Abstracts of Posters 8-th European Conference on Mathematical ...
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<str<strong>on</strong>g>Abstracts</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>Posters</str<strong>on</strong>g><br />

presented at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

8-<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g><br />

<strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology,<br />

and<br />

Annual Meeting <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Society for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology,<br />

Kraków, June 28 - July 2, 2011

C<strong>on</strong>tents<br />

Rasha Abu Eid 22<br />

Cristian Vasile Achim 24<br />

Ben Adams 25<br />

Ben Adams 26<br />

Evans Afenya 27<br />

Maira Aguiar 28<br />

Helmut Ahammer 30<br />

Marco Ajelli 31<br />

Ilya Akberdin 32<br />

Ada Akerman 33<br />

Masakazu Akiyama 34<br />

Tomas Alarcón 36<br />

Maym<strong>on</strong>a Al-husari 37<br />

Samuel Aliz<strong>on</strong> 38<br />

Wolfgang Alt 39<br />

Krystyna Ambroch 40<br />

Jose Amigó 41<br />

Tea Ammunét 42<br />

Anan<str<strong>on</strong>g>th</str<strong>on</strong>g>i Anandanadesan 44<br />

Masahiro Anazawa 46<br />

Alexander Anders<strong>on</strong> 47<br />

Viggo Andreasen 48<br />

Roumen Anguelov 49<br />

Iris Antes 50<br />

Narcisa Apreutesei 51<br />

Mochamad Apri 52<br />

Daniel Arbelaez Alvarado 53<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Argasinski 54<br />

Julian Arndts 55<br />

Anne Arnold 56<br />

Jesus R. Artalejo 57<br />

Yael Artzy-Randrup 58<br />

Takeshi Asakawa 59<br />

Gianluca Ascolani 60<br />

Laura Astola 62<br />

Irem Atac 63<br />

K<strong>on</strong>stantin Avilov 64<br />

Franciane Azevedo 66<br />

Mostafa Bachar 67<br />

3

4<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Stephen Baigent 68<br />

Archana Bajpai 69<br />

Ru<str<strong>on</strong>g>th</str<strong>on</strong>g> Baker 70<br />

Suruchi Bakshi 71<br />

Joanna Balbus 72<br />

Annabelle Ballesta 73<br />

Murad Banaji 74<br />

Leah Band 75<br />

Jörg Bandura 76<br />

Malay Banerjee 77<br />

Maria Barbarossa 78<br />

Susana Barbosa 79<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Bartoszek 80<br />

Wojciech Bartoszek 81<br />

David Basanta 82<br />

David Basanta 83<br />

Andrew Bate 84<br />

Jerry Batzel 85<br />

Robert Bauer 87<br />

Stefan Becker 88<br />

Julio Belm<strong>on</strong>te 90<br />

Sébastien Benzekry 91<br />

Juliana Berbert 92<br />

Ludek Berec 93<br />

Adriana Bernal Escobar 94<br />

Samuel Bernard 95<br />

Roberto Bertolusso 97<br />

Alex Best 98<br />

Anja Be<str<strong>on</strong>g>th</str<strong>on</strong>g>ge 99<br />

Andrzej Bielecki 100<br />

Sebastian Binder 102<br />

Paweł Błażej 103<br />

Jenny Bloomfield 104<br />

Adam Bobrowski 105<br />

Martin Bock 106<br />

Nikolai Bode 107<br />

Christian Bodenstein 108<br />

Marek Bodnar 109<br />

Marek Bodnar 111<br />

Radosław Bogucki 112<br />

Ansgar Bohmann 113<br />

Andreas Bohn 114<br />

Barbara Boldin 115<br />

Dimitra B<strong>on</strong> 116<br />

Axel B<strong>on</strong>acic Marinovic 118<br />

Katarína Boová 119<br />

Wojciech Borkowski 120<br />

Marta Borowska 121

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Evert Bosdriesz 122<br />

Roger Bowers 123<br />

Alexander Bratus 124<br />

Carlos A. Braumann 126<br />

Romulus Breban 127<br />

Romulus Breban 128<br />

Victor F Brena-Medina 129<br />

Nick Britt<strong>on</strong> 130<br />

Tom Britt<strong>on</strong> 131<br />

Ellen Brooks-Pollock 132<br />

Mark Broom 133<br />

Lutz Brusch 134<br />

Lutz Brusch 135<br />

Teodor Buchner 137<br />

Svetlana Bunimovich 138<br />

Bruno Bu<strong>on</strong>omo 139<br />

Zdzislaw Burda 140<br />

Reinhard Bürger 141<br />

Jean Baptiste Burie 142<br />

Peter Buske 144<br />

Katarzyna Buszko 145<br />

Anna Cai 146<br />

Yin Cai 147<br />

Hannah Callender 148<br />

Baba Issa Camara 149<br />

Mario Campanella 150<br />

Vincenzo Capasso 152<br />

Vincenzo Capasso 153<br />

Jose A. Carrillo 155<br />

Magda Castel 156<br />

Isaias Chairez-Hernandez 157<br />

Fabio Chalub 158<br />

Osvaldo Chara 159<br />

Arnaud Chauviere 160<br />

Arnaud Chauviere 162<br />

Andrés Chavarría-Krauser 163<br />

Luis Chaves 165<br />

Ibrahim Cheddadi 166<br />

Roman Cherniha 167<br />

Andrey Cherstvy 168<br />

Chadha Chettaoui 170<br />

Keng-Hwee Chiam 171<br />

Ryan Chisholm 172<br />

Nakul Chitnis 173<br />

Ye<strong>on</strong>taek Choi 174<br />

Catalina Ciric 175<br />

Stanca M Ciupe 177<br />

Jean Clairambault 178<br />

5

6<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

James Clarke 179<br />

Christina Cobbold 180<br />

Daniel C<str<strong>on</strong>g>of</str<strong>on</strong>g>field Jr. 181<br />

Piero Colombatto 182<br />

Ornella Cominetti 184<br />

Carsten C<strong>on</strong>radi 185<br />

Jessica C<strong>on</strong>way 186<br />

Flora Cordoleani 187<br />

Stephen Cornell 188<br />

Andres Cortes 189<br />

Adelle Coster 190<br />

Sim<strong>on</strong> Cotter 191<br />

Markus Covert 192<br />

Gheorghe Craciun 193<br />

Fabien Crauste 194<br />

Vittorio Cristini 196<br />

Huguette Croisier 197<br />

Attila Csikasz-Nagy 198<br />

Jing-an Cui 199<br />

Peter Cummings 200<br />

Andras Czirok 201<br />

Harel Dahari 202<br />

Sascha Dalessi 203<br />

Daniel Damineli 205<br />

Agnieszka Danek 206<br />

Erin Daus<strong>on</strong> 208<br />

Fordyce Davids<strong>on</strong> 209<br />

Fordyce Davids<strong>on</strong> 210<br />

Ross Davids<strong>on</strong> 211<br />

Ant<strong>on</strong>i Le<strong>on</strong> Dawidowicz 212<br />

Troy Day 213<br />

Niall Deakin 214<br />

Walter de Back 215<br />

Malgorzata Debowska 216<br />

Jaber Dehghany 217<br />

Eva Deinum 218<br />

Edgar Delgado-Eckert 219<br />

Aurelio V de los Reyes 221<br />

Sara Del Valle 222<br />

Bernd-Sim<strong>on</strong> Dengel 223<br />

Christophe Deroulers 224<br />

Andreas Deutsch 225<br />

Andreas Deutsch 226<br />

Thanate Dhirasakdan<strong>on</strong> 227<br />

Edgar Diaz Herrera 228<br />

Gabriel Dimitriu 229<br />

Gaelle Diserens 230<br />

Susanne Ditlevsen 231

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Narendra Dixit 232<br />

Radu Dobrescu 233<br />

Marina Dolfin 234<br />

Mirela Domijan 235<br />

Alberto d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio 236<br />

Alberto d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio 237<br />

Alexey Doroshkov 238<br />

Christiana Drake 240<br />

Dirk Drasdo 241<br />

Dirk Drasdo 243<br />

Dirk Drasdo 245<br />

Fátima Drubi Vega 247<br />

Wen Duan 248<br />

Jorge Duarte 249<br />

Claire Dufourd 250<br />

Yves Dum<strong>on</strong>t 252<br />

Sara-Jane Dunn 254<br />

Thomas Dunt<strong>on</strong> 255<br />

Geneviève Dup<strong>on</strong>t 256<br />

Bertram Düring 257<br />

Louise Dys<strong>on</strong> 258<br />

Rosemary Dys<strong>on</strong> 259<br />

Michal Dyzma 260<br />

Ken Eames 261<br />

Hermann Eberl 262<br />

Raluca Eftimie 263<br />

Marisa Eisenberg 264<br />

Maciej Jan Ejsm<strong>on</strong>d 265<br />

Ahmed Elaiw 266<br />

Ait Dads Elhadi 267<br />

Federico Elias Wolff 269<br />

Jerzy Ellert 270<br />

Elizabe<str<strong>on</strong>g>th</str<strong>on</strong>g> Elliott 272<br />

Fadoua El Moustaid 273<br />

German Enciso 274<br />

Heiko Enderling 275<br />

Heiko Enderling 276<br />

Radek Erban 277<br />

Stefano Erm<strong>on</strong> 278<br />

Lourdes Esteva 279<br />

Eunok Jung 280<br />

Roger Evans 281<br />

Joep Evers 283<br />

Yoan Eynaud 284<br />

K<strong>on</strong>stantin Fackeldey 286<br />

James Faeder 287<br />

Martin Falcke 289<br />

Martin Falcke 290<br />

7

8<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Chun Fang 291<br />

Jozsef Farkas 292<br />

Ant<strong>on</strong>io Fasano 293<br />

Sergei Fedotov 295<br />

Elisenda Feliu 296<br />

Justin Fernandez 298<br />

Luis Fernandez Lopez 300<br />

Claudia Ferreira 301<br />

Wils<strong>on</strong> Ferreira Jr. 302<br />

Stephan Fischer 303<br />

K. Renee Fister 305<br />

Ben Fitzpatrick 306<br />

Edward Flach 307<br />

Alexander Fletcher 308<br />

Jasmine Foo 309<br />

J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an Forde 310<br />

J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an Forde 311<br />

Daniel Forger 312<br />

Scott Fortmann-Roe 313<br />

Pawel Foszner 314<br />

John Fozard 316<br />

Benjamin Franz 317<br />

Avner Friedman 318<br />

Avner Friedman 319<br />

Jan Fuhrmann 320<br />

Sebastian Funk 321<br />

Holly Gaff 322<br />

Holly Gaff 323<br />

Eam<strong>on</strong>n Gaffney 325<br />

Przemyslaw Gagat 326<br />

Elżbieta Gajecka-Mirek 327<br />

Magda Galach 328<br />

Jill Gallaher 330<br />

Joerg Galle 331<br />

Martina Gallenberger 332<br />

Alberto Gandolfi 333<br />

Jose A. Garcia 334<br />

Diana Garcia Lopez 335<br />

Astrid Gasselhuber 336<br />

Tomas Gede<strong>on</strong> 337<br />

Eva Gehrmann 338<br />

Richard Gejji 339<br />

Uduak George 340<br />

Sebastian Gerdes 342<br />

Chloe Gerin 344<br />

Philip Gerlee 345<br />

Philip Gerrish 346<br />

Wulfram Gerstner 347

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Philipp Getto 348<br />

Wayne M. Getz 349<br />

Atiyo Ghosh 350<br />

Jan Gierałtowski 351<br />

Kyriaki Giorgakoudi 353<br />

Chiara Giverso 355<br />

Erida Gjini 356<br />

James Glazier 357<br />

Tilmann Glimm 358<br />

Wojciech Goch 359<br />

Julia Gog 360<br />

Chaitanya Gokhale 361<br />

Meltem Gölgeli 362<br />

Gabriela Gomes 363<br />

Didier G<strong>on</strong>ze 364<br />

Jean-Luc Gouzé 365<br />

Isabell Graf 366<br />

Beata Graff 367<br />

Galina Gramotnev 368<br />

J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an Greenman 369<br />

Priscilla Greenwood 370<br />

Fabio Grizzi 371<br />

Frédéric Grognard 372<br />

Christian Groh 373<br />

S<strong>on</strong>ja Gruen 375<br />

Z.J. Grzywna 377<br />

Jeremie Guedj 379<br />

Caterina Guiot 380<br />

Caterina Guiot 381<br />

Piotr Gwiazda 382<br />

Piotr Gwiazda 383<br />

Christ<str<strong>on</strong>g>of</str<strong>on</strong>g>oros Hadjichrysan<str<strong>on</strong>g>th</str<strong>on</strong>g>ou 384<br />

Hiroshi Haeno 385<br />

Saliha Hamdous 386<br />

Christina Hamlet 387<br />

Samuel Handelman 388<br />

Le<strong>on</strong>id Hanin 389<br />

Hea<str<strong>on</strong>g>th</str<strong>on</strong>g>er Hardway 390<br />

Jaroslaw Harezlak 391<br />

Andrew Harris 392<br />

Eleanor Harris<strong>on</strong> 393<br />

S.Naser Hashemi 394<br />

Jan Haskovec 395<br />

Jan Haskovec 396<br />

Beata Hat 397<br />

Haralampos Hatzikirou 398<br />

Hassan Hbid 399<br />

Denis Head<strong>on</strong> 400<br />

9

10<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Robert Heise 401<br />

Christian Hellmich 402<br />

Dorota Herman 403<br />

Joachim Hermiss<strong>on</strong> 404<br />

Ana Hernandez 405<br />

Miguel A. Herrero 406<br />

Miguel A. Herrero 407<br />

Eva Herrmann 408<br />

John Hertz 409<br />

Roslyn Hicks<strong>on</strong> 411<br />

Danielle Hilhorst 412<br />

Gina Himes Boor 413<br />

Erwan Hingant 414<br />

Peter Hinow 416<br />

J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an Hiorns 417<br />

Bar<str<strong>on</strong>g>th</str<strong>on</strong>g>olomaeus Hirt 418<br />

Stefan Hoehme 419<br />

Nadine Hohmann 420<br />

William Holmes 421<br />

Klaus Holst 422<br />

Niels-Henrik Holstein-Ra<str<strong>on</strong>g>th</str<strong>on</strong>g>lou 423<br />

Hermann-Georg Holzhuetter 424<br />

Mary Ann Horn 425<br />

Zhanyuan Hou 426<br />

Thomas House 427<br />

Florence Hubert 428<br />

C. An<str<strong>on</strong>g>th</str<strong>on</strong>g><strong>on</strong>y Hunt 430<br />

Peter Hunter 431<br />

Paul Hurtado 432<br />

Thiemo Hustedt 433<br />

Dagmar Iber 434<br />

Satomi Iino 435<br />

Giuliana Indelicato 436<br />

Jaime Iranzo 437<br />

Shingo Iwami 439<br />

Marta Iwanaszko 440<br />

Sara Jabbari 441<br />

Jędrzej Jabłoski 442<br />

Johannes Jaeger 443<br />

Mehrdad Jafari-Mamaghani 444<br />

Peter Jagers 446<br />

Nick Jagiella 447<br />

Harsh Jain 448<br />

Harsh Jain 449<br />

Roman Jaksik 450<br />

Grzegorz Jamróz 452<br />

Joanna Jaroszewska 453<br />

Joanna Jaruszewicz 454

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Herbert Jelinek 455<br />

W<strong>on</strong>ju Je<strong>on</strong> 456<br />

Yi Jiang 457<br />

Jean-François Joanny 458<br />

Helen Johns<strong>on</strong> 459<br />

Z<str<strong>on</strong>g>of</str<strong>on</strong>g>ia J<strong>on</strong>es 461<br />

Winfried Just 463<br />

Winfried Just 464<br />

Agnieszka Kaczkowska 465<br />

Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ias Kahm 466<br />

Yannis Kalaidzidis 468<br />

Hiroko Kamei 469<br />

Yoshitaka Kameo 470<br />

Atsushi Kamimura 472<br />

Christel Kamp 473<br />

Franz Kappel 474<br />

Irina Kareva 475<br />

Arseny Karkach 476<br />

Ilmari Kar<strong>on</strong>en 477<br />

Khalid Kassara 478<br />

Joanna Kawka 479<br />

Toshiya Kazama 480<br />

Bogdan Kaźmierczak 481<br />

Thomas Keef 482<br />

Jan Kelkel 483<br />

David Kelly 484<br />

Harald Kempf 485<br />

Richard Kerner 487<br />

Helen Kettle 489<br />

Evgeniy Khain 490<br />

Evgeniy Khain 491<br />

Adnan Khan 492<br />

Amjad Khan 493<br />

Nino Khatiashvili 494<br />

Hanifeh Khayyeri 495<br />

Eunjung Kim 496<br />

Yangjin Kim 497<br />

Yangjin Kim 498<br />

Julian King 499<br />

Eva Kisdi 501<br />

Istvan Kiss 502<br />

Agnieszka Kitlas 503<br />

Adam Kleczkowski 505<br />

Sabrina Kleessen 506<br />

Vaclav Klika 507<br />

Wlodzimierz Kl<strong>on</strong>owski 508<br />

Sandra Klu<str<strong>on</strong>g>th</str<strong>on</strong>g> 509<br />

Markus Knappitsch 510<br />

11

12<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Michael Knudsen 511<br />

Ryota Kobayashi 512<br />

Tetsuya Kobayashi 513<br />

Marek Kochanczyk 514<br />

Pawel Kocieniewski 516<br />

Martin Koetzing 517<br />

Alvaro Köhn-Luque 518<br />

Semen Koksal 519<br />

Mikhail Kolev 520<br />

Richard Kollár 521<br />

Andrey Kolobov 522<br />

Michał Komorowski 523<br />

Ryusuke K<strong>on</strong> 524<br />

Shigeru K<strong>on</strong>do 525<br />

Bernhard K<strong>on</strong>rad 526<br />

Wilfried K<strong>on</strong>rad 527<br />

Lubomir Kostal 529<br />

Tanya Kostova Vassilevska 530<br />

Il<strong>on</strong>a Kowalik-Urbaniak 531<br />

T. Kozubowski 533<br />

Roberto Kraenkel 534<br />

Roberto Kraenkel 535<br />

Kseniya Kravchuk 536<br />

Axel Krinner 537<br />

J Krishnan 539<br />

Vlastimil Krivan 540<br />

Pawel Krupinski 541<br />

Pawel Krupinski 543<br />

Michal Krzeminski 544<br />

Wojciech Krzyzanski 545<br />

Akisato Kubo 546<br />

Adam Kucharski 547<br />

Michael Kücken 548<br />

Peter Kühl 549<br />

Paul Kulesa 550<br />

Toshikazu Kuniya 551<br />

Christina Kuttler 552<br />

Julia Kzhyshkowska 553<br />

Paweł Lachor 554<br />

Miroslaw Lachowicz 556<br />

Miroslaw Lachowicz 557<br />

Tanny Lai 558<br />

Christoph Landsberg 559<br />

Michel Langlais 560<br />

Petr Lansky 561<br />

Alexei Lapin 562<br />

Anastasia Lavrova 563<br />

Anita Layt<strong>on</strong> 564

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Harold Layt<strong>on</strong> 565<br />

Urszula Ledzewicz 566<br />

Chang Hye<strong>on</strong>g Lee 567<br />

J<strong>on</strong>ggul Lee 568<br />

Nam-Kyung Lee 569<br />

S. Seirin Lee 570<br />

Karin Leiderman 572<br />

Felix Lenk 573<br />

Anne-Cécile Lesart 574<br />

Jacek Leśkow 575<br />

Sivan Leviyang 576<br />

J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an Li 577<br />

Chelsea Liddell 578<br />

Volkmar Liebscher 579<br />

Magnus Lindh 580<br />

Pietro Lio 581<br />

Tomasz Lipniacki 582<br />

Bartosz Lisowski 584<br />

Alun Lloyd 586<br />

Georgios Lolas 587<br />

Juan Carlos López Alf<strong>on</strong>so 588<br />

MJ Lopez-Herrero 589<br />

Miguel A. Lopez-Marcos 590<br />

Horacio Lopez-Menendez 591<br />

Per Lotstedt 592<br />

Kavi<str<strong>on</strong>g>th</str<strong>on</strong>g>a Louis 593<br />

Jose Lourenço 594<br />

Yoram Louzoun 595<br />

John Lowengrub 596<br />

John Lowengrub 597<br />

Shar<strong>on</strong> Lubkin 598<br />

Torbjörn Lundh 599<br />

Jamie Luo 600<br />

Pavel Lushnikov 601<br />

Angelina Mageni Lutambi 602<br />

Wes Maciejewski 603<br />

Michael C. Mackey 604<br />

Michael C. Mackey 605<br />

Dorota Mackiewicz 606<br />

Paweł Mackiewicz 608<br />

Paul Macklin 609<br />

Paul Macklin 611<br />

Anotida Madzvamuse 613<br />

Carsten Magnus 614<br />

Silvia Mahmood 615<br />

Ludovic Mailleret 616<br />

Danuta Makowiec 617<br />

Danuta Makowiec 619<br />

13

14<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Adam Makuchowski 621<br />

Horst Malchow 622<br />

Solvey Mald<strong>on</strong>ado 623<br />

Jens Malmros 626<br />

Marcin Małogrosz 627<br />

Piero Manfredi 628<br />

Carrie Manore 629<br />

Anna Marciniak-Czochra 630<br />

Anna Marciniak-Czochra 631<br />

Michał Marczyk 632<br />

Glenn Mari<strong>on</strong> 634<br />

Alicia Martinez-G<strong>on</strong>zalez 635<br />

Eduardo Massad 637<br />

Susan Massey 638<br />

Franziska Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>aeus 640<br />

Bertrand Maury 641<br />

Jessica McGillen 642<br />

Alan McKane 643<br />

Nicola McPhers<strong>on</strong> 644<br />

Olesya Melnichenko 645<br />

Renato Mendes Coutinho 646<br />

Berta Mendoza-Juez 647<br />

Aleksander Mendyk 649<br />

Carsten Mente 651<br />

Gülnihal Meral 652<br />

Ge<str<strong>on</strong>g>of</str<strong>on</strong>g>fry Mercer 653<br />

Roeland Merks 654<br />

Roeland Merks 655<br />

Géza Meszéna 656<br />

K<strong>on</strong>radin Metze 657<br />

Michael Meyer-Hermann 659<br />

Alistair Middlet<strong>on</strong> 660<br />

Jacek Miekisz 661<br />

Jacek Miekisz 662<br />

Janusz Mierczynski 663<br />

Florian Milde 664<br />

Judi<str<strong>on</strong>g>th</str<strong>on</strong>g> Miller 665<br />

Harriet Mills 666<br />

Nebojsa Milosevic 667<br />

Maya Mincheva 668<br />

Rachelle Mir<strong>on</strong> 669<br />

Victoria Mir<strong>on</strong>ova 670<br />

Mariola Molenda 672<br />

Rubem M<strong>on</strong>daini 673<br />

Shabnam MoobedMehdiAbadi 674<br />

Yoshihiro Morishita 675<br />

Adam Moroz 676<br />

Charles Mort<strong>on</strong> 677

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Patricia Mostardinha 678<br />

Manuel Mota 679<br />

Iw<strong>on</strong>a Mroz 681<br />

Kalina Mrozek 682<br />

Maciej Mrugala 683<br />

Johannes Müller 684<br />

Sreeharish Muppirisetty 685<br />

Daniele Muraro 686<br />

Philip Murray 688<br />

Robert B. Nachbar 689<br />

Jose Nacher 690<br />

Robyn Nadolny 692<br />

Felix Naef 693<br />

Sundar Nagana<str<strong>on</strong>g>th</str<strong>on</strong>g>an 694<br />

Jun Nakabayashi 695<br />

Tetsuya Nakamura 696<br />

Yukihiko Nakata 697<br />

Toshiyuki Namba 698<br />

Martin Paul Nawrot 700<br />

Bakhyt Nedorezova 701<br />

Jost Neigenfind 702<br />

Zoltan Neufeld 703<br />

Claudia Neuhauser 704<br />

Avidan U. Neumann 705<br />

Sergey Nikolaev 706<br />

Ryosuke Nishi 707<br />

Hiroshi Nishiura 709<br />

Robert Noble 711<br />

Lorette Noiret 713<br />

Robert Nolet 714<br />

Etsuko N<strong>on</strong>aka 715<br />

Ekaterina A. Nosova 716<br />

Ka<str<strong>on</strong>g>th</str<strong>on</strong>g>erine Novoselova 717<br />

Artem Novozhilov 719<br />

Andrzej Nowakowski 720<br />

Tuomas Nurmi 722<br />

Boguslaw Obara 723<br />

Anna Ochab-Marcinek 725<br />

Edward Oczeretko 726<br />

Reuben O’Dea 727<br />

Eryll Ogg 728<br />

Łukasz Olczak 729<br />

Katarzyna Oles 730<br />

Sarah Ols<strong>on</strong> 731<br />

Mette Olufsen 732<br />

Dietmar Ölz 733<br />

Ryosuke Omori 734<br />

Nooshin Omranian 735<br />

15

16<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Natsuki Orita 737<br />

James Osborne 739<br />

Yo-Hey Otake 740<br />

Hans G. O<str<strong>on</strong>g>th</str<strong>on</strong>g>mer 741<br />

Hans G. O<str<strong>on</strong>g>th</str<strong>on</strong>g>mer 742<br />

Johnny Ottesen 743<br />

Aziz Ouhinou 744<br />

Niels Chr Overgaard 745<br />

Marcin Pacholczyk 747<br />

Kevin Painter 748<br />

Kevin Painter 749<br />

Laurence Palk 750<br />

Margriet Palm 751<br />

Peter Pang 752<br />

A. Panorska 753<br />

Casian Pantea 754<br />

Je<strong>on</strong>g-Man Park 755<br />

Su-Chan Park 756<br />

Kalle Parvinen 757<br />

Virginia Pasour 758<br />

Pawel Paszek 759<br />

Kasia Pawelek 760<br />

Jakub Pekalski 761<br />

Zbigniew Peradzyski 763<br />

Victor M. Pérez-García 764<br />

Judi<str<strong>on</strong>g>th</str<strong>on</strong>g> Perez-Velazquez 766<br />

Holger Perfahl 768<br />

Holger Perfahl 770<br />

Valeriy Perminov 771<br />

Fernando Peruani 772<br />

M<strong>on</strong>ika Petelczyc 773<br />

Aleksandra Pfeifer 775<br />

Roland Pieruschka 776<br />

M<strong>on</strong>ika Piotrowska 777<br />

Jaroslaw Piskorski 778<br />

Peter Piv<strong>on</strong>ka 779<br />

Mateusz Plucinski 780<br />

Piotr Podziemski 781<br />

Jean-Christophe Poggiale 783<br />

Ondrej Pokora 784<br />

Sebastian Polak 785<br />

Jan Poleszczuk 786<br />

Andrey Polezhaev 787<br />

Rosalyn Porter 788<br />

Zdenek Pospisil 789<br />

Ilya Potapov 790<br />

Gibin Powa<str<strong>on</strong>g>th</str<strong>on</strong>g>il 792<br />

Sim<strong>on</strong> Praetorius 793

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Jamie Prentice 794<br />

Luigi Preziosi 795<br />

Tadeas Priklopil 796<br />

Stephen Proulx 797<br />

Jens Przybilla 798<br />

Piotr Przymus 799<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Psiuk-Maksymowicz 801<br />

Mariya Ptashnyk 802<br />

Robert Puddicombe 803<br />

Andrea Pugliese 804<br />

Małgorzata Pułka 805<br />

Jan Pyrzowski 806<br />

Amina Qutub 807<br />

Ovidiu Radulescu 808<br />

Marina Rafajlovic 809<br />

Nomenjanahary Alexia Raharinirina 810<br />

Andriamihaja Ramanantoanina 811<br />

Gael Raoul 812<br />

J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an Rault 813<br />

Mario Recker 814<br />

Charles Reichhardt 815<br />

Katarzyna Rejniak 816<br />

Katarzyna A. Rejniak 817<br />

Katarzyna A. Rejniak 818<br />

Timo<str<strong>on</strong>g>th</str<strong>on</strong>g>y Reluga 819<br />

Grzegorz A Rempala 820<br />

Sarunas Repsys 821<br />

Jennifer Reynolds 822<br />

Benjamin Ribba 823<br />

Tim Ricken 824<br />

Rachel Rider 825<br />

Heiko Rieger 826<br />

Jordi Ripoll 827<br />

Ekaterina Roberts 828<br />

Mick Roberts 829<br />

Mark Roberts<strong>on</strong>-Tessi 830<br />

Raina Robeva 831<br />

Susanna Röblitz 832<br />

Russell Rockne 833<br />

Helena S<str<strong>on</strong>g>of</str<strong>on</strong>g>ia Rodrigues 835<br />

Joanna Rodriguez Chrobak 836<br />

Roberto Rosà 837<br />

Anita Ro<str<strong>on</strong>g>th</str<strong>on</strong>g>-Nebelsick 838<br />

Elina Roto 840<br />

Robert Rovetti 841<br />

Peter Rowat 842<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Rykaczewski 843<br />

Laura Sacerdote 844<br />

17

18<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Holly Gaff, Sadie Ryan 845<br />

Michael Sadovsky 846<br />

Koichi Saeki 848<br />

Roberto Saenz 849<br />

Max Sajitz-Hermstein 850<br />

Guillaume Salbreux 851<br />

Adeline Sams<strong>on</strong> 852<br />

Yara Elena Sanchez Corrales 853<br />

Luis Sanz 854<br />

Akira Sasaki 856<br />

Akiko Satake 857<br />

Andrew Savory 858<br />

Sim<strong>on</strong>e Scacchi 859<br />

Andreas Schadschneider 860<br />

Heinz Schaettler 861<br />

Sascha Schäuble 862<br />

Daniella Schittler 863<br />

Daniela Schlueter 864<br />

Christoph Schmal 865<br />

Christine Schmeitz 866<br />

Deena Schmidt 867<br />

Daniel Schneditz 868<br />

Kristan Schneider 870<br />

Santiago Schnell 871<br />

Richard Schugart 872<br />

Anna Schulze 873<br />

Tilo Schwalger 874<br />

Veit Schwämmle 875<br />

Elissa Schwartz 876<br />

Lars Ole Schwen 877<br />

Marco Scianna 878<br />

Jacob Scott 880<br />

Megan Selbach-Allen 881<br />

Lorenzo Sella 882<br />

Hiromi Seno 884<br />

Anne Seppänen 885<br />

Raffaello Seri 886<br />

Robert Service 887<br />

Armin Seyfried 888<br />

Nikolaos Sfakianakis 889<br />

Nazgol Shahbandi 890<br />

Kieran Sharkey 891<br />

Ryan Sharp 892<br />

Eunha Shim 893<br />

Shigeru Shinomoto 894<br />

Andrey Shuvaev 895<br />

Michael Sieber 896<br />

Justyna Signerska 897

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Wer<strong>on</strong>ika Sikora-Wohlfeld 898<br />

Peter Sim<strong>on</strong> 900<br />

Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ew Simps<strong>on</strong> 901<br />

Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ew Simps<strong>on</strong> 902<br />

David Sirl 903<br />

Roberta Sirovich 904<br />

Vladas Skakauskas 905<br />

Alexander Skupin 906<br />

Alexander Skupin 907<br />

Urszula Skwara 908<br />

Jaroslaw Śmieja 909<br />

Charles Smi<str<strong>on</strong>g>th</str<strong>on</strong>g> 910<br />

Robert Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>? 911<br />

Oksana Sorokina 912<br />

Max Souza 913<br />

Eirini Spanou 914<br />

Joanna Stachowska-Piętka 916<br />

Jörn Starruß 918<br />

Michał Startek 919<br />

Tracy Stepien 920<br />

Thomas Stiehl 921<br />

Yv<strong>on</strong>ne Stokes 922<br />

Magdalena Stolarska 923<br />

Nico Stollenwerk 924<br />

Nico Stollenwerk 925<br />

Beatriz Stransky 926<br />

Lior Strauss 928<br />

Zbigniew Struzik 929<br />

Wanda Strychalski 930<br />

Sebastian Student 931<br />

Marc Sturrock 933<br />

Lisa Sundqvist 934<br />

Christina Surulescu 935<br />

Maciej Swat 936<br />

Maciej Swat 938<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Świder 939<br />

David Swig<strong>on</strong> 940<br />

Gabor Szederkenyi 941<br />

Piotr Szopa 942<br />

Joanna Szymanowska-Pułka 943<br />

Paulina Szymanska 945<br />

Zuzanna Szymaska 946<br />

Masoomeh Taghipoor 947<br />

Takenori Takada 949<br />

Daisuke Takahashi 950<br />

Satoshi Takahashi 951<br />

Yasuhiro Takeuchi 952<br />

Massimiliano Tamborrino 953<br />

19

20<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

S<str<strong>on</strong>g>of</str<strong>on</strong>g>ia Tapani 954<br />

Michael Taylor 956<br />

Mickael Teixeira Alves 957<br />

Atsushi Tero 958<br />

Emmanuelle Terry 959<br />

Jeremy Thibodeaux 960<br />

Horst Thieme 961<br />

K<strong>on</strong>stantin Thierbach 962<br />

Michele Thieullen 963<br />

S. Randall Thomas 964<br />

Ruediger Thul 965<br />

Kevin Thurley 966<br />

Sara Tiburtius 967<br />

Marcus Tindall 968<br />

Jaakko Toiv<strong>on</strong>en 969<br />

Christian Tokarski 970<br />

Alina Toma 971<br />

Cristian Tomasetti 972<br />

Paweł Topa 973<br />

Nadine Töpfer 975<br />

Andrea Tosin 977<br />

Suzanne Touzeau 978<br />

Hiroshi Toyoizumi 979<br />

Arne Traulsen 980<br />

Je-Chiang Tsai 981<br />

Reidun Twarock 982<br />

Jacek Tyburczyk 983<br />

Katarzyna Tyc 984<br />

Elpida Tzafestas 985<br />

Agnieszka Ulikowska 987<br />

Margarete Utz 988<br />

Asher Uziel 990<br />

Milan van Hoek 991<br />

Sim<strong>on</strong> van Mourik 993<br />

Bert van Rietbergen 994<br />

Raffaele Vardavas 995<br />

María Vela-Pérez 996<br />

Ezio Venturino 997<br />

Ezio Venturino 998<br />

Paola Vera-Lic<strong>on</strong>a 999<br />

Maurício Vieira Kritz 1000<br />

Irene Vign<strong>on</strong>-Clementel 1002<br />

Fernao Vistulo de Abreu 1003<br />

Guido Vitale 1004<br />

Evgenii Volkov 1005<br />

Vitaly Volpert 1008<br />

Vitaly Volpert 1009<br />

Max v<strong>on</strong> Kleist 1010

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ute v<strong>on</strong> Wangenheim 1012<br />

Anja Voss-Boehme 1013<br />

Joe Yuichiro Wakano 1014<br />

Przemyslaw Waliszewski 1015<br />

Doro<str<strong>on</strong>g>th</str<strong>on</strong>g>y Wallace 1017<br />

Georg Wal<str<strong>on</strong>g>th</str<strong>on</strong>g>er 1018<br />

Xiaojing Wang 1020<br />

John Ward 1021<br />

Michael Wats<strong>on</strong> 1022<br />

Agata Wawrzkiewicz 1023<br />

Rafał Wcisło 1024<br />

William Weens 1025<br />

Sebastian Weitz 1026<br />

Bernt Wennberg 1027<br />

Aleksander Wer<strong>on</strong> 1028<br />

Sergiusz Wesołowski 1029<br />

Bruce West 1031<br />

Andy White 1032<br />

Ruscena Wiederholt 1033<br />

Ka<str<strong>on</strong>g>th</str<strong>on</strong>g>leen Wilkie 1034<br />

Lisa Willis 1035<br />

Christian Winkel 1036<br />

Annelene Wittenfeld 1038<br />

Meike Wittmann 1039<br />

Carsten Wiuf 1040<br />

Tomasz Wojdyla 1041<br />

Carina Wollnik 1042<br />

Dariusz Wrzosek 1043<br />

Michelle Wynn 1044<br />

Norio Yamamura 1045<br />

Atsushi Yamauchi 1046<br />

Ping Yan 1047<br />

Xuxin Yang 1048<br />

Je<strong>on</strong>g-Mi Yo<strong>on</strong> 1049<br />

Hiroshi Yoshida 1050<br />

Marcin Zagórski 1051<br />

Marcin Zagorski 1052<br />

Thomas Zerjatke 1053<br />

Lai Zhang 1054<br />

Qingguo Zhang 1055<br />

Michał Zientek 1057<br />

Ulyana Zubairova 1058<br />

Vladimir Zubkov 1059<br />

Paweł Żuk 1060<br />

K<strong>on</strong>stantinos Zygalakis 1062<br />

K<strong>on</strong>stantinos Zygalakis 1063<br />

Index <str<strong>on</strong>g>of</str<strong>on</strong>g> au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors 1065<br />

21

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Fractals and Complexity II; Wednesday, June 29, 17:00<br />

Rasha Abu Eid<br />

Dental School, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Aberdeen, Aberdeen, Scotland, United<br />

Kingdom<br />

e-mail: r.abueid@abdn.ac.uk<br />

Przemyslaw Waliszewski<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Urology, Philipps University, Marburg, Germany<br />

Faleh Sawair<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Dentistry , The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Jordan, Amman, Jordan<br />

Gabriel Landini<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Dentistry, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Birmingham, Birmingham, England,<br />

United Kingdom<br />

Takashi Saku<br />

uate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical and Dental Science, Niigata University, Niigata,<br />

Japan<br />

Fractal Geometry in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Assessment <str<strong>on</strong>g>of</str<strong>on</strong>g> Oral Epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial<br />

Dysplasia Grading System<br />

Background: Oral epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial dysplasia is linked to <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility <str<strong>on</strong>g>of</str<strong>on</strong>g> progressi<strong>on</strong><br />

to oral squamous cell carcinoma. The severity <str<strong>on</strong>g>of</str<strong>on</strong>g> atypic features and <str<strong>on</strong>g>th</str<strong>on</strong>g>e height<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elium to which <str<strong>on</strong>g>th</str<strong>on</strong>g>ey extend have been used in grading dysplasia into<br />

mild, moderate and severe. Precise grading is a source <str<strong>on</strong>g>of</str<strong>on</strong>g> disagreement as <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

assessment carries a degree <str<strong>on</strong>g>of</str<strong>on</strong>g> subjectivity [1,2]. There is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore a need for<br />

developing new morphological definiti<strong>on</strong>s for grading dysplasia based <strong>on</strong> research<br />

into <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenesis <str<strong>on</strong>g>of</str<strong>on</strong>g> premalignancy [3]. The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is study is developing<br />

objective aids in <str<strong>on</strong>g>th</str<strong>on</strong>g>e diagnosis and classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial dysplasia based <strong>on</strong><br />

image analysis, and using ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical descriptors <str<strong>on</strong>g>of</str<strong>on</strong>g> morphology, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

tissue and cellular levels.<br />

Materials and Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: Eighty images <str<strong>on</strong>g>of</str<strong>on</strong>g> haematoxylin and eosin stained dysplasia<br />

images (mild (25), moderate (27), severe (28)) were analyzed to extract <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial c<strong>on</strong>nective tissue interface (ECTI) pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles using different <str<strong>on</strong>g>th</str<strong>on</strong>g>resholding<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods. Box counting, local and local c<strong>on</strong>nected fractal geometry techniques were<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>en applied to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ECTI pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles. The spatial distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a set <str<strong>on</strong>g>of</str<strong>on</strong>g> dysplasia cell nuclei were also assessed in different dysplasia grades.<br />

Statistical analyses to compare <str<strong>on</strong>g>th</str<strong>on</strong>g>e different grades <str<strong>on</strong>g>of</str<strong>on</strong>g> dysplasia were performed.<br />

Results: Preliminary results showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e global complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> ECTI pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles<br />

as described by <str<strong>on</strong>g>th</str<strong>on</strong>g>e box fractal dimensi<strong>on</strong> (DBOX) was statistically different between<br />

mild (DBOX= 1.09) and bo<str<strong>on</strong>g>th</str<strong>on</strong>g> moderate (DBOX=1.13) and severe dysplasia<br />

(DBOX=1.14) ( p< 0.05, <strong>on</strong>e-way ANOVA), while moderate and severe dysplasia<br />

did not show any significant difference. The local c<strong>on</strong>nected fractal dimensi<strong>on</strong><br />

(LCFD) was not statistically different between mild (LCFD=1.34), moderate<br />

(LCFD=1.34) or severe dysplasia (LCFD=1.34) ( p> 0.05, <strong>on</strong>e- way ANOVA).<br />

C<strong>on</strong>clusi<strong>on</strong>: The initial results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is study agree wi<str<strong>on</strong>g>th</str<strong>on</strong>g> our previous findings<br />

[4,5] and provides fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er evidence <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e traditi<strong>on</strong>al classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dysplastic<br />

changes into <str<strong>on</strong>g>th</str<strong>on</strong>g>ree grades might not represent accurately <str<strong>on</strong>g>th</str<strong>on</strong>g>e morphological characteristic<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e premalignant change This emphasizes <str<strong>on</strong>g>th</str<strong>on</strong>g>e problems <str<strong>on</strong>g>of</str<strong>on</strong>g> using me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at have elements <str<strong>on</strong>g>of</str<strong>on</strong>g> subjectivity. A quantitative classificati<strong>on</strong> system is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore a<br />

22

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

much preferred opti<strong>on</strong>s. The use <str<strong>on</strong>g>of</str<strong>on</strong>g> quantifiable me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods such as different measures<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> fractal geometry might be <str<strong>on</strong>g>of</str<strong>on</strong>g> use in establishing new, reproducible systems.<br />

References.<br />

[1] Pindborg J, Reibel J, Holmstrup P. Subjectivity in evaluating oral epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial dysplasia, carcinoma<br />

in situ and initial carcinoma, J Oral Pa<str<strong>on</strong>g>th</str<strong>on</strong>g> 1985, 14: 698-708.<br />

[2] Warnakulasuriya S. Histological grading <str<strong>on</strong>g>of</str<strong>on</strong>g> oral epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial dysplasia: revisited. J Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ol 2001,<br />

194(3): 294-7.<br />

[3] Bosman FT. Dysplasia classificati<strong>on</strong>: pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology in disgrace? J Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ol 2001, 194(2): 143-4.<br />

[4] Abu Eid R, Landini G. Quantificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e global and local complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elialc<strong>on</strong>nective<br />

tissue interface <str<strong>on</strong>g>of</str<strong>on</strong>g> normal, dysplastic, and neoplastic oral mucosae using digital<br />

imaging. Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>o Res Prac 2003, 199(7):475-482.<br />

[5] Abu-Eid, R. and Landini, G. Oral Epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial Dysplasia: Can Quantifiable Morphological Features<br />

Help in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Grading Dilemma? In: First ImageJ User and Developer <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> Proceedings,<br />

Luxembourg, 2006.<br />

23

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: from physical tools to<br />

applicati<strong>on</strong>s in cancer modeling II; Saturday, July 2, 11:00<br />

Cristian V. Achim<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Physics, Aalto University School <str<strong>on</strong>g>of</str<strong>on</strong>g> Science,Finland<br />

e-mail: criaro@gmail.com<br />

Phase Field Crysyal Model for Liquid Crystals<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> static and dynamical density functi<strong>on</strong>al <str<strong>on</strong>g>th</str<strong>on</strong>g>eory, a phase-field-crystal<br />

model is derived which involves bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e translati<strong>on</strong>al density and <str<strong>on</strong>g>th</str<strong>on</strong>g>e orientati<strong>on</strong>al<br />

degree <str<strong>on</strong>g>of</str<strong>on</strong>g> ordering as well as a local director field. The equilibrium free-energy functi<strong>on</strong>al<br />

involves local powers <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e order parameters up to four<str<strong>on</strong>g>th</str<strong>on</strong>g> order, gradients <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e order parameters up to four<str<strong>on</strong>g>th</str<strong>on</strong>g> order, and different couplings between <str<strong>on</strong>g>th</str<strong>on</strong>g>e order<br />

parameters [1]. The stable phases <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e equilibrium free-energy functi<strong>on</strong>al are calculated<br />

for various coupling parameters. Phase diagrams were obtained by numerical<br />

minimizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e free-energy functi<strong>on</strong>al. Am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e stable liquid-crystalline<br />

states are <str<strong>on</strong>g>th</str<strong>on</strong>g>e isotropic, nematic, columnar, smectic A, and plastic crystalline phases<br />

[2]. The plastic crystals can have triangular, square, and h<strong>on</strong>eycomb lattices and<br />

exhibit orientati<strong>on</strong>al patterns wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a complex topology involving a sublattice wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

topological defects. As far as <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics is c<strong>on</strong>cerned, <str<strong>on</strong>g>th</str<strong>on</strong>g>e translati<strong>on</strong>al density<br />

is a c<strong>on</strong>served order parameter while <str<strong>on</strong>g>th</str<strong>on</strong>g>e orientati<strong>on</strong>al ordering is n<strong>on</strong>-c<strong>on</strong>served.<br />

The derived phase-field-crystal model can serve for use in efficient numerical investigati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> various n<strong>on</strong>equilibrium situati<strong>on</strong>s in liquid crystals.<br />

References.<br />

[1] H. Löwen, A phase-field-crystal model for liquid crystals J. Phys.: C<strong>on</strong>dens. Matter 22 (2010)<br />

364105 1–6.<br />

[2] C. V. Achim, R. Wittkowski and H. Löwen, Stability <str<strong>on</strong>g>of</str<strong>on</strong>g> liquid crystalline phases in <str<strong>on</strong>g>th</str<strong>on</strong>g>e phasefield-crystal<br />

model Submitted to Physical Review E.<br />

24

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Vector-borne diseases; Tuesday, June 28, 14:30<br />

Ben Adams<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Ba<str<strong>on</strong>g>th</str<strong>on</strong>g>, UK<br />

e-mail: b.adams@ba<str<strong>on</strong>g>th</str<strong>on</strong>g>.ac.uk<br />

Durrell D. Kapan<br />

Pacific Biosciences Research Centre, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Hawaii, USA<br />

e-mail: durrell@hawaii.edu<br />

Man bites mosquito: human movement and <str<strong>on</strong>g>th</str<strong>on</strong>g>e urban<br />

epidemiology <str<strong>on</strong>g>of</str<strong>on</strong>g> vector-borne disease<br />

Some vector-borne diseases, such as dengue, <str<strong>on</strong>g>th</str<strong>on</strong>g>rive in urban envir<strong>on</strong>ments. Eradicati<strong>on</strong><br />

and c<strong>on</strong>trol are significant public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> challenges. The mosquito populati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> metropolitan areas may be heterogeneously distributed in patches <str<strong>on</strong>g>of</str<strong>on</strong>g> high and low<br />

density. These mosquito populati<strong>on</strong> patches may remain stable over time, but people<br />

travel frequently and extensively, <str<strong>on</strong>g>of</str<strong>on</strong>g>ten in highly structured patterns. Here we<br />

investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is type <str<strong>on</strong>g>of</str<strong>on</strong>g> human movement in <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemiology <str<strong>on</strong>g>of</str<strong>on</strong>g> vectorborne<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens. We use a metapopulati<strong>on</strong> model in which mobile humans c<strong>on</strong>nect<br />

static mosquito subpopulati<strong>on</strong>s. We focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e size distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mosquito subpopulati<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>e variability in people’s travel patterns. We<br />

assess how <str<strong>on</strong>g>th</str<strong>on</strong>g>ese factors determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> each populati<strong>on</strong> subgroup<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproductive number, <str<strong>on</strong>g>th</str<strong>on</strong>g>e maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e endemic equilibrium and<br />

l<strong>on</strong>g-term disease persistence. We c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at hubs and reservoirs <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong><br />

can be places people visit frequently, even if <strong>on</strong>ly briefly. A few patches wi<str<strong>on</strong>g>th</str<strong>on</strong>g> large<br />

mosquito populati<strong>on</strong>s can make a city vulnerable to disease outbreaks. Variability<br />

in travel people’s travel patterns can reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>is vulnerability, but may also<br />

enhance <str<strong>on</strong>g>th</str<strong>on</strong>g>e rescue effect and so increase <str<strong>on</strong>g>th</str<strong>on</strong>g>e persistence <str<strong>on</strong>g>of</str<strong>on</strong>g> endemic disease. Successful<br />

public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> interventi<strong>on</strong> may require identifying areas wi<str<strong>on</strong>g>th</str<strong>on</strong>g> large mosquito<br />

populati<strong>on</strong>s and a form <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tact tracing <str<strong>on</strong>g>th</str<strong>on</strong>g>at maps <str<strong>on</strong>g>th</str<strong>on</strong>g>e recent movements <str<strong>on</strong>g>of</str<strong>on</strong>g> infected<br />

people to pinpoint <str<strong>on</strong>g>th</str<strong>on</strong>g>e mosquito subpopulati<strong>on</strong> from which <str<strong>on</strong>g>th</str<strong>on</strong>g>ey acquired <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

infecti<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>ose to which <str<strong>on</strong>g>th</str<strong>on</strong>g>ey may have transmitted it.<br />

25

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ben Adams<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Ba<str<strong>on</strong>g>th</str<strong>on</strong>g>, UK<br />

e-mail: b.adams@ba<str<strong>on</strong>g>th</str<strong>on</strong>g>.ac.uk<br />

Immune cross-reacti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase structure <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

subharm<strong>on</strong>ic oscillati<strong>on</strong>s in seas<strong>on</strong>al SIR models<br />

SIR type epidemiological models forced by seas<strong>on</strong>al variati<strong>on</strong> in transmissi<strong>on</strong> may<br />

exhibit subharm<strong>on</strong>ic oscillati<strong>on</strong>s in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic period is an integer multiple<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e forcing period. In models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen strains <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence and<br />

structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese l<strong>on</strong>g period epidemic patterns is influenced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e immunological<br />

cross-reacti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e strains. Here we c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> immunological<br />

cross-protecti<strong>on</strong> and cross-enhancement in an annually forced model for an acute<br />

infectious disease. We focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase relati<strong>on</strong>ship between <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

each strain. We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at most subharm<strong>on</strong>ic soluti<strong>on</strong>s have an in phase structure.<br />

Out <str<strong>on</strong>g>of</str<strong>on</strong>g> phase structures <strong>on</strong>ly occur when <str<strong>on</strong>g>th</str<strong>on</strong>g>e intensity <str<strong>on</strong>g>of</str<strong>on</strong>g> cross-protecti<strong>on</strong> is wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in<br />

a narrow interval. The underlying causes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is relati<strong>on</strong>ship are bound up in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

way <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase structure amplifies or moderates <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune crossreacti<strong>on</strong>.<br />

Time series data for <str<strong>on</strong>g>th</str<strong>on</strong>g>e prevalence <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue virus and RSV show multiannual<br />

epidemics <str<strong>on</strong>g>of</str<strong>on</strong>g> different subtypes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an out <str<strong>on</strong>g>of</str<strong>on</strong>g> phase pattern. Our model<br />

analysis suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese patterns are unusual, and likely to be sensitive to any<br />

changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune cross-reacti<strong>on</strong> between subtypes resulting from interventi<strong>on</strong><br />

or evoluti<strong>on</strong>.<br />

26<br />

;

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

V; Wednesday, June 29, 11:00<br />

Evans Afenya<br />

Elmhurst College<br />

e-mail: evansa@elmhurst.edu<br />

Cancer Modeling: Frameworks, Approaches, and Insights<br />

As biomedicine becomes increasingly quantitative in scope and c<strong>on</strong>tent and various<br />

challenges are encountered in <str<strong>on</strong>g>th</str<strong>on</strong>g>e preventi<strong>on</strong>, detecti<strong>on</strong>, treatment, and management<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancers, ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models corresp<strong>on</strong>dingly assume importance in<br />

syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esizing and comprehending some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics underlying <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cell aggregates and systems. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>is framework, diverse approaches are<br />

adopted for obtaining some models <str<strong>on</strong>g>th</str<strong>on</strong>g>at describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e development and propagati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> malignancy in <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease state. Various techniques are employed in analyzing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e models and biomedical insights <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey engender are discussed and placed<br />

in relevant c<strong>on</strong>text. Predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g>fered by <str<strong>on</strong>g>th</str<strong>on</strong>g>e models are <str<strong>on</strong>g>th</str<strong>on</strong>g>en c<strong>on</strong>sidered and<br />

c<strong>on</strong>clusi<strong>on</strong>s are drawn.<br />

27

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modelling dengue fever epidemiology; Saturday, July 2, 08:30<br />

Maíra Aguiar<br />

Centro de Matemática e Aplicações Fundamentais da Universidade de<br />

Lisboa, Lisb<strong>on</strong>, Portugal.<br />

e-mail: maira@ptmat.fc.ul.pt<br />

Sebastien Ballesteros<br />

Centro de Matemática e Aplicações Fundamentais da Universidade de<br />

Lisboa, Lisb<strong>on</strong>, Portugal.<br />

e-mail: sebastien.ballesteros@gmail.com<br />

Bob W. Kooi<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ear<str<strong>on</strong>g>th</str<strong>on</strong>g> and Life Sciences, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology,Vrije<br />

Universiteit, Amsterdam, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands.<br />

e-mail: kooi@falw.vu.nl<br />

Nico Stollenwerk<br />

Centro de Matemática e Aplicações Fundamentais da Universidade de<br />

Lisboa, Lisb<strong>on</strong>, Portugal.<br />

e-mail: nico@ptmat.fc.ul.pt<br />

Modelling dengue fever epidemiology: complex dynamics<br />

and its implicati<strong>on</strong> for data analysis.<br />

It is estimated <str<strong>on</strong>g>th</str<strong>on</strong>g>at every year, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are 70 − 500 milli<strong>on</strong> dengue infecti<strong>on</strong>s,<br />

36 milli<strong>on</strong> cases <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue fever (DF) and 2.1 milli<strong>on</strong> cases <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue hemorragic<br />

fever (DHF), wi<str<strong>on</strong>g>th</str<strong>on</strong>g> more <str<strong>on</strong>g>th</str<strong>on</strong>g>an 20.000 dea<str<strong>on</strong>g>th</str<strong>on</strong>g>s per year [1, 2]. In many countries<br />

in Asia and Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> America DF and DHF has become a substantial public heal<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

c<strong>on</strong>cern leading to serious social-ec<strong>on</strong>omic costs. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models describing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue viruses has focussed <strong>on</strong> ADE effect and temporary cross<br />

immunity trying to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e irregular behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue epidemics by analyzing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e available data. However, no systematic investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e possible dynamical<br />

structures has been performed so far. Our study focuses <strong>on</strong> a seas<strong>on</strong>ally forced<br />

(n<strong>on</strong>-aut<strong>on</strong>omous) two-strain model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> temporary cross immunity and possible<br />

sec<strong>on</strong>dary infecti<strong>on</strong>, motivated by dengue fever epidemiology. We extend <str<strong>on</strong>g>th</str<strong>on</strong>g>e previous<br />

studied n<strong>on</strong>-seas<strong>on</strong>al (aut<strong>on</strong>omous) model[3, 4, 5]. by adding seas<strong>on</strong>al forcing<br />

and low import rate <str<strong>on</strong>g>of</str<strong>on</strong>g> infected individuals, which is realistic in <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

dengue fever epidemics. A comparative study between <str<strong>on</strong>g>th</str<strong>on</strong>g>ree different scenarios<br />

(n<strong>on</strong>-seas<strong>on</strong>al, low seas<strong>on</strong>al and high seas<strong>on</strong>al wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a low import <str<strong>on</strong>g>of</str<strong>on</strong>g> infected individuals)<br />

is processed and <str<strong>on</strong>g>th</str<strong>on</strong>g>e results are shown and discussed. The extended models<br />

show complex dynamics and qualitatively a very good result when comparing empirical<br />

DHF and simulati<strong>on</strong>. We discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e seas<strong>on</strong>al force and import <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

infected individuals in such systems, <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological relevance and <str<strong>on</strong>g>th</str<strong>on</strong>g>e implicati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e new results in <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e available dengue data [6].<br />

References.<br />

[1] Pediatric Dengue Vaccine Initiative. Global Burden <str<strong>on</strong>g>of</str<strong>on</strong>g> Dengue.<br />

(http://www.pdvi.org/about_dengue/GBD.asp).<br />

[2] Word Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Organizati<strong>on</strong>. (2009). Dengue and Dengue Hemorrhagic Fever. (World Heal<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Org., Geneva, Fact Sheet 117).<br />

[3] M. Aguiar, N. Stollenwerk, A new chaotic attractor in a basic multi-strain epidemiological<br />

model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> temporary cross-immunity. (2007) arXiv:0704.3174v1 [nlin.CD].<br />

28

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[4] M. Aguiar, B. W. Kooi and N. Stollenwerk, Epidemiology <str<strong>on</strong>g>of</str<strong>on</strong>g> Dengue Fever: A Model wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Temporary Cross-Immunity and Possible Sec<strong>on</strong>dary Infecti<strong>on</strong> Shows Bifurcati<strong>on</strong>s and Chaotic<br />

Behaviour in Wide Parameter Regi<strong>on</strong>s. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Model. Nat. Phenom. 4 (2008) 48–70.<br />

[5] M. Aguiar, N. Stollenwerk and B. W. Kooi, Torus bifurcati<strong>on</strong>s, isolas and chaotic attractors<br />

in a simple dengue model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> ADE and temporary cross immunity. Internati<strong>on</strong>al Journal <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Computer Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics 86 (2009) 1867–77.<br />

[6] M. Aguiar, S. Ballesteros, B. Cazelles, B. W. Kooi, and N. Stollenwerk, Seas<strong>on</strong>al two strain<br />

dengue model: complex dynamics and its implicati<strong>on</strong>s for data analysis. Manuscript in preparati<strong>on</strong>.<br />

29

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Fractals and Complexity II; Wednesday, June 29, 17:00<br />

Helmut Ahammer<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biophysics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Graz, Austria<br />

e-mail: helmut.ahammer@medunigraz.at<br />

Roland Sedivy<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, Country Medical Centre St.Pölten, Austria<br />

Fractal Dimensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Anal Intraepi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial Neoplasia (AIN)<br />

AIN is a precancerous c<strong>on</strong>diti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at is interrelated to infecti<strong>on</strong>s by human papillomaviruses<br />

(HPV) and HIV. The histological classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> AIN is getting more<br />

and more important, due to increasing HPV infecti<strong>on</strong> rates <str<strong>on</strong>g>th</str<strong>on</strong>g>roughout human<br />

populati<strong>on</strong>. Distinct grades <str<strong>on</strong>g>of</str<strong>on</strong>g> neoplasia are known, whereas high grades indicate a<br />

high risk for a tumor progressi<strong>on</strong>. Never<str<strong>on</strong>g>th</str<strong>on</strong>g>eless, <str<strong>on</strong>g>th</str<strong>on</strong>g>e grading diagnosis <str<strong>on</strong>g>of</str<strong>on</strong>g> histological<br />

slides is not always clear because <str<strong>on</strong>g>of</str<strong>on</strong>g> varying subjective c<strong>on</strong>diti<strong>on</strong>s. In additi<strong>on</strong> to<br />

subjective diagnoses, quantitative classificati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods would be attractive but sophisticated<br />

soluti<strong>on</strong>s have not quantitatively been developed so far. Therefore, <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

study intends to evaluate digital images <str<strong>on</strong>g>of</str<strong>on</strong>g> AIN tissues by incorporating n<strong>on</strong>linear<br />

morphological analysis. AIN tissues were H&E stained and digitally photographed<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a standard microscope. Three distinct grades were diagnosed by a well trained<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologist in order to get a reference. The fractal dimensi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e images grey<br />

value landscapes using Fourier transformati<strong>on</strong> were calculated and compared to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e subjective diagnoses. Distinct grades <str<strong>on</strong>g>of</str<strong>on</strong>g> AIN led to distinct and well separated<br />

values <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fractal dimensi<strong>on</strong>. Higher grades <str<strong>on</strong>g>of</str<strong>on</strong>g> AIN yielded higher values <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

fractal dimensi<strong>on</strong>. The c<strong>on</strong>clusi<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>at fractal geometry is well suited for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

diagnosis <str<strong>on</strong>g>of</str<strong>on</strong>g> AIN. The fractal dimensi<strong>on</strong> reflects <str<strong>on</strong>g>th</str<strong>on</strong>g>e roughness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e images grey<br />

value distributi<strong>on</strong> and is in accordance wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e grading. Therefore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e fractal<br />

dimensi<strong>on</strong> is a quantitative value <str<strong>on</strong>g>th</str<strong>on</strong>g>at may routinely support subjective diagnoses.<br />

Keywords: intraepi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial neoplasia, image processing, fractal dimensi<strong>on</strong>, Fourier<br />

transformati<strong>on</strong><br />

30

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Informati<strong>on</strong>, human behaviour and disease; Saturday, July 2, 11:00<br />

Marco Ajelli<br />

Bruno Kessler Foundati<strong>on</strong><br />

e-mail: ajelli@fbk.eu<br />

Piero Poletti<br />

Bruno Kessler Foundati<strong>on</strong><br />

Stefano Merler<br />

Bruno Kessler Foundati<strong>on</strong><br />

Risk percepti<strong>on</strong> and 2009 H1N1 pandemic influenza spread<br />

in Italy<br />

In Italy, <str<strong>on</strong>g>th</str<strong>on</strong>g>e 2009 H1N1 pandemic influenza spread in a peculiar way: after an initial<br />

period characterized by a slow exp<strong>on</strong>ential increase in <str<strong>on</strong>g>th</str<strong>on</strong>g>e weekly H1N1 incidence,<br />

a sudden and sharp increase <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate was observed. Were behavioral<br />

changes sp<strong>on</strong>taneously performed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> resp<strong>on</strong>sible for such a notable<br />

pattern? In order to answer <str<strong>on</strong>g>th</str<strong>on</strong>g>is questi<strong>on</strong>, a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> influenza<br />

transmissi<strong>on</strong> is proposed and validated. The performed investigati<strong>on</strong>, based <strong>on</strong><br />

model fit to epidemiological data and <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> antiviral drugs purchase,<br />

reveals <str<strong>on</strong>g>th</str<strong>on</strong>g>at an initial overestimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong> during <str<strong>on</strong>g>th</str<strong>on</strong>g>e early stage<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic, possibly induced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e high c<strong>on</strong>cern for <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> a new<br />

influenza pandemic, results in a pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> spread compliant wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed <strong>on</strong>e.<br />

This study suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at individual choices may have driven <str<strong>on</strong>g>th</str<strong>on</strong>g>e H1N1 dynamics in<br />

Italy during its initial phases and <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey can drastically affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> future<br />

epidemics, by altering timing, dynamics and overall number <str<strong>on</strong>g>of</str<strong>on</strong>g> cases. In c<strong>on</strong>clusi<strong>on</strong>,<br />

to correctly inform public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> decisi<strong>on</strong>s, sp<strong>on</strong>taneous behavioral changes cannot<br />

be neglected in epidemic modeling.<br />

31

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bioinformatics and System Biology; Wednesday, June 29, 14:30<br />

Ilya Akberdin∗,1 Fedor Kazantsev1 Maxim Ri1 Natalya Ri1 Vladimir Tim<strong>on</strong>ov1,2,3 Tamara M. Khlebodarova1 Vitaly A. Likhoshvai1,2 1Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Systems Biology, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Cytology and Genetics,<br />

Siberian Branch <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Russian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Lavrentyev Ave.,<br />

10, Novosibirsk, 630090, Russia<br />

2Novosibirsk State University, Novosibirsk, Pirogova str. 2, 630090,<br />

Russia<br />

3Siberian State University <str<strong>on</strong>g>of</str<strong>on</strong>g> Telecommunicati<strong>on</strong>s and Informati<strong>on</strong><br />

Sciences, Novosibirsk, Kirova str. 86, 630102, Russia<br />

e-mail: ∗akberdin@bi<strong>on</strong>et.nsc.ru Automatic generati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

molecular-genetic systems<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular-genetic systems are based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e informati<strong>on</strong><br />

about <str<strong>on</strong>g>th</str<strong>on</strong>g>e structural and functi<strong>on</strong>al organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> gene networks and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir dynamic<br />

properties <str<strong>on</strong>g>th</str<strong>on</strong>g>at disseminated over hundreds and <str<strong>on</strong>g>th</str<strong>on</strong>g>ousands <str<strong>on</strong>g>of</str<strong>on</strong>g> scientific papers. The<br />

problem arises <str<strong>on</strong>g>of</str<strong>on</strong>g> data comparis<strong>on</strong> and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-uniformed experimental<br />

data, analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> cause-and-effect relati<strong>on</strong>s between molecular structure, dynamics<br />

and phenotypic features <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular-genetic system, and s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware development for<br />

automatic generati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models, storage <str<strong>on</strong>g>of</str<strong>on</strong>g> creating models in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

database and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir numerical analysis. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> solving some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e above<br />

menti<strong>on</strong>ed problems we have developed an integrated computer system and models<br />

database <str<strong>on</strong>g>th</str<strong>on</strong>g>at do not <strong>on</strong>ly render automatically <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models<br />

rec<strong>on</strong>structi<strong>on</strong> based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e structural and functi<strong>on</strong>al organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> gene networks<br />

but also implements original approaches and algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms to modeling and studying<br />

molecular-genetic systems. The examples <str<strong>on</strong>g>of</str<strong>on</strong>g> using <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system are dem<strong>on</strong>strated<br />

<strong>on</strong> a modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> some gene regulatory networks.<br />

32

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Genetics; Friday, July 1, 14:30<br />

Ada Akerman<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Vienna, Austria<br />

e-mail: ada.akerman@univie.ac.at<br />

Reinhard Bürger<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Vienna, Austria<br />

Local adaptati<strong>on</strong> under diversifying selecti<strong>on</strong>: A two-locus<br />

migrati<strong>on</strong>- selecti<strong>on</strong> model<br />

A populati<strong>on</strong>-genetic model <str<strong>on</strong>g>of</str<strong>on</strong>g> local adapti<strong>on</strong> in discrete space and time is studied.<br />

We model a populati<strong>on</strong> inhabiting two discrete demes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> gene flow between <str<strong>on</strong>g>th</str<strong>on</strong>g>em.<br />

Genetic drift is ignored as we assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> size is large. We c<strong>on</strong>sider<br />

two linked loci under selecti<strong>on</strong> and assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment favors alternative<br />

alleles in <str<strong>on</strong>g>th</str<strong>on</strong>g>e two demes. An important interpretati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is in terms <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a quantitative trait <str<strong>on</strong>g>th</str<strong>on</strong>g>at is under directi<strong>on</strong>al selecti<strong>on</strong> acting in opposite directi<strong>on</strong><br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e two demes. The trait is assumed to be determined additively, i.e., wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out<br />

epistasis, by two loci <str<strong>on</strong>g>th</str<strong>on</strong>g>at may exhibit dominance. Thus, essentially, disruptive<br />

selecti<strong>on</strong> acts <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e trait. This scenario allows us to answer interesting questi<strong>on</strong>s<br />

<strong>on</strong> local adaptati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> genetic variati<strong>on</strong>. We derive explicit<br />

results for <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence and amount <str<strong>on</strong>g>of</str<strong>on</strong>g> polymorphism in several limiting cases such<br />

as weak migrati<strong>on</strong>, weak selecti<strong>on</strong>, tight linkage, and free recombinati<strong>on</strong>. In particular,<br />

we present informative approximati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> well-known measures <str<strong>on</strong>g>of</str<strong>on</strong>g> linkage<br />

disequilibrium and investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> linkage and dominance <strong>on</strong> local<br />

adapti<strong>on</strong> and genetic variati<strong>on</strong>.<br />

References.<br />

[1] Akerman, A., and R. Bürger. Local adaptati<strong>on</strong> under diversifying selecti<strong>on</strong>: A two-locus<br />

migrati<strong>on</strong>- selecti<strong>on</strong> model. Manuscript (2011)<br />

33

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Masakazu Akiyama<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Kyushu University<br />

e-mail: masakazu.akiyam@gmail.com<br />

Atsushi Tero<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Kyushu University<br />

e-mail: tero.atsushi@gmail.com<br />

Ryo Kobayashi<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Life Sciences, Hiroshima University<br />

e-mail: ryo@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.sci.hiroshima-u.ac.jp<br />

A Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Model <str<strong>on</strong>g>of</str<strong>on</strong>g> Cleavage<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e present paper, we propose a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> cleavage. Cleavage is<br />

a process during <str<strong>on</strong>g>th</str<strong>on</strong>g>e early stages <str<strong>on</strong>g>of</str<strong>on</strong>g> development in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e fertile egg undergoes<br />

repeated divisi<strong>on</strong> keeping <str<strong>on</strong>g>th</str<strong>on</strong>g>e cluster size almost c<strong>on</strong>stant. During <str<strong>on</strong>g>th</str<strong>on</strong>g>e cleavage<br />

process individual cells repeat cell divisi<strong>on</strong> in an orderly manner to form a blastula,<br />

however, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanism which achieves such a coordinati<strong>on</strong> is still not very clear.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e present research, we took sea urchin as an example and focused <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chemical substances from <str<strong>on</strong>g>th</str<strong>on</strong>g>e animal and vegetal pole. By c<strong>on</strong>sidering<br />

chemotactic moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e centrosomes, we c<strong>on</strong>structed a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e processes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e early stages <str<strong>on</strong>g>of</str<strong>on</strong>g> cleavage.<br />

For example, in a sea urchin, <str<strong>on</strong>g>th</str<strong>on</strong>g>e 1st cleavage and <str<strong>on</strong>g>th</str<strong>on</strong>g>e 2nd cleavage happen<br />

al<strong>on</strong>g a field including an animal pole and a vegetal pole (meridi<strong>on</strong>al cleavage). This<br />

detects <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong> gradient <str<strong>on</strong>g>of</str<strong>on</strong>g> a certain chemical substance from <str<strong>on</strong>g>th</str<strong>on</strong>g>e animal<br />

pole to a vegetal pole, and is c<strong>on</strong>sidered to use for <str<strong>on</strong>g>th</str<strong>on</strong>g>e determinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a cleavage<br />

plane. The 3rd following cleavage is a field which intersects perpendicularly wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e 1st and <str<strong>on</strong>g>th</str<strong>on</strong>g>e 2nd cleavage plane. However, if it inserts wi<str<strong>on</strong>g>th</str<strong>on</strong>g> glass and pressure is<br />

put and changed from two poles, it is known <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e 3rd cleavage will turn into a<br />

meridi<strong>on</strong>al cleavage. It has suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e determinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a cleavage plane is<br />

not necessarily decided <strong>on</strong>ly by distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a chemical substance, and receives<br />

influence in a dynamic factor, a geometric factor, etc. from <str<strong>on</strong>g>th</str<strong>on</strong>g>is. Cell divisi<strong>on</strong><br />

may <str<strong>on</strong>g>th</str<strong>on</strong>g>ink <str<strong>on</strong>g>th</str<strong>on</strong>g>at it is prescribed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e aster. Normal divisi<strong>on</strong> takes place, when<br />

<strong>on</strong>e pair <str<strong>on</strong>g>of</str<strong>on</strong>g> asters exist in <strong>on</strong>e cell, and cleavage does not happen wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out an aster.<br />

When four asters exist in a cell, being divided in four is reported. The centrosome<br />

located at <str<strong>on</strong>g>th</str<strong>on</strong>g>e center <str<strong>on</strong>g>of</str<strong>on</strong>g> an aster determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e positi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an aster. In order to<br />

form <strong>on</strong>e pair <str<strong>on</strong>g>of</str<strong>on</strong>g> asters, it is required to divide a centrosome in two and to arrange<br />

it in advance <str<strong>on</strong>g>of</str<strong>on</strong>g> it, in a suitable positi<strong>on</strong>. As menti<strong>on</strong>ed above, it turns out <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e decisive role is played when <str<strong>on</strong>g>th</str<strong>on</strong>g>e positi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e centrosome which has opted for<br />

arrangement <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e aster determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e geometry <str<strong>on</strong>g>of</str<strong>on</strong>g> cell divisi<strong>on</strong>. Well <str<strong>on</strong>g>th</str<strong>on</strong>g>en, how<br />

does <str<strong>on</strong>g>th</str<strong>on</strong>g>is centrosphere move? The microtubule has c<strong>on</strong>nected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e centrosome<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e aster is c<strong>on</strong>stituted. By work <str<strong>on</strong>g>of</str<strong>on</strong>g> a duplicati<strong>on</strong> regi<strong>on</strong> microtubule, an aster<br />

is repelled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er aster. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e spindle could maintain a fixed<br />

distance wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a cell, in order for an aster microtubule to receive restituti<strong>on</strong> also<br />

34

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

from a film. However, <strong>on</strong>ly in such assumpti<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e directivity <str<strong>on</strong>g>of</str<strong>on</strong>g> divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an<br />

egg does not become settled. Then, we assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e factor <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong><br />

which exists in an animal pole and a vegetal pole exerted taxis <strong>on</strong> a centrosphere.<br />

We did <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical computati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e directivity and <str<strong>on</strong>g>th</str<strong>on</strong>g>e positi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a spindle<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e form and <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> field <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e egg. As a result, it found out <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

c<strong>on</strong>vexity <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>centrati<strong>on</strong> gradient can determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e directivity <str<strong>on</strong>g>of</str<strong>on</strong>g> cell divisi<strong>on</strong>.<br />

We introduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e details about <str<strong>on</strong>g>th</str<strong>on</strong>g>is research.<br />

References.<br />

[1] Scott, F.G., Developmental Biology, 2nd ed. Sinauer Associates, Inc. pp. 84-86.<br />

[2] M. Akiyama, A. Tero and R. Kobayashi, A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> cleavage J. Theor Biol.<br />

2010 May 7;264(1):84-94.<br />

35

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis II; Wednesday, June<br />

29, 11:00<br />

Tomas Alarc<strong>on</strong><br />

Computati<strong>on</strong>al & Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology Group Centre de Recerca<br />

Matematica (CRM) Barcel<strong>on</strong>a, Spain<br />

e-mail: emailtalarc<strong>on</strong>@crm.cat<br />

A flow-coupled phase-field model <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour-induced<br />

angiogenesis<br />

We present a first attempt to formulate a biophysically motivated model <str<strong>on</strong>g>of</str<strong>on</strong>g> structural<br />

vascular adaptati<strong>on</strong> and angiogenesis. In several models <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis so<br />

far, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular structural adaptati<strong>on</strong> being used is <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>e proposed by<br />

Pries, Secomb and co-workers. This model was proposed for modelling blood flow<br />

in rat mesentery and, <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore, is unlikely to be an accurate model for tumour<br />

vasculature. We discuss a model <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular adaptati<strong>on</strong> based <strong>on</strong> a biophysical<br />

(including elasticity, surface tensi<strong>on</strong>, etc) descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> capillaries<br />

to increased demands <str<strong>on</strong>g>of</str<strong>on</strong>g> blood flow.<br />

36

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Tuesday, June 28, 14:30<br />

Maym<strong>on</strong>a Al-husari<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stra<str<strong>on</strong>g>th</str<strong>on</strong>g>clyde, UK, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics<br />

e-mail: maym<strong>on</strong>a.al-husari@stra<str<strong>on</strong>g>th</str<strong>on</strong>g>.ac.uk<br />

Dr Steven Webb<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stra<str<strong>on</strong>g>th</str<strong>on</strong>g>clyde, UK, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics<br />

Regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Tumour Intracellular pH: A Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

Model Examining <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay between hydrogen i<strong>on</strong>s and<br />

lactate<br />

N<strong>on</strong>-invasive measurements <str<strong>on</strong>g>of</str<strong>on</strong>g> pH have shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at bo<str<strong>on</strong>g>th</str<strong>on</strong>g> tumour and normal cells<br />

have intracellular pH (pHi) <str<strong>on</strong>g>th</str<strong>on</strong>g>at lies <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e alkaline side <str<strong>on</strong>g>of</str<strong>on</strong>g> neutrality (7.1-7.2).<br />

However, extracellular pH (pHe) is reported to be more acidic in some tumours<br />

compared to normal tissues. Many cellular processes and <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic agents are<br />

known to be highly pH dependent which makes <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> intracellular pH regulati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> paramount importance. We <str<strong>on</strong>g>th</str<strong>on</strong>g>us develop a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

examines <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> various membrane-based i<strong>on</strong> transporters in tumour pH regulati<strong>on</strong>,<br />

in particular, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay between lactate and H+ i<strong>on</strong>s and<br />

whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e lactate/H+ symporter activity is sufficient to give rise to <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed<br />

reversed pH gradient. Using linear stability analysis and numerical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods, we are<br />

able to gain a clear understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship between lactate and H+ i<strong>on</strong>s.<br />

We extend <str<strong>on</strong>g>th</str<strong>on</strong>g>is analysis using perturbati<strong>on</strong> techniques to specifically examine a<br />

rapid change in <str<strong>on</strong>g>th</str<strong>on</strong>g>e H+ i<strong>on</strong>s c<strong>on</strong>centrati<strong>on</strong>s relative to lactate. We finally perform<br />

a parameter sensitivity analysis to explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> robustness to parameter<br />

variati<strong>on</strong>s. An important result from our study is <str<strong>on</strong>g>th</str<strong>on</strong>g>at a reversed pH gradient is<br />

possible but for unrealistic parameter estimates-pointing to <str<strong>on</strong>g>th</str<strong>on</strong>g>e possible involvement<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er mechanisms in <str<strong>on</strong>g>th</str<strong>on</strong>g>is phenomen<strong>on</strong> such as acidic vesicles, lysosomes,<br />

golgi and endosomes.<br />

37

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ecology and evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases; Friday, July 1, 14:30<br />

Samuel Aliz<strong>on</strong><br />

Laboratoire MIVEGEC (UMR CNRS 5290, IRD 224, UM1, UM2), M<strong>on</strong>tpellier,<br />

France<br />

e-mail: samuel.aliz<strong>on</strong>@ird.fr<br />

Sébastien Li<strong>on</strong><br />

Centre d’Écologie F<strong>on</strong>cti<strong>on</strong>nelle et Évolutive, UMR 5175, M<strong>on</strong>tpellier,<br />

France<br />

e-mail: li<strong>on</strong>@cefe.cnrs.fr<br />

Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-host parasite cooperati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

virulence<br />

Infecti<strong>on</strong>s by multiple genotypes are comm<strong>on</strong> in nature and are known to select<br />

for higher levels <str<strong>on</strong>g>of</str<strong>on</strong>g> virulence in some pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens. It has been argued <str<strong>on</strong>g>th</str<strong>on</strong>g>at for<br />

parasites whose virulence is determined by <str<strong>on</strong>g>th</str<strong>on</strong>g>e producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> public goods, such<br />

co-infecti<strong>on</strong>s can select for lower levels <str<strong>on</strong>g>of</str<strong>on</strong>g> virulence. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>is predicti<strong>on</strong> is<br />

rooted in a perspective <str<strong>on</strong>g>th</str<strong>on</strong>g>at neglects epidemiological feedbacks. Here, we analyse<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> parasites producing a public good, for example siderophore-producing<br />

bacteria, using a nested model <str<strong>on</strong>g>th</str<strong>on</strong>g>at ties toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-host and epidemiological<br />

processes. Making <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemiology explicit wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an SI model reveals <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

current predicti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at co-infecti<strong>on</strong> should select for less virulent strains for publicgoods<br />

producing parasites is <strong>on</strong>ly valid if bo<str<strong>on</strong>g>th</str<strong>on</strong>g> parasite transmissi<strong>on</strong> and virulence<br />

are a linear functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> parasite density. If <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f relati<strong>on</strong>ship such <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

virulence increases more rapidly <str<strong>on</strong>g>th</str<strong>on</strong>g>an transmissi<strong>on</strong>, or if virulence also depends <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e total amount <str<strong>on</strong>g>of</str<strong>on</strong>g> public goods produced, <str<strong>on</strong>g>th</str<strong>on</strong>g>en co-infecti<strong>on</strong>s should select for<br />

more virulent strains. This suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical or empirical studies <str<strong>on</strong>g>th</str<strong>on</strong>g>at seek<br />

to determine optimal virulence wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a single host may not be representative <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e selecti<strong>on</strong> pressures faced by parasites at <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> level. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e same time,<br />

it underlines <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> including epidemiological processes when studying<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases.<br />

38

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Mechanical Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Movement and Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cells and Tissues II;<br />

Wednesday, June 29, 17:00<br />

Wolfgang Alt<br />

Theoretical Biology, University B<strong>on</strong>n, Germany<br />

e-mail: wolf-alt@uni-b<strong>on</strong>n.de<br />

Martin Bock<br />

Theoretical Biology, University B<strong>on</strong>n, Germany<br />

e-mail: mab@uni-b<strong>on</strong>n.de<br />

Mechanical feedback drives cell polarizati<strong>on</strong>, adhesi<strong>on</strong> and<br />

migrati<strong>on</strong><br />

Besides frequently studied regulatory pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways for spatial assembly <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular<br />

motor molecules and cell-cell/matrix adhesi<strong>on</strong> proteins, cf. [1], mainly resp<strong>on</strong>sible<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong>ing <str<strong>on</strong>g>of</str<strong>on</strong>g> cell migrati<strong>on</strong> and tissue formati<strong>on</strong> are primary<br />

biophysical "actors" such as mass flow, tracti<strong>on</strong> force, tensi<strong>on</strong> and pressure. Their<br />

dynamics determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e processes <str<strong>on</strong>g>of</str<strong>on</strong>g> cell deformati<strong>on</strong> and translocati<strong>on</strong> as well as<br />

cell-cell cohesi<strong>on</strong>.<br />

As basis for a most simple mechanical model <str<strong>on</strong>g>of</str<strong>on</strong>g> single cell motility we use<br />

a two-phase "reactive, viscous and c<strong>on</strong>tractive fluid" c<strong>on</strong>tinuum model, written<br />

as a hyperbolic-elliptic PDE system <str<strong>on</strong>g>of</str<strong>on</strong>g> Navier-Stokes type. This model is able<br />

to reproduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed chaotic dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> actin/myosin cluster formati<strong>on</strong> [2].<br />

Then we combine it wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a suitable system <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong>-transport-reacti<strong>on</strong> equati<strong>on</strong>s<br />

for free and bound myosin dimers and integrin adhesi<strong>on</strong> sites [3].<br />

Numerical simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> two- and <strong>on</strong>e-dimensi<strong>on</strong>al model variants reveal sp<strong>on</strong>taneous<br />

and induced fr<strong>on</strong>t-rear polarizati<strong>on</strong> and, subsequently, directi<strong>on</strong>al persistence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cell migrati<strong>on</strong>. Thereby we dem<strong>on</strong>strate, how <str<strong>on</strong>g>th</str<strong>on</strong>g>ese experimentally observed<br />

phenomena <str<strong>on</strong>g>of</str<strong>on</strong>g> cell motility can be traced back to an interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> different<br />

biophysical and biochemical mechanisms such as cell edge protrusi<strong>on</strong>, adhesi<strong>on</strong> site<br />

maturati<strong>on</strong> and force-induced integrin-b<strong>on</strong>d disrupture.<br />

References.<br />

[1] S.M. Rafelski and J.A. Theriot (2004) Crawling toward a unified model <str<strong>on</strong>g>of</str<strong>on</strong>g> cell motility:<br />

spatial and temporal regulat<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> actin dynamics. Annual Review <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemistry 73 209–239.<br />

[2] E. Kuusela and W.Alt (2009) C<strong>on</strong>tinuum model <str<strong>on</strong>g>of</str<strong>on</strong>g> cell adhesi<strong>on</strong> and migrati<strong>on</strong> J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol.<br />

58 135-161.<br />

[3] W. Alt, M. Bock and Ch. Möhl (2010) Coupling <str<strong>on</strong>g>of</str<strong>on</strong>g> cytoplasm and adhesi<strong>on</strong> dynamics<br />

determines cell polarizati<strong>on</strong> and locomoti<strong>on</strong>. In: A. Chauviere, L. Preziosi, C. Verdier (eds.)<br />

Cell Mechanics: From Single Cell-Based Models to Multiscale Modeling. Taylor & Francis.<br />

Chapt. 4, pp. 89-131 (www.ArXiv.org 0907.5078).<br />

39

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Heart rate dynamics: models and measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity (part II);<br />

Wednesday, June 29, 17:00<br />

Krystyna Ambroch<br />

Gdansk University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: ambroch@mif.pg.gda.pl<br />

Time series models for heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y people and patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

LVSD<br />

The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e talk is to discuss time series models which are found as characteristic<br />

for two groups interesting for cardiology. ARIMA models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> GARCH for<br />

residuals <str<strong>on</strong>g>of</str<strong>on</strong>g> ARIMA or squared residuals <str<strong>on</strong>g>of</str<strong>on</strong>g> ARIMA were fitted to RR intervals <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

24h ECG Holter m<strong>on</strong>itoring in group <str<strong>on</strong>g>of</str<strong>on</strong>g> 50 normal subjects wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out past history<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cardiovascular diseases (average age <str<strong>on</strong>g>of</str<strong>on</strong>g> 53 10yrs). Specific subclass od ARIMA<br />

models were fitted to RR intervals <str<strong>on</strong>g>of</str<strong>on</strong>g> 24h ECG Holter m<strong>on</strong>itoring in group <str<strong>on</strong>g>of</str<strong>on</strong>g> 48<br />

patients (average age <str<strong>on</strong>g>of</str<strong>on</strong>g> 57 10yrs) wi<str<strong>on</strong>g>th</str<strong>on</strong>g> LVSD.<br />

40

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Heart rate dynamics: models and measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity (part I);<br />

Wednesday, June 29, 14:30<br />

Jose Amigó<br />

Universidad Miguel Hernandez (Spain)<br />

e-mail: jm.amigo@umh.es<br />

An overview <str<strong>on</strong>g>of</str<strong>on</strong>g> permutati<strong>on</strong> entropy<br />

Permutati<strong>on</strong> entropy was introduced in 2002 by Bandt and Pompe as a complexity<br />

measure for time series. Roughly speaking, permutati<strong>on</strong> entropy replaces <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

probabilities <str<strong>on</strong>g>of</str<strong>on</strong>g> leng<str<strong>on</strong>g>th</str<strong>on</strong>g>-L symbol blocks in <str<strong>on</strong>g>th</str<strong>on</strong>g>e definiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Shann<strong>on</strong>s entropy by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

probabilities <str<strong>on</strong>g>of</str<strong>on</strong>g> leng<str<strong>on</strong>g>th</str<strong>on</strong>g>-L ordinal patterns, each pattern being a digest <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ups and<br />

downs <str<strong>on</strong>g>of</str<strong>on</strong>g> L c<strong>on</strong>secutive elements <str<strong>on</strong>g>of</str<strong>on</strong>g> a time series. Since <str<strong>on</strong>g>th</str<strong>on</strong>g>en permutati<strong>on</strong> entropy<br />

itself, al<strong>on</strong>g wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different tools based <strong>on</strong> ordinal patterns, have found a number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> interesting applicati<strong>on</strong>s. To menti<strong>on</strong> a few: Estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> metric and topological<br />

entropy, complexity analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> time series, detecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> determinism in noisy<br />

time series, recovery <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trol parameters in symbolic sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> unimodal maps,<br />

and characterizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> synchr<strong>on</strong>izati<strong>on</strong>. In all <str<strong>on</strong>g>th</str<strong>on</strong>g>ese applicati<strong>on</strong>s, computati<strong>on</strong>al<br />

efficiency and robustness against observati<strong>on</strong>al noise are a crucial advantage.<br />

The first part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e talk will be a review <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basics <str<strong>on</strong>g>of</str<strong>on</strong>g> permutati<strong>on</strong> entropy.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d part, <str<strong>on</strong>g>th</str<strong>on</strong>g>e focus will be <strong>on</strong> applicati<strong>on</strong>s to <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> biomedical<br />

series. In particular, we expect to report <strong>on</strong> work in progress in <str<strong>on</strong>g>th</str<strong>on</strong>g>is field.<br />

References.<br />

[1] José M. Amigó, Permutati<strong>on</strong> Complexity in Dynamical Systems. Springer Verlag, 2010 (ISBN:<br />

978-3-642-04083-2)<br />

41

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 11:00<br />

Tea Ammunét<br />

Secti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ecology, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Turku,<br />

FI-20014 Turku, Finland<br />

e-mail: tea.ammunet@utu.fi<br />

Tero Klemola<br />

Secti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ecology, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Turku,<br />

FI-20014 Turku, Finland<br />

Kalle Parvinen<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Turku, FI-20014 Turku,<br />

Finland<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e outcome <str<strong>on</strong>g>of</str<strong>on</strong>g> climate change driven invasi<strong>on</strong>:<br />

effects <str<strong>on</strong>g>of</str<strong>on</strong>g> apparent competiti<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resident and invasive<br />

forest herbivore populati<strong>on</strong> dynamics.<br />

Invasive species can have pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ound effects <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resident community via indirect<br />

interacti<strong>on</strong>s. Particularly, forest insect herbivores are known to be able to affect<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e invaded ecosystems by trophic interacti<strong>on</strong>s. Of <str<strong>on</strong>g>th</str<strong>on</strong>g>e indirect mechanisms, apparent<br />

competiti<strong>on</strong> is a highly plausible but less frequently studied structuring<br />

phenomen<strong>on</strong> in terrestrial herbivore communities. Never<str<strong>on</strong>g>th</str<strong>on</strong>g>eless, surprisingly few<br />

studies have been made <str<strong>on</strong>g>of</str<strong>on</strong>g> apparent competiti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> invasive insect<br />

species. The tendency <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g periodic cycles in herbivore populati<strong>on</strong> dynamics can<br />

make <str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e indirect effects difficult using experimental setups.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, dynamic m<strong>on</strong>ophagy in established communities may prevent <str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> apparent competiti<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e community. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

<strong>on</strong>going invasi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-native species into new envir<strong>on</strong>ments create a stage to observe<br />

apparent competiti<strong>on</strong> before adaptati<strong>on</strong> obscures <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s. Modelling<br />

invasi<strong>on</strong>s based <strong>on</strong> real invader-resident communities can <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore be <str<strong>on</strong>g>of</str<strong>on</strong>g> particular<br />

help when determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e undetectable and l<strong>on</strong>g term effects <str<strong>on</strong>g>of</str<strong>on</strong>g> invasive species.<br />

The winter mo<str<strong>on</strong>g>th</str<strong>on</strong>g>, a cyclic foliage feeding geometrid mo<str<strong>on</strong>g>th</str<strong>on</strong>g>, has expanded its<br />

outbreak range during recent years due to warming winter temperatures. The<br />

mountain birches in <str<strong>on</strong>g>th</str<strong>on</strong>g>e new invaded areas (<str<strong>on</strong>g>th</str<strong>on</strong>g>e dominant green leafed tree in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

areas) have previously been defoliated <strong>on</strong> a 9 to 10 year basis by <str<strong>on</strong>g>th</str<strong>on</strong>g>e resident<br />

autumnal mo<str<strong>on</strong>g>th</str<strong>on</strong>g>. The autumnal mo<str<strong>on</strong>g>th</str<strong>on</strong>g> itself is able to cause drastic foliage loss in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

mountain birch forests occasi<strong>on</strong>ally resulting in vast tree dea<str<strong>on</strong>g>th</str<strong>on</strong>g>s. The new invader,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e winter mo<str<strong>on</strong>g>th</str<strong>on</strong>g>, has already been observed to be capable <str<strong>on</strong>g>of</str<strong>on</strong>g> total forest defoliati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> similar magnitude. The two species share, in additi<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e host tree, generalist<br />

predators and parasitoids in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese Fennoscandian areas. Asymmetric preference<br />

at bo<str<strong>on</strong>g>th</str<strong>on</strong>g> parasitism and predati<strong>on</strong> rates has been recently observed. In order to<br />

fully see <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> asymmetric effects <str<strong>on</strong>g>of</str<strong>on</strong>g> natural enemies <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e 9 to<br />

11-year populati<strong>on</strong> cycles, a modelling approach was called for. We were especially<br />

interested in, are <str<strong>on</strong>g>th</str<strong>on</strong>g>ese asymmetries able to cause asynchr<strong>on</strong>ous populati<strong>on</strong> cycles<br />

as seen in <str<strong>on</strong>g>th</str<strong>on</strong>g>e area <str<strong>on</strong>g>of</str<strong>on</strong>g> sympatric occurrence. In additi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g term effects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

invasi<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resident community are <str<strong>on</strong>g>of</str<strong>on</strong>g> particular interest, since recent evidence<br />

shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at winter mo<str<strong>on</strong>g>th</str<strong>on</strong>g>s are interacting in several ways wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e local community<br />

and fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er range expansi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is forest pest does not seem to be restricted by<br />

nei<str<strong>on</strong>g>th</str<strong>on</strong>g>er abiotic nor biotic interacti<strong>on</strong>s.<br />

42

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

We used empirical data from <str<strong>on</strong>g>th</str<strong>on</strong>g>e recent invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cyclic winter mo<str<strong>on</strong>g>th</str<strong>on</strong>g>s in<br />

nor<str<strong>on</strong>g>th</str<strong>on</strong>g>ern Fennoscandia as a starting point and modelled <str<strong>on</strong>g>th</str<strong>on</strong>g>e outcome <str<strong>on</strong>g>of</str<strong>on</strong>g> observed<br />

short term asymmetric effects via generalist predators and parasitoids <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g<br />

term populati<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasive winter and resident autumnal mo<str<strong>on</strong>g>th</str<strong>on</strong>g>s.<br />

Adaptive dynamics <str<strong>on</strong>g>th</str<strong>on</strong>g>eory was used and invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e winter mo<str<strong>on</strong>g>th</str<strong>on</strong>g> into <str<strong>on</strong>g>th</str<strong>on</strong>g>e resident<br />

community was modelled. Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e results, apparent competiti<strong>on</strong> and<br />

asymmetries in <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> generalist predators are able to produce <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed<br />

asynchr<strong>on</strong>ous cycles. However, instead <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary branching resulting in evoluti<strong>on</strong>ary<br />

stable coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two species, <str<strong>on</strong>g>th</str<strong>on</strong>g>e system experiences cycles <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

evoluti<strong>on</strong>ary branching and extincti<strong>on</strong>. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, independent <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e modelled<br />

dynamics, <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasive species was observed have <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential to inflict drastic<br />

changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mountain birch community.<br />

43

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Dynamics; Wednesday, June 29, 17:00<br />

Anan<str<strong>on</strong>g>th</str<strong>on</strong>g>i Anandanadesan<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee<br />

e-mail: anan<str<strong>on</strong>g>th</str<strong>on</strong>g>i@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.dundee.ac.uk<br />

Alis<strong>on</strong> Karley<br />

Scottish Crop Research Institute<br />

e-mail: Alis<strong>on</strong>.Karley@scri.ac.uk<br />

Steven Hubbard<br />

Scottish Crop Research Institute<br />

e-mail: s.f.hubbard@dundee.ac.uk<br />

Pietá Sch<str<strong>on</strong>g>of</str<strong>on</strong>g>ield<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Life Sciences, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee<br />

e-mail: p.sch<str<strong>on</strong>g>of</str<strong>on</strong>g>ield@dundee.ac.uk<br />

Mark Chaplain<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee<br />

e-mail: chaplain@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.dundee.ac.uk<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

aphid-paraistoid-plant-virus interacti<strong>on</strong>s<br />

Aphids cause c<strong>on</strong>siderable damage to agricultural crops, mainly due to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

ability to transmit a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> plant viruses. Understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying processes<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>tribute to plant disease dynamics and how to c<strong>on</strong>tain <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

disease requires a combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biological and <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical study. The <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical<br />

undertaking requires not <strong>on</strong>ly an analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e temporal dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system,<br />

which has been <str<strong>on</strong>g>th</str<strong>on</strong>g>e focus <str<strong>on</strong>g>of</str<strong>on</strong>g> previous work, but also an analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial dynamics.<br />

Envir<strong>on</strong>mental stochasticity operates bo<str<strong>on</strong>g>th</str<strong>on</strong>g> spatially and temporally and<br />

is likely to influence aphid populati<strong>on</strong> processes. As a result, disease transmissi<strong>on</strong><br />

by aphids might be influenced by factors acting in additi<strong>on</strong> to density-dependent<br />

processes.<br />

To c<strong>on</strong>struct a realistic model <str<strong>on</strong>g>of</str<strong>on</strong>g> an aphid-natural enemy-plant-virus system,<br />

we are developing a spatial individual-based model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e aphid Macrosiphum euphorbiae<br />

<strong>on</strong> potato plants. Focus is <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e summer asexual aphid<br />

populati<strong>on</strong>s since aphid outbreaks occur when plant material becomes abundant.<br />

Individuals move randomly and/or via chemotaxis <strong>on</strong> a 2-dimensi<strong>on</strong>al domain representing<br />

<strong>on</strong>e or more plants. We take into account bo<str<strong>on</strong>g>th</str<strong>on</strong>g> parasitoid wasp (e.g.<br />

Aphidius ervi) and predator (e.g. syrphid larvae, coccinellids) natural enemies. Envir<strong>on</strong>mental<br />

stochasticity is incorporated into <str<strong>on</strong>g>th</str<strong>on</strong>g>e model by changing variables such<br />

as patch quality, temperature and light intensity. Parameter estimates for <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

are obtained from experimental quantificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> processes in aphids <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

harbour particular sec<strong>on</strong>dary bacteria or <str<strong>on</strong>g>th</str<strong>on</strong>g>at are free <str<strong>on</strong>g>of</str<strong>on</strong>g> sec<strong>on</strong>dary symbi<strong>on</strong>ts. A<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> aphid cl<strong>on</strong>es have been established in culture and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir sec<strong>on</strong>dary bacteria<br />

status c<strong>on</strong>firmed using diagnostic PCR. The individual-based model is used to<br />

assess how sec<strong>on</strong>dary endosymbi<strong>on</strong>ts affect aphid populati<strong>on</strong> dynamics, vector capacity<br />

and trophic interacti<strong>on</strong>s. Previous work <strong>on</strong> host-parasitoid models (Preedy<br />

et al. 2007; Pearce et al. 2006; Sch<str<strong>on</strong>g>of</str<strong>on</strong>g>ield et al. 2005) suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at a broad-range <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

dynamics including spatio-temporal heterogeneity and chaos can emerge from <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

systems and similar results are observed in our model.<br />

44

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

References.<br />

[1] I.G. Pearce, M.A.J. Chaplain, P.G. Sch<str<strong>on</strong>g>of</str<strong>on</strong>g>ield, S.F. Hubbard, Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> multi-species host-parasitoid interacti<strong>on</strong>s: heterogeneous patterns and ecological implicati<strong>on</strong>s<br />

J. Theoretical Biology 241 876–886.<br />

[2] K. Preedy, P.G. Sch<str<strong>on</strong>g>of</str<strong>on</strong>g>ield, M.A.J. Chaplain, S.F. Hubbard, Disease induced dynamics in hostparasitoid<br />

systems: chaos and coexistence Roy. Soc. Interface 4 463–471.<br />

[3] P.G. Sch<str<strong>on</strong>g>of</str<strong>on</strong>g>ield, M.A.J. Chaplain, S.F. Hubbard, Dynamic heterogeneous spatio-temporal pattern<br />

formati<strong>on</strong> in host-parasitoid systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> synchr<strong>on</strong>ized generati<strong>on</strong>s. J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Biology 50<br />

559-583.<br />

45

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Masahiro Anazawa<br />

Tohoku Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: anazawa@tohtech.ac.jp<br />

Populati<strong>on</strong> Dynamics; Wednesday, June 29, 17:00<br />

Interspecific competiti<strong>on</strong> models derived from competiti<strong>on</strong><br />

between individuals<br />

Populati<strong>on</strong> dynamics, including <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting populati<strong>on</strong>s, result from<br />

behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals comprising populati<strong>on</strong>s and interacti<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>em. It<br />

is important to reveal relati<strong>on</strong>ship between populati<strong>on</strong> dynamics and local interacti<strong>on</strong>s<br />

between individuals, and an effective way to do so is deriving populati<strong>on</strong><br />

models from first principles. In a previous study, I derived various discrete-time<br />

populati<strong>on</strong> models for a single species from first principles, and provided a unified<br />

view to understand how various populati<strong>on</strong> models interrelate wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er.<br />

Extending <str<strong>on</strong>g>th</str<strong>on</strong>g>e study above, <str<strong>on</strong>g>th</str<strong>on</strong>g>is study aims at deriving discrete-time interspecific<br />

competiti<strong>on</strong> models, which describe dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> competing two populati<strong>on</strong>s, by<br />

c<strong>on</strong>sidering competiti<strong>on</strong> for resource between individuals and spatial distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> individuals. Competiti<strong>on</strong> type <str<strong>on</strong>g>of</str<strong>on</strong>g> each species is assumed to be scramble, c<strong>on</strong>test<br />

or an intermediate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two types. Interspecific competiti<strong>on</strong> models are<br />

derived for various combinati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e competiti<strong>on</strong> types <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two species and<br />

several types <str<strong>on</strong>g>of</str<strong>on</strong>g> spatial distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, a general interspecific<br />

competiti<strong>on</strong> model <str<strong>on</strong>g>th</str<strong>on</strong>g>at includes various competiti<strong>on</strong> models as special cases<br />

is derived for each distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals. Finally, I discuss coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> two<br />

species, based <strong>on</strong> competiti<strong>on</strong> models derived for c<strong>on</strong>test vs. scramble case, and<br />

show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e ease <str<strong>on</strong>g>of</str<strong>on</strong>g> coexistence depends greatly <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e type <str<strong>on</strong>g>of</str<strong>on</strong>g> spatial distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> individuals.<br />

46

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

The emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance in cancer using ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling;<br />

Saturday, July 2, 08:30<br />

Alexander Anders<strong>on</strong><br />

Integrated Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Oncology, M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Centre<br />

e-mail: alexander.anders<strong>on</strong>@m<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt.org<br />

David Basanta<br />

Integrated Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Oncology, M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Centre<br />

Regulating drug resistance: Evoluti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e double-bind<br />

Treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cell populati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic drugs is nearly always<br />

associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>set <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance, where minor populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cells escape from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy and c<strong>on</strong>tinue to proliferate and lead to cancer recurrence and subsequent<br />

treatment failure. Resistance is also a comm<strong>on</strong> issue in <str<strong>on</strong>g>th</str<strong>on</strong>g>e ecology field, where<br />

insects become resistant to chemical pesticides after repeated treatments. However,<br />

unlike <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>cology field, <str<strong>on</strong>g>th</str<strong>on</strong>g>e ecologists have used o<str<strong>on</strong>g>th</str<strong>on</strong>g>er strategies to c<strong>on</strong>trol<br />

insect populati<strong>on</strong>s. Specifically, by using biological agents such as predators, parasites,<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens, and parasitoids c<strong>on</strong>trol has been achieved wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out any resulting<br />

resistance. One possible mechanism for <str<strong>on</strong>g>th</str<strong>on</strong>g>e success <str<strong>on</strong>g>of</str<strong>on</strong>g> such biological agents is an<br />

evoluti<strong>on</strong>ary double-bind, where in order to adapt to a given treatment an insect<br />

pays <str<strong>on</strong>g>th</str<strong>on</strong>g>e high cost <str<strong>on</strong>g>of</str<strong>on</strong>g> becoming significantly less fit in comparis<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e unadapted<br />

populati<strong>on</strong>. Here we present an Evoluti<strong>on</strong>ary Game Theory (EGT) model to investigate<br />

such a double-bind approach in <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer. Specifically, we<br />

use EGT to better understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> combinati<strong>on</strong> chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic strategies<br />

when m<strong>on</strong>o-<str<strong>on</strong>g>th</str<strong>on</strong>g>erapies ultimately always lead to drug resistance.<br />

47

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious agents;<br />

Tuesday, June 28, 17:00<br />

Viggo Andreasen<br />

Roskilde University<br />

e-mail: viggo@ruc.dk<br />

The final size <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two competing strains<br />

The competiti<strong>on</strong> between two pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen strains during <str<strong>on</strong>g>th</str<strong>on</strong>g>e course <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic<br />

represents a fundamental step in <str<strong>on</strong>g>th</str<strong>on</strong>g>e early evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> emerging diseases as well as<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e antigenic drift process. The outcome however, depends not <strong>on</strong>ly <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic<br />

properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two strains but also <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e timing and size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e introducti<strong>on</strong>,<br />

characteristics <str<strong>on</strong>g>th</str<strong>on</strong>g>at are poorly captured by deterministic mean-field epidemic models.<br />

I will present a framework <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows us to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>ose aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

competiti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be determined from <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean-field models giving <str<strong>on</strong>g>th</str<strong>on</strong>g>e range<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> possible outcomes <str<strong>on</strong>g>th</str<strong>on</strong>g>at could be observed in an epidemic wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two cross-reacting<br />

strains.<br />

48

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Roumen Anguelov<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Pretoria, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Africa<br />

e-mail: roumen.anguelov@up.ac.za<br />

Kei<str<strong>on</strong>g>th</str<strong>on</strong>g> A. Berven and Meir Shillor<br />

Oakland University, Michigan, USA<br />

e-mail: berven@oakland.edu, shillor@oakland.edu<br />

Populati<strong>on</strong> Dynamics; Wednesday, June 29, 08:30<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> Wood Frog Populati<strong>on</strong><br />

The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is to embed into a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>th</str<strong>on</strong>g>e Wood Frog,<br />

Rana sylvatica, populati<strong>on</strong> data collected by Berven, [3], over more <str<strong>on</strong>g>th</str<strong>on</strong>g>an 25 years.<br />

The life cycle <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e frogs includes aquatic and terrestrial phases, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e competiti<strong>on</strong><br />

in each phase is for different resources. Hence, we deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> separate<br />

populati<strong>on</strong>s, each <strong>on</strong>e providing <str<strong>on</strong>g>th</str<strong>on</strong>g>e new recruits for <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er <strong>on</strong>e, see, e.g., [1].<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Wood Frogs, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are <str<strong>on</strong>g>th</str<strong>on</strong>g>ree main stages <str<strong>on</strong>g>of</str<strong>on</strong>g> development where<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e individuals compete for different resources. The toads live in <str<strong>on</strong>g>th</str<strong>on</strong>g>e water, and<br />

following <str<strong>on</strong>g>th</str<strong>on</strong>g>eir metamorphosis <str<strong>on</strong>g>th</str<strong>on</strong>g>ey become juvenile frogs, not yet large enough to<br />

reproduce. The <str<strong>on</strong>g>th</str<strong>on</strong>g>ird stage is <str<strong>on</strong>g>of</str<strong>on</strong>g> mature egg laying frogs. The populati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ree stages <str<strong>on</strong>g>of</str<strong>on</strong>g> development have different dynamics. Hence, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are modelled<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical tools, which makes assembling <str<strong>on</strong>g>th</str<strong>on</strong>g>e model an interesting<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical problem. Due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e seas<strong>on</strong>s in Michigan, <str<strong>on</strong>g>th</str<strong>on</strong>g>e eggs are laid over<br />

a short time period and <str<strong>on</strong>g>th</str<strong>on</strong>g>e juveniles emerge from <str<strong>on</strong>g>th</str<strong>on</strong>g>e water more or less <str<strong>on</strong>g>th</str<strong>on</strong>g>e same<br />

time, so, we model <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two events by impulses, [4]. The success <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e metamorphosis<br />

depends mainly <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e toads. Hence, <str<strong>on</strong>g>th</str<strong>on</strong>g>e size distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

toads at <str<strong>on</strong>g>th</str<strong>on</strong>g>e time <str<strong>on</strong>g>of</str<strong>on</strong>g> metamorphosis determines bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> juveniles and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir initial size. Similarly, <str<strong>on</strong>g>th</str<strong>on</strong>g>e transfer from juvenile to adults depends mainly <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e frogs. It does not occur at a fixed time, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e juveniles who do not<br />

grow sufficiently to mate need to wait for a year before laying eggs. The grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e toads and <str<strong>on</strong>g>th</str<strong>on</strong>g>e juveniles in size is not uniform across <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> and depends<br />

<strong>on</strong> external factors, as well. It is modelled using PDEs for <str<strong>on</strong>g>th</str<strong>on</strong>g>e density size<br />

distributi<strong>on</strong> at time t. The dea<str<strong>on</strong>g>th</str<strong>on</strong>g> and fertility rates <str<strong>on</strong>g>of</str<strong>on</strong>g> mature frogs are not related<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir age. So <str<strong>on</strong>g>th</str<strong>on</strong>g>eir populati<strong>on</strong> is assumed to be homogeneous and is modelled<br />

by an ODE. Thus, <str<strong>on</strong>g>th</str<strong>on</strong>g>e derived model comprises a system <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary and partial<br />

impulsive differential equati<strong>on</strong>s. The ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> such a model can<br />

be complicated, see, e.g., [1]. Our analysis and numerical simulati<strong>on</strong>s focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

global properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model as a dynamical system, as in [2]. The results show<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e model may have a unique soluti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>verges to a stable periodic cycle.<br />

References.<br />

[1] A Ackleh, K Deng, A N<strong>on</strong>aut<strong>on</strong>omous Juvenile-Adult Model: Well-Posedness and L<strong>on</strong>g Term<br />

Behaivior via Comparis<strong>on</strong> Principle, SIAM Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics 6 (2009) 1644–<br />

1661.<br />

[2] R Anguelov, Y Dum<strong>on</strong>t, J M-S Lubuma, E Murei<str<strong>on</strong>g>th</str<strong>on</strong>g>i, Stability Analysis and Dynamics Preserving<br />

N<strong>on</strong>-Standard Finite Difference Schemes for a Malaria Model, Theoretical Populati<strong>on</strong><br />

Biology, to appear.<br />

[3] K A Berven, Density Dependence in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Terrestrial Stage <str<strong>on</strong>g>of</str<strong>on</strong>g> Wood Frogs: Evidence from a<br />

21-Year Populati<strong>on</strong> Study, Copeia, 2009, No. 2, 328–338<br />

[4] V Lakshmikan<str<strong>on</strong>g>th</str<strong>on</strong>g>an, D D Bainov, P S Sime<strong>on</strong>ov, Theory <str<strong>on</strong>g>of</str<strong>on</strong>g> Impulsive Differential Equati<strong>on</strong>s,<br />

World Scientific Publishing, 1989.<br />

49

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bridging Time Scales in Biological Sciences; Saturday, July 2, 14:30<br />

Iris Antes<br />

Technical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Munich<br />

e-mail: antes@wzw.tum.de<br />

Hierarchical approaches for <str<strong>on</strong>g>th</str<strong>on</strong>g>e investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biomolecular<br />

recogniti<strong>on</strong><br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e major bottlenecks for <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong>al descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biological processes<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular and atomistic level is <str<strong>on</strong>g>th</str<strong>on</strong>g>e limitati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e time scale and<br />

system size which can be treated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e existing <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods. Much research<br />

has been devoted to <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem and many advanced biophysical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

have been developed for <str<strong>on</strong>g>th</str<strong>on</strong>g>is task. Most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em are, however, very time c<strong>on</strong>suming<br />

and not applicable to applicati<strong>on</strong>s for which very complex systems must be investigated<br />

and if many different situati<strong>on</strong>s must be investigated simultaneously, like in<br />

computati<strong>on</strong>al drug or protein design. To be able to deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> such applicati<strong>on</strong>s, we<br />

develop hierarchical models, which combine very efficient, discrete me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods from<br />

computati<strong>on</strong>al biology wi<str<strong>on</strong>g>th</str<strong>on</strong>g> more demanding c<strong>on</strong>tinuous biophysical approaches.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e presentati<strong>on</strong> an overview over <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology will be presented toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> examples for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir practical applicati<strong>on</strong>s.<br />

50

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models in Eco-epidemiology II; Wednesday, June 29, 11:00<br />

Narcisa Apreutesei<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Technical University "Gh. Asachi" Iasi,<br />

Romania<br />

e-mail: napreut@gmail.com<br />

Travelling wave soluti<strong>on</strong>s for integro-differential equati<strong>on</strong>s<br />

from populati<strong>on</strong> dynamics<br />

Our talk c<strong>on</strong>cerns some classes <str<strong>on</strong>g>of</str<strong>on</strong>g> integro-differential equati<strong>on</strong>s from populati<strong>on</strong><br />

dynamics, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e integral term describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>local c<strong>on</strong>sumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> resources.<br />

Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> m<strong>on</strong>ostable case and bistable case are investigated. Fredholm property <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

corresp<strong>on</strong>ding linear operators can help to prove <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> travelling wave soluti<strong>on</strong>s.<br />

For some models, we can prove <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> traveling waves <strong>on</strong>ly when<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e support <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e integral is sufficiently small. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is case, <str<strong>on</strong>g>th</str<strong>on</strong>g>e integro-differential<br />

operator is close to <str<strong>on</strong>g>th</str<strong>on</strong>g>e differential <strong>on</strong>e. One uses a perturbati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od which<br />

combines <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fredholm property <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e linearized operators and <str<strong>on</strong>g>th</str<strong>on</strong>g>e implicit functi<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eorem. For large support, numerical simulati<strong>on</strong>s show <str<strong>on</strong>g>th</str<strong>on</strong>g>e propagati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

periodic travelling waves. For some o<str<strong>on</strong>g>th</str<strong>on</strong>g>er models, Leray-Schauder me<str<strong>on</strong>g>th</str<strong>on</strong>g>od can be<br />

applied. This implies <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a topological degree for <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding<br />

operators and <str<strong>on</strong>g>th</str<strong>on</strong>g>e establishment <str<strong>on</strong>g>of</str<strong>on</strong>g> a priori estimates for <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong>. Some<br />

biological interpretati<strong>on</strong>s follow from <str<strong>on</strong>g>th</str<strong>on</strong>g>is study.<br />

51

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Regulatory Networks; Tuesday, June 28, 17:00<br />

Mochamad Apri<br />

Biometris, Wageningen University, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

e-mail: mochamad.apri@wur.nl<br />

Maarten de Gee<br />

Biometris, Wageningen University, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

Jaap Molenaar<br />

Biometris, Wageningen University, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

Identifying <str<strong>on</strong>g>th</str<strong>on</strong>g>e core <str<strong>on</strong>g>of</str<strong>on</strong>g> biochemical networks: complexity<br />

reducti<strong>on</strong> preserving dynamical behavior<br />

Biochemical systems are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten very complex. The complexity stems from bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> comp<strong>on</strong>ents and <str<strong>on</strong>g>th</str<strong>on</strong>g>e intricate interacti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at may occur. When a<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model is used to describe such a system, its complexity may lead to a<br />

very l<strong>on</strong>g computing time, n<strong>on</strong>-identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters, and most importantly<br />

may hinder us in understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e biochemical system.<br />

Therefore, effective me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are required to capture <str<strong>on</strong>g>th</str<strong>on</strong>g>e key comp<strong>on</strong>ents and<br />

interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system.<br />

We present a novel and efficient reducti<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e core <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

biochemical system. This new me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e explorati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e so-called<br />

admissible regi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>at is <str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters for which <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model<br />

yields <str<strong>on</strong>g>th</str<strong>on</strong>g>e required output. For illustrati<strong>on</strong>al purpose, <str<strong>on</strong>g>th</str<strong>on</strong>g>e reducti<strong>on</strong> is first applied<br />

to a very small artificial network, c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> just <str<strong>on</strong>g>th</str<strong>on</strong>g>ree nodes and <str<strong>on</strong>g>th</str<strong>on</strong>g>ree parameters.<br />

Our me<str<strong>on</strong>g>th</str<strong>on</strong>g>od reveals <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are many parameter sets <str<strong>on</strong>g>th</str<strong>on</strong>g>at give rise to similar<br />

dynamical behavior, which indicates, despite its simplicity, <str<strong>on</strong>g>th</str<strong>on</strong>g>e system is not<br />

identifiable. Next, <str<strong>on</strong>g>th</str<strong>on</strong>g>e reducti<strong>on</strong> is applied to an epidermal grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factor receptor<br />

(EGFR) network model. It turns out <strong>on</strong>ly about 62% <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network comp<strong>on</strong>ents are<br />

required to yield <str<strong>on</strong>g>th</str<strong>on</strong>g>e correct resp<strong>on</strong>se to epidermal grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factor (EGF), whereas<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e rest could be c<strong>on</strong>sidered redundant. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough parameter sensitivity<br />

is expected to give an indicati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e redundancy <str<strong>on</strong>g>of</str<strong>on</strong>g> a parameter, we found<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at a highly sensitive parameter is not always necessarily important, whereas a<br />

slightly sensitive parameter is not always removable. This implies <str<strong>on</strong>g>th</str<strong>on</strong>g>at parameter<br />

sensitivity <strong>on</strong> its own is not a reliable tool for model reducti<strong>on</strong>.<br />

52

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Daniel Arbelaez Alvarado<br />

Universidad de los Andes, Departamento de Ingenieria Civil y Ambiental.<br />

Bogota, Colombia.<br />

e-mail: d.arbelaez36@uniandes.edu.co<br />

Juan Manuel Cordovez Alvarez<br />

Universidad de los Andes, Departamento de Ingenieria Civil y Ambiental.<br />

Bogota, Colombia.<br />

A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for assessing <str<strong>on</strong>g>th</str<strong>on</strong>g>e spraying as a vector<br />

c<strong>on</strong>trol strategy for Chagas disease in Colombia<br />

Chagas disease or American trypanosomiasis is a neglected disease in Latin America,<br />

which means <str<strong>on</strong>g>th</str<strong>on</strong>g>at attacks people already affected by poverty and inequality.<br />

Over time its manifestati<strong>on</strong>s lead to arrhy<str<strong>on</strong>g>th</str<strong>on</strong>g>mias and heart failure, and in some<br />

cases can cause dea<str<strong>on</strong>g>th</str<strong>on</strong>g>. In Colombia <str<strong>on</strong>g>th</str<strong>on</strong>g>is parasitic disease, <str<strong>on</strong>g>th</str<strong>on</strong>g>at affects 1.2 milli<strong>on</strong><br />

people (wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> 3 milli<strong>on</strong> more at risk <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tracting it), is transmitted<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e insect Rhodnius prolixus in a cycle in which wild animals, domestic animals<br />

and humans, act as reservoir. While research aimed at combating <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

country has shown progress in different fields, <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most important questi<strong>on</strong>s<br />

to be answered is how efficacious and efficient are <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol interventi<strong>on</strong>s. Little<br />

is known about <str<strong>on</strong>g>th</str<strong>on</strong>g>em and nowadays <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is no quantitative tool <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows for<br />

predicti<strong>on</strong>, so <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be used for c<strong>on</strong>trol and preventi<strong>on</strong>. The purpose <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

work is to propose a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vector and identifying different scenarios <str<strong>on</strong>g>th</str<strong>on</strong>g>at might c<strong>on</strong>tribute to <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease. In particular we want to explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> insecticide house<br />

spraying. Our approach c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> a system <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear differential equati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> change <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e susceptible and infected classes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree populati<strong>on</strong>s:<br />

domiciliated vectors, domestic animals and man. We present an analytical<br />

approach to get <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproductive number, <str<strong>on</strong>g>th</str<strong>on</strong>g>e steady states and <str<strong>on</strong>g>th</str<strong>on</strong>g>e equilibria<br />

as well as an implementati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model for computer simulati<strong>on</strong>s. In additi<strong>on</strong>,<br />

we show alternatives to reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e domiciliated vector populati<strong>on</strong>. We expect <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese preliminary results can be useful in <str<strong>on</strong>g>th</str<strong>on</strong>g>e reducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> uncertainty <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trol<br />

strategies at local level, and <str<strong>on</strong>g>th</str<strong>on</strong>g>ereby improve decisi<strong>on</strong> making about preventive<br />

management <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease.<br />

53

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Game <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical modelling and optimizati<strong>on</strong> in evoluti<strong>on</strong> and ecology I;<br />

Tuesday, June 28, 11:00<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Argasinski<br />

Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sussex<br />

e-mail: argas1@wp.pl<br />

dr Mark Broom<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Science City University L<strong>on</strong>d<strong>on</strong><br />

In which currency are paid pay<str<strong>on</strong>g>of</str<strong>on</strong>g>fs in evoluti<strong>on</strong>ary games?<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard approach to evoluti<strong>on</strong>ary games and replicator dynamics, differences<br />

in fitness can be interpreted as an excess from mean mal<str<strong>on</strong>g>th</str<strong>on</strong>g>usian grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying reas<strong>on</strong>ing, related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> "costs"<br />

and "benefits", <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a silent assumpti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at fitness can be described in some<br />

kind <str<strong>on</strong>g>of</str<strong>on</strong>g> "units". However, in most cases <str<strong>on</strong>g>th</str<strong>on</strong>g>ese units <str<strong>on</strong>g>of</str<strong>on</strong>g> measure are not explicitly<br />

specified. Then <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong> arises: are <str<strong>on</strong>g>th</str<strong>on</strong>g>ese <str<strong>on</strong>g>th</str<strong>on</strong>g>eories testable? How can we measure<br />

"benefit" or "cost"? It would be useful to describe and justify strategic "costs"<br />

versus "benefits" reas<strong>on</strong>ing in <str<strong>on</strong>g>th</str<strong>on</strong>g>e terminology <str<strong>on</strong>g>of</str<strong>on</strong>g> demography, because basic events<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at shape outcomes <str<strong>on</strong>g>of</str<strong>on</strong>g> natural selecti<strong>on</strong> are bir<str<strong>on</strong>g>th</str<strong>on</strong>g>s and dea<str<strong>on</strong>g>th</str<strong>on</strong>g>s. In our talk, we<br />

will present <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> such an explicit analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> bir<str<strong>on</strong>g>th</str<strong>on</strong>g>s and dea<str<strong>on</strong>g>th</str<strong>on</strong>g>s in an<br />

evoluti<strong>on</strong>ary game <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretic framework.<br />

We will investigate different types <str<strong>on</strong>g>of</str<strong>on</strong>g> mortality pressures, <str<strong>on</strong>g>th</str<strong>on</strong>g>eir combinati<strong>on</strong>s<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility <str<strong>on</strong>g>of</str<strong>on</strong>g> trade <str<strong>on</strong>g>of</str<strong>on</strong>g>fs between mortality and fertility. We will show <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>is new approach it is possible to model how strictly ecological factors,<br />

which seemed neutral in classical <str<strong>on</strong>g>th</str<strong>on</strong>g>eory, can affect outcomes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e game. For<br />

example we will show <str<strong>on</strong>g>th</str<strong>on</strong>g>at density dependence, affecting <str<strong>on</strong>g>th</str<strong>on</strong>g>e mortality <str<strong>on</strong>g>of</str<strong>on</strong>g> newborns,<br />

can seriously change <str<strong>on</strong>g>th</str<strong>on</strong>g>e outcome <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e game.<br />

We will illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>is in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> an example game, <str<strong>on</strong>g>th</str<strong>on</strong>g>e Hawk-Dove Game.<br />

Reformulated in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> our new approach, <str<strong>on</strong>g>th</str<strong>on</strong>g>is game shows new details and produces<br />

new biological predicti<strong>on</strong>s. The soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e new model are less abstract;<br />

instead <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at "cost" should exceed "benefit" we obtain results in<br />

terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fracti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> dead (<str<strong>on</strong>g>th</str<strong>on</strong>g>at can be interpreted as probability <str<strong>on</strong>g>of</str<strong>on</strong>g> dea<str<strong>on</strong>g>th</str<strong>on</strong>g>) individuals<br />

and per capita number <str<strong>on</strong>g>of</str<strong>on</strong>g> newborns, which can be easily estimated from<br />

data. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at in <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical approach to trade<str<strong>on</strong>g>of</str<strong>on</strong>g>f analysis, "cost" caused<br />

by increased mortality, can in some cases depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e value <str<strong>on</strong>g>of</str<strong>on</strong>g> expected benefit<br />

interpreted as an increase in fertility.<br />

References.<br />

[1] K. Argasinski, J. Kozłowski How can we model selectively neutral density dependence in<br />

evoluti<strong>on</strong>ary games Theor. Pop. Biol. 73 250–256 2008<br />

[2] J. H<str<strong>on</strong>g>of</str<strong>on</strong>g>bauer, K. Sigmund, Evoluti<strong>on</strong>ary Games and Populati<strong>on</strong> Dynamics. Cambridge University<br />

Press 1998<br />

[3] G. E. Hutchins<strong>on</strong>, Ecological Theatre and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Evoluti<strong>on</strong>ary Play, Yale University Press 1965<br />

[4] A. Lomnicki, Populati<strong>on</strong> ecology <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals, Princet<strong>on</strong> University Press 1988<br />

[5] J. Maynard Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>, Evoluti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Theory <str<strong>on</strong>g>of</str<strong>on</strong>g> Games. Cambridge University Press 1982<br />

[6] J. Maynard Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>,. Evoluti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Theory <str<strong>on</strong>g>of</str<strong>on</strong>g> Games. Cambridge University Press 1982<br />

[7] J. Weibull, Evoluti<strong>on</strong>ary Game Theory. MIT Press 1995<br />

54

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bioinformatics and System Biology; Wednesday, June 29, 17:00<br />

Julian Arndts<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cambridge; Humboldt University <str<strong>on</strong>g>of</str<strong>on</strong>g> Berlin<br />

e-mail: ja268@cam.ac.uk<br />

Transacti<strong>on</strong> costs and structure formati<strong>on</strong>: an ec<strong>on</strong>omic<br />

approach to biological systems<br />

We harness insights from ec<strong>on</strong>omics and informati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eory and apply <str<strong>on</strong>g>th</str<strong>on</strong>g>em to biological<br />

systems. Using informati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eory as a c<strong>on</strong>ceptual bridge between biology<br />

and ec<strong>on</strong>omics, biological and ec<strong>on</strong>omic systems can be analyzed and compared,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ereby paving <str<strong>on</strong>g>th</str<strong>on</strong>g>e way towards new models in bioec<strong>on</strong>omics. Driven by <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> replicati<strong>on</strong>, variati<strong>on</strong> and selecti<strong>on</strong>, systems in biology and ec<strong>on</strong>omics evolve<br />

towards ever more refined informati<strong>on</strong> architecture, <str<strong>on</strong>g>th</str<strong>on</strong>g>us lowering transacti<strong>on</strong> costs<br />

in general and informati<strong>on</strong> costs in particular. Hence, transacti<strong>on</strong> costs drive structure<br />

formati<strong>on</strong>. To illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>is principle, we present a wide range <str<strong>on</strong>g>of</str<strong>on</strong>g> examples<br />

from biology and ec<strong>on</strong>omics, and explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e following c<strong>on</strong>cepts: First, <str<strong>on</strong>g>th</str<strong>on</strong>g>e role<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> entropy in biological and ec<strong>on</strong>omic systems and <str<strong>on</strong>g>th</str<strong>on</strong>g>ree applicati<strong>on</strong>s: <str<strong>on</strong>g>th</str<strong>on</strong>g>e Kelly<br />

criteri<strong>on</strong>, which relates <str<strong>on</strong>g>th</str<strong>on</strong>g>e Shann<strong>on</strong> informati<strong>on</strong> entropy to <str<strong>on</strong>g>th</str<strong>on</strong>g>e limits <str<strong>on</strong>g>of</str<strong>on</strong>g> biological<br />

and ec<strong>on</strong>omic grow<str<strong>on</strong>g>th</str<strong>on</strong>g>; structure formati<strong>on</strong> as local entropy reducti<strong>on</strong>; and <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximum<br />

entropy principle. Sec<strong>on</strong>d, <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> higher-order informati<strong>on</strong> and Schelling<br />

points in biological and ec<strong>on</strong>omic systems: <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> Schelling points, or<br />

focal points, can transform informati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> first and sec<strong>on</strong>d order into informati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> higher order as well as comm<strong>on</strong> knowledge and hence fundamentally change <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

informati<strong>on</strong> architecture <str<strong>on</strong>g>of</str<strong>on</strong>g> a system. Third, bounded rati<strong>on</strong>ality: due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e limitati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> computati<strong>on</strong>al capacity, biological and ec<strong>on</strong>omic systems face fundamental<br />

trade<str<strong>on</strong>g>of</str<strong>on</strong>g>fs when processing informati<strong>on</strong>. Four<str<strong>on</strong>g>th</str<strong>on</strong>g>, strategic evoluti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptive<br />

market hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis. And fif<str<strong>on</strong>g>th</str<strong>on</strong>g>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-equilibrium: escaping<br />

local maxima in biology and ec<strong>on</strong>omics. Utilizing <str<strong>on</strong>g>th</str<strong>on</strong>g>ese c<strong>on</strong>cepts and comparing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e informati<strong>on</strong> architecture <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems and ec<strong>on</strong>omic systems allows to<br />

determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential <str<strong>on</strong>g>of</str<strong>on</strong>g> applying ec<strong>on</strong>omic <str<strong>on</strong>g>th</str<strong>on</strong>g>eory to biology, as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e limits<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> such applicati<strong>on</strong>s.<br />

55

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bioinformatics and System Biology; Wednesday, June 29, 11:00<br />

Anne Arnold<br />

Zoran Nikoloski<br />

Systems Biology and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling Group<br />

Max-Planck Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular Plant Physiology, 14476 Potsdam,<br />

Germany<br />

e-mail: arnold@mpimp-golm.mpg.de<br />

e-mail: nikoloski@mpimp-golm.mpg.de<br />

Comparative model analyis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Calvin-Bens<strong>on</strong> cycle<br />

Carb<strong>on</strong> fixati<strong>on</strong>, especially <str<strong>on</strong>g>th</str<strong>on</strong>g>e Calvin-Bens<strong>on</strong> cycle (CBC), is <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way<br />

for energy storage in carbohydrate products in C3-plants. Understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay<br />

between regulati<strong>on</strong> and efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> CBC and its end-products (e.g., sucrose,<br />

starch and amino acids) requires <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models which<br />

can explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic transformati<strong>on</strong>s. Here, we address<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is questi<strong>on</strong> by comparing and ranking <str<strong>on</strong>g>th</str<strong>on</strong>g>e existing models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e CBC to<br />

determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> best-performing models.<br />

The importance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e CBC and <str<strong>on</strong>g>th</str<strong>on</strong>g>e related pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways for <str<strong>on</strong>g>th</str<strong>on</strong>g>e increase <str<strong>on</strong>g>of</str<strong>on</strong>g> plant<br />

biomass has already resulted in 15 models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> various level <str<strong>on</strong>g>of</str<strong>on</strong>g> detail. The existing<br />

models can be categorized biologically based <strong>on</strong>: (1) chosen boundaries, i.e.,<br />

models <str<strong>on</strong>g>of</str<strong>on</strong>g> CBC including or excluding end-product syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis, (2) details <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong><br />

modeling, i.e., leaf, cell, or compartment-level, and (3) hierarchy <str<strong>on</strong>g>of</str<strong>on</strong>g> kinetics<br />

[4], translating <str<strong>on</strong>g>th</str<strong>on</strong>g>e model structure into ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical equati<strong>on</strong>s amenable to extensive<br />

analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> spatiotemporal properties. Our focus is placed <strong>on</strong> mass acti<strong>on</strong>,<br />

Michaelis-Menten-like, equilibrium approximati<strong>on</strong>s, and special functi<strong>on</strong>s in c<strong>on</strong>juncti<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong> terms.<br />

The ranking <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e SBML-implemented compendium <str<strong>on</strong>g>of</str<strong>on</strong>g> models is carried out<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>e following criteria: (1) stability analysis [3], (2) sensitivity analysis,<br />

(3) ability to capture key features extracted from <str<strong>on</strong>g>th</str<strong>on</strong>g>e data [1], and (4) analysis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> yield. The obtained scores are <str<strong>on</strong>g>th</str<strong>on</strong>g>en combined <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a comprehensive model<br />

ranking scheme, based <strong>on</strong> which <str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> best-performing models is selected wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

regard to metabolomics data and detecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> candidates for genetic engineering.<br />

References.<br />

[1] S. Arrivault, et al., Use <str<strong>on</strong>g>of</str<strong>on</strong>g> reverse-phase liquid chromatography, linked to tandem mass spectrometry,<br />

to pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile <str<strong>on</strong>g>th</str<strong>on</strong>g>e Calvin cycle and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er metabolic intermediates in arabidopsis rosettes<br />

at different carb<strong>on</strong> dioxide c<strong>on</strong>centrati<strong>on</strong>s Plant J 59 826–839 (2009).<br />

[2] W.W. Chen, M. Niepel, P.K. Sorger, Classic and c<strong>on</strong>temporary approaches to modeling biochemical<br />

reacti<strong>on</strong>s Genes & Development 24 1861–1875 (2010).<br />

[3] S. Grimbs, J. Selbig, S. Bulik, H.G. Holzhutter, R. Steuer, The stability and robustness <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

metabolic states: identifying stabilizing sites in metabolic networks Mol Syst Biol 3 146 (2007).<br />

[4] S. Grimbs, et al., Spatiotemporal dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Calvin cycle: Multistati<strong>on</strong>arity and symmetry<br />

breaking instabilities BioSystems (2011), in press.<br />

56

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Tuesday, June 28, 14:30<br />

Jesus R. Artalejo<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Complutense University 28040 Madrid Spain<br />

e-mail: jesus_artalejo@mat.ucm.es<br />

The ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> expectati<strong>on</strong>s distributi<strong>on</strong> as an alternative to<br />

quasi-stati<strong>on</strong>arity in stochastic biological models<br />

Many stochastic systems, including biological applicati<strong>on</strong>s, use Markov chains in<br />

which <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a set <str<strong>on</strong>g>of</str<strong>on</strong>g> absorbing states. It is <str<strong>on</strong>g>th</str<strong>on</strong>g>en needed to c<strong>on</strong>sider analogues <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e stati<strong>on</strong>ary distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an irreducible chain. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>text, quasi-stati<strong>on</strong>ary<br />

distributi<strong>on</strong>s play a fundamental role to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g-term behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

system. The rati<strong>on</strong>ale for using quasi-stati<strong>on</strong>ary distributi<strong>on</strong> is well established in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e abundant existing literature. The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is study is to reformulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e ratio <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

means approach which provides a simple alternative. We have a two-fold objective<br />

i) to view <str<strong>on</strong>g>th</str<strong>on</strong>g>e quasi-stati<strong>on</strong>arity and ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> expectati<strong>on</strong>s as two different approaches<br />

for understanding he dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system before absorpti<strong>on</strong>, and<br />

ii) to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility <str<strong>on</strong>g>of</str<strong>on</strong>g> using <str<strong>on</strong>g>th</str<strong>on</strong>g>e ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> expectati<strong>on</strong>s distributi<strong>on</strong><br />

as an approximati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e quasi-stati<strong>on</strong>ary distributi<strong>on</strong>.<br />

Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> distributi<strong>on</strong>s are compared for some selected scenarios, which are mainly<br />

inspired in stochastic epidemic models. Previously, <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>vergence to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

quasi-stati<strong>on</strong>ary regime is taking into account in order to make meaningful <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

comparis<strong>on</strong>.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious agents;<br />

Tuesday, June 28, 17:00<br />

Yael Artzy-Randrup<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ecology and Evoluti<strong>on</strong>ary Biology and Howard Hughes<br />

Medical Institute, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Michigan<br />

e-mail: yartzy@umich.edu<br />

Severe First and Mild Later: Temporal Strategies in<br />

Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen Evoluti<strong>on</strong><br />

Because pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens replicate wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in hosts and transmit between <str<strong>on</strong>g>th</str<strong>on</strong>g>em, selecti<strong>on</strong><br />

takes place <strong>on</strong> multiple levels. There has been <strong>on</strong>going interest for more <str<strong>on</strong>g>th</str<strong>on</strong>g>an two<br />

decades in trying to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s favoring <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> acute,<br />

highly transmissible infecti<strong>on</strong>s, focusing <strong>on</strong> trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>fs such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissibilityvirulence<br />

trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f and <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong>-persistence trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f. Studies have shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese types <str<strong>on</strong>g>of</str<strong>on</strong>g> trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>fs lead to intermediate pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen attack rates. These earlier<br />

studies typically c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a single trait under a defined trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f.<br />

However, for some pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens, <str<strong>on</strong>g>th</str<strong>on</strong>g>e course <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e host is likely to be<br />

more complex, determined by more <str<strong>on</strong>g>th</str<strong>on</strong>g>an a single dimensi<strong>on</strong>, opening <str<strong>on</strong>g>th</str<strong>on</strong>g>e door for<br />

more complicated strategies related to disease severity. The protozoa Plasmodium<br />

falciparum (Pf), which causes <str<strong>on</strong>g>th</str<strong>on</strong>g>e most severe type <str<strong>on</strong>g>of</str<strong>on</strong>g> malaria in humans, is <strong>on</strong>e<br />

example <str<strong>on</strong>g>of</str<strong>on</strong>g> such a pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen. During <str<strong>on</strong>g>th</str<strong>on</strong>g>e course <str<strong>on</strong>g>of</str<strong>on</strong>g> an infecti<strong>on</strong>, Pf has <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability<br />

to express up to 60 different variants <str<strong>on</strong>g>of</str<strong>on</strong>g> surface proteins (PfEMP1) encoded by a<br />

family <str<strong>on</strong>g>of</str<strong>on</strong>g> var genes, which are recognized by <str<strong>on</strong>g>th</str<strong>on</strong>g>e host immune system and which<br />

also act as virulence factors.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> temporal variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> life history traits during<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e course <str<strong>on</strong>g>of</str<strong>on</strong>g> an infecti<strong>on</strong>, and we ask whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e additi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a temporal dimensi<strong>on</strong><br />

can assist in reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e burden arising from multiple selective pressures. We<br />

allow <str<strong>on</strong>g>th</str<strong>on</strong>g>e life history traits <str<strong>on</strong>g>of</str<strong>on</strong>g> different stages to evolve independently, and as a case<br />

study, we assume <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f between transmissi<strong>on</strong> and durati<strong>on</strong>. To capture<br />

multiple selective pressures acting <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parasite, we c<strong>on</strong>sider invasi<strong>on</strong> persistence<br />

trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>fs in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> critical community size <str<strong>on</strong>g>of</str<strong>on</strong>g> hosts. We dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at a<br />

composite strategy <str<strong>on</strong>g>th</str<strong>on</strong>g>at is ordered in time and c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> a more transmissible<br />

stage at first, followed by a less transmissible <strong>on</strong>e later, c<strong>on</strong>fers a higher fitness <str<strong>on</strong>g>th</str<strong>on</strong>g>an<br />

any single, c<strong>on</strong>stant, strategy. These results are relevant to ordered expressi<strong>on</strong> in<br />

P. falciparum <str<strong>on</strong>g>of</str<strong>on</strong>g> severe vs. mild var genes, as well as for acute infecti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at are<br />

followed by milder symptoms in some bacterial pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Takeshi Asakawa<br />

System Technologies Laboratories , SONY Corporati<strong>on</strong><br />

e-mail: Takeshi.Asakawa@jp.s<strong>on</strong>y.com<br />

Satoshi Koinuma<br />

Koh-hei Masumoto<br />

Mamoru Nagano<br />

Yasufumi Shigeyoshi<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Anatomy and Neurobiology, School <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine, Kindai<br />

University<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mammalian circadian center as a<br />

many-body system <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e limit cycle oscillators<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e present study, we propose a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mammalian circadian<br />

center, or <str<strong>on</strong>g>th</str<strong>on</strong>g>e suprachiasmatic nucleus (SCN), which is described as a many-body<br />

system composed <str<strong>on</strong>g>of</str<strong>on</strong>g> limit cycle oscillators. Each oscillati<strong>on</strong> unit in <str<strong>on</strong>g>th</str<strong>on</strong>g>e SCN was described<br />

as a limit cycle oscillator based <strong>on</strong> a negative autoregulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> per genes by<br />

its protein product PER previously reported (Goldbeter 1995, Leloup & Goldbeter<br />

1998, Kurosawa et al. 2002, G<strong>on</strong>ze et al. 2006). We adopted ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er assumpti<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at oscillators interacted wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er <strong>on</strong>ly <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a humoral factor, and ignored<br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>er possible neural interacti<strong>on</strong> or network. Then, <str<strong>on</strong>g>th</str<strong>on</strong>g>eir n<strong>on</strong>linear equati<strong>on</strong>s<br />

were reduced to <str<strong>on</strong>g>th</str<strong>on</strong>g>e Stuart Landau equati<strong>on</strong> forms (Kuramoto, 1996). Our present<br />

model was also c<strong>on</strong>structed <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e recent finding <str<strong>on</strong>g>th</str<strong>on</strong>g>at most <str<strong>on</strong>g>of</str<strong>on</strong>g> oscillating neur<strong>on</strong>s<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e SCN shows damping under <str<strong>on</strong>g>th</str<strong>on</strong>g>e isolated envir<strong>on</strong>ment (Webb et al. 2009).<br />

Therefore, we assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at most <str<strong>on</strong>g>of</str<strong>on</strong>g> oscillating neur<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e SCN were damping<br />

oscillators but have potential to generate limit cycle oscillators by appropriate external<br />

forces. In additi<strong>on</strong>, we supposed a phase-dependent gate in <str<strong>on</strong>g>th</str<strong>on</strong>g>e oscillators in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e VLSCN which shut out <str<strong>on</strong>g>th</str<strong>on</strong>g>e photic input to <str<strong>on</strong>g>th</str<strong>on</strong>g>e SCN during <str<strong>on</strong>g>th</str<strong>on</strong>g>e day, which had<br />

been recognized in <str<strong>on</strong>g>th</str<strong>on</strong>g>e VLSCN <str<strong>on</strong>g>of</str<strong>on</strong>g> mammalians. We examined whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

reproduced <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymmetrical resynchr<strong>on</strong>izati<strong>on</strong> process associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e abrupt<br />

shift <str<strong>on</strong>g>of</str<strong>on</strong>g> light: dark cycle (LD cycle; L:D=12h:12h). An abrupt shift <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e LD<br />

cycle yielded internal desynchr<strong>on</strong>y between VLSCN and DMSCN transiently which<br />

caused a jet lag syndrome (Nagano et al. 2003). The asymmetry appeared in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

way <str<strong>on</strong>g>of</str<strong>on</strong>g> resynchr<strong>on</strong>izati<strong>on</strong>; it took five days to restore synchr<strong>on</strong>izati<strong>on</strong> after 10-hour<br />

delay and took more <str<strong>on</strong>g>th</str<strong>on</strong>g>an 10 days after six-hour advance. The present model reproduced<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e asymmetrical expended time spent in resynchr<strong>on</strong>izati<strong>on</strong> process after<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e rapid shift <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e LD cycle. The model also reproduced <str<strong>on</strong>g>th</str<strong>on</strong>g>e intrinsic phase<br />

wave shown in <str<strong>on</strong>g>th</str<strong>on</strong>g>e SCN. The phase wave is propagated from <str<strong>on</strong>g>th</str<strong>on</strong>g>e medial regi<strong>on</strong>s to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e lateral regi<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e SCN. By placing a small regi<strong>on</strong> c<strong>on</strong>taining short period<br />

oscillators (short period regi<strong>on</strong>: SPR: τ < 24h) and remaining large regi<strong>on</strong> c<strong>on</strong>taining<br />

l<strong>on</strong>g period oscillators (l<strong>on</strong>g period regi<strong>on</strong>: LPR: τ > 24h), <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase wave<br />

appeared, being initiated at SPR and propagated to LPR. Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase resp<strong>on</strong>se<br />

curve (PRC) generated from <str<strong>on</strong>g>th</str<strong>on</strong>g>e present model by using <str<strong>on</strong>g>th</str<strong>on</strong>g>e pulse-like input<br />

c<strong>on</strong>siderably corresp<strong>on</strong>ded to empirical PRCs obtained from locomotor activities <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

rats and mice.<br />

59

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Tuesday, June 28, 17:00<br />

Gianluca Ascolani<br />

Laboratory IMNC, CNRS-UMR 8165 and Universities Paris Diderot-<br />

Paris 7 and Paris Sud-11, Orsay, France<br />

e-mail: ascolani@imnc.in2p3.fr<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ilde Badoual<br />

Laboratory IMNC, University Paris Diderot-Paris 7, France<br />

e-mail: badoual@imnc.in2p3.fr<br />

Christophe Deroulers<br />

Laboratory IMNC, University Paris Diderot-Paris 7, France<br />

e-mail: deroulers@imnc.in2p3.fr<br />

Basil Grammaticos<br />

Laboratory IMNC, CNRS-UMR 8165 and Universities Paris Diderot-<br />

Paris 7 and Paris Sud-11, Orsay, France<br />

e-mail: grammaticos@univ-paris-diderot.fr<br />

Migrati<strong>on</strong> processes <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting cancerous cells: bey<strong>on</strong>d<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e mean field approximati<strong>on</strong><br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e main aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> studying diffuse tumors is understanding how <str<strong>on</strong>g>th</str<strong>on</strong>g>ey<br />

diffuse inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e hosting tissues and how fast <str<strong>on</strong>g>th</str<strong>on</strong>g>ey spread. To shed light <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese issues,<br />

we use an approach based <strong>on</strong> a microscopical descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells’ dynamics<br />

to reproduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> at <str<strong>on</strong>g>th</str<strong>on</strong>g>e meso-macroscopical scale. An example <str<strong>on</strong>g>of</str<strong>on</strong>g> a tumor<br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>e glioblastoma which grows in <str<strong>on</strong>g>th</str<strong>on</strong>g>e brain and is very invasive. The glioma cells<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e glioblastoma interact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er cancerous cells exchanging small molecules<br />

and i<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>rough very short links named gap juncti<strong>on</strong> c<strong>on</strong>necti<strong>on</strong>s [1]. In [2], <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors proposed a model in <str<strong>on</strong>g>th</str<strong>on</strong>g>e framework <str<strong>on</strong>g>of</str<strong>on</strong>g> automat<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cancerous<br />

cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at takes into c<strong>on</strong>siderati<strong>on</strong> gap juncti<strong>on</strong> type interacti<strong>on</strong>s. In [3], <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

hydrodynamic limit <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells’ diffusi<strong>on</strong> equati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean field-approximati<strong>on</strong><br />

is found, and some differences wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical simulati<strong>on</strong>s are shown. Using<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e approach proposed in [3], we study and analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong><br />

process <str<strong>on</strong>g>of</str<strong>on</strong>g> cancerous cells <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two-points correlati<strong>on</strong> functi<strong>on</strong>. The cells move<br />

<strong>on</strong> a single occupancy hexag<strong>on</strong>al sites lattice wi<str<strong>on</strong>g>th</str<strong>on</strong>g> periodical border c<strong>on</strong>diti<strong>on</strong>s and<br />

interact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nearest neighbors. The interacti<strong>on</strong> affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells by<br />

imposing <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> preserving at least <strong>on</strong>e gap juncti<strong>on</strong> c<strong>on</strong>necti<strong>on</strong> am<strong>on</strong>g<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e closest neighbors wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a given probability. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tinuous limit <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

correlati<strong>on</strong> functi<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e comparis<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory and numerical simulati<strong>on</strong>s<br />

for different values <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancerous cells’ density and interacti<strong>on</strong> parameter.<br />

The interacti<strong>on</strong> introduces a short leng<str<strong>on</strong>g>th</str<strong>on</strong>g> correlati<strong>on</strong> am<strong>on</strong>g cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at dynamically<br />

evolves toward stable values depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system variables. Numerical simulati<strong>on</strong>s<br />

show <str<strong>on</strong>g>th</str<strong>on</strong>g>e stable c<strong>on</strong>diti<strong>on</strong> differs from <str<strong>on</strong>g>th</str<strong>on</strong>g>e uniform c<strong>on</strong>diti<strong>on</strong> due to spatial<br />

inhomogeneity and clusters formati<strong>on</strong> also in absence <str<strong>on</strong>g>of</str<strong>on</strong>g> sources and sinks.<br />

References.<br />

[1] L. Cr<strong>on</strong>ier, Gap Juncti<strong>on</strong>s and Cancer: New Functi<strong>on</strong>s for an Old Story, Antioxidants &<br />

Redox Signaling, 11, 2 (2009).<br />

[2] M. Aubert et al., A cellular automat<strong>on</strong> model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> glioma cells, Phys Biol., 3,<br />

93-100 (2006).<br />

60

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[3] C. Deroulers et al., Modeling tumor cell migrati<strong>on</strong>: From microscopic to macroscopic models,<br />

Phys. Rev. E, 79, 031917 (2009).<br />

61

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bioinformatics and System Biology; Wednesday, June 29, 08:30<br />

Marian Groenenboom 1,3<br />

e-mail: marian.groenenboom@wur.nl<br />

Laura Astola 1,3<br />

e-mail: laura.astola@wur.nl<br />

Victoria Choserot 2,3<br />

e-mail: victoria.choserot@wur.nl<br />

Jaap Molenaar 1,3<br />

e-mail: jaap.molenaar@wur.nl<br />

1 Biometris, Plant Sciences Group, Wageningen University and Research<br />

Center, Wageningen, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

2 Bioscience, Plant Research Internati<strong>on</strong>al, Wageningen, University<br />

and Research Center, Wageningen, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

3 Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands C<strong>on</strong>sortium for Systems Biology, Amsterdam, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>er-<br />

lands<br />

Glycosylati<strong>on</strong> Networks in Tomato, Top-down and<br />

Bottom-up Inference Combined<br />

Tomato (Solanum Lycopersicum) is a comm<strong>on</strong> element in human diet. In 2009,<br />

more <str<strong>on</strong>g>th</str<strong>on</strong>g>an 140000 milli<strong>on</strong> t<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> tomatoes were produced worldwide. Tomato fruit<br />

c<strong>on</strong>tains relatively large amounts <str<strong>on</strong>g>of</str<strong>on</strong>g> flav<strong>on</strong>oids. Flav<strong>on</strong>oids have recently gained<br />

growing interest due to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir anticipated positive heal<str<strong>on</strong>g>th</str<strong>on</strong>g> effects as antioxidants.<br />

As is <str<strong>on</strong>g>th</str<strong>on</strong>g>e case for many plant metabolites, flav<strong>on</strong>oids mainly occur in glycosylated<br />

form. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough it is widely accepted <str<strong>on</strong>g>th</str<strong>on</strong>g>at glycosylati<strong>on</strong> is <str<strong>on</strong>g>of</str<strong>on</strong>g> great importance<br />

to maintain metabolic homeostasis, <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way leading to <str<strong>on</strong>g>th</str<strong>on</strong>g>e diverse glycosides,<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e specificity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e involved enzymes is not known. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is study, we combine<br />

experiments and ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling to infer <str<strong>on</strong>g>th</str<strong>on</strong>g>e network governing flav<strong>on</strong>ol<br />

glycosylati<strong>on</strong>, and study its functi<strong>on</strong>ing in vivo.<br />

Tomato seedlings are grown under different c<strong>on</strong>diti<strong>on</strong>s, and flav<strong>on</strong>oid glycoside<br />

c<strong>on</strong>centrati<strong>on</strong>s are measured for a number <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>secutive days. To infer <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

flav<strong>on</strong>oid glycosylati<strong>on</strong> network from <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting time-series, we combine two different<br />

approaches. First, we make use <str<strong>on</strong>g>of</str<strong>on</strong>g> a top-down approach <str<strong>on</strong>g>th</str<strong>on</strong>g>at has as starting<br />

point a priori obtained general biological knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular reacti<strong>on</strong>s and<br />

metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways in plants. This knowledge leads to a number <str<strong>on</strong>g>of</str<strong>on</strong>g> candidate<br />

structures for <str<strong>on</strong>g>th</str<strong>on</strong>g>e network. In a fitting procedure, we estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong> rates in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e model, formulated in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary differential equati<strong>on</strong>s, by applying an<br />

iterative minimizati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od in order to match <str<strong>on</strong>g>th</str<strong>on</strong>g>e model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong>s.<br />

The best fitting network is <str<strong>on</strong>g>th</str<strong>on</strong>g>en selected.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e bottom-up approach <strong>on</strong>e directly infers <str<strong>on</strong>g>th</str<strong>on</strong>g>e network structure from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

data via a statistical approach. We explore a me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>th</str<strong>on</strong>g>at involves <strong>on</strong>ly simple<br />

matrix manipulati<strong>on</strong>s and standard statistics. In bo<str<strong>on</strong>g>th</str<strong>on</strong>g> frameworks we inherently<br />

exploit <str<strong>on</strong>g>th</str<strong>on</strong>g>e time-series structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e data. Because <str<strong>on</strong>g>th</str<strong>on</strong>g>e data are noisy, it turned<br />

out difficult to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e flav<strong>on</strong>oid network using ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e top-down or <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

bottom-up approach separately. However, by combining bo<str<strong>on</strong>g>th</str<strong>on</strong>g> approaches we were<br />

able to obtain a reliable estimate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network model for flav<strong>on</strong>oid glycosylati<strong>on</strong><br />

in spite <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>siderable noise.<br />

62

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Irem Atac<br />

Researcher at Kocaeli University, TURKEY<br />

e-mail: irem.atac@kocaeli.edu.trspamuk@kocaeli.edu.tr<br />

Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. Dr. Serdal Pamuk<br />

Kocaeli University, TURKEY<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

On The Stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Steady-State Soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Cell<br />

Equati<strong>on</strong>s in a Tumor Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> Model<br />

The stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e steady-state soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial, pericyte and macrophage<br />

cells equati<strong>on</strong>s in a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model originally presented in Levine, H.A., et<br />

al., A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e roles <str<strong>on</strong>g>of</str<strong>on</strong>g> pericytes and macrophages in <str<strong>on</strong>g>th</str<strong>on</strong>g>e initiati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis. I. The role <str<strong>on</strong>g>of</str<strong>on</strong>g> protease inhibitors in preventing angiogenesis,<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.Biosci., 168(1) 2000, 77-115, is studied. Trajectories near <str<strong>on</strong>g>th</str<strong>on</strong>g>e critical points<br />

are drawn and <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological importance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e results are provided.<br />

63

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Thursday, June 30, 11:30<br />

K.K. Avilov<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Numerical Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics <str<strong>on</strong>g>of</str<strong>on</strong>g> RAS, Moscow, Russia<br />

e-mail: avilov@mail.inm.ras.ru<br />

Case detecti<strong>on</strong> rate: what can be estimated wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out<br />

prevalence surveys?<br />

Case detecti<strong>on</strong> rate (CDR) defined as <str<strong>on</strong>g>th</str<strong>on</strong>g>e proporti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> incident cases <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

disease <str<strong>on</strong>g>th</str<strong>on</strong>g>at are detected (i.e. diagnosed and notified) is <str<strong>on</strong>g>of</str<strong>on</strong>g> great importance bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

for m<strong>on</strong>itoring <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemiological situati<strong>on</strong> and for forecasting and operati<strong>on</strong>al<br />

research. Moreover, case detecti<strong>on</strong> rates are used as target indicators in political<br />

documents (for example, target 70% CDR for smear-positive tuberculosis had been<br />

set by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Millennium Development Goals [1]).<br />

It is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten stated <str<strong>on</strong>g>th</str<strong>on</strong>g>at CDR is hard to estimate because it is calculated as<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e routinely notified incidence to an estimate <str<strong>on</strong>g>of</str<strong>on</strong>g> full (unobserved)<br />

incidence, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e latter being very unreliable. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e field <str<strong>on</strong>g>of</str<strong>on</strong>g> tuberculosis, <str<strong>on</strong>g>th</str<strong>on</strong>g>e usual<br />

recommendati<strong>on</strong> is performing regular prevalence surveys to calculate incidence<br />

ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er directly or indirectly. But representative prevalence surveys are ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er costly<br />

and <str<strong>on</strong>g>of</str<strong>on</strong>g>ten logistically complicated. The workarounds for <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem include using<br />

expert estimates <str<strong>on</strong>g>of</str<strong>on</strong>g> CDR [2] and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g-term trends and interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

HIV [3].<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e talk, presented will be a model <str<strong>on</strong>g>th</str<strong>on</strong>g>at regards case detecti<strong>on</strong> and disease<br />

progressi<strong>on</strong> as competing processes, <str<strong>on</strong>g>th</str<strong>on</strong>g>us deriving a relati<strong>on</strong>ship between <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

intensity <str<strong>on</strong>g>of</str<strong>on</strong>g> case detecti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e severity (or age) <str<strong>on</strong>g>of</str<strong>on</strong>g> disease at <str<strong>on</strong>g>th</str<strong>on</strong>g>e moment <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

detecti<strong>on</strong> [4]. In many settings some kind <str<strong>on</strong>g>of</str<strong>on</strong>g> disease severity measure is available<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e routine notificati<strong>on</strong> data, and so it is possible to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e CDR. For<br />

tuberculosis, such a measure may use data <strong>on</strong> smear microscopy, bacteriological<br />

tests, chest X-ray, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e physician’s diagnosis.<br />

This approach may be extended to incorporate individual socio-ec<strong>on</strong>omical<br />

properties and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir effect <strong>on</strong> individual case detecti<strong>on</strong> intensity [5]. The analysis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e data shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cases substantially differ in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir availability for<br />

detecti<strong>on</strong>, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> “social involvement” and sex being <str<strong>on</strong>g>th</str<strong>on</strong>g>e most significant factors.<br />

This result erects <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong> how much <str<strong>on</strong>g>th</str<strong>on</strong>g>e heterogeneity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong><br />

affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e models based <strong>on</strong> homogeneity assumpti<strong>on</strong>s – in <str<strong>on</strong>g>th</str<strong>on</strong>g>is case, <strong>on</strong> evenly<br />

effective detecti<strong>on</strong> system. In fact, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model estimates CDR for <str<strong>on</strong>g>th</str<strong>on</strong>g>e social strata<br />

readily available for case detecti<strong>on</strong>. This estimate al<strong>on</strong>e may be a useful point<br />

indicator <str<strong>on</strong>g>of</str<strong>on</strong>g> practical efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e case detecti<strong>on</strong> system. But wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some support<br />

form prevalence studies (especially targeting <str<strong>on</strong>g>th</str<strong>on</strong>g>e “ill-detectable” strata) it is possible<br />

to estimate CDR and incidence accurately for <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole populati<strong>on</strong>.<br />

References.<br />

[1] Resoluti<strong>on</strong> A/55/2. United Nati<strong>on</strong>s Millennium Declarati<strong>on</strong>. 32. Fifty-fif<str<strong>on</strong>g>th</str<strong>on</strong>g> United Nati<strong>on</strong>s<br />

General Assembly, New York, 18 September 2000 (Document A/RES/53/202).<br />

[2] Dye C, Scheele S, Dolin P, Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ania V, Ravigli<strong>on</strong>e MC. C<strong>on</strong>sensus statement. Global burden<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tuberculosis: estimated incidence, prevalence, and mortality by country. WHO Global<br />

Surveillance and M<strong>on</strong>itoring Project. JAMA. 1999;282(7):677-86.<br />

64

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[3] Mansoer J, Scheele S, Floyd K, Dye C, Sitienei J, Williams B. New me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for estimating<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e tuberculosis case detecti<strong>on</strong> rate in high-HIV prevalence countries: <str<strong>on</strong>g>th</str<strong>on</strong>g>e example <str<strong>on</strong>g>of</str<strong>on</strong>g> Kenya.<br />

Bull. World. Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>. Organ. 2009;87(3):186-92, 192A-192B.<br />

[4] Avilov KK, Romanyukha AA. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> tuberculosis propagati<strong>on</strong> and patient<br />

detecti<strong>on</strong>. Automati<strong>on</strong> and Remote C<strong>on</strong>trol. 2007; 68(9):1604-1617.<br />

[5] Avilov KK. Statistical descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> factors determining detected tuberculosis incidence. Russian<br />

Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Numerical Analysis and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling. 2009; 24(4):309-324.<br />

65

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Franciane Azevedo<br />

Institute for Theoretical Physics<br />

e-mail: fran@ift.unesp.br<br />

Models in Spatial Ecology; Tuesday, June 28, 17:00<br />

The spatial dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e diphenic plan<str<strong>on</strong>g>th</str<strong>on</strong>g>opper<br />

We study <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> a wing diphenic insect species (when two<br />

phenotypes can arise from <str<strong>on</strong>g>th</str<strong>on</strong>g>e same genotype) where <str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> wings can vary<br />

largely, from almost inexistent (brachypterous) to fully developed (macropterous).<br />

Macropterous individuals are born <strong>on</strong>ly when <str<strong>on</strong>g>th</str<strong>on</strong>g>e total density is higher <str<strong>on</strong>g>th</str<strong>on</strong>g>an<br />

a certain value. This induces a density-dependent diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e species.<br />

We c<strong>on</strong>struct a stage structured (nymphs and adults) model, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> adults fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

sub-divided in macropterous and brachypterous. Space is introduced explicitly by<br />

means <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong> equati<strong>on</strong>s, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> c<strong>on</strong>stant <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e macropterous subpopulati<strong>on</strong><br />

being much higher <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers.<br />

We focus <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics originating from an initially small and c<strong>on</strong>centrated<br />

populati<strong>on</strong>, which is shown to expand, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> macropterous individuals as predecessors<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er stages. The invasi<strong>on</strong> fr<strong>on</strong>t displays a particular form, originating<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e stage-structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model.<br />

66

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling physiological systems: model validati<strong>on</strong> and experimental design<br />

issues; Wednesday, June 29, 11:00<br />

Mostafa Bachar<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, King Saud University, Saudi Arabia<br />

e-mail: mbachar@ksu.edu.sa<br />

Franz Kappel<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Scientific Computing, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Graz,<br />

Austria<br />

e-mail: franz.kappel@uni-graz.at<br />

Peter Kotanko<br />

Renal Research Institute, New York<br />

e-mail: PKotanko@rriny.com<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose insulin system during<br />

hemodialysis using different dialysate glucose c<strong>on</strong>centrati<strong>on</strong>s.<br />

This talk we will presents sensitivity identifiably analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose insulin system during hemodialysis based <strong>on</strong> minimal model. This<br />

model incorporates sufficient structure and complexity to allow for examining <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

metabolic acti<strong>on</strong> and regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose and insulin systems. The complexity <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e model allows for <str<strong>on</strong>g>th</str<strong>on</strong>g>e representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> modes and sites for acti<strong>on</strong> but<br />

at <str<strong>on</strong>g>th</str<strong>on</strong>g>e same time <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters renders <str<strong>on</strong>g>th</str<strong>on</strong>g>e validati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> accessible<br />

data limitati<strong>on</strong> problematic. Subset selecti<strong>on</strong> techniques are employed to examine<br />

which parameters are mostly likely identifiable for a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> potential sources <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

data <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e state <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system.<br />

67

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Recent developments in <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> Lotka-Volterra and Kolmogorov<br />

systems; Saturday, July 2, 14:30<br />

Stephen Baigent<br />

University College L<strong>on</strong>d<strong>on</strong><br />

e-mail: s.baigent@ucl.ac.uk<br />

The curvature <str<strong>on</strong>g>of</str<strong>on</strong>g> carrying simplices for competitive<br />

Lotka-Volterra systems<br />

The N dimensi<strong>on</strong>al totally competitive Lotka-Volterra equati<strong>on</strong>s have a Lipschitz<br />

invariant manifold <str<strong>on</strong>g>th</str<strong>on</strong>g>at attracts all points in <str<strong>on</strong>g>th</str<strong>on</strong>g>e first quadrant except <str<strong>on</strong>g>th</str<strong>on</strong>g>e origin.<br />

For N=2 it is known <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is manifold is ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er c<strong>on</strong>vex or c<strong>on</strong>cave, and for N=3<br />

numerical evidence suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e curvature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e manifold cannot change sign.<br />

I shall discuss a new me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for proving <str<strong>on</strong>g>th</str<strong>on</strong>g>e N=2 case and also outline some recent<br />

progress towards understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e N=3 case, including special cases where <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

manifold can be shown to be c<strong>on</strong>vex, saddle-like or a developable surface.<br />

68

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Archana Bajpai<br />

Micros<str<strong>on</strong>g>of</str<strong>on</strong>g>t Research-University <str<strong>on</strong>g>of</str<strong>on</strong>g> Trento CoSBi<br />

e-mail: archana.bioinfo@gmail.com<br />

F. Vaggi<br />

F. Jordan<br />

A. Csikasz-Nagy<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Computati<strong>on</strong>al analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell grow<str<strong>on</strong>g>th</str<strong>on</strong>g> regulatory<br />

network <str<strong>on</strong>g>of</str<strong>on</strong>g> fissi<strong>on</strong> yeast cells<br />

The rod shaped fissi<strong>on</strong> yeast cells grow <strong>on</strong>ly at <str<strong>on</strong>g>th</str<strong>on</strong>g>eir tip, unidirecti<strong>on</strong>al grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in<br />

G1 is followed by leng<str<strong>on</strong>g>th</str<strong>on</strong>g> extensi<strong>on</strong> also from <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er end in G2. Microtubules are<br />

resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>e proper localizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> z<strong>on</strong>es at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tips and localized<br />

actin polymerizati<strong>on</strong> is needed for grow<str<strong>on</strong>g>th</str<strong>on</strong>g> inducti<strong>on</strong>. Similar actin polymerizati<strong>on</strong><br />

process in <str<strong>on</strong>g>th</str<strong>on</strong>g>e middle <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell is needed for cytokinesis. Several members <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

molecular network <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>nect microtubule and actin dynamics to cell grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and<br />

cell divisi<strong>on</strong> are identified and some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir interacti<strong>on</strong>s are also known, but <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

data do not give a complete picture <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system. After identifying <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>served<br />

regulatory molecules and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir interacti<strong>on</strong>s in o<str<strong>on</strong>g>th</str<strong>on</strong>g>er organisms we perform network<br />

analysis <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e predicted interacti<strong>on</strong> network <str<strong>on</strong>g>of</str<strong>on</strong>g> fissi<strong>on</strong> yeast grow<str<strong>on</strong>g>th</str<strong>on</strong>g> regulatory<br />

system to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e key core comp<strong>on</strong>ents and <str<strong>on</strong>g>th</str<strong>on</strong>g>e links <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>nect cell grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

and cell cycle regulati<strong>on</strong>. We are analyzing <str<strong>on</strong>g>th</str<strong>on</strong>g>e networks also from bottom-up by<br />

creating computati<strong>on</strong>al models for <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e core regulators <str<strong>on</strong>g>of</str<strong>on</strong>g> cell<br />

divisi<strong>on</strong> and cell polarity.<br />

69

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

C<strong>on</strong>necting microscale and macroscale models <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular migrati<strong>on</strong>;<br />

Tuesday, June 28, 17:00<br />

Ru<str<strong>on</strong>g>th</str<strong>on</strong>g> Baker<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: ru<str<strong>on</strong>g>th</str<strong>on</strong>g>.baker@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.yk<br />

Dr Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ew Simps<strong>on</strong><br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Queensland University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Corrected mean-field models for spatially-dependent<br />

advecti<strong>on</strong>-diffusi<strong>on</strong>-reacti<strong>on</strong> phenomena<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e exclusi<strong>on</strong>-process literature, mean-field models are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten derived by assuming<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e occupancy status <str<strong>on</strong>g>of</str<strong>on</strong>g> lattice sites is independent. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>is assumpti<strong>on</strong><br />

is questi<strong>on</strong>able, it is <str<strong>on</strong>g>th</str<strong>on</strong>g>e foundati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> many mean-field models. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we<br />

develop me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to relax <str<strong>on</strong>g>th</str<strong>on</strong>g>e independence assumpti<strong>on</strong> for a range <str<strong>on</strong>g>of</str<strong>on</strong>g> discrete exclusi<strong>on</strong><br />

process-based mechanisms motivated by applicati<strong>on</strong>s from <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell biology<br />

literature. Previous investigati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at focussed <strong>on</strong> relaxing <str<strong>on</strong>g>th</str<strong>on</strong>g>e independence assumpti<strong>on</strong><br />

have been limited to studying initially-uniform populati<strong>on</strong>s and ignored<br />

any spatial variati<strong>on</strong>s. These previous corrected mean-field models could not be<br />

applied to many important problems in cell biology such as invasi<strong>on</strong> waves <str<strong>on</strong>g>of</str<strong>on</strong>g> cells<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at are characterised by moving fr<strong>on</strong>ts. Here we propose me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>th</str<strong>on</strong>g>at relax <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

independence assumpti<strong>on</strong> leading to corrected mean-field descripti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> a range <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

exclusi<strong>on</strong> process-based models <str<strong>on</strong>g>th</str<strong>on</strong>g>at incorporate (i) unbiased motility, (ii) biased<br />

motility, and (iii) unbiased motility wi<str<strong>on</strong>g>th</str<strong>on</strong>g> agent bir<str<strong>on</strong>g>th</str<strong>on</strong>g> and dea<str<strong>on</strong>g>th</str<strong>on</strong>g> processes. The corrected<br />

mean-field models derived here are applicable to spatially-variable processes<br />

including invasi<strong>on</strong> wave-type problems. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere can be large deviati<strong>on</strong>s<br />

between simulati<strong>on</strong> data and traditi<strong>on</strong>al mean-field models based <strong>on</strong> invoking<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e independence assumpti<strong>on</strong>. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e corrected mean-field<br />

models give an improved match to <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> data in all cases c<strong>on</strong>sidered.<br />

70

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Developmental Biology; Wednesday, June 29, 17:00<br />

Suruchi Bakshi<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: bakshi@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

Paul C<strong>on</strong>duit<br />

Sir William Dunn School <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

Omer Dushek<br />

Sir William Dunn School <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

Ru<str<strong>on</strong>g>th</str<strong>on</strong>g> Baker<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

Jordan Raff<br />

Sir William Dunn School <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

Eam<strong>on</strong>n Gaffney<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

Philip Maini<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

Breaking <str<strong>on</strong>g>th</str<strong>on</strong>g>e symmetry: understanding Centrosomin<br />

incorporati<strong>on</strong> in Drosophila centrosomes in order to study<br />

asymmetric divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> neural stem cells.<br />

A size asymmetry between <str<strong>on</strong>g>th</str<strong>on</strong>g>e centrosomes in certain Drosophila stem cells is important<br />

for proper asymmetric cell divisi<strong>on</strong>. How <str<strong>on</strong>g>th</str<strong>on</strong>g>is centrosome size asymmetry<br />

is c<strong>on</strong>trolled is a key questi<strong>on</strong> in stem cell biology. It has recently been shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

differential rates <str<strong>on</strong>g>of</str<strong>on</strong>g> Centrosomin (Cnn) incorporati<strong>on</strong> into centrosomes may lead<br />

to centrosome size asymmetry in Drosophila neural stem cells. Cnn forms a gradient<br />

in pericentriolar matrix (PCM) and live imaging combined wi<str<strong>on</strong>g>th</str<strong>on</strong>g> fluorescence<br />

recovery after photobleaching (FRAP) analysis has revealed <str<strong>on</strong>g>th</str<strong>on</strong>g>at Cnn molecules<br />

first incorporate into <str<strong>on</strong>g>th</str<strong>on</strong>g>e centre <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e PCM and <str<strong>on</strong>g>th</str<strong>on</strong>g>en spreads outwards <str<strong>on</strong>g>th</str<strong>on</strong>g>roughout<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e rest <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e PCM. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we propose a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model composed<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a coupled system <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear reacti<strong>on</strong>-diffusi<strong>on</strong> type equati<strong>on</strong>s to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

observed Cnn behaviour. We hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esise <str<strong>on</strong>g>th</str<strong>on</strong>g>at Cnn binds to its receptors near <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

centre <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e PCM and is c<strong>on</strong>verted into a ’heavy’ form which diffuses slowly as<br />

compared to cytoplasmic Cnn. Diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> heavy Cnn <str<strong>on</strong>g>th</str<strong>on</strong>g>en creates a gradient<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e PCM. Steady state analysis shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at heavy Cnn forms an exp<strong>on</strong>entially<br />

decreasing gradient at steady state, which matches well wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimentally<br />

observed Cnn gradient. Numerical simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model also predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e FRAP<br />

kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> Cnn. Once we understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> Cnn incorporati<strong>on</strong>, we may<br />

be able to predict how <str<strong>on</strong>g>th</str<strong>on</strong>g>is mechanism could be exploited to create centrosome size<br />

asymmetry in Drosophila neural stem cells.<br />

71

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Recent developments in <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> Lotka-Volterra and Kolmogorov<br />

systems; Saturday, July 2, 14:30<br />

Joanna Balbus<br />

Wroclaw University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: joanna.balbus@pwr.wroc.pl<br />

Average c<strong>on</strong>diti<strong>on</strong>s for permanence in N-species<br />

n<strong>on</strong>aut<strong>on</strong>omous competitive systems <str<strong>on</strong>g>of</str<strong>on</strong>g> PDEs<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we c<strong>on</strong>sider a n<strong>on</strong>aut<strong>on</strong>omous systems <str<strong>on</strong>g>of</str<strong>on</strong>g> PDEs<br />

⎧<br />

⎪⎨<br />

∂ui<br />

∂t<br />

⎪⎩<br />

= ∆ui + fi(t, x, u1, . . . , uN )ui, t > 0, x ∈ Ω, i = 1, . . . , N<br />

Bui = 0, t > 0, x ∈ ∂Ω, i = 1, . . . , N,<br />

where Ω is a bounded domain wi<str<strong>on</strong>g>th</str<strong>on</strong>g> sufficiently smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> boundary ∂Ω, ∆ is <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Laplace operator <strong>on</strong> Ω, and B is <str<strong>on</strong>g>th</str<strong>on</strong>g>e boundary operator <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Neumann or Dirichlet<br />

type. Applying <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ahmad and Lazer’s definiti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> lower and upper averages <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a functi<strong>on</strong> we give average c<strong>on</strong>diti<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e permanence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Neumann case we also give a sufficient c<strong>on</strong>diti<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e system to be globally<br />

attractive.<br />

72

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Annabelle Ballesta<br />

INRIA<br />

e-mail: annabelle.ballesta@inria.fr<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

A Combined Experimental and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Approach for<br />

Molecular-based Pers<strong>on</strong>alizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Irinotecan Circadian<br />

Delivery<br />

Irinotecan is an anticancer drug which is currently in use for chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy against<br />

colorectal cancer. Its pharmacokinetics (PK- what <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells do to <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug, e.g.<br />

metabolizati<strong>on</strong>, transport), and pharmacodynamics (PD- what <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug does to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cells, e.g. DNA damage) are largely influenced by 24-hour-period rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

certain proteins including <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug target Topoisomerase I, <str<strong>on</strong>g>th</str<strong>on</strong>g>e activati<strong>on</strong> enzymes<br />

(Carboxylesterases), <str<strong>on</strong>g>th</str<strong>on</strong>g>e deactivati<strong>on</strong> enzymes (UGT1A1,UGT1A9) and <str<strong>on</strong>g>th</str<strong>on</strong>g>e ABC<br />

transporters which are resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>e efflux <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug. Indeed circadian<br />

rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms have been described for most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ose proteins bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in humans and in<br />

mice. A chr<strong>on</strong>omodulated scheme <str<strong>on</strong>g>of</str<strong>on</strong>g> administrati<strong>on</strong> for Irinotecan is already used<br />

in clinic but recent findings highlight <str<strong>on</strong>g>th</str<strong>on</strong>g>e need <str<strong>on</strong>g>of</str<strong>on</strong>g> pers<strong>on</strong>alized chr<strong>on</strong>o<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutics<br />

delivery pattern according to <str<strong>on</strong>g>th</str<strong>on</strong>g>e patient gender and genetic background ([1]).<br />

Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>European</str<strong>on</strong>g> project TEMPO, Irinotecan chr<strong>on</strong>otoxicity has been studied<br />

in mice and <str<strong>on</strong>g>th</str<strong>on</strong>g>ree classes have been determined wi<str<strong>on</strong>g>th</str<strong>on</strong>g> regards to Irinotecan best circadian<br />

hour <str<strong>on</strong>g>of</str<strong>on</strong>g> administrati<strong>on</strong> (i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e hour which induces <str<strong>on</strong>g>th</str<strong>on</strong>g>e minimal toxicity).<br />

Our modeling approach aims at identifying molecular biomarkers which could discriminate<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e classes and at designing optimal chr<strong>on</strong>omodulated infusi<strong>on</strong><br />

scheme for each <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em. A whole body physiologically-based PK-PD model has<br />

been built starting from a previous ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model designed <str<strong>on</strong>g>th</str<strong>on</strong>g>anks to a cell<br />

culture study ([2]) . Parameters have been estimated for each mouse class by fitting<br />

available data <strong>on</strong> tissular PK for two different circadian hours <str<strong>on</strong>g>of</str<strong>on</strong>g> administrati<strong>on</strong> and<br />

<strong>on</strong> circadian rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms <str<strong>on</strong>g>of</str<strong>on</strong>g> relevant proteins. Validati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model<br />

by comparing its output wi<str<strong>on</strong>g>th</str<strong>on</strong>g> independent experimental data is in progress. Then<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter set will be compared in order to find differences between <str<strong>on</strong>g>th</str<strong>on</strong>g>e classes<br />

and optimizati<strong>on</strong> algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms will be applied to <str<strong>on</strong>g>th</str<strong>on</strong>g>e model to design <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretically<br />

optimal chr<strong>on</strong>omodulated scheme <str<strong>on</strong>g>of</str<strong>on</strong>g> administrati<strong>on</strong>. This study in mice may give<br />

a hint for determining molecular biomarkers which should be measured in patients<br />

in order to tailored chr<strong>on</strong>omodulated infusi<strong>on</strong> schemes.<br />

1.Lévi F, Okyar A, Dul<strong>on</strong>g S, Innominato PF, Clairambault J., Circadian timing<br />

in cancer treatments, Annu Rev Pharmacol Toxicol. 2010;50:377-421. 2.Ballesta<br />

A, Dul<strong>on</strong>g S, Abbara C, Cohen B, Okyar A, Clairambault J et al. A combined biological<br />

and ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical approach to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e anticancer drug Irinotecan molecular<br />

pharmacokinetics-pharmacodynamics and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir c<strong>on</strong>trol by <str<strong>on</strong>g>th</str<strong>on</strong>g>e circadian clock,<br />

under revisi<strong>on</strong>.<br />

73

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Structure and Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemical Reacti<strong>on</strong> Networks II; Tuesday, June<br />

28, 17:00<br />

Murad Banaji<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Portsmou<str<strong>on</strong>g>th</str<strong>on</strong>g>, UK<br />

e-mail: murad.banaji@port.ac.uk<br />

M<strong>on</strong>ot<strong>on</strong>e dynamics in chemical reacti<strong>on</strong> networks<br />

Proving <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e allowed dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> certain classes <str<strong>on</strong>g>of</str<strong>on</strong>g> chemical reacti<strong>on</strong> networks<br />

(CRNs) is necessarily simple regardless <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinetics is bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> interest in itself,<br />

and potentially provides insight into how more complex dynamics can arise. Here,<br />

recent <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <strong>on</strong> m<strong>on</strong>ot<strong>on</strong>e dynamical systems is applied to dem<strong>on</strong>strate local and<br />

global stability <str<strong>on</strong>g>of</str<strong>on</strong>g> equilibria for a class <str<strong>on</strong>g>of</str<strong>on</strong>g> CRNs. The stability results arise from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> two structures which occur frequently in CRNs: preservati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a partial order and <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>stants <str<strong>on</strong>g>of</str<strong>on</strong>g> moti<strong>on</strong>. The class shown to have<br />

str<strong>on</strong>g stability properties is defined via <str<strong>on</strong>g>th</str<strong>on</strong>g>e network structure, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <strong>on</strong>ly weak<br />

assumpti<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong> kinetics. The key c<strong>on</strong>diti<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network are (i)<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e stoichiometric matrix can be factorised in a certain way, and (ii) <str<strong>on</strong>g>th</str<strong>on</strong>g>at an<br />

associated digraph is str<strong>on</strong>gly c<strong>on</strong>nected.<br />

74

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Plants, grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and transport processes II; Tuesday, June 28, 14:30<br />

L. R. Band<br />

Centre for Plant Integrative Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, UK<br />

e-mail: Leah.Band@nottingham.ac.uk<br />

S. Úbeda-Tomás<br />

Centre for Plant Integrative Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, UK<br />

e-mail: Susana.Ubeda-Tomas@nottingham.ac.uk<br />

R. J. Dys<strong>on</strong><br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Birmingham, UK<br />

e-mail: R.J.Dys<strong>on</strong>@bham.ac.uk<br />

A. M. Middlet<strong>on</strong><br />

Albert-Ludwigs-Universität, Freiburg, Germany<br />

e-mail: Alistair.Middlet<strong>on</strong>@mail.zbsa.uni-freiburg.de<br />

M. J. Bennett<br />

Centre for Plant Integrative Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, UK<br />

e-mail: Malcolm.Bennett@nottingham.ac.uk<br />

O. E. Jensen<br />

Centre for Plant Integrative Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, UK<br />

e-mail: Oliver.Jensen@nottingham.ac.uk<br />

J. R. King<br />

Centre for Plant Integrative Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, UK<br />

e-mail: John.King@nottingham.ac.uk<br />

Modelling horm<strong>on</strong>e-regulated plant root grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Researchers at <str<strong>on</strong>g>th</str<strong>on</strong>g>e Centre for Plant Integrative Biology are using systems approaches<br />

to investigate plant root grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and development. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, we present<br />

a multiscale model <str<strong>on</strong>g>th</str<strong>on</strong>g>at describes how <str<strong>on</strong>g>th</str<strong>on</strong>g>e horm<strong>on</strong>e GA regulates grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e root<br />

el<strong>on</strong>gati<strong>on</strong> z<strong>on</strong>e. The model includes: (i) horm<strong>on</strong>e diffusi<strong>on</strong> and diluti<strong>on</strong>, (ii) a genetic<br />

regulatory network <str<strong>on</strong>g>th</str<strong>on</strong>g>at details how <str<strong>on</strong>g>th</str<strong>on</strong>g>e horm<strong>on</strong>e affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e DELLA proteins,<br />

(iii) a descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> how <str<strong>on</strong>g>th</str<strong>on</strong>g>e DELLA proteins influence <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell-wall remodelling<br />

enzymes, and finally (iv) a submodel linking cell-wall remodeling to grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. Using<br />

detailed morphological measurements, our model shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at cell grow<str<strong>on</strong>g>th</str<strong>on</strong>g> causes<br />

significant horm<strong>on</strong>e diluti<strong>on</strong> which can led to spatial variati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e key grow<str<strong>on</strong>g>th</str<strong>on</strong>g>regulating<br />

proteins. By modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>is feedback loop, we provide understanding <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e phenotypes observed in wild-type and mutant plants.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Jörg Bandura<br />

Theoretical Biology, IZMB, University <str<strong>on</strong>g>of</str<strong>on</strong>g> B<strong>on</strong>n, Germany<br />

e-mail: bandura@chaos-engine.net<br />

Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. Wolfgang Alt<br />

Theoretical Biology, IZMB, University <str<strong>on</strong>g>of</str<strong>on</strong>g> B<strong>on</strong>n, Germany<br />

e-mail: wolf.alt@uni-b<strong>on</strong>n.de<br />

Cell migrati<strong>on</strong> inspired design <str<strong>on</strong>g>of</str<strong>on</strong>g> crawling robots<br />

Animal tissue cells (as fibroblasts and keratinocytes) are utilising a unique principle<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> locomoti<strong>on</strong>: <str<strong>on</strong>g>th</str<strong>on</strong>g>e adhesive cell migrati<strong>on</strong> for crawling <strong>on</strong> a fixed substratum.<br />

It is a higly complex process involving <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> and multiple regulati<strong>on</strong><br />

mechanisms [1]. The moving cell is polarised as a result <str<strong>on</strong>g>of</str<strong>on</strong>g> asymmetric cytoskelet<strong>on</strong><br />

modificati<strong>on</strong>s by assembling and disassembling micr<str<strong>on</strong>g>of</str<strong>on</strong>g>ilaments [2]. Transmembrane<br />

glycoproteines such as integrins adhere to <str<strong>on</strong>g>th</str<strong>on</strong>g>e substratum and are dynamically coupled<br />

to actin filaments inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell, which are cross-linked to myosin dimers. By<br />

exerti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tractile stress <str<strong>on</strong>g>th</str<strong>on</strong>g>is actomyosin complex is able to transfer a tracti<strong>on</strong><br />

force <strong>on</strong>to <str<strong>on</strong>g>th</str<strong>on</strong>g>e substratum, enhancing cell polarisati<strong>on</strong>: at <str<strong>on</strong>g>th</str<strong>on</strong>g>e fr<strong>on</strong>t, ’s<str<strong>on</strong>g>of</str<strong>on</strong>g>t’ centripetal<br />

forces pull <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell body forwards, whereas in <str<strong>on</strong>g>th</str<strong>on</strong>g>e rear, ’stiff’ centripetal<br />

forces mechanically disrupts <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell from <str<strong>on</strong>g>th</str<strong>on</strong>g>e substratum [3].<br />

This project is using <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic physical principles causing <str<strong>on</strong>g>th</str<strong>on</strong>g>e propulsi<strong>on</strong> during cell<br />

migrati<strong>on</strong> as a bio-inspired approach for designing a new form <str<strong>on</strong>g>of</str<strong>on</strong>g> crawling robot locomoti<strong>on</strong>.<br />

The aim is not to copy <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell migrati<strong>on</strong> mechanism itself but ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er its<br />

basic physical outline. This outline c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> an aut<strong>on</strong>omously induced gradient<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> stiffness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e adhering cell cortex, increasing from fr<strong>on</strong>t to rear, persisting during<br />

migrati<strong>on</strong> due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e successive assembly and streng<str<strong>on</strong>g>th</str<strong>on</strong>g>ening <str<strong>on</strong>g>of</str<strong>on</strong>g> micr<str<strong>on</strong>g>of</str<strong>on</strong>g>ilaments<br />

at <str<strong>on</strong>g>th</str<strong>on</strong>g>e adhesi<strong>on</strong> sites. These physical properties are implemented into a computati<strong>on</strong>al<br />

model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> corresp<strong>on</strong>ding simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> an aut<strong>on</strong>omous self-crawling and<br />

self-deforming robot. The two-dimensi<strong>on</strong>al model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> double elastic chains,<br />

linked by radial elastic segments, which adapt <str<strong>on</strong>g>th</str<strong>on</strong>g>eir stiffness and elasticity to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

adhesi<strong>on</strong> or n<strong>on</strong>-adhesi<strong>on</strong> state over time: building up a gradient <str<strong>on</strong>g>of</str<strong>on</strong>g> stiffness during<br />

adhesi<strong>on</strong> and decreasing it after disrupti<strong>on</strong>.<br />

Simulati<strong>on</strong> runs dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is model is able to move aut<strong>on</strong>omously and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at it is capable to move upwards inclinati<strong>on</strong>s and walls wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out losing stability.<br />

The model is designed simple enough for c<strong>on</strong>structi<strong>on</strong> in reality. This leads to<br />

possibly new forms <str<strong>on</strong>g>of</str<strong>on</strong>g> crawling locomoti<strong>on</strong> in robotics, advantageous in situati<strong>on</strong>s,<br />

where legged and wheeled propulsi<strong>on</strong> is not usable or working.<br />

References.<br />

[1] Lauffenburger DA, Horwitz AF (1996) Cell migrati<strong>on</strong>: a physically integrated molecular process,<br />

Cell, 84, pp. 359–369.<br />

[2] Evans EA, Calderwood DA (2007) Forces and b<strong>on</strong>d dynamics in cell adhesi<strong>on</strong>, Science, 316,<br />

pp. 1148–1153.<br />

[3] Alt W, Bock M, Möhl C (2010) Coupling <str<strong>on</strong>g>of</str<strong>on</strong>g> cytoplasm and adhesi<strong>on</strong> dynamics determines cell<br />

polarizati<strong>on</strong> and locomoti<strong>on</strong>, in: A. Chauvière, L. Preziosi, C. Verdier Cell Mechanics: From<br />

Single Cell-Based Models to Multiscale Modeling, Chapman & Hall CRC, L<strong>on</strong>d<strong>on</strong>, pp. 89–131.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models in Eco-epidemiology I; Wednesday, June 29, 08:30<br />

Malay Banerjee<br />

I. I. T. Kanpur, Kanpur - 208016, INDIA<br />

e-mail: malayb@iitk.ac.in<br />

Deterministic Chaos vs. Stochastic Oscillati<strong>on</strong> in an<br />

Eco-epidemic Model<br />

Eco-epidemiological models <str<strong>on</strong>g>of</str<strong>on</strong>g> prey-predator interacti<strong>on</strong> in presence <str<strong>on</strong>g>of</str<strong>on</strong>g> disease<br />

affecting ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er or bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e species have received significant attenti<strong>on</strong> from various<br />

researchers. Some recent investigati<strong>on</strong> reveals chaotic dynamics for certain range <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

parameter values. Unusual disease related dea<str<strong>on</strong>g>th</str<strong>on</strong>g> or higher grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate <str<strong>on</strong>g>of</str<strong>on</strong>g> susceptible<br />

species or sudden outbreak <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease or high rate <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong> are possible<br />

explanati<strong>on</strong> behind <str<strong>on</strong>g>th</str<strong>on</strong>g>e chaotic dynamics. Most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese modeling approaches neglected<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e demographic stochasticity as well as envir<strong>on</strong>mental stochasticity. Main<br />

objective <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e presentati<strong>on</strong> is to c<strong>on</strong>struct <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic eco-epidemic model based<br />

up<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e existing deterministic model and study <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics for a wide range <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

parameter values. The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic model is investigated for two<br />

types <str<strong>on</strong>g>of</str<strong>on</strong>g> parameter values, first set corresp<strong>on</strong>d to stati<strong>on</strong>ary or periodic scenario<br />

and sec<strong>on</strong>d set corresp<strong>on</strong>d to chaotic oscillati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic model. It is<br />

interesting to note <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er species is not chaotic wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in stochastic<br />

setup ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>ey exhibit n<strong>on</strong>-equilibrium fluctuati<strong>on</strong> around some average<br />

values for bo<str<strong>on</strong>g>th</str<strong>on</strong>g> types <str<strong>on</strong>g>of</str<strong>on</strong>g> parameter values. Chance <str<strong>on</strong>g>of</str<strong>on</strong>g> extincti<strong>on</strong> and expected time<br />

to extincti<strong>on</strong> is also studied wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e help <str<strong>on</strong>g>of</str<strong>on</strong>g> exhaustive numerical simulati<strong>on</strong>s.<br />

77

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Wednesday, June 29, 08:30<br />

Maria Barbarossa<br />

Technische Universität München, Chair for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling<br />

e-mail: barbarossa@ma.tum.de<br />

Christina Kuttler<br />

Technische Universität München, Chair for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling<br />

Delay equati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell cycle <str<strong>on</strong>g>of</str<strong>on</strong>g> tumoral cells<br />

Cancer is nowadays <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most complex severe diseases in <str<strong>on</strong>g>th</str<strong>on</strong>g>e world. To better<br />

understand it, ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical biologists have been working for <str<strong>on</strong>g>th</str<strong>on</strong>g>e last decades <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, we model a combined treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> immuno- and chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy and<br />

its effects <strong>on</strong> a solid tumor.<br />

Many au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors (e.g. Arino, Dys<strong>on</strong> et al.) suggested structured populati<strong>on</strong> models<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer biology. Here, we start wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a tumoral cell populati<strong>on</strong><br />

structured by age and introduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> drugs and immuno<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumoral<br />

mass. For a better descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> phase-specific drugs, we define<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ree sub-populati<strong>on</strong>s for interphase, mitotic and quiescent cells. Effectors from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

immune system work against every kind <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cells, whereas chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy is<br />

assumed to be mitosis-specific <strong>on</strong>ly.<br />

Following a similar approach to <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>of</str<strong>on</strong>g> Bocharov and Hadeler (2000), we derive<br />

a system <str<strong>on</strong>g>of</str<strong>on</strong>g> delay differential equati<strong>on</strong>s equivalent to <str<strong>on</strong>g>th</str<strong>on</strong>g>e original age-structured<br />

model. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough our results apparently resemble <str<strong>on</strong>g>th</str<strong>on</strong>g>ose <str<strong>on</strong>g>of</str<strong>on</strong>g> Villasana (2003) and Liu<br />

(2007), <str<strong>on</strong>g>th</str<strong>on</strong>g>e model here is not deduced from <str<strong>on</strong>g>th</str<strong>on</strong>g>e mass acti<strong>on</strong> kinetics principles. But<br />

our approach allows us to take care <str<strong>on</strong>g>of</str<strong>on</strong>g> all delayed and undelayed variables and to<br />

locate <str<strong>on</strong>g>th</str<strong>on</strong>g>em at <str<strong>on</strong>g>th</str<strong>on</strong>g>e right place in <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>us providing a better descripti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological phenomen<strong>on</strong>.<br />

We investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e delay model bo<str<strong>on</strong>g>th</str<strong>on</strong>g> from <str<strong>on</strong>g>th</str<strong>on</strong>g>e analytical and <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical point <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

view and focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer-free equilibrium. Inspired by <str<strong>on</strong>g>th</str<strong>on</strong>g>e work<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors (e.g. d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio, 2010), we simulate different kinds <str<strong>on</strong>g>of</str<strong>on</strong>g> immuno<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

and estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>eir effects <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. Our aim is to find c<strong>on</strong>diti<strong>on</strong>s<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e eradicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor or for its reducti<strong>on</strong> to a life-compatible<br />

size.<br />

References.<br />

[1] O. Arino, A survey <str<strong>on</strong>g>of</str<strong>on</strong>g> structured cell populati<strong>on</strong> dynamics, Acta Bio<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretica 43 (1995).<br />

[2] G. Bocharov, K.P. Hadeler, Structured populati<strong>on</strong> model, c<strong>on</strong>servati<strong>on</strong> laws and delay equati<strong>on</strong>s,<br />

J. Diff. Equa. 168 (2000).<br />

[3] A. d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio et al., Delay-induced oscillatory dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour-immune system interacti<strong>on</strong>,<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Comp. Mod., Vol.51 (2010)<br />

[4] J. Dys<strong>on</strong>, Asynchr<strong>on</strong>ous exp<strong>on</strong>ential grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in an age-structured populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> proliferating<br />

and quiescent cells, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosc. 177 (2002).<br />

[5] W. Liu et al., A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for M-phase specific chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy including <str<strong>on</strong>g>th</str<strong>on</strong>g>e G0phase<br />

and immunoresp<strong>on</strong>se. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosc. Eng. 4(2), (2007)<br />

[6] M. Villasana, A. Radunskaya, A delay differential equati<strong>on</strong> model for tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

Bio. 47(3), (2003)<br />

[7] M. Barbarossa, C. Kuttler, J. Zinsl, Delay models for tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, in progress.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Mosquito-Borne Diseases; Tuesday, June 28, 11:00<br />

Susana Barbosa<br />

Liverpool School <str<strong>on</strong>g>of</str<strong>on</strong>g> Tropical Medicine<br />

e-mail: sbarbosa@liv.ac.uk<br />

A genetic model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> insecticide resistance in a<br />

heterogeneous envir<strong>on</strong>ment<br />

Protecti<strong>on</strong> measures against insect borne diseases predominantly depend up<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e usage <str<strong>on</strong>g>of</str<strong>on</strong>g> insecticides. Different strategies <str<strong>on</strong>g>of</str<strong>on</strong>g> delivery can use single insecticides<br />

or use <str<strong>on</strong>g>th</str<strong>on</strong>g>em in combinati<strong>on</strong>. The effects <str<strong>on</strong>g>of</str<strong>on</strong>g> combined c<strong>on</strong>trol interventi<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> insecticide resistance in a mosquito populati<strong>on</strong> has not been assessed<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e model presented here is designed to be a starting point.<br />

We incorporate <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> insecticides outside <str<strong>on</strong>g>th</str<strong>on</strong>g>e household and <str<strong>on</strong>g>th</str<strong>on</strong>g>e advent<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> new generati<strong>on</strong> l<strong>on</strong>g-lasting insecticidal nets <str<strong>on</strong>g>th</str<strong>on</strong>g>at allegedly have increased efficacy<br />

against pyre<str<strong>on</strong>g>th</str<strong>on</strong>g>roid-resistant malaria vectors. Here we describe a model <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

allows mosquitoes to encounter insecticides in several envir<strong>on</strong>ments and explicity<br />

investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> synergists <strong>on</strong> bednets.<br />

The model includes two parameters <str<strong>on</strong>g>th</str<strong>on</strong>g>at quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> using a synergist<br />

in combinati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a insecticide: <str<strong>on</strong>g>th</str<strong>on</strong>g>e reduce survival due <str<strong>on</strong>g>th</str<strong>on</strong>g>e synergist and <str<strong>on</strong>g>th</str<strong>on</strong>g>e proporti<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> mosquitoes (males and females) <str<strong>on</strong>g>th</str<strong>on</strong>g>at encounter bo<str<strong>on</strong>g>th</str<strong>on</strong>g> chemicals. These<br />

parameters had a small correlati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> male and female mean fitness suggesting<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>eir impact in <str<strong>on</strong>g>th</str<strong>on</strong>g>e spreading <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance is small. A sensitivity analysis<br />

pinpointed <str<strong>on</strong>g>th</str<strong>on</strong>g>e baseline fitness <str<strong>on</strong>g>of</str<strong>on</strong>g> susceptible homozygotes and <str<strong>on</strong>g>th</str<strong>on</strong>g>e proporti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

mosquitoes <str<strong>on</strong>g>th</str<strong>on</strong>g>at enter <str<strong>on</strong>g>th</str<strong>on</strong>g>e household as <str<strong>on</strong>g>th</str<strong>on</strong>g>e most influential parameters and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

<strong>on</strong>es <str<strong>on</strong>g>th</str<strong>on</strong>g>at play <str<strong>on</strong>g>th</str<strong>on</strong>g>e major role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> insecticide resistance.<br />

79

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 14:30<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Bartoszek<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Chalmers University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg, Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg, Sweden<br />

e-mail: krzbar@chalmers.se<br />

Jas<strong>on</strong> Pienaar<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Genetics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Pretoria, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Africa 0002<br />

e-mail: jas<strong>on</strong>.pienaar@up.ac.za<br />

Thomas Hansen<br />

CEES Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oslo, Oslo Norway<br />

e-mail: t.f.hansen@bio.uio.no<br />

Petter Mostad<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Chalmers University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg, Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg, Sweden<br />

e-mail: mostad@chalmers.se<br />

Multivariate comparative analysis<br />

The need for taking into account phylogenetic dependencies between trait measurements<br />

in comparative analysis is some<str<strong>on</strong>g>th</str<strong>on</strong>g>ing which has become obvious. One<br />

approach to capture <str<strong>on</strong>g>th</str<strong>on</strong>g>is dependency is to assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e trait(s) evolve as a time<br />

dependent branching stochastic differential equati<strong>on</strong> al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e phylogenentic tree.<br />

The development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is branch <str<strong>on</strong>g>of</str<strong>on</strong>g> comparative analysis started wi<str<strong>on</strong>g>th</str<strong>on</strong>g> [1] and was<br />

c<strong>on</strong>tinued in [2],[3],[4],[5]. However all <str<strong>on</strong>g>th</str<strong>on</strong>g>ese proposed me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods lacked a fully multivariate<br />

implementati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed models. We have developed a generalizati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models into <str<strong>on</strong>g>th</str<strong>on</strong>g>e fully multivariate setting and implemented an estimati<strong>on</strong><br />

package in R to analyze comparative data under <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models. The multivariate<br />

setting gives us much more flexibility and allows to e.g. model codevelopment <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

allometry, indicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> a trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f and gain understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> trait coevoluti<strong>on</strong>.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e talk we will discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e multivariate model, possible hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis (allometry,<br />

trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f) <strong>on</strong>e can study wi<str<strong>on</strong>g>th</str<strong>on</strong>g> it and go <str<strong>on</strong>g>th</str<strong>on</strong>g>rough an example study <str<strong>on</strong>g>of</str<strong>on</strong>g> how sexual<br />

selecti<strong>on</strong> acts <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> male canine and body sizes in Primates.<br />

References.<br />

[1] J. Felsenstein Phylogenies and <str<strong>on</strong>g>th</str<strong>on</strong>g>e comparative me<str<strong>on</strong>g>th</str<strong>on</strong>g>od The American Naturalist 1 1–15.<br />

[2] T. Hansen Stabilizing selecti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e comparative analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> adaptati<strong>on</strong> Evoluti<strong>on</strong> 51 1341–<br />

1351.<br />

[3] M. Butler and A. King Phylogenetic comparative analysis: a modelling approach for adaptive<br />

evoluti<strong>on</strong> The American Naturalist 164 683–695.<br />

[4] T. Hansen and J. Pienaar and S. Orzack A comparative me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for studying adaptati<strong>on</strong> to<br />

randomly evolving envir<strong>on</strong>ment Evoluti<strong>on</strong> 62 1965–1977.<br />

[5] J. Pienaar and K. Bartoszek and T. Hansen and K. Voje Overview <str<strong>on</strong>g>of</str<strong>on</strong>g> comparative me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

for studying adaptati<strong>on</strong> <strong>on</strong> adaptive landscapes in prep.<br />

80

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Genetics; Wednesday, June 29, 17:00<br />

Wojciech Bartoszek (1) and Małgorzata Pułka (2)<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Gdańsk University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, ul.<br />

Narutowicza 11/12, 80-233 Gdańsk, Poland<br />

e-mail: bartowk@mifgate.mif.pg.gda.pl (1)<br />

e-mail: mpulka@mif.pg.gda.pl (2)<br />

On dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> quadratic stochastic processes and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

applicati<strong>on</strong>s in biology<br />

A quadratic stochastic operator Q : X → X is defined by a cubic (finite or<br />

infinite) array <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>negative real numbers [qij,k]i,j,k≥1 which satisfy<br />

(1) 0 ≤ qij,k = qji,k ≤ 1 for all i, j, k ≥ 1,<br />

(2) <br />

k=1 qij,k = 1 for any pair (i, j),<br />

where X is ℓ1 or ℓ1 d equipped wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a standard norm. The family <str<strong>on</strong>g>of</str<strong>on</strong>g> all quadratic<br />

stochastic operators is denoted by Q. Any quadratic stochastic operator (process)<br />

Q<br />

<br />

may be viewed as a bilinear mapping Q : X × X → X if we set Q(x, y)(k) =<br />

xiyjqij,k. Clearly Q is m<strong>on</strong>ot<strong>on</strong>e (i.e. Q(x, y) ≥ Q(u, w) whenever x ≥ u ≥<br />

i=1,j=1<br />

0 and y ≥ w ≥ 0) and is bounded as sup x1,y1≤1 Q(x, y)1 = 1 . It follows<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at Q may also be viewed as a mapping Q : D × D → D, where D stands for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

simplex <str<strong>on</strong>g>of</str<strong>on</strong>g> probability vectors. In populati<strong>on</strong> genetics a special attenti<strong>on</strong> is paid to<br />

a n<strong>on</strong>linear mapping D ∋ p → Q(p) = Q(p, p). Here Q : D → D. Roughly speaking<br />

Q(p) represents a distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e next generati<strong>on</strong> if parent’s gens have<br />

a distributi<strong>on</strong> p. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is simplified model <str<strong>on</strong>g>th</str<strong>on</strong>g>e iterates Q k (p), where k = 0, 1, . . . ,<br />

describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a genom. Given an initial distributi<strong>on</strong> p ∈ D <strong>on</strong>e may<br />

ask about asymptotic behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e trajectory (i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e sequence (Q n (p))n≥0).<br />

Because <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linearity, <str<strong>on</strong>g>th</str<strong>on</strong>g>e trajectories enjoy several unexpected features (as it<br />

was c<strong>on</strong>jectured by S. Ulam). In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we discuss some generic properties in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

set Q. We also present c<strong>on</strong>diti<strong>on</strong>s for asymptotic stability <str<strong>on</strong>g>of</str<strong>on</strong>g> Q ∈ Q .<br />

81

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

The emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance in cancer using ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling;<br />

Saturday, July 2, 08:30<br />

David Basanta<br />

M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center<br />

e-mail: david@cancerevo.org<br />

Tumour heterogeneity and its role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

resistance<br />

Cancers are known to be heterogeneous which is <str<strong>on</strong>g>th</str<strong>on</strong>g>e source <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir streng<str<strong>on</strong>g>th</str<strong>on</strong>g> explaining<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> progressi<strong>on</strong> and resistance. N<strong>on</strong>e<str<strong>on</strong>g>th</str<strong>on</strong>g>eless, <str<strong>on</strong>g>th</str<strong>on</strong>g>e nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is heterogeneity<br />

is still poorly understood, especially regarding its impact <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance<br />

to treatment. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we will briefly discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary mechanisms<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>is heterogeneity as well as it is impact in <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance.<br />

Special attenti<strong>on</strong> will be given to <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> interacti<strong>on</strong>s between tumur cells and<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour and stroma and <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese interacti<strong>on</strong>s as a potential<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic target.<br />

82

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

David Basanta<br />

H. Lee M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center & Research Institute<br />

e-mail: david@cancerevo.org<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

The role <str<strong>on</strong>g>of</str<strong>on</strong>g> genetic and envir<strong>on</strong>mental insults in<br />

glioblastoma carcinogenesis<br />

Glioblastoma, <str<strong>on</strong>g>th</str<strong>on</strong>g>e most comm<strong>on</strong> primary brain tumor, is uniformly fatal, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a<br />

majority <str<strong>on</strong>g>of</str<strong>on</strong>g> patients dying wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in 2 years <str<strong>on</strong>g>of</str<strong>on</strong>g> diagnosis. Emerging data suggests<br />

a small subpopulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells in glioblastoma have stem cell-like properties and<br />

are key to tumourigenesis. C<strong>on</strong>certed efforts to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying biology<br />

regulating <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cells are currently underway, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an overarching goal <str<strong>on</strong>g>of</str<strong>on</strong>g> identifying<br />

novel tumor-specific pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways <str<strong>on</strong>g>th</str<strong>on</strong>g>at may be effectively targeted as a strategy for<br />

anti-cancer <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy.<br />

An important advancement towards our understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> glioblastoma stemlike<br />

cells has been identifying <str<strong>on</strong>g>th</str<strong>on</strong>g>e similarities <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cells share wi<str<strong>on</strong>g>th</str<strong>on</strong>g> normal neural<br />

stem cells; most notable being <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>th</str<strong>on</strong>g>e physical microenvir<strong>on</strong>ment plays in regulating<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir phenotype. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e majority <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical work has focused<br />

<strong>on</strong> elements extrinsic to <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour microenvir<strong>on</strong>ment, <str<strong>on</strong>g>th</str<strong>on</strong>g>e microenvir<strong>on</strong>ment <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

has yet to be explored in relati<strong>on</strong> to glioblastoma stem-like cell biology. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er,<br />

current laboratory-based models are limited in providing meaningful insight into<br />

how <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex adaptive systems defining <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor microenvir<strong>on</strong>ment may interact<br />

to c<strong>on</strong>tribute towards glioblastoma tumorigenesis. Our goal is to apply an<br />

integrative approach, coupling ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling wi<str<strong>on</strong>g>th</str<strong>on</strong>g> laboratory-based investigati<strong>on</strong>s,<br />

to better understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay between glioblastoma stem-like cells<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e microenvir<strong>on</strong>ment driving tumour initiati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e role hypoxia may play<br />

in modulating <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor stem-cell niche.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models in Eco-epidemiology II; Wednesday, June 29, 11:00<br />

Andrew Bate<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Ba<str<strong>on</strong>g>th</str<strong>on</strong>g>, Ba<str<strong>on</strong>g>th</str<strong>on</strong>g>, BA2 7AY, UK<br />

e-mail: A.M.Bate@ba<str<strong>on</strong>g>th</str<strong>on</strong>g>.ac.uk<br />

Complex dynamics in an eco-epidemiological model<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, we incorporate a disease <strong>on</strong> a predator in a Holling type II predatorprey<br />

model. We establish <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease can have a stabilising effect <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system,<br />

bringing predator-prey oscillati<strong>on</strong>s to coexistent equilibrium. However, results<br />

become complex when disease dynamics are much faster <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e predator-prey<br />

dynamics, i.e. for high transmissi<strong>on</strong> and disease-induced dea<str<strong>on</strong>g>th</str<strong>on</strong>g> rates. Numerical<br />

soluti<strong>on</strong>s indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> saddle-node and subcritical Hopf bifurcati<strong>on</strong>s,<br />

as well as turning points and branching in periodic soluti<strong>on</strong>s. This means <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ere are regi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> bistability, in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease can have bo<str<strong>on</strong>g>th</str<strong>on</strong>g> a stabilising and<br />

destabilising effect. This holds for bo<str<strong>on</strong>g>th</str<strong>on</strong>g> density-dependent and frequency-dependent<br />

transmissi<strong>on</strong>.<br />

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Modeling physiological systems: model validati<strong>on</strong> and experimental design<br />

issues; Wednesday, June 29, 11:00<br />

Jerry Batel<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Graz<br />

e-mail: jerry.batzel@uni-graz.at<br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> Sensitivity Identifiability Analysis in Modeling<br />

Human Physiological Systems<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we discuss techniques to quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter estimati<strong>on</strong> problem<br />

in models <str<strong>on</strong>g>th</str<strong>on</strong>g>at characterize human physiological systems. In general, <str<strong>on</strong>g>th</str<strong>on</strong>g>e issue is to<br />

balance model complexity and parameter number wi<str<strong>on</strong>g>th</str<strong>on</strong>g> available data, data <str<strong>on</strong>g>th</str<strong>on</strong>g>at is<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g>ten restricted by such c<strong>on</strong>straints as accessibility to measurement sites, <str<strong>on</strong>g>th</str<strong>on</strong>g>e degree<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> error in measurements, cost <str<strong>on</strong>g>of</str<strong>on</strong>g> collecting data, and in <str<strong>on</strong>g>th</str<strong>on</strong>g>e clinical setting, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

need to screen patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> tests <str<strong>on</strong>g>th</str<strong>on</strong>g>at are minimally invasive.<br />

As a template example we will present a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiovascular<br />

c<strong>on</strong>trol system <str<strong>on</strong>g>of</str<strong>on</strong>g> mid-level complexity <str<strong>on</strong>g>th</str<strong>on</strong>g>at reflects <str<strong>on</strong>g>th</str<strong>on</strong>g>e various pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways<br />

for short-term blood pressure c<strong>on</strong>trol in resp<strong>on</strong>se to various cardiovascular stresses.<br />

The model includes 10 vascular compartments and baroreflex feedback c<strong>on</strong>trol <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

can alter resistance, heart rate and heart c<strong>on</strong>tractility, and unstressed volume to<br />

counteract a perturbati<strong>on</strong> in blood pressure, returning <str<strong>on</strong>g>th</str<strong>on</strong>g>e pressure to its more or<br />

less steady state <str<strong>on</strong>g>of</str<strong>on</strong>g> operati<strong>on</strong>. The unstressed blood volume <str<strong>on</strong>g>of</str<strong>on</strong>g> a vascular element is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e natural filling volume <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be accommodated before stretching <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vascular<br />

wall begins. Additi<strong>on</strong>al volume generates transmural pressures <str<strong>on</strong>g>th</str<strong>on</strong>g>at stretch<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e vascular wall (stressed volume). Unstressed volume does not c<strong>on</strong>tribute to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

dynamic pressure which determines blood flow. It is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore a reservoir (particularly<br />

venous unstressed volume) <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be transferred (mobilized) by c<strong>on</strong>trol<br />

mechanisms (<str<strong>on</strong>g>th</str<strong>on</strong>g>rough c<strong>on</strong>stricti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> vessels) to stressed volume when blood volume<br />

is reduced. The model presented is sufficiently complex to characterize resp<strong>on</strong>ses<br />

to a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> system stresses including reducti<strong>on</strong> in blood volume.<br />

Or<str<strong>on</strong>g>th</str<strong>on</strong>g>ostatic stress is caused by blood pooling in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lower limbs when standing<br />

upright, a c<strong>on</strong>sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> gravity. This pooling removes a percentage <str<strong>on</strong>g>of</str<strong>on</strong>g> blood from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamic circulati<strong>on</strong>. In changing from <str<strong>on</strong>g>th</str<strong>on</strong>g>e pr<strong>on</strong>e to standing positi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol<br />

system must compensate for what is in effect a reducti<strong>on</strong> in blood volume. A<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> experimental protocols such as head up tilt (HUT) and lower body negative<br />

pressure (LBNP) are used to examine system resp<strong>on</strong>se to or<str<strong>on</strong>g>th</str<strong>on</strong>g>ostatic stress.<br />

To illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e difficulties <str<strong>on</strong>g>th</str<strong>on</strong>g>at arise in assessing c<strong>on</strong>trol resp<strong>on</strong>se via diagnostic<br />

testing, we note <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e HUT and LBNP protocols each have specific effects <strong>on</strong><br />

overall physiology which can obscure <str<strong>on</strong>g>th</str<strong>on</strong>g>e examinati<strong>on</strong> and characterizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> system<br />

resp<strong>on</strong>se. For example, unstressed blood volume is mobilized in different ways<br />

during LBNP, HUT, and or<str<strong>on</strong>g>th</str<strong>on</strong>g>ostasis [2].<br />

Several aspects and problems <str<strong>on</strong>g>of</str<strong>on</strong>g> model validati<strong>on</strong> will be discussed. Various<br />

tools derived from sensitivity analysis will be applied, including bo<str<strong>on</strong>g>th</str<strong>on</strong>g> classical and<br />

generalized sensitivities and subset selecti<strong>on</strong> [1, 3]. Applied jointly, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese tools can<br />

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provide insight into how specific experimental protocols such as HUT and LBNP<br />

impact model resp<strong>on</strong>se and <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential for parameter estimati<strong>on</strong>.<br />

References.<br />

[1] M. Bur<str<strong>on</strong>g>th</str<strong>on</strong>g>, G. C. Verghese, and M. Vélez-Reyes, Subset selecti<strong>on</strong> for improved parameter<br />

estimati<strong>on</strong> in <strong>on</strong>-line identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a synchr<strong>on</strong>ous generator, IEEE Transacti<strong>on</strong>s <strong>on</strong> Power<br />

Systems 14 (1999), no. 1, 218 – 225.<br />

[2] I. Taneja, C. Moran, M. S. Medow, J. L. Glover, L. D. M<strong>on</strong>tgomery, and J. M. Stewart,<br />

Differential effects <str<strong>on</strong>g>of</str<strong>on</strong>g> lower body negative pressure and upright tilt <strong>on</strong> splanchnic blood volume,<br />

Am J Physiol Heart Circ Physiol 292 (2007), no. 3, H1420 –– H1426.<br />

[3] K. Thomase<str<strong>on</strong>g>th</str<strong>on</strong>g> and C. Cobelli, Generalized sensitivity functi<strong>on</strong>s in physiological system identificati<strong>on</strong>,<br />

Ann Biomed Eng 27 (1999), no. 5, 607 – 616.<br />

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Cell and Tissue Biophysics; Saturday, July 2, 11:00<br />

Robert Bauer<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Illinois at Urbana-Champaign<br />

e-mail: rbauer13@illinois.edu<br />

A queueing <str<strong>on</strong>g>th</str<strong>on</strong>g>eory model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> microtubules<br />

and micr<str<strong>on</strong>g>of</str<strong>on</strong>g>ilaments<br />

Dynamic features <str<strong>on</strong>g>of</str<strong>on</strong>g> microtubules and micr<str<strong>on</strong>g>of</str<strong>on</strong>g>ilaments are essential to cell divisi<strong>on</strong>,<br />

cell motility, and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er cellular processes. ATP-bound m<strong>on</strong>omeric actin and GTPbound<br />

tubulin polymerize to actin filaments and microtubules, respectively. After<br />

assembly into polymers, nucleotide hydrolysis occurs, which can lead to a change<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>- and <str<strong>on</strong>g>of</str<strong>on</strong>g>f-rates at <str<strong>on</strong>g>th</str<strong>on</strong>g>e polymer ends. A simple stochastic model <str<strong>on</strong>g>of</str<strong>on</strong>g> such a<br />

polymer from nucleati<strong>on</strong> until complete depolymerizati<strong>on</strong> is presented. The model<br />

assumes <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a sharp boundary between <str<strong>on</strong>g>th</str<strong>on</strong>g>e “newer” part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e polymer<br />

c<strong>on</strong>taining <strong>on</strong>ly ATP-bound actin—<str<strong>on</strong>g>th</str<strong>on</strong>g>e ATP cap (GTP cap in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> tubulin),<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e “older” part, where all nucleotides have underg<strong>on</strong>e hydrolysis. The ATP<br />

cap and GTP cap are modeled as a single-server queue wi<str<strong>on</strong>g>th</str<strong>on</strong>g> reneging, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

server rate (rate <str<strong>on</strong>g>of</str<strong>on</strong>g> nucleotide hydrolysis) plus <str<strong>on</strong>g>th</str<strong>on</strong>g>e reneging rate (<str<strong>on</strong>g>of</str<strong>on</strong>g>f-rate at plus<br />

end <str<strong>on</strong>g>of</str<strong>on</strong>g> filament) exceeds <str<strong>on</strong>g>th</str<strong>on</strong>g>e arrival rate (<strong>on</strong>-rate at plus end <str<strong>on</strong>g>of</str<strong>on</strong>g> filament). Coupled<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>is queue is ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er single server queue <str<strong>on</strong>g>th</str<strong>on</strong>g>at describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire<br />

filament and whose arrival and reneging rate switch between two regimes depending<br />

<strong>on</strong> whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e ATP cap has disappeared (first server empty) or not. The model exhibits<br />

dynamic instability and treadmilling for proper choice <str<strong>on</strong>g>of</str<strong>on</strong>g> hydrolysis rate and<br />

<strong>on</strong>/<str<strong>on</strong>g>of</str<strong>on</strong>g>f-rates at polymer ends. Analytic expressi<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e life<br />

time and leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> polymers toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> M<strong>on</strong>te Carlo simulati<strong>on</strong>s are presented<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir fit to experimental data discussed.<br />

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Cancer; Wednesday, June 29, 11:00<br />

S. Becker, A. Mang, T.A. Schütz, A. Toma, T.M. Buzug<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Engineering, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Lübeck, Germany<br />

e-mail: {becker,buzug}@imt.uni-luebeck.de<br />

A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> brain tumor and normal tissue<br />

resp<strong>on</strong>ses to radiati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

The present work introduces a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>th</str<strong>on</strong>g>at simulates <str<strong>on</strong>g>th</str<strong>on</strong>g>e progressi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> malignant brain tumors as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy <strong>on</strong> cancerous and<br />

normal tissue. The spatio-temporal dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> a tumor cell density is described<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> a reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong>. In additi<strong>on</strong> to passive diffusi<strong>on</strong> and<br />

proliferati<strong>on</strong> [1–3] <str<strong>on</strong>g>th</str<strong>on</strong>g>is equati<strong>on</strong> incorporates <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> irradiati<strong>on</strong> [2,3]. To account<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e anisotropy <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor diffusi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in white matter, tensor informati<strong>on</strong><br />

deduced from a probabilistic white matter atlas is incorporated into <str<strong>on</strong>g>th</str<strong>on</strong>g>e model.<br />

The model also assumes logistic grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor cell populati<strong>on</strong> resulting in a<br />

lower net proliferati<strong>on</strong> in regi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> high cell density. The spatio-temporal effect <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

radiati<strong>on</strong> is described by <str<strong>on</strong>g>th</str<strong>on</strong>g>e linear-quadratic model.<br />

In current ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models used to predict tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological<br />

effect <str<strong>on</strong>g>of</str<strong>on</strong>g> different treatment schedules, <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> radiati<strong>on</strong><br />

resp<strong>on</strong>se in general is limited to cancerous cells. An optimizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment outcome,<br />

which includes a maximizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor c<strong>on</strong>trol while minimizing normal<br />

tissue toxicity, however necessitates not <strong>on</strong>ly a quantificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological effect<br />

<strong>on</strong> cancerous tissue but also <strong>on</strong> heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y tissue. The present model <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore extends<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e standard approaches [2,3] by also modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy <strong>on</strong><br />

normal tissue. A sec<strong>on</strong>d differential equati<strong>on</strong> describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal progressi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e necrotic density, incorporating <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> irradiati<strong>on</strong> <strong>on</strong> cancerous and<br />

normal tissue and a degradati<strong>on</strong> due to phagocytosis. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor radiosensitivity<br />

is varied according to <str<strong>on</strong>g>th</str<strong>on</strong>g>e local density <str<strong>on</strong>g>of</str<strong>on</strong>g> cancerous cells. This allows<br />

for indirectly c<strong>on</strong>sidering <str<strong>on</strong>g>th</str<strong>on</strong>g>e oxygenati<strong>on</strong> and its influence <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e radiosensitivity,<br />

as <str<strong>on</strong>g>th</str<strong>on</strong>g>e growing tumor increases <str<strong>on</strong>g>th</str<strong>on</strong>g>e lack <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen, which directly corresp<strong>on</strong>ds to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e extent <str<strong>on</strong>g>of</str<strong>on</strong>g> radioresistance.<br />

The numerical results show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e progressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> primary brain tumors can<br />

plausibly be determined. The model is also used to quantitatively study <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficacy<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> irradiati<strong>on</strong> under a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment schedules and dose distributi<strong>on</strong>s.<br />

The results illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed model in finding a trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f<br />

between tumor c<strong>on</strong>trol and normal tissue toxicity. Incorporati<strong>on</strong> into clinical planning<br />

systems could ultimately facilitate <str<strong>on</strong>g>th</str<strong>on</strong>g>e administrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> more appropriate,<br />

patient-specific treatment schedules and <str<strong>on</strong>g>of</str<strong>on</strong>g>fers <str<strong>on</strong>g>th</str<strong>on</strong>g>e promise <str<strong>on</strong>g>of</str<strong>on</strong>g> highly individualized<br />

radiati<strong>on</strong> treatment for cancer patients. Avenues for future research include fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

clinical evaluati<strong>on</strong>s, incorporati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell cycle dynamics and extensi<strong>on</strong> to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

types <str<strong>on</strong>g>of</str<strong>on</strong>g> external beam radiati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy.<br />

References.<br />

[1] S. Becker and A. Mang and A. Toma and T.M. Buzug, In-Silico Oncology: An Approximate<br />

Model <str<strong>on</strong>g>of</str<strong>on</strong>g> Brain Tumor Mass Effect based <strong>on</strong> Directly Manipulated Free Form Deformati<strong>on</strong>,<br />

2010 Int J CARS 5(5) 607–622.<br />

88

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[2] G. Powa<str<strong>on</strong>g>th</str<strong>on</strong>g>il and M. Kohandel and S. Sivalogana<str<strong>on</strong>g>th</str<strong>on</strong>g>an and A. Oza and M. Milosevic, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> brain tumor: Effects <str<strong>on</strong>g>of</str<strong>on</strong>g> radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy and chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, 2007 Phys Med<br />

Biol 52 3291–3306.<br />

[3] R. Rockne and E.C. Alvord jr and J.K. Rockhill and K.R. Swans<strong>on</strong>, A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model<br />

for brain tumor resp<strong>on</strong>se to radiati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, 2009 J Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Biol 58 561–578.<br />

89

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Systems Biology <str<strong>on</strong>g>of</str<strong>on</strong>g> Development; Saturday, July 2, 14:30<br />

Julio Belm<strong>on</strong>te<br />

e-mail: jmbelm<strong>on</strong>@indiana.edu<br />

Susan D. Hester<br />

J. Scott Gens<br />

Sherry Clenden<strong>on</strong><br />

James A. Glazier<br />

Biocomplexity Institute, Indiana University, USA<br />

Multi-cell, Multi-scale Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Vertebrate Somitogenesis<br />

Somitogenesis is an early developmental process <str<strong>on</strong>g>th</str<strong>on</strong>g>at establishes <str<strong>on</strong>g>th</str<strong>on</strong>g>e first signs <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

segmentati<strong>on</strong> in all vertebrates, patterning <str<strong>on</strong>g>th</str<strong>on</strong>g>e precursors <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vertebrae, ribs,<br />

and skeletal muscles <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e back and limbs. This process requires coordinati<strong>on</strong><br />

between biological mechanisms at several scales, ranging from genetic regulatory<br />

networks to structural changes at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue level. Understanding how <str<strong>on</strong>g>th</str<strong>on</strong>g>ese mechanisms<br />

interact across scales and how events are coordinated in space and time is<br />

necessary for a complete comprehensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> somitogenesis, including its evoluti<strong>on</strong>ary<br />

flexibility and how we can best apply observati<strong>on</strong>s at single scales and in different<br />

species to understand, prevent and <strong>on</strong>e day treat somitogenesis defects in humans.<br />

So far, mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> somitogenesis have been studied independently, leading to<br />

a scattered set <str<strong>on</strong>g>of</str<strong>on</strong>g> single-scale models. To test <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sistency, integrability and<br />

combined explanatory power <str<strong>on</strong>g>of</str<strong>on</strong>g> current prevailing hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses, we built a multi-cell<br />

composite clock-and-wavefr<strong>on</strong>t model <str<strong>on</strong>g>th</str<strong>on</strong>g>at includes submodels <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular<br />

segmentati<strong>on</strong> clock, intercellular coupling via Delta/Notch signaling, an FGF8 determinati<strong>on</strong><br />

fr<strong>on</strong>t, delayed differentiati<strong>on</strong>, clock-wavefr<strong>on</strong>t readout and differential<br />

cell-cell adhesi<strong>on</strong>-driven cell sorting. We identify inc<strong>on</strong>sistencies between existing<br />

submodels and gaps in <str<strong>on</strong>g>th</str<strong>on</strong>g>e current understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> somitogenesis mechanisms and<br />

propose novel submodels and extensi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> existing submodels where necessary.<br />

2D simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> our models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> reas<strong>on</strong>able initial c<strong>on</strong>diti<strong>on</strong>s robustly generate<br />

spatially and temporally regular somites, realistic dynamic morphologies and sp<strong>on</strong>taneous<br />

emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> traveling stripes <str<strong>on</strong>g>of</str<strong>on</strong>g> Lfng. Our model is flexible enough to<br />

generate interspecies-like variati<strong>on</strong> in somite size in resp<strong>on</strong>se to changes in PSM<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate and segmentati<strong>on</strong> clock period, and in <str<strong>on</strong>g>th</str<strong>on</strong>g>e number and wid<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Lfng<br />

stripes in resp<strong>on</strong>se to changes in PSM grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate, segmentati<strong>on</strong> clock period and<br />

Wnt3a levels. To our knowledge, our work presents <str<strong>on</strong>g>th</str<strong>on</strong>g>e first embryogenesis model<br />

to successfully combine such a broad range <str<strong>on</strong>g>of</str<strong>on</strong>g> scales and mechanisms, representing<br />

an important step in predictive developmental modeling. The model is modular in<br />

nature, which will allow technically straightforward model extensi<strong>on</strong>s and comparis<strong>on</strong>s<br />

between sets <str<strong>on</strong>g>of</str<strong>on</strong>g> hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esized mechanisms and interacti<strong>on</strong>s.<br />

90

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

III; Tuesday, June 28, 17:00<br />

S. Benzekry<br />

LATP , Université de Provence<br />

Laboratoire de Toxicocinétique et Pharmacocinétique.<br />

Marseille, France.<br />

e-mail: benzekry@phare.normalesup.org<br />

Optimal schedules for <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies in metastatic cancers.<br />

An actual important challenge in <strong>on</strong>cology is to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e best temporal administrati<strong>on</strong><br />

protocols for ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er a given drug or <str<strong>on</strong>g>th</str<strong>on</strong>g>e combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> various treatments,<br />

in order to reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer disease or at least stabilize it. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, we present<br />

a model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e density <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e metastatic populati<strong>on</strong> structured<br />

by size and "angiogenic capacity" (= vasculature) modified by <str<strong>on</strong>g>th</str<strong>on</strong>g>e acti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

an anti-angiogenic treatment which affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e vasculature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumors and a cytotoxic<br />

treatment attacking <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancerous cells. The model is a n<strong>on</strong>-aut<strong>on</strong>omous<br />

transport equati<strong>on</strong> in dimensi<strong>on</strong> 2 wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a n<strong>on</strong>local boundary c<strong>on</strong>diti<strong>on</strong><br />

⎧<br />

⎨ ∂tρ + div(Gρ) = 0 ]0, ∞[×Ω<br />

−G ·<br />

⎩<br />

−→ ν ρ(t, σ) = N(σ) <br />

β(x, θ)ρ(t, x, θ)dxdθ + f(t, σ) ]0, ∞[×∂Ω<br />

Ω<br />

ρ(0, ·) = ρ0 (1)<br />

.<br />

(·) Ω<br />

First, we will show <str<strong>on</strong>g>th</str<strong>on</strong>g>e well-posedness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem : existence and uniqueness <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

soluti<strong>on</strong>s. The existence is proved by c<strong>on</strong>vergence <str<strong>on</strong>g>of</str<strong>on</strong>g> a numerical scheme c<strong>on</strong>sisting<br />

in straightening <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristics and discretize <str<strong>on</strong>g>th</str<strong>on</strong>g>em. We also present <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical<br />

analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is scheme. We use <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>e model to investigate in silico <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

effect <str<strong>on</strong>g>of</str<strong>on</strong>g> various schedules <str<strong>on</strong>g>of</str<strong>on</strong>g> anticancerous drugs bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary tumor and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e metastases, for example in <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a cytotoxic drug<br />

(chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy) and an anti-angiogenic <strong>on</strong>e. These c<strong>on</strong>siderati<strong>on</strong>s lead us to define<br />

and investigate an optimal c<strong>on</strong>trol problem for determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e best schedule <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

drug integrating bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e metastases and primary tumor dynamics.<br />

References.<br />

[1] S. Benzekry, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> a two-dimensi<strong>on</strong>al populati<strong>on</strong> model <str<strong>on</strong>g>of</str<strong>on</strong>g> metastatic<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> including angiogenesis, to appear in J. Evoluti<strong>on</strong> Equati<strong>on</strong>s (2011).<br />

[2] S. Benzekry, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and numerical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> a model for anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy in<br />

metastatic cancers, submitted.<br />

[3] Iwata, K. and Kawasaki, K. and Shigesada N., A dynamical model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and size<br />

distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple metastatic tumors, J. Theor. Biol., 203 177–186, 2000.<br />

[4] Hahnfeldt, P. and Panigraphy, D. and Folkman, J. and Hlatky, L., Tumor development under<br />

angiogenic signaling : a dynamical <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, treatment, resp<strong>on</strong>se and postvascular<br />

dormancy, Cancer Research., 59, 4770–4775, 1999.<br />

[5] A. d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio, U. Ledzewicz, H. Maurer and H. Schättler, On optimal delivery <str<strong>on</strong>g>of</str<strong>on</strong>g> combinati<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy for tumors. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosc. 222 (2009) 13-26.<br />

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Populati<strong>on</strong> Dynamics; Tuesday, June 28, 17:00<br />

Juliana Militão Berbert<br />

Institute for Theoretical Physics - IFT/Unesp - São Paulo/SP/Brazil<br />

e-mail: berbertj@gmail.com<br />

Individual’s memory as a parameter to differentiate<br />

populati<strong>on</strong> distributi<strong>on</strong> patterns<br />

Recent studies including satellite analysis have shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at movement <str<strong>on</strong>g>of</str<strong>on</strong>g> M<strong>on</strong>golian<br />

gazelles can be classified as nomadic. One explanati<strong>on</strong> emerges from <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir habitat is a dynamic envir<strong>on</strong>ment. It was proposed recently <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence<br />

<strong>on</strong> spatial heterogeneity and temporal predictability <str<strong>on</strong>g>of</str<strong>on</strong>g> resources for migrati<strong>on</strong>, nomadism<br />

and residence movement. One can define residence as distributi<strong>on</strong>s in which<br />

an individual over its lifetime occupies a relatively small area compared to <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong><br />

range; migrati<strong>on</strong> as a regular, l<strong>on</strong>g-distance pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> movement, and is<br />

typically observed in systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> regular, seas<strong>on</strong>al fluctuati<strong>on</strong>s in envir<strong>on</strong>mental<br />

c<strong>on</strong>diti<strong>on</strong>s; and nomadism occurs when animals are nei<str<strong>on</strong>g>th</str<strong>on</strong>g>er resident nor migratory,<br />

and instead move across <str<strong>on</strong>g>th</str<strong>on</strong>g>e landscape in routes <str<strong>on</strong>g>th</str<strong>on</strong>g>at do not repeat across years.<br />

Here, we propose, at <str<strong>on</strong>g>th</str<strong>on</strong>g>e individual level, <str<strong>on</strong>g>th</str<strong>on</strong>g>at a dependence <strong>on</strong> memory is also<br />

an important parameter characterizing <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> distributi<strong>on</strong> pattern. The<br />

movement decisi<strong>on</strong>s are based <strong>on</strong> known areas due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e animal’s memory. Migratory<br />

animals may have a l<strong>on</strong>g memory, perhaps <str<strong>on</strong>g>th</str<strong>on</strong>g>ey know all way between different<br />

locati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir journey. In ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er way, nomadic animals remember some last<br />

visited areas, where <str<strong>on</strong>g>th</str<strong>on</strong>g>ey stayed for a while. Therefore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e comparis<strong>on</strong> between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e memories toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e landscape predictability can clarify <str<strong>on</strong>g>th</str<strong>on</strong>g>e individual<br />

behavior behind <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> distributi<strong>on</strong> pattern. Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach, we<br />

propose some tools for analyzing animals movement.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Tuesday, June 28, 17:00<br />

Luděk Berec<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Ecology, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Entomology, Biology<br />

Centre ASCR, Branišovská 31, 37005 České Budějovice, Czech<br />

Republic<br />

e-mail: berec@entu.cas.cz<br />

Daniel Maxin<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science, Valparaiso University,<br />

1900 Chapel Drive, Valparaiso, IN 46383, USA<br />

e-mail: daniel.maxin@valpo.edu<br />

Double impact <str<strong>on</strong>g>of</str<strong>on</strong>g> sterilizing pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens: added value <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

increased life expectancy <strong>on</strong> pest c<strong>on</strong>trol effectiveness<br />

Sterilizing pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens are comm<strong>on</strong>ly assumed not to affect l<strong>on</strong>gevity <str<strong>on</strong>g>of</str<strong>on</strong>g> infected<br />

individuals, and if <str<strong>on</strong>g>th</str<strong>on</strong>g>ey do <str<strong>on</strong>g>th</str<strong>on</strong>g>en negatively. Examples abound, however, <str<strong>on</strong>g>of</str<strong>on</strong>g> species<br />

in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e absence <str<strong>on</strong>g>of</str<strong>on</strong>g> reproducti<strong>on</strong> actually increases life expectancy. This happens<br />

because by decreasing <str<strong>on</strong>g>th</str<strong>on</strong>g>e energy outlay <strong>on</strong> reproducti<strong>on</strong> individuals wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

lowered reproducti<strong>on</strong> can live l<strong>on</strong>ger. Alternatively, fertile individuals are more<br />

susceptible to predators or parasitoids if <str<strong>on</strong>g>th</str<strong>on</strong>g>e latter can capitalize <strong>on</strong> mating signals<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e former. Here we develop and analyze an SI epidemiological model to explore<br />

whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er and to what extent does such a life expectancy prol<strong>on</strong>gati<strong>on</strong> due to sterilizing<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens affect host dynamics. In particular, we are interested in an added<br />

value <str<strong>on</strong>g>of</str<strong>on</strong>g> increased life expectancy <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility <str<strong>on</strong>g>of</str<strong>on</strong>g> successful pest c<strong>on</strong>trol, <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

is, <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> increased lifespan and hence increased potential <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e infected individuals<br />

to spread <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease <strong>on</strong> pest c<strong>on</strong>trol effectiveness. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter range in which we observe an effect <str<strong>on</strong>g>of</str<strong>on</strong>g> increased lifespan <str<strong>on</strong>g>of</str<strong>on</strong>g> infectives<br />

is not large, <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect itself can be significant. In particular, <str<strong>on</strong>g>th</str<strong>on</strong>g>e increase in pest<br />

c<strong>on</strong>trol effectiveness can be very dramatic when disease transmissi<strong>on</strong> efficiency is<br />

close to bir<str<strong>on</strong>g>th</str<strong>on</strong>g> rate, mortality rate <str<strong>on</strong>g>of</str<strong>on</strong>g> susceptibles is relatively high (i.e., <str<strong>on</strong>g>th</str<strong>on</strong>g>e species is<br />

relatively short-lived), and sterilizati<strong>on</strong> efficiency is relatively high. Our results <str<strong>on</strong>g>th</str<strong>on</strong>g>us<br />

characterize pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens <str<strong>on</strong>g>th</str<strong>on</strong>g>at are promising candidates for an effective pest c<strong>on</strong>trol<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>at might possibly be engineered if not occurring naturally.<br />

93

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Adriana Bernal Escobar<br />

Universidad de los Andes<br />

e-mail: ad-berna@uniandes.edu.co<br />

Juan Cordovez<br />

Universidad de los Andes<br />

Esteban Payan<br />

Pan<str<strong>on</strong>g>th</str<strong>on</strong>g>era Foundati<strong>on</strong><br />

Populati<strong>on</strong> Dynamics; Saturday, July 2, 14:30<br />

Spatial explicit dispersal modeling for <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>servati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

jaguars in Colombia<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>th</str<strong>on</strong>g>at go bey<strong>on</strong>d traditi<strong>on</strong>al c<strong>on</strong>servati<strong>on</strong> paradigms <str<strong>on</strong>g>th</str<strong>on</strong>g>at allow<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> corridors and potential areas for species dispersi<strong>on</strong> have<br />

proven to be an important and useful tool in <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposal <str<strong>on</strong>g>of</str<strong>on</strong>g> new c<strong>on</strong>servati<strong>on</strong> and<br />

management plans (Adriaensen et al., 2003; Beier et al., 2009; Ray et al., 2002; Rabinowitz<br />

& Zeller, 2009). Particularly in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>servati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> jaguars, Rabinowitz &<br />

Zeller (2009) gave a first push by analyzing <str<strong>on</strong>g>th</str<strong>on</strong>g>e species at a metapopulati<strong>on</strong> level<br />

and measuring c<strong>on</strong>nectivity as <str<strong>on</strong>g>th</str<strong>on</strong>g>ey produced a complex pa<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> interc<strong>on</strong>nected<br />

populati<strong>on</strong>s. This model was based <strong>on</strong> a least-cost me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology <str<strong>on</strong>g>th</str<strong>on</strong>g>at in spite <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

its virtuosity gave <strong>on</strong>ly a steady state analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>nectivity and distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e jaguars <str<strong>on</strong>g>th</str<strong>on</strong>g>at does not necessarily reflects <str<strong>on</strong>g>th</str<strong>on</strong>g>e current situati<strong>on</strong>. Their<br />

results identified Colombia as a key element for c<strong>on</strong>nectivity between nor<str<strong>on</strong>g>th</str<strong>on</strong>g> and<br />

sou<str<strong>on</strong>g>th</str<strong>on</strong>g> populati<strong>on</strong>s, but for some parts <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e country it did not accurately capture<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e most suitable areas for dispersi<strong>on</strong>. We previously proposed an spatially explicit<br />

dispersal model based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e least-cost matrix obtained from <str<strong>on</strong>g>th</str<strong>on</strong>g>e least-cost<br />

analysis, to provide temporal informati<strong>on</strong> about <str<strong>on</strong>g>th</str<strong>on</strong>g>e sustainability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e areas for<br />

jaguar dispersi<strong>on</strong>, and increase accuracy by scaling <str<strong>on</strong>g>th</str<strong>on</strong>g>e area <str<strong>on</strong>g>of</str<strong>on</strong>g> study to Colombia.<br />

The model proved to be a better tool for dynamical studies, however some<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong>s showed a deviati<strong>on</strong> from total populati<strong>on</strong> predicti<strong>on</strong> respect to<br />

field data. We speculated <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is discrepancy is mainly due to our way to compute<br />

diffusi<strong>on</strong> coefficients, carrying capacities and boundary c<strong>on</strong>diti<strong>on</strong>s. Here we<br />

present a modificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model <str<strong>on</strong>g>th</str<strong>on</strong>g>at includes a new me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology for estimating<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ose parameters <str<strong>on</strong>g>th</str<strong>on</strong>g>at includes <str<strong>on</strong>g>th</str<strong>on</strong>g>e noti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> jaguar c<strong>on</strong>servati<strong>on</strong> units (JCU), as<br />

defined by <str<strong>on</strong>g>th</str<strong>on</strong>g>e current c<strong>on</strong>servati<strong>on</strong> program. Here we present preliminary results<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>is modified model and compare it wi<str<strong>on</strong>g>th</str<strong>on</strong>g> previous simulati<strong>on</strong>s. We found<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at accurately defining <str<strong>on</strong>g>th</str<strong>on</strong>g>e carrying capacity and including boundary c<strong>on</strong>diti<strong>on</strong>s<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at mimic better <str<strong>on</strong>g>th</str<strong>on</strong>g>e ecology <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e specie gives an overall improvement in terms<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> our ability to predict current populati<strong>on</strong> densities and temporal aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

populati<strong>on</strong> dynamics.<br />

94

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Delay Differential Equati<strong>on</strong>s and Applicati<strong>on</strong>s II; Saturday, July 2, 08:30<br />

Samuel Bernard<br />

Université de Ly<strong>on</strong>; Université Ly<strong>on</strong> 1; INSA de Ly<strong>on</strong>, F-69621; Ecole<br />

Centrale de Ly<strong>on</strong>; CNRS, UMR5208, Institut Camille Jordan, 43 blvd<br />

du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France<br />

e-mail: bernard@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.univ-ly<strong>on</strong>1.fr<br />

Fabien Crauste<br />

Université de Ly<strong>on</strong>; Université Ly<strong>on</strong> 1; INSA de Ly<strong>on</strong>, F-69621; Ecole<br />

Centrale de Ly<strong>on</strong>; CNRS, UMR5208, Institut Camille Jordan, 43 blvd<br />

du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France<br />

e-mail: crauste@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.univ-ly<strong>on</strong>1.fr<br />

(1)<br />

Distributed delays stabilize negative feedback loops<br />

We study <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e linear differential equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> distributed delays<br />

˙x = −ax − b<br />

∞<br />

0<br />

x(t − τ)dη(τ)<br />

where <str<strong>on</strong>g>th</str<strong>on</strong>g>e coefficients a and b are c<strong>on</strong>stant, and η(τ) is <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> delays.<br />

In biological applicati<strong>on</strong>s, discrete delays in <str<strong>on</strong>g>th</str<strong>on</strong>g>e feedback loop are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten used to<br />

account for <str<strong>on</strong>g>th</str<strong>on</strong>g>e finite time required to perform essential steps before x(t) is affected.<br />

Linear stability properties <str<strong>on</strong>g>of</str<strong>on</strong>g> scalar delayed equati<strong>on</strong>s are fairly well characterized.<br />

However, lumping intermediate steps into a delayed term can produce broad and<br />

atypical delay distributi<strong>on</strong>s, and it is still not clear how <str<strong>on</strong>g>th</str<strong>on</strong>g>at affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability<br />

compared to a discrete delay [1].<br />

When η is a single discrete delay (a Dirac mass), <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymptotic stability <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e zero soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Eq. (1) is fully determined by a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoren originally due to Hayes<br />

[2].<br />

The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper is to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> delay distributi<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e trivial soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Eq. (1). It has been c<strong>on</strong>jectured <str<strong>on</strong>g>th</str<strong>on</strong>g>at am<strong>on</strong>g distributi<strong>on</strong>s<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a given mean E, <str<strong>on</strong>g>th</str<strong>on</strong>g>e discrete delay is <str<strong>on</strong>g>th</str<strong>on</strong>g>e least stable <strong>on</strong>e [3, 4]. This c<strong>on</strong>jecture<br />

has been proved for a = 0 using Lyapunov-Razumikhin functi<strong>on</strong>s [5], and<br />

for distributi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at are symmetric about <str<strong>on</strong>g>th</str<strong>on</strong>g>eir means [f(E − τ) = f(E + τ)]<br />

[6, 3, 4, 7]. Here, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>jecture is true.<br />

The general strategy for proving <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability <str<strong>on</strong>g>of</str<strong>on</strong>g> distributed delays is <str<strong>on</strong>g>th</str<strong>on</strong>g>e following.<br />

We use a geometric argument to bound <str<strong>on</strong>g>th</str<strong>on</strong>g>e roots <str<strong>on</strong>g>of</str<strong>on</strong>g> characteric equati<strong>on</strong><br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e roots <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristic equati<strong>on</strong> for a single discrete delay. More precisely,<br />

if <str<strong>on</strong>g>th</str<strong>on</strong>g>e leading roots associated to <str<strong>on</strong>g>th</str<strong>on</strong>g>e discrete delay are a pair <str<strong>on</strong>g>of</str<strong>on</strong>g> imaginary<br />

roots, <str<strong>on</strong>g>th</str<strong>on</strong>g>en all <str<strong>on</strong>g>th</str<strong>on</strong>g>e roots associated to <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> delays have negative real<br />

parts. We first state a criteri<strong>on</strong> for stability. We <str<strong>on</strong>g>th</str<strong>on</strong>g>en show <str<strong>on</strong>g>th</str<strong>on</strong>g>at a distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> n discrete delays is more stable <str<strong>on</strong>g>th</str<strong>on</strong>g>an a certain distributi<strong>on</strong> ∗ wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two delays.<br />

We c<strong>on</strong>struct <str<strong>on</strong>g>th</str<strong>on</strong>g>is most “unstable” distributi<strong>on</strong> and determine <str<strong>on</strong>g>th</str<strong>on</strong>g>at <strong>on</strong>ly <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

delays is positive, so <str<strong>on</strong>g>th</str<strong>on</strong>g>at its stability can be determined using Hayes Theorem.<br />

We <str<strong>on</strong>g>th</str<strong>on</strong>g>en generalize for any distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> delays, and obtaine <str<strong>on</strong>g>th</str<strong>on</strong>g>e most complete<br />

picture <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability <str<strong>on</strong>g>of</str<strong>on</strong>g> Eq. (1) when <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>ly informati<strong>on</strong> about <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> delays is <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean.<br />

95

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Theorem 1. The trivial soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Eq. (1) is asymptotically stable if a > −b and<br />

a ≥ |b|, or if b > |a| and <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean E <str<strong>on</strong>g>of</str<strong>on</strong>g> η satisfies<br />

E < arccos(−a/b)<br />

√ .<br />

b2 − a2 The zero soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Eq. (1) may be asymptotically stable (depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e particular<br />

distributi<strong>on</strong>) if b > |a| and<br />

E ≥ arccos(−a/b)<br />

√ .<br />

b2 − a2 The zero soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Eq. (1) is unstable if a ≤ −b.<br />

References.<br />

[1] S. Campbell, R. Jessop, Approximating <str<strong>on</strong>g>th</str<strong>on</strong>g>e Stability Regi<strong>on</strong> for a Differential Equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

a Distributed Delay, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Mod. Nat. Phenom. 4 (2) (2009) 1–27.<br />

[2] N. Hayes, Roots <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transcendental equati<strong>on</strong> associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a certain difference-differential<br />

equati<strong>on</strong>, J. L<strong>on</strong>d. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Soc. 25 (1950) 226–232.<br />

[3] S. Bernard, J. Bélair, M. C. Mackey, Sufficient c<strong>on</strong>diti<strong>on</strong>s for stability <str<strong>on</strong>g>of</str<strong>on</strong>g> linear differential<br />

equati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> distributed delay, Discrete C<strong>on</strong>tin. Dynam. Systems Ser. B 1 (2001) 233–256.<br />

[4] F. Atay, Delayed feedback c<strong>on</strong>trol near Hopf bifurcati<strong>on</strong>, Discrete C<strong>on</strong>tin. Dynam. Systems<br />

Ser. S 1 (2) (2008) 197–205.<br />

[5] T. Krisztin, Stability for functi<strong>on</strong>al differential equati<strong>on</strong>s and some variati<strong>on</strong>al problems, Tohoku<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. J 42 (3) (1990) 407–417.<br />

[6] R. Miyazaki, Characteristic equati<strong>on</strong> and asymptotic behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> delay-differential equati<strong>on</strong>,<br />

Funkcial. Ekvac. 40 (3) (1997) 481–482.<br />

[7] G. Kiss, B. Krauskopf, Stability implicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> delay distributi<strong>on</strong> for first-order and sec<strong>on</strong>dorder<br />

systems, Discrete C<strong>on</strong>tin. Dynam. Systems Ser. B 13 (2) (2010) 327–345.<br />

96

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling I; Tuesday, June 28, 17:00<br />

Roberto Bertolusso<br />

Rice University, Houst<strong>on</strong>, TX, USA<br />

e-mail: rbertolusso@rice.edu<br />

Allan Brasier<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Texas Medical Branch, Galvest<strong>on</strong>, TX, USA<br />

e-mail: arbrasie@utmb.edu<br />

Marek Kimmel<br />

Rice University, Houst<strong>on</strong>, TX, USA<br />

e-mail: kimmel@rice.edu<br />

Tomasz Lipniacki<br />

IPPT, Warszawa, PL<br />

e-mail: tlipnia@ippt.gov.pl<br />

IRF3 and NF-κB: Transcripti<strong>on</strong> factors acting in a<br />

coordinated way under double stranded RNA stimulati<strong>on</strong><br />

Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> innate immunity system under viral attack is still not understood<br />

in detail. However, new insights are emerging based bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <strong>on</strong> novel experiments and<br />

<strong>on</strong> system modeling approach. We report a model <str<strong>on</strong>g>of</str<strong>on</strong>g> coordinated resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> IRF3<br />

and NF-κB transcripti<strong>on</strong> factors pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways in A549 lung cancer cells, under double<br />

stranded RNA (dsRNA) stimulati<strong>on</strong>, itself a model for viral RNA. Viral infecti<strong>on</strong><br />

leads to multiplicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> viral RNA which is sensed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e innate immune system<br />

at a later stage. dsRNA, instead, rapidly activates <str<strong>on</strong>g>th</str<strong>on</strong>g>e IRF3 and NF-κB pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways,<br />

leading to resp<strong>on</strong>ses which are str<strong>on</strong>ger and better localized in time.<br />

dsRNA is sensed bo<str<strong>on</strong>g>th</str<strong>on</strong>g> by RIG-like family <str<strong>on</strong>g>of</str<strong>on</strong>g> helicases (RIG-I) and toll-like receptor<br />

3 (TLR3). Activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> RIG-I leads, via multistep pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way, to <str<strong>on</strong>g>th</str<strong>on</strong>g>e nuclear<br />

translocati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> IRF3. In turn activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> TLR3 leads to phosphorylati<strong>on</strong> and<br />

degradati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> primary NF-κB inhibitor IκBα, freeing NF-κB which also translocates<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e nucleus. IRF3 and NF-κB are independently and cooperatively resp<strong>on</strong>sible<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a number <str<strong>on</strong>g>of</str<strong>on</strong>g> genes involved in innate immune and<br />

inflammatory resp<strong>on</strong>ses, in particular bo<str<strong>on</strong>g>th</str<strong>on</strong>g> IRF3 and NF-κB are needed for <str<strong>on</strong>g>th</str<strong>on</strong>g>e activati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interfer<strong>on</strong> β. In addti<strong>on</strong> NF-κB also activates a number <str<strong>on</strong>g>of</str<strong>on</strong>g> inhibitors,<br />

am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>em IκBα and A20, inhibiting bo<str<strong>on</strong>g>th</str<strong>on</strong>g> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways or selectively <strong>on</strong>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way.<br />

Three kind <str<strong>on</strong>g>of</str<strong>on</strong>g> experiments were performed:<br />

• Time series (0, 0.5, 1, 2, 4 and 6 hours) <str<strong>on</strong>g>of</str<strong>on</strong>g> key mRNAs induced by NFkB<br />

and IRF3 transcripti<strong>on</strong> factors.<br />

• Time series <str<strong>on</strong>g>of</str<strong>on</strong>g> key phosphorylated proteins at same time points as above.<br />

• Knock-down experiments using small interfering RNA (siRNA) <strong>on</strong> NF-κB,<br />

IRF3, RIG-I, and IKKγ wi<str<strong>on</strong>g>th</str<strong>on</strong>g> and wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out dsRNA stimulati<strong>on</strong>.<br />

The emerging deterministic ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model c<strong>on</strong>siders 87 species and 147<br />

reacti<strong>on</strong>. It seems to be <str<strong>on</strong>g>th</str<strong>on</strong>g>e first aggregate model <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> NF-κB and IRF3,<br />

and shows agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental data. In additi<strong>on</strong> we carried out stochastic<br />

simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>etical single-cell experiments, which display bimodality <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

resp<strong>on</strong>ses not visible in cell-populati<strong>on</strong> experiments.<br />

97

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Alex Best<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sheffield<br />

e-mail: a.best@shef.ac.uk<br />

Steve Webb<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stra<str<strong>on</strong>g>th</str<strong>on</strong>g>clyde<br />

e-mail: steven.webb@stra<str<strong>on</strong>g>th</str<strong>on</strong>g>.ac.uk<br />

Andy White<br />

Heriot-Watt University<br />

e-mail: a.r.white@hw.ac.uk<br />

Mike Boots<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sheffield<br />

e-mail: m.boots@shef.ac.uk<br />

Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 08:30<br />

Host resistance and coevoluti<strong>on</strong> in spatially structured<br />

populati<strong>on</strong>s<br />

Most natural, agricultural and human populati<strong>on</strong>s are structured, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a proporti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> interacti<strong>on</strong>s occurring locally or wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in social groups ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an at<br />

random. This wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-populati<strong>on</strong> spatial and social structure is important to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> parasites (e.g. [1]) but little attenti<strong>on</strong> has been paid to how spatial<br />

structure affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> host resistance, and as a c<strong>on</strong>sequence <str<strong>on</strong>g>th</str<strong>on</strong>g>e coevoluti<strong>on</strong>ary<br />

outcome. We examined <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance across a range <str<strong>on</strong>g>of</str<strong>on</strong>g> mixing<br />

patterns using an approximate ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model (pair approximati<strong>on</strong>) and stochastic<br />

simulati<strong>on</strong>s. We found <str<strong>on</strong>g>th</str<strong>on</strong>g>at as reproducti<strong>on</strong> becomes increasingly local,<br />

hosts are always selected to increase resistance. More localised transmissi<strong>on</strong> also<br />

selects for higher resistance, but <strong>on</strong>ly if reproducti<strong>on</strong> is also predominantly local.<br />

If <str<strong>on</strong>g>th</str<strong>on</strong>g>e hosts disperse, lower resistance evolves as transmissi<strong>on</strong> becomes more local.<br />

These effects can be understood as a combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genetic (kin) and ecological<br />

structuring <strong>on</strong> individual fitness. When hosts and parasites coevolve, local interacti<strong>on</strong>s<br />

select for hosts wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high defence and parasites wi<str<strong>on</strong>g>th</str<strong>on</strong>g> low transmissibility<br />

and virulence. Crucially, <str<strong>on</strong>g>th</str<strong>on</strong>g>is means <str<strong>on</strong>g>th</str<strong>on</strong>g>at more populati<strong>on</strong> mixing may lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> fast-transmitting highly virulent parasites and reduced resistance<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e host [2].<br />

References.<br />

[1] Boots, M. and Sasaki, A., ’Small worlds’ and <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> virulence: infecti<strong>on</strong> occurs<br />

locally and at a distance Proc. Roy. Soc. B, 266: 1933-1938.<br />

[2] Best, A., Webb, S., White A. and Boots, M., Host resistance and coevoluti<strong>on</strong> in spatially structured<br />

populati<strong>on</strong>s Proc. Roy. Soc. B, In Press (published <strong>on</strong>line, doi:10.1098/rspb.2010.1978).<br />

98

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Anja Be<str<strong>on</strong>g>th</str<strong>on</strong>g>ge<br />

Competence Center Bioinformatics, Institute for Applied Computer<br />

Science, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Sciences Stralsund, Germany<br />

e-mail: anja.be<str<strong>on</strong>g>th</str<strong>on</strong>g>ge@fh-stralsund.de<br />

Are metastases from metastases clinically relevant? A novel<br />

computer model helps understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e metastatic<br />

progressi<strong>on</strong><br />

The process <str<strong>on</strong>g>of</str<strong>on</strong>g> metastasis formati<strong>on</strong> remains enigmatic. Different models exist<br />

for predicting <str<strong>on</strong>g>th</str<strong>on</strong>g>e metastatic spread <str<strong>on</strong>g>of</str<strong>on</strong>g> malignant tumors. However, it is difficult<br />

to evaluate <str<strong>on</strong>g>th</str<strong>on</strong>g>ese different models for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir clinical relevance. Therefore a novel<br />

computer model was developed which permits comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e different models<br />

quantitatively wi<str<strong>on</strong>g>th</str<strong>on</strong>g> clinical data and which additi<strong>on</strong>ally predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>e outcome <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

treatment interventi<strong>on</strong>s. The computer model is based <strong>on</strong> a discrete events simulati<strong>on</strong><br />

approach. The grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary tumor and <str<strong>on</strong>g>th</str<strong>on</strong>g>e metastases is described<br />

via analytical functi<strong>on</strong>s, while a rate functi<strong>on</strong> models <str<strong>on</strong>g>th</str<strong>on</strong>g>e intravasati<strong>on</strong> events <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e primary tumor and its metastases. Events describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e emitted<br />

malignant cells until <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> new metastases. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e help <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

computer model it was evaluated whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er metastases are able to metastasise and if<br />

late disseminated tumour cells are still capable to form metastases. The simulati<strong>on</strong><br />

results were compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g> clinical data from an untreated patient wi<str<strong>on</strong>g>th</str<strong>on</strong>g> hepatocellular<br />

carcinoma and multiple metastases in <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver. Additi<strong>on</strong>ally, <str<strong>on</strong>g>th</str<strong>on</strong>g>e resecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e primary tumour was simulated. The results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e computer simulati<strong>on</strong>s reveal<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> metastases varies significantly between scenarios where metastases<br />

metastasise and scenarios where <str<strong>on</strong>g>th</str<strong>on</strong>g>ey not. In c<strong>on</strong>trast, <str<strong>on</strong>g>th</str<strong>on</strong>g>e total tumour mass<br />

is nearly unaffected by <str<strong>on</strong>g>th</str<strong>on</strong>g>is mode <str<strong>on</strong>g>of</str<strong>on</strong>g> metastasis formati<strong>on</strong>. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e results<br />

provide evidence <str<strong>on</strong>g>th</str<strong>on</strong>g>at late disseminated tumour cells are still capable <str<strong>on</strong>g>of</str<strong>on</strong>g> forming<br />

metastases. The simulati<strong>on</strong> results show <str<strong>on</strong>g>th</str<strong>on</strong>g>at in <str<strong>on</strong>g>th</str<strong>on</strong>g>is particular case <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatocellular<br />

carcinoma, carcinoma metastases exhibit <str<strong>on</strong>g>th</str<strong>on</strong>g>e same grow<str<strong>on</strong>g>th</str<strong>on</strong>g> pattern as <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary<br />

tumour. Simulati<strong>on</strong>s also allow estimating how <str<strong>on</strong>g>th</str<strong>on</strong>g>e resecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary<br />

tumour delays or even prevents <str<strong>on</strong>g>th</str<strong>on</strong>g>e patients dea<str<strong>on</strong>g>th</str<strong>on</strong>g>. The simulati<strong>on</strong> results indicate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at for <str<strong>on</strong>g>th</str<strong>on</strong>g>is particular case <str<strong>on</strong>g>of</str<strong>on</strong>g> a hepatocellular carcinoma late metastases, i.e.<br />

metastases from metastases, are irrelevant in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> total tumour mass. Hence<br />

metastases seeded from metastases are clinically irrelevant in our model system.<br />

Only <str<strong>on</strong>g>th</str<strong>on</strong>g>e first metastases seeded from <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary tumour c<strong>on</strong>tribute significantly<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour burden and <str<strong>on</strong>g>th</str<strong>on</strong>g>us cause <str<strong>on</strong>g>th</str<strong>on</strong>g>e patients dea<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

99

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Neurosciences; Thursday, June 30, 11:30<br />

Andrzej Bielecki<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science, Jagiell<strong>on</strong>ian University, ul. Łojasiewicza<br />

6, 30-348 Kraków, Poland<br />

e-mail: bielecki@ii.uj.edu.pl<br />

Piotr Kalita<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science, Jagiell<strong>on</strong>ian University, ul. Łojasiewicza<br />

6, 30-348 Kraków, Poland<br />

e-mail: piotr.kalita@ii.uj.edu.pl<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and numerical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> presynaptic phase<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> fast transport<br />

Neurotransmitters in <str<strong>on</strong>g>th</str<strong>on</strong>g>e terminal bout<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a presynaptic neur<strong>on</strong> are stored in vesicles,<br />

which diffuse in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoplasm and, after a stimulati<strong>on</strong> signal is received, fuse<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane and release its c<strong>on</strong>tents into <str<strong>on</strong>g>th</str<strong>on</strong>g>e synaptic cleft. It is comm<strong>on</strong>ly<br />

assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at vesicles bel<strong>on</strong>g to <str<strong>on</strong>g>th</str<strong>on</strong>g>ree pools whose c<strong>on</strong>tent is gradually exploited<br />

during <str<strong>on</strong>g>th</str<strong>on</strong>g>e stimulati<strong>on</strong>.<br />

The physiological assumpti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed model are <str<strong>on</strong>g>th</str<strong>on</strong>g>e following:<br />

1. Terminal bout<strong>on</strong> occupies a fixed domain, a fixed part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e domain<br />

boundary are <str<strong>on</strong>g>th</str<strong>on</strong>g>e vesicle release sites.<br />

2. The unknown <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> vesicles in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoplasm.<br />

The unit in which <str<strong>on</strong>g>th</str<strong>on</strong>g>is value is expressed can ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er be <str<strong>on</strong>g>th</str<strong>on</strong>g>e mass<br />

or <str<strong>on</strong>g>th</str<strong>on</strong>g>e quantity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vesicles or <str<strong>on</strong>g>th</str<strong>on</strong>g>e fracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cytoplasm volume <str<strong>on</strong>g>th</str<strong>on</strong>g>ey<br />

occupy.<br />

3. Vesicles diffuse inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e terminal bout<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esized in<br />

some subdomain <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bout<strong>on</strong>.<br />

4. The efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vesicle syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis is proporti<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e difference<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e equilibrium c<strong>on</strong>centrati<strong>on</strong> (above which <str<strong>on</strong>g>th</str<strong>on</strong>g>e syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis does<br />

not take place) and current c<strong>on</strong>centrati<strong>on</strong>.<br />

5. Vesicles do not leave <str<strong>on</strong>g>th</str<strong>on</strong>g>e domain unless <str<strong>on</strong>g>th</str<strong>on</strong>g>e acti<strong>on</strong> potential arrives. The<br />

arrival <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e acti<strong>on</strong> potential triggers <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vesicles release<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough some fixed period <str<strong>on</strong>g>of</str<strong>on</strong>g> time. The number <str<strong>on</strong>g>of</str<strong>on</strong>g> vesicles <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be<br />

released in a unit time <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e unit area is proporti<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e vesicle<br />

c<strong>on</strong>centrati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e vicinity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e release site.<br />

6. Nei<str<strong>on</strong>g>th</str<strong>on</strong>g>er re-uptake nor recycling <str<strong>on</strong>g>of</str<strong>on</strong>g> released vesicles is c<strong>on</strong>sidered.<br />

7. The availability <str<strong>on</strong>g>of</str<strong>on</strong>g> vesicles for release depends <strong>on</strong>ly <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir locati<strong>on</strong>. The<br />

docking sites are modeled implicitly as <str<strong>on</strong>g>th</str<strong>on</strong>g>e areas in <str<strong>on</strong>g>th</str<strong>on</strong>g>e vicinity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

release sites specified <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bout<strong>on</strong> boundary.<br />

The following variables and parameters which express various physiological quantities<br />

are introduced:<br />

100<br />

(i) Ω ⊂ R N , N ∈ {2, 3} - <str<strong>on</strong>g>th</str<strong>on</strong>g>e domain <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e terminal bout<strong>on</strong>,<br />

(ii) Ω1 ⊂ Ω - <str<strong>on</strong>g>th</str<strong>on</strong>g>e domain <str<strong>on</strong>g>of</str<strong>on</strong>g> neurotransmitter producti<strong>on</strong>,<br />

(iii) ∂Ωd ⊂ ∂Ω - neurotransmitter release sites <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell membrane,<br />

(iv) f : Ω → R - neurotransmitter source density defined, for example, by<br />

f(x) = 0 outside Ω1 and f(x) = fz <strong>on</strong> Ω1,<br />

(v) ¯ρ - <str<strong>on</strong>g>th</str<strong>on</strong>g>e balance c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> neurotransmitter in <str<strong>on</strong>g>th</str<strong>on</strong>g>e bout<strong>on</strong>,

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

(vi) α - <str<strong>on</strong>g>th</str<strong>on</strong>g>e coefficient denoting <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> neurotransmitter exocytosis, α is <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> vesicles (or molecules) which are released <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e unit area<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane in unit time by <str<strong>on</strong>g>th</str<strong>on</strong>g>e unit difference <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong><br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell and outside <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell (1 acti<strong>on</strong> potential activates 300 vesicles<br />

and 1 vesicle c<strong>on</strong>tains 103 − 104 molecules <str<strong>on</strong>g>of</str<strong>on</strong>g> neurotransmitter),<br />

(vii) aij : Ω → R - <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> tensor for <str<strong>on</strong>g>th</str<strong>on</strong>g>e vesicles wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a neurotransmitter,<br />

(viii) τ - <str<strong>on</strong>g>th</str<strong>on</strong>g>e time period <str<strong>on</strong>g>th</str<strong>on</strong>g>rough which <str<strong>on</strong>g>th</str<strong>on</strong>g>e neurotransmitter is released from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e docked vesicles to <str<strong>on</strong>g>th</str<strong>on</strong>g>e cleft (0.2 - 0.5 ms),<br />

(ix) t0 - <str<strong>on</strong>g>th</str<strong>on</strong>g>e arrival moment <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential (it is possible <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are many<br />

such moments during <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong>).<br />

The unknown in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong> ρ : Ω × [0, T ] → R denoting <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vesicles wi<str<strong>on</strong>g>th</str<strong>on</strong>g> neurotransmitter.<br />

The functi<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong><br />

∂ρ(x, t)<br />

(1)<br />

∂t<br />

=<br />

N<br />

<br />

<br />

∂ ∂ρ(x, t)<br />

aij(x) + f(x)(¯ρ − ρ(x, t))<br />

∂xi ∂xj<br />

+ .<br />

i,j=1<br />

The equati<strong>on</strong> is accompanied by boundary and initial c<strong>on</strong>diti<strong>on</strong>s implied directly<br />

by physiology <str<strong>on</strong>g>of</str<strong>on</strong>g> vesicle release as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>eir initial distributi<strong>on</strong> (see [1,2]):<br />

N ∂ρ(x, t)<br />

(2)<br />

aij ni = 0 for (x, t) ∈ (∂Ω − ∂Ωd) × [0, T ],<br />

∂xj<br />

(3)<br />

(4)<br />

N<br />

i,j=1<br />

i,j=1<br />

N<br />

i,j=1<br />

aij<br />

∂ρ(x, t)<br />

ni = 0 for (x, t) ∈ ∂Ωd × ([0, t0) ∪ (t0 + τ, T ]),<br />

∂xj<br />

aij<br />

∂ρ(x, t)<br />

ni = αρ(x, t) for (x, t) ∈ ∂Ωd × [t0, t0 + τ],<br />

∂xj<br />

(5) ρ(x, 0) = ρ0(x) <strong>on</strong> Ω,<br />

where (ni) N i=1 is <str<strong>on</strong>g>th</str<strong>on</strong>g>e unit normal vector directed outside Ω.<br />

The model is analyzed and simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vesicular kinetics using Finite Element<br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g>od are d<strong>on</strong>e.<br />

References.<br />

[1] A. Bielecki, P. Kalita, Model <str<strong>on</strong>g>of</str<strong>on</strong>g> neurotransmitter fast transport in ax<strong>on</strong> terminal <str<strong>on</strong>g>of</str<strong>on</strong>g> presynaptic<br />

neur<strong>on</strong>, J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. 26 (2008) 559–576.<br />

[2] A. Bielecki, P. Kalita, M. Lewandowski, B. Siwek, Numerical simulati<strong>on</strong> for a neurotransmitter<br />

transport model in <str<strong>on</strong>g>th</str<strong>on</strong>g>e ax<strong>on</strong> terminal <str<strong>on</strong>g>of</str<strong>on</strong>g> a presynaptic neur<strong>on</strong>, Biol. Cybern. 102 (2010) 489–<br />

502.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Sebastian Binder<br />

Systems Immunology, Helmholtz Centre for Infecti<strong>on</strong> Research<br />

e-mail: sebastian.binder@helmholtz-hzi.de<br />

Arndt Telschow<br />

Westfälische Wilhelms-Universität Münster<br />

Michael Meyer-Hermann<br />

Systems Immunology, Helmholtz Centre for Infecti<strong>on</strong> Research<br />

Intra-host disseminati<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Borrelia sp. during<br />

Lyme disease<br />

Chr<strong>on</strong>ic inflammatory diseases, caused by bacteria, viruses and eukaryotic parasites<br />

pose a <str<strong>on</strong>g>th</str<strong>on</strong>g>reat to public heal<str<strong>on</strong>g>th</str<strong>on</strong>g>. A str<strong>on</strong>g inflammatory reacti<strong>on</strong> causing tissue<br />

damage <str<strong>on</strong>g>of</str<strong>on</strong>g>ten plays an important role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenesis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese infecti<strong>on</strong>s. Lyme<br />

disease, caused by an infecti<strong>on</strong> by spirochetes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Borrelia burgdorferi sensu lato<br />

group (B. afzelii, B. garinii, B. burgdorferi s.s.), is a comm<strong>on</strong> tick-borne disease<br />

in Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> America, Europe and parts <str<strong>on</strong>g>of</str<strong>on</strong>g> Asia. The early infecti<strong>on</strong> stage c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

mild and mainly localized symptoms. In later stages, <str<strong>on</strong>g>th</str<strong>on</strong>g>e spirochetes can migrate<br />

to different tissues, including <str<strong>on</strong>g>th</str<strong>on</strong>g>e central nervous system, heart and joints, where it<br />

causes str<strong>on</strong>g inflammatory reacti<strong>on</strong>s and tissue damage, leading to severe clinical<br />

symptoms. The infecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese tissues can also become chr<strong>on</strong>ic.<br />

This project aims at modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e disseminati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bacteria from <str<strong>on</strong>g>th</str<strong>on</strong>g>e infected<br />

skin site to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er tissues inside a mouse. The model is based <strong>on</strong> experimental<br />

data <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bacterial c<strong>on</strong>centrati<strong>on</strong>s in different tissues from qPCR studies <str<strong>on</strong>g>of</str<strong>on</strong>g> artificially<br />

infected mice <str<strong>on</strong>g>of</str<strong>on</strong>g> a strain displaying clinical disease symptoms similar to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ose in humans and also develops a systemic infecti<strong>on</strong>. The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

disseminati<strong>on</strong> are described by a simple deterministic model <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> bacterial<br />

populati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>ree different compartments, including <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

macrophages and spirochetes as an important comp<strong>on</strong>ent <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e innate immune<br />

resp<strong>on</strong>se and inflammatory reacti<strong>on</strong> caused by B. burgdorferi. Central questi<strong>on</strong>s<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at may be answered by <str<strong>on</strong>g>th</str<strong>on</strong>g>is model include <str<strong>on</strong>g>th</str<strong>on</strong>g>e infectious bacterial c<strong>on</strong>centrati<strong>on</strong><br />

and elucidati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transiti<strong>on</strong> from <str<strong>on</strong>g>th</str<strong>on</strong>g>e acute to <str<strong>on</strong>g>th</str<strong>on</strong>g>e chr<strong>on</strong>ic infecti<strong>on</strong>.<br />

102

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Genetics and Genomics; Wednesday, June 29, 08:30<br />

Paweł Błażej<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Genomics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Biotechnology, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Wrocław, ul. Przybyszewskiego 63/77, 51-148 Wrocław, Poland<br />

e-mail: blazej.pawel@gmail.com<br />

Paweł Mackiewicz<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Genomics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Biotechnology, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Wrocław, ul. Przybyszewskiego 63/77, 51-148 Wrocław, Poland<br />

Stanisław Cebrat<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Genomics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Biotechnology, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Wrocław, ul. Przybyszewskiego 63/77, 51-148 Wrocław, Poland<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> prokaryotic genome evoluti<strong>on</strong> using coding<br />

signal as selecti<strong>on</strong> pressure<br />

Protein coding genes in prokaryotic chromosomes are subjected to two different<br />

asymmetric mutati<strong>on</strong>al pressures associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> various replicati<strong>on</strong> mechanisms<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> DNA strands (leading and lagging). To simulate evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> prokaryotic protein<br />

coding sequences under <str<strong>on</strong>g>th</str<strong>on</strong>g>is asymmetric mutati<strong>on</strong>al pressure, we elaborated<br />

a simulati<strong>on</strong> model based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Borrelia burgdorferi genome. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutati<strong>on</strong>al<br />

pressure we applied nucleotide substituti<strong>on</strong> matrices empirically found for <str<strong>on</strong>g>th</str<strong>on</strong>g>e leading<br />

and lagging DNA strands <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e genome. The selecti<strong>on</strong> pressure was based <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e modified algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m for protein coding gene finding, trained <strong>on</strong> annotated B.<br />

burgdorferi protein coding genes. We simulated <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genes from differently<br />

replicating strand under <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>stant, opposite and changing mutati<strong>on</strong>al<br />

c<strong>on</strong>diti<strong>on</strong>s, mimicking sequence inversi<strong>on</strong>s.<br />

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The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting cell systems: from intercellular interacti<strong>on</strong><br />

to tissue-level traits I; Wednesday, June 29, 14:30<br />

Jenny Bloomfield<br />

Heriot Watt University<br />

e-mail: jmb7@hw.ac.uk<br />

The effect <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>local cellular interacti<strong>on</strong>s <strong>on</strong> pattern<br />

formati<strong>on</strong><br />

Cells interact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir local envir<strong>on</strong>ment, and <str<strong>on</strong>g>th</str<strong>on</strong>g>ese interacti<strong>on</strong>s affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>e proliferati<strong>on</strong>,<br />

differentiati<strong>on</strong> and movement <str<strong>on</strong>g>of</str<strong>on</strong>g> cells. While modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>ese interacti<strong>on</strong>s<br />

is obviously important, doing so in a c<strong>on</strong>tinuous model has proved difficult.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I will present a c<strong>on</strong>tinuous partial differential equati<strong>on</strong> model <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a two populati<strong>on</strong> system, using integral terms to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> local envir<strong>on</strong>ment<br />

<strong>on</strong> interacting cells. I will use <str<strong>on</strong>g>th</str<strong>on</strong>g>is model to explore particular cellular<br />

interacti<strong>on</strong>s, and present <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial patterning <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be obtained from such a<br />

system.<br />

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Semigroups <str<strong>on</strong>g>of</str<strong>on</strong>g> Operators in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology II; Saturday, July 2, 11:00<br />

Adam Bobrowski<br />

Lublin University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: a.bobrowski@pollub.pl<br />

From a PDE model to an ODE model <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

synaptic depressi<strong>on</strong><br />

We provide a link between two recent models <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> synaptic depressi<strong>on</strong>.<br />

To <str<strong>on</strong>g>th</str<strong>on</strong>g>is end, we correct <str<strong>on</strong>g>th</str<strong>on</strong>g>e err<strong>on</strong>eous boundary c<strong>on</strong>diti<strong>on</strong> and specify <str<strong>on</strong>g>th</str<strong>on</strong>g>e missing<br />

transmissi<strong>on</strong> c<strong>on</strong>diti<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e PDE model <str<strong>on</strong>g>of</str<strong>on</strong>g> Bielecki and Kalita, and show <str<strong>on</strong>g>th</str<strong>on</strong>g>at as<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> coefficients tend to infinity and <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative permeability coefficients<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e membranes involved tend to zero, <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong>s to <str<strong>on</strong>g>th</str<strong>on</strong>g>e PDE model tend to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ose <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e original ODE model <str<strong>on</strong>g>of</str<strong>on</strong>g> Aristizabal and Glavinovič. Hence, from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical point <str<strong>on</strong>g>of</str<strong>on</strong>g> view <str<strong>on</strong>g>th</str<strong>on</strong>g>e ODE model is obtained as a singular perturbati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e PDE model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> singularities bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e operator and in <str<strong>on</strong>g>th</str<strong>on</strong>g>e boundary and<br />

transmissi<strong>on</strong> c<strong>on</strong>diti<strong>on</strong>s. The result is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore c<strong>on</strong>veniently put in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

degenerate c<strong>on</strong>vergence <str<strong>on</strong>g>of</str<strong>on</strong>g> semigroups <str<strong>on</strong>g>of</str<strong>on</strong>g> operators, where a sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> str<strong>on</strong>gly<br />

c<strong>on</strong>tinuous semigroups approaches a semigroup <str<strong>on</strong>g>th</str<strong>on</strong>g>at is str<strong>on</strong>gly c<strong>on</strong>tinuous <strong>on</strong>ly <strong>on</strong><br />

a subspace <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e original Banach space. Biologically, our approach allows a new,<br />

natural interpretati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ODE model’s parameters.<br />

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Martin Bock and Wolfgang Alt<br />

Universität B<strong>on</strong>n, IZMB<br />

Theoretische Biologie<br />

Kirschallee 1–3<br />

53115 B<strong>on</strong>n, Germany<br />

e-mail: mab@uni-b<strong>on</strong>n.de<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

On shape and force – from single to interactive cell moti<strong>on</strong><br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fundamental organizati<strong>on</strong> forms <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue in multi-cellular organisms<br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>e epi- or endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elium, in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells assemble into a single-layered structure<br />

supported by a str<strong>on</strong>g basal membrane. If an injury damages <str<strong>on</strong>g>th</str<strong>on</strong>g>is barrier,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cells perform a so-called epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial-mesenchymal transiti<strong>on</strong>: <str<strong>on</strong>g>th</str<strong>on</strong>g>ey break <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

mutual c<strong>on</strong>necti<strong>on</strong>s and start to migrate. Here we study <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanics <str<strong>on</strong>g>of</str<strong>on</strong>g> cell moti<strong>on</strong><br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese effectively two-dimensi<strong>on</strong>al envir<strong>on</strong>ments, where bo<str<strong>on</strong>g>th</str<strong>on</strong>g> cooperati<strong>on</strong> and<br />

individualism c<strong>on</strong>tribute to <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological functi<strong>on</strong>.<br />

The motility mechanics <str<strong>on</strong>g>of</str<strong>on</strong>g> individual cells can be understood in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> twophase<br />

flow models [1]. Extending our earlier 1D work [2], we project <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying<br />

hyperbolic-elliptic PDE system <str<strong>on</strong>g>of</str<strong>on</strong>g> Stokes type <strong>on</strong>to <str<strong>on</strong>g>th</str<strong>on</strong>g>e unit circle. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e lamella<br />

tip we incorporate enhanced actin polymerizati<strong>on</strong> by prescribing suitable pressure<br />

BCs. This enables us to obtain bo<str<strong>on</strong>g>th</str<strong>on</strong>g> shape dynamics and <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong> trajectory<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a quasi 2D model cell simultaneously. The corresp<strong>on</strong>ding simulati<strong>on</strong>s exhibit a<br />

correlati<strong>on</strong> between migrati<strong>on</strong> speed and cell shape, as observed in experiments.<br />

For cooperative motility, we argue <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells’ moti<strong>on</strong> is governed by essentially<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e same microscopic stochastic process: cadherin cell-cell adhesi<strong>on</strong> molecules<br />

merely add an attractive interacti<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is way, cytoskeletal c<strong>on</strong>tracti<strong>on</strong> stresses<br />

propagate across adjacent cells and determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e shape <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e border in between.<br />

The geometry <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is stress-induced competiti<strong>on</strong> for space can be formalized by<br />

means <str<strong>on</strong>g>of</str<strong>on</strong>g> Vor<strong>on</strong>oi tessellati<strong>on</strong>s. In order overcome <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>venti<strong>on</strong>al polyg<strong>on</strong>al cell<br />

approximati<strong>on</strong>, we propose a c<strong>on</strong>sistent generalizati<strong>on</strong> to partiti<strong>on</strong> space into individual<br />

cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> piecewise spherical or elliptic border [3]. Combined wi<str<strong>on</strong>g>th</str<strong>on</strong>g> aforementi<strong>on</strong>ed<br />

stochastic motility processes, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model tissue displays characteristic<br />

morphogenetic rearrangement patterns.<br />

References.<br />

[1] W. Alt and M. Dembo, Cytoplasm dynamics and cell moti<strong>on</strong>: two-phase flow models, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

Biosciences 156 207 (1999).<br />

[2] W. Alt, M. Bock, and C. Möhl, Coupling <str<strong>on</strong>g>of</str<strong>on</strong>g> cytoplasm and adhesi<strong>on</strong> dynamics determines<br />

cell polarizati<strong>on</strong> and locomoti<strong>on</strong>. In A. Chauviere, L. Preziosi and C. Verdier, editors, Cell<br />

mechanics: From Single Scale-Based Models to Multiscale Modeling, pages 86–125. Chapman<br />

& Hall / CRC, 2010. Preprint http://arxiv.org/abs/0907.5078<br />

[3] M. Bock, A.K. Tyagi, J.-U. Kreft, and W. Alt, Generalized Vor<strong>on</strong>oi tessellati<strong>on</strong> as a model<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> two-dimensi<strong>on</strong>al cell tissue dynamics, Bulletin <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology 72 1696 (2010).<br />

Preprint http://arxiv.org/abs/0901.4469<br />

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Crowd Dynamics: Modeling, Analysis and Simulati<strong>on</strong> (Part 2); Wednesday,<br />

June 29, 14:30<br />

Nikolai Bode<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> York<br />

e-mail: nwfb500@york.ac.uk<br />

Social networks and models for collective moti<strong>on</strong><br />

The <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> collective moti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> social networks have, each individually,<br />

received much attenti<strong>on</strong>. Currently, most models <str<strong>on</strong>g>of</str<strong>on</strong>g> collective moti<strong>on</strong> do<br />

not c<strong>on</strong>sider social network structure. The implicati<strong>on</strong>s for c<strong>on</strong>sidering collective<br />

moti<strong>on</strong> and social networks toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er are likely to be important. Social networks<br />

could determine how populati<strong>on</strong>s move in, split up into and form separate groups<br />

(social networks affecting collective moti<strong>on</strong>). C<strong>on</strong>versely, collective movement could<br />

change <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure <str<strong>on</strong>g>of</str<strong>on</strong>g> social networks by creating social ties <str<strong>on</strong>g>th</str<strong>on</strong>g>at did not exist previously<br />

and maintaining existing ties (collective moti<strong>on</strong> affecting social networks).<br />

Thus, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a need to combine <str<strong>on</strong>g>th</str<strong>on</strong>g>e two areas <str<strong>on</strong>g>of</str<strong>on</strong>g> research and examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship<br />

between network structure and collective moti<strong>on</strong>. I will briefly review<br />

different modelling approaches <str<strong>on</strong>g>th</str<strong>on</strong>g>at combine social network structures and collective<br />

moti<strong>on</strong> (e.g. in pedestrian crowds or evacuati<strong>on</strong> wcenarios) and present examples<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> my own work suggesting how social networks could impact <strong>on</strong> positi<strong>on</strong>ing and<br />

leader-follower relati<strong>on</strong>ships wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in groups and navigati<strong>on</strong> at <str<strong>on</strong>g>th</str<strong>on</strong>g>e group level.<br />

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Regulatory Networks; Friday, July 1, 14:30<br />

C. Bodenstein1 , B. Knoke1 , S. Schuster1 1 Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioinformatics, Friedrich Schiller University Jena, Ernst-<br />

Abbe-Platz 2, D-07743 Jena, Germany<br />

2Current address: Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemical Engineering, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Stuttgart, Germany<br />

e-mail: {christian.bodenstein,stefan.schu}@uni-jena.de<br />

M. Marhl3 , M. Perc3 3 Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Natural Sciences and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia<br />

Protein activati<strong>on</strong> by calcium oscillati<strong>on</strong>s and Jensen’s<br />

Inequality<br />

Oscillating c<strong>on</strong>centrati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular Ca 2+ -i<strong>on</strong>s are <str<strong>on</strong>g>of</str<strong>on</strong>g> great importance for <str<strong>on</strong>g>th</str<strong>on</strong>g>e signalling<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. It is widely believed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e informati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> extracellular stimuli<br />

is encoded into an oscillating Ca 2+ pattern, which subsequently is decoded by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ca 2+ -sensitive proteins. Besides <str<strong>on</strong>g>th</str<strong>on</strong>g>is advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> an oscillating Ca 2+<br />

signal, we here show <str<strong>on</strong>g>th</str<strong>on</strong>g>at oscillati<strong>on</strong>s additi<strong>on</strong>ally lead to a better activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e target proteins compared to a c<strong>on</strong>stant signal. In two asymptotic cases we can<br />

analytically prove <str<strong>on</strong>g>th</str<strong>on</strong>g>is for arbitrary oscillati<strong>on</strong> shapes and a very general decoding<br />

model, which comprises most previous models <str<strong>on</strong>g>of</str<strong>on</strong>g> Ca 2+ -sensitive proteins. For <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

we use Jensen’s inequality <str<strong>on</strong>g>th</str<strong>on</strong>g>at relates <str<strong>on</strong>g>th</str<strong>on</strong>g>e value <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>vex functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an average<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e average <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>vex functi<strong>on</strong>. Moreover, numerical simulati<strong>on</strong>s indicate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at oscillati<strong>on</strong>s lead to a better activati<strong>on</strong> not <strong>on</strong>ly in <str<strong>on</strong>g>th</str<strong>on</strong>g>e two asymptotic cases.<br />

The results underline <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cooperativity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e binding <str<strong>on</strong>g>of</str<strong>on</strong>g> Ca 2+<br />

and <str<strong>on</strong>g>of</str<strong>on</strong>g> zero-order ultrasensitivity, which are two properties <str<strong>on</strong>g>th</str<strong>on</strong>g>at are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten observed<br />

in experiments <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ca 2+ -sensitive target proteins. We compare<br />

our <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical predicti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> data from experimental studies investigating <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> NFAT and Ras by oscillatory and c<strong>on</strong>stant signals.<br />

References.<br />

[1] Dolmetsch et al., Calcium oscillati<strong>on</strong>s increase <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficiency and specificity <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong><br />

Nature 392 933–936, 1998.<br />

[2] Kupzig et al., The frequencies <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium oscillati<strong>on</strong>s are optimized for efficient calciummediated<br />

activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ras and <str<strong>on</strong>g>th</str<strong>on</strong>g>e ERK/MAPK cascade Proc Natl Acad Sci USA 102 7577–<br />

7582, 2005.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Crowd Dynamics: Modeling, Analysis and Simulati<strong>on</strong> (Part 2); Wednesday,<br />

June 29, 14:30<br />

M. Bodnar<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics,<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics and Mechanics,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland<br />

e-mail: mbodnar@mimuw.edu.pl<br />

J.J.L. Velazquez<br />

ICMAT CSIC,<br />

C. Nicolás Cabrera, 13-15, Campus Cantoblanco UAM,<br />

28049 Madrid, Spain<br />

e-mail: velazque@mat.ucm.es<br />

Derivati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> macroscopic equati<strong>on</strong>s<br />

for individual cell-based models.<br />

Typically, in individual cell-based models cells interact by means <str<strong>on</strong>g>of</str<strong>on</strong>g> some pair potential<br />

and are assumed to evolve according to some stochastic or deterministic<br />

dynamics. Because <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models try to describe interacti<strong>on</strong> between individuals<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ey are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten called microscopic models. They can describe quite complicated<br />

phenomena. The rule which governs <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells dynamics can be usually easily implemented<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical simulati<strong>on</strong> might give some soluti<strong>on</strong>s, in particular<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular automata models. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, if we try to give a<br />

precise ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical descripti<strong>on</strong> it is usually complicated and <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> such models is very difficult if possible. Often it is also very difficult to<br />

identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e most relevant parameters or group <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters and its influence <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics.<br />

Our talk will be focused <strong>on</strong> a very particular type <str<strong>on</strong>g>of</str<strong>on</strong>g> models <str<strong>on</strong>g>th</str<strong>on</strong>g>at are analogous<br />

to many <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model studied in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature. We will assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e centres <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cells evolve according to ordinary differential equati<strong>on</strong><br />

d<br />

dt XN(k, t) = −<br />

N<br />

∇VN(XN (k, t) − XN (i, t)) ,<br />

i=1<br />

i=k<br />

where N is a number <str<strong>on</strong>g>of</str<strong>on</strong>g> cells and functi<strong>on</strong>s XN (k, t) describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e positi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e k<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

cell. We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at dominant effect in <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics is cell fricti<strong>on</strong> and for <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

reas<strong>on</strong> <strong>on</strong>ly <strong>on</strong>e derivative appears <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e left-hand side. We will derive a equati<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at can describe a macroscopic behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> ”l<strong>on</strong>g-range”<br />

potentials, <str<strong>on</strong>g>th</str<strong>on</strong>g>is is when <strong>on</strong>e cell/particle interacts wi<str<strong>on</strong>g>th</str<strong>on</strong>g> many o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell/particle density is described by a type <str<strong>on</strong>g>of</str<strong>on</strong>g> porous-medium equati<strong>on</strong>. On<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, if interacti<strong>on</strong> are ”short”, <str<strong>on</strong>g>th</str<strong>on</strong>g>is is a support <str<strong>on</strong>g>of</str<strong>on</strong>g> potential V is <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

order <str<strong>on</strong>g>of</str<strong>on</strong>g> typical distance between cells/particles <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e equilibrium<br />

state <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic system appears in <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic equati<strong>on</strong>. In 1-D <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

leads to a versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> porous-medium equati<strong>on</strong> discrete in space. However for higher<br />

dimensi<strong>on</strong>s a directi<strong>on</strong>al densities have to be c<strong>on</strong>sidered.<br />

References.<br />

[1] M. Bodnar, J.J.L. Velazquez, Derivati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> macroscopic equati<strong>on</strong>s for individual cell-based<br />

models: a formal approach, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods Appl. Sci., 28, (2005), 1757–1779.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[2] M. Bodnar, J.J.L. Velazquez, An integro-differential equati<strong>on</strong> arising as a limit <str<strong>on</strong>g>of</str<strong>on</strong>g> individual<br />

cell-based models, J. Diff. Eqs., 222, (2006), 341–380.<br />

[3] K. Oelschläger, Large systems <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting particles and <str<strong>on</strong>g>th</str<strong>on</strong>g>e porous medium equati<strong>on</strong>, J. Diff.<br />

Eqs. 88 (1990), 294–346.<br />

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Delay Differential Equati<strong>on</strong>s and Applicati<strong>on</strong>s II; Saturday, July 2, 08:30<br />

M. Bodnar<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics,<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics and Mechanics,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland<br />

e-mail: mbodnar@mimuw.edu.pl<br />

T. Płatkowski<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics,<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics and Mechanics,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland<br />

e-mail: tplatk@mimuw.edu.pl<br />

U. Foryś<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics,<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics and Mechanics,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland<br />

e-mail: urszula@mimuw.edu.pl<br />

N. Bielczyk<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics,<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics and Mechanics,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland<br />

e-mail: natalia.bielczyk@gmail.com<br />

J. Poleszczuk<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics,<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics and Mechanics,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland<br />

e-mail: j.poleszczuk@mimuw.edu.pl<br />

Delay can stabilise: populati<strong>on</strong> and love affairs dynamics.<br />

It is well known <str<strong>on</strong>g>th</str<strong>on</strong>g>at time delay may lead to destabilisati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a steady state<br />

and oscillati<strong>on</strong>s may arise due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e Hopf bifurcati<strong>on</strong>. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at for <str<strong>on</strong>g>th</str<strong>on</strong>g>e system<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> two equati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <strong>on</strong>e delay <str<strong>on</strong>g>th</str<strong>on</strong>g>e unstable steady state can be stabilised by time<br />

delay. Namely, if for delay equal to 0 <str<strong>on</strong>g>th</str<strong>on</strong>g>e steady state is an unstable node or<br />

unstable spring, <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>e steady state may gain stability for larger time delays. We<br />

give a c<strong>on</strong>diti<strong>on</strong> which guarantees <str<strong>on</strong>g>th</str<strong>on</strong>g>is kind <str<strong>on</strong>g>of</str<strong>on</strong>g> behaviour and we illustrate it wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

some linear and n<strong>on</strong>-linear sociological models <str<strong>on</strong>g>of</str<strong>on</strong>g> romantic relati<strong>on</strong>ship.<br />

111

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Semigroups <str<strong>on</strong>g>of</str<strong>on</strong>g> Operators in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology II; Saturday, July 2, 11:00<br />

Radosław Bogucki<br />

Ernst & Young Business Advisory Sp. z o.o.<br />

e-mail: radek.bogucki@gmail.com<br />

Adam Bobrowski<br />

Politechnika Lubelska<br />

Two <str<strong>on</strong>g>th</str<strong>on</strong>g>eorems <strong>on</strong> singularly perturbed semigroups wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

applicati<strong>on</strong>s to some genetic models<br />

In our talk we present two <str<strong>on</strong>g>th</str<strong>on</strong>g>eorems <strong>on</strong> c<strong>on</strong>vergence <str<strong>on</strong>g>of</str<strong>on</strong>g> semigroups related to singularly<br />

perturbed abstract Cauchy problems, and apply <str<strong>on</strong>g>th</str<strong>on</strong>g>em to some examples<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> recent models in applied ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics. The semigroups c<strong>on</strong>sidered are related<br />

to piecewise deterministic Markov processes jumping between several copies <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

rectangle in M-dimensi<strong>on</strong>al Euclidean space and moving al<strong>on</strong>g deterministic integral<br />

curves <str<strong>on</strong>g>of</str<strong>on</strong>g> some ODEs between jumps. Our <str<strong>on</strong>g>th</str<strong>on</strong>g>eorems describe limit behavior <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e processes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cases <str<strong>on</strong>g>of</str<strong>on</strong>g> fast jumps and fast moti<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e directi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chosen<br />

variables. These results are motivated by Kepler-Elst<strong>on</strong>’s model <str<strong>on</strong>g>of</str<strong>on</strong>g> gene regulati<strong>on</strong><br />

and Lipniacki’s model <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong>. We will also shortly discuss applicati<strong>on</strong>s<br />

to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er models, including <str<strong>on</strong>g>th</str<strong>on</strong>g>ose <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical ec<strong>on</strong>omics.<br />

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Ansgar Bohmann<br />

Heidelberg University<br />

e-mail: ansgar.bohmann@uni-hd.de<br />

Angela Stevens<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Münster<br />

e-mail: stevens@mis.mpg.de<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Modeling Viral Spread <strong>on</strong> Tissue or Cell Culture Level<br />

Spreading <str<strong>on</strong>g>of</str<strong>on</strong>g> viral infecti<strong>on</strong>s in tissues as well as in artificial cell cultures relies<br />

<strong>on</strong> various microscopical effects between individual cells. Besides <str<strong>on</strong>g>th</str<strong>on</strong>g>e well known<br />

diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> free viri<strong>on</strong>s, which is primitive but important, experimentalist have<br />

recently discovered a vast variety <str<strong>on</strong>g>of</str<strong>on</strong>g> more or less elementary active and directed<br />

transport mechanisms (cf. [1], [2]). Am<strong>on</strong>gst <str<strong>on</strong>g>th</str<strong>on</strong>g>ese viral surfing (cf. [3]) between<br />

cells is particularly interesting, since it may bridge significant distances. In <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

experiments transport <str<strong>on</strong>g>of</str<strong>on</strong>g> a few individual viri<strong>on</strong>s from a single infected towards a<br />

single uninfected cell (wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a culture <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>ly few cells) has been observed via<br />

different techniques such as live cell imaging and electr<strong>on</strong> microscopy. To our<br />

knowledge <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese transport processes <strong>on</strong> a larger scale has not yet been<br />

subject to any systematic studies — nei<str<strong>on</strong>g>th</str<strong>on</strong>g>er experimental nor <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical.<br />

To ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically describe <str<strong>on</strong>g>th</str<strong>on</strong>g>ese phenomena a microscopic model including<br />

different c<strong>on</strong>tributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> transport and replicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> viruses is set up and discussed.<br />

This is c<strong>on</strong>sidered as a preparatory step towards an effective descripti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall viral transport <strong>on</strong> a meso-scale level. The future goal is to use homogenizati<strong>on</strong><br />

techniques to gain more understanding for <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese different<br />

microscopic processes for <str<strong>on</strong>g>th</str<strong>on</strong>g>e quantitative and qualitative effects <strong>on</strong> spreading <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

viral infecti<strong>on</strong>s in living tissues or cell cultures.<br />

References.<br />

[1] Q. Sattentau Avoiding <str<strong>on</strong>g>th</str<strong>on</strong>g>e void: cell-to-cell spread <str<strong>on</strong>g>of</str<strong>on</strong>g> human viruses Nature Reviews Microbiology<br />

6 815 (2008).<br />

[2] W. Mo<str<strong>on</strong>g>th</str<strong>on</strong>g>es, et al. Minireview: virus cell-to-cell transmissi<strong>on</strong> Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Virology 84(17)<br />

8360–8368 (2010).<br />

[3] N. M. Sherer, M. J. Lehmann, et al. Retroviruses can establish filopodial bridges for efficient<br />

cell-to-cell transmissi<strong>on</strong> Nat Cell Biol. 9(3) 310–315 (2007).<br />

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Andreas Bohn<br />

ITQB - New University <str<strong>on</strong>g>of</str<strong>on</strong>g> Lisb<strong>on</strong><br />

e-mail: abohn@itqb.unl.pt<br />

Populati<strong>on</strong> Dynamics; Tuesday, June 28, 14:30<br />

Multi-level modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic spatio-temporal<br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> phototrophic bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms<br />

Phototrophic bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms are complex microbial communities encased in an extracellular<br />

polymeric matrix and fueled by a significantly present photosyn<str<strong>on</strong>g>th</str<strong>on</strong>g>esizing fracti<strong>on</strong><br />

(e.g. cyanobacteria) existing in symbiosis wi<str<strong>on</strong>g>th</str<strong>on</strong>g> heterotrophic bacteria [1]. In<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e present work we present our <strong>on</strong>going work <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> several integrated,<br />

quantitative approaches to modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm life cycle. In particular an SDE model predicting <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic development<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm biomass as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e frequency and size <str<strong>on</strong>g>of</str<strong>on</strong>g> abrupt biomass<br />

detachments, <str<strong>on</strong>g>th</str<strong>on</strong>g>e so-called sloughing events, is discussed [2]. We fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore analyze<br />

a kinetic flux-balance based PDE model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal distributi<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> 16 particulate and solute bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm comp<strong>on</strong>ents [3], which has originally been<br />

developed for <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling framework AQUASIM [4]. Here, we report <strong>on</strong> our<br />

efforts to reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> variables and parameters,<br />

in order to obtain a minimal model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> phototrophic<br />

bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms, and achieve integrati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> generic PDE-modeling approaches<br />

to bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms [5]. Our final aim is to c<strong>on</strong>nect bo<str<strong>on</strong>g>th</str<strong>on</strong>g> models in a coherent fashi<strong>on</strong>, and<br />

fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore adjust <str<strong>on</strong>g>th</str<strong>on</strong>g>em wi<str<strong>on</strong>g>th</str<strong>on</strong>g> evidence from experimental data <str<strong>on</strong>g>of</str<strong>on</strong>g> bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm physiology<br />

and morphology, obtained wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a <str<strong>on</strong>g>European</str<strong>on</strong>g> project <strong>on</strong> phototrophic bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms<br />

(http://www.photobi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms.org).<br />

References.<br />

[1] Roeselers et al. (2008) J Appl Phycol 20:227-235<br />

[2] Bohn et al. (2007) Wat Sci Technol 55(8-9):257-264<br />

[3] Wolf et al. (2007) Biotechnol Bioeng 97:1064-1079<br />

[4] Reichert (1996) Wat Sci Technol 30:21-30<br />

[5] Alpkvist and Klapper (2007) Bull Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Biol 69:765-789<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious agents;<br />

Tuesday, June 28, 17:00<br />

Barbara Boldin<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Natural Sciences and<br />

Informati<strong>on</strong> Technologies<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Primorska<br />

e-mail: barbara.boldin@upr.si<br />

Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-host viral evoluti<strong>on</strong> in a heterogeneous envir<strong>on</strong>ment:<br />

insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e HIV co-receptor switch<br />

From <str<strong>on</strong>g>th</str<strong>on</strong>g>e point <str<strong>on</strong>g>of</str<strong>on</strong>g> view <str<strong>on</strong>g>of</str<strong>on</strong>g> a pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen, a host is a structured and a heterogeneous<br />

envir<strong>on</strong>ment. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV, for instance, <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> spatial structure is<br />

supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus is found in different tissues while envir<strong>on</strong>mental<br />

heterogeneity originates from <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen being able to exploit different types <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

immune cells. We present a simple ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>th</str<strong>on</strong>g>at incorporates two<br />

types <str<strong>on</strong>g>of</str<strong>on</strong>g> target cells and some spatial structuring and discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s under<br />

which viral diversificati<strong>on</strong> occurs wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a host. Applying <str<strong>on</strong>g>th</str<strong>on</strong>g>e model to <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

HIV, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at it captures <str<strong>on</strong>g>th</str<strong>on</strong>g>ree main properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e so called ‘co-receptor<br />

switch’ <str<strong>on</strong>g>th</str<strong>on</strong>g>at is observed in many HIV infecti<strong>on</strong>s: <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial dominance <str<strong>on</strong>g>of</str<strong>on</strong>g> virus<br />

strains <str<strong>on</strong>g>th</str<strong>on</strong>g>at infect CCR5+ cells, <str<strong>on</strong>g>th</str<strong>on</strong>g>e late switch in some (but, importantly, not<br />

all) HIV infecti<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>e associated drop in <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> uninfected T-cells.<br />

This suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e co-receptor switch could result from gradual adaptati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e virus populati<strong>on</strong> to target cell heterogeneity. More generally, we argue <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

evoluti<strong>on</strong>ary ecology can help us better understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e course <str<strong>on</strong>g>of</str<strong>on</strong>g> some infecti<strong>on</strong>s.<br />

The talk is based <strong>on</strong> joint work wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Samuel Aliz<strong>on</strong> [1].<br />

References.<br />

[1] A. Aliz<strong>on</strong>, B. Boldin: Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-host viral evoluti<strong>on</strong> in a heterogeneous envir<strong>on</strong>ment: insights<br />

into <str<strong>on</strong>g>th</str<strong>on</strong>g>e HIV co-receptor switch. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Evoluti<strong>on</strong>ary Biology, 23, No. 12, (2010), pp.<br />

2625-2635.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Dimitra B<strong>on</strong><br />

GOETHE UNIVERSITY FRANKFURT INSTITUTE OF BIOSTATISTICS<br />

AND MATHEMATICAL MODELLING 60590 FRANKFURT (MAIN), GER-<br />

MANY<br />

e-mail: b<strong>on</strong>@med.uni-frankfurt.de<br />

Eva Herrmann<br />

GOETHE UNIVERSITY FRANKFURT INSTITUTE OF BIOSTATISTICS<br />

AND MATHEMATICAL MODELLING<br />

e-mail: herrmann@med.uni-frankfurt.de<br />

Implementati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> PK-PD Models for viral kinetics in<br />

patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> HCV<br />

PK-PD models are used to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> antiviral activity <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

drugs and combinati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> drugs in patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> chr<strong>on</strong>ic viral diseases like HCV.<br />

They play an important role in drug development and optimizing antiviral <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy.<br />

In order to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral kinetics we implemented a full PK-PD model using<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e ordinary differential equati<strong>on</strong> system shown bellow. Target cells, T , are infected<br />

by HCV, V , wi<str<strong>on</strong>g>th</str<strong>on</strong>g> rate β. Infected cells are lost at rate δ per cell and free viri<strong>on</strong>s<br />

are cleared at rate c. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er details are given by <str<strong>on</strong>g>th</str<strong>on</strong>g>e model equati<strong>on</strong>s basing <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e general PK-PD model for Hepatitis C viral kinetics as proposed in Shudo et<br />

al.[1]<br />

VI(t) ˙ = (1 − ε)(1 − ϱ)pI(t) − cV (t)<br />

VN(t) ˙ = (1 − ε)ϱpI(t) − cVn(t)<br />

I(t) ˙ = βT (t)V (t) + pII(t)(1 −<br />

T (t)+I(t)<br />

T (0)+I(0)<br />

) − δI(t)<br />

T ˙<br />

T (t)+I(t)<br />

(t) = γ(1 − T (0)+I(0) )<br />

• T and I are <str<strong>on</strong>g>th</str<strong>on</strong>g>e numbers <str<strong>on</strong>g>of</str<strong>on</strong>g> target cells and infected cells, resp.<br />

• V represents infectious vir<strong>on</strong>s<br />

• VN represents n<strong>on</strong> infectious vir<strong>on</strong>s<br />

• V = VI + VN is <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral load<br />

• p is describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral producti<strong>on</strong> rate in <str<strong>on</strong>g>th</str<strong>on</strong>g>e untreated chr<strong>on</strong>ic patient<br />

• pI is <str<strong>on</strong>g>th</str<strong>on</strong>g>e proliferati<strong>on</strong> rate, as in Dahari et al.[2]<br />

• γ is <str<strong>on</strong>g>th</str<strong>on</strong>g>e regenerati<strong>on</strong> rate as in Herrmann et al.[3]<br />

• ε(t) is <str<strong>on</strong>g>th</str<strong>on</strong>g>e effectiveness <str<strong>on</strong>g>of</str<strong>on</strong>g> IFN<br />

• ϱ is describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e antiviral effect <str<strong>on</strong>g>of</str<strong>on</strong>g> Ribavirin to split <str<strong>on</strong>g>th</str<strong>on</strong>g>e newly produced<br />

virus in infectable virus (VI and VN resp.) as in Dixit et al.[4]<br />

For <str<strong>on</strong>g>th</str<strong>on</strong>g>e PD model, we set ε(t) to ε(t) =<br />

C(t) h<br />

IC h 50 +C(t)h , where C(t) is <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug<br />

c<strong>on</strong>centrati<strong>on</strong> in serum, IC50 is <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug level which blocks <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral producti<strong>on</strong> by<br />

50% and <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter h is <str<strong>on</strong>g>th</str<strong>on</strong>g>e Hill coefficient (h ≥ 1). The drug effectiveness, ε(t)<br />

gradually increases and <str<strong>on</strong>g>th</str<strong>on</strong>g>en decreases during <str<strong>on</strong>g>th</str<strong>on</strong>g>e first week <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, as C(t) does<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e same for each patient. For fitting <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> C(t) to each patient’s PK data,<br />

we estimate all <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong>. Afterwards PK parameters are used<br />

to fit individual patient’s Log HCV RNA kinetic data by maximum likelihood in<br />

order to estimate c, δ, V0, IC50 and h. We used an optimizati<strong>on</strong> algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m basing<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Nelder and Mead me<str<strong>on</strong>g>th</str<strong>on</strong>g>od and an ODE solver for stiff equati<strong>on</strong>s. We also<br />

116

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

present an example <str<strong>on</strong>g>of</str<strong>on</strong>g> such an implementati<strong>on</strong> in MatLab as well as wi<str<strong>on</strong>g>th</str<strong>on</strong>g> R to fit<br />

viral kinetic and pharmacokinetic data wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e described full PK-PD model.<br />

References.<br />

[1] E. Shudo, R.M. Ribeiro and A.S. Perels<strong>on</strong>, Modeling Hepatitis C Virus Kinetics under Therapy<br />

using Pharmacokinetic and Pharmacodynamic Informati<strong>on</strong> Expert Opin. Drug Metab.<br />

Toxicol. 2009, 321-332.<br />

[2] Dahari H, Ribeiro RM, Perels<strong>on</strong> AS., Triphasic decline <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatitis C virus RNA during<br />

antiviral <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy Hepatology. 2007 Jul;46(1):16-21.<br />

[3] Herrmann E, Lee JH, Marinos G, Modi M, Zeuzem S., . Effect <str<strong>on</strong>g>of</str<strong>on</strong>g> ribavirin <strong>on</strong> hepatitis C viral<br />

kinetics in patients treated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> pegylated interfer<strong>on</strong>. Hepatology. 2003 Jun;37(6):1351-8.<br />

[4] Dixit NM, Layden-Almer JE, Layden TJ, Perels<strong>on</strong> AS., Modelling how ribavirin improves<br />

interfer<strong>on</strong> resp<strong>on</strong>se rates in hepatitis C virus infecti<strong>on</strong>. Nature. 2004 Dec 16;432(7019):922-4.<br />

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Recent advances in infectious disease modelling II; Saturday, July 2, 14:30<br />

Axel B<strong>on</strong>acic Marinovic<br />

RIVM / UMC Utrecht, Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

e-mail: axel.b<strong>on</strong>acic.marinovic@rivm.nl<br />

Timeliness <str<strong>on</strong>g>of</str<strong>on</strong>g> interventi<strong>on</strong> in epidemic outbreaks<br />

During an epidemic outbreak <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong> about which interventi<strong>on</strong> measures should<br />

be applied is tightly linked to how timely <str<strong>on</strong>g>th</str<strong>on</strong>g>ese measures can be applied. As a general<br />

rule, <str<strong>on</strong>g>th</str<strong>on</strong>g>e earlier an interventi<strong>on</strong> is applied <str<strong>on</strong>g>th</str<strong>on</strong>g>e better is its result, however, due<br />

to logistics, policies, m<strong>on</strong>ey, people and reality in general, delays <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e applicati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> interventi<strong>on</strong>s are inevitable. Therefore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong> comes down to decide, e.g.,<br />

whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er is it still wor<str<strong>on</strong>g>th</str<strong>on</strong>g> applying a determined interventi<strong>on</strong> (i.e., is it already too<br />

late for it to do some<str<strong>on</strong>g>th</str<strong>on</strong>g>ing?), or whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er a quicker interventi<strong>on</strong> <strong>on</strong> a smaller group<br />

would have a better (or worse) effect <str<strong>on</strong>g>th</str<strong>on</strong>g>an a slower interventi<strong>on</strong> <strong>on</strong> a larger group.<br />

To answer <str<strong>on</strong>g>th</str<strong>on</strong>g>is questi<strong>on</strong> we employ models to analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>e outcome <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics<br />

depending <strong>on</strong> when and to whom are <str<strong>on</strong>g>th</str<strong>on</strong>g>e interventi<strong>on</strong>s applied. We show two examples<br />

where <str<strong>on</strong>g>th</str<strong>on</strong>g>e models can support decisi<strong>on</strong> making. The first case shows <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

effect <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccinati<strong>on</strong> during a measles outbreak in a school depending <strong>on</strong> when after<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e start <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e outbreak vaccinati<strong>on</strong> is implemented. The sec<strong>on</strong>d case investigates<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> employing a quicker but less sensitive test <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e gold standard to<br />

diagnose H1N1, followed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e isolati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> positively diagnosed individuals.<br />

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Genetics and Genomics; Wednesday, June 29, 08:30<br />

Katarína Boďová<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics,<br />

Physics and Informatics, Comenius University, Bratislava, Slovakia<br />

e-mail: bodova@fmph.uniba.sk<br />

Ľubomír Tomáška<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Genetics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Natural Sciences, Comenius University,<br />

Bratislava, Slovakia<br />

Jozef Nosek<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemistry, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Natural Sciences, Comenius<br />

University, Bratislava, Slovakia<br />

Richard Kollár<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, Comenius University,<br />

Bratislava, Slovakia<br />

Factors determining leng<str<strong>on</strong>g>th</str<strong>on</strong>g> distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> telomeric<br />

structures in absence <str<strong>on</strong>g>of</str<strong>on</strong>g> telomerase<br />

Absence <str<strong>on</strong>g>of</str<strong>on</strong>g> telomerase in cellular structures requires an alternative telomeraseindependent<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way for telomeric sequence leng<str<strong>on</strong>g>th</str<strong>on</strong>g> regulati<strong>on</strong>. Telomeric circles<br />

possibly play an important role in a universal mechanism for stabilizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ends <str<strong>on</strong>g>of</str<strong>on</strong>g> linear DNA <str<strong>on</strong>g>th</str<strong>on</strong>g>at possibly dates back to pre-telomerase ages. It was observed<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>eir leng<str<strong>on</strong>g>th</str<strong>on</strong>g> distributi<strong>on</strong> varies significantly in various types <str<strong>on</strong>g>of</str<strong>on</strong>g> organelles and<br />

organisms. How to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>ese different outcomes <str<strong>on</strong>g>of</str<strong>on</strong>g> experiments? In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work<br />

we try to identify and estimate key factors influencing <str<strong>on</strong>g>th</str<strong>on</strong>g>e leng<str<strong>on</strong>g>th</str<strong>on</strong>g> distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

telomeric circles, loops and strand invasi<strong>on</strong>s using numerical simulati<strong>on</strong>s for a model<br />

we have c<strong>on</strong>structed for C. parapsilosis.<br />

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Evoluti<strong>on</strong>ary Ecology; Friday, July 1, 14:30<br />

Wojciech Borkowski<br />

Center for Complex Systems, Institute for Social Studies, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw<br />

e-mail: wborkowski@uw.edu.pl<br />

Cellular automat<strong>on</strong> eco-systems <str<strong>on</strong>g>th</str<strong>on</strong>g>e simple way to simulate<br />

macroevoluti<strong>on</strong><br />

Keywords: Macroevoluti<strong>on</strong>; Coevoluti<strong>on</strong>; Individual-based models; Predator-Prey;<br />

Cellular automata; Artificial life; Phylogenetic Trees; Food Networks;<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is short talk I will present a simple lattice, cellular automat<strong>on</strong> like model <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a multi-species ecosystem suitable for <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> emergent properties <str<strong>on</strong>g>of</str<strong>on</strong>g> macroevoluti<strong>on</strong>.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is model <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> species is not fixednew species c<strong>on</strong>tinuously<br />

emerge by mutati<strong>on</strong> from existing species, <str<strong>on</strong>g>th</str<strong>on</strong>g>en survive or extinct depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

energetic balance between local ecological interacti<strong>on</strong>s. The M<strong>on</strong>te-Carlo numerical<br />

simulati<strong>on</strong>s show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is model is able to qualitatively reproduce phenomena <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

have been empirically observed, like <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence between size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e isolated<br />

area and <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> species inhabiting <str<strong>on</strong>g>th</str<strong>on</strong>g>ere or between primary producti<strong>on</strong> and<br />

complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> food network. The model allows also studying formati<strong>on</strong> and transformati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> food-networks, influence <str<strong>on</strong>g>of</str<strong>on</strong>g> general factors (like intensity <str<strong>on</strong>g>of</str<strong>on</strong>g> primary<br />

producti<strong>on</strong>s) and possible causes <str<strong>on</strong>g>of</str<strong>on</strong>g> mass extincti<strong>on</strong>s, and more generally, <str<strong>on</strong>g>th</str<strong>on</strong>g>e role<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> ecological rules and pure chance in macroevoluti<strong>on</strong>. Some results were published<br />

jet (see below), some new will be presented.<br />

HOMEPAGE: www.iss.uw.edu.pl/borkowski/<br />

References.<br />

[1] Borkowski, W., 2009. Simple Lattice Model <str<strong>on</strong>g>of</str<strong>on</strong>g> Macroevoluti<strong>on</strong>. Planet. Space Sci. Vol. 57. No.<br />

4, pp.: 498-507, doi:10.1016/j.pss.2008.10.001<br />

[2] Borkowski W., 2008. Cellular automata model <str<strong>on</strong>g>of</str<strong>on</strong>g> macroevoluti<strong>on</strong>. In Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Fourteen<str<strong>on</strong>g>th</str<strong>on</strong>g> Nati<strong>on</strong>al <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics in Biology and<br />

Medicine (pp. 18-25), Uniwersytet Warszawski, QPrint Warszawa 2008, ISBN: 83-903893-4-7<br />

(arXiv:0902.3919v1)<br />

[3] Borkowski W., Nowak A., 2009. Zastosowanie modelu samoorganizacji ekosystemów do wyjaśniania<br />

zróżnicowania kulturowego zachowa społecznych. In Układy Złoż<strong>on</strong>e w Naukach<br />

Społecznych - wybrane zagadnienia, pp.: 233-274, Wydawnictwo Naukowe Scholar, Warszawa.<br />

ISBN: 978-83-7383-371-4 (in Polish)<br />

[4] Borkowski W., 2008. Powtarzalność ewolucji w naturze, kulturze i... informatyce. (Repeatability<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Evoluti<strong>on</strong> in nature, culture and computer science) TEKSTY z ULICY nr 12 (pp. 7-28),<br />

Uniwersytet Śląski, OFFMAX, Katowice 2008, ISBN: 978-83-87248-16-1 (in Polish)<br />

[5] Borkowski W., 2006. Ewolucyjna droga do złoż<strong>on</strong>ości. (Evoluti<strong>on</strong>ary way to complexity) TEK-<br />

STY z ULICY nr 10 (pp. 7-24), Uniwersytet Śląski, OFFMAX, Katowice 2006, ISBN: 83-<br />

87248-13-4 (http://www.memetyka.pl/dokumenty/pliki/zm10_1.pdf) (in Polish)<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Marta Borowska<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Informatics, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bialystok, Sosnowa 64, 15-887 Bialystok, Poland<br />

e-mail: mborowska@ii.uwb.edu.pl<br />

Edward Oczeretko<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Mechanical Engineering, Technical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bialystok,<br />

Wiejska 45A, 15-351 Bialystok, Poland<br />

Synchr<strong>on</strong>izati<strong>on</strong> in coupled n<strong>on</strong>linear dynamical systems<br />

The study <str<strong>on</strong>g>of</str<strong>on</strong>g> coupling in dynamical systems has received an increasing interest since<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e 1990s. Recent studies <str<strong>on</strong>g>of</str<strong>on</strong>g> synchr<strong>on</strong>izati<strong>on</strong> have included various measures for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e detecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e different types <str<strong>on</strong>g>of</str<strong>on</strong>g> synchr<strong>on</strong>izati<strong>on</strong>. Never<str<strong>on</strong>g>th</str<strong>on</strong>g>eless, a comparis<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> different measures between coupled dynamical systems in c<strong>on</strong>trolled settings is<br />

still missing. For <str<strong>on</strong>g>th</str<strong>on</strong>g>is aim <str<strong>on</strong>g>th</str<strong>on</strong>g>e noti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> synchr<strong>on</strong>izati<strong>on</strong> will be used in a loose<br />

sense as <str<strong>on</strong>g>th</str<strong>on</strong>g>e syn<strong>on</strong>ym <str<strong>on</strong>g>of</str<strong>on</strong>g> correlati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e similarity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e signals or <str<strong>on</strong>g>th</str<strong>on</strong>g>e similarity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir dynamics. We present some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>linear dynamics me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

synchr<strong>on</strong>izati<strong>on</strong>: <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutual correlati<strong>on</strong> dimensi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e cross-approximate entropy,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e mutual informati<strong>on</strong> functi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>linear interdependencies S, H, N and apply<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese measures to <str<strong>on</strong>g>th</str<strong>on</strong>g>ree coupled model systems. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e reference me<str<strong>on</strong>g>th</str<strong>on</strong>g>od, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

linear cross-correlati<strong>on</strong> functi<strong>on</strong> was used. We use <str<strong>on</strong>g>th</str<strong>on</strong>g>e coupled Lorenz, Rössler and<br />

Lorenz-Rössler systems. Signals appearing here were used to illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e problems<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> rec<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> attractors in <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase space, validati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for<br />

different parameters wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e coupling streng<str<strong>on</strong>g>th</str<strong>on</strong>g>. Mutual correlati<strong>on</strong> dimensi<strong>on</strong> is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e amount <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> exchanged between systems. It allows to specify <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

relati<strong>on</strong>ship between systems dynamics. Cross approximate entropy is a me<str<strong>on</strong>g>th</str<strong>on</strong>g>od<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> measuring <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity or irregularity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e signal. More regular signal has<br />

less value <str<strong>on</strong>g>of</str<strong>on</strong>g> approximate entropy. Mutual informati<strong>on</strong> is a measure <str<strong>on</strong>g>of</str<strong>on</strong>g> statistical<br />

independence <str<strong>on</strong>g>of</str<strong>on</strong>g> signals, if <str<strong>on</strong>g>th</str<strong>on</strong>g>e value <str<strong>on</strong>g>of</str<strong>on</strong>g> zero means <str<strong>on</strong>g>th</str<strong>on</strong>g>at two signals are independent.<br />

Low value (close to zero) measures S, H, N indicates <str<strong>on</strong>g>th</str<strong>on</strong>g>e independence between <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

systems, while a high value indicates <str<strong>on</strong>g>th</str<strong>on</strong>g>e synchr<strong>on</strong>izati<strong>on</strong>. Correlati<strong>on</strong> functi<strong>on</strong> is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e correlati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> two signals. The results obtained by means <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

different algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms failed to answer <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> which me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is <str<strong>on</strong>g>th</str<strong>on</strong>g>e best. It<br />

turns out <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e results depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system and <str<strong>on</strong>g>th</str<strong>on</strong>g>e type <str<strong>on</strong>g>of</str<strong>on</strong>g> coupling.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Evert Bosdriesz<br />

Systems Bioinformatics, Vrije Universiteit Amsterdam<br />

Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands Bioinformatics Center<br />

e-mail: evert.bosdriesz@falw.vu.nl<br />

Jan Berkhout<br />

Systems Bioinformatics, Vrije Universiteit Amsterdam<br />

Frank Bruggeman<br />

Systems Bioinformatics, Vrije Universiteit Amsterdam<br />

Life Sciences, Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science<br />

Douwe Molenaar<br />

Systems Bioinformatics, Vrije Universiteit Amsterdam<br />

Bas Teusink<br />

Systems Bioinformatics, Vrije Universiteit Amsterdam<br />

The cost and benefit <str<strong>on</strong>g>of</str<strong>on</strong>g> enzyme expressi<strong>on</strong><br />

The resources a microorganism has at it’s disposal are limited. Am<strong>on</strong>g o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ings, <str<strong>on</strong>g>th</str<strong>on</strong>g>is implies <str<strong>on</strong>g>th</str<strong>on</strong>g>at expressing enzymes is costly. C<strong>on</strong>sider for instance <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

specific grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate, which is <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> biomass syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis per unit biomass. Expressing<br />

a certain enzyme increases <str<strong>on</strong>g>th</str<strong>on</strong>g>e total biomass and <str<strong>on</strong>g>th</str<strong>on</strong>g>us, unless it c<strong>on</strong>tributes<br />

in some way to <str<strong>on</strong>g>th</str<strong>on</strong>g>e biomass syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis rate, will decreases <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate. Indeed,<br />

it has been observed <str<strong>on</strong>g>th</str<strong>on</strong>g>at expressing "dummy" proteins has a negative effect <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate [1,2].<br />

In order to quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e cost and benefit <str<strong>on</strong>g>of</str<strong>on</strong>g> enzyme expressi<strong>on</strong>, we generalized<br />

a definiti<strong>on</strong> previously proposed by Dekel and Al<strong>on</strong> [1]. The benefit functi<strong>on</strong> is<br />

closely related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e flux c<strong>on</strong>trol coefficient, <str<strong>on</strong>g>th</str<strong>on</strong>g>e cost is <str<strong>on</strong>g>th</str<strong>on</strong>g>e directly related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

fracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resources dedicated to <str<strong>on</strong>g>th</str<strong>on</strong>g>e enzyme. The flux is optimized if for each<br />

enzyme its c<strong>on</strong>trol coefficient equals its c<strong>on</strong>tributi<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e total resource usages.<br />

This is generalizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g>, and c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g>, earlier observati<strong>on</strong>s by Klipp and He<br />

[3].<br />

The relati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e benefit functi<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e flux c<strong>on</strong>trol coefficients allows<br />

us to intuitively understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> kinetic parameters such as catalytic<br />

c<strong>on</strong>stants and Michaelis-Menten c<strong>on</strong>stants <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e (optimal) flux, at least for small<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways. For instance, an enzyme wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a high catalytic c<strong>on</strong>stant typically has a<br />

flux c<strong>on</strong>trol coefficient <str<strong>on</strong>g>th</str<strong>on</strong>g>at rapidly decreases wi<str<strong>on</strong>g>th</str<strong>on</strong>g> it’s c<strong>on</strong>centrati<strong>on</strong>, and we expect<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is enzyme to have a low expressi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal state.<br />

We are currently applying <str<strong>on</strong>g>th</str<strong>on</strong>g>e cost-benefit analysis to self-replicator models<br />

[4].<br />

References.<br />

[1] E. Dekel and U. Al<strong>on</strong> (2005), Optimality and evoluti<strong>on</strong>ary tuning <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e expressi<strong>on</strong> level <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

protein Nature 436 588–92.<br />

[2] D. M. Stoebel, A.M. Dean, D.E. and Dykhuizen (2008), The cost <str<strong>on</strong>g>of</str<strong>on</strong>g> expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Escherichia<br />

coli lac oper<strong>on</strong> proteins is in <str<strong>on</strong>g>th</str<strong>on</strong>g>e process, not in <str<strong>on</strong>g>th</str<strong>on</strong>g>e product Genetics 178 1653–60.<br />

[3] E. Klipp and R. Heinrich (1999), Competiti<strong>on</strong> for enzymes in metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways: implicati<strong>on</strong>s<br />

for optimal distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> enzyme c<strong>on</strong>centrati<strong>on</strong>s and for <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> flux c<strong>on</strong>trol Bio<br />

Systems 54 1–14.<br />

[4] D. Molenaar, R. van Berlo, D. de Ridder and B. Teusink (2009), Shifts in grow<str<strong>on</strong>g>th</str<strong>on</strong>g> strategies<br />

reflect trade<str<strong>on</strong>g>of</str<strong>on</strong>g>fs in cellular ec<strong>on</strong>omics Molecular Systems Biology 5.<br />

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Evoluti<strong>on</strong>ary Ecology; Thursday, June 30, 11:30<br />

Roger Bowers<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Liverpool,<br />

Liverpool, L69 7ZL, U.K.<br />

e-mail: sx04@liv.ac.uk<br />

Andy Hoyle<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Computing Science and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Stirling, Stirling, FK9 4LA, U.K.<br />

Andy White<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Maxwell Institute for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

Sciences, Heriot Watt University, Edinburgh, EH14 4AS, U.K.<br />

Evoluti<strong>on</strong>ary behaviour in single-species discrete-time<br />

models: <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>fs, <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying<br />

populati<strong>on</strong> dynamics and density dependence<br />

We study a class <str<strong>on</strong>g>of</str<strong>on</strong>g> discrete-time single-species models typified by <str<strong>on</strong>g>th</str<strong>on</strong>g>e logistic, Hassell<br />

and Ricker forms. These have been used to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> behaviour<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> ecological systems as, despite <str<strong>on</strong>g>th</str<strong>on</strong>g>eir relative simplicity, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey can produce a wide<br />

variety <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamics from stable equilibria and cycles to chaos. Here, we investigate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models which has received much less attenti<strong>on</strong>.<br />

We use adaptive dynamics (supported by simulati<strong>on</strong>s) and assume <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are two<br />

evolving parameters linked by a trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at, for equilibrium underlying<br />

populati<strong>on</strong> dynamics, <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary behaviour is restricted to an evoluti<strong>on</strong>ary attractor<br />

or an evoluti<strong>on</strong>ary repellor depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e shape <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f; branching<br />

cannot be exhibited. We fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er show <str<strong>on</strong>g>th</str<strong>on</strong>g>at, in c<strong>on</strong>trast to recent studies, <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

restricti<strong>on</strong> in evoluti<strong>on</strong>ary behaviour is maintained in <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard Hassell model,<br />

and models which have a similar separable form, when <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying populati<strong>on</strong><br />

dynamics are cyclic. To gain a broader range <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary behaviour requires<br />

c<strong>on</strong>sidering models in which density-dependence operates differently <strong>on</strong> reproducti<strong>on</strong><br />

and survival. Such models can additi<strong>on</strong>ally for some trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f shapes exhibit<br />

evoluti<strong>on</strong>ary branching or Garden <str<strong>on</strong>g>of</str<strong>on</strong>g> Eden evoluti<strong>on</strong>ary behaviour when <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying<br />

populati<strong>on</strong> dynamics are n<strong>on</strong>-equilibrium. Fundamental to such outcomes are<br />

disc<strong>on</strong>tinuous changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e boundary for c<strong>on</strong>vergence stability (wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to<br />

a measure <str<strong>on</strong>g>of</str<strong>on</strong>g> trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f shape) across transiti<strong>on</strong>s (induced by parameter variati<strong>on</strong>)<br />

between different types <str<strong>on</strong>g>of</str<strong>on</strong>g> underlying populati<strong>on</strong> dynamics. Trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f shape and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying populati<strong>on</strong> dynamics can bo<str<strong>on</strong>g>th</str<strong>on</strong>g> have a marked effect<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> ecological systems<br />

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Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 08:30<br />

Alexander S. Bratus<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Computati<strong>on</strong>al Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Cybernetics, Moscow State<br />

University, Moscow, 119992, Russia<br />

e-mail: alexander.bratus@yandex.ru<br />

Vladimir P. Posvyanskii<br />

Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics–1, Moscow State University <str<strong>on</strong>g>of</str<strong>on</strong>g> Railway Engineering,<br />

Moscow<br />

Artem S. Novozhilov<br />

Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics–1, Moscow State University <str<strong>on</strong>g>of</str<strong>on</strong>g> Railway Engineering,<br />

Moscow<br />

e-mail: anovozhilov@gmail.com<br />

Stability and limit behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> a distributed replicator<br />

system<br />

The replicator equati<strong>on</strong> is known to provide a general modeling framework for several<br />

distinct areas in ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical biology. In particular, it arises as a selecti<strong>on</strong><br />

equati<strong>on</strong> in populati<strong>on</strong> genetics, as a dynamic descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary game<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eory, and as a model for putative chemical reacti<strong>on</strong>s describing prebiotic evoluti<strong>on</strong>.<br />

In its simplest form, when <str<strong>on</strong>g>th</str<strong>on</strong>g>e fitness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e species is a linear functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

relative abundances <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er species, <str<strong>on</strong>g>th</str<strong>on</strong>g>e replicator equati<strong>on</strong> takes <str<strong>on</strong>g>th</str<strong>on</strong>g>e form<br />

<br />

(1) ˙vi = vi (Av)i − f loc (t) , i = 1, . . . , n,<br />

where v = v(t) = (v1, . . . , vn), A is an n × n matrix wi<str<strong>on</strong>g>th</str<strong>on</strong>g> elements aij describing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e j-<str<strong>on</strong>g>th</str<strong>on</strong>g> species to <str<strong>on</strong>g>th</str<strong>on</strong>g>e fitness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e i-<str<strong>on</strong>g>th</str<strong>on</strong>g> species, (Av)i =<br />

n<br />

j=1 aijvj, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean fitness f loc (t) = 〈Av, v〉 = n<br />

i=1 (Av)ivi is chosen such<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at v ∈ Sn = {v : n<br />

i=1 vi = 1}.<br />

There are several different approaches to add space to (1). We suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e global regulati<strong>on</strong> represents a natural and c<strong>on</strong>venient approach to c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

replicator equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an explicit spatial structure. To be exact, as a counterpart<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e local model (1) we c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

(2)<br />

∂ui<br />

∂t = ui [(Au)i − f sp (t)] + di∆ui, i = 1, . . . , n,<br />

where now u = u(x, t), x ∈ Ω ⊂ Rk , k = 1, 2, 3, di > 0 are diffusi<strong>on</strong> coefficients,<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean integral fitness is given, assuming Niemann’s boundary c<strong>on</strong>diti<strong>on</strong>s,<br />

by f sp (t) = <br />

〈Au, u〉 dx. This approach allows analytical investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> (2):<br />

Ω<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e tool which was mainly missing in <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> replicator equati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

explicit space. In particular, it is possible to find <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s for asymptotically<br />

stable rest points <str<strong>on</strong>g>of</str<strong>on</strong>g> (1) to be asymptotically stable homogeneous equilibria <str<strong>on</strong>g>of</str<strong>on</strong>g> (2).<br />

In our work, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at for some values <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> coefficients spatially<br />

heterogeneous soluti<strong>on</strong>s appear. Using a definiti<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean<br />

integral sense we prove <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese heterogeneous soluti<strong>on</strong>s can be attracting; in<br />

particular <str<strong>on</strong>g>th</str<strong>on</strong>g>is is <str<strong>on</strong>g>th</str<strong>on</strong>g>e case for Eigen’s hypercycle. Defining in some natural way<br />

evoluti<strong>on</strong>ary stable states for <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributed system (2), we provide <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>is distributed state to be an asymptotically stable stati<strong>on</strong>ary soluti<strong>on</strong> to (2).<br />

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References.<br />

[1] A. S. Bratus, V. P. Posvyanskii. Stati<strong>on</strong>ary soluti<strong>on</strong>s in a closed distributed Eigen–Schuster<br />

evoluti<strong>on</strong> system. Differential equati<strong>on</strong>s, 42:1762–1774, 2006.<br />

[2] A. S. Bratus, V. P. Posvyanskii, and A. S. Novozhilov. Existence and stability <str<strong>on</strong>g>of</str<strong>on</strong>g> stati<strong>on</strong>ary<br />

soluti<strong>on</strong>s to spatially extended autocatalytic and hypercyclic systems under global regulati<strong>on</strong><br />

and wi<str<strong>on</strong>g>th</str<strong>on</strong>g> n<strong>on</strong>linear grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rates. N<strong>on</strong>linear Analysis: Real World Applicati<strong>on</strong>s, 11:1897–1917,<br />

2010.<br />

[3] A. S. Bratus, V. P. Posvyanskii, and A. S. Novozhilov. A note <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e replicator equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

explicit space and global regulati<strong>on</strong>. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences and Engineering, in press, 2011.<br />

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Populati<strong>on</strong> Dynamics; Tuesday, June 28, 11:00<br />

Carlos A. Braumann<br />

Centro de Investigação em Matemática e Aplicaçes, Universidade de<br />

Évora<br />

e-mail: braumann@uevora.pt<br />

Patrícia A. Filipe<br />

Centro de Investigação em Matemática e Aplicaçes, Universidade de<br />

Évora<br />

Clara Carlos<br />

Escola Superior de Tecnologia do Barreiro, Insytituto Politécnico<br />

de Setúbal<br />

Nuno M. Brites<br />

Universidade de Évora<br />

Carlos J. Roquete<br />

Instituto de Ciências Agrárias e Ambientais Mediterrânicas, Universidade<br />

de Évora<br />

Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>it optimizati<strong>on</strong> issues in livestock producti<strong>on</strong> in a<br />

randomly variable envir<strong>on</strong>ment<br />

We use quite general stochastic differential equati<strong>on</strong> models to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical<br />

behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e individual grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> animals raised in a randomly varying<br />

envir<strong>on</strong>ment. These models are c<strong>on</strong>ceptually more adequate to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> random envir<strong>on</strong>mental variati<strong>on</strong>s <strong>on</strong> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical regressi<strong>on</strong><br />

techniques (which are appropriate to describe measurement errors). We describe<br />

parameter estimati<strong>on</strong> and predicti<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods, illustrating wi<str<strong>on</strong>g>th</str<strong>on</strong>g> data <strong>on</strong> cow grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Mertolengo breed raised in Alentejo (Portugal) under natural c<strong>on</strong>diti<strong>on</strong>s and<br />

show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey outperform <str<strong>on</strong>g>th</str<strong>on</strong>g>e traditi<strong>on</strong>al regressi<strong>on</strong> models in predictive power.<br />

Mixed models, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> random variati<strong>on</strong> am<strong>on</strong>g animals <str<strong>on</strong>g>of</str<strong>on</strong>g> average asymptotic size,<br />

are also c<strong>on</strong>sidered.<br />

An applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models to pr<str<strong>on</strong>g>of</str<strong>on</strong>g>it optimizati<strong>on</strong> in livestock producti<strong>on</strong><br />

is shown.<br />

Assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>e animal is to be sold when it reaches some prescribed age and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are fixed and variable costs (per unit time) in raising <str<strong>on</strong>g>th</str<strong>on</strong>g>e animal and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

selling price is proporti<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e animal’s weight, we determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal age<br />

at which an animal should be sold in order to maximize pr<str<strong>on</strong>g>of</str<strong>on</strong>g>it.<br />

The first passage time distributi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a prescribed size is studied and used<br />

to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal size at which <str<strong>on</strong>g>th</str<strong>on</strong>g>e animal should be sold. We can <str<strong>on</strong>g>th</str<strong>on</strong>g>en<br />

determine which policy (selling at a fixed age or selling at a fixed size) is preferable<br />

in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> expected pr<str<strong>on</strong>g>of</str<strong>on</strong>g>it.<br />

Some issues related to optimizati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e simultaneous raising <str<strong>on</strong>g>of</str<strong>on</strong>g> several animals<br />

will also be discussed.<br />

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Recent advances in infectious disease modelling II; Saturday, July 2, 14:30<br />

Romulus Breban<br />

Unité d’Epidémiologie des Maladies Emergentes,<br />

Institut Pasteur, 75724 Paris Cedex 15, France<br />

e-mail: romulus.breban@pasteur.fr<br />

The nati<strong>on</strong>wide incidence <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatitis C in Egypt: Toward<br />

realistic estimates<br />

Recently, <str<strong>on</strong>g>th</str<strong>on</strong>g>e nati<strong>on</strong>wide incidence <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatitis C in Egypt has attracted much<br />

attenti<strong>on</strong> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e scientific literature and mass media. Alarming new estimates<br />

exceeding 500 000 new cases per year (6.9/1000 per pers<strong>on</strong>-year) have been made<br />

based <strong>on</strong> data originating from <str<strong>on</strong>g>th</str<strong>on</strong>g>e Egyptian Demographic and Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Survey performed<br />

in 2008. However, a more complete analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hepatitis C epidemiology<br />

in Egypt, based <strong>on</strong> additi<strong>on</strong>al nati<strong>on</strong>al-level as well as cohort-level data, reveals a<br />

very different story. First, it unveils a complex epidemic dynamics <str<strong>on</strong>g>th</str<strong>on</strong>g>at violates <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

simplistic me<str<strong>on</strong>g>th</str<strong>on</strong>g>odological assumpti<strong>on</strong>s made for <str<strong>on</strong>g>th</str<strong>on</strong>g>e incidence estimates; it <str<strong>on</strong>g>th</str<strong>on</strong>g>us becomes<br />

obvious <str<strong>on</strong>g>th</str<strong>on</strong>g>at incidence has been overestimated. Sec<strong>on</strong>d, a comparis<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

direct incidence measurements in rural cohorts suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e overestimati<strong>on</strong> is<br />

by at least a factor <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree. Accurate estimate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hepatitis C incidence in<br />

Egypt remains a task for <str<strong>on</strong>g>th</str<strong>on</strong>g>e future.<br />

References.<br />

[1] F.D. Miller, L.J. Abu-Raddad Evidence <str<strong>on</strong>g>of</str<strong>on</strong>g> intense <strong>on</strong>going endemic transmissi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatitis<br />

C virus in Egypt Proc Natl Acad Sci U S A 107 14757-14762, 2010.<br />

[2] E.M. Lehman, M.L. Wils<strong>on</strong> Epidemic hepatitis C virus infecti<strong>on</strong> in Egypt: estimates <str<strong>on</strong>g>of</str<strong>on</strong>g> past<br />

incidence and future morbidity and mortality J Vir Hep 16 650-658, 2009.<br />

[3] C. Frank C, M.K. Mohamed, G.T. Strickland, D. Lavanchy, R. Ar<str<strong>on</strong>g>th</str<strong>on</strong>g>ur, L.S. Magder, T. Khoby,<br />

Y. Abdel-Wahab, E. Ohn, W. Anwar, I. Sallam The role <str<strong>on</strong>g>of</str<strong>on</strong>g> parenteral antischistosomal <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatitis C virus in Egypt Lancet 355 887-891, 2000.<br />

[4] A. Mostafa, S. Taylor, M. El-Daly, M. El Hoseiny, I. Bakr, N. Arafa, V. Thiers, F. Rimlinger,<br />

M. Abdel-Hamid, A. F<strong>on</strong>tanet, M.K. Mohamed Is <str<strong>on</strong>g>th</str<strong>on</strong>g>e hepatitis C virus epidemic over in<br />

Egypt? Incidence and risk factors <str<strong>on</strong>g>of</str<strong>on</strong>g> new hepatitis C virus infecti<strong>on</strong>s Liver Int 30 560-566,<br />

2010.<br />

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Informati<strong>on</strong>, human behaviour and disease; Saturday, July 2, 11:00<br />

Romulus Breban<br />

Unité d’Epidémiologie des Maladies Emergentes,<br />

Institut Pasteur, 75724 Paris Cedex 15, France<br />

e-mail: romulus.breban@pasteur.fr<br />

Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> newscasts for increasing influenza vaccinati<strong>on</strong><br />

coverage: How much is too much?<br />

Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> pandemic and seas<strong>on</strong>al influenza are receiving more attenti<strong>on</strong> from massmedia<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>an ever before. Frequent topics are epidemic severity, vaccinati<strong>on</strong>, etc.,<br />

changing <str<strong>on</strong>g>th</str<strong>on</strong>g>e way in which we perceive <str<strong>on</strong>g>th</str<strong>on</strong>g>e utility <str<strong>on</strong>g>of</str<strong>on</strong>g> disease preventi<strong>on</strong>. Voluntary<br />

influenza vaccinati<strong>on</strong> has been recently modeled using inductive reas<strong>on</strong>ing games.<br />

Thus, it has been found <str<strong>on</strong>g>th</str<strong>on</strong>g>at severe epidemics cannot be prevented by voluntary<br />

vaccinati<strong>on</strong> unless vaccinati<strong>on</strong> incentives are <str<strong>on</strong>g>of</str<strong>on</strong>g>fered. However, a key assumpti<strong>on</strong><br />

has been <str<strong>on</strong>g>th</str<strong>on</strong>g>at individuals make vaccinati<strong>on</strong> decisi<strong>on</strong>s based <strong>on</strong> whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>ere was<br />

an epidemic each influenza seas<strong>on</strong>; no o<str<strong>on</strong>g>th</str<strong>on</strong>g>er epidemiological informati<strong>on</strong> is available<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>em. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, we relax <str<strong>on</strong>g>th</str<strong>on</strong>g>is assumpti<strong>on</strong> and investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sequences<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> making more informed vaccinati<strong>on</strong> decisi<strong>on</strong>s while no incentives are <str<strong>on</strong>g>of</str<strong>on</strong>g>fered. We<br />

obtain two major results. First, providing additi<strong>on</strong>al epidemiological informati<strong>on</strong><br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e public may stabilize <str<strong>on</strong>g>th</str<strong>on</strong>g>e vaccinati<strong>on</strong> coverage and suppress severe influenza<br />

epidemics. Sec<strong>on</strong>d, when severe epidemics are prevented, if even more epidemiological<br />

informati<strong>on</strong> is released to <str<strong>on</strong>g>th</str<strong>on</strong>g>e public, <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>e vaccinati<strong>on</strong> coverage decreases.<br />

We discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>ree scenarios where individuals know (i) <str<strong>on</strong>g>th</str<strong>on</strong>g>e prevalence, (ii) <str<strong>on</strong>g>th</str<strong>on</strong>g>e vaccinati<strong>on</strong><br />

coverage and (iii) bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e prevalence and <str<strong>on</strong>g>th</str<strong>on</strong>g>e vaccinati<strong>on</strong> coverage every<br />

influenza seas<strong>on</strong>, in additi<strong>on</strong> to whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>ere was an epidemic.<br />

References.<br />

[1] R. Vardavas, R. Breban, S. Blower, Can influenza epidemics be prevented by voluntary vaccinati<strong>on</strong>?<br />

PLoS Comput Biol 3 e85, 2007.<br />

[2] R. Breban, R. Vardavas, S. Blower, Mean-field analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> an inductive reas<strong>on</strong>ing game: applicati<strong>on</strong><br />

to influenza vaccinati<strong>on</strong> Phys Rev E 76 031127, 2007.<br />

128

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Víctor F. Breña–Medina<br />

Applied N<strong>on</strong>linear Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bristol<br />

e-mail: envfbm@bris.ac.uk<br />

Alan R. Champneys<br />

Applied N<strong>on</strong>linear Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bristol<br />

e-mail: A.R.Champneys@bristol.ac.uk<br />

Wave–pinning Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Model <str<strong>on</strong>g>of</str<strong>on</strong>g> Plant Root Hair<br />

Initiati<strong>on</strong><br />

A simple ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model is developed <str<strong>on</strong>g>of</str<strong>on</strong>g> a key cellular–level process in plant<br />

morphogenesis, namely <str<strong>on</strong>g>th</str<strong>on</strong>g>e biochemical process wich triggers outgrow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> a hair<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a root hair cell <str<strong>on</strong>g>of</str<strong>on</strong>g> Arabidopsis. It involves <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e small G–<br />

proteins known as ROPs which bind to a specific locati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell membrane,<br />

triggering cell wall s<str<strong>on</strong>g>of</str<strong>on</strong>g>tening and subsequent hair grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. A n<strong>on</strong>–homogeneous<br />

reacti<strong>on</strong>–diffusi<strong>on</strong> model is taking into account where a catalytic effect <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e horm<strong>on</strong>e<br />

auxin is described which is experimentally known to play an important role<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e locati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hair <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. Local analysis, numerical bifurcati<strong>on</strong> analysis<br />

and numerical simulati<strong>on</strong> in 1D are used to <str<strong>on</strong>g>th</str<strong>on</strong>g>e better understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> locati<strong>on</strong> point <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e root hair formati<strong>on</strong>.<br />

References.<br />

[1] Chen W. (2009). Localized Patterns in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Gray-Scott Model: An Asymptotic and Numerical<br />

Study <str<strong>on</strong>g>of</str<strong>on</strong>g> Dynamics and Stability. Vancouver: University <str<strong>on</strong>g>of</str<strong>on</strong>g> British Columbia.<br />

[2] Ir<strong>on</strong>, D., Wei J. and Winter M. (2004). Stability analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Turing patterns generated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Schnakenberg model. J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. 49(4), pp. 358–390.<br />

[3] J<strong>on</strong>es A.R., Kramer E. M., Knox K., Swarup R., Bennett M. J., Lazary C. M., Ottoline<br />

Leyser H. M. & Griers<strong>on</strong> C. S. (2009). Auxin transport <str<strong>on</strong>g>th</str<strong>on</strong>g>rough n<strong>on</strong>-hair cells sustains roo<str<strong>on</strong>g>th</str<strong>on</strong>g>air<br />

development. Nat. Cell. Biol. 11(1), pp.78–84.<br />

[4] Payne R. J. H. & Griers<strong>on</strong> C. S. (2009). A Theoretical Model for ROP Localisati<strong>on</strong> by Auxin<br />

in Arabidopsis Root Hair Cells. PLoS ONE 4(12): e8337. doi:10.1371/journal.p<strong>on</strong>e.0008337<br />

129

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Populati<strong>on</strong> Dynamics; Wednesday, June 29, 11:00<br />

Nicholas F. Britt<strong>on</strong><br />

Dept <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Sciences & Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Biology, Univ <str<strong>on</strong>g>of</str<strong>on</strong>g> Ba<str<strong>on</strong>g>th</str<strong>on</strong>g>, UK<br />

e-mail: n.f.britt<strong>on</strong>@ba<str<strong>on</strong>g>th</str<strong>on</strong>g>.ac.uk<br />

Interspecific kleptoparasitism<br />

Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough interspecific kleptoparasitism is widespread, <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical models have<br />

focussed <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intraspecific case. We develop a game-<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretic model <str<strong>on</strong>g>of</str<strong>on</strong>g> interspecific<br />

kleptoparasitism, ultimately based <strong>on</strong> Ruxt<strong>on</strong> and Moody [1], c<strong>on</strong>sidering<br />

optimal host and parasite strategies. We explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility <str<strong>on</strong>g>th</str<strong>on</strong>g>at, <strong>on</strong> an ecological<br />

time scale, <str<strong>on</strong>g>th</str<strong>on</strong>g>e system does not settle to a steady state but to oscillatory<br />

behaviour in strategy space.<br />

References.<br />

[1] G D Ruxt<strong>on</strong> and A L Moody, The ideal free distributi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> kleptoparasitism, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Theoretical Biology 186, 449–458, 1997.<br />

130

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Epidemic models: Networks and stochasticity II; Thursday, June 30, 11:30<br />

Tom Britt<strong>on</strong><br />

Stockholm University<br />

e-mail: tom.britt<strong>on</strong>@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.su.se<br />

Dynamic networks in dynamic populati<strong>on</strong>s<br />

We study a randomly growing populati<strong>on</strong> (where new individuals are born and<br />

old die) in which edges between individuals appear and disappear randomly over<br />

time. A specific feature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is <str<strong>on</strong>g>th</str<strong>on</strong>g>at individuals are born wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a "social<br />

index" which affects how frequently <str<strong>on</strong>g>th</str<strong>on</strong>g>ey create new neighbours. For <str<strong>on</strong>g>th</str<strong>on</strong>g>is model<br />

we study asymptotic properties valid after a l<strong>on</strong>g time: <str<strong>on</strong>g>th</str<strong>on</strong>g>e degree distributi<strong>on</strong>,<br />

degree correlati<strong>on</strong> and a <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold c<strong>on</strong>diti<strong>on</strong> determining whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er a giant c<strong>on</strong>nected<br />

comp<strong>on</strong>ent exists or not. (Joint work wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ias Lindholm and Tatyana Turova)<br />

131

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Ellen Brooks-Pollock<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cambridge<br />

e-mail: ellen.brooks.pollock@gmail.com<br />

Tuberculosis - <str<strong>on</strong>g>th</str<strong>on</strong>g>e family disease?<br />

Epidemics; Tuesday, June 28, 11:00<br />

Tuberculosis (TB) cases have been l<strong>on</strong>g been noted to cluster wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in households.<br />

In 1820, when <str<strong>on</strong>g>th</str<strong>on</strong>g>e famous English poet John Keats died <str<strong>on</strong>g>of</str<strong>on</strong>g> TB, he was <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ird<br />

in his family to do so: two years earlier, his bro<str<strong>on</strong>g>th</str<strong>on</strong>g>er died <str<strong>on</strong>g>of</str<strong>on</strong>g> TB, and eight years<br />

before <str<strong>on</strong>g>th</str<strong>on</strong>g>at, <str<strong>on</strong>g>th</str<strong>on</strong>g>eir mo<str<strong>on</strong>g>th</str<strong>on</strong>g>er had also died <str<strong>on</strong>g>of</str<strong>on</strong>g> TB. Years later in 1841, a <str<strong>on</strong>g>th</str<strong>on</strong>g>ird bro<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

developed and died <str<strong>on</strong>g>of</str<strong>on</strong>g> TB.<br />

It is unclear whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er clustering <str<strong>on</strong>g>of</str<strong>on</strong>g> cases represents household transmissi<strong>on</strong> or<br />

shared household risk factors. TB is a chr<strong>on</strong>ic disease and <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g timescales between<br />

infecti<strong>on</strong> and disease mean <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> processes can be difficult to<br />

untangle. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is presentati<strong>on</strong>, I examine cross-secti<strong>on</strong>al TB data from households<br />

in Lima, Peru, to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> household transmissi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e average<br />

time between cases, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e immunity afforded by a previous TB infecti<strong>on</strong>. Using<br />

probabilistic and SIR-type models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> household structure, we investigate how<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cases changes during <str<strong>on</strong>g>th</str<strong>on</strong>g>e course <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic. The framework<br />

lends itself for investigating <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple reinfecti<strong>on</strong>s and immunity in<br />

transmissi<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is populati<strong>on</strong>, we estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>at protective immunity c<strong>on</strong>ferred<br />

up to 35% reducti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk <str<strong>on</strong>g>of</str<strong>on</strong>g> disease. Like <str<strong>on</strong>g>th</str<strong>on</strong>g>e Keats family, we find <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

household cases can occur decades apart, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e average time between cases<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in households is 3.8 years.<br />

References.<br />

[1] Brooks-Pollock, Becerra, Goldstein, Cohen and Murray (2011) Epidemiological inference from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tuberculosis cases in households in Lima, Peru The Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Infectious<br />

Diseases, in press.<br />

[2] L<strong>on</strong>gini and Koopman (1982) Household and community transmissi<strong>on</strong> parameters from final<br />

distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong>s in households Biometrics 38 115–126.<br />

[3] Ball, Mollis<strong>on</strong> and Scalia-Tomba (1997) Epidemics wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two levels <str<strong>on</strong>g>of</str<strong>on</strong>g> mixing Annals <str<strong>on</strong>g>of</str<strong>on</strong>g> applied<br />

probability 7 46–89.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Game <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical modelling and optimizati<strong>on</strong> in evoluti<strong>on</strong> and ecology II;<br />

Tuesday, June 28, 14:30<br />

Mark Broom<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Science, City University<br />

e-mail: mark.broom@city.ac.uk<br />

Jan Rychtar<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina<br />

at Greensboro<br />

Evoluti<strong>on</strong> in structured populati<strong>on</strong>s: modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals and groups<br />

Recently models <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong> have begun to incorporate structured populati<strong>on</strong>s,<br />

including spatial structure, <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary processes <strong>on</strong><br />

graphs (evoluti<strong>on</strong>ary graph <str<strong>on</strong>g>th</str<strong>on</strong>g>eory). One limitati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is o<str<strong>on</strong>g>th</str<strong>on</strong>g>erwise quite general<br />

framework is <str<strong>on</strong>g>th</str<strong>on</strong>g>at interacti<strong>on</strong>s are restricted to pairwise <strong>on</strong>es, <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

edges c<strong>on</strong>necting pairs <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals. Yet many animal interacti<strong>on</strong>s can involve<br />

many players, and <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical models also describe such multi-player interacti<strong>on</strong>s.<br />

We shall discuss a more general modelling framework <str<strong>on</strong>g>of</str<strong>on</strong>g> interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> structured<br />

populati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e focus <strong>on</strong> competiti<strong>on</strong> between territorial animals, where each<br />

animal or animal group has a "home range" which overlaps wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a number <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers,<br />

and interacti<strong>on</strong>s between various group sizes are possible. Depending up<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour c<strong>on</strong>cerned we can embed <str<strong>on</strong>g>th</str<strong>on</strong>g>e results <str<strong>on</strong>g>of</str<strong>on</strong>g> different evoluti<strong>on</strong>ary games<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in our structure, as occurs for pairwise games such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e pris<strong>on</strong>er’s dilemma<br />

or <str<strong>on</strong>g>th</str<strong>on</strong>g>e Hawk-Dove game <strong>on</strong> graphs. We discuss some examples toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some<br />

important differences between <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach and evoluti<strong>on</strong>ary graph <str<strong>on</strong>g>th</str<strong>on</strong>g>eory.<br />

133

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Lutz Brusch<br />

Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Germany<br />

e-mail: lutz.brusch@tu-dresden.de<br />

Elan Gin<br />

DKFZ Heidelberg, Germany<br />

Elly M. Tanaka<br />

CRTD Dresden, Germany<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

A model for cyst lumen expansi<strong>on</strong> and size regulati<strong>on</strong> via<br />

fluid secreti<strong>on</strong><br />

Many internal epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial organs derive from cysts, which are tissues comprised <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

bent epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cell layers enclosing a lumen. I<strong>on</strong> accumulati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lumen drives<br />

water influx and c<strong>on</strong>sequently water accumulati<strong>on</strong> and cyst expansi<strong>on</strong>. Lumensize<br />

recogniti<strong>on</strong> is important for <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> organ size. When lumen size<br />

and cyst size are not c<strong>on</strong>trolled, diseases can result; for instance, renal failure <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e kidney. We develop a mechanistic ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> lumen expansi<strong>on</strong> in<br />

order to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms for saturati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cyst grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. We include fluid<br />

accumulati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lumen, osmotic and elastic pressure, i<strong>on</strong> transport and stretchinduced<br />

cell divisi<strong>on</strong>. We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e lumen volume increases in two phases: first,<br />

due to fluid accumulati<strong>on</strong> stretching <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells, <str<strong>on</strong>g>th</str<strong>on</strong>g>en in <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d phase, <str<strong>on</strong>g>th</str<strong>on</strong>g>e volume<br />

increase follows <str<strong>on</strong>g>th</str<strong>on</strong>g>e increase in cell number until proliferati<strong>on</strong> ceases as stretch<br />

forces relax. The model is quantitatively fitted to published data <str<strong>on</strong>g>of</str<strong>on</strong>g> in vitro cyst<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and predicts steady state lumen size as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model parameters.<br />

134

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multi-scale ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver: From intracellular signaling to<br />

intercellular interacti<strong>on</strong>; Wednesday, June 29, 08:30<br />

Lutz Brusch<br />

Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: lutz.brusch@tu-dresden.de<br />

Ca<str<strong>on</strong>g>th</str<strong>on</strong>g>leen Heil<br />

Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Martin Sander<br />

Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Fabian Rost<br />

Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Andreas Deutsch<br />

Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Modelling Endocytosis - from <str<strong>on</strong>g>th</str<strong>on</strong>g>e Molecules to <str<strong>on</strong>g>th</str<strong>on</strong>g>e Liver Cell<br />

Endocytosis is a c<strong>on</strong>served cellular process in eukaryotes by which nutrients are assimilated<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. Internalized material is transported by endosomes and sorted<br />

by means <str<strong>on</strong>g>of</str<strong>on</strong>g> endosome transiti<strong>on</strong>s. Endosome transiti<strong>on</strong>s result from dynamic interacti<strong>on</strong>s<br />

am<strong>on</strong>g Rab GTPases. We focus <strong>on</strong> Rab5-Rab7 and Rab5-Rab4/11 interacti<strong>on</strong>s<br />

underlying respectively early-to-late and early-to-recycling endosome transiti<strong>on</strong>s<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at select am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e degradative, recycling and transcytotic routes in liver<br />

cells. As a model <str<strong>on</strong>g>of</str<strong>on</strong>g> endosome transiti<strong>on</strong>s, we c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial c<strong>on</strong>centrati<strong>on</strong><br />

pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles <str<strong>on</strong>g>of</str<strong>on</strong>g> competing GTPases and <str<strong>on</strong>g>th</str<strong>on</strong>g>e shift <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting c<strong>on</strong>centrati<strong>on</strong> fr<strong>on</strong>t<br />

in a <strong>on</strong>e-dimensi<strong>on</strong>al system across <str<strong>on</strong>g>th</str<strong>on</strong>g>e endosomal membrane. Locally, interacting<br />

GTPases can be modelled as a bistable system <str<strong>on</strong>g>of</str<strong>on</strong>g> ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e cut-out switch or <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

toggle switch type [1]. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e toggle switch, all stable steady state soluti<strong>on</strong>s depend<br />

m<strong>on</strong>ot<strong>on</strong>ically <strong>on</strong> parameters whereas <str<strong>on</strong>g>th</str<strong>on</strong>g>e cut-out switch yields an increasing<br />

soluti<strong>on</strong> which <str<strong>on</strong>g>th</str<strong>on</strong>g>en switches <str<strong>on</strong>g>of</str<strong>on</strong>g>f. We extend <str<strong>on</strong>g>th</str<strong>on</strong>g>ose two models by diffusive spatial<br />

coupling. Heterogeneous initial c<strong>on</strong>diti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong>-diffusi<strong>on</strong> system lead to<br />

spatially alternating GTPase c<strong>on</strong>centrati<strong>on</strong> domains and interjacent c<strong>on</strong>centrati<strong>on</strong><br />

fr<strong>on</strong>ts. In general, <str<strong>on</strong>g>th</str<strong>on</strong>g>e fr<strong>on</strong>t is invading <str<strong>on</strong>g>th</str<strong>on</strong>g>at domain which has <str<strong>on</strong>g>th</str<strong>on</strong>g>e smaller c<strong>on</strong>centrati<strong>on</strong><br />

difference from <str<strong>on</strong>g>th</str<strong>on</strong>g>e unstable saddle soluti<strong>on</strong>. Hence, an intermediate<br />

parameter value exists at which <str<strong>on</strong>g>th</str<strong>on</strong>g>e fr<strong>on</strong>t remains stati<strong>on</strong>ary. The toggle switch<br />

kinetics yields <str<strong>on</strong>g>th</str<strong>on</strong>g>is expected behaviour whereas <str<strong>on</strong>g>th</str<strong>on</strong>g>e cut-out switch system shows<br />

novel behaviour. Corresp<strong>on</strong>ding to <str<strong>on</strong>g>th</str<strong>on</strong>g>e toggle switch properties, we propose <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is mechanism underlies <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> Rab5-Rab4/11 domains during<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e early-to-recycling endosome transiti<strong>on</strong>. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatially extended cut-out switch system reinforces <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cut-out<br />

switch for early-to-late endosome transiti<strong>on</strong>s. Moreover, we link <str<strong>on</strong>g>th</str<strong>on</strong>g>is molecular<br />

understanding to <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell level by means <str<strong>on</strong>g>of</str<strong>on</strong>g> an agent-based model representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> and biophysical interacti<strong>on</strong>s between early endosomes wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <strong>on</strong>e cell.<br />

Simulati<strong>on</strong> results identify critical regulatory steps <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trol efficient cargo flux<br />

which is essential for liver cells.<br />

References.<br />

[1] P. del C<strong>on</strong>te-Zerial, L. Brusch, J. Rink, C. Collinet, Y. Kalaidzidis, M. Zerial and A. Deutsch,<br />

Membrane identity and GTPase cascades regulated by toggle and cut-out switches, Mol. Syst.<br />

Biol. 4, 206, 2008.<br />

135

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Keywords: endocytosis, Rab GTPAses, reacti<strong>on</strong>-diffusi<strong>on</strong> system, travelingwave<br />

soluti<strong>on</strong>s, cut-out switch, toggle switch<br />

136

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Heart rate dynamics: models and measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity (part II);<br />

Wednesday, June 29, 17:00<br />

Teodor Buchner<br />

Cardiovascular Physics Group, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, Warsaw University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: buchner@if.pw.edu.pl<br />

Oscillati<strong>on</strong>s and synchr<strong>on</strong>izati<strong>on</strong> in human circulatory<br />

system<br />

Human cardiovascular system exhibits interesting dynamics, which is expressed<br />

in beat-by-beat changes <str<strong>on</strong>g>of</str<strong>on</strong>g> such variables as heart rate (interbeat interval) and blood<br />

pressure. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e system is complex, <str<strong>on</strong>g>th</str<strong>on</strong>g>e origin <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is dynamics is complex as well.<br />

Part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics is <str<strong>on</strong>g>of</str<strong>on</strong>g> neural or electrophysiological nature, depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

functi<strong>on</strong>al state <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart muscle, which is an example <str<strong>on</strong>g>of</str<strong>on</strong>g> an active medium, subject<br />

to neural c<strong>on</strong>trol. Ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics is related wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vascular<br />

resp<strong>on</strong>se to <str<strong>on</strong>g>th</str<strong>on</strong>g>e hemodynamic heart acti<strong>on</strong>. This resp<strong>on</strong>se depends <strong>on</strong> vascular resistance<br />

and <strong>on</strong> elastic properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vascular wall. The resulting blood pressure<br />

and chemical properties (pH) are c<strong>on</strong>stantly m<strong>on</strong>itored by specific receptors <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

initiate neural reflexes, which applies neural c<strong>on</strong>trol to specific variables. There<br />

are many independent mechanisms <str<strong>on</strong>g>th</str<strong>on</strong>g>at may be activated in order to resp<strong>on</strong>d to<br />

certain fluctuati<strong>on</strong>s. Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristic times <str<strong>on</strong>g>of</str<strong>on</strong>g> different c<strong>on</strong>trol loops<br />

may differ by order <str<strong>on</strong>g>of</str<strong>on</strong>g> magnitude.<br />

Ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er source <str<strong>on</strong>g>of</str<strong>on</strong>g> complex oscillati<strong>on</strong>s, crucially important for homeostasis is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e respiratory system. All <str<strong>on</strong>g>th</str<strong>on</strong>g>e systems are interrelated in a complex way and give<br />

rise to <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex cardiovascular dynamics. One <str<strong>on</strong>g>of</str<strong>on</strong>g> interesting phenomena <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

arises in such a system is <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiorespiratory synchr<strong>on</strong>izati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e related phenomen<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interdependence between short-term dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> blood pressure,<br />

heart rate and brea<str<strong>on</strong>g>th</str<strong>on</strong>g>ing. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> problems will be addressed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e talk.<br />

137

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

III; Tuesday, June 28, 17:00<br />

Svetlana Bunimovich<br />

University Center, Ariel, Israel<br />

e-mail: SvetlanaBu@ariel.ac.il<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e activati<strong>on</strong><br />

killer cells after <str<strong>on</strong>g>th</str<strong>on</strong>g>e BCG treatment in bladder cancer<br />

Bladder cancer (BC) is <str<strong>on</strong>g>th</str<strong>on</strong>g>e most frequently occurring urological cancer and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

fif<str<strong>on</strong>g>th</str<strong>on</strong>g> most comm<strong>on</strong> cancer am<strong>on</strong>g men, accounting for approximately 200,000 new<br />

cases worldwide annually. I would like to present a new ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> superficial bladder cancer and <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>th</str<strong>on</strong>g>ereup<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> immuno<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e administrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Bacillus Calmette-Guerin (BCG) combined<br />

or not wi<str<strong>on</strong>g>th</str<strong>on</strong>g> interleukin-2 (IL-2). Intravesical instillati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> BCG performed<br />

after surgical removal <str<strong>on</strong>g>of</str<strong>on</strong>g> tumors represents an established treatment wi<str<strong>on</strong>g>th</str<strong>on</strong>g> approximately<br />

50% success rate. So far, attempts to improve <str<strong>on</strong>g>th</str<strong>on</strong>g>is efficiency have not led to<br />

essential changes. However, c<strong>on</strong>vincing clinical results have been reported <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> IL-2 to BCG, even <str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>is is still not applied in current practice.<br />

The present model provides insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical outcomes arising in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

bladder from <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> immune cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> tumor cells in <str<strong>on</strong>g>th</str<strong>on</strong>g>e course <str<strong>on</strong>g>of</str<strong>on</strong>g> BCG<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy associated or not wi<str<strong>on</strong>g>th</str<strong>on</strong>g> IL-2. Specifically, from <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong>s performed<br />

using nine ordinary and n<strong>on</strong>-linear differential equati<strong>on</strong>s we obtained indicati<strong>on</strong>s <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at would result in successful bladder cancer treatment. We show<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at immune cells effector lymphocytes, natural killer cells and antigen-presenting<br />

cells expand and reach a sustainable plateau under BCG treatment, which may<br />

account for its beneficial effect, resulting from inflammatory "side-effects" which<br />

eliminate residual or eventual newly arising tumor cells, providing <str<strong>on</strong>g>th</str<strong>on</strong>g>us protecti<strong>on</strong><br />

from fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er cancer development.<br />

138

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Informati<strong>on</strong>, human behaviour and infecti<strong>on</strong> c<strong>on</strong>trol; Saturday, July 2, 08:30<br />

Bruno Bu<strong>on</strong>omo<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Applicati<strong>on</strong>s, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Naples<br />

Federico II, via Cintia, 80126 Naples, Italy<br />

e-mail: bu<strong>on</strong>omo@unina.it<br />

N<strong>on</strong>linear stability <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemic models including<br />

informati<strong>on</strong>-related human behaviour<br />

We study <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>linear stability properties <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemic models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a feedback<br />

mechanism, which describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong>, and <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong>- related<br />

delays, <strong>on</strong> human behaviour [3,4]. In particular, we give a special example<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> two stability me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: <str<strong>on</strong>g>th</str<strong>on</strong>g>e geometric me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for global stability,<br />

due to Li and Muldowney [5], and a Lyapunov-based approach, which provides<br />

necessary and sufficient c<strong>on</strong>diti<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e local n<strong>on</strong>linear stability <str<strong>on</strong>g>of</str<strong>on</strong>g> equilibria [6].<br />

Some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e results presented here are included in <str<strong>on</strong>g>th</str<strong>on</strong>g>e recent papers [1] and [2].<br />

References.<br />

[1] B. Bu<strong>on</strong>omo, A. d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio, D. Lacitignola, Global stability <str<strong>on</strong>g>of</str<strong>on</strong>g> an SIR epidemic model wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

informati<strong>on</strong> dependent vaccinati<strong>on</strong>, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci., 216 9–16 (2008).<br />

[2] B. Bu<strong>on</strong>omo, A. d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio, D. Lacitignola, Rati<strong>on</strong>al exempti<strong>on</strong> to vaccinati<strong>on</strong> for n<strong>on</strong>-fatal<br />

SIS diseases: globally stable and oscillatory endemicity. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci. Eng., 7 561–578 (2010).<br />

[3] A. d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio, P. Manfredi, Informati<strong>on</strong>-related changes in c<strong>on</strong>tact patterns may trigger oscillati<strong>on</strong>s<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e endemic prevalence <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases, J. Theor. Biol., 256 473–478 (2009).<br />

[4] A. d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio, P. Manfredi, E. Salinelli, Vaccinating behaviour, informati<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> SIR vaccine preventable diseases, Theor. Popul. Biol. 71 301–317 (2007).<br />

[5] M. Y. Li, J. S. Muldowney, A geometric approach to global-stability problems, SIAM J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

Anal., 27 1070–1083 (1996).<br />

[6] S. Ri<strong>on</strong>ero, A rigorous reducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e L 2 -stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong>s to a n<strong>on</strong>linear binary<br />

reacti<strong>on</strong>-diffusi<strong>on</strong> system <str<strong>on</strong>g>of</str<strong>on</strong>g> P.D.E.s to <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong>s to a linear binary system<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> ODE’s, J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Anal. Appl. 319 377–397 (2006).<br />

139

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Z. Burda<br />

Marian Smoluchowski Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics and Mark Kac Complex<br />

Systems Research Centre, Jagell<strong>on</strong>ian University, Reym<strong>on</strong>ta 4, 30-059<br />

Krakow, Poland<br />

e-mail: zdzislaw.burda@uj.edu.pl<br />

A. Krzywicki<br />

Univ Paris-Sud, LPT ; CNRS, UMR8627, Orsay, F-91405, France<br />

e-mail: Andre.Krzywicki@<str<strong>on</strong>g>th</str<strong>on</strong>g>.u-psud.fr<br />

O.C. Martin<br />

Univ Paris-Sud, LPTMS ; CNRS, UMR8626, F-91405, Orsay, France,<br />

INRA, CNRS, UMR0320 / UMR 8120 Génétique Végétale, F-91190 Gifsur-Yvette,<br />

France<br />

e-mail: olivier.martin@u-psud.fr<br />

M. Zagorski<br />

Marian Smoluchowski Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics and Mark Kac Complex<br />

Systems Research Centre, Jagell<strong>on</strong>ian University, Reym<strong>on</strong>ta 4, 30-059<br />

Krakow, Poland<br />

e-mail: Marcin.Zagorskii@gmail.com<br />

Emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> sparsity and motifs in gene regulatory<br />

networks<br />

We c<strong>on</strong>sider a simple model <str<strong>on</strong>g>of</str<strong>on</strong>g> gene regulatory dynamics derived from <str<strong>on</strong>g>th</str<strong>on</strong>g>e statistical<br />

framework describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e binding <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong> factors to DNA. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

networks representing essential interacti<strong>on</strong>s in gene regulati<strong>on</strong> have a minimal c<strong>on</strong>nectivity<br />

compatible wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a given functi<strong>on</strong>. We discuss statistical properties using<br />

M<strong>on</strong>te Carlo sampling. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at functi<strong>on</strong>al networks have a specific motifs statistics.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e case where <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulatory networks are to exhibit multi-stability, we<br />

find a high frequency <str<strong>on</strong>g>of</str<strong>on</strong>g> gene pairs <str<strong>on</strong>g>th</str<strong>on</strong>g>at are mutually inhibitory and self-activating.<br />

In c<strong>on</strong>trast, networks having periodic gene expressi<strong>on</strong> patterns (mimicking for instance<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cell cycle) have a high frequency <str<strong>on</strong>g>of</str<strong>on</strong>g> bifan-like motifs involving four genes<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> at least <strong>on</strong>e activating and <strong>on</strong>e inhibitory interacti<strong>on</strong>.<br />

140<br />

;

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Reinhard Bürger<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Vienna<br />

e-mail: reinhard.buerger@univie.ac.at<br />

Ada Akerman<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Vienna<br />

Populati<strong>on</strong> Genetics; Friday, July 1, 14:30<br />

The effects <str<strong>on</strong>g>of</str<strong>on</strong>g> linkage and gene flow <strong>on</strong> local adaptati<strong>on</strong>: A<br />

two-locus c<strong>on</strong>tinent-island model<br />

We study a populati<strong>on</strong>-genetic model <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong> in a derived (island) populati<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at experiences altered envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s and maladaptive gene flow<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e ancestral (c<strong>on</strong>tinental) populati<strong>on</strong>. It is assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at locally advantageous<br />

mutati<strong>on</strong>s have arisen <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e island at two linked loci. Gene flow in c<strong>on</strong>cert<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> selecti<strong>on</strong> induces substantial linkage disequilibrium. This has a number <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

c<strong>on</strong>sequences for evoluti<strong>on</strong>. The central ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical result is an explicit characterizati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> all possible equilibrium c<strong>on</strong>figurati<strong>on</strong>s. From <str<strong>on</strong>g>th</str<strong>on</strong>g>is, we deduce explicit<br />

expressi<strong>on</strong>s for two measures <str<strong>on</strong>g>of</str<strong>on</strong>g> linkage disequilibrium. We determine explicitly<br />

how <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximum amount <str<strong>on</strong>g>of</str<strong>on</strong>g> gene flow <str<strong>on</strong>g>th</str<strong>on</strong>g>at admits <str<strong>on</strong>g>th</str<strong>on</strong>g>e preservati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e locally<br />

adapted haplotype depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> recombinati<strong>on</strong> and selecti<strong>on</strong>. We also<br />

study <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> beneficial mutants <str<strong>on</strong>g>of</str<strong>on</strong>g> small effect <str<strong>on</strong>g>th</str<strong>on</strong>g>at are linked to an already<br />

present, locally adapted allele. As a c<strong>on</strong>sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> linkage disequilibrium, mutants<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> much smaller effect can invade successfully <str<strong>on</strong>g>th</str<strong>on</strong>g>an predicted by naive single-locus<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eory. This raises interesting questi<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic architecture,<br />

in particular, about <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> clusters <str<strong>on</strong>g>of</str<strong>on</strong>g> tightly linked, slightly beneficial<br />

mutati<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> recombinati<strong>on</strong> and chromosome inversi<strong>on</strong>s. Finally,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> linkage <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e degree <str<strong>on</strong>g>of</str<strong>on</strong>g> local adaptati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong> load is<br />

explored.<br />

References.<br />

[1] Bürger, R., and A. Akerman. The effects <str<strong>on</strong>g>of</str<strong>on</strong>g> linkage and gene flow <strong>on</strong> local adaptati<strong>on</strong>: A<br />

two-locus c<strong>on</strong>tinent-island model. Submitted manuscript (2011)<br />

141

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models in Eco-epidemiology II; Wednesday, June 29, 11:00<br />

J.-B. Burie<br />

UMR CNRS 5251 IMB<br />

INRIA Bordeaux Sud-Ouest, EPI Anubis<br />

Université <str<strong>on</strong>g>of</str<strong>on</strong>g> Bordeaux<br />

3 ter, Place de la Victoire, 33076 Bordeaux, France<br />

e-mail: jean-baptiste.burie@u-bordeaux2.fr<br />

A. Ducrot<br />

UMR CNRS 5251 IMB<br />

INRIA Bordeaux Sud-Ouest, EPI Anubis<br />

Université <str<strong>on</strong>g>of</str<strong>on</strong>g> Bordeaux<br />

3 ter, Place de la Victoire, 33076 Bordeaux, France<br />

e-mail: arnaud.ducrot@u-bordeaux2.fr<br />

Homogenizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a model <str<strong>on</strong>g>of</str<strong>on</strong>g> propagati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a fungal<br />

disease in a heterogenous crop field<br />

For producti<strong>on</strong> purpose, crop fields usually display a high degree <str<strong>on</strong>g>of</str<strong>on</strong>g> periodic<br />

spatial structure: vineyards are made <str<strong>on</strong>g>of</str<strong>on</strong>g> vine rows, orchards <str<strong>on</strong>g>of</str<strong>on</strong>g> regularly spaced<br />

trees...<br />

To model <str<strong>on</strong>g>th</str<strong>on</strong>g>is, we introduce a small parameter ε > 0. The crop field, assumed<br />

to be large, is described by a domain Ω ⊂ R N , N = 1, 2 or 3. Let Y = [0, 1] N <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

reference cell, and Y1 ⊂ Y . The set Y1 describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e part <str<strong>on</strong>g>of</str<strong>on</strong>g> Y occupied by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

crop. The domain Ω is <str<strong>on</strong>g>th</str<strong>on</strong>g>en equal to Ω ε 1 ∪ Ω ε 2 where<br />

Ω ε 1 = {x ∈ Ω, χY1(x/ε) = 1}, Ω ε 2 = {x ∈ Ω, χY1(x/ε) = 0}.<br />

For example, in a orchard or in a vineyard, each cell Y could c<strong>on</strong>tain a single tree<br />

or vine stock. For a vineyard, each cell Y could also c<strong>on</strong>tain an entire row <str<strong>on</strong>g>of</str<strong>on</strong>g> vine<br />

stocks. This modeling formalism also applies to <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> cultivar mixture fields<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at could be used for disease c<strong>on</strong>trol [2].<br />

We study <str<strong>on</strong>g>th</str<strong>on</strong>g>e propagati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a fungal disease over <str<strong>on</strong>g>th</str<strong>on</strong>g>is field. The following<br />

model is a simplified versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>e in [1]. The vectors <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e propagati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease are <str<strong>on</strong>g>th</str<strong>on</strong>g>e spores produced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e fungus lesi<strong>on</strong>s. We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese spores disperse according to a Fickian diffusi<strong>on</strong> process. Moreover <str<strong>on</strong>g>th</str<strong>on</strong>g>ey may<br />

disperse at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell range, hence <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> coefficient will be or order ε 2 , or at<br />

l<strong>on</strong>g range. A very simple model for <str<strong>on</strong>g>th</str<strong>on</strong>g>is is given by <str<strong>on</strong>g>th</str<strong>on</strong>g>e following system <str<strong>on</strong>g>of</str<strong>on</strong>g> partial<br />

differential equati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e spores producti<strong>on</strong> and dispersal, coupled<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an ordinary differential equati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> SI type <str<strong>on</strong>g>th</str<strong>on</strong>g>at describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e inoculati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e crop by <str<strong>on</strong>g>th</str<strong>on</strong>g>e fungus:<br />

⎧<br />

⎪⎨<br />

⎪⎩<br />

142<br />

∂Sε S (t, x)<br />

− ε<br />

∂t<br />

2 ∇.(dS(x, x/ε)∇S ε S(t, x)) + S ε S(t, x) = (1 − P (t, x, x/ε))I ε (t, x),<br />

∂Sε L (t, x)<br />

− ∆S<br />

∂t<br />

ε L(t, x) + S ε L(t, x) = P (t, x, x/ε)I ε (t, x),<br />

∂I ε (t, x)<br />

∂t<br />

= χY1<br />

<br />

x<br />

<br />

(S<br />

ε<br />

ε S(t, x) + S ε L(t, x)) (1 − I ε (t, x))

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

for t > 0 and x ∈ Ω a regular bounded open subset <str<strong>on</strong>g>of</str<strong>on</strong>g> R N , supplemented wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Neumann boundary c<strong>on</strong>diti<strong>on</strong>s<br />

and wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some initial data.<br />

∂νS ε S(t, x) = ∂νS ε L(t, x) = 0, ∀t > 0 and x ∈ ∂Ω<br />

The state variables are: Sε S <str<strong>on</strong>g>th</str<strong>on</strong>g>e short range spores density, Sε L <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g range<br />

spores density and Iε <str<strong>on</strong>g>th</str<strong>on</strong>g>e diseased foliar surface density. The ode describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Iε is n<strong>on</strong> trivial <strong>on</strong>ly if x ∈ Y1.<br />

Now we are able to show <str<strong>on</strong>g>th</str<strong>on</strong>g>at as ε tend to 0, up to a subsequence, <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model c<strong>on</strong>verges towards <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a homogenized problem. This homogenized<br />

problem is a coupled system <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s at <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic scale (in<br />

Ω) and at <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic <strong>on</strong>e (in Y ). To prove <str<strong>on</strong>g>th</str<strong>on</strong>g>is result, we use standard results<br />

from homogeneizati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eory, see e.g. [3]. The benefit from <str<strong>on</strong>g>th</str<strong>on</strong>g>is homogeneizati<strong>on</strong><br />

process is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical computati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e homogenized<br />

problem is easier <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e original <strong>on</strong>e.<br />

References.<br />

[1] B. Burie, A. Cal<strong>on</strong>nec, M. Langlais, Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a fungal disease over a vineyard,<br />

in: A. Deutsch, R. Bravo de la Parra, R. deBoer, O. Diekmann, P. Jagers, E. Kisdi, M.<br />

Kretzschmar, P. Lansky, H. Metz (Eds.), Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Systems, vol.<br />

II, Birkhauser, Bost<strong>on</strong>, 2007, pp. 11-21.<br />

[2] F. Didelot, L. Brun and L. Parisi, Effects <str<strong>on</strong>g>of</str<strong>on</strong>g> cultivar mixtures <strong>on</strong> scab c<strong>on</strong>trol in apple orchards,<br />

Plant Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, 56 (2007), pp. 1014-1022.<br />

[3] G. Allaire,Homogeneizati<strong>on</strong> and two-scale c<strong>on</strong>vergence, Siam J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Anal., 23 (1992), pp.<br />

1482-1518.<br />

143

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cellular Systems Biology; Tuesday, June 28, 14:30<br />

Peter Buske<br />

Interdisciplinary Center for Bioinformatics, Leipzig University<br />

e-mail: buske@izbi.uni-leipzig.de<br />

Markus Loeffler<br />

Interdisciplinary Center for Bioinformatics, Leipzig University<br />

e-mail: markus.loeffler@imise..uni-leipzig.de<br />

Joerg Galle<br />

Interdisciplinary Center for Bioinformatics, Leipzig University<br />

e-mail: galle@izbi.uni-leipzig.de<br />

Modelling in vitro crypt formati<strong>on</strong><br />

In vitro cultures <str<strong>on</strong>g>of</str<strong>on</strong>g> intestinal tissue have been tried for decades. Only recently<br />

Sato and co-workers succeeded in establishing organoid cultures from single cells [1].<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cultures intestinal cells expressing <str<strong>on</strong>g>th</str<strong>on</strong>g>e stem cell marker Lgr5 form cryptlike<br />

structures similar to <str<strong>on</strong>g>th</str<strong>on</strong>g>ose found in vivo. The mechanisms <str<strong>on</strong>g>th</str<strong>on</strong>g>at underlie <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese spatially-organised structures are currently a matter <str<strong>on</strong>g>of</str<strong>on</strong>g> debate.<br />

We here present a 3D biophysical model <str<strong>on</strong>g>of</str<strong>on</strong>g> de novo crypt formati<strong>on</strong> in vitro. The<br />

model builds <strong>on</strong> an individual cell-based model <str<strong>on</strong>g>of</str<strong>on</strong>g> crypt dynamics recently published<br />

by us [2]. We extended <str<strong>on</strong>g>th</str<strong>on</strong>g>is model by introducing a flexible basal membrane. This<br />

membrane can be reorganised by cells showing active matrix metabolism.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is model, shape changes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basal membrane result from a feedback<br />

loop between its curvature and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Wnt-activity <str<strong>on</strong>g>of</str<strong>on</strong>g> adherent cells. Thereby, increased<br />

Wnt-activity increases <str<strong>on</strong>g>th</str<strong>on</strong>g>e adhesi<strong>on</strong> streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells and <str<strong>on</strong>g>th</str<strong>on</strong>g>us, forces<br />

local shape changes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basal membrane. We dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

crypt-like structures wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>is model depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e elasticity and stiffness <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e basal membrane and <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e adhesi<strong>on</strong> properties and matrix metabolisms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

different cell types.<br />

We suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed mechanism to be a principal <strong>on</strong>e in epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial gland<br />

formati<strong>on</strong>.<br />

References.<br />

[1] T. Sato, Single Lgr5 stem cells build crypt-villus structures in vitro wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out a mesenchymal<br />

niche. Nature 459(7244):262-51–2.<br />

[2] P. Buske, A comprehensive model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal stem cell and tissue organisati<strong>on</strong> in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e intestinal crypt. PLoS Comput Biol. 7(1): e1001045.<br />

144

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

K. Buszko<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Foundati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Bio-medical Science and<br />

Medical Informatics,Nicolaus Copernicus University, Collegium Medicum<br />

in Bydgoszcz, ul. Jagiellońska 13, 85-094 Bydgoszcz, Poland<br />

e-mail: buszko@cm.umk.pl<br />

K. Stefański<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Foundati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Bio-medical Science and<br />

Medical Informatics,Nicolaus Copernicus University, Collegium Medicum<br />

in Bydgoszcz, ul. Jagiellońska 13, 85-094 Bydgoszcz, Poland<br />

e-mail: stefan@phys.uni.torun.pl<br />

Transient chaos measurements using finite-time Lyapunov<br />

exp<strong>on</strong>ents in model <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> dynamics<br />

The family <str<strong>on</strong>g>of</str<strong>on</strong>g> logistic maps is <str<strong>on</strong>g>th</str<strong>on</strong>g>e best known n<strong>on</strong>linear model <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong><br />

dynamics. The typical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model is c<strong>on</strong>centrated <strong>on</strong> its asymptotic<br />

behaviour. Special attenti<strong>on</strong> is payed to properties <str<strong>on</strong>g>of</str<strong>on</strong>g> trajectories generated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

maps inside periodic windows, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e periodic behaviour occurs [1]-[3]. However<br />

such periodic behaviour is preceded by chaotic transient behaviour. The durati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> such transient chaos can be prol<strong>on</strong>ged [4],[5] .<br />

We propose a model for estimating <str<strong>on</strong>g>th</str<strong>on</strong>g>e durati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> transient chaos based <strong>on</strong><br />

calculati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> finite-time Lyapunov exp<strong>on</strong>ents. Lyapunov exp<strong>on</strong>ents bel<strong>on</strong>g to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

most useful tools applied for measuring sensitivity to initial c<strong>on</strong>diti<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> asymptotic chaos. We used Lyapunov exp<strong>on</strong>ents for characterizing sensitivity<br />

to initial c<strong>on</strong>diti<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> transient chaos. Before doing <str<strong>on</strong>g>th</str<strong>on</strong>g>at we modify<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e noti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> finite-time Lyapunov exp<strong>on</strong>ent averaging <str<strong>on</strong>g>th</str<strong>on</strong>g>em over a set <str<strong>on</strong>g>of</str<strong>on</strong>g> initial<br />

c<strong>on</strong>diti<strong>on</strong>s and we report results <str<strong>on</strong>g>of</str<strong>on</strong>g> tests providing evidence in favor <str<strong>on</strong>g>of</str<strong>on</strong>g> correctness<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> such an approach. We also present a model reproducing correctly variati<strong>on</strong> in<br />

time <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e finite-time Lyapunov exp<strong>on</strong>ents corresp<strong>on</strong>ding to transient chaos.The<br />

dependence <strong>on</strong> time is verified by comparing <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretically predicted values wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ose obtained numerically.<br />

References.<br />

[1] Hasselblatt B. and Katok A., A first Course in Dynamics, Cambrige, Cambrige University<br />

Press, 2003.<br />

[2] Schuster H. G., Deterministic Chaos, Germany, VCH Verlagsgesellschaft mbH, 1988.<br />

[3] Collet P. and Eckmann J.-P., Iterated Maps <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Interval as Dynamical Systems, Bost<strong>on</strong>,<br />

Birkhauser - Bost<strong>on</strong>, 1980.<br />

[4] Jacobs J., Ott E. and Hunt R.,Scaling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e durati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> chaotic transients in windows <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

attracting periodicity, Physical Review E, 1997, vol. 56, 6508.<br />

[5] Buszko K. and Stefański K.,Measuring transient chaos in n<strong>on</strong>linear <strong>on</strong>e- and two-dimensi<strong>on</strong>al<br />

maps, Chaos, Solit<strong>on</strong>s and Fractals, 2006, vol. 27, 630.<br />

145

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Biological Systems; Tuesday, June 28, 17:00<br />

Anna Cai<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> California, Irvine<br />

e-mail: acai@uci.edu<br />

Kelly Radtke<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Developmental and Cell Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> California,<br />

Irvine<br />

Thomas F. Schilling<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Developmental and Cell Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> California,<br />

Irvine<br />

Qing Nie<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics , University <str<strong>on</strong>g>of</str<strong>on</strong>g> California, Irvine<br />

Critical roles for intracellular binding proteins in creating a<br />

robust retinoic acid morphogen gradient<br />

Retinoic acid (RA) is a vitamin A derivative <str<strong>on</strong>g>th</str<strong>on</strong>g>at acts as a graded morphogen to<br />

promote posterior cell fates in <str<strong>on</strong>g>th</str<strong>on</strong>g>e vertebrate central nervous system (CNS). CNS<br />

development occurs normally over a 20-fold range <str<strong>on</strong>g>of</str<strong>on</strong>g> RA c<strong>on</strong>centrati<strong>on</strong>s, indicating<br />

a remarkable degree <str<strong>on</strong>g>of</str<strong>on</strong>g> gradient robustness.<br />

Cellular retinoic acid binding proteins (Crabps) transport RA intracellularly<br />

but <str<strong>on</strong>g>th</str<strong>on</strong>g>eir roles in morphogen gradient formati<strong>on</strong> remain unclear. Using a combinati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> computati<strong>on</strong>al and experimental approaches in zebrafish, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

positive and negative feedback by Crabps <strong>on</strong> RA signaling dramatically improves<br />

robustness. Crabps improve robustness wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in an optimal c<strong>on</strong>centrati<strong>on</strong> range and<br />

transport <str<strong>on</strong>g>of</str<strong>on</strong>g> Crabp bound RA to Cyp26 degradati<strong>on</strong> enzymes appears to be critical<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>ese robustness gains. These results suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at Crabps are essential for modulating<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e RA signaling gradient in <str<strong>on</strong>g>th</str<strong>on</strong>g>e face <str<strong>on</strong>g>of</str<strong>on</strong>g> varying levels <str<strong>on</strong>g>of</str<strong>on</strong>g> dietary vitamin A.<br />

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Immunology; Wednesday, June 29, 17:00<br />

Yin Cai<br />

Research Group Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Systems, German Cancer Research<br />

Center, Heidelberg, Germany<br />

e-mail: yin.cai@bioquant.uni-heidelberg.de<br />

Thomas Höfer<br />

Research Group Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Systems, German Cancer Research<br />

Center, Heidelberg, Germany<br />

Spatially-resolved ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> T cell antigen<br />

recogniti<strong>on</strong><br />

T cells play a crucial role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptive immune resp<strong>on</strong>se. Interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

specific antigens initiate T cell signaling but also ensure <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e majority <str<strong>on</strong>g>of</str<strong>on</strong>g> selfreactive<br />

cells are selectively deleted in <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ymus during its maturati<strong>on</strong>. However,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying mechanisms remain unclear as to why T cells can reliably distinguish<br />

cognate antigens from o<str<strong>on</strong>g>th</str<strong>on</strong>g>er peptides <str<strong>on</strong>g>th</str<strong>on</strong>g>at have <strong>on</strong>ly slightly weaker affinity<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e T cell receptor (TCR). Recent data indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e clustering <str<strong>on</strong>g>of</str<strong>on</strong>g> TCRs at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e interface <str<strong>on</strong>g>of</str<strong>on</strong>g> T cell and antigen-presenting cell could be <str<strong>on</strong>g>th</str<strong>on</strong>g>e key to <str<strong>on</strong>g>th</str<strong>on</strong>g>e exquisite<br />

ligand recogniti<strong>on</strong> specificity. We develop a spatially-resolved ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model<br />

based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong>-diffusi<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> individual TCRs. We use stochastic<br />

M<strong>on</strong>te Carlo simulati<strong>on</strong>s to analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e model and its ability to exhibit TCR clustering.<br />

The model aims at rati<strong>on</strong>alizing experiments <str<strong>on</strong>g>th</str<strong>on</strong>g>at have dem<strong>on</strong>strated a<br />

sharp affinity <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold for <str<strong>on</strong>g>th</str<strong>on</strong>g>ymic selecti<strong>on</strong>. It will help us to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

TCR clustering and <str<strong>on</strong>g>th</str<strong>on</strong>g>e core elements initializing T cell signaling during antigen<br />

recogniti<strong>on</strong> and will inform new experimental work.<br />

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Undergraduate Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Educati<strong>on</strong> Bey<strong>on</strong>d BIO 2010 (Part II);<br />

Saturday, July 2, 08:30<br />

Hannah Callender<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Portland<br />

What My Biology Students Taught Me About Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

Many colleges and universities struggle wi<str<strong>on</strong>g>th</str<strong>on</strong>g> finding ways to meet <str<strong>on</strong>g>th</str<strong>on</strong>g>e quantitative<br />

needs <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir biology and life science majors. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e University <str<strong>on</strong>g>of</str<strong>on</strong>g> Portland,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese students have in <str<strong>on</strong>g>th</str<strong>on</strong>g>e past been enrolled in <str<strong>on</strong>g>th</str<strong>on</strong>g>e traditi<strong>on</strong>al calculus sequence,<br />

where <str<strong>on</strong>g>th</str<strong>on</strong>g>e majority <str<strong>on</strong>g>of</str<strong>on</strong>g> applicati<strong>on</strong>s are geared heavily towards engineering<br />

and physics. Our biology and life science majors come out <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is course not <strong>on</strong>ly<br />

feeling as <str<strong>on</strong>g>th</str<strong>on</strong>g>ough calculus had no c<strong>on</strong>necti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir discipline, but also struggling<br />

more <str<strong>on</strong>g>th</str<strong>on</strong>g>an students in o<str<strong>on</strong>g>th</str<strong>on</strong>g>er disciplines, possibly from lack <str<strong>on</strong>g>of</str<strong>on</strong>g> motivati<strong>on</strong>. Here I<br />

will share my experiences in <str<strong>on</strong>g>th</str<strong>on</strong>g>e development and implementati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a first semester<br />

biocalculus course and what I learned from my students, including <str<strong>on</strong>g>th</str<strong>on</strong>g>eir beliefs<br />

about ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics pre- and post-biocalculus as well as similarities and differences<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir styles <str<strong>on</strong>g>of</str<strong>on</strong>g> learning ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics.<br />

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Ecosystems Dynamics; Tuesday, June 28, 11:00<br />

Baba Issa Camara<br />

UMR 077 Plant Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, French Nati<strong>on</strong>al Agricultural Institute,<br />

42, rue Georges Morel - BP 60057 49071 Beaucouzé, Angers, France.<br />

e-mail: bicamara@angers.inra.fr<br />

Natalia Sapoukhina<br />

UMR 077 Plant Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, French Nati<strong>on</strong>al Agricultural Institute,<br />

42, rue Georges Morel - BP 60057 49071 Beaucouzé, Angers, France.<br />

e-mail: natalia.sapoukhina@angers.inra.fr<br />

Estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stratified dispersal rate<br />

The establishment and spread <str<strong>on</strong>g>of</str<strong>on</strong>g> invading organisms have dramatic c<strong>on</strong>sequences<br />

for ecosystems. Many organisms expand <str<strong>on</strong>g>th</str<strong>on</strong>g>eir range by being transferred passively<br />

over short and l<strong>on</strong>g distances simultaneously, <str<strong>on</strong>g>th</str<strong>on</strong>g>us resulting in a stratified dispersal<br />

process [1, 2] . The stochastic events <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g-distance dispersal complicate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread rate <str<strong>on</strong>g>of</str<strong>on</strong>g> an invading populati<strong>on</strong>. Our goal is to measure <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

accelerating effect <str<strong>on</strong>g>of</str<strong>on</strong>g> sec<strong>on</strong>dary foci created by l<strong>on</strong>g-distance dispersal <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong><br />

spread rate. We developed a spatially explicit host-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen model describing<br />

independently c<strong>on</strong>tinuous short- and stochastic l<strong>on</strong>g-distance dispersal processes.<br />

Comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> exact soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusive spread wi<str<strong>on</strong>g>th</str<strong>on</strong>g> results <str<strong>on</strong>g>of</str<strong>on</strong>g> M<strong>on</strong>te Carlo simulati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> stratified dispersal allowed us to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g-distance<br />

dispersal events <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread rate. Due to independent descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two<br />

modes <str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal, <str<strong>on</strong>g>th</str<strong>on</strong>g>e developed model can be parameterized easily and used in<br />

epidemiology. The explicit representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two-dimensi<strong>on</strong>al habitat allows<br />

coupling our model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a landscape optimizati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od to design landscapes<br />

unfavorable to fast epidemics spread.<br />

References.<br />

[1] Hengeveld, R. 1989. Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> biological invasi<strong>on</strong>s. Chapman and Hall, L<strong>on</strong>d<strong>on</strong>, UK.<br />

[2] Sapoukhina N., Tyutyunov Y., Sache I. and Arditi R. 2010. Spatially mixed crops to c<strong>on</strong>trol<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e stratified dispersal <str<strong>on</strong>g>of</str<strong>on</strong>g> airborne fungal diseases. Ecological Modelling 221 2793–2800.<br />

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Crowd Dynamics: Modeling, Analysis and Simulati<strong>on</strong> (Part 1); Wednesday,<br />

June 29, 11:00<br />

Mario Campanella<br />

Delft University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: m.c.campanella@tudelft.nl<br />

Serge Hoogendoorn<br />

Delft University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: s.p.hoogendoorn@tudelft.nl<br />

Winnie Daamen<br />

Delft University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: w.daamen@tudelft.nl<br />

Calibrating walker models: variati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters due to<br />

traffic regimes<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e wide range <str<strong>on</strong>g>of</str<strong>on</strong>g> walking behaviours is not a simple task and several<br />

type <str<strong>on</strong>g>of</str<strong>on</strong>g> walker models have been proposed such as CA [1], discrete choice [2],<br />

social force [3] and utility based models [4]. Albeit different in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

properties, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models share a modelling assumpti<strong>on</strong> in dividing <str<strong>on</strong>g>th</str<strong>on</strong>g>e pedestrian<br />

behaviours in comp<strong>on</strong>ents such as pa<str<strong>on</strong>g>th</str<strong>on</strong>g> following, pedestrian avoidance and obstacle<br />

avoidance behaviours. In all <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g> following comp<strong>on</strong>ent describes<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e free-flow c<strong>on</strong>diti<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er two comp<strong>on</strong>ents describe how pedestrians<br />

deviate from <str<strong>on</strong>g>th</str<strong>on</strong>g>eir free-flow behaviours due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er pedestrians. The<br />

effects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e comp<strong>on</strong>ents are simply added and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir parameters remain c<strong>on</strong>stant<br />

regardless <str<strong>on</strong>g>of</str<strong>on</strong>g> external c<strong>on</strong>diti<strong>on</strong>s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is investigati<strong>on</strong> we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> invariance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters is incorrect leading to significant modelling errors.<br />

To investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e pedestrian behaviours we perform a series <str<strong>on</strong>g>of</str<strong>on</strong>g> calibrati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Nomad model [4] wi<str<strong>on</strong>g>th</str<strong>on</strong>g> empirical data from experiments representing different<br />

types <str<strong>on</strong>g>of</str<strong>on</strong>g> flows such as bidirecti<strong>on</strong>al, crossing and unidirecti<strong>on</strong>al flows. Each pedestrian<br />

trajectory is used to estimate <strong>on</strong>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters using <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology<br />

developed in [5]. The estimated parameter set is <str<strong>on</strong>g>th</str<strong>on</strong>g>en associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e average<br />

speed <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pedestrian <str<strong>on</strong>g>th</str<strong>on</strong>g>at produced <str<strong>on</strong>g>th</str<strong>on</strong>g>e trajectory. The average speed accounts<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e traffic flow intensity <str<strong>on</strong>g>th</str<strong>on</strong>g>at pedestrians had encountered. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

values <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g> following parameter display two distinct regimes <str<strong>on</strong>g>th</str<strong>on</strong>g>at corresp<strong>on</strong>d<br />

to free-flow and c<strong>on</strong>gesti<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>at between <str<strong>on</strong>g>th</str<strong>on</strong>g>e two regimes <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a smoo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

variati<strong>on</strong> resembling a sigmoid curve. The parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pedestrian avoidance<br />

comp<strong>on</strong>ent also display significant variati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> walking speeds. The c<strong>on</strong>sequences<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese findings is <str<strong>on</strong>g>th</str<strong>on</strong>g>at by showing <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavioural comp<strong>on</strong>ents are affected<br />

by traffic regimes, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey should incorporate variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters to improve <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

estimati<strong>on</strong> quality.<br />

References.<br />

[1] Blue, V.J. and J.L. Adler (1998), Emergent fundamental pedestrian flows from cellular automata<br />

microsimulati<strong>on</strong> Transportati<strong>on</strong> Research Record 1644 29–36.<br />

[2] Ant<strong>on</strong>ini, G., Bierlaire, M. and Weber, M. (2006), Discrete choice models <str<strong>on</strong>g>of</str<strong>on</strong>g> pedestrian walking<br />

behavior Transportati<strong>on</strong> Research Part B: Me<str<strong>on</strong>g>th</str<strong>on</strong>g>odological 40 667–687.<br />

[3] Helbing, D and Molnar, P (1995), Social force model for pedestrian dynamics Physical review<br />

E 51 4282–4286.<br />

[4] Hoogendoorn, S.P. and Bovy, P. H. L. (2003), Simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> pedestrian flows by optimal c<strong>on</strong>trol<br />

and differential games Optim. C<strong>on</strong>trol Appl. Me<str<strong>on</strong>g>th</str<strong>on</strong>g>. 24 153–172.<br />

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[5] Campanella, M. and Hoogendoorn, S.P. and Daamen, W.(2010), A me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology to calibrate<br />

pedestrian walker models using multiple-objectives to appear in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g> The Pedestrian<br />

and Evacuati<strong>on</strong> Dynamics, PED2010.<br />

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Vincenzo Capasso<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Milan<br />

e-mail: vincenzo.capasso@unimi.it<br />

Edoardo Beretta<br />

CIMAB, Italy<br />

Nadya Morozova<br />

CNRS, France<br />

Cancer; Tuesday, June 28, 11:00<br />

Populati<strong>on</strong> behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer stem cells<br />

Stem cells are cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two specific features - <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability to differentiate into all<br />

range <str<strong>on</strong>g>of</str<strong>on</strong>g> specialized cell types and <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability to renew <str<strong>on</strong>g>th</str<strong>on</strong>g>emselves. There are several<br />

possible scenarios <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer stem cells evoluti<strong>on</strong>, am<strong>on</strong>g which <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymmetric<br />

cell divisi<strong>on</strong>s providing self-renewing, is <str<strong>on</strong>g>th</str<strong>on</strong>g>e main <strong>on</strong>e. The main <str<strong>on</strong>g>th</str<strong>on</strong>g>eory for today<br />

for ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er normal or cancer stem cells is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey differentiate when <str<strong>on</strong>g>th</str<strong>on</strong>g>ey receive<br />

some kind <str<strong>on</strong>g>of</str<strong>on</strong>g> “instructive" signal influencing <str<strong>on</strong>g>th</str<strong>on</strong>g>e pattern and speed <str<strong>on</strong>g>of</str<strong>on</strong>g> cell divisi<strong>on</strong>s<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e given c<strong>on</strong>diti<strong>on</strong>s. All current experiments reporting <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer<br />

stem cell populati<strong>on</strong>s in culture allow to c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e main feature is <str<strong>on</strong>g>th</str<strong>on</strong>g>e same<br />

- <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e percentages <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cell populati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole populati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells, independently <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e starting c<strong>on</strong>diti<strong>on</strong>s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper we compare<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e qualitative behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> stem cells evoluti<strong>on</strong>, wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out<br />

and wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an underlying signal. In absence <str<strong>on</strong>g>of</str<strong>on</strong>g> an underlying field, we propose a<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model described by a system <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary differential equati<strong>on</strong>s, while<br />

in presence <str<strong>on</strong>g>of</str<strong>on</strong>g> an underlying field it is described by a system <str<strong>on</strong>g>of</str<strong>on</strong>g> delay differential<br />

equati<strong>on</strong>s, by admitting a delayed signal originated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e existing cells. In particular<br />

we show <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability <str<strong>on</strong>g>of</str<strong>on</strong>g> percentages for <str<strong>on</strong>g>th</str<strong>on</strong>g>e ODE system, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> oscillati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell populati<strong>on</strong>s <strong>on</strong>ly in presence <str<strong>on</strong>g>of</str<strong>on</strong>g> an underlying field. The<br />

hope is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper may stimulate fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er experiments to ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

validate or not <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e above menti<strong>on</strong>ed “instructive" signals.<br />

Keywords: Cancer stem cells, delay differential equati<strong>on</strong>s, qualitative behavior,<br />

stability, oscillati<strong>on</strong>s.<br />

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Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

II; Tuesday, June 28, 14:30<br />

Vincenzo Capasso<br />

ADAMSS (Interdisciplinary Centre for Advanced Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

and Statistical Sciences) and Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Universita’<br />

degli Studi di Milano, Italy<br />

e-mail: vincenzo.capasso@unimi.it<br />

Daniela Morale<br />

ADAMSS (Interdisciplinary Centre for Advanced Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

and Statistical Sciences) and Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Universita’<br />

degli Studi di Milano, Italy<br />

An hybrid analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> multiscale models for angiogenesis<br />

Angiogenesis, <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> new blood vessels, is an important natural process<br />

occurring in <str<strong>on</strong>g>th</str<strong>on</strong>g>e body, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in heal<str<strong>on</strong>g>th</str<strong>on</strong>g> and in disease. It is an example <str<strong>on</strong>g>of</str<strong>on</strong>g> complex<br />

system: <str<strong>on</strong>g>th</str<strong>on</strong>g>e endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells are <str<strong>on</strong>g>th</str<strong>on</strong>g>e building blocks for <str<strong>on</strong>g>th</str<strong>on</strong>g>e vessels and <str<strong>on</strong>g>th</str<strong>on</strong>g>ey interact<br />

by regulati<strong>on</strong> signals, forming a network <str<strong>on</strong>g>of</str<strong>on</strong>g> capillaries in order to reach every part<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e body.<br />

As examples <str<strong>on</strong>g>of</str<strong>on</strong>g> real experimental systems we c<strong>on</strong>sider tumour driven angiogenesis<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e embry<strong>on</strong>ic mouse retinal angiogenesis.<br />

An angiogenic system is extremely complex, due to its intrinsic multiscale structure;<br />

a major source <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity in <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling derives from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

str<strong>on</strong>g coupling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinetic parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relevant stochastic branching-andgrow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e capillary network at <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscale, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a family <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting<br />

underlying fields at a macroscale. This is <str<strong>on</strong>g>th</str<strong>on</strong>g>e reas<strong>on</strong> why in literature we may<br />

find a large variety <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models addressing some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e features <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

angiogenic process, and still integrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> all relevant features <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e process is an<br />

open problem.<br />

Thus our main goal is not in providing additi<strong>on</strong>al models for <str<strong>on</strong>g>th</str<strong>on</strong>g>e angiogenic<br />

phenomen<strong>on</strong> but in addressing <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical problem <str<strong>on</strong>g>of</str<strong>on</strong>g> reducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> such systems by taking advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir intrinsic multiscale structure.<br />

A satisfactory ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis and <str<strong>on</strong>g>of</str<strong>on</strong>g> many o<str<strong>on</strong>g>th</str<strong>on</strong>g>er fiber processes<br />

requires a geometric <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic fibre processes. We present here a<br />

simplified stochastic geometric model, largely inspired by current literature, bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and biological <strong>on</strong>es, for a spatially structured angiogenic process,<br />

str<strong>on</strong>gly coupled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a family <str<strong>on</strong>g>of</str<strong>on</strong>g> relevant underlying fields.<br />

The branching mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> blood vessels is modelled as a stochastic marked<br />

counting process describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e bir<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells, while <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole network<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> vessels is modelled as <str<strong>on</strong>g>th</str<strong>on</strong>g>e uni<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir trajectories; finally, capillary extensi<strong>on</strong>s<br />

are expressed by a system <str<strong>on</strong>g>of</str<strong>on</strong>g> a random number <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic differential equati<strong>on</strong>s,<br />

coupled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e PDEs describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying fields involved in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e process. On <strong>on</strong>e side <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinetic parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e capillary<br />

network depend up<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e family <str<strong>on</strong>g>of</str<strong>on</strong>g> underlying fields, <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er side <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying fields relies <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evolving capillary network. Since <str<strong>on</strong>g>th</str<strong>on</strong>g>is <strong>on</strong>e is<br />

a stochastic process, <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> equati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese fields will be a set <str<strong>on</strong>g>of</str<strong>on</strong>g> random<br />

partial differential equati<strong>on</strong>s, leading to random kinetic parameters. We are <str<strong>on</strong>g>th</str<strong>on</strong>g>us<br />

facing a problem <str<strong>on</strong>g>of</str<strong>on</strong>g> double stochasticity. This is a major source <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity<br />

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which may tremendously increase as <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> cells becomes extremely large,<br />

as it may happen in many cases <str<strong>on</strong>g>of</str<strong>on</strong>g> real interest. Under <str<strong>on</strong>g>th</str<strong>on</strong>g>ese last circumstances,<br />

by taking into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e natural multiple scale nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system a mesoscale<br />

may be introduced, which is sufficiently small wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscale <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

underlying fields, and sufficiently large wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to typical cell size. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e level<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is mesoscale, we may <str<strong>on</strong>g>th</str<strong>on</strong>g>en approximate (law <str<strong>on</strong>g>of</str<strong>on</strong>g> large numbers) <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tributi<strong>on</strong><br />

due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e vascularizati<strong>on</strong> process by local mean values, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

underlying fields <str<strong>on</strong>g>th</str<strong>on</strong>g>us providing a family <str<strong>on</strong>g>of</str<strong>on</strong>g> underlying deterministic fields. We<br />

may <str<strong>on</strong>g>th</str<strong>on</strong>g>en use <str<strong>on</strong>g>th</str<strong>on</strong>g>ese approximate mean fields to drive <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relevant<br />

stochastic processes cells at <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscale. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is way <strong>on</strong>ly <str<strong>on</strong>g>th</str<strong>on</strong>g>e simple stochasticity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e geometric processes <str<strong>on</strong>g>of</str<strong>on</strong>g> bir<str<strong>on</strong>g>th</str<strong>on</strong>g> (branching) and grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is kept, and it is possible<br />

to generate a n<strong>on</strong>trivial and realistic geometric pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e capillary network.<br />

This kind <str<strong>on</strong>g>of</str<strong>on</strong>g> models are known as hybrid models since we have substituted all<br />

stochastic underlying fields by <str<strong>on</strong>g>th</str<strong>on</strong>g>eir averaged counterparts; most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e current<br />

literature could now be reinterpreted al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>ese lines. It is necessary to stress<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at anyhow substituting mean geometric densities <str<strong>on</strong>g>of</str<strong>on</strong>g> tips, or <str<strong>on</strong>g>of</str<strong>on</strong>g> full vessels to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

corresp<strong>on</strong>ding stochastic quantities leads to an acceptable coefficient <str<strong>on</strong>g>of</str<strong>on</strong>g> variati<strong>on</strong><br />

(percentage error) <strong>on</strong>ly when a law <str<strong>on</strong>g>of</str<strong>on</strong>g> large numbers can be applied, i.e. whenever<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e relevant numbers per unit volume are sufficiently large; o<str<strong>on</strong>g>th</str<strong>on</strong>g>erwise stochasticity<br />

cannot be avoided, and in additi<strong>on</strong> to mean values, <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis<br />

and/or simulati<strong>on</strong>s should provide c<strong>on</strong>fidence bands for all quantities <str<strong>on</strong>g>of</str<strong>on</strong>g> interest.<br />

This fact is well evidenced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical simulati<strong>on</strong>s. If we homogenize <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

underlying fields ab initio we obtain a trivial capillary network, which c<strong>on</strong>firms<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at during <str<strong>on</strong>g>th</str<strong>on</strong>g>e early phases <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network formati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial<br />

cells is not sufficiently large to let us apply laws <str<strong>on</strong>g>of</str<strong>on</strong>g> large numbers yet.<br />

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Applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>negative Rad<strong>on</strong> measure spaces wi<str<strong>on</strong>g>th</str<strong>on</strong>g> metric structure<br />

to populati<strong>on</strong> dynamic models; Wednesday, June 29, 17:00<br />

Jose A. Carrillo<br />

ICREA & UAB<br />

e-mail: carrillo@mat.uab.es<br />

On some kinetic models <str<strong>on</strong>g>of</str<strong>on</strong>g> swarming<br />

We will present a kinetic <str<strong>on</strong>g>th</str<strong>on</strong>g>eory for swarming systems <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting, self-propelled<br />

discrete particles. Starting from <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>e particle model, <strong>on</strong>e can c<strong>on</strong>struct soluti<strong>on</strong>s<br />

to a kinetic equati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e single particle probability distributi<strong>on</strong> functi<strong>on</strong> using<br />

distances between measures. Moreover, I will introduce related macroscopic hydrodynamic<br />

equati<strong>on</strong>s. General soluti<strong>on</strong>s include flocks <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>stant density and fixed<br />

velocity and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er n<strong>on</strong>-trivial morphologies such as compactly supported rotating<br />

mills. The kinetic <str<strong>on</strong>g>th</str<strong>on</strong>g>eory approach leads us to <str<strong>on</strong>g>th</str<strong>on</strong>g>e identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> macroscopic<br />

structures o<str<strong>on</strong>g>th</str<strong>on</strong>g>erwise not recognized as soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hydrodynamic equati<strong>on</strong>s,<br />

such as double mills <str<strong>on</strong>g>of</str<strong>on</strong>g> two superimposed flows. I will also present and analyse<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e asymptotic behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tinuous kinetic versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> flocking<br />

by Cucker and Smale, which describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e collective behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> an ensemble <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

organisms, animals or devices. This kinetic versi<strong>on</strong> introduced in Ha and Tadmor<br />

is obtained from a particle model. The large-time behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> in<br />

phase space is subsequently studied by means <str<strong>on</strong>g>of</str<strong>on</strong>g> particle approximati<strong>on</strong>s and a<br />

stability property in distances between measures. A c<strong>on</strong>tinuous analogue <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eorems <str<strong>on</strong>g>of</str<strong>on</strong>g> Cucker-Smale will be shown to hold for <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinetic<br />

model. More precisely, <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong>s c<strong>on</strong>centrate exp<strong>on</strong>entially fast <str<strong>on</strong>g>th</str<strong>on</strong>g>eir velocity<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir mean while in space <str<strong>on</strong>g>th</str<strong>on</strong>g>ey will c<strong>on</strong>verge towards a translati<strong>on</strong>al flocking<br />

soluti<strong>on</strong>.<br />

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Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 11:00<br />

Magda Castel<br />

Agrocampus Ouest, UMR1099 BiO3P, 35042 Rennes, France<br />

e-mail: castel@agrocampus-ouest.fr<br />

Frederic M. Hamelin<br />

Agrocampus Ouest, UMR1099 BiO3P, 35042 Rennes, France<br />

Sylvain Poggi<br />

INRA, UMR1099 BiO3P, 35653 Le Rheu, France.<br />

Didier Andriv<strong>on</strong><br />

INRA, UMR1099 BiO3P, 35653 Le Rheu, France.<br />

Ludovic Mailleret<br />

INRA, UR880 URIH, 06903 Sophia Antipolis, France.<br />

Evoluti<strong>on</strong>ary insights from semi-discrete plant epidemic<br />

models.<br />

The coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> closely related plant parasitic species is ubiquitous in agriculture.<br />

However, understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e ecological determinants <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary divergence in<br />

parasites still represents an issue, in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> evoluti<strong>on</strong>ary biology and agricultural sciences.<br />

To our knowledge, <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>ly ecological mechanism which has been generically<br />

shown to promote phenotypic divergence in plant parasitic species is spatial host<br />

heterogeneity. However, spaceis not <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>ly source <str<strong>on</strong>g>of</str<strong>on</strong>g> ecological heterogeneity. Interestingly,<br />

crop plant parasites face abrupt, periodic changes in host density due to<br />

planting and harvesting. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper, we investigate whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er such heterogeneity<br />

in time can promote evoluti<strong>on</strong>ary divergence as well. We make use <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic<br />

model <str<strong>on</strong>g>th</str<strong>on</strong>g>at combines c<strong>on</strong>tinuous and discrete dynamics, to capture sharp seas<strong>on</strong>al<br />

events. Performing an evoluti<strong>on</strong>ary invasi<strong>on</strong> analysis, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at evoluti<strong>on</strong>ary<br />

branching <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parasite phenotype can occur, assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f between<br />

intra- and inter-seas<strong>on</strong> transmissi<strong>on</strong> abilities. Since <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are experimental<br />

evidence for such a trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f, <str<strong>on</strong>g>th</str<strong>on</strong>g>is study provides fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er ecological bases for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> closely related plant parasite species. Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>is study provides<br />

original insights regarding <str<strong>on</strong>g>th</str<strong>on</strong>g>e coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> m<strong>on</strong>o- and poly-cyclic sibling plant<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens.<br />

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Populati<strong>on</strong> Dynamics; Saturday, July 2, 14:30<br />

Isaias Chairez Hernández 1 , J. Natividad Gurrola Reyes 1 and Cipriano<br />

García Gutiérrez 2<br />

1 IPN CIIDIR Durango México, 2 IPN CIIDIR Sinaloa México, Becarios<br />

de COFAA<br />

e-mail: ichairez@hotmail.com<br />

e-mail: ngurrola@ipn.mx<br />

e-mail: garciacipriano@hotmail.com<br />

Grasshopper populati<strong>on</strong> interpolati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Generalized<br />

linear models<br />

This study was carried up in grassland areas in Durango México. Between latitude<br />

(23.916 o , 25.983 o ) and l<strong>on</strong>gitude ( -104.997 o , -104.010 o ). There were established<br />

sampling sites. At each <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese sites, twice a m<strong>on</strong><str<strong>on</strong>g>th</str<strong>on</strong>g> a grasshopper sampling was<br />

d<strong>on</strong>e from June to November 2003. Three were <str<strong>on</strong>g>th</str<strong>on</strong>g>e most abundant species. The<br />

purpose <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is study was to create grasshopper populati<strong>on</strong> maps wi<str<strong>on</strong>g>th</str<strong>on</strong>g> linear regressi<strong>on</strong>.<br />

Since <str<strong>on</strong>g>th</str<strong>on</strong>g>e assumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> normality failed for <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependent variables, <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong>s<br />

Poiss<strong>on</strong>, Gamma and Inverse binomial <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e generalized linear models were<br />

analyzed. taking as dependent variable <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> grasshopper surveyed <str<strong>on</strong>g>of</str<strong>on</strong>g> each<br />

species and <str<strong>on</strong>g>th</str<strong>on</strong>g>e independent variables were, latitude ( o ), l<strong>on</strong>gitude ( o ), altitude (m),<br />

slope (percentage), temperature (annual average o C), precipitati<strong>on</strong> (annual mm),<br />

landcover, type <str<strong>on</strong>g>of</str<strong>on</strong>g> vegetati<strong>on</strong>, type <str<strong>on</strong>g>of</str<strong>on</strong>g> soil and vegetati<strong>on</strong> index. According to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

deviance criteria <str<strong>on</strong>g>th</str<strong>on</strong>g>e best model was Gamma wi<str<strong>on</strong>g>th</str<strong>on</strong>g> logari<str<strong>on</strong>g>th</str<strong>on</strong>g>mic link functi<strong>on</strong> since<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e deviance 11.211 wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 9 d. f. was lower <str<strong>on</strong>g>th</str<strong>on</strong>g>an 16.91 <str<strong>on</strong>g>th</str<strong>on</strong>g>e 95-<str<strong>on</strong>g>th</str<strong>on</strong>g> percentile <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

chi-squared wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 9 d.f. The distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e residuals were heterogeneous at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ree grasshopper species and <str<strong>on</strong>g>th</str<strong>on</strong>g>e lowest correlati<strong>on</strong> coefficient between predicted<br />

grasshopper and observed was R 2 =0.83. The generalized linear models are alternative<br />

models when <str<strong>on</strong>g>th</str<strong>on</strong>g>e normal assumpti<strong>on</strong> has not been reached and when <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

dependent variable is a count data.<br />

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Fabio Chalub<br />

Universidade Nova de Lisboa<br />

e-mail: chalub@fct.unl.pt<br />

Max Souza<br />

Universidade Federal Fluminense<br />

Populati<strong>on</strong> Dynamics; Thursday, June 30, 11:30<br />

Discrete and c<strong>on</strong>tinous models in evoluti<strong>on</strong>ary dynamics<br />

We study <str<strong>on</strong>g>th</str<strong>on</strong>g>e large populati<strong>on</strong> limit <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Moran and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Wright-Fisher process,<br />

under <str<strong>on</strong>g>th</str<strong>on</strong>g>e assumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> weak-selecti<strong>on</strong>, and for different scalings. Depending <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e particular choice <str<strong>on</strong>g>of</str<strong>on</strong>g> scalings, we obtain a c<strong>on</strong>tinuous model <str<strong>on</strong>g>th</str<strong>on</strong>g>at may highlight<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic-drift (neutral evoluti<strong>on</strong>) or natural selecti<strong>on</strong>; for <strong>on</strong>e precise scaling,<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> effects are present. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e scalings <str<strong>on</strong>g>th</str<strong>on</strong>g>at take <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic-drift into account,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tinuous model is given by a singular diffusi<strong>on</strong> equati<strong>on</strong>, toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two<br />

c<strong>on</strong>servati<strong>on</strong> laws <str<strong>on</strong>g>th</str<strong>on</strong>g>at are already present at <str<strong>on</strong>g>th</str<strong>on</strong>g>e discrete level. For scalings <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

take into account <strong>on</strong>ly natural selecti<strong>on</strong>, we obtain a hyperbolic singular equati<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at embeds <str<strong>on</strong>g>th</str<strong>on</strong>g>e Replicator Dynamics and satisfies <strong>on</strong>ly <strong>on</strong>e c<strong>on</strong>servati<strong>on</strong> law. The<br />

derivati<strong>on</strong> is made in two steps: a formal <strong>on</strong>e, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e candidate limit model<br />

is obtained, and a rigorous <strong>on</strong>e, where c<strong>on</strong>vergence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability density is<br />

proved. Additi<strong>on</strong>al results <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fixati<strong>on</strong> probabilities are also presented.<br />

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Systems Biology <str<strong>on</strong>g>of</str<strong>on</strong>g> Development; Saturday, July 2, 14:30<br />

Osvaldo Chara<br />

Zentrum für Informati<strong>on</strong>sdienste und Hochleistungsrechnen (ZIH), Technische<br />

Universität Dresden, Germany<br />

e-mail: osvaldo.chara@tu-dresden.de<br />

Lutz Brusch<br />

Zentrum für Informati<strong>on</strong>sdienste und Hochleistungsrechnen (ZIH), Technische<br />

Universität Dresden, Germany<br />

Brigitte Galliot<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Zoology and Animal Biology, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Geneva, Switzerland<br />

Andreas Deutsch<br />

Zentrum für Informati<strong>on</strong>sdienste und Hochleistungsrechnen (ZIH), Technische<br />

Universität Dresden, Germany<br />

The role <str<strong>on</strong>g>of</str<strong>on</strong>g> Wnt3 in early Hydra head regenerati<strong>on</strong><br />

Several organisms including planaria, fish, insects and salamanders resp<strong>on</strong>d to injury<br />

and amputati<strong>on</strong> by regenerating <str<strong>on</strong>g>th</str<strong>on</strong>g>e lost body part. A general open questi<strong>on</strong><br />

is: How does <str<strong>on</strong>g>th</str<strong>on</strong>g>e remaining tissue ’measure’ <str<strong>on</strong>g>th</str<strong>on</strong>g>e degree <str<strong>on</strong>g>of</str<strong>on</strong>g> injury and mount a regenerati<strong>on</strong><br />

resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> adequate magnitude? This questi<strong>on</strong> is studied in <str<strong>on</strong>g>th</str<strong>on</strong>g>e fresh<br />

water polyp Hydra. The Hydra body column can be viewed as a hollow bilayered<br />

tissue cylinder wi<str<strong>on</strong>g>th</str<strong>on</strong>g> head and foot <strong>on</strong> opposite ends referred to as apical and basal,<br />

respectively. The tissue c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e following cell types: ectodermal and endodermal<br />

cells (in <str<strong>on</strong>g>th</str<strong>on</strong>g>e epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial lineage), interstitial stem cells, progenitors, neur<strong>on</strong>s,<br />

nematocytes and gland cells (in <str<strong>on</strong>g>th</str<strong>on</strong>g>e interstitial lineage). Previous experiments <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cutting Hydra into two halves showed secreti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Wnt3 molecules by cells undergoing<br />

apoptosis near <str<strong>on</strong>g>th</str<strong>on</strong>g>e amputati<strong>on</strong> plane <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basal half [1].<br />

We model <str<strong>on</strong>g>th</str<strong>on</strong>g>is immediate Wnt3 resp<strong>on</strong>se and <str<strong>on</strong>g>th</str<strong>on</strong>g>e following resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

different cell types by a system <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled partial differential equati<strong>on</strong>s. We assume<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at Wnt3 is produced by apoptotic cells near <str<strong>on</strong>g>th</str<strong>on</strong>g>e amputati<strong>on</strong> plane, diffuses deeper<br />

into <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue and subsequently undergoes a lytic degradati<strong>on</strong>. We model <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cell dynamics c<strong>on</strong>sidering cell differentiati<strong>on</strong>, self-renewal, apoptosis (triggered by<br />

amputati<strong>on</strong>), basal loss <str<strong>on</strong>g>of</str<strong>on</strong>g> cells due to migrati<strong>on</strong> toward <str<strong>on</strong>g>th</str<strong>on</strong>g>e extremities al<strong>on</strong>g wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

increases in cell proliferati<strong>on</strong> and cell migrati<strong>on</strong> in resp<strong>on</strong>se to <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong><br />

and spatial gradient <str<strong>on</strong>g>of</str<strong>on</strong>g> Wnt3, respectively.<br />

We implemented <str<strong>on</strong>g>th</str<strong>on</strong>g>e model in a simulati<strong>on</strong> program coded in C++. Modeldependent<br />

fitting simulati<strong>on</strong>s to <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental data [1] dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

mechanisms could be resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>e measured cell dynamics, corroborating an<br />

important role <str<strong>on</strong>g>of</str<strong>on</strong>g> Wnt3 wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e injury resp<strong>on</strong>se <str<strong>on</strong>g>th</str<strong>on</strong>g>at ultimately determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

fate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e regenerati<strong>on</strong> process in Hydra.<br />

References.<br />

[1] Chera S, Ghila L, Dobretz K, Wenger Y, Bauer C, Buzgariu W, Martinou JC, Galliot B.<br />

2009. Apoptotic cells provide an unexpected source <str<strong>on</strong>g>of</str<strong>on</strong>g> Wnt3 signaling to drive hydra head<br />

regenerati<strong>on</strong>. Dev Cell. 17(2):279-89.<br />

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Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

III; Tuesday, June 28, 17:00<br />

Arnaud Chauviere<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, University New Mexico, Albuquerque, USA<br />

e-mail: AChauviere@salud.unm.edu<br />

Haralambos Hatzikirou, Vittorio Cristini<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, University New Mexico, Albuquerque, USA<br />

Kara Pham, John Lowengrub<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> California at Irvine, USA<br />

Helen Byrne<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, UK<br />

Andreas Deutsch<br />

ZIH, Technische Universität Dresden, Germany<br />

The “Go-or-Grow” hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis in glioma grow<str<strong>on</strong>g>th</str<strong>on</strong>g>:<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and analysis<br />

Gliomas are very aggressive brain tumors, in which tumor cells gain <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability<br />

to penetrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding normal tissue. The invasi<strong>on</strong> mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

type <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor are not yet fully understood. Our work is motivated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong>/proliferati<strong>on</strong><br />

dichotomy (“Go-or-Grow” hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis), i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e antag<strong>on</strong>istic<br />

migratory and proliferating cellular behaviors in a cell populati<strong>on</strong>, which may play<br />

a central role in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese tumors [3].<br />

In a first part, we present results obtained by using a lattice-gas cellular automat<strong>on</strong><br />

and show <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Go-or-Grow mechanism <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

glioma grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, which we qualitatively compare to in vitro data [5].<br />

In a sec<strong>on</strong>d part, we formulate c<strong>on</strong>tinuum models to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> quiescence phases <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> a populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> glioma cells. We propose a<br />

“Go-or-Rest” model and describe cell migrati<strong>on</strong> as a velocity-jump process including<br />

resting phases. We derive <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding macroscopic model and show <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

anomalous diffusi<strong>on</strong> arises from <str<strong>on</strong>g>th</str<strong>on</strong>g>e switch between motile and quiescent phases. In<br />

particular, sub- and super-diffusi<strong>on</strong> regimes can be observed and are governed by a<br />

parameter describing intrinsic migratory properties <str<strong>on</strong>g>of</str<strong>on</strong>g> cells [2]. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at our<br />

results are in excellent agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> in vitro data <str<strong>on</strong>g>of</str<strong>on</strong>g> glioma tumor expansi<strong>on</strong> [1]<br />

when <str<strong>on</strong>g>th</str<strong>on</strong>g>e switch to quiescence is regulated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell density. We fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore show<br />

how <str<strong>on</strong>g>th</str<strong>on</strong>g>is density-regulati<strong>on</strong> allows for <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> immotile aggregates in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Turing instability. We use a combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> numerical and analytical<br />

techniques to characterize <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> spatio-temporal instabilities<br />

and traveling wave soluti<strong>on</strong>s generated by our model. We dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

density-dependent Go-or-Grow mechanism can produce complex dynamics similar<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>ose associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> tumor heterogeneity and invasi<strong>on</strong>.<br />

References.<br />

[1] M. Aubert et al., A cellular automat<strong>on</strong> model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> glioma cells, Phys. Biol. 3,<br />

pp. 93-100 (2006).<br />

[2] A. Chauviere et al., Anomalous diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> glioma cells (2011, in preparati<strong>on</strong>).<br />

[3] A. Giese et al., Cost <str<strong>on</strong>g>of</str<strong>on</strong>g> migrati<strong>on</strong>: invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> malignant gliomas and implicati<strong>on</strong>s for treatment,<br />

J. Clin. Onc. 21, pp. 1624–1636 (2003).<br />

160

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[4] K. Pham et al., Density-dependent quiescence in glioma invasi<strong>on</strong>: instability in a simple<br />

reacti<strong>on</strong>-diffusi<strong>on</strong> model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong>/proliferati<strong>on</strong> dichotomy, J. Biol. Dyn. (2011, in<br />

review).<br />

[5] M. Tekt<strong>on</strong>idis et al., Identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> intrinsic in vitro cellular mechanisms for glioma invasi<strong>on</strong>,<br />

J. Theor. Biol. (2011, in review).<br />

161

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: from physical tools to<br />

applicati<strong>on</strong>s in cancer modeling II; Saturday, July 2, 11:00<br />

Arnaud Chauviere, Haralambos Hatzikirou<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, University New Mexico, Albuquerque, USA<br />

e-mail: AChauviere@salud.unm.edu, HHatzikirou@salud.unm.edu<br />

John Lowengrub<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> California at Irvine, USA<br />

Vittorio Cristini<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, University New Mexico, Albuquerque, USA<br />

Multiscale modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems<br />

Modeling phenomena in biology <str<strong>on</strong>g>of</str<strong>on</strong>g>ten requires <str<strong>on</strong>g>th</str<strong>on</strong>g>e inclusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> processes occurring<br />

at different spatial and temporal scales. There is an urgent and challenging<br />

need to describe biological systems utilizing a multiscale landscape and not just a<br />

single scale view. To <str<strong>on</strong>g>th</str<strong>on</strong>g>is end, <str<strong>on</strong>g>th</str<strong>on</strong>g>eories from Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Physics can provide<br />

tools for <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> multiscale phenomena. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk,<br />

we present a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical multiscale framework inspired from Physics, <str<strong>on</strong>g>th</str<strong>on</strong>g>e Dynamic<br />

Density Functi<strong>on</strong>al Theory, which we apply to derive a modeling approach for biological<br />

systems <str<strong>on</strong>g>th</str<strong>on</strong>g>at is c<strong>on</strong>sistent across <str<strong>on</strong>g>th</str<strong>on</strong>g>e scales.<br />

Our starting point is to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a multi-cellular<br />

system by means <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic Langevin equati<strong>on</strong>s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach, each<br />

cell moves as <str<strong>on</strong>g>th</str<strong>on</strong>g>e result <str<strong>on</strong>g>of</str<strong>on</strong>g> a balance <str<strong>on</strong>g>of</str<strong>on</strong>g> forces exerted am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding cells<br />

and by <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell microenvir<strong>on</strong>ment. A random c<strong>on</strong>tributi<strong>on</strong> arises from <str<strong>on</strong>g>th</str<strong>on</strong>g>e local<br />

explorati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e neighborhood by <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells.<br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods from statistical physics can be used to derive <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding generalized<br />

Fokker-Planck equati<strong>on</strong>, which gives <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

probability distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> finding <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system at specific locati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

domain.<br />

An interesting level <str<strong>on</strong>g>of</str<strong>on</strong>g> descripti<strong>on</strong> c<strong>on</strong>sists in assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>e scalar density field<br />

as <str<strong>on</strong>g>th</str<strong>on</strong>g>e relevant variable for describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system. We show how<br />

to derive <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding functi<strong>on</strong>al Fokker-Planck equati<strong>on</strong>, which gives <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

spatio-temporal evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells adopt a particular density<br />

pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile. At <str<strong>on</strong>g>th</str<strong>on</strong>g>is level <str<strong>on</strong>g>of</str<strong>on</strong>g> descripti<strong>on</strong>, we show how to include cell proliferati<strong>on</strong> and<br />

apoptosis as a stochastic bir<str<strong>on</strong>g>th</str<strong>on</strong>g>-dea<str<strong>on</strong>g>th</str<strong>on</strong>g> process in our framework.<br />

Finally, we present <str<strong>on</strong>g>th</str<strong>on</strong>g>e derivati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a deterministic macroscopic equati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell density, including cell movement<br />

as a result <str<strong>on</strong>g>of</str<strong>on</strong>g> a balance <str<strong>on</strong>g>of</str<strong>on</strong>g> forces, and cell proliferati<strong>on</strong> and dea<str<strong>on</strong>g>th</str<strong>on</strong>g>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is equati<strong>on</strong>,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell density are regulated by a free energy functi<strong>on</strong>al <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

accounts for interacti<strong>on</strong>s am<strong>on</strong>g cells and wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microenvir<strong>on</strong>ment.<br />

This Dynamic Density Functi<strong>on</strong>al Theory is applied to simple interacting multicellular<br />

systems. We show how microscopic interacti<strong>on</strong>s at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular level (e.g.,<br />

cell-cell adhesi<strong>on</strong> and repulsi<strong>on</strong>) generate correlati<strong>on</strong> terms <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>tribute to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

corresp<strong>on</strong>ding macroscopic descripti<strong>on</strong> at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue level. We illustrate our approach<br />

for well-established mean-field approximati<strong>on</strong>s such as Keller-Segel- and<br />

Fisher-Kolmogorov-like models.<br />

162

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Plants, grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and transport processes II; Tuesday, June 28, 14:30<br />

Andrés Chavarría-Krauser<br />

Center for Modelling and Simulati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Biosciences (BIOMS), Universität<br />

Heidelberg<br />

e-mail: andres.chavarria@bioquant.uni-heidelberg.de<br />

Yejie Du<br />

Heidelberg Institute for Plant Science, Universität Heidelberg<br />

e-mail: duyejie@hip.uni-heidelberg.de<br />

A model <str<strong>on</strong>g>of</str<strong>on</strong>g> plasma membrane flow and cytosis regulati<strong>on</strong> in<br />

growing pollen tubes<br />

In plant sexual reproducti<strong>on</strong>, pollen tubes carry <str<strong>on</strong>g>th</str<strong>on</strong>g>e male genetic informati<strong>on</strong><br />

from pollen grains to ovules. These single cells traverse <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire female tissue to<br />

reach <str<strong>on</strong>g>th</str<strong>on</strong>g>e eggs. Ast<strong>on</strong>ishing high expansi<strong>on</strong> rates and total leng<str<strong>on</strong>g>th</str<strong>on</strong>g>s are achieved:<br />

rates <str<strong>on</strong>g>of</str<strong>on</strong>g> 1 mm/h in lily flowers and leng<str<strong>on</strong>g>th</str<strong>on</strong>g>s <str<strong>on</strong>g>of</str<strong>on</strong>g> 30 cm in maize. This extreme grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

rates and total leng<str<strong>on</strong>g>th</str<strong>on</strong>g>s demand perfect coordinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell wall expansi<strong>on</strong>, cell wall<br />

material depositi<strong>on</strong> and membrane recycling.<br />

During grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, pollen tubes have to have a well defined and tightly regulated<br />

distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell wall extensibility. Regulati<strong>on</strong> is achieved by influencing <str<strong>on</strong>g>th</str<strong>on</strong>g>e esterificati<strong>on</strong><br />

degree <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell wall material (mostly pectins) <str<strong>on</strong>g>th</str<strong>on</strong>g>rough Pectin Me<str<strong>on</strong>g>th</str<strong>on</strong>g>yl<br />

Esterases (PME), which activity is in turn regulated by an inhibitor (PMEI). Distinct<br />

patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> PME and PMEI are found in pollen tubes. While PME is widely<br />

distributed al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e flanks <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pollen tube, PMEI is <strong>on</strong>ly present at <str<strong>on</strong>g>th</str<strong>on</strong>g>e apical<br />

cell wall. To achieve <str<strong>on</strong>g>th</str<strong>on</strong>g>ese distinct distributi<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese enzymes are subjected to<br />

specific cytosis patterns. The cell wall material, pectin, reaches also <str<strong>on</strong>g>th</str<strong>on</strong>g>e wall by<br />

means <str<strong>on</strong>g>of</str<strong>on</strong>g> exocytosis. It stands to reas<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at, mechanics <str<strong>on</strong>g>of</str<strong>on</strong>g> growing pollen tubes<br />

can <strong>on</strong>ly be understood completely, if <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> endocytosis and exocytosis<br />

are also c<strong>on</strong>sidered.<br />

We present a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical approach to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>ese patterns. A model <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cytosis regulati<strong>on</strong> is developed and simulati<strong>on</strong>s presented. We address in particular<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e minimal assumpti<strong>on</strong>s needed to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterns reported<br />

recently by Z<strong>on</strong>ia and Munnik, [1]. The movement <str<strong>on</strong>g>of</str<strong>on</strong>g> plasma membrane in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

tip is described by using c<strong>on</strong>cepts <str<strong>on</strong>g>of</str<strong>on</strong>g> flow and c<strong>on</strong>servati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> membrane material.<br />

After obtaining <str<strong>on</strong>g>th</str<strong>on</strong>g>e central equati<strong>on</strong>s, relati<strong>on</strong>s describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e rates <str<strong>on</strong>g>of</str<strong>on</strong>g> endocytosis<br />

and exocytosis are proposed. We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at two cytosis receptors (for exocytosis and<br />

endocytosis), which have different recycling rates and activati<strong>on</strong> times, suffice to<br />

describe a stable growing tube. The simulati<strong>on</strong>s show a very good spatial separati<strong>on</strong><br />

between endocytosis and exocytosis, and separati<strong>on</strong> is shown to depend str<strong>on</strong>gly <strong>on</strong><br />

exocytic vesicle delivery. The model shows also <str<strong>on</strong>g>th</str<strong>on</strong>g>at most vesicles in <str<strong>on</strong>g>th</str<strong>on</strong>g>e clear z<strong>on</strong>e<br />

have to be endocytic, in accordance wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature. Membrane flow is essential<br />

to maintain cell polarity, and bi-directi<strong>on</strong>al flow is a natural c<strong>on</strong>sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

proposed mechanism. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e first time, a model addressing plasma membrane<br />

flow and cytosis regulati<strong>on</strong> was posed. Therefore, it represents a missing piece in an<br />

integrative model <str<strong>on</strong>g>of</str<strong>on</strong>g> pollen tube grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, in which cell wall mechanics, hydrodynamic<br />

fluxes and regulati<strong>on</strong> mechanisms are combined.<br />

References.<br />

163

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[1] Z<strong>on</strong>ia and Munnik, Uncovering hidden treasures in pollen tube grow<str<strong>on</strong>g>th</str<strong>on</strong>g> mechanics, Trends in<br />

Plant Science 14: 318–327.<br />

164

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Populati<strong>on</strong> Dynamics; Wednesday, June 29, 14:30<br />

Luis Fernando Chaves<br />

Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Envir<strong>on</strong>mental Science, Hokkaido University, Sapporo,<br />

Japan<br />

e-mail: lchaves@ees.hokudai.ac.jp<br />

N<strong>on</strong>-linear impacts <str<strong>on</strong>g>of</str<strong>on</strong>g> climatic variability <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e density<br />

dependent regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an insect vector <str<strong>on</strong>g>of</str<strong>on</strong>g> disease<br />

Aedes aegypti is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most comm<strong>on</strong> urban tropical mosquito species and an<br />

important vector <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue, chikungunya, and yellow fever viruses. It is also an organism<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a complex life history where larval stages are aquatic and adults are terrestrial.<br />

This <strong>on</strong>togenetic niche shift could shape <str<strong>on</strong>g>th</str<strong>on</strong>g>e density dependent regulati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er mosquito species because events <str<strong>on</strong>g>th</str<strong>on</strong>g>at occur during <str<strong>on</strong>g>th</str<strong>on</strong>g>e larval stages<br />

impact adult densities. Here, we present results from simple density-dependence<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models fitted using maximum likelihood me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to weekly time<br />

series data from Puerto Rico and Thailand. Density dependent regulati<strong>on</strong> was<br />

str<strong>on</strong>g in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> populati<strong>on</strong>s. Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> climatic forcing indicated <str<strong>on</strong>g>th</str<strong>on</strong>g>at populati<strong>on</strong>s<br />

were more sensitive to climatic variables wi<str<strong>on</strong>g>th</str<strong>on</strong>g> low kurtosis (i.e., highly variable<br />

around <str<strong>on</strong>g>th</str<strong>on</strong>g>e median) rainfall in Puerto Rico and temperature in Thailand. Changes<br />

in envir<strong>on</strong>mental variability appear to drive sharp increases in <str<strong>on</strong>g>th</str<strong>on</strong>g>e abundance <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

mosquitoes. The identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> exogenous factors forcing <str<strong>on</strong>g>th</str<strong>on</strong>g>e sharp increases in<br />

disease vector populati<strong>on</strong>s using <str<strong>on</strong>g>th</str<strong>on</strong>g>eir statistical properties, such as kurtosis, could<br />

be useful to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e impacts <str<strong>on</strong>g>of</str<strong>on</strong>g> changing climate patterns <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

vector-borne diseases.<br />

165

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Cancer; Friday, July 1, 14:30<br />

Ibrahim Cheddadi<br />

INRIA-Rocquencourt, France<br />

e-mail: ibrahim.cheddadi@inria.fr<br />

Dirk Drasdo<br />

INRIA-Rocquencourt, France<br />

Benoît Per<str<strong>on</strong>g>th</str<strong>on</strong>g>ame<br />

Laboratoire Jacques-Louis Li<strong>on</strong>s, Université Pierre et Marie Curie,<br />

Paris, France<br />

Min Tang<br />

Laboratoire Jacques-Louis Li<strong>on</strong>s, Université Pierre et Marie Curie,<br />

Paris, France<br />

Nicolas Vauchelet<br />

Laboratoire Jacques-Louis Li<strong>on</strong>s, Université Pierre et Marie Curie,<br />

Paris, France<br />

Irène Vign<strong>on</strong>-Clémentel<br />

INRIA-Rocquencourt, France<br />

Towards quantitative individual-based and c<strong>on</strong>tinuum<br />

models <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor multicellular aggregates<br />

Recent development <str<strong>on</strong>g>of</str<strong>on</strong>g> experimental techniques permits <str<strong>on</strong>g>th</str<strong>on</strong>g>e measurement <str<strong>on</strong>g>of</str<strong>on</strong>g> an<br />

increasing number <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters necessary to parameterize quantitative models<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and cancer development.On <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>e hand, Individual-cell Based<br />

Models (IBMs) allow to incorporate a lot <str<strong>on</strong>g>of</str<strong>on</strong>g> details <str<strong>on</strong>g>of</str<strong>on</strong>g> cell-level behavior but are<br />

limited to <str<strong>on</strong>g>th</str<strong>on</strong>g>e millimeter scale. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, c<strong>on</strong>tinuum models are well<br />

adapted to larger scales but do not permit such a detailed descripti<strong>on</strong>. Building<br />

a hybrid c<strong>on</strong>tinuum/discrete model is a promising way to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e multiscale<br />

behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> tumors from <str<strong>on</strong>g>th</str<strong>on</strong>g>e single cell up to centimeter scale. However, it requires<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at bo<str<strong>on</strong>g>th</str<strong>on</strong>g> approaches lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e same predicti<strong>on</strong>s. Recently, Byrne and Drasdo<br />

(J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. 2009) studied c<strong>on</strong>tinuum models able to capture important aspects<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er compact or very diluted tumor aggregates <str<strong>on</strong>g>of</str<strong>on</strong>g> a previously introduced IBM<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at has been shown to reproduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e typical grow<str<strong>on</strong>g>th</str<strong>on</strong>g> kinetic <str<strong>on</strong>g>of</str<strong>on</strong>g> m<strong>on</strong>olayers and<br />

multi-cellular spheroids (Drasdo et al., J. Stat. Phys. 2007) . Here we extend<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>cept towards a c<strong>on</strong>tinuum model <str<strong>on</strong>g>th</str<strong>on</strong>g>at describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e intermediate range <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

phenotypes by representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e different aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e IBM in more detail. The<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> dynamics predicted by <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two models are quantitatively compared.<br />

166

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> physiological processes in patients <strong>on</strong> dialysis;<br />

Saturday, July 2, 11:00<br />

Roman Cherniha<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Ukrainian Nati<strong>on</strong>al Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences,<br />

Tereshchenkivs’ka Street 3, Kyiv 01601, Ukraine;<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Kyiv-Mohyla Academy,<br />

Skovoroda Street 2, Kyiv 04070 , Ukraine<br />

e-mail: cherniha@ima<str<strong>on</strong>g>th</str<strong>on</strong>g>.kiev.ua<br />

Jacek Waniewski<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biocybernetics and Biomedical Engineering, PAS,<br />

Ks. Trojdena 4, 02 796 Warszawa, Poland<br />

e-mail: jacekwan@ibib.waw.pl<br />

New exact soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models<br />

describing perit<strong>on</strong>eal transport<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> fluid and solute transport between blood and dialysis<br />

fluid in <str<strong>on</strong>g>th</str<strong>on</strong>g>e perit<strong>on</strong>eal cavity has not been formulated fully yet, in spite <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

well known basic physical laws for such transport. Recent ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical, <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical<br />

and numerical studies introduced new c<strong>on</strong>cepts <strong>on</strong> perit<strong>on</strong>eal transport and<br />

yielded better results for <str<strong>on</strong>g>th</str<strong>on</strong>g>e transport <str<strong>on</strong>g>of</str<strong>on</strong>g> fluid and osmotic agent [1]–[4]. However,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> a combined descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> osmotic ultrafiltrati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e perit<strong>on</strong>eal<br />

cavity, absorpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> osmotic agent from <str<strong>on</strong>g>th</str<strong>on</strong>g>e perit<strong>on</strong>eal cavity and leak <str<strong>on</strong>g>of</str<strong>on</strong>g> macromolecules<br />

(proteins, e.g., albumin) from blood to <str<strong>on</strong>g>th</str<strong>on</strong>g>e perit<strong>on</strong>eal cavity has not<br />

been addressed yet. Therefore, we present here a new extended model for <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

phenomena and investigate its ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical structure. The model is based <strong>on</strong><br />

a <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-comp<strong>on</strong>ent n<strong>on</strong>linear system <str<strong>on</strong>g>of</str<strong>on</strong>g> two-dimensi<strong>on</strong>al partial differential equati<strong>on</strong>s<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relevant boundary and initial c<strong>on</strong>diti<strong>on</strong>s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e particular case, <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

model produces <strong>on</strong>e, which was studied earlier in papers [1]–[3]. The n<strong>on</strong>-c<strong>on</strong>stant<br />

steady-state soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model obtained are studied. The realistic restricti<strong>on</strong>s<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters arising in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model were established wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e aim to obtain<br />

exact formulae for <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>-c<strong>on</strong>stant steady-state soluti<strong>on</strong>s. As result, <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact<br />

formulae for <str<strong>on</strong>g>th</str<strong>on</strong>g>e density <str<strong>on</strong>g>of</str<strong>on</strong>g> fluid flux from blood to tissue and <str<strong>on</strong>g>th</str<strong>on</strong>g>e volumetric flux<br />

across <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue were c<strong>on</strong>structed, and two linear aut<strong>on</strong>omous ordinary differential<br />

equati<strong>on</strong>s to find <str<strong>on</strong>g>th</str<strong>on</strong>g>e glucose and albumin c<strong>on</strong>centrati<strong>on</strong>s were derived. The analytical<br />

results were checked, whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are applicable for <str<strong>on</strong>g>th</str<strong>on</strong>g>e descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

glucose-albumin transport in perit<strong>on</strong>eal dialysis.<br />

References.<br />

[1] Cherniha, R., Waniewski, J.: Exact soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for fluid transport in<br />

perit<strong>on</strong>eal dialysis. Ukrainian Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. J., 57, 1112–1119 (2005)<br />

[2] R. Cherniha, V.Dutka, J.Stachowska-Pietka and J.Waniewski. Fluid transport in perit<strong>on</strong>eal<br />

dialysis: a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model and numerical soluti<strong>on</strong>s. //Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological<br />

Systems, Vol.I. Ed. by A.Deutsch et al., Birkhaeuser, P.291-298, 2007<br />

[3] Waniewski J, Dutka V, Stachowska-Pietka J, Cherniha R: Distributed modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> glucoseinduced<br />

osmotic flow. Adv Perit Dial 2007;23:2-6.<br />

[4] Waniewski J, Stachowska-Pietka J, Flessner MF: Distributed modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> osmotically driven<br />

fluid transport in perit<strong>on</strong>eal dialysis: <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical and computati<strong>on</strong>al investigati<strong>on</strong>s. Am J<br />

Physiol Heart Circ Physiol 2009;296:H1960-1968.<br />

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Andrey Cherstvy<br />

ICS-2, FZ Juelich, 52425 Juelich, Germany<br />

e-mail: a.cherstvy@gmail.com<br />

A. Kolomeisky<br />

Rice University, Houst<strong>on</strong>, Texas 77005, USA<br />

A. Kornyshev<br />

Imperial College L<strong>on</strong>d<strong>on</strong>, SW7 2AZ, L<strong>on</strong>d<strong>on</strong>, UK<br />

Bioengineering; Tuesday, June 28, 14:30<br />

Protein-DNA interacti<strong>on</strong>s: reaching and recognizing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

targets<br />

Search and recogniti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> targets <strong>on</strong> DNA by DNA-binding proteins is a vital<br />

biological process. Some proteins find <str<strong>on</strong>g>th</str<strong>on</strong>g>eir target sequences <strong>on</strong> DNA wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

rates <str<strong>on</strong>g>th</str<strong>on</strong>g>at are 100-1000 times faster <str<strong>on</strong>g>th</str<strong>on</strong>g>an predicted by Smoluchowski diffusi<strong>on</strong> in<br />

3D space. It is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten claimed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e reducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dimensi<strong>on</strong>ality from 3D in<br />

soluti<strong>on</strong> to 1D <strong>on</strong> DNA is <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic key to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>is facilitated diffusi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> DNA-sliding proteins. Recent experiments have shown however <str<strong>on</strong>g>th</str<strong>on</strong>g>at protein<br />

diffusi<strong>on</strong> al<strong>on</strong>g DNA is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten much slower <str<strong>on</strong>g>th</str<strong>on</strong>g>an in soluti<strong>on</strong> (see data <str<strong>on</strong>g>of</str<strong>on</strong>g> Ref. [1]<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e lac repressor). Thus, <str<strong>on</strong>g>th</str<strong>on</strong>g>e 3D1D space reducti<strong>on</strong> by itself does not ensure a<br />

faster target search. That c<strong>on</strong>troversy pushed us to revisit <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem [2].<br />

We present two <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical models <str<strong>on</strong>g>th</str<strong>on</strong>g>at describe some physical and chemical<br />

aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> protein target search and mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> DNA-protein electrostatic recogniti<strong>on</strong>.<br />

First, we c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein target search as a sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> cycles <str<strong>on</strong>g>of</str<strong>on</strong>g> 3D diffusi<strong>on</strong><br />

in soluti<strong>on</strong> and 1D sliding al<strong>on</strong>g DNA. Our n<strong>on</strong>-equilibrium model accounts<br />

for protein binding/unbinding to DNA [2]. The model c<strong>on</strong>tains a new correlati<strong>on</strong><br />

term, missing in previous <str<strong>on</strong>g>th</str<strong>on</strong>g>eories, <str<strong>on</strong>g>th</str<strong>on</strong>g>at comes from <str<strong>on</strong>g>th</str<strong>on</strong>g>e accurate descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> protein<br />

diffusi<strong>on</strong> process in stochastic DNA-protein potential. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e search<br />

time is optimal for an intermediate streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> protein-DNA interacti<strong>on</strong>s and intermediate<br />

protein c<strong>on</strong>centrati<strong>on</strong>s. The fast search is achieved by a parallel scanning<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> DNA by many proteins. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>clusi<strong>on</strong>s are c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e outcomes <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

recent large-scale M<strong>on</strong>te Carlo simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> protein diffusi<strong>on</strong> [3].<br />

Then, we focus <strong>on</strong> DNA-protein electrostatic interacti<strong>on</strong>s, known to give a<br />

large c<strong>on</strong>tributi<strong>on</strong> to protein-DNA binding affinity. C<strong>on</strong>trary to hydrogen b<strong>on</strong>ding,<br />

electrostatic protein-DNA forces are believed to be largely insensitive to DNA<br />

sequence. We show however how <str<strong>on</strong>g>th</str<strong>on</strong>g>e complementarity <str<strong>on</strong>g>of</str<strong>on</strong>g> charge patterns <strong>on</strong> target<br />

DNA sequence and <strong>on</strong> a model protein can result in electrostatic recogniti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a specific track <strong>on</strong> DNA. This recogniti<strong>on</strong> provokes protein pinning near <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

homologous regi<strong>on</strong> <strong>on</strong> DNA. We obtain analytical expressi<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e shape <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

capturing well and typical times proteins spend in it before <str<strong>on</strong>g>th</str<strong>on</strong>g>ermal escape. These<br />

times are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten l<strong>on</strong>g enough to allow a reorganizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein structure, socalled<br />

interacti<strong>on</strong>-induced protein folding, and formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> str<strong>on</strong>ger (hydrogen)<br />

b<strong>on</strong>ds wi<str<strong>on</strong>g>th</str<strong>on</strong>g> DNA. One can <str<strong>on</strong>g>th</str<strong>on</strong>g>us suggest a two-step mechanism for DNA-protein<br />

recogniti<strong>on</strong> [2]: electrostatically mediated protein sliding and pinning followed by<br />

chemical recogniti<strong>on</strong> interacti<strong>on</strong>s.<br />

This mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> protein-DNA recogniti<strong>on</strong> is reminiscent <str<strong>on</strong>g>of</str<strong>on</strong>g> charge adjustment<br />

predicted by us for sequence-specific DNA-DNA electrostatic interacti<strong>on</strong> [4].<br />

The charge complementarity is also known to dominate <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> many<br />

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protein-protein complexes in soluti<strong>on</strong> [5], rendering such charge zipper complexati<strong>on</strong><br />

pretty general.<br />

Theoretical model <str<strong>on</strong>g>of</str<strong>on</strong>g> protein-DNA charge recogniti<strong>on</strong> has been validated by<br />

our recent analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> real DNA-protein complexes [6]. Structure visualizati<strong>on</strong> for<br />

many DNA-binding proteins indeed reveals a close proximity <str<strong>on</strong>g>of</str<strong>on</strong>g> positively charged<br />

protein residues (Arg, Lys, and Hist) to negative DNA phosphate groups [6]. A<br />

detailed computati<strong>on</strong>al analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Protein Data Bank files <str<strong>on</strong>g>of</str<strong>on</strong>g> crystallized DNAprotein<br />

complexes performed has indicated several important features. We have<br />

observed for instance <str<strong>on</strong>g>th</str<strong>on</strong>g>at in particularly for large structural proteins such as nucleosome<br />

core particles, <str<strong>on</strong>g>th</str<strong>on</strong>g>e sequence-specific DNA-protein charge zipper effects are<br />

str<strong>on</strong>gly pr<strong>on</strong>ounced. Namely, <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Lys and Arg <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein surface<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e vicinity <str<strong>on</strong>g>of</str<strong>on</strong>g> bound DNA fragment is adjusted to provide a better fit to<br />

sequence-specific pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> DNA phosphates. This indicates sequence-specificity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> electrostatic interacti<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>ese complexes, <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact largely overlooked in literature<br />

before. Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> relatively small DNA-protein complexes, <str<strong>on</strong>g>th</str<strong>on</strong>g>at implement<br />

standard motifs <str<strong>on</strong>g>of</str<strong>on</strong>g> DNA recogniti<strong>on</strong>, <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trary, did not reveal any statistical<br />

preference in distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> positively charged protein amino acids wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tacting DNA phosphates [6,7].<br />

References.<br />

[1] R. Austin et al., Phys. Rev. Lett., 97 048302 (2006).<br />

[2] A. G. Cherstvy et al., J. Phys. Chem. B, 112 4741 (2008).<br />

[3] R. K. Das and A. B. Kolomeisky, PCCP, 12 2999 (2010).<br />

[4] A. G. Cherstvy et al., J. Phys. Chem. B, 108 6508 (2004).<br />

[5] A. J. McCoy et al., J. Mol. Biol., 268 570 (1997).<br />

[6] A. G. Cherstvy, J. Phys. Chem. B, 113 4242 (2009).<br />

[7] A. G. Cherstvy, Phys. Chem. Chem. Phys, accepted (2011).<br />

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Chadha Chettaoui<br />

INRIA Rocquencourt / INRA Jouy en Josas<br />

e-mail: chadha.chettaoui@gmail.com<br />

Dirk Drasdo<br />

INRIA Rocquencourt<br />

Michel Guillomot<br />

INRA Jouy en Josas<br />

Isabelle Hue<br />

INRA Jouy en Josas<br />

Alain Trubuil<br />

INRA Jouy en Josas<br />

Juhui Wang<br />

INRA Jouy en Josas<br />

Developmental Biology; Thursday, June 30, 11:30<br />

Towards a single-cell-based model <str<strong>on</strong>g>of</str<strong>on</strong>g> early development in<br />

ruminants<br />

Embry<strong>on</strong>ic losses and, after bir<str<strong>on</strong>g>th</str<strong>on</strong>g>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chr<strong>on</strong>ic diseases <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic origins<br />

such as obesity, diabetes, arterial hypertensi<strong>on</strong>, have been observed as critical<br />

in early ruminant (sheep, cow) development.<br />

In order to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e possible mechanisms leading to such failures, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

mechanisms c<strong>on</strong>trolling two developmental phases, <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e blastocyst (a<br />

hollow sphere <str<strong>on</strong>g>of</str<strong>on</strong>g> cells) during late blastula formati<strong>on</strong> as well as early trophoblast<br />

development needs to be understood. The trophoblast is <str<strong>on</strong>g>th</str<strong>on</strong>g>e first epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elium <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

appears at <str<strong>on</strong>g>th</str<strong>on</strong>g>e beginning <str<strong>on</strong>g>of</str<strong>on</strong>g> embryogenesis in mammals. It forms <str<strong>on</strong>g>th</str<strong>on</strong>g>e wall <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

blastocyst and helps for implantati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e uterine wall. During early development<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e trophoblast, a temporal window <str<strong>on</strong>g>of</str<strong>on</strong>g> 15 days from <str<strong>on</strong>g>th</str<strong>on</strong>g>e blastocyst stage, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

trophoblast floats in <str<strong>on</strong>g>th</str<strong>on</strong>g>e uterine liquid, and undergoes an extremely fast grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and<br />

el<strong>on</strong>gati<strong>on</strong>. This period <str<strong>on</strong>g>of</str<strong>on</strong>g> early morphogenesis is fundamental for a normal development<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e embryo. We established a process chain to quantitatively analyze<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e two developmental phases by experiments, analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> images from <str<strong>on</strong>g>th</str<strong>on</strong>g>e embryos<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> different stages, and ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling. We analyze c<strong>on</strong>focal images<br />

to infer <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular organizati<strong>on</strong> into <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue sheet, and determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cell size and cell shapes prior and during <str<strong>on</strong>g>th</str<strong>on</strong>g>e embryo shape transiti<strong>on</strong>.<br />

Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is analysis, we set up a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical single-cell-based<br />

model. Our model cells are parametrized by measurable biophysical and cell biological<br />

quantities. They can migrate, grow and divide, and interact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er cells<br />

and extracellular matrix by forces. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e first step we c<strong>on</strong>sidered a representative<br />

secti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e developing embryo and studied different mechanisms to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

deformati<strong>on</strong>. The model permits predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> several manipulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cells and<br />

embryo <str<strong>on</strong>g>th</str<strong>on</strong>g>at are currently experimentally tested.<br />

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Cell and Tissue Biophysics; Friday, July 1, 14:30<br />

Keng-Hwee Chiam<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> High Performance Computing, Singapore<br />

e-mail: chiamkh@ihpc.a-star.edu.sg<br />

F<strong>on</strong>g Yin Lim<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> High Performance Computing, Singapore<br />

e-mail: limfy@ihpc.a-star.edu.sg<br />

L. Mahadevan<br />

Havard University, USA<br />

Bleb Statics, Dynamics, Adaptati<strong>on</strong> and Directed Cell<br />

Migrati<strong>on</strong><br />

Cellular blebs are spherical cell membrane protrusi<strong>on</strong>s powered by cytoplasmic flow.<br />

To understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular blebs, we develop a quantitative model to<br />

study how a bleb develops when a porti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell membrane detaches from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying cortex. From <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, we calculate <str<strong>on</strong>g>th</str<strong>on</strong>g>e minimum cytoplasmic<br />

pressure and minimum unsupported membrane leng<str<strong>on</strong>g>th</str<strong>on</strong>g> for a bleb to nucleate and<br />

grow. We also show how a bleb may travel around <str<strong>on</strong>g>th</str<strong>on</strong>g>e periphery <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. We find<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e traveling speed <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bleb is governed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e speed <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pressure pulse<br />

induced by local cortical c<strong>on</strong>tracti<strong>on</strong> and we c<strong>on</strong>struct a phase diagram for bleb<br />

existence and moti<strong>on</strong>. Finally, we propose a bleb-based mechanism for directed<br />

migrati<strong>on</strong> during chemotaxis based <strong>on</strong> adaptati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e variance <str<strong>on</strong>g>of</str<strong>on</strong>g> blebbing. This<br />

adaptati<strong>on</strong> is shown to be robust and is insensitive to perturbati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a wide<br />

range <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters.<br />

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Ryan Chisholm<br />

Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>s<strong>on</strong>ian Tropical Research Institute<br />

e-mail: ryan.chis@gmail.com<br />

Populati<strong>on</strong> Dynamics; Saturday, July 2, 11:00<br />

A <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical model linking interspecific variati<strong>on</strong> in density<br />

dependence to species abundances<br />

Understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e factors <str<strong>on</strong>g>th</str<strong>on</strong>g>at govern <str<strong>on</strong>g>th</str<strong>on</strong>g>e comm<strong>on</strong>ness and rarity <str<strong>on</strong>g>of</str<strong>on</strong>g> individual<br />

species is a central challenge in community ecology. Empirical studies have <str<strong>on</strong>g>of</str<strong>on</strong>g>ten<br />

found <str<strong>on</strong>g>th</str<strong>on</strong>g>at abundance is related to traits associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> competitive ability and<br />

suitability to <str<strong>on</strong>g>th</str<strong>on</strong>g>e local envir<strong>on</strong>ment, and more recently also to negative c<strong>on</strong>specific<br />

density dependence. Here, we c<strong>on</strong>struct a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical framework to show how a<br />

species abundance is in general expected to be dependent <strong>on</strong> its per-capita grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

rate when rare and <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate at which its grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate declines wi<str<strong>on</strong>g>th</str<strong>on</strong>g> increasing abundance<br />

(streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> stabilizati<strong>on</strong>). We argue <str<strong>on</strong>g>th</str<strong>on</strong>g>at per-capita grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate when rare<br />

can be interpreted as competitive ability and <str<strong>on</strong>g>th</str<strong>on</strong>g>at streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> stabilizati<strong>on</strong> largely<br />

reflects negative c<strong>on</strong>specific inhibiti<strong>on</strong>. We <str<strong>on</strong>g>th</str<strong>on</strong>g>en analyze a simple spatially implicit<br />

model in which each species is defined by <str<strong>on</strong>g>th</str<strong>on</strong>g>ree parameters <str<strong>on</strong>g>th</str<strong>on</strong>g>at affect its juvenile<br />

survival: its generalized competitive effect <strong>on</strong> o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers, its generalized resp<strong>on</strong>se to<br />

competiti<strong>on</strong>, and an additi<strong>on</strong>al negative effect <strong>on</strong> c<strong>on</strong>specifics. This model facilitates<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e stable coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> an arbitrarily large number <str<strong>on</strong>g>of</str<strong>on</strong>g> species and qualitatively<br />

reproduces empirical relati<strong>on</strong>ships between abundance, competitive ability<br />

and negative c<strong>on</strong>specific density dependence. Our results provide <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical support<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e combined roles <str<strong>on</strong>g>of</str<strong>on</strong>g> competitive ability and negative density dependence<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e determinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> species abundances in real ecosystems, and suggest new avenues<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> research for understanding abundance in models and in real communities.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Mosquito-Borne Diseases; Tuesday, June 28, 11:00<br />

Nakul Chitnis<br />

Swiss Tropical and Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Institute<br />

e-mail: Nakul.Chitnis@unibas.ch<br />

Diggory Hardy, Nicolas Maire, Amanda Ross, Melissa Penny, Valerie<br />

Crowell, Olivier Briët, Thomas Smi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Swiss Tropical and Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Institute<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling to Support Malaria C<strong>on</strong>trol and<br />

Eliminati<strong>on</strong><br />

We use numerical simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an ensemble <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> malaria in<br />

humans and mosquitoes to help develop target product pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles for new interventi<strong>on</strong>s<br />

and to provide robust quantitative predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> effectiveness and cost-effectiveness<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> different strategies in reducing transmissi<strong>on</strong>, morbidity and mortality.<br />

The individual-based stochastic simulati<strong>on</strong> models include seas<strong>on</strong>ality <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong>;<br />

multiple mosquito populati<strong>on</strong>s; superinfecti<strong>on</strong>, acquired immunity, and variati<strong>on</strong>s<br />

in parasite densities in humans; and <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> heal<str<strong>on</strong>g>th</str<strong>on</strong>g> systems. We describe<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e model and show results <str<strong>on</strong>g>of</str<strong>on</strong>g> simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> combinati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> different interventi<strong>on</strong>s<br />

including indoor residual spraying (IRS), insecticide-treated nets (ITNs), improved<br />

case management, intermittent preventive treatment, and potential vaccine candidates.<br />

Our results suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at sustained coverage <str<strong>on</strong>g>of</str<strong>on</strong>g> ITNs and/or IRS reduces malaria<br />

prevalence in two to <str<strong>on</strong>g>th</str<strong>on</strong>g>ree years but does not lead to fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er gains. However, in<br />

some settings, even wi<str<strong>on</strong>g>th</str<strong>on</strong>g> sustained coverage, clinical incidence <str<strong>on</strong>g>of</str<strong>on</strong>g> malaria increases<br />

as <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> loses its naturally acquired immunity. In some low to medium<br />

transmissi<strong>on</strong> settings, our simulati<strong>on</strong>s suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at high coverage <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> interventi<strong>on</strong>s<br />

can lead to interrupti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> transmissi<strong>on</strong>, especially if coupled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an effective<br />

transmissi<strong>on</strong> blocking vaccine.<br />

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Populati<strong>on</strong> Dynamics; Tuesday, June 28, 11:00<br />

Ye<strong>on</strong>taek Choi<br />

Nati<strong>on</strong>al Institute for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Korea<br />

e-mail: ytchoi@nims.re.kr<br />

Ngo van Thanh<br />

Nati<strong>on</strong>al Institute for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Korea<br />

Tae-Soo Ch<strong>on</strong><br />

Pusan Nati<strong>on</strong>al University, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Korea<br />

Sang-Hee Lee<br />

Nati<strong>on</strong>al Institute for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Korea<br />

Movement pattern analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> C.elegans based <strong>on</strong><br />

Box-Sized-Distributi<strong>on</strong><br />

It is already known <str<strong>on</strong>g>th</str<strong>on</strong>g>at locomoti<strong>on</strong> by C.elegans delivers characteristic patterns <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

movements, e.g. forward and backward movement, rest, omega-turn, and coil-type<br />

turn. However <str<strong>on</strong>g>th</str<strong>on</strong>g>e previous studies, being interested in <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> C.elegans<br />

movement, have had limitati<strong>on</strong> to give enough explanati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immediate c<strong>on</strong>necti<strong>on</strong><br />

between movement and pattern. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is study, we introduced a way to<br />

deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> C.elegans movement patterns, called Box-Sized-Distributi<strong>on</strong> (BSD), in<br />

order to look to <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong> between movement and its pattern. BSD is defined by<br />

introducing a rectangular box which c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e wid<str<strong>on</strong>g>th</str<strong>on</strong>g>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>gest line formed<br />

by any two points <strong>on</strong> C.elegans, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e height, <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>gest vertical line determined<br />

by wid<str<strong>on</strong>g>th</str<strong>on</strong>g> line. We used experimental data sets for 50 individuals, being obtained<br />

after each c<strong>on</strong>trolled C.elegans was observed by real-time recording system for <str<strong>on</strong>g>th</str<strong>on</strong>g>ree<br />

hours <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e agar plate. As a result, BSD delivers a few interesting facts <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

movement patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> C.elegans : 1) The ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> wid<str<strong>on</strong>g>th</str<strong>on</strong>g> to height <str<strong>on</strong>g>of</str<strong>on</strong>g> a box can<br />

measure <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical activity <str<strong>on</strong>g>of</str<strong>on</strong>g> C.elegans, i.e., speed <str<strong>on</strong>g>of</str<strong>on</strong>g> movement and turn. 2)<br />

BSD makes it possible to explain pattern transiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> C.elegans movements. 3)<br />

BSD also obeys a Boltzmann statistics based <strong>on</strong> shape itself.<br />

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Ecosystems Dynamics; Tuesday, June 28, 17:00<br />

Catalina Ciric<br />

EDF; Divisi<strong>on</strong> Recherche et Développement; Département Laboratoire<br />

Nati<strong>on</strong>al d’Hydraulique et Envir<strong>on</strong>nement; 6 quai Watier, 78401 Chatou,<br />

France<br />

e-mail: ciric.cata@gmail.com<br />

Sandrine Charles<br />

Université de Ly<strong>on</strong>, F-69000, Ly<strong>on</strong>; Université Ly<strong>on</strong> 1; CNRS, UMR5558,<br />

Laboratoire de Biométrie et Biologie Évolutive, F-69622, Villeurbanne,<br />

France<br />

Philippe Ciffroy<br />

EDF; Divisi<strong>on</strong> Recherche et Développement; Département Laboratoire<br />

Nati<strong>on</strong>al d’Hydraulique et Envir<strong>on</strong>nement; 6 quai Watier, 78401 Chatou,<br />

France<br />

Aquatic ecosystem modeling: use <str<strong>on</strong>g>of</str<strong>on</strong>g> screening sensitivity<br />

analysis me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to facilitate <str<strong>on</strong>g>th</str<strong>on</strong>g>e calibrati<strong>on</strong> process<br />

In ecological risk assessments, risks imputable to chemicals at <str<strong>on</strong>g>th</str<strong>on</strong>g>e ecosystem level<br />

are usually estimated by extrapolati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> single-species toxicity test results. But<br />

such approaches fail to account for <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at inevitably exist am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

comp<strong>on</strong>ent species [1]. Alternately, modeling at <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole ecosystem level reveals<br />

to be a powerful tool by c<strong>on</strong>sidering species interacti<strong>on</strong>s, and by predicting toxic<br />

effects <strong>on</strong> n<strong>on</strong>-target species populati<strong>on</strong>s (indirect effects). The aims <str<strong>on</strong>g>of</str<strong>on</strong>g> our work<br />

are: (i) to develop a new ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model which comprehensively describes<br />

a whole aquatic ecosystem accounting for species interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a clear set <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

equati<strong>on</strong>s including bo<str<strong>on</strong>g>th</str<strong>on</strong>g> abiotic and biotic factors; (ii) to incorporate perturbati<strong>on</strong><br />

functi<strong>on</strong>s <strong>on</strong> chosen processes wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model in order to predict potential<br />

toxic effects at <str<strong>on</strong>g>th</str<strong>on</strong>g>e ecosystem level and to identify functi<strong>on</strong>al groups at risk; (iii) to<br />

perform a sensitivity analysis, i.e., to screen parameters having <str<strong>on</strong>g>th</str<strong>on</strong>g>e greatest influence<br />

<strong>on</strong> calculated target endpoints. An extensive literature review allowed us to<br />

c<strong>on</strong>ceptualize a whole n<strong>on</strong>-c<strong>on</strong>taminated aquatic ecosystem wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a compartmental<br />

ecological model [2]. Compartments include primary producers (macrophytes and<br />

algae from phytoplankt<strong>on</strong> and periphyt<strong>on</strong>), primary c<strong>on</strong>sumers (juvenile fish and<br />

invertebrate grazers, shredders and collectors) and sec<strong>on</strong>dary c<strong>on</strong>sumers (invertebrate<br />

predators and fish). All compartments are related wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a food web as well<br />

as to abiotic factors such as light, temperature and nutrients. Ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er literature<br />

review was carried <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most relevant perturbati<strong>on</strong> functi<strong>on</strong>s ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically<br />

describing how c<strong>on</strong>taminants impact populati<strong>on</strong> dynamics, trophic relati<strong>on</strong>ships<br />

and ecosystem functi<strong>on</strong>ning. These two literature reviews also provided for all parameters<br />

point estimates as well as some probability distributi<strong>on</strong>s. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 13 state<br />

variables (compartments), 23 interacti<strong>on</strong>s between species and 63 ecological processes,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> model parameters was necessarily very high ( 260), making<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e calibrati<strong>on</strong> process very complex and computati<strong>on</strong>ally expensive. To overcome<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese difficulties, sensitivity analyses (SA) seem particularly relevant [3]. They<br />

allow identifying n<strong>on</strong>-influential parameters <str<strong>on</strong>g>th</str<strong>on</strong>g>at can <str<strong>on</strong>g>th</str<strong>on</strong>g>en be fixed at a nominal<br />

value wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out significantly reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e variance <str<strong>on</strong>g>of</str<strong>on</strong>g> outputs. Am<strong>on</strong>g SA me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods,<br />

screening <strong>on</strong>es could be preferred as <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are computati<strong>on</strong>ally cheap, compared to<br />

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global <strong>on</strong>es. But screening SA me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are <strong>on</strong>ly qualitative and do not compute<br />

an output variance decompositi<strong>on</strong> based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e input uncertainties. Hence, we first<br />

tested and compared two screening SA me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: <str<strong>on</strong>g>th</str<strong>on</strong>g>e Morris [4] me<str<strong>on</strong>g>th</str<strong>on</strong>g>od and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>od developed by Klepper [4]. In order to check <str<strong>on</strong>g>th</str<strong>on</strong>g>e reliability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir results,<br />

we sec<strong>on</strong>d carried out a comparis<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> results given by two global quantitative<br />

SA me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: <str<strong>on</strong>g>th</str<strong>on</strong>g>e Standardized Regressi<strong>on</strong> Coefficients (SRC) me<str<strong>on</strong>g>th</str<strong>on</strong>g>od and me<str<strong>on</strong>g>th</str<strong>on</strong>g>od<br />

FAST. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e last two me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are computati<strong>on</strong>ally expensive, we were <strong>on</strong>ly able<br />

to perform all our comparis<strong>on</strong>s <strong>on</strong> a reduced versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> our model, <str<strong>on</strong>g>th</str<strong>on</strong>g>e "Periphyt<strong>on</strong>-<br />

Grazers" submodel, which c<strong>on</strong>tained a very small number <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters ( 20). The<br />

Morris me<str<strong>on</strong>g>th</str<strong>on</strong>g>od was finally <str<strong>on</strong>g>th</str<strong>on</strong>g>e best compromise to screen n<strong>on</strong>-influential parameters.<br />

Applied to <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole aquatic model, such a me<str<strong>on</strong>g>th</str<strong>on</strong>g>od allows <strong>on</strong>e to reduce<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying equati<strong>on</strong>s (some parameters are fixed, <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers<br />

have to be calibrated), and c<strong>on</strong>sequently to facilitate <str<strong>on</strong>g>th</str<strong>on</strong>g>e calibrati<strong>on</strong> process from<br />

experimental data.<br />

References.<br />

[1] F.DeLaender; K.A.C.De Schamphelaere, P.A.Vanrolleghem, C.R.Janssen. 2008. Validati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

an ecosystem modelling approach as a tool for ecological effect assessments. Chemosphere<br />

71:529-545.<br />

[2] S.M.Bartell, G.Lefebvre, G.Kaminski, M.Carreau, K.Rouse Campbell. 1999. An ecosystem<br />

model for assessing ecological risks in Québec rivers, lakes, and reservoirs. Ecological Modelling<br />

124:43-67.<br />

[3] A. Saltelli, K.Chan, E.M.Scott. 2008. Sensitivity analysis. Chicheter. UK: John Wiley & S<strong>on</strong>s<br />

Ltd. 475p.<br />

[4] Max D.Morris. 1991. Factorial sampling plans for preliminary computati<strong>on</strong>al experiments.<br />

Technometrics 33(2):161-174<br />

[5] O. Klepper. 1997. Multivariate aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> model uncertainty analysis: tools for sensitivity<br />

analysis and calibrati<strong>on</strong>. Ecological Modelling 101:1-13<br />

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Recent advances in infectious disease modelling I; Saturday, July 2, 11:00<br />

Stanca M. Ciupe<br />

UL Lafayette<br />

e-mail: msc6503@louisiana.edu<br />

Ruy Ribeiro<br />

Los Alamos Nati<strong>on</strong>al Laboratory<br />

e-mail: ruy@lanl.gov<br />

Alan Perels<strong>on</strong><br />

Los Alamos Nati<strong>on</strong>al Laboratory<br />

e-mail: asp@lanl.gov<br />

Antibody resp<strong>on</strong>ses during Hepatitis B viral infecti<strong>on</strong><br />

Infecti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> hepatitis B virus results in <str<strong>on</strong>g>th</str<strong>on</strong>g>e syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>of</str<strong>on</strong>g> a large excess <str<strong>on</strong>g>of</str<strong>on</strong>g> subviral<br />

particles, which are empty particles wi<str<strong>on</strong>g>th</str<strong>on</strong>g> viral proteins <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir surface but wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out<br />

viral nucleic acids. The reas<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir overproducti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tributi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ey<br />

play in HBV pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenesis is not understood. Here, we investigate whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er subviral<br />

particles can serve as a decoy by adsorbing neutralizing antibodies and <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore<br />

delaying <str<strong>on</strong>g>th</str<strong>on</strong>g>e clearance <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong>. We develop a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> HBVantibody<br />

interacti<strong>on</strong> and determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e quantitative c<strong>on</strong>tributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> virus-antibody<br />

and subviral particles-antibody formati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong>. We extend<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e results to account for <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple Hepatitis B surface proteins,<br />

each <str<strong>on</strong>g>of</str<strong>on</strong>g> which can potentially facilitate infecti<strong>on</strong>. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>is extended model we<br />

investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e necessity for <str<strong>on</strong>g>th</str<strong>on</strong>g>e antibody to bind all available surface proteins to<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g>fer protecti<strong>on</strong>.<br />

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Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

V; Wednesday, June 29, 11:00<br />

Jean Clairambault<br />

INRIA Paris-Rocquencourt, France<br />

e-mail: jean.clairambault@inria.fr<br />

Numerical optimisati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> anticancer <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutics, especially<br />

chr<strong>on</strong>o<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutics, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> toxicity c<strong>on</strong>straints<br />

I will firstly recall previous results <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimisati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a chr<strong>on</strong>o<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy delivered<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e general circulati<strong>on</strong>, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> targets <strong>on</strong> two separate cell populati<strong>on</strong>s, heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y<br />

and tumour. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is representati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e proliferating cell populati<strong>on</strong>s under attack<br />

are modelled by simple ordinary differential equati<strong>on</strong>s (ODEs). The variables under<br />

c<strong>on</strong>trol are numbers or densities <str<strong>on</strong>g>of</str<strong>on</strong>g> cells in homogeneous populati<strong>on</strong>s, heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y or tumour,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e actual drug targets being cell dea<str<strong>on</strong>g>th</str<strong>on</strong>g> rates. A Lagrangian is designed from<br />

objective (killing cancer cells) and c<strong>on</strong>straint (preserving heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y cells) functi<strong>on</strong>s.<br />

Its numerical maximizati<strong>on</strong> yields suboptimal soluti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be implemented<br />

as c<strong>on</strong>tinuous drug delivery schedules in programmable pumps <str<strong>on</strong>g>th</str<strong>on</strong>g>at are in use in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e clinic. Chr<strong>on</strong>o<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutics, a me<str<strong>on</strong>g>th</str<strong>on</strong>g>od used in <str<strong>on</strong>g>th</str<strong>on</strong>g>e clinical treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> cancers,<br />

takes advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> circadian clock phase differences <str<strong>on</strong>g>th</str<strong>on</strong>g>at exist between heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y and<br />

cancer cells to optimise drug delivery using such pumps. These differences are represented<br />

as differences between 24 h-periodic modulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug effects in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cell populati<strong>on</strong> models.<br />

Then I will develop more recent aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same optimisati<strong>on</strong> problem,<br />

where, instead <str<strong>on</strong>g>of</str<strong>on</strong>g> ODEs, physiologically structured partial differential equati<strong>on</strong>s<br />

(PDEs) representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e divisi<strong>on</strong> cycle in proliferating cell populati<strong>on</strong>s are used<br />

here, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> as variables cell populati<strong>on</strong> number or densities, heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y and tumour.<br />

The variables under c<strong>on</strong>trol are however here not cell numbers, but grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rates<br />

(first eigenvalues <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e linear PDE systems), yielding bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e objective functi<strong>on</strong><br />

(for tumour cells) and <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>straint functi<strong>on</strong> (for heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y cells), from which a Lagrangian<br />

is also designed. The actual targets <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trol are in <str<strong>on</strong>g>th</str<strong>on</strong>g>is representati<strong>on</strong><br />

cell cycle phase transiti<strong>on</strong> rates, which is much more realistic <str<strong>on</strong>g>th</str<strong>on</strong>g>an cell dea<str<strong>on</strong>g>th</str<strong>on</strong>g> rates<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> cytotoxic drugs, since <str<strong>on</strong>g>th</str<strong>on</strong>g>eir effects are not directly exerted by enhancing<br />

dea<str<strong>on</strong>g>th</str<strong>on</strong>g> rates, but ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er by blocking cell cycle checkpoints. These checkpoints<br />

are bo<str<strong>on</strong>g>th</str<strong>on</strong>g> physiologically (by circadian clocks) and pharmacologically c<strong>on</strong>trolled.<br />

Differences between heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y and tumour cells are here modelled as different synchr<strong>on</strong>isati<strong>on</strong>s<br />

between cell cycle phases, since heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y cell populati<strong>on</strong>s are assumed<br />

to be more synchr<strong>on</strong>ised, i.e., wi<str<strong>on</strong>g>th</str<strong>on</strong>g> steeper transiti<strong>on</strong> functi<strong>on</strong>s between cell cycle<br />

phases, <str<strong>on</strong>g>th</str<strong>on</strong>g>an tumour cell populati<strong>on</strong>s.<br />

Finally I will present a prospective view, adapted to pers<strong>on</strong>alised medicine,<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic optimisati<strong>on</strong> in <strong>on</strong>cology, which is based <strong>on</strong> physiological modelling<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>roughout <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e targets (cell populati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole body) and <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol<br />

means (fate <str<strong>on</strong>g>of</str<strong>on</strong>g> drugs, from <str<strong>on</strong>g>th</str<strong>on</strong>g>eir infusi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e general circulati<strong>on</strong> until <str<strong>on</strong>g>th</str<strong>on</strong>g>eir molecular<br />

acti<strong>on</strong> at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell and tissue level). To make <str<strong>on</strong>g>th</str<strong>on</strong>g>ese views more complete, I will<br />

also present extended principles <str<strong>on</strong>g>of</str<strong>on</strong>g> drug delivery optimisati<strong>on</strong>, presently using <strong>on</strong>ly<br />

toxicity c<strong>on</strong>straints <strong>on</strong> heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y cells, but also in <str<strong>on</strong>g>th</str<strong>on</strong>g>e future, at a different time scale,<br />

simultaneously using drug resistance c<strong>on</strong>straints <strong>on</strong> tumours wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a cell Darwinian<br />

point <str<strong>on</strong>g>of</str<strong>on</strong>g> view.<br />

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James Clarke<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Ba<str<strong>on</strong>g>th</str<strong>on</strong>g>, UK<br />

e-mail: J.P.Clarke@ba<str<strong>on</strong>g>th</str<strong>on</strong>g>.ac.uk<br />

Dr. K.A. Jane White<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Ba<str<strong>on</strong>g>th</str<strong>on</strong>g>, UK<br />

e-mail: maskajw@ba<str<strong>on</strong>g>th</str<strong>on</strong>g>.ac.uk<br />

Dr. Katy Turner<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bristol, UK<br />

e-mail: katy.turner@bristol.ac.uk<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

C<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> Chlamydia from a public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> viewpoint<br />

Infecti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Chlamydia trachomatis poses a significant public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> problem in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e UK and worldwide. Left untreated <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong> can cause fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er problems<br />

in individuals, including PID, epididymitis, and infertility. People wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Chlamydia<br />

infecti<strong>on</strong>, (or o<str<strong>on</strong>g>th</str<strong>on</strong>g>er bacterial STIs) are also more likely to be infected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> HIV<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough sexual c<strong>on</strong>tact. We have been comparing <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficacy <str<strong>on</strong>g>of</str<strong>on</strong>g> random screening,<br />

c<strong>on</strong>tact tracing, and combinati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to c<strong>on</strong>trolling Chlamydia<br />

levels in a populati<strong>on</strong> in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong> is already endemic. Our model<br />

system involves a pair approximati<strong>on</strong> approach to mimic sexual c<strong>on</strong>tact structure<br />

and we explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> changes in key c<strong>on</strong>trol parameters over timescales <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

relevance to public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> policy makers. In particular we use our model analysis<br />

to answer <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong>: what combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> screening and c<strong>on</strong>tact tracing should<br />

be employed to minimise prevalence <str<strong>on</strong>g>of</str<strong>on</strong>g> Chlamydia over realistic time intervals?<br />

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Christina Cobbold<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Glasgow<br />

e-mail: cc@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.gla.ac.uk<br />

Populati<strong>on</strong> Dynamics; Friday, July 1, 14:30<br />

Emerging spatio-temporal patterns in a model <str<strong>on</strong>g>of</str<strong>on</strong>g> insect<br />

invasi<strong>on</strong><br />

Recent empirical studies <str<strong>on</strong>g>of</str<strong>on</strong>g> insect invasi<strong>on</strong>s have provided evidence for invasive<br />

waves wi<str<strong>on</strong>g>th</str<strong>on</strong>g> endogenously generated variance in spread rates. Integrodifference equati<strong>on</strong>s<br />

provide a general framework to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> an invasive species when<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e species has distinct grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and dispersal phases. Many insects from temporate<br />

climates satisfy <str<strong>on</strong>g>th</str<strong>on</strong>g>is descripti<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I will present an integrodifference<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> insect host-parasitoid co-invasi<strong>on</strong> which exhibits endogenously generated<br />

variance in spread rate. The emerging spatio-temporal patterns which form in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

wake <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pulsed wavefr<strong>on</strong>t may provide insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms <str<strong>on</strong>g>th</str<strong>on</strong>g>at lead to<br />

collapse and generati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> insect outbreaks at <str<strong>on</strong>g>th</str<strong>on</strong>g>e landscape scale.<br />

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Daniel C<str<strong>on</strong>g>of</str<strong>on</strong>g>field Jr.<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Michigan-Flint<br />

e-mail: dc<str<strong>on</strong>g>of</str<strong>on</strong>g>fiel@umflint.edu<br />

Vector-borne diseases; Tuesday, June 28, 14:30<br />

A Model for Chagas Disease wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Vector C<strong>on</strong>sumpti<strong>on</strong> and<br />

Transplacental Transmissi<strong>on</strong><br />

Chagas disease is caused by <str<strong>on</strong>g>th</str<strong>on</strong>g>e parasite Trypanosoma cruzi, which is spread primarily<br />

by domestic vectors in <str<strong>on</strong>g>th</str<strong>on</strong>g>e reduviid family, and affects humans and domestic<br />

mammals <str<strong>on</strong>g>th</str<strong>on</strong>g>roughout rural areas in Central and Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> America. An epidemiological<br />

model for Chagas disease in a hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>etical village setting will be presented.<br />

The model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> a n<strong>on</strong>linear coupled system <str<strong>on</strong>g>of</str<strong>on</strong>g> four differential equati<strong>on</strong>s,<br />

<strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> which has a delay, <str<strong>on</strong>g>th</str<strong>on</strong>g>at describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> change <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e total number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vectors, infected vectors, infected humans, and infected domestic mammals.<br />

In additi<strong>on</strong> to bir<str<strong>on</strong>g>th</str<strong>on</strong>g>, dea<str<strong>on</strong>g>th</str<strong>on</strong>g>, and parasite transmissi<strong>on</strong> due to vectors, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

takes into account insecticide spraying, transplacental transmissi<strong>on</strong>, and c<strong>on</strong>sumpti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vector by domestic mammals. Steady state analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

c<strong>on</strong>stant coefficients provides a stability c<strong>on</strong>diti<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model parameters. In representative<br />

examples, <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory and computer simulati<strong>on</strong>s reveal <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e endemic<br />

equilibrium is locally asymptotically stable.<br />

181

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Modeling viral hepatitis dynamics in-vivo and in-vitro in <str<strong>on</strong>g>th</str<strong>on</strong>g>e era <str<strong>on</strong>g>of</str<strong>on</strong>g> direct<br />

anti-viral agents II; Wednesday, June 29, 08:30<br />

Piero Colombatto<br />

Hepatology Unit, University Hospital <str<strong>on</strong>g>of</str<strong>on</strong>g> Pisa, Pisa, Italy<br />

e-mail: p.colombatto@ao-pisa.toscana.it<br />

Luigi Civitano<br />

Hepatology Unit, University Hospital <str<strong>on</strong>g>of</str<strong>on</strong>g> Pisa, Pisa, Italy<br />

Ver<strong>on</strong>ica Romagnoli<br />

Hepatology Unit, University Hospital <str<strong>on</strong>g>of</str<strong>on</strong>g> Pisa, Pisa, Italy<br />

Pietro Ciccorossi<br />

Hepatology Unit, University Hospital <str<strong>on</strong>g>of</str<strong>on</strong>g> Pisa, Pisa, Italy<br />

Ferruccio B<strong>on</strong>ino<br />

Hepatology Unit, University Hospital <str<strong>on</strong>g>of</str<strong>on</strong>g> Pisa, Pisa, Italy<br />

Maurizia Rossana Brunetto<br />

Hepatology Unit, University Hospital <str<strong>on</strong>g>of</str<strong>on</strong>g> Pisa, Pisa, Italy<br />

Simulating <str<strong>on</strong>g>th</str<strong>on</strong>g>e decline <str<strong>on</strong>g>of</str<strong>on</strong>g> HCV infected hepatocytes by<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling allows for individual tailoring <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Peg-IFN+RBV <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy and for a better selecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

candidates to <str<strong>on</strong>g>th</str<strong>on</strong>g>e new direct antiviral agents.<br />

Background. We have already shown in a retrospective study <str<strong>on</strong>g>th</str<strong>on</strong>g>at modelling infected<br />

cells dynamics by ALT and HCV RNA decline during <str<strong>on</strong>g>th</str<strong>on</strong>g>e first 4 weeks <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy warrants accurate predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment outcome and <str<strong>on</strong>g>of</str<strong>on</strong>g>fer <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility<br />

to compute individual treatment durati<strong>on</strong>. We compared in a randomised c<strong>on</strong>trolled<br />

trial <str<strong>on</strong>g>th</str<strong>on</strong>g>e durati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficacy <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e new model tailored (MT) schedule vs <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

traditi<strong>on</strong>al Guide Line (GL). Patients and me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods. 100 c<strong>on</strong>secutive patients stratified<br />

by previous <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy (38 nave, 62 retreated), HCV genotype (60 G1-G4 and 40<br />

G2-G3)and peg-IFN type (60 2a and 40 2b), randomly received GL or MT schedules.<br />

GL pts were treated 24 weeks if G2-G3 and 48 weeks if G1-G4 applying week<br />

12 stopping rule in G1 n<strong>on</strong> resp<strong>on</strong>ders (NR). In MT patients ALT and HCV RNA<br />

were measured at day 0-2-4-7-14-21-28 to compute <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> infected cells at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e end <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy (Ieot), treatment was stopped at week 6 if computed Ieot at<br />

GL durati<strong>on</strong> > 5000 (NR), o<str<strong>on</strong>g>th</str<strong>on</strong>g>erwise tailored to achieve Ieot < 250. Results. Ieot<br />

could be computed in 42 (84%) MT patients, <str<strong>on</strong>g>th</str<strong>on</strong>g>e remaining 8 pts showed ALT<br />

or HCV-RNA data <str<strong>on</strong>g>th</str<strong>on</strong>g>at did not fit into <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, <str<strong>on</strong>g>th</str<strong>on</strong>g>us <str<strong>on</strong>g>th</str<strong>on</strong>g>ey were treated wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

GL schedules and not included in <str<strong>on</strong>g>th</str<strong>on</strong>g>is analysis. Therapy was wi<str<strong>on</strong>g>th</str<strong>on</strong>g>drawn/modified<br />

because <str<strong>on</strong>g>of</str<strong>on</strong>g> side effects in 13 (26%) MT and in 9 (18%) GL pts. Therapy was disc<strong>on</strong>tinued<br />

at week 6 because <str<strong>on</strong>g>of</str<strong>on</strong>g> NR in 11 (22%) MT pts and at week 12 in 8 (16%)<br />

GL pts. The SVR rate in <str<strong>on</strong>g>th</str<strong>on</strong>g>ose who completed <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy was 85% according to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

MT (mean durati<strong>on</strong> 32 weeks, range:13-56) and 82% according to <str<strong>on</strong>g>th</str<strong>on</strong>g>e GL (mean<br />

durati<strong>on</strong> 38 weeks, range:24-48). Treatment durati<strong>on</strong> in SVR pts ranged between<br />

18-55 weeks in 7 G1 pts, 13-21 weeks in 3 G2 pts and 21-56 weeks in 5 G3 pts.<br />

Mean durati<strong>on</strong> for SVR <str<strong>on</strong>g>of</str<strong>on</strong>g> GL schedules was 21% l<strong>on</strong>ger in resp<strong>on</strong>der patients and<br />

100% in NR. C<strong>on</strong>clusi<strong>on</strong>s. The prospective applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> our model c<strong>on</strong>firmed <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

wide diversificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment durati<strong>on</strong> required for SVR, as predicted by<br />

our previous retrospective study, and allowed in clinical practice a fine pers<strong>on</strong>alizati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e antiviral treatment at <str<strong>on</strong>g>th</str<strong>on</strong>g>e single patient level. Tailoring treatment to<br />

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Ieot

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chaste framework;<br />

Tuesday, June 28, 11:00<br />

Ornella Cominetti<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: cominetti@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. Philip Maini<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. Helen Byrne<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. Angela Shifflet<br />

W<str<strong>on</strong>g>of</str<strong>on</strong>g>ford College<br />

Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. George Shifflet<br />

W<str<strong>on</strong>g>of</str<strong>on</strong>g>ford College<br />

Using a cell-vertex model to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> differential<br />

adhesi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e intestinal crypt<br />

A cell-based vertex model in Chaste was used to study differential adhesi<strong>on</strong> and cell<br />

positi<strong>on</strong>ing in <str<strong>on</strong>g>th</str<strong>on</strong>g>e intestinal crypt. The results were compared to <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>es obtained<br />

using a different modelling framework, namely <str<strong>on</strong>g>th</str<strong>on</strong>g>e Potts model.<br />

When directly comparing <str<strong>on</strong>g>th</str<strong>on</strong>g>e models simulati<strong>on</strong>s we see <str<strong>on</strong>g>th</str<strong>on</strong>g>at bo<str<strong>on</strong>g>th</str<strong>on</strong>g> models agree<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental data in transit time, migratory velocities and migratory patterns<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cells. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>is is not <str<strong>on</strong>g>th</str<strong>on</strong>g>e case when comparing <str<strong>on</strong>g>th</str<strong>on</strong>g>e boundary between<br />

differentiated and transit amplifying cells: while using <str<strong>on</strong>g>th</str<strong>on</strong>g>e Potts model a sharp<br />

boundary can be observed, using <str<strong>on</strong>g>th</str<strong>on</strong>g>e vertex model such boundary is not seen.<br />

Our results suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at different modelling frameworks can give different answers<br />

when studying <str<strong>on</strong>g>th</str<strong>on</strong>g>e same phenomen<strong>on</strong>, reinforcing <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> testing<br />

in more <str<strong>on</strong>g>th</str<strong>on</strong>g>an <strong>on</strong>e modelling platform in order to obtain robust results.<br />

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Structure and Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemical Reacti<strong>on</strong> Networks I; Tuesday, June<br />

28, 14:30<br />

Carsten C<strong>on</strong>radi<br />

MPI Magdeburg<br />

e-mail: c<strong>on</strong>radi@mpi-magdeburg.mpg.de<br />

Dietrich Flockerzi<br />

MPI Magdeburg<br />

Multistati<strong>on</strong>arity in mass acti<strong>on</strong> networks by linear<br />

inequality systems<br />

Ordinary Differential Equati<strong>on</strong>s (ODEs) are an important tool in many areas <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Quantitative Biology. For many ODE systems multistati<strong>on</strong>arity (i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> at least two positive steady states) is a desired feature. In general establishing<br />

multistati<strong>on</strong>arity is a difficult task as realistic biological models are large in terms <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

states and (unknown) parameters and in most cases poorly parameterized (because<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> noisy measurement data <str<strong>on</strong>g>of</str<strong>on</strong>g> few comp<strong>on</strong>ents, a very small number <str<strong>on</strong>g>of</str<strong>on</strong>g> data points<br />

and <strong>on</strong>ly a limited number <str<strong>on</strong>g>of</str<strong>on</strong>g> repetiti<strong>on</strong>s). For mass acti<strong>on</strong> networks establishing<br />

multistati<strong>on</strong>arity hence is equivalent to establishing <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> at least two<br />

positive soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> a large polynomial system wi<str<strong>on</strong>g>th</str<strong>on</strong>g> unknown coefficients. For<br />

mass acti<strong>on</strong> networks wi<str<strong>on</strong>g>th</str<strong>on</strong>g> certain structural properties, expressed in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

stoichiometric matrix and <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong> rate-exp<strong>on</strong>ent matrix, we present necessary<br />

and sufficient c<strong>on</strong>diti<strong>on</strong>s for multistati<strong>on</strong>arity <str<strong>on</strong>g>th</str<strong>on</strong>g>at take <str<strong>on</strong>g>th</str<strong>on</strong>g>e form linear inequality<br />

systems. Soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese inequality systems define pairs <str<strong>on</strong>g>of</str<strong>on</strong>g> steady states and<br />

parameter values. We also present a sufficient c<strong>on</strong>diti<strong>on</strong> to identify networks where<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e aforementi<strong>on</strong>ed c<strong>on</strong>diti<strong>on</strong>s hold.<br />

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Jessica C<strong>on</strong>way<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> British Columbia<br />

e-mail: c<strong>on</strong>way@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ubc.ca<br />

Dr. Daniel Coombs<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> British Columbia<br />

Immunology; Wednesday, June 29, 17:00<br />

C<strong>on</strong>tinuous-time branching processes to model viral load in<br />

treated HIV+ individuals<br />

We will discuss a c<strong>on</strong>tinuous-time, multi-type branching model <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV viral dynamics<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood stream. We are motivated by observati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> viral load in<br />

HIV+ patients <strong>on</strong> anti-retroviral treatment (ART). ARTs very effectively limit viral<br />

replicati<strong>on</strong>. However, while <strong>on</strong> ARTs, an HIV+ individual’s viral load remains<br />

n<strong>on</strong>-zero, and blood tests show occasi<strong>on</strong>al viral blips: short periods <str<strong>on</strong>g>of</str<strong>on</strong>g> increased<br />

viral load. We hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esize <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is low viral load can be attributed to activati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cells latently infected by HIV before treatment initiati<strong>on</strong>. Blips <str<strong>on</strong>g>th</str<strong>on</strong>g>en represent<br />

small-probability deviati<strong>on</strong>s from <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean. Modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>is system as a branching<br />

process, we derive equati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability generating functi<strong>on</strong>. Using a novel<br />

numerical approach we extract probability distributi<strong>on</strong>s for viral load yielding blip<br />

amplitudes c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> patient data. We <str<strong>on</strong>g>th</str<strong>on</strong>g>en compute distributi<strong>on</strong>s <strong>on</strong> durati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese blips <str<strong>on</strong>g>th</str<strong>on</strong>g>rough direct numerical simulati<strong>on</strong>. Our stochastic model <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

latent cell activati<strong>on</strong> reproduces features <str<strong>on</strong>g>of</str<strong>on</strong>g> treated HIV infecti<strong>on</strong>. It can be used<br />

to provide insight into variability <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment outcomes for HIV+ individuals not<br />

available in deterministic models.<br />

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Populati<strong>on</strong> Dynamics; Wednesday, June 29, 11:00<br />

Flora Cordoleani<br />

Jean-Christophe Poggiale<br />

David Nerini<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ias Gauduch<strong>on</strong><br />

Andrew Morozov<br />

Centre d’Oceanologie de Marseille, Universite de la Mediterranee,<br />

UMR LMGEM 6117 CNRS, Campus de Luminy, Case 901,13288 Marseille<br />

Cedex 09, FRANCE<br />

e-mail: flora.cordoleani@univmed.fr<br />

Development <str<strong>on</strong>g>of</str<strong>on</strong>g> structure sensitivity analysis me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

Most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e time, sensitivity analyses performed <strong>on</strong> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models are<br />

limited to <str<strong>on</strong>g>th</str<strong>on</strong>g>ose c<strong>on</strong>cerning <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters. Though, it has been shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical formulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological processes <str<strong>on</strong>g>th</str<strong>on</strong>g>at <strong>on</strong>e wants to model can<br />

also be very important for <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> ecological systems. For instance, several<br />

au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors have highlighted <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e choice <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong>al resp<strong>on</strong>se formulati<strong>on</strong>,<br />

which gives <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sumpti<strong>on</strong> rate <str<strong>on</strong>g>of</str<strong>on</strong>g> predators as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> prey density, can have<br />

a str<strong>on</strong>g impact <strong>on</strong> predator-prey models behavior and stability. This is referred by<br />

[1] as a new type <str<strong>on</strong>g>of</str<strong>on</strong>g> model sensitivity, called <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure sensitivity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model.<br />

The formulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biological processes can be very complex and it is not rare<br />

to find several possible ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical expressi<strong>on</strong>s to model <strong>on</strong>e process. Indeed,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e process studied is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten difficult to measure in <str<strong>on</strong>g>th</str<strong>on</strong>g>e natural medium and it is<br />

approximated by functi<strong>on</strong>s estimated from laboratory or in situ experiments. These<br />

functi<strong>on</strong>s are c<strong>on</strong>sidered as a good approximati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e phenomen<strong>on</strong> observed in<br />

natural systems, which is <str<strong>on</strong>g>of</str<strong>on</strong>g> course questi<strong>on</strong>able since it has been dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

natural systems are much more heterogeneous <str<strong>on</strong>g>th</str<strong>on</strong>g>an simplified laboratory systems.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>text, we have decided to develop some simple ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at will help modelers to detect and to measure if <str<strong>on</strong>g>th</str<strong>on</strong>g>eir system is sensitive to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e formulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e process studied. We argue <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is type <str<strong>on</strong>g>of</str<strong>on</strong>g> analysis is<br />

essential if <strong>on</strong>e wants to be able to use and comment informati<strong>on</strong>s obtained from<br />

model simulati<strong>on</strong>s. We show an example <str<strong>on</strong>g>of</str<strong>on</strong>g> applicati<strong>on</strong> by investigating <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong>al resp<strong>on</strong>se formulati<strong>on</strong> <strong>on</strong> a chemostat-type predator-prey model<br />

dynamics. We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e system does exhibit structure sensitivity, which is even<br />

str<strong>on</strong>ger <str<strong>on</strong>g>th</str<strong>on</strong>g>an system parameters sensitivity.<br />

References.<br />

[1] Wood, S. N. and Thomas, M. B., 1999. Super-sensitivity to structure in biological models.<br />

Proc. R. Soc. L<strong>on</strong>d. B 266, 565-570.<br />

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Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 11:00<br />

Stephen Cornell<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Leeds, Leeds LS2 9JT,<br />

UK<br />

e-mail: s.j.cornell@leeds.ac.uk<br />

Space, coexistence, and mutual invasibility<br />

Two possible c<strong>on</strong>diti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at will lead to two species coexisting are: (i) <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a<br />

stable equilibrium point where bo<str<strong>on</strong>g>th</str<strong>on</strong>g> densities are n<strong>on</strong>zero; and (ii) ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er species<br />

can invade <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er when rare. For many simple models <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two c<strong>on</strong>diti<strong>on</strong>s<br />

are equivalent, but <str<strong>on</strong>g>th</str<strong>on</strong>g>is need not be <str<strong>on</strong>g>th</str<strong>on</strong>g>e case. Unfortunately, a dear<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> exact<br />

analytical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods hampers <str<strong>on</strong>g>th</str<strong>on</strong>g>e explorati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is questi<strong>on</strong> for spatial, stochastic<br />

systems. However, asymptotically exact results can be computed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e limit where<br />

interacti<strong>on</strong>s take place <strong>on</strong> a large but finite leng<str<strong>on</strong>g>th</str<strong>on</strong>g> scale [1]. Here, I study a spatial,<br />

stochastic Lotka-Volterra competiti<strong>on</strong> model, which is selectively neutral except<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial kernels <str<strong>on</strong>g>th</str<strong>on</strong>g>at describe wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in- and between-species interacti<strong>on</strong>s [2].<br />

The equilibrium stability eigenvalue gives a weal<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> (asymptotically exact) results<br />

for when coexistence is to be expected. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasibility eigenvalues give<br />

different prediti<strong>on</strong>s. I argue <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is is because exp<strong>on</strong>ential grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is not an<br />

appropriate descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> successful invasi<strong>on</strong> in spatial systems. This means <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

approximati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for computing invasi<strong>on</strong> eigenvalues can give misleading<br />

results in evoluti<strong>on</strong>ary studies <str<strong>on</strong>g>of</str<strong>on</strong>g> spatial systems.<br />

References.<br />

[1] O. Ovaskainen and S. J. Cornell Space and Stochasticity in populati<strong>on</strong> dynamics Proc. Natl.<br />

Acad. Sci. USA 103 12781–12786 (2006).<br />

[2] D. J. Murrell and R. Law Heteromyopia and <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> similar competitors<br />

Ecology Letters 6 48–19 (2003).<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Andres Cortes<br />

Uppsala University, Sweden<br />

e-mail: aj.cortes235@gmail.com<br />

Fredy M<strong>on</strong>serrate<br />

Centro Internaci<strong>on</strong>al de Agricultura Tropical, Cali, Colombia<br />

Santiago Madriñán<br />

Universidad de los Andes, Bogotá, Colombia<br />

Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ew W. Blair<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Plant Breeding and Genetics, Cornell University, I<str<strong>on</strong>g>th</str<strong>on</strong>g>aca<br />

NY<br />

The Utility <str<strong>on</strong>g>of</str<strong>on</strong>g> Thorn<str<strong>on</strong>g>th</str<strong>on</strong>g>waite and Ham<strong>on</strong> Models for<br />

Potential Evotranspirati<strong>on</strong> and Drought Index Calculati<strong>on</strong>:<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Case <str<strong>on</strong>g>of</str<strong>on</strong>g> Wild Comm<strong>on</strong> Bean<br />

Potential Evotranspirati<strong>on</strong> (PET) is a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical value <str<strong>on</strong>g>th</str<strong>on</strong>g>at aims to characterize<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e quantity <str<strong>on</strong>g>of</str<strong>on</strong>g> water <str<strong>on</strong>g>th</str<strong>on</strong>g>at will flux from <str<strong>on</strong>g>th</str<strong>on</strong>g>e soil-biosphere system towards <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

atmosphere as a c<strong>on</strong>sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> evaporati<strong>on</strong> and transpirati<strong>on</strong>, based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e suppositi<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at available water is infinite. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is research, an agroecological diversity<br />

study based <strong>on</strong> PET was c<strong>on</strong>ducted <strong>on</strong> 104 wild comm<strong>on</strong> beans to estimate drought<br />

tolerance in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir natural habitats. Our wild populati<strong>on</strong> samples covered a range<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> mesic to very dry habitats from Mexico to Argentina. Two PET models which<br />

c<strong>on</strong>sidered <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> temperature and radiati<strong>on</strong> were coupled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e precipitati<strong>on</strong><br />

regimens for each collecti<strong>on</strong> site during <str<strong>on</strong>g>th</str<strong>on</strong>g>e last fifty years. We detected<br />

a broader geographic distributi<strong>on</strong> in wild comm<strong>on</strong> beans <str<strong>on</strong>g>th</str<strong>on</strong>g>an in cultivated <strong>on</strong>es.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we found <str<strong>on</strong>g>th</str<strong>on</strong>g>at wild accessi<strong>on</strong>s were distributed am<strong>on</strong>g different precipitati<strong>on</strong><br />

regimens following a latitudinal gradient and <str<strong>on</strong>g>th</str<strong>on</strong>g>at agroecological diversity<br />

was structured into natural populati<strong>on</strong>s. Habitat drought stress index based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Thorn<str<strong>on</strong>g>th</str<strong>on</strong>g>waite potential evotranspirati<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>e most promising predictor <str<strong>on</strong>g>of</str<strong>on</strong>g> drought<br />

tolerance. This resource should be coupled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>siderati<strong>on</strong>s about populati<strong>on</strong><br />

structure as a c<strong>on</strong>sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary history and diversificati<strong>on</strong> process<br />

suffered by <str<strong>on</strong>g>th</str<strong>on</strong>g>e species. Finally, <str<strong>on</strong>g>th</str<strong>on</strong>g>is modeling tool suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at informati<strong>on</strong> from<br />

wild comm<strong>on</strong> bean accessi<strong>on</strong>s should be taken into account in order to exploit variati<strong>on</strong><br />

for drought tolerance in order to minimize significant depleti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e yield<br />

comp<strong>on</strong>ents.<br />

Key words: Bioclimatic variables, potential evotranspirati<strong>on</strong> models, PET, precipitati<strong>on</strong>,<br />

Thorn<str<strong>on</strong>g>th</str<strong>on</strong>g>waite estimator, Ham<strong>on</strong> estimator<br />

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Adelle Coster<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> New Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Wales, Australia<br />

e-mail: A.Coster@unsw.edu.au<br />

Cell and Tissue Biophysics; Friday, July 1, 14:30<br />

Modelling Insulin Acti<strong>on</strong> <strong>on</strong> Glucose Transporters<br />

The applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> insulin to a cell causes membrane-embedded glucose transporter<br />

proteins to be transported to <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell surface. An experimental technique <str<strong>on</strong>g>th</str<strong>on</strong>g>at is<br />

ideally suited to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>is dynamic process is total internal reflecti<strong>on</strong> microscopy<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> single cells, where fluorescent markers are attached to <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecules<br />

and movements recorded. To create s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware capable <str<strong>on</strong>g>of</str<strong>on</strong>g> annotating <str<strong>on</strong>g>th</str<strong>on</strong>g>e recordings<br />

automatically, ideal ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models are required. Features <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e models and<br />

s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware are outlined and compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g> biological recordings.<br />

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Multiscale modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong> kinetics in biology; Tuesday, June 28, 14:30<br />

Sim<strong>on</strong> Cotter<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: cotter@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

A c<strong>on</strong>strained multiscale approach to modelling biochemical<br />

systems<br />

It is well known <str<strong>on</strong>g>th</str<strong>on</strong>g>at intrinsic noise can play a significant role in biological systems.<br />

Stochastic descripti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese types <str<strong>on</strong>g>of</str<strong>on</strong>g> systems give far more accurate representati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e true dynamics. Exact me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

systems exist, but can be very computati<strong>on</strong>ally expensive, particularly in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> multiple timescales. Many different me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods exist for reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e system<br />

to <strong>on</strong>e which is <strong>on</strong>ly c<strong>on</strong>cerned wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e slowly evolving variables.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we introduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e C<strong>on</strong>diti<strong>on</strong>al SSA (CSSA), a me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for sampling<br />

directly from <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>al distributi<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fast variables, given a value for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e slow variables. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>is, we go <strong>on</strong> to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e C<strong>on</strong>strained Multiscale<br />

Algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m (CMA), which uses simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e CSSA to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e drift and<br />

diffusi<strong>on</strong> terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effective dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e slow variables. We show how <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

approach can give accurate estimates for quantities <str<strong>on</strong>g>of</str<strong>on</strong>g> interest, such as average<br />

period <str<strong>on</strong>g>of</str<strong>on</strong>g> oscillati<strong>on</strong> in biological processes. This is joint work wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Radek Erban<br />

and Kostas Zygalakis (Oxford), and Ioannis Kevrekidis (Princet<strong>on</strong>).<br />

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling I; Tuesday, June 28, 17:00<br />

Markus Covert<br />

Stanford University<br />

e-mail: mcovert@stanford.edu<br />

Heterogeneous cellular resp<strong>on</strong>ses via noisy paracrine signals<br />

The mammalian immune resp<strong>on</strong>se is a striking example <str<strong>on</strong>g>of</str<strong>on</strong>g> coordinati<strong>on</strong> between<br />

individual cells. We previously discovered <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> wild-type murine<br />

embry<strong>on</strong>ic fibroblasts (MEFs) to lipopolysaccharide (LPS) depends <strong>on</strong> paracrine<br />

secreti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor necrosis factor (TNF). We <str<strong>on</strong>g>th</str<strong>on</strong>g>en dem<strong>on</strong>strated in single cells<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e low c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e paracrine TNF signal results in two qualitatively<br />

different resp<strong>on</strong>ses to LPS: roughly <strong>on</strong>e-half <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells exhibit a transient NFkappaB<br />

resp<strong>on</strong>se, while <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er half exhibit a persistent resp<strong>on</strong>se wi<str<strong>on</strong>g>th</str<strong>on</strong>g> NF-kappaB<br />

remaining in <str<strong>on</strong>g>th</str<strong>on</strong>g>e nucleus for hours. Only cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at sense <str<strong>on</strong>g>th</str<strong>on</strong>g>e low TNF c<strong>on</strong>centrati<strong>on</strong><br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore resp<strong>on</strong>d to <str<strong>on</strong>g>th</str<strong>on</strong>g>e paracrine signal exhibit <str<strong>on</strong>g>th</str<strong>on</strong>g>e persistent resp<strong>on</strong>se. The<br />

ability <str<strong>on</strong>g>of</str<strong>on</strong>g> a low c<strong>on</strong>centrati<strong>on</strong> signal to create qualitatively different subpopulati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cells in resp<strong>on</strong>se to <strong>on</strong>e stimulus led us to ask, how does a single cell resp<strong>on</strong>d to low<br />

c<strong>on</strong>centrati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> TNF? To answer <str<strong>on</strong>g>th</str<strong>on</strong>g>is questi<strong>on</strong>, we measured NF-kappaB activity<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>ousands <str<strong>on</strong>g>of</str<strong>on</strong>g> living cells under TNF doses covering four orders <str<strong>on</strong>g>of</str<strong>on</strong>g> magnitude to<br />

determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> individual cell resp<strong>on</strong>ses which occur in a populati<strong>on</strong>, and<br />

what effect <str<strong>on</strong>g>th</str<strong>on</strong>g>ese resp<strong>on</strong>ses might have <strong>on</strong> NF-kappaB dependent gene expressi<strong>on</strong>.<br />

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Structure and Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemical Reacti<strong>on</strong> Networks I; Tuesday, June<br />

28, 14:30<br />

Gheorghe Craciun<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Wisc<strong>on</strong>sin-Madis<strong>on</strong><br />

e-mail: craciun@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.wisc.edu<br />

Persistence and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Global Attractor C<strong>on</strong>jecture: The Big<br />

Picture<br />

We discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g-term behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> systems, and in particular <str<strong>on</strong>g>of</str<strong>on</strong>g> chemical<br />

reacti<strong>on</strong> systems modeled by mass-acti<strong>on</strong> kinetics. We especially focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

property <str<strong>on</strong>g>of</str<strong>on</strong>g> "persistence", and its c<strong>on</strong>necti<strong>on</strong>s to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er dynamical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

systems. A system is called persistent if no positive trajectory has a limit point<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e boundary <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e positive or<str<strong>on</strong>g>th</str<strong>on</strong>g>ant. Persistence is important in understanding<br />

properties <str<strong>on</strong>g>of</str<strong>on</strong>g> biochemical networks (e.g., will each chemical species be available<br />

indenitely in <str<strong>on</strong>g>th</str<strong>on</strong>g>e future), and also in ecology (e.g., will a species become extinct in<br />

an ecosystem), and in <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases (e.g., will an infecti<strong>on</strong> die<br />

o, or will it infect <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole populati<strong>on</strong>). We describe two important open problems<br />

for mass-acti<strong>on</strong> systems: <str<strong>on</strong>g>th</str<strong>on</strong>g>e Persistence C<strong>on</strong>jecture and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Global Attractor<br />

C<strong>on</strong>jecture. The Persistence C<strong>on</strong>jecture says <str<strong>on</strong>g>th</str<strong>on</strong>g>at weakly reversible mass-acti<strong>on</strong><br />

systems are persistent, independent <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e values <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong> rate parameters.<br />

A pro<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Persistence C<strong>on</strong>jecture would also imply <str<strong>on</strong>g>th</str<strong>on</strong>g>e Global Attractor C<strong>on</strong>jecture,<br />

which says <str<strong>on</strong>g>th</str<strong>on</strong>g>at complex balanced systems have a global attractor. We<br />

explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship between <str<strong>on</strong>g>th</str<strong>on</strong>g>ese c<strong>on</strong>jectures, and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er recent results. This<br />

is joint work wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Casian Pantea and Fedor Nazarov.<br />

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Cellular Systems Biology; Tuesday, June 28, 14:30<br />

Fabien Crauste<br />

Institut Camille Jordan UMR 5208, Université Claude Bernard Ly<strong>on</strong><br />

1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France;<br />

INRIA Team Dracula, INRIA Center Grenoble Rh<strong>on</strong>e-Alpes<br />

e-mail: crauste@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.univ-ly<strong>on</strong>1.fr<br />

Multiscale Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> Red Blood Cell Producti<strong>on</strong> using<br />

C<strong>on</strong>tinuous and Hybrid Models<br />

This presentati<strong>on</strong> will be devoted to multiscale ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> ery<str<strong>on</strong>g>th</str<strong>on</strong>g>ropoiesis,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> producti<strong>on</strong> and regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> red blood cells. It lies up<strong>on</strong><br />

works recently published [1, 2, 3, 4], in collaborati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> N. Bess<strong>on</strong><strong>on</strong>v (Institute<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Mechanical Engineering Problems, St Petersburg, Russia), I. Demin (Novartis<br />

Pharma, Basel, Switzerland), O. Gandrill<strong>on</strong> (University Ly<strong>on</strong> 1, France), S. Genieys<br />

(INSA de Toulouse, France), P. Kurbatova (University Ly<strong>on</strong> 1), S. Fisher (INSA de<br />

Ly<strong>on</strong>, France), L. Pujo-Menjouet (University Ly<strong>on</strong> 1) and V. Volpert (University<br />

Ly<strong>on</strong> 1, France), wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e INRIA Team Dracula (Ly<strong>on</strong>, France).<br />

Ery<str<strong>on</strong>g>th</str<strong>on</strong>g>ropoiesis is a complex process, involving cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different maturities,<br />

from very immature stem cells to circulating mature red blood cells. It is regulated<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> at <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular level and at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell populati<strong>on</strong> scale. We propose<br />

two complementary approaches for a multiscale model <str<strong>on</strong>g>of</str<strong>on</strong>g> ery<str<strong>on</strong>g>th</str<strong>on</strong>g>ropoiesis [1, 2, 4],<br />

in which we describe toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er ery<str<strong>on</strong>g>th</str<strong>on</strong>g>roid progenitor (immature red cells) dynamics<br />

and intracellular regulatory network <str<strong>on</strong>g>th</str<strong>on</strong>g>at determines ery<str<strong>on</strong>g>th</str<strong>on</strong>g>roid cell fate. The intracellular<br />

regulati<strong>on</strong> model is based <strong>on</strong> several proteins inhibiting and activating<br />

<strong>on</strong>e an o<str<strong>on</strong>g>th</str<strong>on</strong>g>er, under external acti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factors <str<strong>on</strong>g>th</str<strong>on</strong>g>at influence <str<strong>on</strong>g>th</str<strong>on</strong>g>eir producti<strong>on</strong>.<br />

The levels <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese proteins will decide <str<strong>on</strong>g>of</str<strong>on</strong>g> cell self-renewal, differentiati<strong>on</strong> or<br />

dea<str<strong>on</strong>g>th</str<strong>on</strong>g> by apoptosis. Ery<str<strong>on</strong>g>th</str<strong>on</strong>g>roid progenitors dynamics are ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er described wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an<br />

individual-based model as discrete elements [1] or wi<str<strong>on</strong>g>th</str<strong>on</strong>g> structured models, ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

compartmental models (systems <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary differential equati<strong>on</strong>s) [2, 4] or partial<br />

differential equati<strong>on</strong>s [3]. In bo<str<strong>on</strong>g>th</str<strong>on</strong>g> cases, n<strong>on</strong>linearities are c<strong>on</strong>sidered in <str<strong>on</strong>g>th</str<strong>on</strong>g>e models<br />

to account for cell fate regulati<strong>on</strong>.<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tinuous models is performed and simulati<strong>on</strong>s are carried out<br />

to c<strong>on</strong>fr<strong>on</strong>t <str<strong>on</strong>g>th</str<strong>on</strong>g>e models to experimental data <str<strong>on</strong>g>of</str<strong>on</strong>g> anemia (blood loss). The IBM is<br />

also c<strong>on</strong>fr<strong>on</strong>ted to experimental data, and <str<strong>on</strong>g>th</str<strong>on</strong>g>is allows c<strong>on</strong>cluding <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e roles <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

different feedback c<strong>on</strong>trols and <str<strong>on</strong>g>th</str<strong>on</strong>g>e relevance <str<strong>on</strong>g>of</str<strong>on</strong>g> such models, in order to provide<br />

more insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ery<str<strong>on</strong>g>th</str<strong>on</strong>g>ropoiesis.<br />

References.<br />

[1] N. Bess<strong>on</strong>ov, F. Crauste, S. Fisher, P. Kurbatova, V. Volpert (2010) Applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Hybrid<br />

Models to Blood Cell Producti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e B<strong>on</strong>e Marrow, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Model Nat Phenom 6 (7). DOI:<br />

10.1051/mmnp/20116701<br />

[2] F. Crauste, I. Demin, O. Gandrill<strong>on</strong>, V. Volpert (2010) Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical study <str<strong>on</strong>g>of</str<strong>on</strong>g> feedback c<strong>on</strong>trol<br />

roles and relevance in stress ery<str<strong>on</strong>g>th</str<strong>on</strong>g>ropoiesis, J Theo Biol 263 (3), 303–316.<br />

[3] F. Crauste, L. Pujo-Menjouet, S. Genieys, C. Molina, O. Gandrill<strong>on</strong> (2008) Adding Self-<br />

Renewal in Committed Ery<str<strong>on</strong>g>th</str<strong>on</strong>g>roid Progenitors Improves <str<strong>on</strong>g>th</str<strong>on</strong>g>e Biological Relevance <str<strong>on</strong>g>of</str<strong>on</strong>g> a Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

Model <str<strong>on</strong>g>of</str<strong>on</strong>g> Ery<str<strong>on</strong>g>th</str<strong>on</strong>g>ropoiesis, J Theo Biol 250, 322–338.<br />

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[4] I. Demin, F. Crauste, O. Gandrill<strong>on</strong>, V. Volpert (2010) A multi-scale model <str<strong>on</strong>g>of</str<strong>on</strong>g> ery<str<strong>on</strong>g>th</str<strong>on</strong>g>ropoiesis,<br />

J Biol Dynamics 4 (1), 59–70.<br />

195

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Modeling and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor invasi<strong>on</strong> I; Tuesday, June 28, 11:00<br />

Vittorio Cristini<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> New Mexico<br />

e-mail: vcristini@salud.unm.edu<br />

Multiparameter Computati<strong>on</strong>al Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Tumor Invasi<strong>on</strong><br />

Clinical outcome prognosticati<strong>on</strong> in <strong>on</strong>cology is a guiding principle in <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic<br />

choice. A weal<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> qualitative empirical evidence links disease progressi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

tumor morphology, histopa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, invasi<strong>on</strong>, and associated molecular phenomena.<br />

However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e quantitative c<strong>on</strong>tributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> each <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e known parameters in <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

progressi<strong>on</strong> remains elusive. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling can provide <str<strong>on</strong>g>th</str<strong>on</strong>g>e capability to<br />

quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>necti<strong>on</strong> between variables governing grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, prognosis, and treatment<br />

outcome. By quantifying <str<strong>on</strong>g>th</str<strong>on</strong>g>e link between <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor boundary morphology<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasive phenotype, <str<strong>on</strong>g>th</str<strong>on</strong>g>is work provides a quantitative tool for <str<strong>on</strong>g>th</str<strong>on</strong>g>e study<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tumor progressi<strong>on</strong> and diagnostic/prognostic applicati<strong>on</strong>s. This establishes a<br />

framework for m<strong>on</strong>itoring system perturbati<strong>on</strong> towards development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic<br />

strategies and correlati<strong>on</strong> to clinical outcome for prognosis.<br />

196

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

H. Croisier, R. Thul, S. Coombes, I.P. Hall, and B.S. Brook<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, United Kingdom<br />

e-mail: huguette.croisier@nottingham.ac.uk<br />

A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium dynamics in airway<br />

smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> muscle cells including store-operated calcium entry<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e principal causes <str<strong>on</strong>g>of</str<strong>on</strong>g> airway narrowing in as<str<strong>on</strong>g>th</str<strong>on</strong>g>ma is <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tracti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> muscle cells lining <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>ducting airways. This c<strong>on</strong>tracti<strong>on</strong> is regulated<br />

by changes in intracellular calcium c<strong>on</strong>centrati<strong>on</strong> ([Ca 2+ ]i). The mechanism<br />

c<strong>on</strong>trolling [Ca 2+ ]i primarily involves ag<strong>on</strong>ist-induced release <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium from internal<br />

stores. Appropriate refilling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese stores is achieved via calcium influx<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular medium into <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoplasm, which is <str<strong>on</strong>g>th</str<strong>on</strong>g>en pumped back<br />

into <str<strong>on</strong>g>th</str<strong>on</strong>g>e stores by sarcoplasmic/endoplasmic reticulum calcium APTase (SERCA).<br />

However, in c<strong>on</strong>trast to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er types <str<strong>on</strong>g>of</str<strong>on</strong>g> muscle cells, calcium influx in airway smoo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

muscle cells (ASMC) occurs mainly <str<strong>on</strong>g>th</str<strong>on</strong>g>rough n<strong>on</strong>-voltage-dependent pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways. In<br />

particular, store-operated calcium entry (SOCE), in which calcium influx is triggered<br />

by store depleti<strong>on</strong>, has been shown to play an important role. Therefore, in<br />

order to account for <str<strong>on</strong>g>th</str<strong>on</strong>g>e characterics <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium influx observed in human ASMC<br />

subject to SERCA block or ag<strong>on</strong>ist stimulati<strong>on</strong> [1,2], we develop a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium dynamics in ASMC <str<strong>on</strong>g>th</str<strong>on</strong>g>at includes SOCE. Preliminary simulati<strong>on</strong>s<br />

and phase-plane analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>at ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er direct SOCE into <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

internal stores, in additi<strong>on</strong> to cytosolic SOCE, or desensitizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cytosolic SOCE<br />

by [Ca 2+ ]i, is required to account for <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental resp<strong>on</strong>ses reported in [1,2].<br />

This modelling work is part <str<strong>on</strong>g>of</str<strong>on</strong>g> a larger project aiming at developing a multiscale<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> airway hyper-resp<strong>on</strong>siveness in as<str<strong>on</strong>g>th</str<strong>on</strong>g>ma, from <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular mechanisms<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> airway c<strong>on</strong>tracti<strong>on</strong> at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular level to <str<strong>on</strong>g>th</str<strong>on</strong>g>e biomechanics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole tissue<br />

[3,4].<br />

References.<br />

[1] S.E. Peel, B. Liu, and I.P. Hall, A key role for STIM1 in store-operated calcium channel<br />

activati<strong>on</strong> in airway smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> muscle. Resp. Research 7: 119 (2006)<br />

[2] S.E. Peel, B. Liu, and I.P. Hall, ORAI and store-operated calcium influx in human airway<br />

smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> muscle cells. Am. J. Resp. Cell and Molec. Biol. 38: 744–749 (2008)<br />

[3] B.S. Brook, S.E. Peel, I.P. Hall, A.Z. Politi, J. Sneyd, Y. Bai, M.J. Sanders<strong>on</strong>, and O.E Jensen,<br />

A biomechanical model <str<strong>on</strong>g>of</str<strong>on</strong>g> ag<strong>on</strong>ist-initiated c<strong>on</strong>tracti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e as<str<strong>on</strong>g>th</str<strong>on</strong>g>matic airway. Resp. Physiol.<br />

and Neurobiol. 170: 44–58 (2010)<br />

[4] A.Z. Politi, G.M. D<strong>on</strong>ovan, M.H. Tawhai, M.J. Sanders<strong>on</strong>, A.-M. Lauz<strong>on</strong>, J.H.T. Bates, and<br />

J. Sneyd, A multiscale, spatially distributed model <str<strong>on</strong>g>of</str<strong>on</strong>g> as<str<strong>on</strong>g>th</str<strong>on</strong>g>matic airway hyper-resp<strong>on</strong>siveness.<br />

J. Theore. Biol. 266: 614–624 (2010)<br />

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Cellular Systems Biology; Saturday, July 2, 11:00<br />

Attila Csikasz-Nagy<br />

The Micros<str<strong>on</strong>g>of</str<strong>on</strong>g>t Research University <str<strong>on</strong>g>of</str<strong>on</strong>g> Trento Centre for Computati<strong>on</strong>al<br />

and Systems Biology<br />

e-mail: csikasz@cosbi.eu<br />

Cell signaling network unit dynamics<br />

Cells use a dense network <str<strong>on</strong>g>of</str<strong>on</strong>g> signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways to decide how to resp<strong>on</strong>d to various<br />

external stimuli. Several dynamic aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> complex pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways have been<br />

already described. Here we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at simple generic motifs <str<strong>on</strong>g>of</str<strong>on</strong>g> signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways<br />

(wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out any feedback) could show some interesting dynamics. We investigated <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e simplest dynamical elements in biochemical networks: we analyzed<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>se dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> a signaling protein when it enters <str<strong>on</strong>g>th</str<strong>on</strong>g>e signaling pool in<br />

<strong>on</strong>e state (modified or unmodified) and exits in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese states. When <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

exit rates <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two states are comparable, a persistent stimulus results in step<br />

resp<strong>on</strong>ses and can produce ultrasensitivity, however, when <str<strong>on</strong>g>th</str<strong>on</strong>g>e exit rates are imbalanced,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e signaling protein gives transient resp<strong>on</strong>ses to persistent stimuli. Such<br />

adaptive behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways could be used by many organisms. We also<br />

investigated <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical features <str<strong>on</strong>g>of</str<strong>on</strong>g> phosphorelays: phosphorelays are extended<br />

two-comp<strong>on</strong>ent signaling systems found in diverse bacteria, lower eukaryotes and<br />

plants. We found <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e intermediate layers <str<strong>on</strong>g>of</str<strong>on</strong>g> phosphorelays can display ultrasensitivity<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at could result in tolerance <str<strong>on</strong>g>of</str<strong>on</strong>g> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way cross-talk. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, it<br />

leads to a high signal to noise ratio for <str<strong>on</strong>g>th</str<strong>on</strong>g>e relay output. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese features<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> phosporelays might be employed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e sporulati<strong>on</strong> network <str<strong>on</strong>g>of</str<strong>on</strong>g> B. subtilis.<br />

198

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Epidemics; Saturday, July 2, 08:30<br />

Jing-an Cui, Guohua S<strong>on</strong>g<br />

Beijing University <str<strong>on</strong>g>of</str<strong>on</strong>g> Civil Engineering & Architecture, Beijing 100044,<br />

China<br />

e-mail: cuijingan@bucea.edu.cn<br />

Models <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious disease c<strong>on</strong>trol wi<str<strong>on</strong>g>th</str<strong>on</strong>g> limit treatment<br />

resource<br />

The number <str<strong>on</strong>g>of</str<strong>on</strong>g> patients need to be treated may exceed <str<strong>on</strong>g>th</str<strong>on</strong>g>e carry capacity <str<strong>on</strong>g>of</str<strong>on</strong>g> local<br />

hospitals during <str<strong>on</strong>g>th</str<strong>on</strong>g>e spreading <str<strong>on</strong>g>of</str<strong>on</strong>g> a severe infectious disease. We propose an epidemic<br />

model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> saturati<strong>on</strong> recovery from infective individuals to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

effect <str<strong>on</strong>g>of</str<strong>on</strong>g> limited resources for treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> infectives <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergency disease c<strong>on</strong>trol.<br />

It is shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at saturati<strong>on</strong> recovery from infective individuals leads to vital<br />

dynamics, such as bistability and periodicity, when <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproducti<strong>on</strong> number<br />

R0 is less <str<strong>on</strong>g>th</str<strong>on</strong>g>an unity.<br />

References.<br />

[1] J.Cui, X.Mu, H.Wan,Saturati<strong>on</strong> Recovery Leads to Multiple Endemic Equilibria and Backward<br />

Bifurcati<strong>on</strong>. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology 254 275–283.<br />

[2] W. Wang, S. Ruan, Bifurcati<strong>on</strong>s in an epidemic model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>stant removal rate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

infectives. J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Anal. Appl. 291 775–793.<br />

[3] W. Wang, Backward bifurcati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> treatment. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci. 201<br />

58–71.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biomechanical regulati<strong>on</strong> in b<strong>on</strong>e tissue (Sessi<strong>on</strong><br />

I); Wednesday, June 29, 08:30<br />

Peter Cummings<br />

Vanderbilt University<br />

e-mail: peter.cummings@vanderbilt.edu<br />

A Computati<strong>on</strong>al Model <str<strong>on</strong>g>of</str<strong>on</strong>g> B<strong>on</strong>e Resorpti<strong>on</strong> Behavior<br />

B<strong>on</strong>e resorpti<strong>on</strong> by osteoclasts plays a fundamental role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e remodeling<br />

cycle which serves <str<strong>on</strong>g>th</str<strong>on</strong>g>e purpose <str<strong>on</strong>g>of</str<strong>on</strong>g> repairing micro-damage and/or achieving mineral<br />

homeostasis. This process is also essential in grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and remodeling <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e,<br />

where it is tightly coupled to b<strong>on</strong>e formati<strong>on</strong> by osteoblasts. In order to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

static and dynamic behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e resorpti<strong>on</strong>, a computati<strong>on</strong>al model <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e<br />

resorpti<strong>on</strong> has been developed using a cellular automat<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od and its hybrid<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>od wi<str<strong>on</strong>g>th</str<strong>on</strong>g> finite element calculati<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, essential features <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e resorpti<strong>on</strong><br />

include <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> osteoclasts wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e matrix and wi<str<strong>on</strong>g>th</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

osteoclasts, and a recruiting signal for osteoclasts from osteocytes <str<strong>on</strong>g>th</str<strong>on</strong>g>at can sense<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e change in mechanical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e matrix such as strain and strainenergy<br />

density. The computati<strong>on</strong>al model provides a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical tool to address<br />

various questi<strong>on</strong>s <strong>on</strong> b<strong>on</strong>e resorpti<strong>on</strong> in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e shape and size <str<strong>on</strong>g>of</str<strong>on</strong>g> resorbed<br />

b<strong>on</strong>e. From <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong>al model <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e resorpti<strong>on</strong>, it is<br />

found <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e resorpti<strong>on</strong> is str<strong>on</strong>gly affected by <str<strong>on</strong>g>th</str<strong>on</strong>g>e streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

interacti<strong>on</strong>s between osteoclasts wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e matrix and wi<str<strong>on</strong>g>th</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er osteoclasts,<br />

external mechanical loads, and velocity <str<strong>on</strong>g>of</str<strong>on</strong>g> a blood vessel.<br />

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The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting cell systems: from intercellular interacti<strong>on</strong><br />

to tissue-level traits I; Wednesday, June 29, 14:30<br />

Andras Czirok<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Kansas Medical Ctr<br />

e-mail: ACZIROK@KUMC.EDU<br />

Vasculogenesis and collective movement <str<strong>on</strong>g>of</str<strong>on</strong>g> endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells<br />

The early vascular network is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e simplest functi<strong>on</strong>ing organs in <str<strong>on</strong>g>th</str<strong>on</strong>g>e embryo.<br />

Its formati<strong>on</strong> involves <strong>on</strong>ly <strong>on</strong>e cell type and it can be readily observed and<br />

manipulated in avian embryos or in vitro explants. The early vascular network <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

warm-blooded vertebrates self-organizes by <str<strong>on</strong>g>th</str<strong>on</strong>g>e collective motility <str<strong>on</strong>g>of</str<strong>on</strong>g> cell streams, or<br />

multicellular "sprouts". The el<strong>on</strong>gati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese future vascular network segments<br />

depends <strong>on</strong> a c<strong>on</strong>tinuous supply <str<strong>on</strong>g>of</str<strong>on</strong>g> cells, moving al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e sprout towards its tip.<br />

To understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed self-organizati<strong>on</strong> process, we investigate computati<strong>on</strong>al<br />

models c<strong>on</strong>taining interacti<strong>on</strong>s between adherent, polarized and self-propelled cells.<br />

By comparing <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> data from in vivo or simplistic in vitro experiments,<br />

we explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> active migrati<strong>on</strong>, tip cells, invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ECM, and<br />

cell guidance by micromechanical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> adjacent cell surfaces.<br />

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Modeling viral hepatitis dynamics in-vivo and in-vitro in <str<strong>on</strong>g>th</str<strong>on</strong>g>e era <str<strong>on</strong>g>of</str<strong>on</strong>g> direct<br />

anti-viral agents II; Wednesday, June 29, 08:30<br />

Harel Dahari<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Illinois at Chicago<br />

e-mail: daharih@uic.edu<br />

Modeling hepatitis C virus (HCV) RNA kinetics during<br />

treatment: in vitro and in vivo<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e last decade HCV kinetic modeling in vivo has played an important role<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> HCV dynamics and <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> antiviral <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy and <str<strong>on</strong>g>th</str<strong>on</strong>g>ey<br />

have suggested mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> acti<strong>on</strong> (MOA) for bo<str<strong>on</strong>g>th</str<strong>on</strong>g> interfer<strong>on</strong>-alpha (IFN) and<br />

ribavirin. While we still do not fully understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e MOAs <str<strong>on</strong>g>of</str<strong>on</strong>g> IFN and ribavirin,<br />

understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed HCV RNA pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles during <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy wi<str<strong>on</strong>g>th</str<strong>on</strong>g> new direct<br />

acting agents (DAA) against HCV will shed light <strong>on</strong> HCV-host interacti<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e MOA <str<strong>on</strong>g>of</str<strong>on</strong>g> antivirals. The new cell-culture systems<br />

(in vitro) <str<strong>on</strong>g>th</str<strong>on</strong>g>at allow <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> HCV replicati<strong>on</strong>, infecti<strong>on</strong> and treatment at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular level will provide valuable insights into HCV-host-drug dynamics<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in infected cells; a feature <str<strong>on</strong>g>th</str<strong>on</strong>g>at has been c<strong>on</strong>sidered as a black box. Recent<br />

experimental data (in vitro and in vivo) and modeling efforts in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

IFN/ribavirin/DAAs will be presented.<br />

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Developmental Biology; Thursday, June 30, 11:30<br />

Sascha Dalessi<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Genetics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Lausanne, Lausanne,<br />

Switzerland<br />

Swiss Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioinformatics<br />

e-mail: sascha.dalessi@unil.ch<br />

Gerald Schwank<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular Life Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Zurich, Zurich,<br />

Switzerland<br />

Aitana Mort<strong>on</strong> de Lachapelle<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Genetics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Lausanne, Lausanne,<br />

Switzerland<br />

Swiss Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioinformatics<br />

K<strong>on</strong>rad Basler<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular Life Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Zurich, Zurich,<br />

Switzerland<br />

Sven Bergmann<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Genetics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Lausanne, Lausanne,<br />

Switzerland<br />

Swiss Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioinformatics<br />

Analytical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Dpp wt pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile and tkv cl<strong>on</strong>es in<br />

Drosophila wing imaginal discs<br />

Morphogen c<strong>on</strong>centrati<strong>on</strong> gradients in developing organisms or tissues provide<br />

positi<strong>on</strong>al informati<strong>on</strong> which can induce patterning and space-dependent cell fates<br />

[1]. A well known example is Decapentaplegic (Dpp), involved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterning<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Drosophila wing imaginal discs, which forms a c<strong>on</strong>centrati<strong>on</strong> gradient al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Anterior-Posterior axis [2].<br />

In a recent work [3], we developed and compared to experimental data a 1D analytical<br />

model describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e Dpp steady state gradient pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile and tkv mutant<br />

cl<strong>on</strong>e effects. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is model, we identify <str<strong>on</strong>g>th</str<strong>on</strong>g>ree distinct Dpp comp<strong>on</strong>ents: external<br />

Dpp, Tkv-bound Dpp and internalized Dpp. We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e external Dpp diffuses<br />

from a finite-size producti<strong>on</strong> regi<strong>on</strong> and can bind to <str<strong>on</strong>g>th</str<strong>on</strong>g>e Tkv receptors. The<br />

bound Dpp can unbind or be internalized. The internalized Dpp can be degraded or<br />

transported cell by cell by transcytosis. We c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>at transcytosis is receptormediated<br />

and we model it in a pure diffusive way. Assuming a large number <str<strong>on</strong>g>of</str<strong>on</strong>g> free<br />

receptors allows for <str<strong>on</strong>g>th</str<strong>on</strong>g>e linearizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding differential equati<strong>on</strong>s,<br />

from which we obtain simple analytical expressi<strong>on</strong>s for each Dpp comp<strong>on</strong>ent.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e tkv cl<strong>on</strong>al regi<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> receptors as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e receptor-mediated<br />

transcytosis are affected. We c<strong>on</strong>sider loss-<str<strong>on</strong>g>of</str<strong>on</strong>g>-functi<strong>on</strong> (LOF) experiments, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> no<br />

receptors inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e cl<strong>on</strong>e, and gain-<str<strong>on</strong>g>of</str<strong>on</strong>g>-functi<strong>on</strong> (GOF) experiments, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a n−fold<br />

increase <str<strong>on</strong>g>of</str<strong>on</strong>g> receptors.<br />

An extensive qualitative analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> LOF experiments and quantitative data extracti<strong>on</strong><br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e GOF images allows to (i) c<strong>on</strong>strain <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters space and<br />

find a set <str<strong>on</strong>g>of</str<strong>on</strong>g> optimal parameters (ii) understand which <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e external diffusi<strong>on</strong> or<br />

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transcytosis is <str<strong>on</strong>g>th</str<strong>on</strong>g>e dominating mechanism in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Dpp gradient formati<strong>on</strong> (iii) obtain<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e relative abundance <str<strong>on</strong>g>of</str<strong>on</strong>g> external, Tkv-bound and internalized Dpp. All <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

experimental data and <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical results are reported in [3].<br />

References.<br />

[1] L. Wolpert L Positi<strong>on</strong>al informati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular differentiati<strong>on</strong> J. Theor.<br />

Biol. 25(1) 1–47<br />

[2] E. V. Entchev et al. Gradient formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e TGF-beta homolog Dpp Cell 103(6) 981–991<br />

[3] G. Schwank, S. Dalessi et al. Formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g range Dpp morphogen gradient Manuscript<br />

submitted<br />

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Cellular Systems Biology; Tuesday, June 28, 17:00<br />

Daniel Damineli<br />

PhD Program in Computati<strong>on</strong>al Biology - Instituto Gulbenkian de<br />

Ciências; Instituto de Tecnologia Química e Biológica - Universidade<br />

Nova de Lisboa<br />

e-mail: damineli@itqb.unl.pt<br />

Andreas Bohn<br />

Instituto de Tecnologia Química e Biológica<br />

Minimal modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> two-oscillator circadian systems under<br />

c<strong>on</strong>flicting envir<strong>on</strong>mental cues<br />

Multiple coupled oscillators have been presumed to c<strong>on</strong>stitute <str<strong>on</strong>g>th</str<strong>on</strong>g>e circadian system<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> many organisms. In some cases <str<strong>on</strong>g>th</str<strong>on</strong>g>e different oscillators are driven by<br />

diverse envir<strong>on</strong>mental cues (zeitgebers), as suggested by <str<strong>on</strong>g>th</str<strong>on</strong>g>e light- versus foodentrainable<br />

oscillators in mice and <str<strong>on</strong>g>th</str<strong>on</strong>g>e light- versus temperature-entrainable oscillators<br />

in Drosophila. In order to survey <str<strong>on</strong>g>th</str<strong>on</strong>g>e spectrum <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamics <str<strong>on</strong>g>th</str<strong>on</strong>g>at could emerge<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> potentially c<strong>on</strong>flicting zeitgebers wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a multi-oscillator circadian<br />

system, we assume a minimal model c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> two mutually coupled<br />

oscillators, each being exclusively driven by a periodic envir<strong>on</strong>mental signal. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically<br />

we represent <str<strong>on</strong>g>th</str<strong>on</strong>g>e circadian system by 2 mutually coupled phase oscillators<br />

[1], A and B, each wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an arbitrary individual period. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e two envir<strong>on</strong>mental<br />

signals are assumed to have <str<strong>on</strong>g>th</str<strong>on</strong>g>e same period (24 h) and are <strong>on</strong>ly separated by a<br />

phase shift DELTA, <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment can be represent by a <str<strong>on</strong>g>th</str<strong>on</strong>g>ird phase oscillator,<br />

which is unidirecti<strong>on</strong>ally coupled to oscillators A and B, respectively, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

DELTA being reflected in a delayed coupling to oscillator B. Performing numerical<br />

studies <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> DELTA, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e balance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>mental<br />

and intra-oscillator coupling streng<str<strong>on</strong>g>th</str<strong>on</strong>g>, rich dynamic behavior like bistability and<br />

hysteresis, as well as loss <str<strong>on</strong>g>of</str<strong>on</strong>g> entrainment and quasi-periodicity is observable. Our<br />

study provides insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e putative coupling network required<br />

to maintain <str<strong>on</strong>g>th</str<strong>on</strong>g>e organism in a stable phase-relati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment, even<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e face <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tradictory signals. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, our results can indicate appropriate<br />

experimental strategies to evaluate <str<strong>on</strong>g>th</str<strong>on</strong>g>e streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> inter-oscillator coupling<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative zeitgeber streng<str<strong>on</strong>g>th</str<strong>on</strong>g>, which have been performed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e past, but<br />

mostly lacked guidelines for correct design and interpretati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e results. We<br />

finally compare our minimal model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a more complex model, using limit-cycle<br />

oscillators [2], showing <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e principal dynamics are not altered by <str<strong>on</strong>g>th</str<strong>on</strong>g>e inclusi<strong>on</strong><br />

or exclusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> more details.<br />

References.<br />

[1] Kuramoto, Y. (1984) Chemical oscillati<strong>on</strong>s, waves and turbulence. Springer-Verlag, Berlin,<br />

DE.<br />

[2] Oda, G.A. and Friesen, W.O. (2002) A model for splitting <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e running wheel activity in<br />

hamsters. J. Biol. Rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms 17(1): 76-88.<br />

205

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Genetics and Genomics; Wednesday, June 29, 08:30<br />

Agnieszka Danek<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science,<br />

Poland<br />

e-mail: agnieszka.danek@polsl.pl<br />

Rafał Pokrzywa<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science,<br />

Poland<br />

e-mail: rafal.pokrzywa@polsl.pl<br />

Algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m for Searching for Approximate Tandem Repeats<br />

based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Burrows-Wheeler transform<br />

Genomic sequences tend to c<strong>on</strong>tain many types <str<strong>on</strong>g>of</str<strong>on</strong>g> repetitive structures <str<strong>on</strong>g>of</str<strong>on</strong>g> different<br />

leng<str<strong>on</strong>g>th</str<strong>on</strong>g>, ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er interspersed or tandem. Tandem repeats play an important role<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene expressi<strong>on</strong> and transcripti<strong>on</strong> regulati<strong>on</strong>s. They can be used as markers<br />

for DNA mapping and DNA fingerprinting. Some, when occurring in increased,<br />

abnormal number, are known to be <str<strong>on</strong>g>th</str<strong>on</strong>g>e cause <str<strong>on</strong>g>of</str<strong>on</strong>g> inherited diseases. All functi<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tandem repeats in genomic sequences are still not well defined and understood.<br />

However, growing biological databases toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> tools for efficient identificati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese repeats may lead to discovery <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir specific role or correlati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

particular symptoms or diseases.<br />

Perfect tandem repeat c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> successive duplicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> some motif. Typically<br />

tandem copies are approximate due to mutati<strong>on</strong>s. Hence approximate tandem<br />

repeat (ATR) can be defined as a c<strong>on</strong>secutive, inexact copies <str<strong>on</strong>g>of</str<strong>on</strong>g> some motif. In our<br />

c<strong>on</strong>siderati<strong>on</strong>s we are assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>at two such successive repeats must be <str<strong>on</strong>g>of</str<strong>on</strong>g> equal<br />

leng<str<strong>on</strong>g>th</str<strong>on</strong>g>s and can differ <strong>on</strong>ly by an established number <str<strong>on</strong>g>of</str<strong>on</strong>g> mismatches. Dissimilarity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two approximate copies is measured using Hamming distance between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>em. We are interested in finding approximate tandem repeat when each repeated<br />

motif is similar enough to <str<strong>on</strong>g>th</str<strong>on</strong>g>e adjacent duplicate.<br />

Algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m presented is an enhancement <str<strong>on</strong>g>of</str<strong>on</strong>g> a me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for finding perfect tandem<br />

repeats in DNA sequences based <strong>on</strong> Burrows-Wheeler transform (BWT). It uses its<br />

intermediate results, groups <str<strong>on</strong>g>of</str<strong>on</strong>g> particular sequences repeated wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole input<br />

string, to find candidates for double ATR — <str<strong>on</strong>g>th</str<strong>on</strong>g>at is <str<strong>on</strong>g>th</str<strong>on</strong>g>e first stage <str<strong>on</strong>g>of</str<strong>on</strong>g> searching. The<br />

sec<strong>on</strong>d stage c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> investigating found candidates and accepting or rejecting<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>em as a pair <str<strong>on</strong>g>of</str<strong>on</strong>g> ATRs. Finally, in last stage, located double ATRs are extended<br />

to c<strong>on</strong>tain as much successive, similar copies, as possible.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e first stage <str<strong>on</strong>g>th</str<strong>on</strong>g>e input string is c<strong>on</strong>verted according to BWT. This, toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some auxiliary arrays, allows to make use <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e alphabetically sorted array <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

input string suffixes, wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out <str<strong>on</strong>g>th</str<strong>on</strong>g>e need <str<strong>on</strong>g>of</str<strong>on</strong>g> storing <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole suffix array structure.<br />

The algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m finds <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> positi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e repeated pattern in <str<strong>on</strong>g>th</str<strong>on</strong>g>e suffix<br />

array. It starts wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e empty pattern P and recursively appends, in fr<strong>on</strong>t <str<strong>on</strong>g>of</str<strong>on</strong>g> P ,<br />

characters from <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sidered alphabet. This approach uses <str<strong>on</strong>g>th</str<strong>on</strong>g>e results from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

previous iterati<strong>on</strong> to calculate a range <str<strong>on</strong>g>of</str<strong>on</strong>g> positi<strong>on</strong>s for a l<strong>on</strong>ger pattern and it is<br />

d<strong>on</strong>e in a c<strong>on</strong>stant time, according to <str<strong>on</strong>g>th</str<strong>on</strong>g>e idea <str<strong>on</strong>g>of</str<strong>on</strong>g> Ferragina and Manzini. Two<br />

sequences from <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> repeated patterns are c<strong>on</strong>sidered a candidate for a<br />

double approximate tandem repeat if <str<strong>on</strong>g>th</str<strong>on</strong>g>ey lay close enough to each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e input string, in particular, if it is possible <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey will form an approximate<br />

206

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

tandem repeat wi<str<strong>on</strong>g>th</str<strong>on</strong>g> established, maximum dissimilarity. To limit <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

redundant candidates <str<strong>on</strong>g>th</str<strong>on</strong>g>e algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m makes use <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e property <str<strong>on</strong>g>of</str<strong>on</strong>g> two strings <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

leng<str<strong>on</strong>g>th</str<strong>on</strong>g> n and wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Hamming distance h between <str<strong>on</strong>g>th</str<strong>on</strong>g>em, which states <str<strong>on</strong>g>th</str<strong>on</strong>g>at two such<br />

strings have always a comm<strong>on</strong>, matching substring at corresp<strong>on</strong>ding positi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

leng<str<strong>on</strong>g>th</str<strong>on</strong>g> ⌊ n<br />

h+1⌋ at least. Hence, repeated patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> leng<str<strong>on</strong>g>th</str<strong>on</strong>g> d are used to search<br />

<strong>on</strong>ly for ATRs <str<strong>on</strong>g>of</str<strong>on</strong>g> leng<str<strong>on</strong>g>th</str<strong>on</strong>g> n <str<strong>on</strong>g>th</str<strong>on</strong>g>at satisfies <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong> d = ⌊ n<br />

h+1⌋ for all acceptable<br />

h. Additi<strong>on</strong>ally, as positi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> previously found ATRs are known, qualifying as a<br />

candidate <str<strong>on</strong>g>th</str<strong>on</strong>g>e ATR discovered before is avoided.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e next stage Hamming distance between found pairs <str<strong>on</strong>g>of</str<strong>on</strong>g> candidates is measured<br />

(checking all possible alignments <str<strong>on</strong>g>of</str<strong>on</strong>g> found candidates) and if it satisfies <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

assumpti<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e double approximate tandem repeat is reported. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ird, final<br />

stage, Hamming distance is measured between marginal motif <str<strong>on</strong>g>of</str<strong>on</strong>g> found ATR and<br />

a neighboring string. As l<strong>on</strong>g as it is not greater <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e assumed maximum, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ATR is extended in <str<strong>on</strong>g>th</str<strong>on</strong>g>at directi<strong>on</strong>.<br />

The developed algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m exploits <str<strong>on</strong>g>th</str<strong>on</strong>g>e advantages <str<strong>on</strong>g>of</str<strong>on</strong>g>fered by <str<strong>on</strong>g>th</str<strong>on</strong>g>e BWT algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e suffix array data structure to return ATRs from <str<strong>on</strong>g>th</str<strong>on</strong>g>e input string, assuming<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at any two c<strong>on</strong>secutive copies wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in ATR differ at most by a provided Hamming<br />

distance.<br />

Acknowledgement: This work was supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>European</str<strong>on</strong>g> Uni<strong>on</strong> from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> Social Fund.<br />

References.<br />

[1] R. Pokrzywa, Applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Burrows-Wheeler Transform for searching for tandem repeats<br />

in DNA sequences Int. J. Bioinform. Res. Appl. vol. 5 (4) (2009) 432–446.<br />

[2] R. Pokrzywa and A. Polański, BWtrs: A tool for searching for tandem repeats in DNA sequences<br />

based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Burrows-Wheeler transform Genomics 96 (2010) 316–321.<br />

[3] M. Burrows and D.J. Wheeler, A block-sorting lossless data compressi<strong>on</strong> algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m SRC Research<br />

Report 124, Digital Equipment Corporati<strong>on</strong>, Palo Alto, California, May 10 1994.<br />

[4] P. Ferragina and G. Manzini, Opportunistic data structures wi<str<strong>on</strong>g>th</str<strong>on</strong>g> applicati<strong>on</strong>s Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e 41st Annual Symposium <strong>on</strong> Foundati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science, 2000, pp. 390–398.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Erin Daus<strong>on</strong><br />

Dartmou<str<strong>on</strong>g>th</str<strong>on</strong>g> College<br />

Ben Bier<br />

Dartmou<str<strong>on</strong>g>th</str<strong>on</strong>g> College<br />

Clyde Martin<br />

Texas Tech University<br />

Models in Spatial Ecology; Tuesday, June 28, 17:00<br />

Repopulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ambystoma tigrinum in <str<strong>on</strong>g>th</str<strong>on</strong>g>e West Texas<br />

playas in <str<strong>on</strong>g>th</str<strong>on</strong>g>e period following Antevs Alti<str<strong>on</strong>g>th</str<strong>on</strong>g>ermal: a<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model<br />

We c<strong>on</strong>sider a populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> amphibians in transient wetlands. The effect <str<strong>on</strong>g>of</str<strong>on</strong>g> predati<strong>on</strong>,<br />

migrati<strong>on</strong> and finite resources is examined <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a series <str<strong>on</strong>g>of</str<strong>on</strong>g> models based<br />

<strong>on</strong> differential equati<strong>on</strong>s. Logistic grow<str<strong>on</strong>g>th</str<strong>on</strong>g> coupled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> predati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> satiati<strong>on</strong><br />

can, depending <strong>on</strong> parameters, produce an Allee effect in an isolated habitat. In<br />

particular, a populati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at might <str<strong>on</strong>g>th</str<strong>on</strong>g>rive in isolati<strong>on</strong> may go extinct if migrati<strong>on</strong><br />

becomes an opti<strong>on</strong> and an equilibrium <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong>s in a coupled system does not<br />

necessarily lead to stable n<strong>on</strong>zero populati<strong>on</strong>s when migrati<strong>on</strong> stops. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

under some circumstances periods <str<strong>on</strong>g>of</str<strong>on</strong>g> migrati<strong>on</strong> followed by periods <str<strong>on</strong>g>of</str<strong>on</strong>g> isolati<strong>on</strong> is a<br />

faster way to repopulate a system <str<strong>on</strong>g>th</str<strong>on</strong>g>an a single l<strong>on</strong>g period <str<strong>on</strong>g>of</str<strong>on</strong>g> migrati<strong>on</strong>. We apply<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is model to <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ambystoma tigrinum populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e highland playas <str<strong>on</strong>g>of</str<strong>on</strong>g> west<br />

Texas to show <str<strong>on</strong>g>th</str<strong>on</strong>g>at in a given rainy period it is unlikely <str<strong>on</strong>g>th</str<strong>on</strong>g>at migrati<strong>on</strong> will occur<br />

except to nearest adjacent p<strong>on</strong>ds. Coupling <str<strong>on</strong>g>th</str<strong>on</strong>g>is result wi<str<strong>on</strong>g>th</str<strong>on</strong>g> rainfall data gives a<br />

rough probability for migrati<strong>on</strong> in a given rainy seas<strong>on</strong>. Field data give an indicati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> extincti<strong>on</strong> rates for individual playas. Coupling <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two probabilities<br />

in a percolati<strong>on</strong> process <strong>on</strong> a finite grid gives an indicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> how many years are<br />

required to restock a whole system <str<strong>on</strong>g>of</str<strong>on</strong>g> playas from a single populated p<strong>on</strong>d. We<br />

show under what assumpti<strong>on</strong>s it is possible for <str<strong>on</strong>g>th</str<strong>on</strong>g>e system <str<strong>on</strong>g>of</str<strong>on</strong>g> about 20,000 playas<br />

to be restocked from a single source by Ambystoma tigrinum in <str<strong>on</strong>g>th</str<strong>on</strong>g>e interval since<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e intense dry period known as Antevs Alti<str<strong>on</strong>g>th</str<strong>on</strong>g>ermal.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Mai Jaffar<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee<br />

e-mail: mzamjaffar@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.dundee.ac.uk<br />

Fordyce A. Davids<strong>on</strong><br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee<br />

e-mail: fdavids<strong>on</strong>@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.dundee.ac.uk<br />

Hyphal tip morphogenesis<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Tip grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is a mechanism by which cells can expand in a preferred directi<strong>on</strong>. It<br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>e defining feature <str<strong>on</strong>g>of</str<strong>on</strong>g> filamentous organisms such vegetative fungi and actinomycete<br />

bacteria. The ability to extend by apical grow<str<strong>on</strong>g>th</str<strong>on</strong>g> allows <str<strong>on</strong>g>th</str<strong>on</strong>g>ese organisms<br />

to optimally explore and exploit <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex envir<strong>on</strong>ments <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey normally<br />

inhabit. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> tip grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is a mature subject. However, recent<br />

advances in imaging and genetic manipulati<strong>on</strong> has brought new impetuous<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>is area, as <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms by which cell wall building material is brought<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e tip and subsequently used to extend <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypha, are now beginning to be<br />

revealed. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are still many open questi<strong>on</strong>s regarding <str<strong>on</strong>g>th</str<strong>on</strong>g>e organisati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese complex processes. In particular, how <str<strong>on</strong>g>th</str<strong>on</strong>g>e biomechanics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell wallplasma<br />

membrane complex and vesicle supply centre (Spitzenkorper) interact is<br />

still largely unknown. We discuss models <str<strong>on</strong>g>th</str<strong>on</strong>g>at treat <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell-wall development as a<br />

c<strong>on</strong>sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er geometry or elasticity and detail what progress can be made<br />

regarding tip morphologies from <str<strong>on</strong>g>th</str<strong>on</strong>g>ese basic assumpti<strong>on</strong>s.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modelling bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms: from gene regulati<strong>on</strong> to large-scale structure and<br />

functi<strong>on</strong>; Wednesday, June 29, 17:00<br />

Fordyce A. Davids<strong>on</strong><br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee<br />

e-mail: fdavids<strong>on</strong>@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.dundee.ac.uk<br />

Chung-Se<strong>on</strong> Yi<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee<br />

Nicola Stanley-Wall<br />

Molecular Micriobiology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee<br />

Cell differentiati<strong>on</strong> in bacterial bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms<br />

It has been l<strong>on</strong>g understood <str<strong>on</strong>g>th</str<strong>on</strong>g>at isogenic (genetically identical) cells in complex<br />

living organisms can perform different, but co-ordinated roles. This is called cell<br />

differentiati<strong>on</strong> and until recently, it was <str<strong>on</strong>g>th</str<strong>on</strong>g>ought <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is behaviour was restricted<br />

to multi-cellular organisms. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>rough recent technical advances it has<br />

been shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at simple, single-celled organisms such as bacteria, also display cell<br />

differentiati<strong>on</strong> and so to some extent can behave as "multi-cellular collectives". It<br />

has been postulated <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-species variati<strong>on</strong> may be essential for survival<br />

in a changing envir<strong>on</strong>ment.<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most striking examples <str<strong>on</strong>g>of</str<strong>on</strong>g> bacterial cell differentiati<strong>on</strong> is wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a<br />

bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm: a multicellular sessile community <str<strong>on</strong>g>of</str<strong>on</strong>g> bacteria encased wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a self-produced<br />

polymeric matrix. It is <str<strong>on</strong>g>th</str<strong>on</strong>g>ought <str<strong>on</strong>g>th</str<strong>on</strong>g>at over 90% <str<strong>on</strong>g>of</str<strong>on</strong>g> bacterial col<strong>on</strong>ies in <str<strong>on</strong>g>th</str<strong>on</strong>g>e natural<br />

envir<strong>on</strong>ment exist in <str<strong>on</strong>g>th</str<strong>on</strong>g>is form. Bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms are important in all sectors <str<strong>on</strong>g>of</str<strong>on</strong>g> our ec<strong>on</strong>omy<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> examples ranging from human heal<str<strong>on</strong>g>th</str<strong>on</strong>g> (e.g. <str<strong>on</strong>g>th</str<strong>on</strong>g>ey form <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> chr<strong>on</strong>ic<br />

infecti<strong>on</strong>s) to bioremediati<strong>on</strong> (e.g. <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are required for <str<strong>on</strong>g>th</str<strong>on</strong>g>e effective treatment <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

sewage). The Gram positive bacterium Bacillus subtilis is extensively used in an<br />

industrial c<strong>on</strong>text to produce enzymes for cleaning products and has growing potential<br />

as an alternative and envir<strong>on</strong>mentally friendly pesticide. It has recently been<br />

shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms <str<strong>on</strong>g>of</str<strong>on</strong>g> B. subtilis, <strong>on</strong>ly a subpopulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e isogenic cells<br />

produce <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular matrix which surrounds all <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells, while a different<br />

subset retain <str<strong>on</strong>g>th</str<strong>on</strong>g>eir flagella (and <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore remain motile) and a fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er subset will<br />

undergo sporulati<strong>on</strong>. We discuss a regulatory network <str<strong>on</strong>g>th</str<strong>on</strong>g>at may shed some light<br />

<strong>on</strong> comp<strong>on</strong>ent processes in cell differentiati<strong>on</strong> in B. subtilis. In particular we focus<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e phosphorylati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>se regulator DegU and its c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> cell fate,<br />

detailing how a n<strong>on</strong>-unimodal distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> "<strong>on</strong>" cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a populati<strong>on</strong> does<br />

not necessarily come from a classical bistability in <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

regulatory network.<br />

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Ross Davids<strong>on</strong><br />

SAC<br />

e-mail: ross.davids<strong>on</strong>@sac.ac.uk<br />

Leo Zijerveld<br />

SAC<br />

Glenn Mari<strong>on</strong><br />

Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics Scotland<br />

Mike Hutchings<br />

SAC<br />

Epidemics; Wednesday, June 29, 08:30<br />

The impact <str<strong>on</strong>g>of</str<strong>on</strong>g> social structure <strong>on</strong> spatially explicit<br />

epidemiological models<br />

We investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>th</str<strong>on</strong>g>at social structure plays in influencing <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong><br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in spatial and n<strong>on</strong>-spatial epidemiological models. Social hierarchy is<br />

introduced into such models <str<strong>on</strong>g>th</str<strong>on</strong>g>rough covariates which affect individuals fecundity,<br />

giving rise to realistic populati<strong>on</strong> distributi<strong>on</strong>s. The effect <str<strong>on</strong>g>of</str<strong>on</strong>g> correlati<strong>on</strong>s between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese covariates and <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease prevalence is examined <str<strong>on</strong>g>th</str<strong>on</strong>g>rough analytical and<br />

numerical approaches. Heterogeneous distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> sizes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e various subpopulati<strong>on</strong>s,<br />

arising from <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>-uniform fecundity, tend to increase disease prevalence<br />

compared to homogeneous models, and <str<strong>on</strong>g>th</str<strong>on</strong>g>ese differences are larger when spatial<br />

structure is taken into account. These findings have implicati<strong>on</strong>s for epidemiological<br />

models, and for <str<strong>on</strong>g>th</str<strong>on</strong>g>e deployment <str<strong>on</strong>g>of</str<strong>on</strong>g> disease c<strong>on</strong>trol strategies.<br />

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Delay Differential Equati<strong>on</strong>s and Applicati<strong>on</strong>s II; Saturday, July 2, 08:30<br />

Ant<strong>on</strong>i Le<strong>on</strong> Dawidowicz<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Jagiell<strong>on</strong>ian University, ul. Łojasiewicza<br />

6, 30-348 Kraków, Poland<br />

e-mail: Ant<strong>on</strong>i.Le<strong>on</strong>.Dawidowicz@im.uj.edu.pl<br />

Anna Poskrobko<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science, Bialystok University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology,<br />

ul. Wiejska 45A, 15-351 Białystok, Poland<br />

e-mail: a.poskrobko@pb.edu.pl<br />

Jerzy Leszek Zalasiński<br />

Tarnów Regi<strong>on</strong>al Development Agency SA, ul.Szujskiego 66, 33-100<br />

Tarnów, Poland<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> bioenergetic process in green plants<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> delayed argument<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is presentati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary differential equati<strong>on</strong>s which describe<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e bioenergetics <str<strong>on</strong>g>of</str<strong>on</strong>g> green plants is c<strong>on</strong>structed. This model is <str<strong>on</strong>g>th</str<strong>on</strong>g>e mosificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

presented in [1] We use <str<strong>on</strong>g>th</str<strong>on</strong>g>ree variables in <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed model:<br />

• x - <str<strong>on</strong>g>th</str<strong>on</strong>g>e part <str<strong>on</strong>g>of</str<strong>on</strong>g> biomass <str<strong>on</strong>g>of</str<strong>on</strong>g> green plants participating in bioenergetic processes;<br />

• y - <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> ATP i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e mass <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is compound;<br />

• z - <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-organic phosphorus taking part in bioenergetic i.e.<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e total mass <str<strong>on</strong>g>of</str<strong>on</strong>g> ani<strong>on</strong>s P O 3−<br />

4 absorbed from soil after dissociati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

phosphates.<br />

We c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e following n<strong>on</strong>linear system <str<strong>on</strong>g>of</str<strong>on</strong>g> first order equati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> delayed<br />

argument describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e bioenergetic processes in green plants<br />

⎧<br />

⎨<br />

.<br />

⎩<br />

x ′ (t) = ϕ(t)x(t) − c1(x(t)y(t)) γ<br />

y ′ (t) = c2x(t)z(t)(Ax(t − τ) − y(t − τ)) + − c3(x(t)y(t)) γ<br />

z ′ (t) = H(x)c4(c5x(t) − z(t)) − c6x(t)z(t)(Ax(t − τ) − y(t − τ)) +<br />

We present pro<str<strong>on</strong>g>of</str<strong>on</strong>g>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence and <str<strong>on</strong>g>th</str<strong>on</strong>g>e uniqueness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem<br />

and results <str<strong>on</strong>g>of</str<strong>on</strong>g> computer experiments.<br />

References.<br />

[1] A. L. Dawidowicz, J. L. Zalasiński Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> bioenergetic process in green plants<br />

Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e XVI Nati<strong>on</strong>al <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> Applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics to Biology and<br />

Medicine, Krynica, September 14-18, 2010<br />

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Ecology and evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases; Friday, July 1, 14:30<br />

Troy Day<br />

Queen’s University<br />

e-mail: tday@mast.queensu.ca<br />

Optimal c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> drug resistant pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens and <str<strong>on</strong>g>th</str<strong>on</strong>g>e mixing<br />

versus cycling c<strong>on</strong>troversy<br />

The evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> drug resistance presents a major challenge for <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases. Numerous recent simulati<strong>on</strong> studies suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at deploying<br />

drugs at an intermediate level in <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> can sometimes minimize <str<strong>on</strong>g>th</str<strong>on</strong>g>e total<br />

size <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious disease outbreaks. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I will revisit <str<strong>on</strong>g>th</str<strong>on</strong>g>is issue from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

standpoint <str<strong>on</strong>g>of</str<strong>on</strong>g> optimal c<strong>on</strong>trol <str<strong>on</strong>g>th</str<strong>on</strong>g>eory. I will dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal drug<br />

deployment strategy is, in fact, <strong>on</strong>e <str<strong>on</strong>g>th</str<strong>on</strong>g>at uses a maximal treatment level but <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

times <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment appropriately during <str<strong>on</strong>g>th</str<strong>on</strong>g>e outbreak. From <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>clusi<strong>on</strong> I will<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>en go <strong>on</strong> to c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal deployment <str<strong>on</strong>g>of</str<strong>on</strong>g> two drugs. Again, optimal c<strong>on</strong>trol<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eory will be used to shed light <strong>on</strong> recent c<strong>on</strong>troversies about drug mixing versus<br />

drug cycling. I present analytical results dem<strong>on</strong>strating how some situati<strong>on</strong>s lead<br />

to mixing being optimal and o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers lead to a form <str<strong>on</strong>g>of</str<strong>on</strong>g> cycling being optimal. These<br />

results help to partially resolve some discrepancies am<strong>on</strong>g o<str<strong>on</strong>g>th</str<strong>on</strong>g>er studies.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Niall Deakin<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee<br />

e-mail: niall@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.dundee.ac.uk<br />

Cancer; Friday, July 1, 14:30<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> Cancer Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and Spread: The<br />

Role <str<strong>on</strong>g>of</str<strong>on</strong>g> Enzyme Degradati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Tissue<br />

Metastatic spread <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer is <str<strong>on</strong>g>th</str<strong>on</strong>g>e main cause <str<strong>on</strong>g>of</str<strong>on</strong>g> dea<str<strong>on</strong>g>th</str<strong>on</strong>g> in patients suffering from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e disease - cancer cells from a primary tumour break away from <str<strong>on</strong>g>th</str<strong>on</strong>g>e central mass<br />

and are disseminated <str<strong>on</strong>g>th</str<strong>on</strong>g>roughout <str<strong>on</strong>g>th</str<strong>on</strong>g>e body where <str<strong>on</strong>g>th</str<strong>on</strong>g>ey re-grow to form sec<strong>on</strong>dary<br />

tumours or metastases. A crucial aspect <str<strong>on</strong>g>of</str<strong>on</strong>g> metastatic spread is <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> local<br />

invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding tissue. The cancer cells achieve <str<strong>on</strong>g>th</str<strong>on</strong>g>is by <str<strong>on</strong>g>th</str<strong>on</strong>g>e secreti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

certain enzymes involved in proteolysis (tissue degradati<strong>on</strong>), namely plasmin and<br />

matrix metalloproteinases (MMPs). These overly-expressed proteolytic enzymes<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>en proceed to degrade <str<strong>on</strong>g>th</str<strong>on</strong>g>e host tissue allowing <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer cells to spread <str<strong>on</strong>g>th</str<strong>on</strong>g>roughout<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e microenvir<strong>on</strong>ment by active migrati<strong>on</strong> and interacti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> comp<strong>on</strong>ents <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular matrix such as collagen.<br />

Here, we present a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cell invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a host tissue<br />

at <str<strong>on</strong>g>th</str<strong>on</strong>g>e macro-scale (cell populati<strong>on</strong>) level. The model c<strong>on</strong>siders cancer cells and<br />

a number <str<strong>on</strong>g>of</str<strong>on</strong>g> different matrix-degrading enzymes (MDEs) from <str<strong>on</strong>g>th</str<strong>on</strong>g>e MMP family<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir interacti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>, and effect <strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular matrix (ECM) using<br />

systems <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong>-diffusi<strong>on</strong>-taxis partial differential equati<strong>on</strong>s in an attempt to<br />

capture <str<strong>on</strong>g>th</str<strong>on</strong>g>e qualitative dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e migratory resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer cells,<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a specific focus placed <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane-bound MMPs. We use ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

analysis and computati<strong>on</strong>al simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong>s in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <strong>on</strong>e- and two-space<br />

dimensi<strong>on</strong>s to predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer cell density, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

c<strong>on</strong>centrati<strong>on</strong> levels <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e various enzymes and <str<strong>on</strong>g>th</str<strong>on</strong>g>e density <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular<br />

matrix. The model exhibits ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er travelling-wave soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells, which<br />

can be used to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximum speed <str<strong>on</strong>g>of</str<strong>on</strong>g> invasi<strong>on</strong> into <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue, or very<br />

dynamic and heterogeneous spatio-temporal soluti<strong>on</strong>s, which match experimentally<br />

and clinically observed results for aggressive invading carcinoma.<br />

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Multi-scale ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver: From intracellular signaling to<br />

intercellular interacti<strong>on</strong>; Wednesday, June 29, 08:30<br />

Walter de Back<br />

Technische Universität Dresden<br />

e-mail: walter.deback@tu-dresden.de<br />

Lutz Brusch<br />

Technische Universität Dresden<br />

e-mail: lutz.brusch@tu-dresden.de<br />

Andreas Deutsch<br />

Technische Universität Dresden<br />

e-mail: andreas.deutsch@tu-dresden.de<br />

From hepatocyte polarizati<strong>on</strong><br />

to canalicular network formati<strong>on</strong>:<br />

a multiscale approach<br />

The generati<strong>on</strong> and maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatocyte polarity is crucial for <str<strong>on</strong>g>th</str<strong>on</strong>g>e proper<br />

functi<strong>on</strong>ing <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver, and is important in development, as well as liver regenerati<strong>on</strong>.<br />

It is well-known <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex polarity <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatocytes is characterized by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple basolateral and apical/canalicular poles per cell. Yet, it<br />

remains unclear what molecular and cellular interacti<strong>on</strong>s regulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e generati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

segregated membrane domains, and how <str<strong>on</strong>g>th</str<strong>on</strong>g>is affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e morphology <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hepatic<br />

epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elium and <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> bile canulicular network.<br />

To investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e feedback between <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular and cellular interacti<strong>on</strong>s, we<br />

have developed a multiscale modeling envir<strong>on</strong>ment called Morpheus. This modeling<br />

and simulati<strong>on</strong> framework facilitates <str<strong>on</strong>g>th</str<strong>on</strong>g>e integrative modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> multiscale<br />

cellular systems, and includes solvers for discrete and c<strong>on</strong>tinuous models, a XMLbased<br />

modeling language, and a graphical modeling interface.<br />

To study <str<strong>on</strong>g>th</str<strong>on</strong>g>e generati<strong>on</strong> and c<strong>on</strong>sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatocyte polarity, we established a<br />

hybrid model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> two modules. The molecular interacti<strong>on</strong>s between Rho GT-<br />

Pases and phosphoinositides (PIPs) are modeled using a reacti<strong>on</strong>-diffusi<strong>on</strong> (PDE)<br />

formalism. Anisotropic adhesi<strong>on</strong> and bile secreti<strong>on</strong> between cells are represented in<br />

a cellular Potts model. The integrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e modules is based <strong>on</strong> cell-cell and cellmatrix<br />

signals <str<strong>on</strong>g>th</str<strong>on</strong>g>at trigger polarizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> membrane proteins, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e downstream<br />

effects <str<strong>on</strong>g>of</str<strong>on</strong>g> membrane domains <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tight juncti<strong>on</strong>s and bile secreti<strong>on</strong><br />

at <str<strong>on</strong>g>th</str<strong>on</strong>g>e apical/canalicular domain. Our results are compared to quantitative data<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e polarity and tissue morphology <str<strong>on</strong>g>of</str<strong>on</strong>g> murine hepatocytes in in vitro sandwich<br />

cultures.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> physiological processes in patients <strong>on</strong> dialysis;<br />

Saturday, July 2, 11:00<br />

Malgorzata Debowska<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biocybernetics and Biomedical Engineering, Polish Academy<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warsaw, Poland<br />

e-mail: mdebowska@ibib.waw.pl<br />

Jacek Waniewski<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biocybernetics and Biomedical Engineering, Polish Academy<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warsaw, Poland<br />

Compartmental modeling and adequacy <str<strong>on</strong>g>of</str<strong>on</strong>g> dialysis<br />

In compartmental modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e patient body may be c<strong>on</strong>sidered as a single compartment,<br />

two compartments (intracellular and extracellular or perfused and n<strong>on</strong>perfused)<br />

or more compartments, as appropriate to <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> investigated solute.<br />

Then <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> solute kinetics can be used for <str<strong>on</strong>g>th</str<strong>on</strong>g>e descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dialysis<br />

and provide support for <str<strong>on</strong>g>th</str<strong>on</strong>g>e assessment <str<strong>on</strong>g>of</str<strong>on</strong>g> its efficiency. Two compartment variable<br />

volume urea kinetic model, based <strong>on</strong> ordinary differential equati<strong>on</strong>s, was used<br />

to simulate numerically different dialysis modalities: 1) c<strong>on</strong>venti<strong>on</strong>al hemodialysis<br />

(HD) wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree dialysis sessi<strong>on</strong>s per week, 2) daily HD wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 6 short sessi<strong>on</strong>s per<br />

week, 3) nocturnal HD wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 6 l<strong>on</strong>g sessi<strong>on</strong>s per week, 4) c<strong>on</strong>tinuous ambulatory<br />

perit<strong>on</strong>eal dialysis (PD) wi<str<strong>on</strong>g>th</str<strong>on</strong>g> four exchanges <str<strong>on</strong>g>of</str<strong>on</strong>g> dialysis fluid per day and 5) bimodal<br />

dialysis, i.e., a combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> 5 days <strong>on</strong> PD and two HD sessi<strong>on</strong>s. The<br />

volumes <str<strong>on</strong>g>of</str<strong>on</strong>g> extracellular (Ve) and intracellular (Vi) compartments were related to<br />

total body volume V as Ve(t) = 1/3V(t) and Vi(t) = 2/3V(t), respectively. The<br />

obtained urea c<strong>on</strong>centrati<strong>on</strong>, mass and distributi<strong>on</strong> volume pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles in patient body<br />

and solute c<strong>on</strong>centrati<strong>on</strong>, mass and dialysate volume pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles allow to calculate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

following dialysis adequacy indices, DAI: 1) fracti<strong>on</strong>al solute removal, FSR; and<br />

2) equivalent c<strong>on</strong>tinuous clearance, ECC. FSR is defined as total solute mass removed<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e body normalized by solute mass in <str<strong>on</strong>g>th</str<strong>on</strong>g>e body. ECC is defined as<br />

solute removal rate over solute c<strong>on</strong>centrati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular compartment <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

patient body. In general, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are four variants <str<strong>on</strong>g>of</str<strong>on</strong>g> DAI linked to <str<strong>on</strong>g>th</str<strong>on</strong>g>e variability <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

solute c<strong>on</strong>centrati<strong>on</strong>, mass and fluid volume during intermittent dialysis treatment<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different time intervals between treatments. FSR and ECC are related to 1)<br />

peak, 2) peak average, 3) time average and 4) treatment time average reference<br />

values <str<strong>on</strong>g>of</str<strong>on</strong>g> mass and c<strong>on</strong>centrati<strong>on</strong>, respectively. The system <str<strong>on</strong>g>of</str<strong>on</strong>g> DAI was applied 1)<br />

to compare c<strong>on</strong>venti<strong>on</strong>al, daily and nocturnal HD and c<strong>on</strong>tinuous ambulatory PD,<br />

i.e., treatments wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different dialysis dose and time schedules, 2) to calculate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> bimodal dialysis, 3) to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> residual renal functi<strong>on</strong><br />

and dialysis into <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment, and 4) to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

dialysis dose in metabolically unstable patients. The results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is investigati<strong>on</strong><br />

are important for practical applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> dialysis. Using compartmental models<br />

and solute kinetic analysis we were able to evaluate dialysis adequacy, FSR and<br />

ECC, for simulated dialysis modalities in anuric and n<strong>on</strong>-anuric patients taking<br />

into account <str<strong>on</strong>g>th</str<strong>on</strong>g>eir metabolic state.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Jaber Dehghany<br />

Helmholtz Centre for Infecti<strong>on</strong> Research, Braunschweig, Germany<br />

e-mail: jaber.dehghany@helmholtz-hzi.de<br />

Michael Meyer-Hermann<br />

Helmholtz Centre for Infecti<strong>on</strong> Research, Braunschweig, Germany<br />

e-mail: michael.meyer-hermann@helmholtz-hzi.de<br />

Computer modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> insulin secretory granules’ dynamics<br />

in pancreatic betacell<br />

Insulin is <str<strong>on</strong>g>th</str<strong>on</strong>g>e body’s glucose lowering horm<strong>on</strong>e which is stored in dense-core secretory<br />

granules in pancreatic beta-cells. Glucose-induced insulin secreti<strong>on</strong> follows a<br />

two phase time course: <strong>on</strong>e rapid and transient phase and a week but sustained<br />

phase. Loss <str<strong>on</strong>g>of</str<strong>on</strong>g> first phase in insulin secreti<strong>on</strong> results in Type 2 Diabetes, a metabolic<br />

disorder which is rapidly increasing worldwide. Therefore it is important<br />

to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular mechanism underlying biphasic insulin secreti<strong>on</strong>. Total<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> granules, size distributi<strong>on</strong> and spatial distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> granules in a typical<br />

betacell are important in <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed models for stimulated insulin secreti<strong>on</strong><br />

from betacells. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is project we develop an in-silico model based <strong>on</strong> experimental<br />

results to find <str<strong>on</strong>g>th</str<strong>on</strong>g>e true size distributi<strong>on</strong> (TSD), 3D density pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile and total number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> granules (N) in a typical betacell. Then we make an agent-based model for<br />

granules dynamics inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell and try to find <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanism and explanati<strong>on</strong><br />

behind <str<strong>on</strong>g>th</str<strong>on</strong>g>e two-phase insulin release.<br />

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Developmental Biology; Friday, July 1, 14:30<br />

E.E. Deinum<br />

FOM Institute AMOLF, Amsterdam, <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands; Laboratory for<br />

molecular biology, Wageningen University, <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

e-mail: deinum@amolf.nl<br />

R. Geurts<br />

Laboratory for molecular biology, Wageningen University, <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

T. Bisseling<br />

Laboratory for molecular biology, Wageningen University, <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

B.M. Mulder<br />

FOM Institute AMOLF, Amsterdam, <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands; Laboratory for<br />

plant cell biology, Wageningen University, <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

Manipulating auxin transport: different strategies leave<br />

different signatures<br />

Auxin is a key horm<strong>on</strong>e in plant development. Am<strong>on</strong>g its roles is <str<strong>on</strong>g>th</str<strong>on</strong>g>e determinati<strong>on</strong><br />

and maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> root meristem identity. When a root forms a lateral organ,<br />

differentiated cells turn into a de novo meristem, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e aid <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin.<br />

From a developmental perspective, Legume roots are a particularly interesting<br />

example: <str<strong>on</strong>g>th</str<strong>on</strong>g>ey can sprout two different lateral organs: lateral roots and nitrogen<br />

fixing root nodules. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese are formed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e same regi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e root, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

differentiati<strong>on</strong> z<strong>on</strong>e. In bo<str<strong>on</strong>g>th</str<strong>on</strong>g> cases auxin accumulati<strong>on</strong> is found at <str<strong>on</strong>g>th</str<strong>on</strong>g>e locati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e organ primordium. The primordia, however, originate from different cell layers<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e organs are induced in different ways. This implies <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanism<br />

behind <str<strong>on</strong>g>th</str<strong>on</strong>g>e local auxin accumulati<strong>on</strong> most likely differs between <str<strong>on</strong>g>th</str<strong>on</strong>g>e two cases.<br />

Inspired by <str<strong>on</strong>g>th</str<strong>on</strong>g>is, we analyzed <str<strong>on</strong>g>th</str<strong>on</strong>g>e general characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree plausible<br />

generic strategies for increasing <str<strong>on</strong>g>th</str<strong>on</strong>g>e local auxin c<strong>on</strong>centrati<strong>on</strong>: increasing influx,<br />

decreasing efflux and local producti<strong>on</strong>.<br />

Each strategy results in a pattern wi<str<strong>on</strong>g>th</str<strong>on</strong>g> its own characteristic signature. This<br />

holds in a simple 1D model, but also shows up in a more complex root-like envir<strong>on</strong>ment.<br />

Returning to <str<strong>on</strong>g>th</str<strong>on</strong>g>e legumes: are <str<strong>on</strong>g>th</str<strong>on</strong>g>e differences large enough to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

early differences between bo<str<strong>on</strong>g>th</str<strong>on</strong>g> lateral organ primordia?<br />

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Immunology; Wednesday, June 29, 14:30<br />

Edgar Delgado-Eckert<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosystems Science and Engineering, ETH Zürich, Mattenstrasse<br />

26, 4058 Basel, Switzerland.<br />

e-mail: edgar.delgado-eckert@bsse.e<str<strong>on</strong>g>th</str<strong>on</strong>g>z.ch<br />

Michael Shapiro<br />

Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology Department, Tufts University, 150 Harris<strong>on</strong> Ave., Bost<strong>on</strong>,<br />

MA 02111, U.S.A.<br />

e-mail: Michael.Shapiro@tufts.edu<br />

A model <str<strong>on</strong>g>of</str<strong>on</strong>g> host resp<strong>on</strong>se to a multi-stage pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen<br />

Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens <str<strong>on</strong>g>th</str<strong>on</strong>g>at traverse different stages during <str<strong>on</strong>g>th</str<strong>on</strong>g>eir life cycle or during an<br />

infecti<strong>on</strong> process have been studied since <str<strong>on</strong>g>th</str<strong>on</strong>g>e late nineteen<str<strong>on</strong>g>th</str<strong>on</strong>g> century. The most<br />

prominent genus is Plasmodium, causer <str<strong>on</strong>g>of</str<strong>on</strong>g> Malaria. O<str<strong>on</strong>g>th</str<strong>on</strong>g>er important examples are<br />

Trypanosoma and <str<strong>on</strong>g>th</str<strong>on</strong>g>e family <str<strong>on</strong>g>of</str<strong>on</strong>g> herpes viruses. Our focus is <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e herpes virus<br />

Epstein-Barr (EBV), which is known to cycle <str<strong>on</strong>g>th</str<strong>on</strong>g>rough at least four different stages<br />

during infecti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e human body. One remarkable characteristic <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong>s<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> many <str<strong>on</strong>g>of</str<strong>on</strong>g> such pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens is life-l<strong>on</strong>g persistent infecti<strong>on</strong>.<br />

The main goal <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune resp<strong>on</strong>se<br />

to such a pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen using ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling. In particular, we are interested<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence and properties <str<strong>on</strong>g>of</str<strong>on</strong>g> steady-state behavior corresp<strong>on</strong>ding to life-l<strong>on</strong>g<br />

persistent infecti<strong>on</strong>. Our ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical approach is based <strong>on</strong> standard ODE models<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> viral infecti<strong>on</strong>. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e postulated system <str<strong>on</strong>g>of</str<strong>on</strong>g> ODEs, we were able to characterize<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e equilibria in full generality regarding <str<strong>on</strong>g>th</str<strong>on</strong>g>e number n <str<strong>on</strong>g>of</str<strong>on</strong>g> stages <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen<br />

cycles <str<strong>on</strong>g>th</str<strong>on</strong>g>rough. To establish <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e models’ equilibria, we<br />

successfully applied techniques from modern c<strong>on</strong>trol engineering.<br />

If <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen is able to establish infecti<strong>on</strong>, (i.e., <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproductive number<br />

R0 satisfies R0 > 1), <str<strong>on</strong>g>th</str<strong>on</strong>g>e model’s parameters induce a partial order <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen’s stages. This binary relati<strong>on</strong> j ≻ k is based <strong>on</strong> comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate<br />

at which stage j produces stage k wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate at which stage k is lost to dea<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

and transformati<strong>on</strong> into <str<strong>on</strong>g>th</str<strong>on</strong>g>e next stage k + 1. We say stage j starves stage k if<br />

immune regulati<strong>on</strong> at stage j deprives stage k <str<strong>on</strong>g>of</str<strong>on</strong>g> sufficient populati<strong>on</strong> to support<br />

immune regulati<strong>on</strong>. A stage k is called starvable if <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er stage j such<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at j ≻ k. If no such j exists, k is called unstarvable. One <str<strong>on</strong>g>of</str<strong>on</strong>g> our main results<br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at, generically, <str<strong>on</strong>g>th</str<strong>on</strong>g>e system has a unique (local) asymptotically stable<br />

fixed point, namely, <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>e at which all unstarvable stages are regulated and all<br />

starvable stages are unregulated. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is sense, <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> unstarvable<br />

stages is sufficient to immunologically c<strong>on</strong>trol <str<strong>on</strong>g>th</str<strong>on</strong>g>e starvable stages. At steady<br />

state, immune regulati<strong>on</strong> is <strong>on</strong>ly required against <str<strong>on</strong>g>th</str<strong>on</strong>g>ose stages <str<strong>on</strong>g>th</str<strong>on</strong>g>at are produced<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> relatively higher yield.<br />

This puts wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in reach a principled quantitative explanati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chr<strong>on</strong>ic infecti<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens such as EBV, including <str<strong>on</strong>g>th</str<strong>on</strong>g>e pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> regulati<strong>on</strong> (which is known to<br />

vary from pers<strong>on</strong> to pers<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> EBV), <str<strong>on</strong>g>th</str<strong>on</strong>g>e sizes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e infected populati<strong>on</strong>s<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e host resp<strong>on</strong>se.<br />

References.<br />

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[1] E. Delgado-Eckert and M. Shapiro, A model <str<strong>on</strong>g>of</str<strong>on</strong>g> host resp<strong>on</strong>se to a multi-stage pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen. Journal<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology. 2010 Oct. 2. [Epub ahead <str<strong>on</strong>g>of</str<strong>on</strong>g> print]. DOI 10.1007/s11538-010-9596-2.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Aurelio de los Reyes V<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular Life Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Zurich<br />

e-mail: aurelio.delosreyes@imls.uzh.ch<br />

Attila Becskei<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular Life Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Zurich<br />

e-mail: attila.becskei@imls.uzh.ch<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Feedback in GAL Signalling Cascade<br />

The GAL network cascade in yeast (Saccharomyces cerevisiae) c<strong>on</strong>tains dynamic<br />

molecular interacti<strong>on</strong>s. The complex interplay <str<strong>on</strong>g>of</str<strong>on</strong>g> galactose, Gal3p, Gal80p<br />

and Gal4p regulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e transcripti<strong>on</strong>al activity <str<strong>on</strong>g>of</str<strong>on</strong>g> enzymes in galactose utilizati<strong>on</strong>.<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models have been proposed to understand such biological<br />

signalling processes. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er studies suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e models exhibit bistability/multistability<br />

due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e systems’ positive feedback loop, ultrasensitivity, etc.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is study, an ODE model in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e feedback possesses a sigmoidal characteristic<br />

is used. We are interested to investigate how robustly positive feedback<br />

loop gives rise to bistability depending <strong>on</strong> whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er it is mediated by stoichiometric<br />

complexes <str<strong>on</strong>g>of</str<strong>on</strong>g> signalling proteins, enzymes, or transporter molecules. In particular,<br />

we will examine how feedback in GAL signalling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way can be used to apprehend<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e enhancement <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular memory.<br />

References.<br />

[1] M. Acar, A. Becskei & A. van Oudenaarden, Enhancement <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular memory by reducing<br />

stochastic transiti<strong>on</strong>s Nature 435 228–231.<br />

[2] D. Angeli, J. Ferrell Jr. & E. S<strong>on</strong>tag, Detecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> multistability, bifurcati<strong>on</strong>s, and hysteresis<br />

in a large class <str<strong>on</strong>g>of</str<strong>on</strong>g> biological positive-feedback systems PNAS 101 1822–1827.<br />

[3] P.J. Bhat & R. Iyer, Epigenetics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e yeast galactose genetic switch J. Biosci. 4 513–522.<br />

[4] V. Kulkarni, V. Kareenhalli, P. Malakar, L. Pao, M. Saf<strong>on</strong>ov, & G. Viswana<str<strong>on</strong>g>th</str<strong>on</strong>g>an, Stability<br />

analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e GAL regulatory network in Saccharomyces cerevisiae and Kluyveromyces lactis<br />

BMC Bioinformatics 11 (Suppl 1):S43.<br />

[5] S. Smidtas, V, Schächter & F. Képès, The adaptive filter <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e yeast galactose pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way J.<br />

Theor. Biol. 242 372–381.<br />

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Informati<strong>on</strong>, human behaviour and disease; Saturday, July 2, 11:00<br />

Sara Y. Del Valle<br />

Los Alamos Nati<strong>on</strong>al Laboratory,<br />

e-mail: sdelvall@lanl.gov<br />

James M. Hyman<br />

Tulane University and Los Alamos Nati<strong>on</strong>al Laboratory<br />

e-mail: mhyman@tulane.edu<br />

Herbert W. He<str<strong>on</strong>g>th</str<strong>on</strong>g>cote<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Iowa<br />

e-mail: herbert-he<str<strong>on</strong>g>th</str<strong>on</strong>g>cote@uiowa.edu<br />

Carlos Castillo-Chavez<br />

Ariz<strong>on</strong>a State University<br />

e-mail: chavez@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.asu.edu<br />

Saman<str<strong>on</strong>g>th</str<strong>on</strong>g>a M. Tracht<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Tennessee<br />

e-mail: saman<str<strong>on</strong>g>th</str<strong>on</strong>g>a.tracht@gmail.com<br />

Effects <str<strong>on</strong>g>of</str<strong>on</strong>g> Behavioral Changes in Smallpox and Influenza<br />

Models<br />

Communicable diseases are highly sensitive to how rapidly people reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

c<strong>on</strong>tact activity patterns and to <str<strong>on</strong>g>th</str<strong>on</strong>g>e precauti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> takes to reduce<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease. Recent experiences wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e H1N1 pandemic show<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at an outbreak <str<strong>on</strong>g>of</str<strong>on</strong>g> a deadly disease would generate dramatic behavioral changes.<br />

However, models for infectious diseases have focused <strong>on</strong> analyzing <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

traditi<strong>on</strong>al interventi<strong>on</strong> strategies such as isolati<strong>on</strong> and vaccinati<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I<br />

will present a model in which some individuals lower <str<strong>on</strong>g>th</str<strong>on</strong>g>eir daily c<strong>on</strong>tact activity<br />

rates or wear masks <strong>on</strong>ce an epidemic has been identified in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir community. I will<br />

dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at even gradual and mild behavioral changes can have a dramatic<br />

impact in slowing <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic and reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e total number <str<strong>on</strong>g>of</str<strong>on</strong>g> cases. I c<strong>on</strong>clude<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at for simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases to be useful, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey must c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

impact <str<strong>on</strong>g>of</str<strong>on</strong>g> behavioral changes. This is especially true if <str<strong>on</strong>g>th</str<strong>on</strong>g>e model predicti<strong>on</strong>s are<br />

being used to guide public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> policy.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Bernd-Sim<strong>on</strong> Dengel, Holger Perfahl, Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ias Reuss<br />

Center Systems Biology, University Stuttgart, Germany<br />

e-mail: Bernd.Dengel@gmx.de<br />

3D image rec<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biological tissues<br />

To analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>e movement and reacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> drugs in tissues, a detailed knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue structure is needed. To acquire a better understanding and provide a<br />

model for ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis and simulati<strong>on</strong>s, we c<strong>on</strong>struct a 3D-model from<br />

given image stacks showing various tissues. This model builds <str<strong>on</strong>g>th</str<strong>on</strong>g>e foundati<strong>on</strong> for<br />

particle simulati<strong>on</strong>s and narrows <str<strong>on</strong>g>th</str<strong>on</strong>g>e gap from a discrete to an experimental approach.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore <str<strong>on</strong>g>th</str<strong>on</strong>g>e model serves as a verificati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for simulati<strong>on</strong> data<br />

and provides feedback to refine <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> process.<br />

The image recogniti<strong>on</strong> is implemented using OpenCV, which is <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard<br />

library for computer visi<strong>on</strong> and comes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> efficient algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m useful<br />

to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e different tissue structures. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> an image stack <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

distinguished tissue structure can be c<strong>on</strong>structed to a geometrical model. For verificati<strong>on</strong><br />

and better understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e results we generate a 3D visualisati<strong>on</strong><br />

using OpenGL. Statistical data can also be calculated using <str<strong>on</strong>g>th</str<strong>on</strong>g>e generated model,<br />

for instance cell volume fracti<strong>on</strong> or mean cell density.<br />

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The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting cell systems: from intercellular interacti<strong>on</strong><br />

to tissue-level traits II; Wednesday, June 29, 17:00<br />

Christophe Deroulers<br />

Université Paris Diderot-Paris 7, Laboratoire IMNC, Campus d’Orsay<br />

bat. 440, 91406 Orsay CEDEX, France<br />

e-mail: deroulers.remove<str<strong>on</strong>g>th</str<strong>on</strong>g>is@imnc.in2p3.fr<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ilde Badoual<br />

Université Paris Diderot-Paris 7, Laboratoire IMNC, Campus d’Orsay<br />

bat. 440, 91406 Orsay CEDEX, France<br />

e-mail: badoual.remove<str<strong>on</strong>g>th</str<strong>on</strong>g>is@imnc.in2p3.fr<br />

Basile Grammaticos<br />

CNRS, Laboratoire IMNC, Campus d’Orsay bat. 440, 91406 Orsay CEDEX,<br />

France<br />

e-mail: grammaticos.remove<str<strong>on</strong>g>th</str<strong>on</strong>g>is@univ-paris-diderot.fr<br />

Two examples <str<strong>on</strong>g>of</str<strong>on</strong>g> influence <str<strong>on</strong>g>of</str<strong>on</strong>g> cell-cell interacti<strong>on</strong>s <strong>on</strong><br />

populati<strong>on</strong>s: migrating cancer cells and magnetic<br />

manipulati<strong>on</strong> for tissue engineering<br />

Cell interacti<strong>on</strong>s can have a str<strong>on</strong>g influence <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir populati<strong>on</strong>,<br />

qualitatively as well as quantitatively. Often, <str<strong>on</strong>g>th</str<strong>on</strong>g>e link between <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic<br />

law <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir interacti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic behaviour is not straightforward, and<br />

requires computer simulati<strong>on</strong>s and/or analytic techniques which can be successfully<br />

borrowed from c<strong>on</strong>densed matter physics.<br />

Here we give two examples <str<strong>on</strong>g>of</str<strong>on</strong>g> experimental situati<strong>on</strong>s where a macroscopic<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells was derived (in a n<strong>on</strong>-rigorous way)<br />

from postulated microscopic interacti<strong>on</strong>s. In bo<str<strong>on</strong>g>th</str<strong>on</strong>g> cases, <str<strong>on</strong>g>th</str<strong>on</strong>g>e aim is two-fold. Since<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e models succeed in reproducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e experiments, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey can make predicti<strong>on</strong>s<br />

about more complicated, or even unattainable, experimental c<strong>on</strong>diti<strong>on</strong>s. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, in a c<strong>on</strong>text where <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic mechanisms at stake are difficult<br />

to investigate directly, <str<strong>on</strong>g>th</str<strong>on</strong>g>e quantitative match <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

experiments indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying microscopic hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses may be true.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e first experiment, <str<strong>on</strong>g>th</str<strong>on</strong>g>e excluded volume and adhesi<strong>on</strong>, or c<strong>on</strong>tact inhibiti<strong>on</strong>,<br />

interacti<strong>on</strong>s between migrating cancer cells governs <str<strong>on</strong>g>th</str<strong>on</strong>g>e way <str<strong>on</strong>g>th</str<strong>on</strong>g>ey collectively<br />

spread, making it far from a simple diffusi<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d <strong>on</strong>e, heaps <str<strong>on</strong>g>of</str<strong>on</strong>g> cells<br />

were prepared using magnetic nanomanipulati<strong>on</strong>. The shape <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heaps and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

evoluti<strong>on</strong> depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tact interacti<strong>on</strong>s, and can be understood <str<strong>on</strong>g>th</str<strong>on</strong>g>anks to<br />

simulati<strong>on</strong>s and to a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model.<br />

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective phenomena in biological systems; Saturday, July 2,<br />

08:30<br />

Andreas Deutsch<br />

Centre for Informati<strong>on</strong> Services and High Performance Computing,<br />

Technical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dresden<br />

e-mail: andreas.deutsch@tu-dresden.de<br />

Analyzing emergent behaviour in interacting cell systems<br />

Examples <str<strong>on</strong>g>of</str<strong>on</strong>g> emergent behaviour in interacting cell systems are life cycles <str<strong>on</strong>g>of</str<strong>on</strong>g> bacteria<br />

and social amoebae, embry<strong>on</strong>ic tissue formati<strong>on</strong>, wound healing or tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

Thereby, development <str<strong>on</strong>g>of</str<strong>on</strong>g> a particular spatio-temporal ”multi-cellular” pattern may<br />

be interpreted as cooperative phenomen<strong>on</strong> emerging from an intricate interplay <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

local (e.g. by adhesi<strong>on</strong>) and n<strong>on</strong>-local (e.g. via diffusing signals) cell interacti<strong>on</strong>s.<br />

What are cooperative phenomena in interacting cell systems and how can <str<strong>on</strong>g>th</str<strong>on</strong>g>ey be<br />

studied by ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models and computer simulati<strong>on</strong>s?<br />

Typical modelling attempts focus <strong>on</strong> a macroscopic perspective, i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e models<br />

(e.g. partial differential equati<strong>on</strong>s) describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> cell<br />

c<strong>on</strong>centrati<strong>on</strong>s. More recently, cell-based models have been suggested in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

fate <str<strong>on</strong>g>of</str<strong>on</strong>g> each individual cell can be tracked. Cellular automata are discrete dynamical<br />

systems and may be utilized as cell-based models.<br />

Here, we analyze spatio-temporal pattern formati<strong>on</strong> in cellular automat<strong>on</strong> models<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> interacting discrete cells. We introduce lattice-gas cellular automata and a<br />

cellular automat<strong>on</strong> based <strong>on</strong> an extended Potts model <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows to c<strong>on</strong>sider cell<br />

shapes. Model applicati<strong>on</strong>s are bacterial pattern formati<strong>on</strong> and tumour invasi<strong>on</strong>.<br />

DEUTSCH, A. AND DORMANN, S. (2005) Cellular Automat<strong>on</strong> Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Biological Pattern Formati<strong>on</strong>. Birkhauser, Bost<strong>on</strong><br />

225

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Modeling and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor invasi<strong>on</strong> II; Tuesday, June 28, 14:30<br />

Andreas Deutsch<br />

Centre for Informati<strong>on</strong> Services and High Performance Computing,<br />

Technical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dresden<br />

e-mail: andreas.deutsch@tu-dresden.de<br />

Analyzing emergent behaviour in cellular automat<strong>on</strong> models<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cancer invasi<strong>on</strong><br />

Deciphering <str<strong>on</strong>g>th</str<strong>on</strong>g>e principles <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer invasi<strong>on</strong> is crucial for <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> new<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy c<strong>on</strong>cepts. While molecular biology me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are required for a better characterizati<strong>on</strong><br />

and identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individual cancer cells, ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling<br />

and computer simulati<strong>on</strong> is needed for investigating collective effects <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer invasi<strong>on</strong>.<br />

Here, we dem<strong>on</strong>strate how lattice-gas cellular automat<strong>on</strong> (LGCA) models<br />

allow for an adequate descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individual invasive cancer cell behaviour. We<br />

will <str<strong>on</strong>g>th</str<strong>on</strong>g>en show how analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e LGCA models allows for predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> emerging<br />

properties (in particular <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong> speed). Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we propose <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

transiti<strong>on</strong> to invasive tumour phenotypes in some brain tumours can be explained<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic Go or Grow mechanism (migrati<strong>on</strong>/proliferati<strong>on</strong><br />

dichotomy) and oxygen shortage, i.e. hypoxia, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment <str<strong>on</strong>g>of</str<strong>on</strong>g> a growing<br />

tumour. We test <str<strong>on</strong>g>th</str<strong>on</strong>g>is hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis again wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e help <str<strong>on</strong>g>of</str<strong>on</strong>g> a lattice-gas cellular automat<strong>on</strong>.<br />

Finally, we will use our LGCA models for <str<strong>on</strong>g>th</str<strong>on</strong>g>e interpretati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> data from<br />

in vitro glioma cancer cell invasi<strong>on</strong> assays.<br />

References.<br />

[1] DEUTSCH, A. AND DORMANN, S. (2005) Cellular Automat<strong>on</strong> Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Pattern<br />

Formati<strong>on</strong>. Birkhauser, Bost<strong>on</strong>.<br />

[2] GIESE, A., BJERKVIG, R., BERENS, M. AND WESTPHAL, M. (2003) Cost <str<strong>on</strong>g>of</str<strong>on</strong>g> migrati<strong>on</strong>:<br />

invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> malignant gliomas and implicati<strong>on</strong>s for treatment. J. Clin. Oncol., 21, 16241636.<br />

[3] GODLEWSKI, J., NOWICKI, M. O., BRONISZ, A., NUOVO, G., PALATINI, J., LAY, M.<br />

D., BROCKLYN, J. V., OSTROWSKI, M. C. AND CHIOCCA, E. A. (2010) Microrna-451<br />

regulates lkb1/ampk signaling and allows adaptati<strong>on</strong> to metabolic stress in glioma cells. Mol.<br />

Cell, 37, 620632.<br />

226

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Thanate Dhirasakdan<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Helsinki<br />

e-mail: <str<strong>on</strong>g>th</str<strong>on</strong>g>anate.dhirasakdan<strong>on</strong>@helsinki.fi<br />

Stanley H. Fae<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina at Greensboro<br />

Karl P. Hadeler<br />

Ariz<strong>on</strong>a State University<br />

Horst R. Thieme<br />

Ariz<strong>on</strong>a State University<br />

Epidemics; Wednesday, June 29, 08:30<br />

Coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> vertically and horiz<strong>on</strong>tally transmitted<br />

parasite strains in a simple SI type model<br />

We study an SI type endemic model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <strong>on</strong>e host and two parasite strains wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

complete cross protecti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e strains. We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <strong>on</strong>e strain is exclusively<br />

vertically transmitted and <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er strain is horiz<strong>on</strong>tally (and possibly<br />

also vertically) transmitted. We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at each strain reduces fertility and/or<br />

increases mortality <str<strong>on</strong>g>of</str<strong>on</strong>g> infected hosts. Our model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> just <str<strong>on</strong>g>th</str<strong>on</strong>g>ree ordinary<br />

differential equati<strong>on</strong>s. We use <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> persistence to show <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e (exclusively) vertically transmitted strain <str<strong>on</strong>g>th</str<strong>on</strong>g>at would go extinct by itself can<br />

persist by protecting <str<strong>on</strong>g>th</str<strong>on</strong>g>e host against <str<strong>on</strong>g>th</str<strong>on</strong>g>e more virulent horiz<strong>on</strong>tally transmitted<br />

strain [2]. There are two more interesting properties <str<strong>on</strong>g>of</str<strong>on</strong>g> our model. First, <str<strong>on</strong>g>th</str<strong>on</strong>g>e ratio<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> horiz<strong>on</strong>tal to vertical transmissi<strong>on</strong> decreases if <str<strong>on</strong>g>th</str<strong>on</strong>g>e coefficient <str<strong>on</strong>g>of</str<strong>on</strong>g> horiz<strong>on</strong>tal<br />

transmissi<strong>on</strong> increases, c<strong>on</strong>trary to what <strong>on</strong>e might expects [1]. Sec<strong>on</strong>d, <str<strong>on</strong>g>th</str<strong>on</strong>g>e equilibrium<br />

where bo<str<strong>on</strong>g>th</str<strong>on</strong>g> parasite strains coexist is always locally asymptotically stable<br />

if <str<strong>on</strong>g>th</str<strong>on</strong>g>e horiz<strong>on</strong>tal transmissi<strong>on</strong> is <str<strong>on</strong>g>of</str<strong>on</strong>g> density-dependent (mass-acti<strong>on</strong>) type, but can<br />

loses its stability and gives rise to a limit cycle if <str<strong>on</strong>g>th</str<strong>on</strong>g>e horiz<strong>on</strong>tal transmissi<strong>on</strong> is <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

frequency-dependent (standard) type [3].<br />

References.<br />

[1] Stanley H. Fae<str<strong>on</strong>g>th</str<strong>on</strong>g>, Karl P. Hadeler, and Horst R. Thieme. An apparent paradox <str<strong>on</strong>g>of</str<strong>on</strong>g> horiz<strong>on</strong>tal<br />

and vertical disease transmissi<strong>on</strong>. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Dynamics, 1(1):45-62, 2007.<br />

[2] Thanate Dhirasakdan<strong>on</strong> and Horst R. Thieme. Persistence <str<strong>on</strong>g>of</str<strong>on</strong>g> vertically transmitted parasite<br />

strains which protect against more virulent horiz<strong>on</strong>tally transmitted strains. In Z. Ma, Y. Zhou,<br />

and J. Wu, editors, Modeling and Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Infectious Diseases, 187-215, World Scientific,<br />

2009.<br />

[3] Thanate Dhirasakdan<strong>on</strong> and Horst R. Thieme. Stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e endemic coexistence equilibrium<br />

for <strong>on</strong>e host and two parasites. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> Natural Phenomena, 5(6):109-138,<br />

2010.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Edgar Díaz Herrera<br />

California State University, Los Angeles and<br />

California Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, C<strong>on</strong>trol Dynamical Systems<br />

e-mail: ediazh@caltech.edu<br />

Turing Theory in an Epidemiological Model<br />

Spatial models quantify disease spread in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemiological parameters<br />

(infecti<strong>on</strong> and recovery rates) <str<strong>on</strong>g>th</str<strong>on</strong>g>at influence <str<strong>on</strong>g>th</str<strong>on</strong>g>e speed <str<strong>on</strong>g>of</str<strong>on</strong>g> disease propagati<strong>on</strong><br />

traveling epidemic fr<strong>on</strong>ts. A recurrent assumpti<strong>on</strong> behind bo<str<strong>on</strong>g>th</str<strong>on</strong>g> type <str<strong>on</strong>g>of</str<strong>on</strong>g> models is<br />

uniformity in disease propagati<strong>on</strong>. Such an assumpti<strong>on</strong> while unrealistic facilitates<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is dissertati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e assumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> uniform mixing<br />

(homogeneity) is relaxed, spatial heterogeneity in <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> process is<br />

allowed. A novel reacti<strong>on</strong> diffusi<strong>on</strong> model is introduced and used to identify necessary<br />

and sufficient c<strong>on</strong>diti<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e aggregati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals <str<strong>on</strong>g>th</str<strong>on</strong>g>at may result<br />

in resp<strong>on</strong>se to <str<strong>on</strong>g>th</str<strong>on</strong>g>e introducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a communicable disease. The me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology and<br />

techniques used in <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model, which exhibits diffusive instability,<br />

include Turing <str<strong>on</strong>g>th</str<strong>on</strong>g>eory, which as far as I know, has not been used in <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>text.<br />

228

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Gabriel Dimitriu<br />

“Gr. T. Popa” University <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine and Pharmacy,<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Informatics,<br />

16 Universitatii street, 700115, Iaşi, Romania<br />

e-mail: dimitriu.gabriel@gmail.com<br />

Immunology; Saturday, July 2, 08:30<br />

Optimal c<strong>on</strong>trols for enhancing natural resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

immune system in obesity-related chr<strong>on</strong>ic inflammati<strong>on</strong><br />

Recent researches shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e prevalence <str<strong>on</strong>g>of</str<strong>on</strong>g> obesity has increased by 70 percent<br />

over <str<strong>on</strong>g>th</str<strong>on</strong>g>e past decade [2]. According to World Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Organizati<strong>on</strong> estimates,<br />

over 300 milli<strong>on</strong> adults are obese [4]. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e severity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem c<strong>on</strong>tinues to<br />

grow worldwide, many scientific experts c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e obesity crisis a pandemic [3].<br />

Chr<strong>on</strong>ic inflammati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in fat tissue is now recognized as a c<strong>on</strong>tributor to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

many ill heal<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>sequences <str<strong>on</strong>g>th</str<strong>on</strong>g>at come wi<str<strong>on</strong>g>th</str<strong>on</strong>g> obesity, from diabetes to cardiovascular<br />

disease. The new discovery may <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore point to a targeted <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy designed<br />

to limit <str<strong>on</strong>g>th</str<strong>on</strong>g>e heal<str<strong>on</strong>g>th</str<strong>on</strong>g> impact <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e obesity epidemic, <str<strong>on</strong>g>th</str<strong>on</strong>g>e researchers say. Unlike<br />

acute inflammati<strong>on</strong>, which is <str<strong>on</strong>g>th</str<strong>on</strong>g>e natural resp<strong>on</strong>se to injury or infecti<strong>on</strong>, chr<strong>on</strong>ic<br />

inflammati<strong>on</strong> results from a defective immune resp<strong>on</strong>se. The excessive activity <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

pro-inflammatory cells and proteins can result in additi<strong>on</strong>al defects for surrounding<br />

tissues. These effects <str<strong>on</strong>g>of</str<strong>on</strong>g> chr<strong>on</strong>ic inflammati<strong>on</strong> can lead to diseases such as cancer,<br />

kidney failure, a<str<strong>on</strong>g>th</str<strong>on</strong>g>erosclerosis, and type 2 diabetes mellitus.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal c<strong>on</strong>trol <str<strong>on</strong>g>th</str<strong>on</strong>g>eory is applied to an extended versi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model introduced by P. Díaz et al. in [1]. The model is defined by a<br />

system <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary differential equati<strong>on</strong>s and reflects <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular and cellular<br />

interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e macrophages, T cells, chemokines, and cytokines <str<strong>on</strong>g>th</str<strong>on</strong>g>at cause<br />

chr<strong>on</strong>ic inflammati<strong>on</strong>, after <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>set <str<strong>on</strong>g>of</str<strong>on</strong>g> adipocyte hypertrophy. The model does<br />

not account for <str<strong>on</strong>g>th</str<strong>on</strong>g>e time period in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e subject becomes obese. In comparis<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model in [1], here a linear model for pharmacokinetics has been added.<br />

Seeking to maximize <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> drug treatments to <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, we use a c<strong>on</strong>trol<br />

representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment. The optimal c<strong>on</strong>trol is characterized in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

optimality system, which is solved numerically for several scenarios.<br />

References.<br />

[1] P. Díaz, M. Gillespie, J. Krueger, J. Pérez, A. Radebaughe, T. Shearman, G. Vo, and C.<br />

Wheatley, A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune system’s role in obesity-related chr<strong>on</strong>ic inflammati<strong>on</strong><br />

ICAM, Virginia Bioinformatics Institute, 2(2) (2009), 26–45.<br />

[2] A. Mokdad, B. Bowman, E. Ford, F. Vinikor, J. Marks, and J. Koplan, The c<strong>on</strong>tinuing<br />

epidemics <str<strong>on</strong>g>of</str<strong>on</strong>g> obesity and diabetes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e United States, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e American Medical<br />

Associati<strong>on</strong>, 286 (2001), 1195–1200.<br />

[3] B. Popkin and C. Doak, The obesity epidemic is a worldwide phenomen<strong>on</strong>, Nutriti<strong>on</strong> Review,<br />

56 (1998), 106–114.<br />

[4] P. Puska, C. Nishida, and D. Porter, World Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Organizati<strong>on</strong> strategy <strong>on</strong> diet, physical<br />

activity, and heal<str<strong>on</strong>g>th</str<strong>on</strong>g>: obesity and overweight, Data and statistics. WHO, 2007.<br />

229

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Gaelle Diserens, Gregory Vuillaume, Thomas Mueller, Marja Talikka,<br />

Yiming Cheng, Julia Hoeng<br />

Philip Morris Internati<strong>on</strong>al R&D, Philip Morris Products S.A., Neuchâtel,<br />

Switzerland<br />

e-mail: Gaelle.Diserens@c<strong>on</strong>tracted.pmi.com, gregory.vuillaume@pmintl.com<br />

Philip Morris Internati<strong>on</strong>al R&D, Philip Morris Research Laboratories<br />

GmbH, Cologne, Germany<br />

Frank Tobin<br />

Tobin C<strong>on</strong>sulting LLC, Newtown Square, Pennsylvania, US<br />

Modeling Early Initiati<strong>on</strong> Processes in Smoking-Induced<br />

Lung Adenocarcinomas<br />

While most cancer models focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor itself, our objective<br />

is to build a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e early initiati<strong>on</strong> processes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

development <str<strong>on</strong>g>of</str<strong>on</strong>g> lung adenocarcinomas induced by smoking. Our goal is to produce<br />

a model <str<strong>on</strong>g>th</str<strong>on</strong>g>at is accurate enough to account for <str<strong>on</strong>g>th</str<strong>on</strong>g>e major phenomenology involved<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese initiati<strong>on</strong> processes, <str<strong>on</strong>g>th</str<strong>on</strong>g>at is able to reproduce all <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental data, and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at can explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e timings <str<strong>on</strong>g>of</str<strong>on</strong>g> tumorigenesis based <strong>on</strong> demographic differences.<br />

We have approached <str<strong>on</strong>g>th</str<strong>on</strong>g>e model building in four steps. First, <str<strong>on</strong>g>th</str<strong>on</strong>g>e poorly understood<br />

biology was triaged to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e key biological behaviors causing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

phenotype transiti<strong>on</strong> from normal cells (prior to any smoke exposure) to <str<strong>on</strong>g>th</str<strong>on</strong>g>e earliest<br />

phenotype <str<strong>on</strong>g>th</str<strong>on</strong>g>at could be c<strong>on</strong>sidered a neoplasm. Sec<strong>on</strong>d, <str<strong>on</strong>g>th</str<strong>on</strong>g>e biology was translated<br />

into a n<strong>on</strong>linear ODE model <str<strong>on</strong>g>th</str<strong>on</strong>g>at can reas<strong>on</strong>ably explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> smoking and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at is nei<str<strong>on</strong>g>th</str<strong>on</strong>g>er too complex nor too simplistic. The resulting rate equati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

phenotype dynamics c<strong>on</strong>tain first and sec<strong>on</strong>d order terms. The model is augmented<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>straint functi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at have a dual role <str<strong>on</strong>g>th</str<strong>on</strong>g>ey can be used for checking <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> results obey <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling assumpti<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>ey can be used in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

optimizati<strong>on</strong> step to insure more reas<strong>on</strong>able parameters.<br />

The <str<strong>on</strong>g>th</str<strong>on</strong>g>ird modeling step c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e acquisiti<strong>on</strong> and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> quantitative<br />

biological data to calibrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e model. Because <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount <str<strong>on</strong>g>of</str<strong>on</strong>g> quantitative data<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e scope <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is limited, we have adopted a rigorous surrogate<br />

strategy. This allows us to use bo<str<strong>on</strong>g>th</str<strong>on</strong>g> clinical and animal data (including omics).<br />

The use <str<strong>on</strong>g>of</str<strong>on</strong>g> animal data requires care to make sure <str<strong>on</strong>g>th</str<strong>on</strong>g>at bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dose and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

age <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e animals can be properly incorporated into a human model <str<strong>on</strong>g>th</str<strong>on</strong>g>at extends<br />

across an entire adult lifespan. Finally, a strategy <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>strained optimizati<strong>on</strong> is<br />

used to obtain a single set <str<strong>on</strong>g>of</str<strong>on</strong>g> model parameters <str<strong>on</strong>g>th</str<strong>on</strong>g>at simultaneously provides a good<br />

fit to all <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental data sets and accurately reproduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e key biological<br />

phenomena, wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out producing any unacceptable <strong>on</strong>es.<br />

The model is currently being built and so far c<strong>on</strong>tains approximately 20 differential<br />

equati<strong>on</strong>s involving 50 parameters. We will discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e model building<br />

process, some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e associated ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and computati<strong>on</strong>al challenges, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

need for good data collecti<strong>on</strong> practices, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e value <str<strong>on</strong>g>of</str<strong>on</strong>g> a formal ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

language for <str<strong>on</strong>g>th</str<strong>on</strong>g>e expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> complex biological knowledge.<br />

230

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Neurosciences; Wednesday, June 29, 08:30<br />

Susanne Ditlevsen<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Copenhagen, Denmark<br />

e-mail: susanne@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ku.dk<br />

Priscilla Greenwood<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> British Columbia, Vancouver, Canada<br />

e-mail: Priscilla.Greenwood@asu.edu<br />

The stochastic Morris-Lecar neur<strong>on</strong> model embeds a<br />

<strong>on</strong>e-dimensi<strong>on</strong>al diffusi<strong>on</strong> and its first-passage-time crossings<br />

Stochastic leaky integrate-and-fire models, i.e. <strong>on</strong>e-dimensi<strong>on</strong>al mean-reverting<br />

diffusi<strong>on</strong>s, are popular tools to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic fluctuati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e neur<strong>on</strong>al<br />

membrane potential dynamics due to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir simplicity and statistical tractability.<br />

They have been widely applied to gain understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying mechanisms<br />

for spike timing in neur<strong>on</strong>s, and have served as building blocks for more elaborate<br />

models. Especially <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ornstein-Uhlenbeck process is popular, but also o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

models like <str<strong>on</strong>g>th</str<strong>on</strong>g>e square-root model or models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a n<strong>on</strong>-linear drift are sometimes<br />

applied. However, experimental data show varying time c<strong>on</strong>stants, state dependent<br />

noise, a graded firing <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold and time-inhomogeneous input, and higher<br />

dimensi<strong>on</strong>al, more biophysical models are called for.<br />

The stochastic Morris-Lecar neur<strong>on</strong> is a two-dimensi<strong>on</strong>al diffusi<strong>on</strong> which includes<br />

i<strong>on</strong> channel dynamics. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at in a neighborhood <str<strong>on</strong>g>of</str<strong>on</strong>g> its stable point,<br />

it can be approximated by a two-dimensi<strong>on</strong>al Ornstein-Uhlenbeck modulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

c<strong>on</strong>stant circular moti<strong>on</strong>. The associated radial Ornstein-Uhlenbeck process is an<br />

example <str<strong>on</strong>g>of</str<strong>on</strong>g> a leaky integrate-and-fire model prior to firing. A new model c<strong>on</strong>structed<br />

from a radial Ornstein-Uhlenbeck process toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a simple firing mechanism<br />

based <strong>on</strong> detailed Morris-Lecar firing statistics reproduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e interspike interval<br />

distributi<strong>on</strong>, and has <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong>al advantages <str<strong>on</strong>g>of</str<strong>on</strong>g> a <strong>on</strong>e-dimensi<strong>on</strong>al model.<br />

The result justifies <str<strong>on</strong>g>th</str<strong>on</strong>g>e large amount <str<strong>on</strong>g>of</str<strong>on</strong>g> attenti<strong>on</strong> paid to <str<strong>on</strong>g>th</str<strong>on</strong>g>e leaky integrate-andfire<br />

models.<br />

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Modeling viral hepatitis dynamics in-vivo and in-vitro in <str<strong>on</strong>g>th</str<strong>on</strong>g>e era <str<strong>on</strong>g>of</str<strong>on</strong>g> direct<br />

anti-viral agents II; Wednesday, June 29, 08:30<br />

Narendra Dixit<br />

Indian Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Science, Bangalore, India<br />

e-mail: narendra@chemeng.iisc.ernet.in<br />

Pranesh Padmanabhan<br />

Indian Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Science, Bangalore, India<br />

Modelling HCV kinetics in vitro yields estimates <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> E2-CD81 complexes necessary for viral entry into<br />

target cells<br />

Interacti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e hepatitis C virus (HCV) envelop protein E2 and <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell<br />

surface receptor CD81 is necessary for HCV entry into target cells. Blocking <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

interacti<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore a promising strategy for <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic and preventive interventi<strong>on</strong>.<br />

The minimum number <str<strong>on</strong>g>of</str<strong>on</strong>g> E2-CD81 complexes <str<strong>on</strong>g>th</str<strong>on</strong>g>at must form across a<br />

virus-cell interface to facilitate virus entry, however, remains unknown. The recently<br />

developed cell culture systems <str<strong>on</strong>g>th</str<strong>on</strong>g>at allow persistent HCV infecti<strong>on</strong> in vitro<br />

present data <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e susceptibility <str<strong>on</strong>g>of</str<strong>on</strong>g> cells to virus entry <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

CD81 expressi<strong>on</strong> level <strong>on</strong> cells. We develop a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>th</str<strong>on</strong>g>at quantitatively<br />

describes several independent experimental observati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> viral kinetics<br />

in vitro and <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e frequency <str<strong>on</strong>g>of</str<strong>on</strong>g> virus entry as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e CD81 expressi<strong>on</strong><br />

level. Comparis<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> model predicti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experiments yield estimates <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>reshold number <str<strong>on</strong>g>of</str<strong>on</strong>g> E2-CD81 complexes necessary for virus entry. The <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold<br />

number depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e affinity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e E2-CD81 complex and presents guidelines<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e design and optimal usage <str<strong>on</strong>g>of</str<strong>on</strong>g> entry inhibitors and vaccines <str<strong>on</strong>g>th</str<strong>on</strong>g>at target <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

E2-CD81 interacti<strong>on</strong>.<br />

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Radu Dobrescu<br />

e-mail: rd_dobrescu@yahoo.com<br />

Mihai Tanase<br />

POLITEHNICA University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bucharest<br />

Fractals and Complexity I; Wednesday, June 29, 14:30<br />

Using a mix <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular automata in tumor margin analysis<br />

Cellular automata are classical examples <str<strong>on</strong>g>of</str<strong>on</strong>g> models for many complex systems<br />

related to biology, being suitable tools for modeling grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and diffusi<strong>on</strong> phenomena,<br />

especially tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, c<strong>on</strong>sidering <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey have in comm<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> tumors<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> cell and local interacti<strong>on</strong>. The goal in obtaining a good tumor<br />

model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> cellular automata, as in any o<str<strong>on</strong>g>th</str<strong>on</strong>g>er model, is a better understanding<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tumor dynamics and <str<strong>on</strong>g>th</str<strong>on</strong>g>e developing <str<strong>on</strong>g>of</str<strong>on</strong>g> better techniques for <str<strong>on</strong>g>th</str<strong>on</strong>g>e predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir evoluti<strong>on</strong> in real instances. The <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical ingredients <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is experiment are<br />

mixed cellular automata, <str<strong>on</strong>g>th</str<strong>on</strong>g>e fractal dimensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure generated by an<br />

automat<strong>on</strong> (estimated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e box counting dimensi<strong>on</strong>), <str<strong>on</strong>g>th</str<strong>on</strong>g>e fr<strong>on</strong>tier fractal dimensi<strong>on</strong><br />

between two mixed cellular automata (estimated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e compass dimensi<strong>on</strong>)<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Langt<strong>on</strong>’s Lambda parameter <str<strong>on</strong>g>of</str<strong>on</strong>g> a cellular automat<strong>on</strong>.<br />

References.<br />

[1] B. Pfeifer, K. Kugler, M.M. Tejada. A cellular automat<strong>on</strong> framework for infectious disease<br />

spread simulati<strong>on</strong>. The Open Medical Informatics Journal, 2008; 2: 70-81<br />

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Marina Dolfin<br />

Dep. <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics - University <str<strong>on</strong>g>of</str<strong>on</strong>g> Messina<br />

e-mail: mdolfin@unime.it<br />

Immunology; Wednesday, June 29, 14:30<br />

A phenomenological approach to <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> cl<strong>on</strong>al<br />

expansi<strong>on</strong> and immune competiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> T cells<br />

This presentati<strong>on</strong> deals wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> cl<strong>on</strong>al expansi<strong>on</strong> and<br />

immune competiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> T cells [1] based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e approach <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tinuum mechanics.<br />

Field equati<strong>on</strong>s are ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically c<strong>on</strong>structed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic framework <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ermodynamic <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> reacting fluid mixtures [2, 3], adapted to <str<strong>on</strong>g>th</str<strong>on</strong>g>e case<br />

in which proliferative events occur [4, 5]. The introduced ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model is<br />

inspired by <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental observati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at during <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> type I hypersensitivity<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Specific ImmunoTherapy, <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative fracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> allergen<br />

specific Th1 cells increases [6] and its principal scope is to individuate key parameters<br />

and to evaluate <str<strong>on</strong>g>th</str<strong>on</strong>g>eir effect up<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dominati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Th1 cell populati<strong>on</strong> over<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Th2 <strong>on</strong>e and viceversa.<br />

References.<br />

[1] N. Bellomo, G. Forni, Complex multicellular systems and immune competiti<strong>on</strong>: New paradigms<br />

looking for a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical <str<strong>on</strong>g>th</str<strong>on</strong>g>eory Current Topics in Developmental Biology 81 (2008) 485–<br />

502.<br />

[2] I. Muller, Thermodynamics, Pitman Advanced Publishing Program (1985).<br />

[3] I. Muller, T. Ruggeri, Rati<strong>on</strong>al Extended Thermodynamics, Springer Tracts in Natural Philosophy,<br />

37 (1998) 84–92.<br />

[4] J.D. Humphrey, K.R. Rajagopal, A c<strong>on</strong>strained mixture model for grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and remodeling <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

s<str<strong>on</strong>g>of</str<strong>on</strong>g>t tissues Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models and Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in Applied Sciences 12 (2002) 407-430.<br />

[5] N. Bellomo, N.K. Li, P.K. Maini, On <str<strong>on</strong>g>th</str<strong>on</strong>g>e foundati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer modelling: selected topics,<br />

speculati<strong>on</strong>s and perspectives Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models and Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in Applied Sciences 18 (2008)<br />

593–646.<br />

[6] Pers<strong>on</strong>al communicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. S. Gangemi <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Policlinico Hospital <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Messina to <str<strong>on</strong>g>th</str<strong>on</strong>g>e au<str<strong>on</strong>g>th</str<strong>on</strong>g>or.<br />

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Bioinformatics and System Biology; Wednesday, June 29, 14:30<br />

Mirela Domijan<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warwick<br />

e-mail: mirela.domijan@warwick.ac.uk<br />

Light and temperature effects <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e circadian clock<br />

The circadian clock is endogenous 24h timer driving numerous metabolic, physiological,<br />

biochemical and developmental processes. The clock has a complex interacti<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> its envir<strong>on</strong>ment as it resp<strong>on</strong>ds to light and temperature cues. It can be<br />

entrained to daily cycles <str<strong>on</strong>g>of</str<strong>on</strong>g> light and temperature, yet it also remains very robust to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir stochastic fluctuati<strong>on</strong>s. Ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er key striking feature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e clock is <str<strong>on</strong>g>th</str<strong>on</strong>g>at it can<br />

maintain nearly c<strong>on</strong>stant period over a broad range <str<strong>on</strong>g>of</str<strong>on</strong>g> physiological temperatures<br />

(a feature called temperature compensati<strong>on</strong>). These properties enable <str<strong>on</strong>g>th</str<strong>on</strong>g>e clock to<br />

do a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong>s: it can be used to predict transiti<strong>on</strong>s at dusk and dawn,<br />

measure day leng<str<strong>on</strong>g>th</str<strong>on</strong>g>, and it allows an organism to resp<strong>on</strong>d accurately to seas<strong>on</strong>al<br />

rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms. Elucidating <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e clock wi<str<strong>on</strong>g>th</str<strong>on</strong>g> its envir<strong>on</strong>ment can help us<br />

gain greater understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e design principles <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is important mechanism.<br />

Here I will present some recent work in <str<strong>on</strong>g>th</str<strong>on</strong>g>is directi<strong>on</strong> [1, 2].<br />

References.<br />

[1] M. Domijan and D.A. Rand, Balance equati<strong>on</strong>s can buffer noisy and sustained envir<strong>on</strong>mental<br />

perturbati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> circadian clocks Interface Focus 1 177–186.<br />

[2] P.D. Gould , N. Ugarte, J. Foreman, M. Domijan, D. McGregor, S. Penfield, D.A. Rand, A.<br />

Hall, K. Halliday, A.J. Millar, Photoreceptors c<strong>on</strong>tribute temperature-specific regulati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

biological clock in Arabidopsis, preprint.<br />

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Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part I;<br />

Tuesday, June 28, 11:00<br />

Alberto d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Experimental Oncology, <str<strong>on</strong>g>European</str<strong>on</strong>g> Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Oncology,<br />

Milan, Italy<br />

e-mail: alberto.d<strong>on</strong><str<strong>on</strong>g>of</str<strong>on</strong>g>rio@ifom-ieo-campus.it<br />

The noisy life <str<strong>on</strong>g>of</str<strong>on</strong>g> tumors<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we shall survey some recent <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical results <str<strong>on</strong>g>of</str<strong>on</strong>g> our group <strong>on</strong> how<br />

much and how noise can deeply affect bo<str<strong>on</strong>g>th</str<strong>on</strong>g> natural history <str<strong>on</strong>g>of</str<strong>on</strong>g> tumours and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapies. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e first part we shall show how intrinsic noise might beneficial since<br />

it might trigger tumour suppressi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough evasi<strong>on</strong> form immune surveillance.<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, we shall show how extrinsic noise may be negative, since it<br />

might trigger, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in absence and in presence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies, bounded-noise-induced<br />

induced phase transiti<strong>on</strong>s leading to tumour expansi<strong>on</strong>.<br />

References.<br />

[1] A. d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio, Phys Rev E (2010)<br />

[2] A. d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio and A. Gandolfi, Phys Rev E (2010)<br />

[3] G. Caravagna, A. d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio, P. Milazzo and R. Barbuti, J Theor Biol (2010)<br />

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Delay Differential Equati<strong>on</strong>s and Applicati<strong>on</strong>s I; Friday, July 1, 14:30<br />

Alberto d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Experimental Oncology, <str<strong>on</strong>g>European</str<strong>on</strong>g> Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Oncology,<br />

Milan, Italy<br />

e-mail: alberto.d<strong>on</strong><str<strong>on</strong>g>of</str<strong>on</strong>g>rio@ifom-ieo-campus.it<br />

Malay Banerjee<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics Indian Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Kanpur, India<br />

The interplay between delays and bounded noises in immune<br />

reacti<strong>on</strong> to tumors<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we shall summarize some recent results c<strong>on</strong>cerning <str<strong>on</strong>g>th</str<strong>on</strong>g>e subtle interplays<br />

existing between <str<strong>on</strong>g>th</str<strong>on</strong>g>e statistical fluctuati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e baseline levels <str<strong>on</strong>g>of</str<strong>on</strong>g> immunity and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e delays in <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor-stimulated activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune system. We set our<br />

analysis in <str<strong>on</strong>g>th</str<strong>on</strong>g>e framework <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> bounded noises.<br />

237

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Bioimaging; Tuesday, June 28, 11:00<br />

Alexey Doroshkov<br />

THE INSTITUTE OF CYTOLOGY AND GENETICS The Siberian Branch<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Russian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

e-mail: ad@bi<strong>on</strong>et.nsc.ru<br />

Mikhail Genaev<br />

Tatyana Pshenichnikova<br />

Dmitry Af<strong>on</strong>nikov<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> leaf hairiness in wheat Triticum Aestivum L.<br />

using image processing technique<br />

Leaf hairiness in wheat is <str<strong>on</strong>g>of</str<strong>on</strong>g> great importance for adaptati<strong>on</strong> to envir<strong>on</strong>mental factors<br />

including protecti<strong>on</strong> from pests. For example, <str<strong>on</strong>g>th</str<strong>on</strong>g>is trait is <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristic<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a number <str<strong>on</strong>g>of</str<strong>on</strong>g> drought resistant wheat cultivars referred to <str<strong>on</strong>g>th</str<strong>on</strong>g>e steppe ecological<br />

group. Study <str<strong>on</strong>g>of</str<strong>on</strong>g> leaf hairiness morphology and identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding<br />

genes will allow obtaining <str<strong>on</strong>g>th</str<strong>on</strong>g>e varieties which are resistant to hard climatic c<strong>on</strong>diti<strong>on</strong>s<br />

and certain pests. To identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e genes resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>e leaf hairiness,<br />

mass analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> a great number <str<strong>on</strong>g>of</str<strong>on</strong>g> plants bel<strong>on</strong>ging to different hybrid populati<strong>on</strong>s<br />

is needed, accompanying wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a laborious manual job. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

more accurate descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e morphological properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e trait for correct<br />

determinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> phenotypic classes is timely. We developed <str<strong>on</strong>g>th</str<strong>on</strong>g>e computerbased<br />

technology for descripti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> quantitative traits <str<strong>on</strong>g>of</str<strong>on</strong>g> leaf hairiness. It c<strong>on</strong>tains <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

LHDetect program wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e feature <str<strong>on</strong>g>of</str<strong>on</strong>g> image processing [1,2]. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>e LHDetect<br />

<strong>on</strong>e can count <str<strong>on</strong>g>th</str<strong>on</strong>g>e trichome number, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e trichomes, and evaluate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e trichome leng<str<strong>on</strong>g>th</str<strong>on</strong>g> distributi<strong>on</strong> vector for each leaf sample. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e investigati<strong>on</strong>,<br />

we used <str<strong>on</strong>g>th</str<strong>on</strong>g>e LHDetect program for determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e morphological properties <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

leaf hairiness <strong>on</strong> a number <str<strong>on</strong>g>of</str<strong>on</strong>g> wheat genotypes. The technology appeared to be <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

effective approach for a large scale analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> leaf hairiness morphological peculiarities<br />

in individual plants. In according wi<str<strong>on</strong>g>th</str<strong>on</strong>g> genotyping <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach can be useful<br />

for quantitative trait loci (QTL) mapping. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is study we carried out <str<strong>on</strong>g>th</str<strong>on</strong>g>e detailed<br />

morphology analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> leaf hairiness in 8 wheat cultivars: Golubka, Saratovskaya<br />

29, Rodina (almost glabrous leaf), Rodina introgressi<strong>on</strong> line 102/00i (genome c<strong>on</strong>tains<br />

Aegilops speltoides gene, resp<strong>on</strong>sible for trichomes, line has well-haired leaf),<br />

Houng mang may, Janetzkis probat, Chinese syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic and Diamant 2. Chosen cultivares<br />

represent a wide range <str<strong>on</strong>g>of</str<strong>on</strong>g> leaf hairiness morphology: <str<strong>on</strong>g>th</str<strong>on</strong>g>e trichome density,<br />

leng<str<strong>on</strong>g>th</str<strong>on</strong>g> and distributi<strong>on</strong> pattern greatly varied. Golubka cultivar plants was grown<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e various c<strong>on</strong>diti<strong>on</strong>s. It was shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at drought stressed Golubka plants form<br />

more trichomes <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e leaf surface, but <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are significantly shorter <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>ose<br />

from plants grown in a favourable c<strong>on</strong>diti<strong>on</strong>s. There are at least two possible explanati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong>s. First, much more trichomes are needed to form <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

microclimat in <str<strong>on</strong>g>th</str<strong>on</strong>g>e drought c<strong>on</strong>diti<strong>on</strong>s. Sec<strong>on</strong>d, plant cells cant produce enough<br />

turgor pressure to form a l<strong>on</strong>g trichomes while <str<strong>on</strong>g>th</str<strong>on</strong>g>e drougt stress.<br />

References.<br />

[1] Using <str<strong>on</strong>g>th</str<strong>on</strong>g>e computer-based image processing technique in genetic analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> leaf hairiness<br />

in wheat Triticum aestivum L./ A.V.Doroshkov, M.A.Genaev, T.A.Pshenichnikova,<br />

D.A.Af<strong>on</strong>nikov //<str<strong>on</strong>g>th</str<strong>on</strong>g>e 7-<str<strong>on</strong>g>th</str<strong>on</strong>g> internati<strong>on</strong>al c<strong>on</strong>ference <strong>on</strong> bioinformatics <str<strong>on</strong>g>of</str<strong>on</strong>g> genome regulati<strong>on</strong><br />

and structure/ systems biology, june 20-27 2010 Novosibirsk, Russia.<br />

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[2] WheatPGE system for analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ships between phenotype, genotype and envir<strong>on</strong>ment<br />

in wheat/ M.A.Genaev, A.V.Doroshkov, D.A.Af<strong>on</strong>nikov //<str<strong>on</strong>g>th</str<strong>on</strong>g>e 7-<str<strong>on</strong>g>th</str<strong>on</strong>g> internati<strong>on</strong>al<br />

c<strong>on</strong>ference <strong>on</strong> bioinformatics <str<strong>on</strong>g>of</str<strong>on</strong>g> genome regulati<strong>on</strong> and structure/ systems biology, june 20-27<br />

2010 Novosibirsk, Russia.<br />

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Statistical Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Signals I; Saturday, July 2, 08:30<br />

Christiana Drake<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Statistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> California, Davis<br />

e-mail: cmdrake@ucdavis.edu<br />

Travis Loux<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Statistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> California, Davis<br />

Not Missing at Random and Combined Odds Ratios from<br />

Mixture Models<br />

L<strong>on</strong>gitudinal studies and surveys <str<strong>on</strong>g>of</str<strong>on</strong>g>ten deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> incomplete observati<strong>on</strong>s. The validity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> inference depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e missingness mechanism [Little J.A, and Rubin,<br />

D.B., 2002]. When <str<strong>on</strong>g>th</str<strong>on</strong>g>e missing data mechanism depends <strong>on</strong> observed data <strong>on</strong>ly, estimati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> means and/or regressi<strong>on</strong> coefficients requires adjustment but is possible<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er informati<strong>on</strong>. If <str<strong>on</strong>g>th</str<strong>on</strong>g>e missingness mechanism depends <strong>on</strong> unobserved<br />

data, unbiased estimati<strong>on</strong> requires fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er informati<strong>on</strong>. The informati<strong>on</strong> from random<br />

sub-samples <str<strong>on</strong>g>of</str<strong>on</strong>g> subjects whose resp<strong>on</strong>ses are obtained, can be used to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

data using selecti<strong>on</strong>, shared parameter or pattern mixture models [Allis<strong>on</strong>, 1994],<br />

which are identifiable in <str<strong>on</strong>g>th</str<strong>on</strong>g>is case. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters obtained may not be<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>es <str<strong>on</strong>g>of</str<strong>on</strong>g> interest to an investigator. A separate regressi<strong>on</strong> fit to resp<strong>on</strong>ders and<br />

n<strong>on</strong>resp<strong>on</strong>ders will result in two regressi<strong>on</strong> coefficients when a single coefficient for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e whole populati<strong>on</strong> is <str<strong>on</strong>g>of</str<strong>on</strong>g> interest. Multiple imputati<strong>on</strong> [Rubin, D.B. 1987, Glynn<br />

etal, 1993] can lead to standard statistical analysis. Very large surveys can have<br />

more <str<strong>on</strong>g>th</str<strong>on</strong>g>an 50% n<strong>on</strong>-resp<strong>on</strong>se. A naive approach using multiple imputati<strong>on</strong> results<br />

in data sets wi<str<strong>on</strong>g>th</str<strong>on</strong>g> more <str<strong>on</strong>g>th</str<strong>on</strong>g>an 50% imputed values. We will discuss logistic regressi<strong>on</strong><br />

for a mixture model and compare it to multiple imputati<strong>on</strong> when missingness<br />

depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e unobserved data., The me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are illustrated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Project<br />

Talent data set. The original survey was very large and baseline informati<strong>on</strong> is<br />

available for all participants. Study attriti<strong>on</strong> exceeds 50% but random sub-samples<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>resp<strong>on</strong>dents have almost complete follow-up.<br />

Little, R.J.A. and Rubin, D.B. (2002). Statistical Analysis wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Missing Data,<br />

2nd editi<strong>on</strong>. New York: John Wiley<br />

Rubin, D.B. (1987). Multiple Imputati<strong>on</strong> for N<strong>on</strong>resp<strong>on</strong>se in Surveys, New<br />

York: John Wiley<br />

Glynn, R., Laird, N., and Rubin, D.B. (1993), The Performance <str<strong>on</strong>g>of</str<strong>on</strong>g> Mixture<br />

Models for N<strong>on</strong>ignorable N<strong>on</strong>resp<strong>on</strong>se Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Followups. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e American<br />

Statistical Associati<strong>on</strong>, 88: 984-993.<br />

240

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From <strong>on</strong>e to many: Cell-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective, emergent behaviors<br />

in biology -I; Tuesday, June 28, 11:00<br />

Dirk Drasdo<br />

Rocquencourt<br />

e-mail: dirk.drasdo@inria.fr<br />

Helen Byrne<br />

Nottingham<br />

Jan G. Hengstler<br />

IFADO<br />

Stefan Hoehme<br />

Leipzig<br />

Possible cell behavior strategies to escape biomechanical<br />

c<strong>on</strong>straints in liver regenerati<strong>on</strong> and tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we will show how cells can escape possible biomechanical c<strong>on</strong>straints.<br />

We c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e examples <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e growing m<strong>on</strong>olayers and multi-cellular spheroids, as<br />

well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e proliferati<strong>on</strong> and regenerati<strong>on</strong> pattern in liver after drug-induced damage<br />

and after hepatectomy. For each example we compare experimental results wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

simulati<strong>on</strong> results <str<strong>on</strong>g>of</str<strong>on</strong>g> single-cell-based models. Our model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e center-based type<br />

c<strong>on</strong>siders each cell as an individual unit parameterized by cell- biophysical and cellbiological<br />

quantities. Cell migrati<strong>on</strong> is mimicked by an equati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> moti<strong>on</strong> for each<br />

cell, representing all forces <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at cell and including <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells micro-motility. Part<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e models is parameterized from image analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er bright field or laser<br />

scanning micrographs for quantitative comparis<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> data. We dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> m<strong>on</strong>olayers and multi-cellular spheroids can be c<strong>on</strong>sistently<br />

explained if proliferati<strong>on</strong> is c<strong>on</strong>trolled not <strong>on</strong>ly by molecular factors but also by a<br />

biomechanical proliferati<strong>on</strong> c<strong>on</strong>trol. The same type <str<strong>on</strong>g>of</str<strong>on</strong>g> proliferati<strong>on</strong> c<strong>on</strong>trol is able<br />

to ensure <str<strong>on</strong>g>th</str<strong>on</strong>g>at unrealistically compressed cell volumes during regenerati<strong>on</strong> after<br />

partial hepatectomy in liver does not occur, and <str<strong>on</strong>g>th</str<strong>on</strong>g>at during tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in liver<br />

vessels are not pushed out <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor cell mass. After drug induced liver damage<br />

cells around <str<strong>on</strong>g>th</str<strong>on</strong>g>e so called central veins show massive necrosis. The central vein<br />

forms <str<strong>on</strong>g>th</str<strong>on</strong>g>e center <str<strong>on</strong>g>of</str<strong>on</strong>g> a liver lobule, <str<strong>on</strong>g>th</str<strong>on</strong>g>e repetitive functi<strong>on</strong>al unit <str<strong>on</strong>g>of</str<strong>on</strong>g> liver. Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y<br />

cells must move actively to escape unrealistic compressi<strong>on</strong>s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e absence <str<strong>on</strong>g>of</str<strong>on</strong>g> such<br />

a mechanism, <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimentally observed regenerati<strong>on</strong> and proliferati<strong>on</strong> pattern<br />

cannot be reproduced. The models <str<strong>on</strong>g>of</str<strong>on</strong>g> regenerati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> liver after drug induced<br />

damage and after partial hepatectomy made predicti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at could subsequently<br />

be validated.<br />

References.<br />

[1] Drasdo, D., Hoehme, S. and Block, M. (2007) On <str<strong>on</strong>g>th</str<strong>on</strong>g>e Role <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and<br />

Pattern Formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Multi-Cellular Systems: What can we Learn from Individual-Cell Based<br />

Models? Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Statistical Physics, Volume 128, Numbers 1-2, pp. 287-345(59)<br />

[2] Hoehme, S., Brulport, M., Bauer, A., Bedawy, E., Schormann, W., Gebhardt, R., Zellmer,<br />

S., Schwarz, M., Bockamp, E., Timmel, T., G. Hengstler, J.G., and Drasdo, D. (2010). Predicti<strong>on</strong><br />

and validati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell alignment al<strong>on</strong>g microvessels as order principle to restore tissue<br />

architecture in liver regenerati<strong>on</strong>. Proc. Natl. Acad. Sci. (USA), 107(23), 10371-10376.<br />

[3] Hoehme and Drasdo, (2010) Biomechanical versus nutrient c<strong>on</strong>trol: what determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> mammalian cell populati<strong>on</strong>s? Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Populati<strong>on</strong> Studies, Volume<br />

17, Issue 3, 2010, 166187.<br />

241

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[4] Byrne and Drasdo, (2009) Individual-based and c<strong>on</strong>tinuum models <str<strong>on</strong>g>of</str<strong>on</strong>g> growing cell populati<strong>on</strong>s:<br />

a comparis<strong>on</strong>. J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. Apr;58(4-5):657-87.<br />

242

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multi-scale ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver: From intracellular signaling to<br />

intercellular interacti<strong>on</strong>; Wednesday, June 29, 08:30<br />

Dirk Drasdo<br />

Institut Nati<strong>on</strong>al de Recherche en Informatique et en Automatique<br />

(INRIA), Rocquencourt/Paris, France<br />

e-mail: dirk.drasdo@inria.fr<br />

Stefan Hoehme<br />

Research group Multicellular systems // IZBI // University <str<strong>on</strong>g>of</str<strong>on</strong>g> Leipzig,<br />

Germany<br />

Marc Brulport<br />

Leibniz, Research Centre for Working Envir<strong>on</strong>ment and Human Factors,<br />

Dortmund, Germany<br />

Jan G. Hengstler<br />

Leibniz, Research Centre for Working Envir<strong>on</strong>ment and Human Factors,<br />

Dortmund, Germany<br />

Predicti<strong>on</strong> and validati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an order principle to restore<br />

tissue architecture in liver regenerati<strong>on</strong> after drug-induced<br />

damage: from experiments to modeling and back<br />

Not much is known about how cells coordinately behave to establish functi<strong>on</strong>al<br />

tissue structure and to restore micro-architecture during regenerati<strong>on</strong>. Research<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>is field suffers from a lack <str<strong>on</strong>g>of</str<strong>on</strong>g> techniques <str<strong>on</strong>g>th</str<strong>on</strong>g>at permits quantificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue<br />

architecture and its development. To bridge <str<strong>on</strong>g>th</str<strong>on</strong>g>is gap we have established a<br />

procedure based <strong>on</strong> c<strong>on</strong>focal laser scans, image processing and <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-dimensi<strong>on</strong>al<br />

tissue rec<strong>on</strong>structi<strong>on</strong>, as well as <strong>on</strong> quantitative ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling. To illustrate<br />

our me<str<strong>on</strong>g>th</str<strong>on</strong>g>od we studied regenerati<strong>on</strong> after toxic liver damage. We have<br />

chosen <str<strong>on</strong>g>th</str<strong>on</strong>g>e example <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e regenerating liver, because liver functi<strong>on</strong> depends <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e complex micro-architecture formed by hepatocytes (<str<strong>on</strong>g>th</str<strong>on</strong>g>e main type <str<strong>on</strong>g>of</str<strong>on</strong>g> cells in<br />

liver) and micro-vessels (sinusoids) <str<strong>on</strong>g>th</str<strong>on</strong>g>at ensures optimal exchange <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolites<br />

between blood and hepatocytes. Our model <str<strong>on</strong>g>of</str<strong>on</strong>g> regenerati<strong>on</strong> after toxic damage captures<br />

hepatocytes and sinusoids <str<strong>on</strong>g>of</str<strong>on</strong>g> a liver lobule during <str<strong>on</strong>g>th</str<strong>on</strong>g>e regenerati<strong>on</strong> process.<br />

Hepatocytes are modeled as individual agents parameterized by measurable biophysical<br />

and cell-biological quantities. Cell migrati<strong>on</strong> is mimicked by an equati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> moti<strong>on</strong> for each cell subject to cell-cell-, cell-extra-cellular matrix-, and cellsinusoid-forces,<br />

as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell micro-motility. We dem<strong>on</strong>strate how by iterative<br />

applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e above procedure <str<strong>on</strong>g>of</str<strong>on</strong>g> experiments, image processing and modeling<br />

a final model emerged <str<strong>on</strong>g>th</str<strong>on</strong>g>at unambiguously predicted a so far unrecognized mechanism,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e alignment <str<strong>on</strong>g>of</str<strong>on</strong>g> daughter hepatocytes al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e closest sinusoids as essential<br />

for liver regenerati<strong>on</strong>. In absence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is mechanism, <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulated tissue architecture<br />

was in dis-agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimentally obtained data and no o<str<strong>on</strong>g>th</str<strong>on</strong>g>er likely<br />

mechanism could replace it. To experimentally validate <str<strong>on</strong>g>th</str<strong>on</strong>g>e model predicti<strong>on</strong>, we<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ree-dimensi<strong>on</strong>ally analyzed <str<strong>on</strong>g>th</str<strong>on</strong>g>e orientati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> daughter hepatocytes in relati<strong>on</strong> to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e sinusoids. The results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is analysis clearly c<strong>on</strong>firmed <str<strong>on</strong>g>th</str<strong>on</strong>g>e model predicti<strong>on</strong>.<br />

References.<br />

243

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[1] Hoehme, S., Brulport, M., Bauer, A., Bedawy, E., Schormann, W., Gebhardt, R., Zellmer,<br />

S., Schwarz, M., Bockamp, E., Timmel, T., G. Hengstler, J.G., and Drasdo, D. (2010). Predicti<strong>on</strong><br />

and validati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell alignment al<strong>on</strong>g microvessels as order principle to restore tissue<br />

architecture in liver regenerati<strong>on</strong>. Proc. Natl. Acad. Sci. (USA), 107(23), 10371-10376.<br />

[2] Hoehme, S., Hengstler J.G., Brulport M., Schäfer M., Bauer A., Gebhardt R. and Drasdo<br />

D. (2007) Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> liver regenerati<strong>on</strong> after intoxicati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> CCl. Chemico-<br />

Biological Interacti<strong>on</strong>, 168, 74-93.<br />

244

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Multiscale modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: from physical tools to<br />

applicati<strong>on</strong>s in cancer modeling I; Saturday, July 2, 08:30<br />

Dirk Drasdo<br />

INRIA, Paris-Rocquencourt, France & IZBI, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Leipzig,<br />

Germany<br />

e-mail: dirk.drasdo@inria.fr<br />

Ignacio Ramis C<strong>on</strong>de<br />

UDM, Spain<br />

Helen Byrne<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, UK<br />

Markus Radszuweit<br />

TU Berlin, Germany<br />

Axel Krinner<br />

Univ. Leipzig, Germany<br />

Joerg Galle<br />

Univ. Leipzig, Germany<br />

Eckehard Schoell<br />

Univ. Leipzig, Germany<br />

Multi-scale modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> cells: c<strong>on</strong>cepts and open questi<strong>on</strong>s<br />

The analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue organizati<strong>on</strong> and tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is inherently <str<strong>on</strong>g>of</str<strong>on</strong>g> multi-scale<br />

nature. Extracellular signal molecules, metabolites, mutati<strong>on</strong>s may due to cascades<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> molecular intermediates modify <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior and <str<strong>on</strong>g>th</str<strong>on</strong>g>e physical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

cell resulting in re-organizati<strong>on</strong> processes <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue and organ level. Vice-versa,<br />

changes <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue can feed back to <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular regulati<strong>on</strong> processes.<br />

Limits in computati<strong>on</strong> time requirements and <str<strong>on</strong>g>th</str<strong>on</strong>g>e great complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> cells and<br />

tissues make it impossible to simulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e different scales ranging<br />

from molecules to whole organs in great detail. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, many details<br />

<strong>on</strong> smaller scales have <strong>on</strong>ly small or no effects <strong>on</strong> processes <strong>on</strong> larger scales. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

talk we discuss different individual-based models to tissue organizati<strong>on</strong> including<br />

hybrid and multi-scale models.<br />

(1) In <str<strong>on</strong>g>th</str<strong>on</strong>g>e first part we introduce individual-based model c<strong>on</strong>cepts and dem<strong>on</strong>strate<br />

how <str<strong>on</strong>g>th</str<strong>on</strong>g>ey can be used to explain grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in biological models <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor development,<br />

namely, m<strong>on</strong>olayer, multi-cellular spheroids, and Xenografts (Drasdo et.<br />

al., J. Stat. Phys. 2007 and refs <str<strong>on</strong>g>th</str<strong>on</strong>g>erein, Radszuweit et. al., Phys. Rev. E, 2009).<br />

We c<strong>on</strong>sider two model types: cellular automat<strong>on</strong> models and center-based models.<br />

The first model is parameterized by rules while <str<strong>on</strong>g>th</str<strong>on</strong>g>e latter model is parameterized<br />

by measurable quantities, and directly represents physical forces between <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells,<br />

and between cells and extra-cellular structures. We will critically discuss advantages<br />

and pitfalls <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e different model types and show how <str<strong>on</strong>g>th</str<strong>on</strong>g>ey can be linked to<br />

extracellular molecular c<strong>on</strong>centrati<strong>on</strong>s to hybrid models.<br />

(2) In a sec<strong>on</strong>d step we show how intra-cellular, molecular core modules can be<br />

embedded into a single-cell-based model to a multi-scale model. We c<strong>on</strong>sider several<br />

examples: <str<strong>on</strong>g>th</str<strong>on</strong>g>e integrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e beta-catenin core module to mimic <str<strong>on</strong>g>th</str<strong>on</strong>g>e epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elialmesenchymal<br />

transiti<strong>on</strong> during cancer invasi<strong>on</strong> (Ramis-C<strong>on</strong>de et. al., Biophys.<br />

J. 2008), intravasati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e process by which a tumor cells enters a blood vessel<br />

(Ramis-C<strong>on</strong>de et. al., Phys. Biol. 2009), mesenchymal stem cell differentiati<strong>on</strong><br />

245

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

(Krinner et. al., Cell Prol. 2009; BMC Syst. Biol. 2010), and <str<strong>on</strong>g>th</str<strong>on</strong>g>e change <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cell metabolism during liver regenerati<strong>on</strong> after drug-induced damage. (3) Finally<br />

we show how individual-based models can be used to guide <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

c<strong>on</strong>tinuum models c<strong>on</strong>sidering grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> disperse and compact tumor phenotypes<br />

(Byrne and Drasdo, J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. 2009).<br />

246

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Fátima Drubi<br />

Leiden University<br />

e-mail: drubi@cml.leidenuniv.nl<br />

Patsy Haccou<br />

Leiden University<br />

e-mail: haccou@cml.leidenuniv.nl<br />

Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 14:30<br />

Do bacteria form spores as a bet-hedging strategy in<br />

stochastic envir<strong>on</strong>ments?<br />

Many bacteria form spores to survive extreme c<strong>on</strong>diti<strong>on</strong>s, such as lack <str<strong>on</strong>g>of</str<strong>on</strong>g> nutrients,<br />

periods <str<strong>on</strong>g>of</str<strong>on</strong>g> drought, or extraordinary high or low temperatures. Detailed observati<strong>on</strong>s<br />

by microbiologists have revealed <str<strong>on</strong>g>th</str<strong>on</strong>g>at even in isogenic populati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>ere<br />

is substantial intra-individual variati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e timing <str<strong>on</strong>g>of</str<strong>on</strong>g> sporulati<strong>on</strong> initiati<strong>on</strong>. This<br />

has led to <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at sporulati<strong>on</strong> is a ‘bet hedging strategy’, which has<br />

evolved to cope wi<str<strong>on</strong>g>th</str<strong>on</strong>g> unpredictably varying envir<strong>on</strong>ments. The idea behind <str<strong>on</strong>g>th</str<strong>on</strong>g>is is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at early sporulators have an advantage if <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment gets worse, whereas late<br />

sporulators can pr<str<strong>on</strong>g>of</str<strong>on</strong>g>it more quickly from improving envir<strong>on</strong>ments. Genotypes <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

produce individuals <str<strong>on</strong>g>of</str<strong>on</strong>g> different types <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore ‘spread <str<strong>on</strong>g>th</str<strong>on</strong>g>eir risks’. We will present<br />

a model for studying <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> sporulati<strong>on</strong> strategies in envir<strong>on</strong>ments where<br />

new resources arrive at stochastic times. Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model we make predicti<strong>on</strong>s<br />

about <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s under which bet hedging sporulati<strong>on</strong> strategies might indeed<br />

evolve. The problem is complicated, since it involves density dependent processes<br />

(due to resource depleti<strong>on</strong>) as well as envir<strong>on</strong>mental fluctuati<strong>on</strong>.<br />

Keywords: Evoluti<strong>on</strong>ary modeling; Bed-hedging strategy; Stochastic envir<strong>on</strong>ments;<br />

Sporulati<strong>on</strong>.<br />

References.<br />

[1] T. G. Bent<strong>on</strong> and A. Grant, Optimal reproductive effort in stochastic, density-dependent envir<strong>on</strong>ments.<br />

Evoluti<strong>on</strong> 53(3) 677–688. (1999)<br />

[2] BetNet Project, The evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastis heterogeneous networks as bet-hedging adaptati<strong>on</strong>s<br />

to fluctuating envir<strong>on</strong>ments. Financed by The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands Organisati<strong>on</strong> for Scientific Reseach<br />

(NWO). (2009-2011)<br />

[3] A. Grant, Selecti<strong>on</strong> pressures <strong>on</strong> vital rates in density-dependent populati<strong>on</strong>s. Proc. R. Soc.<br />

L<strong>on</strong>d. B 264 303–306. (1997)<br />

[4] P. Haccou and J. McNamara, Effects <str<strong>on</strong>g>of</str<strong>on</strong>g> parental survival <strong>on</strong> clutch size decisi<strong>on</strong>s in fluctuating<br />

envir<strong>on</strong>ments. Evoluti<strong>on</strong>ary ecology 12 459–475. (1998)<br />

[5] E. Kussell, R. Kish<strong>on</strong>y, N. Q. Balaban and S. Leibler, Bacterial persistence: A model <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

survival in changing envir<strong>on</strong>ments. Genetics 168 1807–1814. (2005)<br />

[6] J. Seger and H. J. Brockmann, What is bet-hedging? Oxford Surveys in Evoluti<strong>on</strong>ary Biology<br />

4 182–211. (1988)<br />

[7] W. M. Schaffer, Optimal effort in fluctuating envir<strong>on</strong>ments. Am. Nat. 108 783–790. (1974)<br />

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Wen Duan<br />

Auckland University, New Zealand<br />

e-mail: wdua004@aucklanduni.ac.nz<br />

Kiho Lee<br />

Otago University, New Zealand<br />

Allan E. Herbis<strong>on</strong><br />

Otago University, New Zealand<br />

James Sneyd<br />

Auckland University, New Zealand<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> adult GnRH neur<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

mouse brain<br />

G<strong>on</strong>adotropin-releasing horm<strong>on</strong>e (GnRH) neur<strong>on</strong>s are cells in <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>alamus<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at produce GnRH, <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e major horm<strong>on</strong>es <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trols fertility and reproducti<strong>on</strong>.<br />

However, despite <str<strong>on</strong>g>th</str<strong>on</strong>g>eir importance, little is known about <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms<br />

by which GnRH is produced. GnRH neur<strong>on</strong>s exhibit complicated membrane potential<br />

dynamics, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> electrical bursting, and <str<strong>on</strong>g>th</str<strong>on</strong>g>is bursting is closely<br />

coupled to <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> intracellular calcium (Ca 2+ ) in ways <str<strong>on</strong>g>th</str<strong>on</strong>g>at are not yet<br />

well understood.<br />

A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model has been c<strong>on</strong>structed to help understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms<br />

underlying <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed behaviours <str<strong>on</strong>g>of</str<strong>on</strong>g> GnRH neur<strong>on</strong>s, and how electrical<br />

bursting synchr<strong>on</strong>izes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> transients in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytosolic Ca 2+ c<strong>on</strong>centrati<strong>on</strong> ([Ca 2+ ]i).<br />

Simulati<strong>on</strong>s show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> all <str<strong>on</strong>g>th</str<strong>on</strong>g>e crucial experimental<br />

data. Most importantly, <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model predicted <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> particular<br />

[Ca 2+ ]i-activated potassium (K + ) channel (sIAHP−UCL), which was <str<strong>on</strong>g>th</str<strong>on</strong>g>en<br />

c<strong>on</strong>firmed experimentally. In c<strong>on</strong>trast to <str<strong>on</strong>g>th</str<strong>on</strong>g>e apamin-sensitive [Ca 2+ ]i-activated<br />

K + channels (sIAHP−SK), which c<strong>on</strong>trol bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure <str<strong>on</strong>g>of</str<strong>on</strong>g> firing wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in bursts<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e interburst intervals, sIAHP−UCL solely determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e interburst dynamics.<br />

The work has been published in Lee et al., 2010 and Duan et al., 2011.<br />

References.<br />

[1] Kiho Lee, Wen Duan, James Sneyd, Allan E. Herbis<strong>on</strong>, Two slow calcium-activated afterhyperpolarizati<strong>on</strong><br />

currents c<strong>on</strong>trol burst firing dynamics in g<strong>on</strong>adotropin-releasing horm<strong>on</strong>e<br />

neur<strong>on</strong>s The Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Neuroscience 30(18) 6214–6224.<br />

[2] Wen Duan, Kiho Lee, Allan E. Herbis<strong>on</strong>, James Sneyd, A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> adult GnRH<br />

neur<strong>on</strong>s in mouse brain and its bifurcati<strong>on</strong> analysis Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology 276 22–34.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Jorge Duarte 1,2 , Cristina Januário 1 , Nuno Martins 2 and Josep Sardanyés 3<br />

e-mail: jduarte@deq.isel.ipl.pt<br />

e-mail: cjanuario@deq.isel.ipl.pt<br />

e-mail: nmartins@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ist.utl.pt<br />

e-mail: josep.sardanes@upf.edu<br />

1 ISEL - Engineering Superior Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Lisb<strong>on</strong>, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Department,<br />

Rua C<strong>on</strong>selheiro Emídio Navarro, 1, 1949-014 Lisboa, Portugal<br />

2 Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento<br />

de Matemática„ Instituto Superior Técnico, Av. Rovisco<br />

Pais 1, 1049-001 Lisboa, Portugal<br />

3 Instituto de Biologıa Molecular y Celular de Plantas, Centro Superior<br />

de Investigaci<strong>on</strong>es Científicas-UPV, Ingeniero Fausto Elio s/n,<br />

46022 Valência, Spain<br />

Chaos and crises in a model for cooperative hunting<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> cooperative hunting<br />

extending <str<strong>on</strong>g>th</str<strong>on</strong>g>e McCann and Yodzis model for a <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-species food chain system wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

a predator, a prey, and a resource species. The new model c<strong>on</strong>siders <str<strong>on</strong>g>th</str<strong>on</strong>g>at a given<br />

fracti<strong>on</strong> σ <str<strong>on</strong>g>of</str<strong>on</strong>g> predators cooperates in prey’s hunting, while <str<strong>on</strong>g>th</str<strong>on</strong>g>e rest <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong><br />

1 − σ hunts wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out cooperati<strong>on</strong>. We use <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> symbolic dynamics to<br />

study <str<strong>on</strong>g>th</str<strong>on</strong>g>e topological entropy and <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter space ordering <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e kneading<br />

sequences associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <strong>on</strong>e-dimensi<strong>on</strong>al maps <str<strong>on</strong>g>th</str<strong>on</strong>g>at reproduce significant aspects<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e species under several degrees <str<strong>on</strong>g>of</str<strong>on</strong>g> cooperative hunting. Our<br />

model also allows us to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e so-called deterministic extincti<strong>on</strong> via chaotic<br />

crisis and transient chaos in <str<strong>on</strong>g>th</str<strong>on</strong>g>e framework <str<strong>on</strong>g>of</str<strong>on</strong>g> cooperative hunting.<br />

249

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Claire Dufourd<br />

Umr PVBMT - CIRAD, FR-974200 Saint Pierre<br />

e-mail: claire.dufourd@gmail.com<br />

Yves Dum<strong>on</strong>t<br />

Umr AMAP - CIRAD, FR-34980 M<strong>on</strong>tpellier<br />

e-mail: yves.dum<strong>on</strong>t@cirad.fr<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Spatio-temporal modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Aedes albopictus dispersal in<br />

Réuni<strong>on</strong> Island. Applicati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e release <str<strong>on</strong>g>of</str<strong>on</strong>g> Sterile Insects.<br />

This work is part <str<strong>on</strong>g>of</str<strong>on</strong>g> a project, called <str<strong>on</strong>g>th</str<strong>on</strong>g>e SIT-project, <str<strong>on</strong>g>th</str<strong>on</strong>g>at aims to develop biological<br />

c<strong>on</strong>trol tools to prevent or stop a Chikungunya epidemic. Chikungunya is somehow<br />

a uncomm<strong>on</strong> disease and before <str<strong>on</strong>g>th</str<strong>on</strong>g>e huge epidemic in Réuni<strong>on</strong> island and in India in<br />

2006, our knowledges <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is virus were small. Recently, in September 2010, a few<br />

cases <str<strong>on</strong>g>of</str<strong>on</strong>g> Chikungunya appeared in Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> France, indicating <str<strong>on</strong>g>th</str<strong>on</strong>g>at Chikungunya is<br />

not <strong>on</strong>ly a tropical disease but can potentially appear in Europe. The appearance<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Chikungunya is str<strong>on</strong>gly c<strong>on</strong>nected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spreading <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> its principal<br />

vector, Aedes albopictus. This mosquito is now well established in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Europe. In [1] and [2], we were mainly c<strong>on</strong>cerned <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic<br />

and <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> chemical vector c<strong>on</strong>trol tools, like adulticides and larvicides, and<br />

mechanical c<strong>on</strong>trol, which c<strong>on</strong>sists in reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e breeding sites. Unfortunately,<br />

using chemical c<strong>on</strong>trol tools, in Réuni<strong>on</strong> Island is not really a good idea. First,<br />

because Réuni<strong>on</strong> Island is a hot spot <str<strong>on</strong>g>of</str<strong>on</strong>g> endemicity, and sec<strong>on</strong>d because mosquito<br />

can develop a resistance to insecticides. In a recent paper, we have developed a<br />

new model <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Sterile Insect Technique (SIT) as an alternative to<br />

insecticides [3].<br />

All published models are temporal models, i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>ey d<strong>on</strong>’t take into account<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial comp<strong>on</strong>ent. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>e previous works, we began to fill <str<strong>on</strong>g>th</str<strong>on</strong>g>is gap. Using<br />

mark-release-capture experiments, we have developed a system <str<strong>on</strong>g>of</str<strong>on</strong>g> partial differential<br />

equati<strong>on</strong>s (PDES) in order to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e spreading/displacement <str<strong>on</strong>g>of</str<strong>on</strong>g> an Aedes<br />

albopictus mosquito populati<strong>on</strong>. In a first approach, we have splitted <str<strong>on</strong>g>th</str<strong>on</strong>g>e females<br />

in two biological stages: <strong>on</strong>e representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e female looking for breeding sites, and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er representing females looking for blood meal. This led to a system <str<strong>on</strong>g>of</str<strong>on</strong>g> two<br />

coupled partial differential equati<strong>on</strong>s. Then, we have c<strong>on</strong>sidered a full model wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

more compartments including <str<strong>on</strong>g>th</str<strong>on</strong>g>e aquatic stage, imature females, female looking for<br />

blood meals, female looking for breeding sites, and males, for mating. These led to<br />

a system <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled advecti<strong>on</strong>-reacti<strong>on</strong>-diffusi<strong>on</strong> PDES. Taking into account entomological<br />

knowledges, we have included biological facts into <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong>s in order<br />

to be as realistic as possible. We developed appropriate numerical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in order<br />

to get realistic numerical simulati<strong>on</strong>s to be able to compare wi<str<strong>on</strong>g>th</str<strong>on</strong>g> "experiments" in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e fields.<br />

The main applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is to optimize vector c<strong>on</strong>trol, using releases<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> sterile males combined wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mechanical c<strong>on</strong>trol.<br />

References.<br />

[1] Y. Dum<strong>on</strong>t, F. Chiroleu and C. Domerg, On a temporal model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chikungunya disease:<br />

modeling, <str<strong>on</strong>g>th</str<strong>on</strong>g>eory and numerics, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci. 213 (2008), 70-81.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[2] Y. Dum<strong>on</strong>t and F. Chiroleu, Vector C<strong>on</strong>trol for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chikungunya Disease, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Bioscience<br />

and Engineering, 7(2) (2010), 315-348.<br />

[3] Y. Dum<strong>on</strong>t and J.M. Tchuenche, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical studies <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Sterile Insect Technique for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Chikungunya Disease and Aedes albopictus, submitted.<br />

251

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Yves Dum<strong>on</strong>t<br />

Umr AMAP - CIRAD, FR-34980 M<strong>on</strong>tpellier<br />

e-mail: yves.dum<strong>on</strong>t@cirad.fr<br />

Vector-borne diseases; Tuesday, June 28, 14:30<br />

Chikungunya: an unusual vector-borne disease. Overview<br />

and new research trends.<br />

In 2006 Réuni<strong>on</strong> Island faced a huge Chikungunya epidemic. Since <str<strong>on</strong>g>th</str<strong>on</strong>g>en, in<br />

2007, and more recently, in september 2010, a few cases <str<strong>on</strong>g>of</str<strong>on</strong>g> Chikungunya appeared<br />

in Italy and in Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> France. Since <str<strong>on</strong>g>th</str<strong>on</strong>g>e explosive epidemic in Réuni<strong>on</strong> Island, our<br />

knowledges <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chikungunya virus and its principal vector, Aedes albopictus,<br />

have increased (see [6] for instance). In some sense, Chikungunya is an unusual<br />

vector-borne disease: it has been proved <str<strong>on</strong>g>th</str<strong>on</strong>g>at a mutati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus in 2005<br />

has led to an increase in <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>of</str<strong>on</strong>g> transmissi<strong>on</strong> from human to mosquito,<br />

and had also a str<strong>on</strong>g impact <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e life-span <str<strong>on</strong>g>of</str<strong>on</strong>g> infected mosquitoes [6], which<br />

may explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e explosive epidemic in 2006 in Réuni<strong>on</strong> Island. All <str<strong>on</strong>g>th</str<strong>on</strong>g>ese biological<br />

assumpti<strong>on</strong>s have been taken into account in <str<strong>on</strong>g>th</str<strong>on</strong>g>e models studied in [2,3]. After some<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical works [1, 2] <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic and <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> chemical<br />

vector c<strong>on</strong>trol tools, like adulticides and larvicides, we recently have studied <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

"Pulsed" Sterile Insect Technique (SIT) as a biological alternative to insecticides,<br />

because mosquito can develop a resistance to insecticides [3]. Moreover SIT is<br />

known to be a species-specific envir<strong>on</strong>mentally n<strong>on</strong>polluting me<str<strong>on</strong>g>th</str<strong>on</strong>g>od. In particular,<br />

we showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at frequent and small releases <str<strong>on</strong>g>of</str<strong>on</strong>g> sterile males can be efficient to c<strong>on</strong>trol<br />

an epidemic, but <strong>on</strong>ly if it is c<strong>on</strong>sidered early in <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic.<br />

All published models are temporal models, i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>ey d<strong>on</strong>’t take into account<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial comp<strong>on</strong>ent. Based <strong>on</strong> [2], we have filled <str<strong>on</strong>g>th</str<strong>on</strong>g>is gap, c<strong>on</strong>sidering a patchy<br />

model in order to take into account human displacements between cities in Réuni<strong>on</strong><br />

Island [1]. We have computed <str<strong>on</strong>g>th</str<strong>on</strong>g>e Global Basic Reproducti<strong>on</strong> Number, R0,G, for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e patchy model, and we have showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at even if locally R0 is less <str<strong>on</strong>g>th</str<strong>on</strong>g>an 1, R0,G<br />

can be greater <str<strong>on</strong>g>th</str<strong>on</strong>g>an 1, indicating <str<strong>on</strong>g>th</str<strong>on</strong>g>at populati<strong>on</strong> displacements could have an effect<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e global dynamic <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e outbreak. For practical purposes, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at vector<br />

c<strong>on</strong>trol in cities where R0 is large, could be efficient to c<strong>on</strong>trol globally <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic.<br />

Finally, based <strong>on</strong> field experiments, we have include <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial comp<strong>on</strong>ent in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mosquito populati<strong>on</strong>. This leads to a complicate system <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

n<strong>on</strong> linear partial differential equati<strong>on</strong>s [5]. The final aim is to "optimize" locally<br />

vector c<strong>on</strong>trol by reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e breeding sites or/and by using <str<strong>on</strong>g>th</str<strong>on</strong>g>e Pulsed SIT. We<br />

will illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e presentati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> numerical simulati<strong>on</strong>s.<br />

References.<br />

[1] S. Bow<strong>on</strong>g, Y. Dum<strong>on</strong>t, and J.J. Tewa, A patchy model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chikungunya Disease in<br />

Réuni<strong>on</strong> Island, submitted.<br />

[2] Y. Dum<strong>on</strong>t, F. Chiroleu and C. Domerg, On a temporal model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chikungunya disease:<br />

modeling, <str<strong>on</strong>g>th</str<strong>on</strong>g>eory and numerics, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci. 213 (2008), 70-81.<br />

[3] Y. Dum<strong>on</strong>t and F. Chiroleu, Vector C<strong>on</strong>trol for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chikungunya Disease, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Bioscience<br />

and Engineering, 7(2) (2010), 315-348.<br />

[4] Y. Dum<strong>on</strong>t and J.M. Tchuenche, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical studies <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Sterile Insect Technique for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Chikungunya Disease and Aedes albopictus, submitted.<br />

[5] Y. Dum<strong>on</strong>t, and C. Dufourd, Spatio-temporal modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Aedes albopictus dispersal in Réuni<strong>on</strong><br />

Island. Applicati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e release <str<strong>on</strong>g>of</str<strong>on</strong>g> Sterile Insects, submitted to ECMTB 2011.<br />

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[6] E. Martin, S. Moutailler, Y. Madec, and A.B. Failloux, Differential resp<strong>on</strong>ses <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mosquito<br />

Aedes albopictus from <str<strong>on</strong>g>th</str<strong>on</strong>g>e Indian Ocean regi<strong>on</strong> to two chikungunya isolates, BMC Ecol. 10:8<br />

(2010).<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chaste framework;<br />

Tuesday, June 28, 11:00<br />

Sara-Jane Dunn<br />

Computing Laboratory, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: sara-jane.dunn@comlab.ox.ac.uk<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e Effect <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Actin Basket and Basement<br />

Membrane in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Deformati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Col<strong>on</strong>ic Crypt<br />

The role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basement membrane is vital in maintaining <str<strong>on</strong>g>th</str<strong>on</strong>g>e integrity and<br />

structure <str<strong>on</strong>g>of</str<strong>on</strong>g> an epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial layer, acting as bo<str<strong>on</strong>g>th</str<strong>on</strong>g> a mechanical support and forming<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e physical interface between epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells and <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding c<strong>on</strong>nective tissue.<br />

The functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is membrane is explored here in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial<br />

m<strong>on</strong>olayer <str<strong>on</strong>g>th</str<strong>on</strong>g>at lines <str<strong>on</strong>g>th</str<strong>on</strong>g>e col<strong>on</strong>ic crypt, a test tube shaped gland resp<strong>on</strong>sible for<br />

renewing <str<strong>on</strong>g>th</str<strong>on</strong>g>e intestinal surface <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a coordinated sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> cell divisi<strong>on</strong>, migrati<strong>on</strong><br />

and dea<str<strong>on</strong>g>th</str<strong>on</strong>g>. It is believed <str<strong>on</strong>g>th</str<strong>on</strong>g>at in <str<strong>on</strong>g>th</str<strong>on</strong>g>e first step in colorectal carcinogenesis,<br />

crypts acquire genetic mutati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at disrupt <str<strong>on</strong>g>th</str<strong>on</strong>g>e normal patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> cell proliferati<strong>on</strong><br />

and migrati<strong>on</strong>, which can lead to crypt buckling and fissi<strong>on</strong>. To identify<br />

mechanisms resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>is, a model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e crypt wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a realistic, deformable<br />

geometry is required, which takes into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding tissue<br />

stroma in maintaining crypt homeostasis <str<strong>on</strong>g>th</str<strong>on</strong>g>roughout <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cell events.<br />

A model is proposed here to directly address <str<strong>on</strong>g>th</str<strong>on</strong>g>ese criteria. An <str<strong>on</strong>g>of</str<strong>on</strong>g>f-lattice<br />

cell-centre modelling approach is adopted, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> cell-cell c<strong>on</strong>nectivity defined by a<br />

Delaunay triangulati<strong>on</strong>, and polyg<strong>on</strong>al cell shapes realistically prescribed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

dual Vor<strong>on</strong>oi tessellati<strong>on</strong>. As such, cell centres are defined by nodes <str<strong>on</strong>g>th</str<strong>on</strong>g>at are free<br />

to move in space, which are c<strong>on</strong>nected to neighbouring cells al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e lines <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

triangulati<strong>on</strong>. A novel me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basement membrane<br />

benea<str<strong>on</strong>g>th</str<strong>on</strong>g> a growing epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elium is presented, which subsequently allows <str<strong>on</strong>g>th</str<strong>on</strong>g>e desired<br />

crypt geometry to develop, ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an to be imposed. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er to <str<strong>on</strong>g>th</str<strong>on</strong>g>is, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

takes into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tinuous meshwork <str<strong>on</strong>g>of</str<strong>on</strong>g> actin <str<strong>on</strong>g>th</str<strong>on</strong>g>at forms a basket below each<br />

crypt base, and which provides stability to <str<strong>on</strong>g>th</str<strong>on</strong>g>is regi<strong>on</strong>.<br />

Results from in silico simulati<strong>on</strong>s show <str<strong>on</strong>g>th</str<strong>on</strong>g>at homeostasis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e growing epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial<br />

m<strong>on</strong>olayer can be achieved and sustained wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>is modelling framework,<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e necessary balance <str<strong>on</strong>g>of</str<strong>on</strong>g> interactive cell forces, cell migrati<strong>on</strong> and cell dea<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

are presented. This work forms <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis for investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e deformati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e crypt structure <str<strong>on</strong>g>th</str<strong>on</strong>g>at can occur due to proliferati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells exhibiting mutant<br />

phenotypes, experiments <str<strong>on</strong>g>th</str<strong>on</strong>g>at would not be possible in vivo or in vitro.<br />

This model is proposed as <str<strong>on</strong>g>th</str<strong>on</strong>g>e foundati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a realistic representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> an epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial sheet in a deformable envir<strong>on</strong>ment. Whilst it is applied here specifically<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e col<strong>on</strong>ic crypt, <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic principles extend to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er biological epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elia,<br />

such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e interfollicular epidermis, or <str<strong>on</strong>g>th</str<strong>on</strong>g>e olfactory mucous membrane. Thus, <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

work and <str<strong>on</strong>g>th</str<strong>on</strong>g>e results presented, hold potential for future research in o<str<strong>on</strong>g>th</str<strong>on</strong>g>er biological<br />

c<strong>on</strong>texts.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Thomas A. Dunt<strong>on</strong><br />

e-mail: <str<strong>on</strong>g>th</str<strong>on</strong>g>omas.dunt<strong>on</strong>@comlab.ox.ac.uk<br />

James M. Osborne<br />

e-mail: james.osborne@comlab.ox.ac.uk<br />

David J. Gavaghan<br />

e-mail: david.gavaghan@comlab.ox.ac.uk<br />

Mark S.P. Sansom<br />

e-mail: mark.sansom@bioch.ox.ac.uk<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

A discrete simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> protein movement and<br />

protein-protein interacti<strong>on</strong>s in a biological membrane<br />

The membrane is a complex and dynamic system <str<strong>on</strong>g>th</str<strong>on</strong>g>at plays a major role in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolic processes <str<strong>on</strong>g>of</str<strong>on</strong>g> organisms. The lateral organizati<strong>on</strong> and dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

proteins in <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane are important factors in c<strong>on</strong>trolling membrane bioactivity.<br />

Simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane, which strive to maintain biological realism, enable<br />

us to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>ese processes. The purpose <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is to explore time and<br />

leng<str<strong>on</strong>g>th</str<strong>on</strong>g> scales <str<strong>on</strong>g>th</str<strong>on</strong>g>at are not accessible to all-atom, or even coarse-grained, molecular<br />

dynamics (MD) simulati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at are currently undertaken. Here we present a novel<br />

simulati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for a system <str<strong>on</strong>g>of</str<strong>on</strong>g> syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic membrane peptides, WALP-23, in a<br />

DPPC phospholipid bilayer.<br />

We are able to investigate many <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e features <str<strong>on</strong>g>th</str<strong>on</strong>g>at are observable in MD simulati<strong>on</strong>s,<br />

but at a fracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong>al cost. The ability to simulate l<strong>on</strong>ger<br />

time and leng<str<strong>on</strong>g>th</str<strong>on</strong>g> scales also enables us to investigate aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulated system<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at we would be unable to investigate wi<str<strong>on</strong>g>th</str<strong>on</strong>g> MD. We can look at <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>ger-term<br />

evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> protein clusters, investigating <str<strong>on</strong>g>th</str<strong>on</strong>g>eir mobility, lifetime and rates <str<strong>on</strong>g>of</str<strong>on</strong>g> coalescence.<br />

We are also able to look at <str<strong>on</strong>g>th</str<strong>on</strong>g>e larger-scale structures <str<strong>on</strong>g>th</str<strong>on</strong>g>at form, allowing<br />

us to make comparis<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental data from techniques like atomic force<br />

microscopy.<br />

We employ an <str<strong>on</strong>g>of</str<strong>on</strong>g>f-lattice model, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane represented as a two dimensi<strong>on</strong>al<br />

sheet and <str<strong>on</strong>g>th</str<strong>on</strong>g>e proteins described by <str<strong>on</strong>g>th</str<strong>on</strong>g>e positi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir centre <str<strong>on</strong>g>of</str<strong>on</strong>g> mass.<br />

The simulati<strong>on</strong> uses stochastic Brownian dynamics to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proteins<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough a lipid c<strong>on</strong>tinuum. Forces between proteins, mostly a result <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

hydrophobic mismatch between <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein and <str<strong>on</strong>g>th</str<strong>on</strong>g>e bilayer, act al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e line <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

centres. The influence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding lipids <strong>on</strong> each protein is manifested bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Brownian moti<strong>on</strong>, and in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir c<strong>on</strong>tributi<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

inter-protein forces.<br />

We use MD simulati<strong>on</strong>s to characterise <str<strong>on</strong>g>th</str<strong>on</strong>g>e force between proteins. The interprotein<br />

force for a pair <str<strong>on</strong>g>of</str<strong>on</strong>g> WALP-23 proteins in a DPPC bilayer can be measured<br />

whilst varying <str<strong>on</strong>g>th</str<strong>on</strong>g>e separati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir centres <str<strong>on</strong>g>of</str<strong>on</strong>g> mass. The benefit <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach<br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e inter-protein force includes c<strong>on</strong>tributi<strong>on</strong>s from different sources. Some <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese, such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e hydrophobic mismatch, would be difficult to characterise wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out<br />

such a calculati<strong>on</strong>. By improving <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameterizati<strong>on</strong> process and looking at<br />

more protein species we can work towards a more varied and realistic membrane<br />

simulati<strong>on</strong>.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling III; Wednesday, June 29,<br />

17:00<br />

Geneviève Dup<strong>on</strong>t<br />

Université Libre de Bruxelles<br />

e-mail: gdup<strong>on</strong>t@ulb.ac.be<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal organisati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> intracellular<br />

calcium signalling : from mechanism to physiology<br />

Signal-induced Ca2+ oscillati<strong>on</strong>s have been observed in many cell types and play a<br />

primary role in cell physiology. They mediate vital physiological processes such as<br />

secreti<strong>on</strong>, gene expressi<strong>on</strong> or fertilizati<strong>on</strong>. Specificity in <str<strong>on</strong>g>th</str<strong>on</strong>g>e physiological resp<strong>on</strong>ses<br />

is ensured by <str<strong>on</strong>g>th</str<strong>on</strong>g>e high level <str<strong>on</strong>g>of</str<strong>on</strong>g> spatio-temporal organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ca2+ dynamics<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic sub-cellular increases, regular oscillati<strong>on</strong>s and intra- or<br />

intercellular Ca2+ waves. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, I’ll illustrate <strong>on</strong> some specific examples how<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay between experiments and modelling can help uncovering <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular<br />

mechanisms resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> intracellular Ca2+<br />

dynamics and for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir physiological role. The peculiarities <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ca2+ oscillati<strong>on</strong>s<br />

induced by stimulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> mGluR5 will be presented in more details.<br />

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Crowd Dynamics: Modeling, Analysis and Simulati<strong>on</strong> (Part 2); Wednesday,<br />

June 29, 14:30<br />

Bertram Düring<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sussex<br />

e-mail: b.during@sussex.ac.uk<br />

Kinetic modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> opini<strong>on</strong> leadership<br />

We propose a kinetic model for opini<strong>on</strong> formati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> str<strong>on</strong>g opini<strong>on</strong><br />

leaders. Our approach is based <strong>on</strong> an opini<strong>on</strong> formati<strong>on</strong> model introduced in<br />

Toscani (2006) and borrows ideas from <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinetic <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> mixtures <str<strong>on</strong>g>of</str<strong>on</strong>g> rarefied<br />

gases. Starting from microscopic interacti<strong>on</strong>s am<strong>on</strong>g individuals, we arrive at a<br />

macroscopic descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e opini<strong>on</strong> formati<strong>on</strong> process which is characterized by<br />

a system <str<strong>on</strong>g>of</str<strong>on</strong>g> Fokker-Planck type equati<strong>on</strong>s. We discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e steady states <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

system and present numerical results.<br />

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Cell migrati<strong>on</strong> during development: modelling and experiment; Saturday,<br />

July 2, 08:30<br />

Louise Dys<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: louise.dys<strong>on</strong>@balliol.ox.ac.uk<br />

Ru<str<strong>on</strong>g>th</str<strong>on</strong>g> Baker<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: ru<str<strong>on</strong>g>th</str<strong>on</strong>g>.baker@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

Philip Maini<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: maini@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

Paul Kulesa<br />

Stowers Institute for Medical Research<br />

e-mail: PMK@stowers.org<br />

Models <str<strong>on</strong>g>of</str<strong>on</strong>g> neural crest cell migrati<strong>on</strong> during development<br />

Elucidating <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms underlying <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell movement and rearrangement <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

turn a clump <str<strong>on</strong>g>of</str<strong>on</strong>g> cells into a functi<strong>on</strong>ing organism requires close collaborati<strong>on</strong>s between<br />

experimentalists and ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modellers. One such important phenomen<strong>on</strong><br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>of</str<strong>on</strong>g> neural crest cell migrati<strong>on</strong> during embryogenesis. A two-dimensi<strong>on</strong>al<br />

individual-based model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cranial neural crest cells in <str<strong>on</strong>g>th</str<strong>on</strong>g>e developing<br />

chick embryo has been formulated. The model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple agent<br />

types and predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>ses <str<strong>on</strong>g>of</str<strong>on</strong>g> cells to an underlying chemoattractant which<br />

is used up by <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells. The model is used to make predicti<strong>on</strong>s which are <str<strong>on</strong>g>th</str<strong>on</strong>g>en<br />

tested experimentally. This talk will outline <str<strong>on</strong>g>th</str<strong>on</strong>g>e stages <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e modelling process,<br />

dem<strong>on</strong>strating how repeated cycles <str<strong>on</strong>g>of</str<strong>on</strong>g> model c<strong>on</strong>structi<strong>on</strong>, experimental validati<strong>on</strong><br />

and testing are vital for fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ering our understanding in <str<strong>on</strong>g>th</str<strong>on</strong>g>e area.<br />

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Plants, grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and transport processes II; Tuesday, June 28, 14:30<br />

R.J. Dys<strong>on</strong><br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Birmingham<br />

e-mail: R.J.Dys<strong>on</strong>@bham.ac.uk<br />

The mechanics <str<strong>on</strong>g>of</str<strong>on</strong>g> plant root grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Many growing plant cells undergo rapid axial el<strong>on</strong>gati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> negligible radial<br />

expansi<strong>on</strong>. Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is driven by high internal turgor pressure causing viscous<br />

stretching <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell wall, a complex structure c<strong>on</strong>taining stiff cellulose micr<str<strong>on</strong>g>of</str<strong>on</strong>g>ibrils,<br />

embedded wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a pectin ground matrix and linked <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a network <str<strong>on</strong>g>of</str<strong>on</strong>g> hemicellulose<br />

crosslinks. This microstructure produces n<strong>on</strong>-linear anisotropic mechanical<br />

behaviour, and can be manipulated under enzymatic c<strong>on</strong>trol to alter <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

rate. We first present a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical model <str<strong>on</strong>g>of</str<strong>on</strong>g> a growing cell, representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary<br />

cell wall as a <str<strong>on</strong>g>th</str<strong>on</strong>g>in axisymmetric fibre-reinforced viscous sheet supported between<br />

rigid end plates. Asymptotic reducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e governing equati<strong>on</strong>s, under simple<br />

sets <str<strong>on</strong>g>of</str<strong>on</strong>g> assumpti<strong>on</strong>s about <str<strong>on</strong>g>th</str<strong>on</strong>g>e fibre and wall properties, yields variants <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e traditi<strong>on</strong>al<br />

Lockhart equati<strong>on</strong>, which relates <str<strong>on</strong>g>th</str<strong>on</strong>g>e axial cell grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate to <str<strong>on</strong>g>th</str<strong>on</strong>g>e internal<br />

pressure. The model provides insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e geometric and biomechanical parameters<br />

underlying bulk quantities such as wall extensibility and shows how ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

dynamical changes in wall material properties or passive fibre reorientati<strong>on</strong> may<br />

suppress cell el<strong>on</strong>gati<strong>on</strong>. We <str<strong>on</strong>g>th</str<strong>on</strong>g>en investigate how <str<strong>on</strong>g>th</str<strong>on</strong>g>e acti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> enzymes <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cell wall microstructure can lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e required dynamic changes in macroscale<br />

wall material properties, and <str<strong>on</strong>g>th</str<strong>on</strong>g>us dem<strong>on</strong>strate a mechanism by which horm<strong>on</strong>es<br />

may regulate plant grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. Using knowledge gained from <str<strong>on</strong>g>th</str<strong>on</strong>g>e single cell model, we<br />

c<strong>on</strong>sider a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> hemicellulose crosslink dynamics incorporating<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> strain-enhanced breakage and enzyme-mediated breakage and reformati<strong>on</strong>.<br />

The relati<strong>on</strong>ship between stress and strain-rate is shown to exhibit <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristic<br />

yielding-type behaviour seen experimentally. The model shows how <str<strong>on</strong>g>th</str<strong>on</strong>g>is stress<br />

strain-rate relati<strong>on</strong>ship is modified in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> enzymes and predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> crosslinks and stress wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell wall.<br />

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling V; Saturday, July 2, 11:00<br />

Michal Dyzma<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research<br />

Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warsaw<br />

e-mail: mdyzma@ippt.gov.pl<br />

Piotr Szopa<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research<br />

Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warsaw<br />

e-mail: pszopa@ippt.gov.pl<br />

Bogdan Kazmierczak<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research<br />

Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warsaw<br />

e-mail: bkazmier@ippt.gov.pl<br />

Three pool model <str<strong>on</strong>g>of</str<strong>on</strong>g> self sustained calcium oscilati<strong>on</strong>s<br />

In additi<strong>on</strong> to energy producti<strong>on</strong>, mitoch<strong>on</strong>dria are involved in crucial cellular<br />

signaling processes. They are <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most important organelles resp<strong>on</strong>sible for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Ca 2+ regulatory pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. Several ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models explaining<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese mechanisms were created but <strong>on</strong>ly few <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em describe an interplay between<br />

calcium c<strong>on</strong>centrati<strong>on</strong> in endoplasmic reticulum (ER), cytoplasm and mitoch<strong>on</strong>dria<br />

(see e.g. [1]). Experiments measuring calcium c<strong>on</strong>centrati<strong>on</strong>s in mitoch<strong>on</strong>dria and<br />

ER suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> cytosolic microdomains wi<str<strong>on</strong>g>th</str<strong>on</strong>g> locally increased calcium<br />

c<strong>on</strong>centrati<strong>on</strong> (CMDs) in <str<strong>on</strong>g>th</str<strong>on</strong>g>e nearest vicinity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e outer mitoch<strong>on</strong>drial membrane.<br />

CMDs allow Ca 2+ to be taken up by mitoch<strong>on</strong>dria rapidly and form a steep c<strong>on</strong>centrati<strong>on</strong><br />

gradient. Such microdomains have been described lately as a MAM -<br />

mitoch<strong>on</strong>dria-associated ER membrane. To simulate calcium oscillati<strong>on</strong>s more accurately,<br />

we propose a model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an additi<strong>on</strong>al direct calcium flow between ER<br />

and mitoch<strong>on</strong>dria which takes into account recently discovered specific physical<br />

c<strong>on</strong>necti<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two organelles. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed model we have shown<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e global existence <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>negative soluti<strong>on</strong>s. We examined numerically <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> stable limit cycles <str<strong>on</strong>g>of</str<strong>on</strong>g> Ca 2+ oscillati<strong>on</strong>s, basin <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir attracti<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cycles period <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters.<br />

References.<br />

[1] M. Marhl, T. Haberichter, M. Brumen, R. Heinrich Complex calcium oscillati<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>e role<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> mitoch<strong>on</strong>dria and cytosolic proteins BioSystems 57 75–86.<br />

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Epidemic models: Networks and stochasticity I; Wednesday, June 29, 14:30<br />

Ken Eames<br />

L<strong>on</strong>d<strong>on</strong> School <str<strong>on</strong>g>of</str<strong>on</strong>g> Hygiene and Tropical Medicine<br />

e-mail: Ken.Eames@lshtm.ac.uk<br />

Measuring and modelling changing social c<strong>on</strong>tact patterns<br />

Social networks <str<strong>on</strong>g>of</str<strong>on</strong>g>fer an attractive way <str<strong>on</strong>g>of</str<strong>on</strong>g> viewing patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> human c<strong>on</strong>tacts;<br />

however, it is seldom (never?) possible to accurately measure an epidemiologicallyrelevant<br />

network in all its detail and complexity. In practice, <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore, models <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

disease spread are obliged to make a range <str<strong>on</strong>g>of</str<strong>on</strong>g> simplificati<strong>on</strong>s. One comm<strong>on</strong> simplificati<strong>on</strong><br />

is to assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tacts do not change over time; more ambitious<br />

models make plausible, <str<strong>on</strong>g>th</str<strong>on</strong>g>ough somewhat ad hoc, assumpti<strong>on</strong>s to capture <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

effects <str<strong>on</strong>g>of</str<strong>on</strong>g>, for example, school holidays. In c<strong>on</strong>trast, we present an age-structured<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> H1N1v influenza (swine flu) in <str<strong>on</strong>g>th</str<strong>on</strong>g>e UK in 2009, parameterised<br />

using data from a social c<strong>on</strong>tact survey completed by an internet-based<br />

cohort <str<strong>on</strong>g>th</str<strong>on</strong>g>roughout <str<strong>on</strong>g>th</str<strong>on</strong>g>e course <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic. We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is simple model can<br />

provide remarkably satisfying representati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> disease incidence data. We c<strong>on</strong>clude<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at even when detailed social network data are unavailable all is not lost.<br />

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Modelling bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms: from gene regulati<strong>on</strong> to large-scale structure and<br />

functi<strong>on</strong>; Wednesday, June 29, 17:00<br />

Hermann Eberl<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Guelph<br />

e-mail: heberl@uoguelph.ca<br />

A numerical me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for a doubly degenrate<br />

diffusi<strong>on</strong>-reacti<strong>on</strong> model describing bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm processes<br />

Some bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm systems and processes can be described by quasilinear parabolic equati<strong>on</strong>s<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two n<strong>on</strong>-Fickian diffusi<strong>on</strong> effects: (i) degeneracy <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> coefficients<br />

for vanishing biomass density, and (ii) a super-diffusi<strong>on</strong> singularity when <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

maximum biomass density is reached. Phenomen<strong>on</strong> (i) guarantees a well defined<br />

interface between <str<strong>on</strong>g>th</str<strong>on</strong>g>e bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm and <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding aqueous phase <str<strong>on</strong>g>th</str<strong>on</strong>g>at moves at<br />

finite speed, phenomen<strong>on</strong> (ii) ensures <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximum biomass density is not exceeded.<br />

In numerical simulati<strong>on</strong>s bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese aspects are not easy to deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g>. We<br />

discuss a simple, yet relatively robust numerical me<str<strong>on</strong>g>th</str<strong>on</strong>g>od. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at under <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

numerical realisati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> (i) and (ii) are maintained, we give a stability<br />

result, show c<strong>on</strong>vergence numerically by grid refinement, and discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e parallel<br />

speed-up gained <strong>on</strong> OpenMP platforms.<br />

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Recent advances in infectious disease modelling II; Saturday, July 2, 14:30<br />

Raluca Eftimie<br />

McMaster University<br />

e-mail: reftimie@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.mcmaster.ca<br />

Using viruses to eliminate tumours: <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

multi-stability and multi-instability phenomena<br />

Recent advances in virology, gene <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy and molecular and cell biology have<br />

provided insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms <str<strong>on</strong>g>th</str<strong>on</strong>g>rough which viruses can boost <str<strong>on</strong>g>th</str<strong>on</strong>g>e antitumour<br />

immune resp<strong>on</strong>se, or can infect and kill directly tumour cells. Here, we<br />

derive a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e anti-tumour effect <str<strong>on</strong>g>of</str<strong>on</strong>g> two viruses<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune cells. We <str<strong>on</strong>g>th</str<strong>on</strong>g>en discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> virus persistence<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e eliminati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour cells. To <str<strong>on</strong>g>th</str<strong>on</strong>g>is end, we focus <strong>on</strong> multi-stability<br />

and multi-instability, two complex phenomena <str<strong>on</strong>g>th</str<strong>on</strong>g>at can cause abrupt transiti<strong>on</strong>s<br />

between different states in biological and physical systems. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer<br />

immuno<str<strong>on</strong>g>th</str<strong>on</strong>g>erapies, <str<strong>on</strong>g>th</str<strong>on</strong>g>e transiti<strong>on</strong>s between a tumour-free and a tumour-present<br />

state were so far associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e multi-stability phenomen<strong>on</strong>. Here, we show<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e multi-instability phenomen<strong>on</strong> can lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a homoclinic<br />

bifurcati<strong>on</strong>, which causes <str<strong>on</strong>g>th</str<strong>on</strong>g>e system to switch from a tumour-present to a tumourfree<br />

state. This multi-instability phenomen<strong>on</strong> is driven by <str<strong>on</strong>g>th</str<strong>on</strong>g>e persistence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

virus, while <str<strong>on</strong>g>th</str<strong>on</strong>g>e multi-stability phenomen<strong>on</strong> is driven by <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune resp<strong>on</strong>se.<br />

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Bridging <str<strong>on</strong>g>th</str<strong>on</strong>g>e Divide: Cancer Models in Clinical Practice; Thursday, June 30,<br />

11:30<br />

Marisa Eisenberg<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences Institute, The Ohio State University<br />

e-mail: meisenberg@mbi.osu.edu<br />

Modeling Remnant Ablati<strong>on</strong> Protocols in Thyroid Cancer<br />

Thyroidectomy <str<strong>on</strong>g>of</str<strong>on</strong>g> pediatric and adult patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> differentiated <str<strong>on</strong>g>th</str<strong>on</strong>g>yroid cancer is<br />

typically followed by radioactive iodine treatment to ablate <str<strong>on</strong>g>th</str<strong>on</strong>g>yroid remnants. A<br />

comm<strong>on</strong> protocol for <str<strong>on</strong>g>th</str<strong>on</strong>g>is followup treatment is to give replacement <str<strong>on</strong>g>th</str<strong>on</strong>g>yroid horm<strong>on</strong>e<br />

T4 after surgery as <str<strong>on</strong>g>th</str<strong>on</strong>g>e patient recovers, and <str<strong>on</strong>g>th</str<strong>on</strong>g>en wi<str<strong>on</strong>g>th</str<strong>on</strong>g>draw replacement horm<strong>on</strong>e<br />

for 2-3 weeks to raise TSH levels to 30 mU/L or higher, as radioiodine uptake is<br />

improved when TSH levels are high. Patients may be quite sick and impaired during<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese several weeks, due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e severe clinically hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>yroid c<strong>on</strong>diti<strong>on</strong> generated. To<br />

explore whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>is protocol can be improved, we adapted a physiologically based<br />

ODE model <str<strong>on</strong>g>of</str<strong>on</strong>g> adult hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>alamic-pituitary-<str<strong>on</strong>g>th</str<strong>on</strong>g>yroid axis regulati<strong>on</strong> to incorporate<br />

severe hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>yroid effects, as well as adjusting <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters to model pediatric<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>yroid cancer using pediatric clinical data. We simulated a range <str<strong>on</strong>g>of</str<strong>on</strong>g> replacement<br />

protocols to establish wi<str<strong>on</strong>g>th</str<strong>on</strong>g>drawal times needed to raise TSH levels > 30 mU/L, each<br />

for a range <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue remnant percentages based <strong>on</strong> typical clinical remnants after<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>yroidectomy. We found <str<strong>on</strong>g>th</str<strong>on</strong>g>at use <str<strong>on</strong>g>of</str<strong>on</strong>g> T3-<strong>on</strong>ly after <str<strong>on</strong>g>th</str<strong>on</strong>g>yroidectomy, ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an T4,<br />

can substantially reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e wi<str<strong>on</strong>g>th</str<strong>on</strong>g>drawal time needed prior to radioiodine ablati<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, <str<strong>on</strong>g>th</str<strong>on</strong>g>ereby decreasing patient morbidity.<br />

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Game <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical modelling and optimizati<strong>on</strong> in evoluti<strong>on</strong> and ecology I;<br />

Tuesday, June 28, 11:00<br />

Maciej Jan Ejsm<strong>on</strong>d<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Envir<strong>on</strong>mental Sciences, Jagiell<strong>on</strong>ian University<br />

e-mail: maciek.ejsm<strong>on</strong>d@uj.edu.pl<br />

Filip Kapustka<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Envir<strong>on</strong>mental Sciences, Jagiell<strong>on</strong>ian University<br />

Macrin Czarnołęski<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Envir<strong>on</strong>mental Sciences, Jagiell<strong>on</strong>ian University<br />

Jan Kozłowski<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Envir<strong>on</strong>mental Sciences, Jagiell<strong>on</strong>ian University<br />

More capital or income breeding optimal strategies for<br />

indeterminate growers in <str<strong>on</strong>g>th</str<strong>on</strong>g>e seas<strong>on</strong>al envir<strong>on</strong>ment<br />

We use dynamic optimizati<strong>on</strong> algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m to find adaptive schedules <str<strong>on</strong>g>of</str<strong>on</strong>g> energy allocati<strong>on</strong><br />

to grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and reproducti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e seas<strong>on</strong>al envir<strong>on</strong>ment for an organism <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

can be capital or income breeder. Value <str<strong>on</strong>g>of</str<strong>on</strong>g> newborns in our model is related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

timing <str<strong>on</strong>g>of</str<strong>on</strong>g> reproducti<strong>on</strong>. Our results show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship between newborns<br />

value and storing reserves for reproducti<strong>on</strong> can be highly negatively correlated.<br />

Importantly <str<strong>on</strong>g>th</str<strong>on</strong>g>e reliance <strong>on</strong> reserves in reproducti<strong>on</strong> may be optimal wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

stochastic changes in envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s usually assumed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e models <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

capital breeding evoluti<strong>on</strong>. Our results c<strong>on</strong>firm also <str<strong>on</strong>g>th</str<strong>on</strong>g>e idea <str<strong>on</strong>g>th</str<strong>on</strong>g>at optimality <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

capital breeding strategy depends <strong>on</strong> efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> energy channeling from reserves<br />

to reproducti<strong>on</strong>.<br />

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Epidemics; Saturday, July 2, 08:30<br />

A. M. Elaiw<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Science, King Abdulaziz University,<br />

P.O. Box 80203, Jeddah 21589, Saudi Arabia.<br />

e-mail: a_m_elaiw@yahoo.com<br />

Global properties <str<strong>on</strong>g>of</str<strong>on</strong>g> virus dynamics models wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

multi-target cells and delays<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper, we propose a class <str<strong>on</strong>g>of</str<strong>on</strong>g> virus dynamics models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multi-target cells<br />

and intracellular delays and study <str<strong>on</strong>g>th</str<strong>on</strong>g>eir global properties. We first study <str<strong>on</strong>g>th</str<strong>on</strong>g>e global<br />

properties <str<strong>on</strong>g>of</str<strong>on</strong>g> a virus dynamics model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two target cells and delays. Then we<br />

introduce two new virus dynamics models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multi-target cells and delays. The<br />

first model is a (2n + 1)-dimensi<strong>on</strong>al n<strong>on</strong>linear delay ODEs <str<strong>on</strong>g>th</str<strong>on</strong>g>at describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus, n class <str<strong>on</strong>g>of</str<strong>on</strong>g> target cells (uninfected cells) and n class <str<strong>on</strong>g>of</str<strong>on</strong>g> infected<br />

target cells. The sec<strong>on</strong>d model generalizes <str<strong>on</strong>g>th</str<strong>on</strong>g>e first <strong>on</strong>e by assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong><br />

rate is given by saturati<strong>on</strong> functi<strong>on</strong>al resp<strong>on</strong>se. Two classes <str<strong>on</strong>g>of</str<strong>on</strong>g> time delays<br />

are incorporated into <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models, (i) <str<strong>on</strong>g>th</str<strong>on</strong>g>e times needed for newly infected cells<br />

to start to produce viruses, (ii) <str<strong>on</strong>g>th</str<strong>on</strong>g>e time for newly produced virus to become infectious<br />

(matures). Lyapunov functi<strong>on</strong>als are c<strong>on</strong>structed to establish <str<strong>on</strong>g>th</str<strong>on</strong>g>e global<br />

asymptotic stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e uninfected and infected steady states <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models.<br />

We have proven <str<strong>on</strong>g>th</str<strong>on</strong>g>at if <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproducti<strong>on</strong> number R0 is less <str<strong>on</strong>g>th</str<strong>on</strong>g>an unity <str<strong>on</strong>g>th</str<strong>on</strong>g>en<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e uninfected steady state is globally asymptotically stable, and if R0 > 1 (or if<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e infected steady state exists) <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>e infected steady state is globally asymptotically<br />

stable.<br />

Keywords: Global stability; viral infecti<strong>on</strong>; intracellular delays; direct Lyapunov<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>od.<br />

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Epidemics; Wednesday, June 29, 08:30<br />

E.Ait Dads<br />

Université Cadi Ayyad, Département de Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ématiques, Faculté des<br />

Sciences, B.P. 2390 Marrakech, Morocco<br />

e-mail: aitdads@ucam.ac.ma<br />

P. Cieutat<br />

Laboratoire de Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ématiques de Versailles, Université de Versailles<br />

Saint-Quentin en Yvelines, 45 Avenue des Etats-Unis, 78035 Versailles<br />

Cedex, France<br />

e-mail: Philippe.Cieutat@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.uvsq.fr<br />

L. Lhachimi<br />

Université Cadi Ayyad, Département de Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ématiques, Faculté des<br />

Sciences, B.P. 2390 Marrakech, Morocco<br />

e-mail: lhachimi@voila.fr<br />

Existence <str<strong>on</strong>g>of</str<strong>on</strong>g> Positive Almost Periodic or Ergodic Soluti<strong>on</strong>s<br />

for Some Neutral N<strong>on</strong>linear Integral Equati<strong>on</strong>s<br />

As we all know, <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> periodic soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong>al differential<br />

equati<strong>on</strong>s (FDE) has great <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical and practical significance and is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

problems <str<strong>on</strong>g>of</str<strong>on</strong>g> great interest to scholars in <str<strong>on</strong>g>th</str<strong>on</strong>g>e field. Since Yoshizawa [2] presented an<br />

excellent result for <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> periodic soluti<strong>on</strong>s to FDE wi<str<strong>on</strong>g>th</str<strong>on</strong>g> bounded delay,<br />

Cooke and Huang [3], Burt<strong>on</strong> and Hatvani [1] generalized Yoshizawa’s result to<br />

FDE wi<str<strong>on</strong>g>th</str<strong>on</strong>g> infinite delay. We remark <str<strong>on</strong>g>th</str<strong>on</strong>g>at, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e nature, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is no phenomen<strong>on</strong><br />

which is purely periodic, <str<strong>on</strong>g>th</str<strong>on</strong>g>is gives <str<strong>on</strong>g>th</str<strong>on</strong>g>e idea to c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e almost periodic situati<strong>on</strong>.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper, we c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e following neutral n<strong>on</strong>linear integral equati<strong>on</strong><br />

(1) x(t) = γx(t − σ) + (1 − γ)<br />

t<br />

t−σ<br />

f(s, x(s)) ds,<br />

where 0 ≤ γ < 1, σ > 0 and f : R × R + → R + is a c<strong>on</strong>tinuous map.<br />

We give sufficient c<strong>on</strong>diti<strong>on</strong>s which guarantee <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> almost periodic<br />

soluti<strong>on</strong>s for Equati<strong>on</strong> (1). We also treat <str<strong>on</strong>g>th</str<strong>on</strong>g>e ergodic soluti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at means <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

asymptotically almost periodic, <str<strong>on</strong>g>th</str<strong>on</strong>g>e weakly almost periodic and pseudo almost periodic<br />

soluti<strong>on</strong>s. Hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses <str<strong>on</strong>g>of</str<strong>on</strong>g> our results do not impose <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong> f(t, .)<br />

is m<strong>on</strong>ot<strong>on</strong>e. To state our results, we use a variant <str<strong>on</strong>g>of</str<strong>on</strong>g> Hilbert’s projective metric<br />

<strong>on</strong> a subset <str<strong>on</strong>g>of</str<strong>on</strong>g> a space <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tinuous and bounded functi<strong>on</strong>s.<br />

References.<br />

[1] T. A. Burt<strong>on</strong> and L. Hatvani, On <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> periodic soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> some n<strong>on</strong>linear<br />

functi<strong>on</strong>al-differential equati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> unbounded delay, N<strong>on</strong>linear Anal. TMA 16, 389-396,<br />

(1991).<br />

[2] T. Yoshizawa, Stability <str<strong>on</strong>g>th</str<strong>on</strong>g>eory by Liapunov’s sec<strong>on</strong>d me<str<strong>on</strong>g>th</str<strong>on</strong>g>od, Publicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

Society <str<strong>on</strong>g>of</str<strong>on</strong>g> Japan, No. 9 The Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Society <str<strong>on</strong>g>of</str<strong>on</strong>g> Japan, Tokio, 1966.<br />

[3] K. L. Cooke and W. Z. Huang, On <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem for linearizati<strong>on</strong> for state-dependent delay<br />

differential equati<strong>on</strong>s, Proc. Amer. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Soc. 124, 1417-1426, (1996).<br />

[4] E. Ait Dads, O. Arino, K. Ezzinbi, Existence <str<strong>on</strong>g>of</str<strong>on</strong>g> periodic soluti<strong>on</strong> for some neutral n<strong>on</strong>linear<br />

integral equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> delay time dependent, Facta Univ. Ser. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Inform. 11 (1996), 79-92.<br />

[5] E. Ait Dads, K. Ezzinbi, Existence <str<strong>on</strong>g>of</str<strong>on</strong>g> positive pseudo-almost periodic soluti<strong>on</strong> for a class<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong>al equati<strong>on</strong>s arising in epidemic problems, Cybernet. Systems Anal. 30 (1994),<br />

900-910.<br />

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[6] E. Ait Dads, K. Ezzinbi, Existence <str<strong>on</strong>g>of</str<strong>on</strong>g> positive pseudo-almost-periodic soluti<strong>on</strong> for some n<strong>on</strong>linear<br />

infinite delay integral equati<strong>on</strong>s arising in epidemic problems, N<strong>on</strong>linear Anal. 41<br />

(2000), 1-13.<br />

[7] S. Busenberg, K. Cooke, Periodic soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> delay differential equati<strong>on</strong>s arising in some<br />

models <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics, Applied N<strong>on</strong>linear Analysis (Proc. Third Internat. C<strong>on</strong>f., Univ. Texas,<br />

Arlingt<strong>on</strong>, Tex., 1978), pp. 67-78, Academic Press, New York, 1979.<br />

[8] K. Cooke, J. Kaplan, A periodicity <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold <str<strong>on</strong>g>th</str<strong>on</strong>g>eorem for epidemics and populati<strong>on</strong> grow<str<strong>on</strong>g>th</str<strong>on</strong>g>,<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci. 31 (1976), 87-104.<br />

[9] K. Ezzinbi, M. Hachimi, Existence <str<strong>on</strong>g>of</str<strong>on</strong>g> positive almost periodic soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong>al equati<strong>on</strong>s<br />

via Hilbert’s projective metric, N<strong>on</strong>linear Anal. 26 (1996), 1169-1176.<br />

[10] D. Guo, V. Lakshmikan<str<strong>on</strong>g>th</str<strong>on</strong>g>am, Positive soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear integral equati<strong>on</strong>s arising in<br />

infectious diseases, J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Anal. Appl. 134 (1988), 1-8.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Federico Elias Wolff<br />

Chalmers University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Physics<br />

e-mail: federice@student.chalmers.se<br />

Anders Erikss<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cambridge, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Zoology<br />

Bernhard Mehlig<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics<br />

Models for extincti<strong>on</strong> in metapopulati<strong>on</strong>s<br />

Standard metapopulati<strong>on</strong> models assume a timescale separati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e local<br />

dynamics (fast), and <str<strong>on</strong>g>th</str<strong>on</strong>g>e global dynamics, allowing for a much simpler treatment<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole populati<strong>on</strong>. This assumpti<strong>on</strong> is however not realistic. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a Master<br />

equati<strong>on</strong> we implement a metapopulati<strong>on</strong> model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> general wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-patch dynamics.<br />

We implement a Fokker-Planck approximati<strong>on</strong>, by means <str<strong>on</strong>g>of</str<strong>on</strong>g> expanding <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

inverse number <str<strong>on</strong>g>of</str<strong>on</strong>g> patches, to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e quasi-steady state and <str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> typical<br />

fluctuati<strong>on</strong>s. We use also WKB <str<strong>on</strong>g>th</str<strong>on</strong>g>eory in order to calculate <str<strong>on</strong>g>th</str<strong>on</strong>g>e expected time to<br />

extincti<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong>. We compare our results to numerical simulati<strong>on</strong>s,<br />

and lastly to <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard metapopulati<strong>on</strong> model.<br />

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Heart rate dynamics: models and measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity (part II);<br />

Wednesday, June 29, 17:00<br />

J. Ellert<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Cardiology - Intensive Therapy and Internal Diseases,<br />

Poznan University <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Sciences, Przybyszewskiego 49, Poznan,<br />

Poland<br />

e-mail: jeel@epoczta.pl<br />

J. Piskorski<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Ziel<strong>on</strong>a Gora, Szafrana 4a, Ziel<strong>on</strong>a<br />

Gora, Poland<br />

e-mail: jaropis@zg.home.pl<br />

T. Krauze<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Cardiology - Intensive Therapy and Internal Diseases,<br />

Poznan University <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Sciences, Przybyszewskiego 49, Poznan,<br />

Poland<br />

e-mail: tomaszkrauze@wp.pl<br />

P. Guzik<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Cardiology - Intensive Therapy and Internal Diseases,<br />

Poznan University <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Sciences, Przybyszewskiego 49, Poznan,<br />

Poland<br />

e-mail: pguzik@ptkardio.pl<br />

Heart rate asymmetry and its reflecti<strong>on</strong> in HRV complexity<br />

measures<br />

Heart rate asymmetry (HRA) is a physiological phenomen<strong>on</strong> by which <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> decelerati<strong>on</strong>s to short-term variability is greater <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>of</str<strong>on</strong>g> accelerati<strong>on</strong>s,<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> accelerati<strong>on</strong>s to l<strong>on</strong>g -term variability is greater <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> decelerati<strong>on</strong>s. After shuffling <str<strong>on</strong>g>th</str<strong>on</strong>g>e above differences vanish, so it was c<strong>on</strong>cluded<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at HRA depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e RR intervals series. Complexity based<br />

measures, such as sample entropy or symbolic dynamics, try to quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a dataset trying it <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tinuum between perfect order and randomness.<br />

It is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore interesting to see if <str<strong>on</strong>g>th</str<strong>on</strong>g>e two approaches are related.<br />

Materials and me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: 30-min ECG recordings were obtained from 200<br />

heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y subjects, 87 women. Variance based asymmetry descriptors (SD1a, SD1d,<br />

SD2a, SD2d, SDNNa, SDNNd, C1d, C2d, Cd) and sample entropy (SampEn) as<br />

well as parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> symbolic dynamics (V0, V1, V2, SymbEnt) were calculated<br />

for each <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em. The associati<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>ese parameters was studied wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

use <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>-parametric Kendall correlati<strong>on</strong>.<br />

Results: The variance based HRA descriptors are not associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> SampEn.<br />

C1d, C2d and Cd are statistically significantly correlated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> SampEn for<br />

m=1 (τ=−0.3, −0.13, −0.12) and <strong>on</strong>ly C1d is correlated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> SampEn for m=2<br />

(τ = −0.25). All variance parameters are correlated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> symbolic<br />

dynamic, negatively wi<str<strong>on</strong>g>th</str<strong>on</strong>g> V0 and positively wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e remaining parameters.<br />

C1d is negatively correlated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> V0 (τ = 0.3) and positively wi<str<strong>on</strong>g>th</str<strong>on</strong>g> all <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

symbolic dynamic parameters, a similar observati<strong>on</strong> can be made <str<strong>on</strong>g>of</str<strong>on</strong>g> C2d and Cd,<br />

but <str<strong>on</strong>g>th</str<strong>on</strong>g>e magnitude <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e correlati<strong>on</strong> coefficient is very small.<br />

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Discussi<strong>on</strong>: HRA descriptors are associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e studied complexity based<br />

parameters. The nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is associati<strong>on</strong> is, however unclear, and needs fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

study.<br />

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Elizabe<str<strong>on</strong>g>th</str<strong>on</strong>g> Elliott<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Leeds<br />

e-mail: jhs5ece@leeds.ac.uk<br />

Stephen Cornell<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Leeds<br />

Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 14:30<br />

Dispersal polymorphism and species’ invasi<strong>on</strong>s<br />

The speed at which species range expansi<strong>on</strong>s occur has important c<strong>on</strong>sequences<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>servati<strong>on</strong> management <str<strong>on</strong>g>of</str<strong>on</strong>g> species experiencing climate change and for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> exotic organisms. Dispersal and populati<strong>on</strong> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate are known<br />

to affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e speed <str<strong>on</strong>g>of</str<strong>on</strong>g> invasi<strong>on</strong>, however, little is known about what <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

having a community <str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal phenotypes is <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> range expansi<strong>on</strong>.<br />

We use reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong>s to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a species wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two<br />

dispersal phenotypes into a previously unoccupied landscape. These phenotypes<br />

differ in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir dispersal rate and populati<strong>on</strong> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate. We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

presence <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> phenotypes can result in faster range expansi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>an if <strong>on</strong>ly a<br />

single phenotype is present in <str<strong>on</strong>g>th</str<strong>on</strong>g>e landscape. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at typically <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong><br />

can occur up to twice as fast as a result <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is polymorphism. This has implicati<strong>on</strong>s<br />

for predicting <str<strong>on</strong>g>th</str<strong>on</strong>g>e speed <str<strong>on</strong>g>of</str<strong>on</strong>g> invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> species, suggesting <str<strong>on</strong>g>th</str<strong>on</strong>g>at speeds cannot just be<br />

predicted from looking at a single phenotype and <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> a community<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> phenotypes needs to be taken into c<strong>on</strong>siderati<strong>on</strong>.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Fadoua El Moustaid<br />

e-mail: fadoua@aims.ac.za<br />

Dr. Aziz Ouhinou<br />

e-mail: aziz@aims.ac.za<br />

Dr. Lafras Uys<br />

e-mail: Lafras@aims.ac.za<br />

African Institute for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences,<br />

Stellenbosch University,<br />

6-8 Melrose road, Muizenberg 7945, Cape town, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Africa<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> bacterial attachment to surfaces:<br />

Bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm initiati<strong>on</strong><br />

The development <str<strong>on</strong>g>of</str<strong>on</strong>g> bacterial bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm is a multi-stage process c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> five<br />

stages, namely, initial attachment <str<strong>on</strong>g>of</str<strong>on</strong>g> bacteria to surfaces or interfaces, irreversible<br />

attachment, first maturati<strong>on</strong>, sec<strong>on</strong>d maturati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e detachment <str<strong>on</strong>g>of</str<strong>on</strong>g> bacteria.<br />

Our interest in <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, is to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm initiati<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e early stage at<br />

low bacterial density, we use a stochastic model to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e bacterial movement<br />

towards <str<strong>on</strong>g>th</str<strong>on</strong>g>e interfaces. Then when <str<strong>on</strong>g>th</str<strong>on</strong>g>e density is significantly high we develop<br />

a n<strong>on</strong>-linear system <str<strong>on</strong>g>of</str<strong>on</strong>g> partial differential equati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Keller-Segel type model to<br />

illustrate more biological facts such as chemotaxis and sensing chemicals producti<strong>on</strong>.<br />

The numerical simulati<strong>on</strong>s to <str<strong>on</strong>g>th</str<strong>on</strong>g>e models show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e sensing chemicals are highly<br />

c<strong>on</strong>centrated in <str<strong>on</strong>g>th</str<strong>on</strong>g>e interfaces which attract more bacteria to <str<strong>on</strong>g>th</str<strong>on</strong>g>e boundaries, and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is makes a good agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological observati<strong>on</strong>s.<br />

References.<br />

[1] J.W. Costert<strong>on</strong>, Introducti<strong>on</strong> to bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm Internati<strong>on</strong>al Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Antimicrobial Agents 11<br />

217–221.<br />

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Modeling Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Biological Systems; Tuesday, June 28, 17:00<br />

German A. Enciso<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> California, Irvine<br />

e-mail: enciso@uci.edu<br />

Protein scaffolds can enhance <str<strong>on</strong>g>th</str<strong>on</strong>g>e bistability <str<strong>on</strong>g>of</str<strong>on</strong>g> multisite<br />

phosphorylati<strong>on</strong> systems<br />

The phosphorylati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a substrate at multiple sites is a comm<strong>on</strong> protein modificati<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at can give rise to important structural and electrostatic changes. Scaffold<br />

proteins can enhance protein phosphorylati<strong>on</strong> by facilitating interacti<strong>on</strong> between a<br />

protein kinase enzyme and its target substrate. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, we c<strong>on</strong>sider a simple<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> a scaffold protein and show <str<strong>on</strong>g>th</str<strong>on</strong>g>at under certain c<strong>on</strong>diti<strong>on</strong>s,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e scaffold can substantially raise <str<strong>on</strong>g>th</str<strong>on</strong>g>e likelihood <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting<br />

system will exhibit bistable behavior. This phenomen<strong>on</strong> is especially pr<strong>on</strong>ounced<br />

when <str<strong>on</strong>g>th</str<strong>on</strong>g>e enzymatic reacti<strong>on</strong>s have a Km larger <str<strong>on</strong>g>th</str<strong>on</strong>g>an 10 micromolar. We also find<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at bistable systems tend to have a specific kinetic c<strong>on</strong>formati<strong>on</strong>, and we provide<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis a number <str<strong>on</strong>g>of</str<strong>on</strong>g> necessary c<strong>on</strong>diti<strong>on</strong>s for bistability,<br />

such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple phosphorylati<strong>on</strong> sites and <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

scaffold binding/unbinding rates <strong>on</strong> number <str<strong>on</strong>g>of</str<strong>on</strong>g> phosphorylated sites.<br />

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From <strong>on</strong>e to many: Cell-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective, emergent behaviors<br />

in biology -II; Tuesday, June 28, 14:30<br />

Heiko Enderling<br />

Center <str<strong>on</strong>g>of</str<strong>on</strong>g> Cancer Systems Biology, Tufts University School <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine<br />

e-mail: heiko.enderling@tufts.ed<br />

Emerging tumor morphologies from cancer cell interacti<strong>on</strong>s<br />

We present a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical model <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer<br />

stem cells and n<strong>on</strong>-stem cancer cells. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is driven by<br />

cancer stem cells and modulated by n<strong>on</strong>-stem cancer cells. Intrinsic cell parameters<br />

yield different kinetics and populati<strong>on</strong> ratios, and a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor morphologies<br />

emerge.<br />

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The emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance in cancer using ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling;<br />

Saturday, July 2, 08:30<br />

Heiko Enderling<br />

Center <str<strong>on</strong>g>of</str<strong>on</strong>g> Cancer Systems Biology, Tufts University School <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine<br />

e-mail: heiko.enderling@tufts.ed<br />

Emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> radioresistance <str<strong>on</strong>g>th</str<strong>on</strong>g>rough selecti<strong>on</strong> for cancer<br />

stem cells in solid tumors<br />

Tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and progressi<strong>on</strong> is a complex phenomen<strong>on</strong> dependent <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong><str<strong>on</strong>g>of</str<strong>on</strong>g><br />

multiple intrinsic and extrinsic factors. Necessary for tumor development is a<br />

small subpopulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> potent cells, so-called cancer stem cells, which also produce<br />

a distinct populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-stem cancer cells. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> populati<strong>on</strong>s compete wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er yielding interesting tumor dynamics. During radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy treatment<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e intrinsic tumor dynamics are perturbed, resulting in selecti<strong>on</strong> and expansi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

resistant cancer stem cells.<br />

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Radek Erban<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Institute, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: erban@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

Cellular Systems Biology; Thursday, June 30, 11:30<br />

Stochastic modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong>-diffusi<strong>on</strong> processes in<br />

biology<br />

Many cellular and subcellular biological processes can be described in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusing<br />

and chemically reacting species. Several stochastic simulati<strong>on</strong> algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms<br />

(SSAs) suitable for <str<strong>on</strong>g>th</str<strong>on</strong>g>e modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> such reacti<strong>on</strong>-diffusi<strong>on</strong> processes have been<br />

recently proposed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, two comm<strong>on</strong>ly used SSAs will be<br />

studied. The first SSA is an <strong>on</strong>-lattice model described by <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong>-diffusi<strong>on</strong><br />

master equati<strong>on</strong>. The sec<strong>on</strong>d SSA is an <str<strong>on</strong>g>of</str<strong>on</strong>g>f-lattice model based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Brownian moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individual molecules and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir reactive collisi<strong>on</strong>s. The c<strong>on</strong>necti<strong>on</strong>s<br />

between SSAs and <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic models (based <strong>on</strong> reacti<strong>on</strong>-diffusi<strong>on</strong><br />

PDEs) will be presented. I will c<strong>on</strong>sider chemical reacti<strong>on</strong>s bo<str<strong>on</strong>g>th</str<strong>on</strong>g> at a surface and<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e bulk. I will show how <str<strong>on</strong>g>th</str<strong>on</strong>g>e "microscopic" parameters should be chosen to<br />

achieve <str<strong>on</strong>g>th</str<strong>on</strong>g>e correct "macroscopic" reacti<strong>on</strong> rate. This choice is found to depend <strong>on</strong><br />

which SSA is used. I will also present multiscale algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms which use models wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

a different level <str<strong>on</strong>g>of</str<strong>on</strong>g> detail in different parts <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong>al domain.<br />

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Reports from US - African BioMa<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Initiative: C<strong>on</strong>servati<strong>on</strong><br />

Biology; Saturday, July 2, 14:30<br />

Stefano Erm<strong>on</strong><br />

Cornell University<br />

e-mail: erm<strong>on</strong>ste@cs.cornell.edu<br />

Chata Sanogo<br />

Université Ibn-T<str<strong>on</strong>g>of</str<strong>on</strong>g>ail<br />

A Bio-ec<strong>on</strong>omic Model For Tropical Forest Harvesting and<br />

Habitat Loss<br />

We plan to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> between tropical forest harvesting and <str<strong>on</strong>g>th</str<strong>on</strong>g>e habitat<br />

loss for <str<strong>on</strong>g>th</str<strong>on</strong>g>e B<strong>on</strong>obos and Pygmy Chimpanzees (Pan paniscus) living in <str<strong>on</strong>g>th</str<strong>on</strong>g>e forest.<br />

Starting from data collected for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Idanre Forest Reserve in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lowland rain<br />

forest z<strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> -Western Nigeria (and literature review), we c<strong>on</strong>structed an<br />

analytic model <str<strong>on</strong>g>th</str<strong>on</strong>g>at classifies <str<strong>on</strong>g>th</str<strong>on</strong>g>e trees into 6 size classes according to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir diameter<br />

and captures <str<strong>on</strong>g>th</str<strong>on</strong>g>e forest grow<str<strong>on</strong>g>th</str<strong>on</strong>g> over time. Our model assumes linear dynamics and<br />

uses a Leslie-like matrix <str<strong>on</strong>g>th</str<strong>on</strong>g>at was fitted to historical time series.<br />

We modeled <str<strong>on</strong>g>th</str<strong>on</strong>g>e ec<strong>on</strong>omic aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e logging activity by introducing variable<br />

(dependent <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effort) and fixed (independent <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effort) costs, estimated from<br />

real world data. Moreover, to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e ec<strong>on</strong>omic value <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e trees in each size<br />

class, we c<strong>on</strong>structed a functi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at relates <str<strong>on</strong>g>th</str<strong>on</strong>g>e diameter to <str<strong>on</strong>g>th</str<strong>on</strong>g>e volume, from which<br />

we obtain a m<strong>on</strong>etary value by looking at market prices <str<strong>on</strong>g>of</str<strong>on</strong>g> tropical wood.<br />

We plan to include a populati<strong>on</strong> dynamic model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e animal populati<strong>on</strong>s<br />

living in <str<strong>on</strong>g>th</str<strong>on</strong>g>e area <str<strong>on</strong>g>th</str<strong>on</strong>g>at is dynamically coupled to <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> processes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e forest.<br />

In particular, we plan to capture <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> each size class <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e carrying capacity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e B<strong>on</strong>obos and Chimpanzees populati<strong>on</strong>s.<br />

Our final goal is to quantitatively study <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> harvesting policies in terms<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> ec<strong>on</strong>omic benefits and <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> survival probability, in order to obtain<br />

insights <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure <str<strong>on</strong>g>of</str<strong>on</strong>g> more sustainable logging practices.<br />

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Epidemics <str<strong>on</strong>g>of</str<strong>on</strong>g> Neglected Tropical Diseases; Wednesday, June 29, 11:00<br />

Lourdes Esteva<br />

Facultad de Ciencias, UNAM<br />

e-mail: lesteva@lya.fciencias.unam.mx<br />

Gustavo Cruz-Pacheco<br />

Instituto de Investigaci<strong>on</strong>es en Matemáticas Aplicadas y en Sistemas,<br />

UNAM<br />

e-mail: cruz@mym.iimas.unam.mx<br />

Cristobal Vargas<br />

Departamento de C<strong>on</strong>trol Automático, CINVESTAV-IPN<br />

e-mail: cvargas@ctrl.cinvestav.mx<br />

Modelling transmissi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Chagas’ disease<br />

Chagas disease, also known as American trypanosomiasis, is a potentially life<str<strong>on</strong>g>th</str<strong>on</strong>g>reatening<br />

illness caused by <str<strong>on</strong>g>th</str<strong>on</strong>g>e protozoan parasite, Trypanosoma cruzi (T. cruzi)<br />

which is found mainly in Latin America. The main mode <str<strong>on</strong>g>of</str<strong>on</strong>g> transmissi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Chagas<br />

disease in endemic areas is <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e bite <str<strong>on</strong>g>of</str<strong>on</strong>g> an insect vector called a triatomine<br />

bug. The disease may also be spread <str<strong>on</strong>g>th</str<strong>on</strong>g>rough blood transfusi<strong>on</strong> and organ transplantati<strong>on</strong>,<br />

ingesti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> food c<strong>on</strong>taminated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> parasites, and from a mo<str<strong>on</strong>g>th</str<strong>on</strong>g>er to<br />

her fetus. C<strong>on</strong>trol measures are limited since vaccines to prevent <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease are<br />

not available, and drugs are effective <strong>on</strong>ly in <str<strong>on</strong>g>th</str<strong>on</strong>g>e acute and early chr<strong>on</strong>ic phase <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

infecti<strong>on</strong>, but have adverse effects. C<strong>on</strong>trol measures include insecticides to kill <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

vector, screening blood d<strong>on</strong>ors, and treatment to patients in <str<strong>on</strong>g>th</str<strong>on</strong>g>e acute phase. Recently,<br />

a c<strong>on</strong>troversial strategy, Zooprophylaxis, has been proposed for <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> vector transmitted diseases. This technique refers to <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> vector-borne<br />

diseases by attracting vectors to domestic animals in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen cannot<br />

amplify (a dead-end host).<br />

In order to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e different c<strong>on</strong>trol measures for Chagas<br />

disease, in <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we develop a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model c<strong>on</strong>sidering four populati<strong>on</strong>s:<br />

humans, vectors, and susceptible and no susceptible domestic animals to Chagas<br />

infecti<strong>on</strong>. We obtain <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproductive number <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease, and <str<strong>on</strong>g>th</str<strong>on</strong>g>rough it<br />

we evaluate <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol measures.<br />

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Fluid-structure interacti<strong>on</strong> problems in biomechanics; Saturday, July 2, 08:30<br />

Jung Eunok<br />

K<strong>on</strong>kuk University<br />

e-mail: junge@k<strong>on</strong>kuk.ac.kr<br />

Yung Sam Kim<br />

Chung-Ang University<br />

Wanho Lee<br />

K<strong>on</strong>kuk University<br />

A heart model in <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole circulatory system<br />

We present a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> left heart governed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e partial differential<br />

equati<strong>on</strong>s. This heart is coupled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a lumped model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole circulatory<br />

system governed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e ordinary differential equati<strong>on</strong>s. The immersed boundary<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is used to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracardiac blood flow and <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiac valve<br />

moti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e normal circulati<strong>on</strong> in humans. We investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e intraventricular<br />

velocity field and <str<strong>on</strong>g>th</str<strong>on</strong>g>e velocity curves over <str<strong>on</strong>g>th</str<strong>on</strong>g>e mitral ring and across outflow tract.<br />

The pressure and flow are also measured in <str<strong>on</strong>g>th</str<strong>on</strong>g>e left and right heart and <str<strong>on</strong>g>th</str<strong>on</strong>g>e systemic<br />

and pulm<strong>on</strong>ary arteries. The simulati<strong>on</strong> results are comparable to <str<strong>on</strong>g>th</str<strong>on</strong>g>e existing<br />

measurements.<br />

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Bi<str<strong>on</strong>g>of</str<strong>on</strong>g>luids, Solute Transport, and Hemodynamics; Wednesday, June 29, 11:00<br />

Roger Evans<br />

M<strong>on</strong>ash University, Australia<br />

e-mail: roger.evans@m<strong>on</strong>ash.edu<br />

Bruce S. Gardiner<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Western Australia<br />

David W. Smi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Western Australia<br />

Paul M. O’C<strong>on</strong>nor<br />

Medical College <str<strong>on</strong>g>of</str<strong>on</strong>g> Wisc<strong>on</strong>sin<br />

A computati<strong>on</strong>al model <str<strong>on</strong>g>of</str<strong>on</strong>g> whole kidney oxygen regulati<strong>on</strong><br />

incorporating arterial to venous oxygen shunting<br />

Background: Our understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> renal tissue oxygenati<strong>on</strong> is complicated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ability <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen to diffuse directly from arteries to veins in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cortex; referred<br />

to here as arterial-to-venous (AV) oxygen shunting. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

delivery <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen in renal arterial blood, and in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen by<br />

kidney tissue, affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e PO2 gradients driving AV oxygen shunting. To understand<br />

how AV oxygen shunting influences kidney oxygenati<strong>on</strong>, we c<strong>on</strong>structed a<br />

computati<strong>on</strong>al model <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen transport in <str<strong>on</strong>g>th</str<strong>on</strong>g>e renal cortex. Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: The model<br />

is based <strong>on</strong> a quantitative analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ree dimensi<strong>on</strong>al morphology <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e rat<br />

renal circulati<strong>on</strong> (1). It c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> a multiscale hierarchy <str<strong>on</strong>g>of</str<strong>on</strong>g> eleven counter-current<br />

vascular modules, representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e various branch levels <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cortical vasculature.<br />

At each level equati<strong>on</strong>s describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e reactive-advecti<strong>on</strong>-diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen are<br />

solved. Factors critical in renal oxygen transport incorporated into <str<strong>on</strong>g>th</str<strong>on</strong>g>e model include:<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e parallel geometry <str<strong>on</strong>g>of</str<strong>on</strong>g> arteries and veins and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir size, variati<strong>on</strong> in blood<br />

velocity in each vessel, oxygen c<strong>on</strong>sumpti<strong>on</strong> and transport, and n<strong>on</strong>-linear binding<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen to hemoglobin. Because quantitative informati<strong>on</strong> regarding <str<strong>on</strong>g>th</str<strong>on</strong>g>e barriers<br />

to AV oxygen diffusi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e kidney is not available, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model was calibrated<br />

against published measurements <str<strong>on</strong>g>of</str<strong>on</strong>g> outer cortical microvascular PO2 and renal venous<br />

PO2 (2). As <str<strong>on</strong>g>th</str<strong>on</strong>g>e outer cortex is <str<strong>on</strong>g>th</str<strong>on</strong>g>e most well oxygenated part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e kidney,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is approach provides a c<strong>on</strong>servative estimate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e magnitude <str<strong>on</strong>g>of</str<strong>on</strong>g> AV oxygen<br />

shunting. Results: The model predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>at AV oxygen shunting is quantitatively<br />

similar to total renal oxygen c<strong>on</strong>sumpti<strong>on</strong> under basal physiological c<strong>on</strong>diti<strong>on</strong>s. It is<br />

predicted <str<strong>on</strong>g>th</str<strong>on</strong>g>at oxygen shunting increases as renal oxygen c<strong>on</strong>sumpti<strong>on</strong> increases or<br />

arterial PO2 increases, or when renal blood flow or hematocrit are reduced. Assuming<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e barriers for AV oxygen diffusi<strong>on</strong> are quantitatively similar <str<strong>on</strong>g>th</str<strong>on</strong>g>roughout <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cortical circulati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>at AV oxygen shunting occurs mostly in<br />

distal vascular elements. Regardless, in severe ischemia or anemia, or when kidney<br />

oxygen c<strong>on</strong>sumpti<strong>on</strong> increases, AV oxygen shunting in proximal vascular elements<br />

may reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e oxygen c<strong>on</strong>tent <str<strong>on</strong>g>of</str<strong>on</strong>g> blood destined for <str<strong>on</strong>g>th</str<strong>on</strong>g>e medullary circulati<strong>on</strong>.<br />

C<strong>on</strong>clusi<strong>on</strong>s: Cortical AV oxygen shunting limits oxygen delivery to cortical tissue<br />

and stabilizes tissue PO2 when arterial PO2 changes, but renders bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cortex<br />

and medulla susceptible to hypoxia when oxygen delivery falls or c<strong>on</strong>sumpti<strong>on</strong><br />

increases. The model also predicts how much kidney oxygen c<strong>on</strong>sumpti<strong>on</strong> must<br />

change, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e face <str<strong>on</strong>g>of</str<strong>on</strong>g> altered renal blood flow, to maintain cortical tissue PO2 at a<br />

stable level.<br />

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References.<br />

[1] Nordsletten DA et al. Structural morphology <str<strong>on</strong>g>of</str<strong>on</strong>g> renal vasculature. Am J Physiol Heart Circ<br />

Physiol 291: H296-309, 2006.<br />

[2] Welch WJ et al. Nephr<strong>on</strong> pO2 and renal oxygen usage in <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypertensive rat kidney. Kidney<br />

Int 59: 230-237, 2001.<br />

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Crowd Dynamics: Modeling, Analysis and Simulati<strong>on</strong> (Part 1); Wednesday,<br />

June 29, 11:00<br />

Joep Evers<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science, TU Eindhoven,<br />

The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

e-mail: j.h.m.evers@student.tue.nl<br />

Modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> a multi-comp<strong>on</strong>ent crowd via a<br />

two-scale approach, working in a setting <str<strong>on</strong>g>of</str<strong>on</strong>g> measure-<str<strong>on</strong>g>th</str<strong>on</strong>g>eory,<br />

mixture-<str<strong>on</strong>g>th</str<strong>on</strong>g>eory and <str<strong>on</strong>g>th</str<strong>on</strong>g>ermodynamics<br />

We present a strategy to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> crowds in heterogeneous domains.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is framework, <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e crowd is c<strong>on</strong>sidered from a two-fold perspective:<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> macroscopically and microscopically. This means <str<strong>on</strong>g>th</str<strong>on</strong>g>at we are enabled<br />

to examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e large scale behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e crowd (where <str<strong>on</strong>g>th</str<strong>on</strong>g>e crowd is essentially<br />

c<strong>on</strong>sidered as a c<strong>on</strong>tinuum), and simultaneously we are able to capture phenomena<br />

happening at <str<strong>on</strong>g>th</str<strong>on</strong>g>e individual pedestrian’s level. On bo<str<strong>on</strong>g>th</str<strong>on</strong>g> scales we specify mass<br />

measures and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir transport, and we unify <str<strong>on</strong>g>th</str<strong>on</strong>g>e micro and macro approaches in a<br />

single model. Thus we benefit from <str<strong>on</strong>g>th</str<strong>on</strong>g>e advantages <str<strong>on</strong>g>of</str<strong>on</strong>g> working wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a c<strong>on</strong>tinuum<br />

descripti<strong>on</strong>, while we can also tract (i.e. zoom in to) microscopic features. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

model we couple <str<strong>on</strong>g>th</str<strong>on</strong>g>e measure-<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical framework described above to <str<strong>on</strong>g>th</str<strong>on</strong>g>e ideas<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> mixture <str<strong>on</strong>g>th</str<strong>on</strong>g>eory in c<strong>on</strong>tinuum mechanics (formulated in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> measures). This<br />

allows us to define several c<strong>on</strong>stituents (read: sub-populati<strong>on</strong>s) <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e large crowd,<br />

each having its own partial velocity field. We <str<strong>on</strong>g>th</str<strong>on</strong>g>us have <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility to examine<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e interactive behavior between sub-groups <str<strong>on</strong>g>th</str<strong>on</strong>g>at have distinct characteristics. We<br />

especially aim at giving special properties to <str<strong>on</strong>g>th</str<strong>on</strong>g>ose pedestrians <str<strong>on</strong>g>th</str<strong>on</strong>g>at are represented<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic (discrete) part in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model. In real life situati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>ey would<br />

play <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> firemen, tourist guides, leaders, terrorists, predators (c<strong>on</strong>sidering<br />

animals instead <str<strong>on</strong>g>of</str<strong>on</strong>g> people) etc. Since typically <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is <strong>on</strong>ly a relatively small number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> such people in a crowd, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are most naturally modeled as individuals <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e micro-scale. However, we are not interested in <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> pedestrians<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e rest <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e (large) crowd, <str<strong>on</strong>g>th</str<strong>on</strong>g>us it suffices to simplify here, and model<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>em as a c<strong>on</strong>tinuum. By identifying a suitable c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> entropy for <str<strong>on</strong>g>th</str<strong>on</strong>g>e system,<br />

we derive an entropy inequality. From <str<strong>on</strong>g>th</str<strong>on</strong>g>is inequality restricti<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed<br />

velocity fields follow. Obeying <str<strong>on</strong>g>th</str<strong>on</strong>g>ese restricti<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling phase, we make<br />

our assumpti<strong>on</strong>s more feasible. Joint work wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Adrian Muntean.<br />

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Ecosystems Dynamics; Tuesday, June 28, 11:00<br />

Yoan Eynaud<br />

Laboratoire de Microbiologie, de Géochimie et d’Ecologie Marines,<br />

UMR CNRS 6117, Centre d’Océanologie de Marseille (OSU) Université<br />

de la Méditerranée - Campus de Luminy, case 901 13288 Marseille<br />

cedex 9<br />

e-mail: yoan.eynaud@univmed.fr<br />

Melika Baklouti<br />

Laboratoire d’Océanographie Physique et Biogéochimique, UMR CNRS<br />

6535, Centre d’Océanologie de Marseille (OSU) Université de la Méditerranée<br />

- Campus de Luminy, case 901 13288 Marseille cedex 9<br />

e-mail: melika.baklouti@univmed.fr<br />

Jean-Christophe Poggiale<br />

Laboratoire de Microbiologie, de Géochimie et d’Ecologie Marines,<br />

UMR CNRS 6117, Centre d’Océanologie de Marseille (OSU) Université<br />

de la Méditerranée - Campus de Luminy, case 901 13288 Marseille<br />

cedex 9<br />

e-mail: jean-christophe.poggiale@univmed.fr<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e mesopelagic ecosystem: how far details are<br />

important ?<br />

The role played by carb<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e global change led researchers to focus <strong>on</strong> its<br />

cycle wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e biosphere. Since 70% <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ear<str<strong>on</strong>g>th</str<strong>on</strong>g> surface is covered by <str<strong>on</strong>g>th</str<strong>on</strong>g>e ocean,<br />

understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e remineralizati<strong>on</strong> processes occuring am<strong>on</strong>g oceanic realms is crucial.<br />

However our knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mesopelagic layer is still poor and if logistical<br />

issues can partially explain <str<strong>on</strong>g>th</str<strong>on</strong>g>is lack, our limited capacity in modelling marine<br />

ecosystems are resp<strong>on</strong>sible as well. Thus we need to improve our way to model<br />

marine ecosystems and more precisely, how <str<strong>on</strong>g>th</str<strong>on</strong>g>ey behave. An analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e role<br />

played by details in ecological modelling is essential, and if some works have been<br />

d<strong>on</strong>e <strong>on</strong> simple model (Fussmann and Blazius, 2005; Poggiale et al., 2010), it appears<br />

interesting to study more complex systems, such as a mesopelagic model.<br />

A few models already exist (Anders<strong>on</strong> and Tang, 2010; Jacks<strong>on</strong> et al.,2001; Stemmann<br />

et al., 2004) but n<strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em have used <str<strong>on</strong>g>th</str<strong>on</strong>g>e DEB <str<strong>on</strong>g>th</str<strong>on</strong>g>eory in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir c<strong>on</strong>structi<strong>on</strong><br />

hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses, which leads in a complexificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model at <str<strong>on</strong>g>th</str<strong>on</strong>g>e physiological scale.<br />

Since we aim to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e role played by details in modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e mesopelagic<br />

layer, we here work <strong>on</strong> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> different level <str<strong>on</strong>g>of</str<strong>on</strong>g> physiological complexicity and trophic<br />

web organizati<strong>on</strong>. Thus, we have built 3 mesopelagic model <str<strong>on</strong>g>of</str<strong>on</strong>g> different trophic web<br />

complexicity, all using DEB <str<strong>on</strong>g>th</str<strong>on</strong>g>eory and compare it to n<strong>on</strong>-mecanistic approaches.<br />

Our results shows <str<strong>on</strong>g>th</str<strong>on</strong>g>e details required in modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e mesopelagic ecosystem and<br />

enhance our knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> trophic web modelling.<br />

References.<br />

[1] G.F. Fussmann and B. Blasius, “Community resp<strong>on</strong>se to enrichment is highly sensitive to<br />

model structure.,” Biology letters, vol. 1, Mar. 2005, pp. 9-12.<br />

284

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[2] J.-C. Poggiale, M. Baklouti, B. Queguiner, and S. a L.M. Kooijman, “How far details are<br />

important in ecosystem modelling: <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> multi-limiting nutrients in phytoplankt<strong>on</strong>zooplankt<strong>on</strong><br />

interacti<strong>on</strong>s.,” Philosophical transacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Royal Society <str<strong>on</strong>g>of</str<strong>on</strong>g> L<strong>on</strong>d<strong>on</strong>. Series<br />

B, Biological sciences, vol. 365, Nov. 2010, pp. 3495-507.<br />

[3] T.R. Anders<strong>on</strong> and K.W. Tang, “Carb<strong>on</strong> cycling and POC turnover in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mesopelagic z<strong>on</strong>e<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ocean: Insights from a simple model,” Deep Sea Research Part II: Topical Studies in<br />

Oceanography, vol. 57, Aug. 2010, pp. 1581-1592.<br />

[4] G. a Jacks<strong>on</strong> and A.B. Burd, “A model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> particle flux in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mid-water<br />

column c<strong>on</strong>trolled by subsurface biotic interacti<strong>on</strong>s,” Deep Sea Research Part II: Topical<br />

Studies in Oceanography, vol. 49, 2001, pp. 193-217.<br />

[5] L. Stemmann, G. a Jacks<strong>on</strong>, and D. Ians<strong>on</strong>, “A vertical model <str<strong>on</strong>g>of</str<strong>on</strong>g> particle size distributi<strong>on</strong>s<br />

and fluxes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e midwater column <str<strong>on</strong>g>th</str<strong>on</strong>g>at includes biological and physical processes—Part I:<br />

model formulati<strong>on</strong>,” Deep Sea Research Part I: Oceanographic Research Papers, vol. 51, Jul.<br />

2004, pp. 865-884.<br />

285

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bridging Time Scales in Biological Sciences; Saturday, July 2, 14:30<br />

K<strong>on</strong>stantin Fackeldey<br />

Zuse Institute Berlin, Takustrasse 7, 14195 Berlin<br />

e-mail: fackeldey@zib.de<br />

Efficient Simulati<strong>on</strong> in Protein Modelling and<br />

N<strong>on</strong>-equilibrium Processes<br />

The behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> a molecule is described by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Boltzmann distributi<strong>on</strong> in c<strong>on</strong>formati<strong>on</strong><br />

space. In classical molecular dynamics a trajectory describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e time<br />

dependent dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> a protein. Thereby <str<strong>on</strong>g>th</str<strong>on</strong>g>e time step is c<strong>on</strong>fined to <str<strong>on</strong>g>th</str<strong>on</strong>g>e fastest<br />

oscillati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e covalent b<strong>on</strong>ds and <str<strong>on</strong>g>th</str<strong>on</strong>g>us shortens <str<strong>on</strong>g>th</str<strong>on</strong>g>e absolute simulati<strong>on</strong> time.<br />

C<strong>on</strong>trary, events which are relevant for protein design, such as protein folding occur<br />

<strong>on</strong>ly after comparably l<strong>on</strong>g time. Thus we have a time gap, between <str<strong>on</strong>g>th</str<strong>on</strong>g>e fastest<br />

simulati<strong>on</strong> which determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximum possible simulati<strong>on</strong> time and <str<strong>on</strong>g>th</str<strong>on</strong>g>e rare<br />

events which have a great impact <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>figurati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein. Additi<strong>on</strong>ally<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> increasing size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecule <str<strong>on</strong>g>th</str<strong>on</strong>g>e dimensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding c<strong>on</strong>formati<strong>on</strong><br />

space and <str<strong>on</strong>g>th</str<strong>on</strong>g>us <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong>al complexity grow<str<strong>on</strong>g>th</str<strong>on</strong>g>s.<br />

C<strong>on</strong>sequently <strong>on</strong>e seeks for me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods which extract <str<strong>on</strong>g>th</str<strong>on</strong>g>e relevant informati<strong>on</strong> out <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> data wi<str<strong>on</strong>g>th</str<strong>on</strong>g> less computati<strong>on</strong>al complexity. This is <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic c<strong>on</strong>cept<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e coarse graining techniques. These me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods take advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact, <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e rare events can be “detected” by ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e last few decades<br />

various coarse graining techniques have been developed in order to bridge <str<strong>on</strong>g>th</str<strong>on</strong>g>is time<br />

gap in biological processes. Here, we focus <strong>on</strong> c<strong>on</strong>formati<strong>on</strong> dynamics, where in<br />

c<strong>on</strong>trast to classical MD <strong>on</strong>e is interested in <str<strong>on</strong>g>th</str<strong>on</strong>g>e identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> metastable states<br />

and transiti<strong>on</strong> probabilities. Moreover meshfree me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are introduced for a suitable<br />

discretizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>formati<strong>on</strong> space in high dimensi<strong>on</strong>s.<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>is basis, we focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e force simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong> equilibrium processes which<br />

play an important role in protein miss folding diseases such as Alzheimer’s disease.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we motivate how results from computer simulati<strong>on</strong> and experimental<br />

data from laboratory can be combined in a meaningful way.<br />

286

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling II; Wednesday, June 29,<br />

14:30<br />

James R. Faeder<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Computati<strong>on</strong>al and Systems Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Pittsburgh<br />

e-mail: faeder@pitt.edu<br />

Rule-Based Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular and Cellular Processes<br />

Cells possess complex sensory mechanisms <str<strong>on</strong>g>th</str<strong>on</strong>g>at are governed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e biochemical<br />

interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> proteins. A typical signaling protein possesses multiple interacti<strong>on</strong><br />

sites, whose activity can be modified bo<str<strong>on</strong>g>th</str<strong>on</strong>g> by direct chemical modificati<strong>on</strong> (termed<br />

”post-translati<strong>on</strong>al modificati<strong>on</strong>”) and by <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> modificati<strong>on</strong> or interacti<strong>on</strong><br />

at o<str<strong>on</strong>g>th</str<strong>on</strong>g>er sites (termed ”allostery”). This complexity at <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein level leads to<br />

combinatorial complexity at <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> signaling networks - an individual protein<br />

has many potential states <str<strong>on</strong>g>of</str<strong>on</strong>g> modificati<strong>on</strong> and interacti<strong>on</strong>, which gives rise to an<br />

ever-multiplying set <str<strong>on</strong>g>of</str<strong>on</strong>g> possible complexes and poses a major barrier to traditi<strong>on</strong>al<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> modeling and simulati<strong>on</strong> [1]. Here, I will review major developments in<br />

modeling, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> from my work and <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers, <str<strong>on</strong>g>th</str<strong>on</strong>g>at have helped to tame <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

difficulties.<br />

The need to simplify <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> signal transducti<strong>on</strong> models and to expand<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir scope has motivated <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> rule-based modeling languages,<br />

such as BioNetGen [2] and Kappa [3], which provide a rich and yet c<strong>on</strong>cise descripti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> signaling proteins and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir interacti<strong>on</strong>s. Their success is dem<strong>on</strong>strated by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e growing community <str<strong>on</strong>g>of</str<strong>on</strong>g> users and <str<strong>on</strong>g>th</str<strong>on</strong>g>e substantial number <str<strong>on</strong>g>of</str<strong>on</strong>g> models <str<strong>on</strong>g>th</str<strong>on</strong>g>at have<br />

been developed and published. While greatly facilitating <str<strong>on</strong>g>th</str<strong>on</strong>g>e translati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> knowledge<br />

about signaling biochemistry into models, however, rule-based languages do<br />

not directly address <str<strong>on</strong>g>th</str<strong>on</strong>g>e combinatorial challenges involved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> such<br />

models, which arise from <str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong> network implied by <str<strong>on</strong>g>th</str<strong>on</strong>g>e rules. For<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese, new agent-based stochastic simulati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods have been developed for rulebased<br />

models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> computati<strong>on</strong>al requirements <str<strong>on</strong>g>th</str<strong>on</strong>g>at are independent <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> possible species (i.e., complexes) and proporti<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> molecules<br />

(e.g., proteins) being simulated. In additi<strong>on</strong>, general and efficient implementati<strong>on</strong>s<br />

are now available <str<strong>on</strong>g>th</str<strong>on</strong>g>at enable <str<strong>on</strong>g>th</str<strong>on</strong>g>e rapid simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> rule-based models <str<strong>on</strong>g>of</str<strong>on</strong>g> virtually<br />

any complexity. NFsim is <strong>on</strong>e such simulator <str<strong>on</strong>g>th</str<strong>on</strong>g>at stands out because <str<strong>on</strong>g>of</str<strong>on</strong>g> its<br />

efficiency and <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability to course-grain complex interacti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e incorporati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> high-level functi<strong>on</strong>s into <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate laws <str<strong>on</strong>g>th</str<strong>on</strong>g>at govern rule applicati<strong>on</strong> [4]. The<br />

use <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic simulati<strong>on</strong>s, however, exacerbates <str<strong>on</strong>g>th</str<strong>on</strong>g>e already difficult problems<br />

comm<strong>on</strong> to all complex models <str<strong>on</strong>g>of</str<strong>on</strong>g> relating model parameters to model behavior<br />

and <str<strong>on</strong>g>of</str<strong>on</strong>g> estimating parameter values based <strong>on</strong> experimental observati<strong>on</strong>s and data.<br />

For <str<strong>on</strong>g>th</str<strong>on</strong>g>ese, new statistical model checking algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms and tools have been developed<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at allow model properties to be determined from a minimal number <str<strong>on</strong>g>of</str<strong>on</strong>g> simulati<strong>on</strong><br />

runs [5]. Taken toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er, rule-based modeling languages and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir associated tools<br />

address <str<strong>on</strong>g>th</str<strong>on</strong>g>e issue <str<strong>on</strong>g>of</str<strong>on</strong>g> combinatorial complexity in cell regulatory networks, allowing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e development, simulati<strong>on</strong>, and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> unprecedented scope and<br />

detail and, we hope, predictive capability.<br />

References.<br />

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[1] W. S. Hlavacek and J. R. Faeder (2009) Sci. Signaling 2 pe46.<br />

[2] J. R. Faeder, M. L. Blinov, and W. S. Hlavacek (2009) Me<str<strong>on</strong>g>th</str<strong>on</strong>g>. Mol. Biol. 500, 113–167.<br />

[3] V. Danos, J. Feret, W. F<strong>on</strong>tana, and J. Krivine (2007) Lect. Notes. Comput. Sci 4807,139-157.<br />

[4] M. W. Snedd<strong>on</strong>, J. R. Faeder, and T. Em<strong>on</strong>et (2011) Nature Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods 8, 177–183.<br />

[5] E. M. Clarke, et al. (2008) Lect. Notes. Comput. Sci. 5307, 231-250.<br />

288

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Martin Falcke<br />

Max Delbrück Center for Molecular Medicine<br />

e-mail: martin.falcke@mdc-berlin.de<br />

Kevin Thurley<br />

Max Delbrück Center for Molecular Medicine<br />

Noisy Cells; Saturday, July 2, 14:30<br />

Random but reliable: Properties <str<strong>on</strong>g>of</str<strong>on</strong>g> spike sequences <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

IP3-induced Ca2+ signaling<br />

Ca2+ is a universal sec<strong>on</strong>d messenger in eucaryotic cells transmitting informati<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>centrati<strong>on</strong> spikes. A prominent mechanism to generate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese spikes involves Ca2+ release from <str<strong>on</strong>g>th</str<strong>on</strong>g>e endoplasmic reticulum (ER) Ca2+<br />

store via IP3-sensitive channels. Puffs are elemental events <str<strong>on</strong>g>of</str<strong>on</strong>g> IP3-induced Ca2+<br />

release <str<strong>on</strong>g>th</str<strong>on</strong>g>rough single clusters <str<strong>on</strong>g>of</str<strong>on</strong>g> channels. Intracellular Ca2+ dynamics are a<br />

stochastic system, but a complete stochastic <str<strong>on</strong>g>th</str<strong>on</strong>g>eory has not been developed yet.<br />

As a new c<strong>on</strong>cept, we formulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> interpuff interval and puff<br />

durati<strong>on</strong> distributi<strong>on</strong>s, since unlike <str<strong>on</strong>g>th</str<strong>on</strong>g>e properties <str<strong>on</strong>g>of</str<strong>on</strong>g> individual channels, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey can<br />

be measured in vivo. Our <str<strong>on</strong>g>th</str<strong>on</strong>g>eory reproduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e typical spectrum <str<strong>on</strong>g>of</str<strong>on</strong>g> Ca2+ signals<br />

like puffs, spiking and bursting in analytically treatable test cases as well as in more<br />

realistic simulati<strong>on</strong>s. We find c<strong>on</strong>diti<strong>on</strong>s for spiking and calculate interspike interval<br />

(ISI) distributi<strong>on</strong>s. Signal form, average ISI and ISI distributi<strong>on</strong>s depend sensitively<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e details <str<strong>on</strong>g>of</str<strong>on</strong>g> cluster properties and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir spatial arrangement. In difference to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at, <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e average and <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard deviati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ISIs does not<br />

depend <strong>on</strong> cluster properties and cluster arrangement, and is robust wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect<br />

to cell variability. It is c<strong>on</strong>trolled by <str<strong>on</strong>g>th</str<strong>on</strong>g>e global feedback processes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ca2+<br />

signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way (e.g. via IP3-3-kinase or ER depleti<strong>on</strong>). That relati<strong>on</strong> is essential<br />

for pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way functi<strong>on</strong>, since it ensures frequency encoding despite <str<strong>on</strong>g>th</str<strong>on</strong>g>e randomness<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> ISIs and determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximal spike train informati<strong>on</strong> c<strong>on</strong>tent. Hence, we<br />

find a divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tasks between global feedbacks and local cluster properties which<br />

guarantees robustness <str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong> while maintaining sensitivity <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

average ISI.<br />

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling IV; Saturday, July 2, 08:30<br />

Martin Falcke<br />

Max Delbrück Center for Molecular Medicine<br />

e-mail: martin.falcke@mdc-berlin.de<br />

Kevin Thurley<br />

Max Delbrück Center for Molecular Medicine<br />

How does single channel behavior cause cellular Ca2+<br />

spiking?<br />

The behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways is determined by <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular properties <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir comp<strong>on</strong>ents, feedbacks and self-organizati<strong>on</strong> am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e participating molecules.<br />

But usually systems are too complex to understand in detail how cellular behavior<br />

relates to molecular behavior. Intracellular Ca2+ signaling <str<strong>on</strong>g>of</str<strong>on</strong>g>fers an opportunity to<br />

understand <str<strong>on</strong>g>th</str<strong>on</strong>g>at relati<strong>on</strong> in detail, since it is comprised from relatively few different<br />

types <str<strong>on</strong>g>of</str<strong>on</strong>g> molecules. A well-studied system involves Ca2+ liberati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough inositol<br />

trisphosphate receptor (IP3R) channels wherein <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular dynamics emerge<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough a hierarchy <str<strong>on</strong>g>of</str<strong>on</strong>g> events. Opening <str<strong>on</strong>g>of</str<strong>on</strong>g> single Ca2+ channels can induce local<br />

Ca2+ release events evoked by channel clusters (called puffs), <str<strong>on</strong>g>th</str<strong>on</strong>g>e combined acti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> which results in repetitive global cellular Ca2+ spikes. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough cellular behavior<br />

and single channel properties have been characterized in detail before, <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

study investigates statistical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cluster dynamics by analyzing highresoluti<strong>on</strong><br />

data from TIRF microscopy in two mammalian cell lines. We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

interpuff intervals (IPIs) are significantly shorter <str<strong>on</strong>g>th</str<strong>on</strong>g>an cellular interspike intervals<br />

(ISIs), <str<strong>on</strong>g>th</str<strong>on</strong>g>at puff-activity is stochastic wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a recovery time much shorter <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cellular refractory period, and <str<strong>on</strong>g>th</str<strong>on</strong>g>at IPIs show no sign <str<strong>on</strong>g>of</str<strong>on</strong>g> periodicity. These results<br />

str<strong>on</strong>gly suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at Ca2+ spikes do not arise from oscillatory cluster dynamics,<br />

but <str<strong>on</strong>g>th</str<strong>on</strong>g>at cellular repetitive spiking and its typical time scales arise from collective<br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole cluster array.<br />

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Populati<strong>on</strong> Dynamics; Tuesday, June 28, 11:00<br />

Chun Fang<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Helsinki<br />

e-mail: chun.fang@helsinki.fi<br />

Mats Gyllenberg and Yi Wang<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Helsinki<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Technology<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> China<br />

e-mail: mats.gyllenberg@helsinki.fi and yi.wang@helsinki.fi<br />

Asymptotic almost periodicity <str<strong>on</strong>g>of</str<strong>on</strong>g> competitive-cooperative<br />

systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> almost periodic time dependence<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is report, we are interested in <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymptotic almost periodicity for a<br />

positively bounded moti<strong>on</strong> πt(x, g) by investigating its ω-limit set. We proved if<br />

ω(x, g) is hyperbolic, <str<strong>on</strong>g>th</str<strong>on</strong>g>at is, <str<strong>on</strong>g>th</str<strong>on</strong>g>e linearized equati<strong>on</strong> about <str<strong>on</strong>g>th</str<strong>on</strong>g>e flow <strong>on</strong> ω(x, g) has<br />

an Exp<strong>on</strong>ential Dichotomy <strong>on</strong> ω(x, g). Then ω(x, g) is 1-cover <str<strong>on</strong>g>of</str<strong>on</strong>g> H(f), <str<strong>on</strong>g>th</str<strong>on</strong>g>at is,<br />

πt(x, g) is asymptotically almost periodic.<br />

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Semigroups <str<strong>on</strong>g>of</str<strong>on</strong>g> Operators in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology II; Saturday, July 2, 11:00<br />

Jozsef Farkas<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling<br />

e-mail: jzf@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.stir.ac.uk<br />

Wentzell semigroups in biology<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we are going to introduce linear and n<strong>on</strong>linear physiologically structured<br />

populati<strong>on</strong> models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> diffusi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e size-space. We equip our model wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Wentzell boundary c<strong>on</strong>diti<strong>on</strong>s which can be recast as dynamic c<strong>on</strong>diti<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

boundary. We apply our model for a populati<strong>on</strong> in which individuals are structured<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to a pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen load which represents <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tinuous structuring variable.<br />

Then <str<strong>on</strong>g>th</str<strong>on</strong>g>e compartment <str<strong>on</strong>g>of</str<strong>on</strong>g> uninfected individuals carries mass. For a much<br />

earlier attempt see: Waldstaetter et al. in SIAM JMA (1988). We will discuss<br />

existence and positivity <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s and qualitative questi<strong>on</strong>s: such as existence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> steady states and asymptotic behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s. We will be working in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e framework <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> str<strong>on</strong>gly c<strong>on</strong>tinuous semigroups and utilising some<br />

earlier results, see e.g. Favini et al. in J. Evol. Eq. (2002).<br />

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Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

IV; Wednesday, June 29, 08:30<br />

Ant<strong>on</strong>io Fasano<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics "Ulisse Dini", University <str<strong>on</strong>g>of</str<strong>on</strong>g> Florence,<br />

Italy<br />

e-mail: fasano@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.unifi.it<br />

Alessandro Bertuzzi<br />

IASI CNR, Rome, Italy<br />

Alberto Gandolfi<br />

IASI CNR, Rome, Italy<br />

Carmela Sinisgalli<br />

IASI CNR, Rome, Italy<br />

Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor spheroids: adopting a Bingham scheme<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell comp<strong>on</strong>ent<br />

Avascular multicellular spheroids are <str<strong>on</strong>g>th</str<strong>on</strong>g>e simplest form <str<strong>on</strong>g>of</str<strong>on</strong>g> tumours <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be<br />

studied experimentally under c<strong>on</strong>trolled c<strong>on</strong>diti<strong>on</strong>s. They can be grown in suspensi<strong>on</strong>s<br />

(<str<strong>on</strong>g>th</str<strong>on</strong>g>us being subject to atmospheric pressure) or in a gel which <str<strong>on</strong>g>of</str<strong>on</strong>g>fers some<br />

mechanical resistance to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir expansi<strong>on</strong>. They are made <str<strong>on</strong>g>of</str<strong>on</strong>g> proliferating cells,<br />

quiescent cell and <str<strong>on</strong>g>of</str<strong>on</strong>g> dead cells progressively degrading to liquid. The whole cell<br />

populati<strong>on</strong> is embedded in an extracellular fluid, which provides <str<strong>on</strong>g>th</str<strong>on</strong>g>e mass required<br />

for cell replicati<strong>on</strong>.<br />

During <str<strong>on</strong>g>th</str<strong>on</strong>g>e last years it has become evident <str<strong>on</strong>g>th</str<strong>on</strong>g>at, despite <str<strong>on</strong>g>th</str<strong>on</strong>g>e advantage <str<strong>on</strong>g>of</str<strong>on</strong>g>fered<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e simple geometry, <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> (or even <str<strong>on</strong>g>th</str<strong>on</strong>g>e steady<br />

state) <str<strong>on</strong>g>of</str<strong>on</strong>g> a multicellular spheroid is generally very complicated and requires <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

choice <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>stitutive equati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system. A<br />

peculiar difficulty is originated by its composite nature. Various papers have been<br />

devoted to <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> spheroids evoluti<strong>on</strong>, assigning an important role to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

deformability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system <str<strong>on</strong>g>of</str<strong>on</strong>g> mutually interacting cells by introducing interacti<strong>on</strong><br />

potentials (depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell volume fracti<strong>on</strong>) and c<strong>on</strong>stitutive laws <str<strong>on</strong>g>th</str<strong>on</strong>g>at may<br />

include yield stress and elasticity (see [1]).<br />

Here we want to present an evoluti<strong>on</strong> model in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e main assumpti<strong>on</strong>s<br />

are:<br />

(i)<str<strong>on</strong>g>th</str<strong>on</strong>g>e cell volume fracti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e viable regi<strong>on</strong> is c<strong>on</strong>stant,<br />

(ii)<str<strong>on</strong>g>th</str<strong>on</strong>g>e rheological properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> cells in <str<strong>on</strong>g>th</str<strong>on</strong>g>e viable z<strong>on</strong>e are <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>es<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a Bingham fluid,<br />

(iii)<str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>ly species c<strong>on</strong>sidered in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells metabolism is oxygen and <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> metabolites is neglected.<br />

Thus our model is in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two-fluid approach. The inspiring<br />

criteri<strong>on</strong> was to incorporate some physically relevant feature (as it can be <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> intercellular links providing a stress <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold for flow), but introducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

minimum possible number <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>stitutive quantities. Formulating a Bingham-like<br />

scheme proved to be not so simple, since some classical models are not compatible<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> velocity fields <str<strong>on</strong>g>th</str<strong>on</strong>g>at have necessarily to occur in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> a growing spheroid.<br />

Thus <str<strong>on</strong>g>th</str<strong>on</strong>g>is aspect <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis is particularly delicate. The spheroid evoluti<strong>on</strong><br />

is followed from <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial fully proliferating phase, to <str<strong>on</strong>g>th</str<strong>on</strong>g>e stage which includes a<br />

necrotic liquid core, possibly reaching an asymptotic equilibrium (<str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

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steady states has been studied in <str<strong>on</strong>g>th</str<strong>on</strong>g>e same framework in <str<strong>on</strong>g>th</str<strong>on</strong>g>e paper [2]). Despite <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

many simplificati<strong>on</strong>s (to which we add some less important assumpti<strong>on</strong>s, like <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

existence <str<strong>on</strong>g>of</str<strong>on</strong>g> interfaces separating <str<strong>on</strong>g>th</str<strong>on</strong>g>e various classes <str<strong>on</strong>g>of</str<strong>on</strong>g> cells), <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem turns out<br />

to be c<strong>on</strong>siderably complicated. An existence <str<strong>on</strong>g>th</str<strong>on</strong>g>eorem and numerical simulati<strong>on</strong>s<br />

will be presented.<br />

References.<br />

[1] D. Ambrosi, L. Preziosi. Cell adhesi<strong>on</strong> mechanisms and stress relaxati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

tumours. Biomech. Model. MechanoBiol. 8 (2009) 397-413.<br />

[2] A. FASANO, M. GABRIELLI, A. GANDOLFI. Investigating <str<strong>on</strong>g>th</str<strong>on</strong>g>e steady state <str<strong>on</strong>g>of</str<strong>on</strong>g> multicellular<br />

spheroids by revisiting <str<strong>on</strong>g>th</str<strong>on</strong>g>e two-fluid model. To appear <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci. Eng.<br />

294

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Modeling and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor invasi<strong>on</strong> II; Tuesday, June 28, 14:30<br />

Sergei Fedotov<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Manchester<br />

e-mail: sergei.fedotov@manchester.ac.uk<br />

Migrati<strong>on</strong>-Proliferati<strong>on</strong> Dichotomy in Tumor Cell<br />

Proliferati<strong>on</strong> and migrati<strong>on</strong> dichotomy <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor cell invasi<strong>on</strong> is examined wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in<br />

a two-state c<strong>on</strong>tinuous time random walk (CTRW) model. The overall spreading<br />

rate <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells is obtained by using a Hamilt<strong>on</strong>-Jacobi formalism. Random<br />

switching between cell proliferati<strong>on</strong> and migrati<strong>on</strong> is taken into account, and its<br />

influence <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fr<strong>on</strong>t propagati<strong>on</strong> rate is studied.<br />

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Elisenda Feliu, Carsten Wiuf<br />

Bioinformatics Research Centre<br />

e-mail: feliu.elisenda@gmail.com, wiuf@cs.au.dk<br />

Cellular Systems Biology; Thursday, June 30, 11:30<br />

Enzyme sharing as a cause <str<strong>on</strong>g>of</str<strong>on</strong>g> multistati<strong>on</strong>arity in signaling<br />

systems<br />

Bistability, and more generally multistability, in biological systems is seen as a<br />

mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular decisi<strong>on</strong> making. Compared to systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a single steady<br />

state, <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple stable steady states provide a possible switch between<br />

different resp<strong>on</strong>ses and increased robustness wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to envir<strong>on</strong>mental<br />

noise. To understand cellular signaling, it is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore <str<strong>on</strong>g>of</str<strong>on</strong>g> fundamental importance to<br />

know i) which systems can exhibit multistati<strong>on</strong>arity and ii) what are <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological<br />

c<strong>on</strong>diti<strong>on</strong>s enabling it.<br />

Here, we c<strong>on</strong>sider biological systems where a signal is transmitted by phosphorylati<strong>on</strong>.<br />

Kinases catalyze phosphorylati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> (protein) substrates, and phosphatases<br />

catalyse dephosphorylati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same substrates. Biological systems are<br />

known in which several different kinases phosphorylate a single substrate and o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers<br />

where a single kinase phosphorylate several different substrates. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore,<br />

phosphorylati<strong>on</strong> in more <str<strong>on</strong>g>th</str<strong>on</strong>g>an <strong>on</strong>e site can be carried out by a unique kinase or, as<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> priming kinases, different <strong>on</strong>es. The same phenomena are observed<br />

c<strong>on</strong>cerning phosphatases and dephosphorylati<strong>on</strong>.<br />

The interplay between kinases, phosphatases and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir substrates increases <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is presentati<strong>on</strong> we determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> multistati<strong>on</strong>arity in small motifs <str<strong>on</strong>g>th</str<strong>on</strong>g>at repeatedly occur in signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways.<br />

Our simple modules are built <strong>on</strong> a <strong>on</strong>e-site modificati<strong>on</strong> cycle and c<strong>on</strong>tain <strong>on</strong>e or two<br />

cycles combined in all possible ways wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e above features regarding <str<strong>on</strong>g>th</str<strong>on</strong>g>e number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> modificati<strong>on</strong> sites, and competiti<strong>on</strong> and n<strong>on</strong>-specificity <str<strong>on</strong>g>of</str<strong>on</strong>g> enzymes, incorporated.<br />

We c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

a) Multistati<strong>on</strong>arity arises whenever a single enzyme is resp<strong>on</strong>sible for catalyzing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e modificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> two different but linked substrates.<br />

b) The presence <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple steady states requires substrate saturati<strong>on</strong> and<br />

two opposing dynamics acting <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same substrate.<br />

c) Multistati<strong>on</strong>arity in some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e systems occurs independently <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong><br />

rates.<br />

The ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling is based <strong>on</strong> mass-acti<strong>on</strong> kinetics. This implies <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

steady states are soluti<strong>on</strong>s to a system <str<strong>on</strong>g>of</str<strong>on</strong>g> polynomial equati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e chemical<br />

c<strong>on</strong>centrati<strong>on</strong>s and enables <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> algebraic arguments as previously proven<br />

successful, e.g. [1], [3]. In particular, <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>clusi<strong>on</strong>s are derived in full generality<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out restoring to simulati<strong>on</strong>s or random generati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters. See [2].<br />

References.<br />

[1] E. Feliu, M. Knudsen, L. N. Andersen, and C. Wiuf. An algebraic approach to signaling<br />

cascades wi<str<strong>on</strong>g>th</str<strong>on</strong>g> n layers. arXiv, q-bio.QM, Aug 2010.<br />

[2] E. Feliu, and C. Wiuf. Enzyme sharing as a cause <str<strong>on</strong>g>of</str<strong>on</strong>g> multistati<strong>on</strong>arity in signaling systems.<br />

arXiv, q-bio.QM, Feb 2011.<br />

296

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[3] M. Thoms<strong>on</strong> and J. Gunawardena. Unlimited multistability in multisite phosphorylati<strong>on</strong> systems.<br />

Nature, 460:274–277, 2009.<br />

297

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biomechanical regulati<strong>on</strong> in b<strong>on</strong>e tissue (Sessi<strong>on</strong><br />

II); Wednesday, June 29, 11:00<br />

J. Fernandez<br />

Auckland Bioengineering Institute, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Auckland, 70<br />

Sym<strong>on</strong>ds St, Auckland, New Zealand<br />

e-mail: j.fernandez@auckland.ac.nz<br />

R. Das<br />

Mechanical Engineering, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Auckland, New Zealand<br />

e-mail: r.das@auckland.ac.nz<br />

J. Cornish<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Auckland, New Zealand<br />

e-mail: j.cornish@auckland.ac.nz<br />

D. Thomas<br />

Melbourne Dental School, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Melboune, Australia<br />

e-mail: cd<str<strong>on</strong>g>th</str<strong>on</strong>g>omas@unimelb.edu.au<br />

J. Clement<br />

Melbourne Dental School, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Melboune, Australia<br />

e-mail: johngc@unimelb.edu.au<br />

P. Piv<strong>on</strong>ka<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science and S<str<strong>on</strong>g>of</str<strong>on</strong>g>tware Engineering, The University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Western Australia, Australia<br />

e-mail: peter.piv<strong>on</strong>ka@uwa.edu.au<br />

P. Hunter<br />

Auckland Bioengineering Institute, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> auckland, New<br />

Zealand<br />

e-mail: p.hunter@auckland.ac.nz<br />

A multiscale b<strong>on</strong>e remodelling framework using <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Physiome Project markup languages<br />

Numerous computati<strong>on</strong>al b<strong>on</strong>e models have explored remodelling and b<strong>on</strong>e resp<strong>on</strong>se<br />

at ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell level, micro level or macro level (whole b<strong>on</strong>e). However,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ere have been limited attempts to link informati<strong>on</strong> across <str<strong>on</strong>g>th</str<strong>on</strong>g>ese spatial scales<br />

[1]. Treatments such as milk-derived Lact<str<strong>on</strong>g>of</str<strong>on</strong>g>errin <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy [2], have been shown to<br />

increase mineralised b<strong>on</strong>e by modifiying <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> active b<strong>on</strong>e absorbing cells<br />

(osteoclasts) and b<strong>on</strong>e forming cells (osteoblasts). This, in turn, changes <str<strong>on</strong>g>th</str<strong>on</strong>g>e micro<br />

b<strong>on</strong>e architecture and <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall c<strong>on</strong>tinuum streng<str<strong>on</strong>g>th</str<strong>on</strong>g> observed at <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole<br />

b<strong>on</strong>e level. A multiscale computati<strong>on</strong>al framework <str<strong>on</strong>g>th</str<strong>on</strong>g>at passes informati<strong>on</strong> across<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial scales will allow us to evaluate treatments and study disease progressi<strong>on</strong>.<br />

The focus <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is study is to (i) outline <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial linkages from <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

whole b<strong>on</strong>e using <str<strong>on</strong>g>th</str<strong>on</strong>g>e framework and markup languages developed for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Physiome<br />

Project [3]; and (ii) dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>is framework by looking at an anabolic treatment,<br />

Lact<str<strong>on</strong>g>of</str<strong>on</strong>g>errin, and how it modifies osteoblast/osteoclast numbers, influences<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e strain pattern at <str<strong>on</strong>g>th</str<strong>on</strong>g>e micro b<strong>on</strong>e level and changes whole b<strong>on</strong>e streng<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

The multiscale modelling framework developed as part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e IUPS Physiome<br />

Project [4] was used to link <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial scales. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell level <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e remodelling<br />

process describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e RANK-RANKL-OPG pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way [5] was implemented in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e CellML markup language [6]. This describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount <str<strong>on</strong>g>of</str<strong>on</strong>g> osteoblasts (b<strong>on</strong>e<br />

298

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

forming) and osteoclasts (b<strong>on</strong>e resorbing) cells in resp<strong>on</strong>se to a heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y, diseased or<br />

treatment state. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e micro level a particulate me<str<strong>on</strong>g>th</str<strong>on</strong>g>od, ’Smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> Particle Hydrodynamics’<br />

(SPH) was used to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e micro strain <str<strong>on</strong>g>of</str<strong>on</strong>g> a b<strong>on</strong>e cube (1mm x 1mm x<br />

1mm) [7]. SPH has <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability to handle highly fragmenting solid structures, b<strong>on</strong>e<br />

additi<strong>on</strong> and removal. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e micro level a b<strong>on</strong>e remodelling algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m based <strong>on</strong><br />

strain excitati<strong>on</strong> adapted from <str<strong>on</strong>g>th</str<strong>on</strong>g>e work <str<strong>on</strong>g>of</str<strong>on</strong>g> Prendergast [8] was used to add or remove<br />

b<strong>on</strong>e in order to maintain b<strong>on</strong>e density. At <str<strong>on</strong>g>th</str<strong>on</strong>g>is level <str<strong>on</strong>g>th</str<strong>on</strong>g>e oste<strong>on</strong> cortical pore<br />

structure was visible and <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and resorpti<strong>on</strong> patterns based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> osteoclasts/osteoblasts lead to a changing architecture and overall b<strong>on</strong>e<br />

streng<str<strong>on</strong>g>th</str<strong>on</strong>g>. The macro model (whole b<strong>on</strong>e) was a Femur geometry from <str<strong>on</strong>g>th</str<strong>on</strong>g>e AnatML<br />

database, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> material properties described using FieldML. A spatially varying<br />

density and Young’s modulus was fitted from CT images using <str<strong>on</strong>g>th</str<strong>on</strong>g>e CT number<br />

and a grey-scale mapping. The macro level models are physiologically loaded from<br />

muscle forces and ground reacti<strong>on</strong> force data taken from gait experiments [9]. The<br />

whole b<strong>on</strong>e model provides <str<strong>on</strong>g>th</str<strong>on</strong>g>e boundary c<strong>on</strong>diti<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e micro models. The<br />

proposed computati<strong>on</strong>al framework has <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential to improve understanding <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

how cellular level changes influence whole b<strong>on</strong>e streng<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

References.<br />

[1] Webster D and Mueller R., WIREs Systems Biology and Medicine. Review: 1-11, 2010<br />

[2] Naot D, et al., Clin Med Res. 3(2):93-101, 2005.<br />

[3] Hunter, P.J. and T.K, Borg, Nat Rev Mol Cell Biol 4(3):237-43, 2003.<br />

[4] Lloyd, C.M., et al., Bioinformatics 24(18):2122-3, 2008.<br />

[5] Piv<strong>on</strong>ka P, et al., B<strong>on</strong>e 43(2):249-263, 2008.<br />

[6] CellML, www.cellml.org/.<br />

[7] Fernandez JW, et al., Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g> 6<str<strong>on</strong>g>th</str<strong>on</strong>g> World C<strong>on</strong>gress <strong>on</strong> Biomechanics, Singapore, 1-6<br />

August. 31:784-787, 2010.<br />

[8] McNamara L and Prendergast P, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Biomechanics, 40(6):1381-1391, 2007<br />

[9] Fernandez JW and Pandy MG, Exp Phys 91(2): 371-382, 2006<br />

299

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Luis F. Lopez<br />

Eduardo Massad<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sao Paulo Medical School<br />

e-mail: lopez@usp.br<br />

Epidemics; Thursday, June 30, 11:30<br />

Time-dependent discret, Ising-like model for SIS epidemic<br />

systems<br />

Standard SIS (Susceptible-Infected-Susceptible), SIR and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er similar epidemic<br />

systems are comm<strong>on</strong>ly modeled as mean field dynamic systems or simulated<br />

as different kinds <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular automata. We model a SIS system as an asymmetric<br />

Ising model. In its simplest versi<strong>on</strong>, each individual is c<strong>on</strong>sidered fixed to <str<strong>on</strong>g>th</str<strong>on</strong>g>e nodes<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a square lattice <str<strong>on</strong>g>of</str<strong>on</strong>g> linear size L and <str<strong>on</strong>g>th</str<strong>on</strong>g>ey interact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir nearest neighbors<br />

<strong>on</strong>ly. Then each individual is represented by a vector which may assume <str<strong>on</strong>g>th</str<strong>on</strong>g>e values<br />

1 (susceptible) or −1 (infected) and <str<strong>on</strong>g>th</str<strong>on</strong>g>e probabilities <str<strong>on</strong>g>of</str<strong>on</strong>g> a susceptible to become<br />

infected and an infected to recover depend respectively <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> infected<br />

neighbors and a c<strong>on</strong>stant field H. Here we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e SIS model is c<strong>on</strong>sistent<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> time dependent probabilities in a Glauber fashi<strong>on</strong>, derive <str<strong>on</strong>g>th</str<strong>on</strong>g>e classic meanfield<br />

equati<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>rough extensive M<strong>on</strong>te Carlo simulati<strong>on</strong>s, we show how spatial<br />

heterogeneities arise naturally from <str<strong>on</strong>g>th</str<strong>on</strong>g>e model.<br />

300

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics <str<strong>on</strong>g>of</str<strong>on</strong>g> Neglected Tropical Diseases; Wednesday, June 29, 11:00<br />

C.P. Ferreira<br />

Depto de Bioestatística, Instituto de Biociências, Univ. Estadual<br />

Paulista, 18618-000, Botucatu, SP, Brazil<br />

e-mail: pio@ibb.unesp.br<br />

S.T.R. Pinho<br />

Instituto de Física, Universidade Federal da Bahia, 40210-340, Salvador,<br />

BA, Brazil<br />

e-mail: suani@ufba.br<br />

L. Esteva<br />

Facultad de Ciencias, Universidad Naci<strong>on</strong>al Autónoma de México, 04510,<br />

México, D.F., Mexico<br />

e-mail: esteva@lya.fciencias.unam.mx<br />

F.R. Barreto 1<br />

V.C.M. Silva 2<br />

M.G.L. Teixeira 3<br />

Instituto de Saúde Coletiva, Universidade Federal da Bahia, 0110-040,<br />

Salvador, BA, Brazil<br />

e-mail: 1 florisneide@ufba.br, 2 morato@gmail.com, 3 magloria@ufba.br<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue real epidemics<br />

The infectious diseases are still a relevant problem for human life. Nowadays, due to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e intense flow <str<strong>on</strong>g>of</str<strong>on</strong>g> people around <str<strong>on</strong>g>th</str<strong>on</strong>g>e world and wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cities, <str<strong>on</strong>g>th</str<strong>on</strong>g>e understanding<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir complex dynamics is a multidisciplinary issue. C<strong>on</strong>cerning dengue, a vector<br />

transmitted disease, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is no vaccine against any <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e four serotypes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

virus, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough many efforts have been d<strong>on</strong>e in <str<strong>on</strong>g>th</str<strong>on</strong>g>at directi<strong>on</strong>. As a result, dengue<br />

transmissi<strong>on</strong> c<strong>on</strong>trol is based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e aquatic and adult mosquito<br />

forms. So far, <str<strong>on</strong>g>th</str<strong>on</strong>g>e modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue may be very helpful for<br />

testing bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e adopted vector c<strong>on</strong>trol strategies and <str<strong>on</strong>g>th</str<strong>on</strong>g>e acti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> future vaccines.<br />

In Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> and Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> America, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are records <str<strong>on</strong>g>of</str<strong>on</strong>g> occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> all serotypes<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> dengue virus, while in Brazil, until now, <strong>on</strong>ly 3 serotypes (DENV1, DENV2 and<br />

DENV3) have been reported. However, Brazil is resp<strong>on</strong>sible for 80% <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue cases<br />

in Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> America and 60% <str<strong>on</strong>g>of</str<strong>on</strong>g> notified cases around <str<strong>on</strong>g>th</str<strong>on</strong>g>e world. The circulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ree serotypes represent an important risk factor for <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue<br />

hemorrhagic fever (DHF). Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough all <str<strong>on</strong>g>th</str<strong>on</strong>g>e efforts applied by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Brazilian dengue<br />

c<strong>on</strong>trol program to stop dengue transmissi<strong>on</strong>, it is still a relevant problem in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

first decade <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is century. Two factors had been associated to <str<strong>on</strong>g>th</str<strong>on</strong>g>e failure <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue<br />

c<strong>on</strong>trol: <str<strong>on</strong>g>th</str<strong>on</strong>g>e vector’s adaptive capacity and <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> new virus strains.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we use a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for dengue transmissi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

aim to analyze and compare two dengue epidemics <str<strong>on</strong>g>th</str<strong>on</strong>g>at occurred at Salvador, Brazil<br />

in 1995-1996 and 2002. Using real data, we obtain <str<strong>on</strong>g>th</str<strong>on</strong>g>e force <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong>, Λ, and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproductive number,R0 for bo<str<strong>on</strong>g>th</str<strong>on</strong>g> epidemics. We also obtain <str<strong>on</strong>g>th</str<strong>on</strong>g>e time<br />

evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effective reproducti<strong>on</strong> number, R(t), which result to be a very<br />

asuitable measure to comparing <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> epidemics. Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

estimati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> R0 and R(t) we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trol applied <strong>on</strong>ly <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e adult stage <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e mosquito populati<strong>on</strong> is not sufficient to stop dengue transmissi<strong>on</strong>, emphasizing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol applied <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e aquatic mosquito phase.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Wils<strong>on</strong> Ferreira Jr.<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Campinas - SP - Brazil<br />

e-mail: wils<strong>on</strong>@ime.unicamp.br<br />

Lucy T. Takahashi<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Vicosa - MG - Brazil<br />

Populati<strong>on</strong> Dynamics; Tuesday, June 28, 14:30<br />

Dengue Epidemics : Urbi et Orbi<br />

Dengue is a viral disease which plagues most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tropical regi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e world,<br />

mainly <str<strong>on</strong>g>th</str<strong>on</strong>g>ose wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high humidity and dense populati<strong>on</strong>. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease is not<br />

permanent (since it is <str<strong>on</strong>g>th</str<strong>on</strong>g>rough in about 3 weeks) and in most cases not fatal, never<str<strong>on</strong>g>th</str<strong>on</strong>g>eless<br />

it has an enormous impact in <str<strong>on</strong>g>th</str<strong>on</strong>g>e public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> system and in <str<strong>on</strong>g>th</str<strong>on</strong>g>e ec<strong>on</strong>omic<br />

activity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e affected regi<strong>on</strong>s. The viral infecti<strong>on</strong> is <strong>on</strong>ly transmitted by infected<br />

mosquito Aedes egypti which <strong>on</strong>ly get <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus by biting infected humans. So, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dengue epidemics depends str<strong>on</strong>gly <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e human movement (<str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

infected individuals) and <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> a large populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> mosquitoes vectors.<br />

The coupling <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> populati<strong>on</strong>s plus <str<strong>on</strong>g>th</str<strong>on</strong>g>e movement <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e human populati<strong>on</strong><br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis for <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>th</str<strong>on</strong>g>at we present, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e vector populati<strong>on</strong><br />

evolves locally (in urban areas) while <str<strong>on</strong>g>th</str<strong>on</strong>g>e infected humans are resp<strong>on</strong>sible<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e large distance phenomena (orbi). We have tested <str<strong>on</strong>g>th</str<strong>on</strong>g>e model in <str<strong>on</strong>g>th</str<strong>on</strong>g>e State <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Sao Paulo-Brazil by devising a network c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> its largest 60 cities linked by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e highway traffic between <str<strong>on</strong>g>th</str<strong>on</strong>g>em as a measure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir inter c<strong>on</strong>necti<strong>on</strong>s. At each<br />

city we have used a simple and homogeneous model <str<strong>on</strong>g>of</str<strong>on</strong>g> vector-epidemic dynamics.<br />

The simulati<strong>on</strong> were made by starting a focus <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong> in a far west city <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

state (which is comm<strong>on</strong>ly observed) and <str<strong>on</strong>g>th</str<strong>on</strong>g>e geographical and time evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

results are quite close to <str<strong>on</strong>g>th</str<strong>on</strong>g>e data obtained from <str<strong>on</strong>g>th</str<strong>on</strong>g>e State Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Department in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e last decade. The main goal <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is to have a reliable s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware to predict<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic burst , detect its main spreading nodes so <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

resp<strong>on</strong>sible public system can act sparsely (which is <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>ly way it can afford to<br />

do) but quickly in order to block <str<strong>on</strong>g>th</str<strong>on</strong>g>e fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er propagati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong>.<br />

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Populati<strong>on</strong> Genetics; Wednesday, June 29, 17:00<br />

Stephan Fischer<br />

INSA-Ly<strong>on</strong>, CNRS, INRIA, LIRIS, UMR5205, F-69621, France<br />

e-mail: stephan.fischer@insa-ly<strong>on</strong>.fr<br />

Carole Knibbe<br />

Université Ly<strong>on</strong> 1, CNRS, INRIA, LIRIS, UMR5205, F-69622, France<br />

e-mail: carole.knibbe@liris.cnrs.fr<br />

Samuel Bernard<br />

Université Ly<strong>on</strong> 1, CNRS, INRIA, Institut Camille Jordan, UMR 5208,<br />

F-69222, France<br />

e-mail: bernard@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.univ-ly<strong>on</strong>1.fr<br />

Guillaume Besl<strong>on</strong><br />

INSA-Ly<strong>on</strong>, CNRS, INRIA, LIRIS, UMR5205, F-69621, France<br />

e-mail: guillaume.besl<strong>on</strong>@liris.cnrs.fr<br />

Unravelling laws <str<strong>on</strong>g>of</str<strong>on</strong>g> genome evoluti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and individual-based models<br />

In order to investigate laws <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genome organizati<strong>on</strong> over large evoluti<strong>on</strong>ary<br />

time scales, our lab has developed an individual-based model simulating<br />

Darwinian selecti<strong>on</strong> and most <str<strong>on</strong>g>of</str<strong>on</strong>g> mutati<strong>on</strong>s and rearrangements underg<strong>on</strong>e by a<br />

chromosome during asexual reproducti<strong>on</strong>. In particular, <str<strong>on</strong>g>th</str<strong>on</strong>g>e leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e chromosome<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e number and leng<str<strong>on</strong>g>th</str<strong>on</strong>g>s <str<strong>on</strong>g>of</str<strong>on</strong>g> genes are free to vary. It was shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

evoluti<strong>on</strong>ary success depends not <strong>on</strong>ly <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fitness but also <strong>on</strong> an appropriate<br />

trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f between genome robustness and variability. This indirect selective pressure<br />

regulates <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount <str<strong>on</strong>g>of</str<strong>on</strong>g> coding DNA, but also, more surprisingly, <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-coding DNA, if large rearrangements are taken into account. The higher <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

sp<strong>on</strong>taneous rate <str<strong>on</strong>g>of</str<strong>on</strong>g> duplicati<strong>on</strong>s and deleti<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e more compact <str<strong>on</strong>g>th</str<strong>on</strong>g>e genome in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e surviving lineages [1].<br />

This phenomen<strong>on</strong> is reminiscent <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e error-<str<strong>on</strong>g>th</str<strong>on</strong>g>reshold effect described by Eigen<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e quasispecies <str<strong>on</strong>g>th</str<strong>on</strong>g>eory [2, 3], where <str<strong>on</strong>g>th</str<strong>on</strong>g>e per-digit mutati<strong>on</strong> rate q sets a maximum<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> digits ν <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be reproducibly preserved: ν < − ln(σ0)<br />

ln(q) , where σ0 is a<br />

parameter quantifying <str<strong>on</strong>g>th</str<strong>on</strong>g>e fitness superiority <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fittest sequence. If <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutati<strong>on</strong><br />

rate is increased bey<strong>on</strong>d <str<strong>on</strong>g>th</str<strong>on</strong>g>is limit, <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> structure breaks down, and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> disperses over sequence space. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>is effect was mostly<br />

studied in <str<strong>on</strong>g>th</str<strong>on</strong>g>e special case where all sequences have an equal leng<str<strong>on</strong>g>th</str<strong>on</strong>g> and <strong>on</strong>ly point<br />

mutati<strong>on</strong>s can occur. In <str<strong>on</strong>g>th</str<strong>on</strong>g>ese c<strong>on</strong>diti<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximum chain leng<str<strong>on</strong>g>th</str<strong>on</strong>g> νmax applies<br />

<strong>on</strong>ly to <str<strong>on</strong>g>th</str<strong>on</strong>g>e segments <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>tribute to fitness [3], and <str<strong>on</strong>g>th</str<strong>on</strong>g>us cannot directly explain<br />

our results regarding <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-coding DNA.<br />

The computati<strong>on</strong>al model cannot be c<strong>on</strong>sidered as an analytic pro<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

observed relati<strong>on</strong>. Here, we combine <str<strong>on</strong>g>th</str<strong>on</strong>g>e intuiti<strong>on</strong> and power <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis. By relaxing Eigen’s hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses, we developed simpler<br />

dynamical models <str<strong>on</strong>g>th</str<strong>on</strong>g>at exhibit essentially <str<strong>on</strong>g>th</str<strong>on</strong>g>e same behavior as <str<strong>on</strong>g>th</str<strong>on</strong>g>e original computati<strong>on</strong>al<br />

model as far as genome leng<str<strong>on</strong>g>th</str<strong>on</strong>g> and coding/n<strong>on</strong>-coding ratio is c<strong>on</strong>cerned.<br />

These models yield a better insight <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> essential parameters and<br />

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provide valuable feedback for computati<strong>on</strong>al simulati<strong>on</strong>s. In return, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese computati<strong>on</strong>al<br />

improvements lead to new relati<strong>on</strong>s and limits <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be investigated<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically, closing <str<strong>on</strong>g>th</str<strong>on</strong>g>e emulati<strong>on</strong> loop.<br />

References.<br />

[1] C. Knibbe, A. Coul<strong>on</strong>, O. Mazet, J.M. Fayard, G. Besl<strong>on</strong> (2007). A L<strong>on</strong>g-Term Evoluti<strong>on</strong>ary<br />

Pressure <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Amount <str<strong>on</strong>g>of</str<strong>on</strong>g> N<strong>on</strong>coding DNA. Molecular Biology and Evoluti<strong>on</strong> 24(10) 2344–<br />

2353.<br />

[2] M. Eigen (1971), Selforganizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> matter and <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biological macromolecules.<br />

Naturwissenschaften 58(10) 465–523.<br />

[3] M. Eigen, J. McCaskill, P. Schuster (1988). Molecular Quasi-Species. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Physical<br />

Chemistry 92:6881-6891.<br />

304

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

II; Tuesday, June 28, 14:30<br />

K. Renee Fister<br />

Murray State University<br />

e-mail: renee.fister@murraystate.edu<br />

Optimal c<strong>on</strong>trol scenarios in cancer treatment strategies<br />

Models depicting cancer dynamics are investigated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e inclusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> optimal<br />

c<strong>on</strong>trol strategies to minimize <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer cells, toxicity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e drugs, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e cost<br />

associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e regimen. The ordinary differential equati<strong>on</strong> models coupled<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> state c<strong>on</strong>straints will be studied and some numerical results will be discussed.<br />

305

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ben Fitzpatrick<br />

Loyola Marymount University<br />

e-mail: bfitzpatrick@lmu.edu<br />

Regulatory Networks; Saturday, July 2, 11:00<br />

Modeling and Estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Gene Regulatory Networks and<br />

Envir<strong>on</strong>mental Stress Resp<strong>on</strong>se<br />

This talk investigates <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> gene regulatory networks governing cold<br />

shack resp<strong>on</strong>se in budding yeast, Saccharomyces cerevisiae, <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

differential equati<strong>on</strong> model. The inverse problem <str<strong>on</strong>g>of</str<strong>on</strong>g> determining model parameters<br />

from observed data is our primary interest. We fit <str<strong>on</strong>g>th</str<strong>on</strong>g>e differential equati<strong>on</strong> model to<br />

microarray data from a cold shock experiment using a Bayesian maximum likelihood<br />

approach, and we discuss future efforts involving gene deleti<strong>on</strong> experiments and<br />

related modeling problems.<br />

306

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

The emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance in cancer using ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling;<br />

Saturday, July 2, 08:30<br />

Edward H. Flach<br />

Integrated Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Oncology, M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center, Tampa,<br />

FL, USA<br />

Inna Fedorenko<br />

Molecular Oncology, M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center, Tampa, FL, USA<br />

Kim Paraiso<br />

Molecular Oncology, M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center, Tampa, FL, USA<br />

Keiran S. M. Smalley<br />

Molecular Oncology, M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center, Tampa, FL, USA<br />

Cutaneous Oncology, M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center, Tampa, FL, USA<br />

Alexander R. M. Anders<strong>on</strong><br />

Integrated Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Oncology, M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center, Tampa,<br />

FL, USA<br />

Cancer drug treatment is unnatural selecti<strong>on</strong><br />

Targeted drug treatment reduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour volume, but <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is almost always<br />

recurrence even under chr<strong>on</strong>ic treatment. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour populati<strong>on</strong> is<br />

heterogenous. Then <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug treatment is a selecti<strong>on</strong> process, targeting specific<br />

subpopulati<strong>on</strong>s. If treatment is stopped, phenotypic drift causes reversi<strong>on</strong> towards<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e original wild-type populati<strong>on</strong>.<br />

Our model is a discrete populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells, <str<strong>on</strong>g>th</str<strong>on</strong>g>e individual equivalent <str<strong>on</strong>g>of</str<strong>on</strong>g> an ODE.<br />

The cells each have a distinct phenotype. This phenotype determines <str<strong>on</strong>g>th</str<strong>on</strong>g>eir fitness.<br />

The fitness changes under drug c<strong>on</strong>diti<strong>on</strong>s: we define a fitness landscape for bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

drug and drug-free c<strong>on</strong>diti<strong>on</strong>s.<br />

Experimentati<strong>on</strong> shows evidence <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>ly partial reversi<strong>on</strong> to wild-type. We<br />

extend <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fitness landscape to multiple fitness “wells”. Reversi<strong>on</strong><br />

after drug treatment <strong>on</strong>ly fills <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e wells. The overall behaviour matches<br />

experimental observati<strong>on</strong>s.<br />

Our model c<strong>on</strong>cept extends to c<strong>on</strong>sidering alternative treatments. Temporal<br />

variati<strong>on</strong> appears unhelpful but well-chosen combinati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies could be effective.<br />

This approach gives a quantitative predicrti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment strategies.<br />

307

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chaste framework;<br />

Tuesday, June 28, 11:00<br />

Dr Alexander Fletcher<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: alexander.fletcher@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

Modelling biological systems in Chaste: an overview<br />

Computati<strong>on</strong>al models <str<strong>on</strong>g>of</str<strong>on</strong>g> a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> biological processes have been implemented<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chaste framework (http://web.comlab.ox.ac.uk/chaste). In <str<strong>on</strong>g>th</str<strong>on</strong>g>is,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d talk <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mini-symposium, we provide an overview <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, focusing<br />

in particular <strong>on</strong> models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intestinal crypt. We discuss how multiscale<br />

modelling may be used to gain insight into processes such as crypt homeostasis,<br />

m<strong>on</strong>ocl<strong>on</strong>al c<strong>on</strong>versi<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> dysregulated proliferati<strong>on</strong> and adhesi<strong>on</strong><br />

<strong>on</strong> crypt dynamics. We also dem<strong>on</strong>strate how <str<strong>on</strong>g>th</str<strong>on</strong>g>e generality <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chaste framework<br />

allows a quantitative comparis<strong>on</strong> to be made <str<strong>on</strong>g>of</str<strong>on</strong>g> different cell-based modelling<br />

frameworks. We c<strong>on</strong>clude wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a discussi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er biological systems <str<strong>on</strong>g>th</str<strong>on</strong>g>at are<br />

being modelled wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in Chaste.<br />

308

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

The emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance in cancer using ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling;<br />

Saturday, July 2, 08:30<br />

Jasmine Foo<br />

Harvard University, Dana Farber Cancer Institute<br />

e-mail: jfoo@jimmy.harvard.edu<br />

Modeling diversity in drug-resistant populati<strong>on</strong>s using<br />

multitype branching processes<br />

I will discuss a c<strong>on</strong>tinuous-time bir<str<strong>on</strong>g>th</str<strong>on</strong>g>-dea<str<strong>on</strong>g>th</str<strong>on</strong>g> process model <str<strong>on</strong>g>of</str<strong>on</strong>g> tumorigenesis<br />

where resistance mutati<strong>on</strong>s c<strong>on</strong>fer random additive fitness (bir<str<strong>on</strong>g>th</str<strong>on</strong>g> rate) changes<br />

sampled from a mutati<strong>on</strong>al fitness distributi<strong>on</strong>. We investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

rate and diversity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resistant populati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymptotic limit, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese features <strong>on</strong> parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fitness landscape. We study <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

generati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance from bo<str<strong>on</strong>g>th</str<strong>on</strong>g> exp<strong>on</strong>entially increasing sensitive cell populati<strong>on</strong>s<br />

(pre-treatment) and exp<strong>on</strong>entially declining populati<strong>on</strong>s (during treatment).<br />

Using experimental data, we apply <str<strong>on</strong>g>th</str<strong>on</strong>g>is model to study characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> a drugresistant<br />

subpopulati<strong>on</strong> at <str<strong>on</strong>g>th</str<strong>on</strong>g>e time <str<strong>on</strong>g>of</str<strong>on</strong>g> diagnosis <str<strong>on</strong>g>of</str<strong>on</strong>g> chr<strong>on</strong>ic myeloid leukemia, and<br />

discuss implicati<strong>on</strong>s for treatment strategies. (Joint work w/R. Durrett, K. Leder,<br />

J. Mayberry. F. Michor)<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Recent advances in infectious disease modelling I; Saturday, July 2, 11:00<br />

J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an Forde<br />

Hobart and William Smi<str<strong>on</strong>g>th</str<strong>on</strong>g> Colleges; Geneva, NY, USA<br />

e-mail: forde@hws.edu<br />

Stanca Ciupe<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Louisiana at Lafayette, Lafayette, LA, USA<br />

e-mail: msc6503@louisiana.edu<br />

Reducing HIV Reservoirs by Induced Activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Latently<br />

Infected Cells<br />

Treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> patients infected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> HIV is effective at lowering <str<strong>on</strong>g>th</str<strong>on</strong>g>e serum viral<br />

c<strong>on</strong>centrati<strong>on</strong> to below <str<strong>on</strong>g>th</str<strong>on</strong>g>e limits <str<strong>on</strong>g>of</str<strong>on</strong>g> detecti<strong>on</strong>, but <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus persists in reservoirs<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> latently infected cells, such as resting memory T cells. Because <str<strong>on</strong>g>th</str<strong>on</strong>g>e latent pool<br />

may serve as a source for reemergence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus after <str<strong>on</strong>g>th</str<strong>on</strong>g>e cessati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment,<br />

speeding its decay is a necessary step toward eradicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV from <str<strong>on</strong>g>th</str<strong>on</strong>g>e patient.<br />

One strategy for reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e latent pool is to artificially activate memory T cells.<br />

We present a model <str<strong>on</strong>g>of</str<strong>on</strong>g> viral infecti<strong>on</strong> including anti-retroviral <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy and<br />

activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> latently infected cells. We explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative roles <str<strong>on</strong>g>of</str<strong>on</strong>g> homeostatic<br />

proliferati<strong>on</strong> and transient viremic events in maintaining <str<strong>on</strong>g>th</str<strong>on</strong>g>e latent pool. Using<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is model, we evaluate <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential use <str<strong>on</strong>g>of</str<strong>on</strong>g> artificial activati<strong>on</strong> to enhance HIV<br />

treatment.<br />

310

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling viral hepatitis dynamics in-vivo and in-vitro in <str<strong>on</strong>g>th</str<strong>on</strong>g>e era <str<strong>on</strong>g>of</str<strong>on</strong>g> direct<br />

anti-viral agents II; Wednesday, June 29, 08:30<br />

J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an Forde<br />

Hobart and William Smi<str<strong>on</strong>g>th</str<strong>on</strong>g> Colleges; Geneva, NY, USA<br />

e-mail: forde@hws.edu<br />

Yang Kuang<br />

Ariz<strong>on</strong>a State University, Tempe, AZ, USA<br />

e-mail: kuang@asu.edu<br />

Aar<strong>on</strong> Packer<br />

Ariz<strong>on</strong>a State University, Tempe, AZ, USA<br />

e-mail: aar<strong>on</strong>.packer@asu.edu<br />

Modeling Early Events in Hepatitis Delta Virus Infecti<strong>on</strong><br />

Delta hepatitis virus (HDV) is a dependent satellite virus <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatitis B virus.<br />

HDV relies <strong>on</strong> surface proteins produced by HBV to create new virus particles, but<br />

also has an inhibitory effect <str<strong>on</strong>g>of</str<strong>on</strong>g> HBV replicati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e two species compete for<br />

comm<strong>on</strong> resources inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. Understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>is dependence and competiti<strong>on</strong><br />

could provide targets for antiviral <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies to eliminate or prevent chr<strong>on</strong>ic HDV<br />

superinfecti<strong>on</strong>.<br />

By exploring <str<strong>on</strong>g>th</str<strong>on</strong>g>e early events in HDV replicati<strong>on</strong>, we explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

viral release from newly infected hepatocytes, including a delay in <str<strong>on</strong>g>th</str<strong>on</strong>g>e initiati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

viral release and a precipitous decline in producti<strong>on</strong> after 12 days. We fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er explore<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese dynamics for <str<strong>on</strong>g>th</str<strong>on</strong>g>e establishment <str<strong>on</strong>g>of</str<strong>on</strong>g> chr<strong>on</strong>ic hepatitis<br />

delta in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cases <str<strong>on</strong>g>of</str<strong>on</strong>g> coinfecti<strong>on</strong> and superinfecti<strong>on</strong>.<br />

311

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Neurosciences; Wednesday, June 29, 08:30<br />

Daniel Forger<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Michigan<br />

e-mail: forger@umich.edu<br />

Casey O. Diekman<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences Institute, Ohio State University<br />

The surprising complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> signal processing in clock<br />

neur<strong>on</strong>s<br />

Neur<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e suprachiasmatic nucleus (SCN) <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>alamus act as <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

central daily pacemakers in mammals. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese neur<strong>on</strong>s, a molecular circadian<br />

clock is closely coupled to <str<strong>on</strong>g>th</str<strong>on</strong>g>e neur<strong>on</strong>s electrical activity to process timekeeping<br />

signals from <str<strong>on</strong>g>th</str<strong>on</strong>g>e external world, and to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e signals <str<strong>on</strong>g>th</str<strong>on</strong>g>e neur<strong>on</strong>s will send<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e rest <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e body. This is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> many emerging examples <str<strong>on</strong>g>of</str<strong>on</strong>g> how neur<strong>on</strong>al<br />

firing influences, and is influenced by, intracellular biochemical systems.<br />

For as l<strong>on</strong>g as <str<strong>on</strong>g>th</str<strong>on</strong>g>ese neur<strong>on</strong>s had been studied, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey had been assumed to<br />

encode <str<strong>on</strong>g>th</str<strong>on</strong>g>e time <str<strong>on</strong>g>of</str<strong>on</strong>g> day indicated by <str<strong>on</strong>g>th</str<strong>on</strong>g>eir internal molecular clock by <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate at<br />

which <str<strong>on</strong>g>th</str<strong>on</strong>g>ey fire acti<strong>on</strong> potentials. Here, I will present analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at suggests much more complex coding, largely based <strong>on</strong> a balance between<br />

calcium and sodium dynamics. Bifurcati<strong>on</strong> analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model we<br />

have developed <str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>s which c<strong>on</strong>trol daily timekeeping in mammals suggested<br />

a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> electrical states, including depolarized low amplitude membrane oscillati<strong>on</strong>s<br />

and depolarizati<strong>on</strong> block. These states were c<strong>on</strong>firmed experimentally<br />

by colleagues. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er simulati<strong>on</strong>s suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at rest membrane potential may be<br />

more important <str<strong>on</strong>g>th</str<strong>on</strong>g>an spike rate for signaling in clock neur<strong>on</strong>s. This suggests a new<br />

modeling paradigm when c<strong>on</strong>sidering signaling from membrane to DNA and back.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bioinformatics and System Biology; Wednesday, June 29, 08:30<br />

Scott Fortmann-Roe<br />

UC Berkeley<br />

e-mail: scottfr@berkeley.edu<br />

Orr Spiegel<br />

Hebrew University <str<strong>on</strong>g>of</str<strong>on</strong>g> Jerusalem<br />

Roi Harel<br />

Hebrew University <str<strong>on</strong>g>of</str<strong>on</strong>g> Jerusalem<br />

Wayne Getz<br />

UC Berkeley<br />

Ran Na<str<strong>on</strong>g>th</str<strong>on</strong>g>an<br />

Hebrew University <str<strong>on</strong>g>of</str<strong>on</strong>g> Jerusalem<br />

Automatic Classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Vulture Behavior using Machine<br />

Learning Algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms Applied to Accelerometer Data<br />

Accelerometer data has been shown to be an effective tool for identifying certain<br />

animal behaviors. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, I present <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> tri-axial accelerometer data<br />

as a predictor <str<strong>on</strong>g>of</str<strong>on</strong>g> seven ground-tru<str<strong>on</strong>g>th</str<strong>on</strong>g>ed Griff<strong>on</strong> vulture (Gyps fulvus) behaviors:<br />

active flight, eating, laying down, passive flight, preening, running, and standing.<br />

Five different machine learning algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms were trained and validated <strong>on</strong> subsets<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> over nine-hundred observati<strong>on</strong>s, each 16 to 25 sec<strong>on</strong>ds in leng<str<strong>on</strong>g>th</str<strong>on</strong>g>. Prior to classificati<strong>on</strong>,<br />

summary statistics for <str<strong>on</strong>g>th</str<strong>on</strong>g>e accelerometer data were calculated and used<br />

as inputs into <str<strong>on</strong>g>th</str<strong>on</strong>g>e machine learning algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms. The algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms tested were Linear<br />

Discriminate Analysis, Classificati<strong>on</strong> and Regressi<strong>on</strong> Trees, Random Forests,<br />

Artificial Neural Networks, and Support Vector Machines. Of <str<strong>on</strong>g>th</str<strong>on</strong>g>ese me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Random Forest predictors were found to be <str<strong>on</strong>g>th</str<strong>on</strong>g>e most accurate while Linear Discriminate<br />

Analysis predictors were <str<strong>on</strong>g>th</str<strong>on</strong>g>e least accurate. Classificati<strong>on</strong> accuracies for<br />

all predictors were in <str<strong>on</strong>g>th</str<strong>on</strong>g>e 80% to 90% range. Using results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e machine learning<br />

algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms we determined <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e different summary statistics for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e classificati<strong>on</strong> effort. Generally, measures <str<strong>on</strong>g>of</str<strong>on</strong>g> variance were found to be more<br />

important <str<strong>on</strong>g>th</str<strong>on</strong>g>an measures <str<strong>on</strong>g>of</str<strong>on</strong>g> central tendency or correlati<strong>on</strong>.<br />

313

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bioinformatics and System Biology; Wednesday, June 29, 08:30<br />

Pawel Foszner<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: Pawel.Foszner@polsl.pl<br />

Roman Jaksik<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: Roman.Jaksik@polsl.pl<br />

Aleksandra Gruca<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: Aleksandra.Gruca@polsl.pl<br />

Joanna Polanska<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: Joanna.Polanska@polsl.pl<br />

Andrzej Polanski<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: Andrzej.Polanski@polsl.pl<br />

Efficient reannotati<strong>on</strong> system for verifying genomic targets<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> DNA microarray probes<br />

Systems for data cleaning for supporting analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> results <str<strong>on</strong>g>of</str<strong>on</strong>g> DNA microarray<br />

experiments are becoming important elements <str<strong>on</strong>g>of</str<strong>on</strong>g> bioinformatics aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> gene<br />

expressi<strong>on</strong> analysis [1]. It has been dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at data cleaning at <str<strong>on</strong>g>th</str<strong>on</strong>g>e level<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> microarray probes, based <strong>on</strong> most recent knowledge <strong>on</strong> genomic data, can substantially<br />

improve results <str<strong>on</strong>g>of</str<strong>on</strong>g> predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular classifiers. However, due to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e difficulty <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole genome browsing projects, available services and data for<br />

reannotati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> microarray probes are still quite sparse. In our research we have<br />

created an efficient reannotati<strong>on</strong> tool by combining <str<strong>on</strong>g>th</str<strong>on</strong>g>e well known gene search tool<br />

BLAT [2] wi<str<strong>on</strong>g>th</str<strong>on</strong>g> appropriately designed database and tools for operati<strong>on</strong>s <strong>on</strong> it.<br />

We show properties <str<strong>on</strong>g>of</str<strong>on</strong>g> our tool by using two Affymetrix chips HG U133A and<br />

HG 1.0 ST. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e Affymetrix microarrays, <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene intensity is calculated <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

basis <str<strong>on</strong>g>of</str<strong>on</strong>g> gene probes c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> 25-mer oligo-nucleotides. For many reas<strong>on</strong>s, in<br />

many cases, <str<strong>on</strong>g>th</str<strong>on</strong>g>e calculated value does not match <str<strong>on</strong>g>th</str<strong>on</strong>g>e real expressi<strong>on</strong>. These reas<strong>on</strong>s<br />

include single nucleotide polymorphism, adjusting <str<strong>on</strong>g>th</str<strong>on</strong>g>e probe to ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er gene or intr<strong>on</strong>.<br />

Our task was to check how many probes can truly determine gene expressi<strong>on</strong>.<br />

We have developed a database which c<strong>on</strong>tains informati<strong>on</strong> about how <str<strong>on</strong>g>th</str<strong>on</strong>g>e probes<br />

are aligned to <str<strong>on</strong>g>th</str<strong>on</strong>g>e latest human genome. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>ose matches to <str<strong>on</strong>g>th</str<strong>on</strong>g>e genome, for<br />

each probe we found mRNA and EST sequences. In our presentati<strong>on</strong> we compare<br />

reannotati<strong>on</strong> results for analyzed Affymetrix chips, based <strong>on</strong> two different built <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Human Genome, HG18 and HG19. Improving <str<strong>on</strong>g>th</str<strong>on</strong>g>e quality <str<strong>on</strong>g>of</str<strong>on</strong>g> data can be fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

verified by comparing <str<strong>on</strong>g>th</str<strong>on</strong>g>e misclassificati<strong>on</strong> rates for classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> microarray data<br />

obtained using <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>of</str<strong>on</strong>g>ficial affymetrix CDF files and CDF file created by us. The<br />

informati<strong>on</strong> obtained from reannotati<strong>on</strong>s can help to update <str<strong>on</strong>g>th</str<strong>on</strong>g>e CDF files, and can<br />

significantly improve <str<strong>on</strong>g>th</str<strong>on</strong>g>e quality <str<strong>on</strong>g>of</str<strong>on</strong>g> classificati<strong>on</strong>.<br />

Acknowledgements. This work was supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>European</str<strong>on</strong>g> Community<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>European</str<strong>on</strong>g> Social Fund.<br />

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References.<br />

[1] Ramil N. Nurtdinov, Mikhail O. Vasiliev,Anna S. Ershova, Ilia S. Lossev and Anna S. Karyagina,<br />

PLANdbAffy: probe-level annotati<strong>on</strong> database for Affymetrix expressi<strong>on</strong> microarrays Nucleic<br />

Acids Research, 2010, 38 D726–D730.<br />

[2] Kent,W.J., BLAT–<str<strong>on</strong>g>th</str<strong>on</strong>g>e BLAST-like alignment tool. Genome Res. 12 656–664.<br />

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C<strong>on</strong>necting microscale and macroscale models <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular migrati<strong>on</strong>;<br />

Tuesday, June 28, 17:00<br />

John Fozard<br />

CPIB, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham<br />

e-mail: john.fozard@nottingham.ac.uk<br />

Helen Byrne<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham<br />

e-mail: helen.byrne@nottingham.ac.uk<br />

Oliver Jensen<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham<br />

e-mail: oliver.jensen@nottingham.ac.uk<br />

John King<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham<br />

e-mail: john.king@nottingham.ac.uk<br />

Discrete and c<strong>on</strong>tinuum modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and signalling<br />

in biological tissue<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e recent work [1], we examined me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for deriving c<strong>on</strong>tinuum approximati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>e-dimensi<strong>on</strong>al individual-based models (IBM) for systems <str<strong>on</strong>g>of</str<strong>on</strong>g> tightly adherent<br />

cells, such as an epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial m<strong>on</strong>olayer. Each cell occupies a bounded regi<strong>on</strong>, defined<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e locati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> its endpoints, has bo<str<strong>on</strong>g>th</str<strong>on</strong>g> elastic and viscous mechanical properties<br />

and is subject to drag generated by adhesi<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e substrate. The evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e discrete system is governed by a system <str<strong>on</strong>g>of</str<strong>on</strong>g> differential-algebraic equati<strong>on</strong>s. This<br />

IBM is <str<strong>on</strong>g>th</str<strong>on</strong>g>en approximated by a system <str<strong>on</strong>g>of</str<strong>on</strong>g> partial differential equati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e limit <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a large number <str<strong>on</strong>g>of</str<strong>on</strong>g> cells. We c<strong>on</strong>sider two different techniques: <str<strong>on</strong>g>th</str<strong>on</strong>g>e usual c<strong>on</strong>tinuum<br />

approximati<strong>on</strong> which is appropriate when cellular properties vary slowly between<br />

neighbouring cells, and a multiple-scales approach which is appropriate when cellular<br />

properties are spatially periodic (so may be heterogeneous, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> substantial<br />

variati<strong>on</strong> between adjacent cells). In <str<strong>on</strong>g>th</str<strong>on</strong>g>e latter case, <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship between mean<br />

cell pressure and mean cell leng<str<strong>on</strong>g>th</str<strong>on</strong>g>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tinuum model is found to be historydependent<br />

when cell viscosity is significant. We apply <str<strong>on</strong>g>th</str<strong>on</strong>g>is model to examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

accelerati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a wound edge observed in wound-healing assays.<br />

References.<br />

[1] Fozard JA, Byrne HM, Jensen OE, King JR, C<strong>on</strong>tinuum approximati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> individual-based<br />

models for epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial m<strong>on</strong>olayers. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Med Biol. (2010) 27(1) 39–74.<br />

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Benjamin Franz<br />

Oxford University (OCCAM)<br />

e-mail: franz@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

Populati<strong>on</strong> Dynamics; Wednesday, June 29, 17:00<br />

Hybrid modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> cell migrati<strong>on</strong>: coupling<br />

individual-based models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> partial differential equati<strong>on</strong>s<br />

Two approaches to ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> cell migrati<strong>on</strong> are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten used in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

literature: (i) individual-based (agent-based) models, which describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> each cell, and (ii) macroscopic partial differential equati<strong>on</strong>s (PDEs), which are<br />

written for cell c<strong>on</strong>centrati<strong>on</strong>s. A widely studied example <str<strong>on</strong>g>of</str<strong>on</strong>g> cell migrati<strong>on</strong> is chemotaxis,<br />

where cells move according to extracellular chemicals <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be altered by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cells <str<strong>on</strong>g>th</str<strong>on</strong>g>emselves. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is case, systems <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled PDEs are used to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

c<strong>on</strong>centrati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cells and external chemicals. A more detailed descripti<strong>on</strong> is given<br />

by hybrid models <str<strong>on</strong>g>th</str<strong>on</strong>g>at couple an individual-based model <str<strong>on</strong>g>of</str<strong>on</strong>g> cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> PDEs for<br />

extracellular chemicals. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, we will give an overview <str<strong>on</strong>g>of</str<strong>on</strong>g> hybrid models used<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature. Examples will include chemotaxis <str<strong>on</strong>g>of</str<strong>on</strong>g> bacteria and eukaryotic cells.<br />

We will analyse similarities and differences between hybrid models and macroscopic<br />

PDEs.<br />

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Bridging <str<strong>on</strong>g>th</str<strong>on</strong>g>e Divide: Cancer Models in Clinical Practice; Thursday, June 30,<br />

11:30<br />

Avner Friedman<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences Institute, Ohio State University<br />

e-mail: afriedman@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ohio-state.edu<br />

Therapeutic approaches to brain cancer<br />

The standard treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> newly diagnosed glioblastoma, <str<strong>on</strong>g>th</str<strong>on</strong>g>e most aggressive brain<br />

cancer, is surgical resecti<strong>on</strong> followed by radiati<strong>on</strong> and chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy. This treatment,<br />

however, has failed to signi<br />

cantly extend <str<strong>on</strong>g>th</str<strong>on</strong>g>e patient’s life expectancy which is typically <strong>on</strong>e year. By <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

time <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease is diagnosed, tumor cells have already migrated to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er parts <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e brain. Based <strong>on</strong> clinical data, we shall evaluate dierent combinati<strong>on</strong> protocols <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

resecti<strong>on</strong>, radiati<strong>on</strong> and chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy <str<strong>on</strong>g>th</str<strong>on</strong>g>at may increase a patient’s survival time.<br />

We shall also c<strong>on</strong>sider viral <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, currently at <str<strong>on</strong>g>th</str<strong>on</strong>g>e preclinical stage, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e eect<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> drugs <str<strong>on</strong>g>th</str<strong>on</strong>g>at slow down glioma cell migrati<strong>on</strong>. The ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models used in<br />

our analysis are based, primarily, <strong>on</strong> systems <str<strong>on</strong>g>of</str<strong>on</strong>g> partial dierential equati<strong>on</strong>s.<br />

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Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part I;<br />

Tuesday, June 28, 11:00<br />

Avner Friedman<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences Institute, and Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics,<br />

The Ohio State University, Columbus, USA<br />

e-mail: afriedman@mbi.osu.edu<br />

Bei Hu<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Notre Dame, Notre Dame,<br />

USA<br />

The development <str<strong>on</strong>g>of</str<strong>on</strong>g> fingers in solid tumors<br />

We c<strong>on</strong>sider a solid tumor in a regi<strong>on</strong> which is modeled ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er as a porous medium<br />

(by Darcy’s law) or as fluid-like tissue (by Stokes equati<strong>on</strong>). We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

proliferating and dying cells move around wi<str<strong>on</strong>g>th</str<strong>on</strong>g> velocity v in a way <str<strong>on</strong>g>th</str<strong>on</strong>g>at keeps <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

density c<strong>on</strong>stant in <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor regi<strong>on</strong> D(t). The nutrient c<strong>on</strong>centrati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

velocity v satisfy a system <str<strong>on</strong>g>of</str<strong>on</strong>g> PDEs in D(t). The aggressivity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor is<br />

represented by a parameter µ which relates nutrient c<strong>on</strong>centrati<strong>on</strong> to proliferating<br />

rate <str<strong>on</strong>g>of</str<strong>on</strong>g> cells. It is shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a stati<strong>on</strong>ary spherically symmetric soluti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> radius R which depends <strong>on</strong> some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model parameters but not <str<strong>on</strong>g>of</str<strong>on</strong>g> µ. We<br />

prove <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is soluti<strong>on</strong> is asymptotically stable for µ > µ∗ and <str<strong>on</strong>g>th</str<strong>on</strong>g>ere exist infinite<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> branches <str<strong>on</strong>g>of</str<strong>on</strong>g> stati<strong>on</strong>ary soluti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> arbitrarily large number <str<strong>on</strong>g>of</str<strong>on</strong>g> fingers,<br />

indicating <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>set <str<strong>on</strong>g>of</str<strong>on</strong>g> metastasis. We also prove <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluid-like tumor develops<br />

more fingers <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor wi<str<strong>on</strong>g>th</str<strong>on</strong>g> porous medium c<strong>on</strong>sistency.<br />

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Cell and Tissue Biophysics; Thursday, June 30, 11:30<br />

Jan Fuhrmann<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Universität Heidelberg<br />

e-mail: jan.fuhrmann@uni-hd.de<br />

Angela Stevens<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Numerical and Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Universität Münster;<br />

formerly Universität Heidelberg<br />

e-mail: stevens@mis.mpg.de<br />

On a parabolic model for particle alignment<br />

In [1] we proposed a model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e initiati<strong>on</strong> <strong>on</strong> cell polarizati<strong>on</strong> at <str<strong>on</strong>g>th</str<strong>on</strong>g>e first<br />

steps <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular moti<strong>on</strong>. Now, numerical simulati<strong>on</strong>s indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

shocks in <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>ese equati<strong>on</strong>s which may be interpreted as fr<strong>on</strong>ts <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

active barbed ends <str<strong>on</strong>g>of</str<strong>on</strong>g> actin filaments being established in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell.<br />

The original model included <str<strong>on</strong>g>th</str<strong>on</strong>g>e descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> actin m<strong>on</strong>omers and filaments<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out taking into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutual alignment <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e latter. In order to understand<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> aligning filaments we deduced from <str<strong>on</strong>g>th</str<strong>on</strong>g>e given model a simple<br />

parabolic system describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> oriented particles wi<str<strong>on</strong>g>th</str<strong>on</strong>g> fixed velocity,<br />

undergoing diffusi<strong>on</strong> and mutual alignment. This system, c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> no more<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>an two equati<strong>on</strong>s, may be used to model different kinds <str<strong>on</strong>g>of</str<strong>on</strong>g> aligning particles, e.g.<br />

myxobacteria.<br />

For <str<strong>on</strong>g>th</str<strong>on</strong>g>is model we analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e totally symmetric state which<br />

corresp<strong>on</strong>ds to a n<strong>on</strong> polarized cell against small perturbati<strong>on</strong>s. Here, <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> different types <str<strong>on</strong>g>of</str<strong>on</strong>g> alignment terms will be discussed. We fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore derive<br />

traveling wave soluti<strong>on</strong>s to <str<strong>on</strong>g>th</str<strong>on</strong>g>e system and show how <str<strong>on</strong>g>th</str<strong>on</strong>g>ey emerge numerically from<br />

small initial data. We will <str<strong>on</strong>g>th</str<strong>on</strong>g>us observe polarizati<strong>on</strong> fr<strong>on</strong>ts developing from an<br />

initially almost symmetric state.<br />

References.<br />

[1] J. Fuhrmann, J. Käs, A. Stevens, Initiati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cytoskeletal asymmetry for cell polarizati<strong>on</strong><br />

and movement. J Theor Biol 249.2 278–288.<br />

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Informati<strong>on</strong>, human behaviour and infecti<strong>on</strong> c<strong>on</strong>trol; Saturday, July 2, 08:30<br />

Sebastian Funk<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Zoology, Zoological Society <str<strong>on</strong>g>of</str<strong>on</strong>g> L<strong>on</strong>d<strong>on</strong><br />

e-mail: sf429@cam.ac.uk<br />

Marcel Sala<str<strong>on</strong>g>th</str<strong>on</strong>g>é<br />

Pennsylvania State University<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e Influence <str<strong>on</strong>g>of</str<strong>on</strong>g> Human Behaviour <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Spread<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Infectious Diseases<br />

People can protect <str<strong>on</strong>g>th</str<strong>on</strong>g>emselves against being infected by a disease by changing <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

behaviour in resp<strong>on</strong>se to an outbreak, for example, <str<strong>on</strong>g>th</str<strong>on</strong>g>rough wearing face masks or<br />

reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>eir number <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious c<strong>on</strong>tacts. This type <str<strong>on</strong>g>of</str<strong>on</strong>g> behavioural change can<br />

affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemiology <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease itself. Here, I will discuss different ways to<br />

model <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> human behaviour <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases, as well<br />

as challenges <str<strong>on</strong>g>th</str<strong>on</strong>g>erein. As an example, I will present a model in which individuals<br />

are influenced by <str<strong>on</strong>g>th</str<strong>on</strong>g>eir peers as awareness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> a disease as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

disease itself spread in <str<strong>on</strong>g>th</str<strong>on</strong>g>e social networks <str<strong>on</strong>g>of</str<strong>on</strong>g> influence and disease.<br />

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Undergraduate Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Educati<strong>on</strong> Bey<strong>on</strong>d BIO 2010 (Part I);<br />

Wednesday, June 29, 14:30<br />

Holly Gaff<br />

Old Domini<strong>on</strong> University<br />

e-mail: hgaff@odu.edu<br />

Agent-based models <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting populati<strong>on</strong>s<br />

Agent-based models, also called individual-based models, are computer-based models<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at simulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e acti<strong>on</strong>s and interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> aut<strong>on</strong>omous agents <str<strong>on</strong>g>th</str<strong>on</strong>g>at represent<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e individuals <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong>. These models are powerful simulati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at can<br />

capture <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergent phenomena <str<strong>on</strong>g>of</str<strong>on</strong>g> a natural system. These types <str<strong>on</strong>g>of</str<strong>on</strong>g> models have<br />

been applied to many different areas <str<strong>on</strong>g>of</str<strong>on</strong>g> research such as ecology, e.g., white-tailed<br />

deer and pan<str<strong>on</strong>g>th</str<strong>on</strong>g>er populati<strong>on</strong>s in Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Florida, and epidemiology, e.g., human disease<br />

outbreaks in a realistic urban area. One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most beneficial aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

models is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are easily understood and explainable to bo<str<strong>on</strong>g>th</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g> and biology<br />

students. A framework for teaching how to develop an agent-based model and<br />

examples <str<strong>on</strong>g>of</str<strong>on</strong>g> such models will be presented.<br />

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Reports from US - African BioMa<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Initiative: C<strong>on</strong>servati<strong>on</strong><br />

Biology; Saturday, July 2, 14:30<br />

Holly Gaff<br />

Old Domini<strong>on</strong> University<br />

e-mail: hgaff@odu.edu<br />

Sadie Ryan<br />

College <str<strong>on</strong>g>of</str<strong>on</strong>g> Envir<strong>on</strong>mental Science and Forestry, SUNY<br />

Overview: Reports from US - African BioMa<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

Initiative: C<strong>on</strong>servati<strong>on</strong> Biology<br />

How do you combine <str<strong>on</strong>g>th</str<strong>on</strong>g>e expertise <str<strong>on</strong>g>of</str<strong>on</strong>g> graduate students trained as ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematicians<br />

and c<strong>on</strong>servati<strong>on</strong> biologists, from two c<strong>on</strong>tinents, to explore important questi<strong>on</strong>s in<br />

African c<strong>on</strong>servati<strong>on</strong> biology? This questi<strong>on</strong> was at <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e US-African BioMa<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Initiative: C<strong>on</strong>servati<strong>on</strong> Biology, a jointly funded<br />

enterprise <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Center for Discrete Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Theoretical Computer Science<br />

(DIMACS), <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences Institute at Ohio State University<br />

(MBI), <str<strong>on</strong>g>th</str<strong>on</strong>g>e Society <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology (SMB), <str<strong>on</strong>g>th</str<strong>on</strong>g>e L<strong>on</strong>d<strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Society<br />

(LMS), and <str<strong>on</strong>g>th</str<strong>on</strong>g>e US Nati<strong>on</strong>al Science Foundati<strong>on</strong> (NSF). Two advanced studies<br />

institutes, or ASIs, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> guest lecturers, a follow-up workshop and fieldtrips to see,<br />

first-hand, <str<strong>on</strong>g>th</str<strong>on</strong>g>e local c<strong>on</strong>servati<strong>on</strong> needs in questi<strong>on</strong>, were held in Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Africa (2010)<br />

and Kenya (2011).<br />

Researchers working in <str<strong>on</strong>g>th</str<strong>on</strong>g>e fields <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and c<strong>on</strong>servati<strong>on</strong><br />

biology provided a series <str<strong>on</strong>g>of</str<strong>on</strong>g> lectures in populati<strong>on</strong> viability analysis, global climate<br />

change, harvesting, disease modeling, c<strong>on</strong>servati<strong>on</strong> genetics, remote sensing,<br />

reserve design, agent-based modeling and practical c<strong>on</strong>cerns in real-world c<strong>on</strong>servati<strong>on</strong><br />

and management. These lectures established a comm<strong>on</strong> background am<strong>on</strong>g<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e students, while examining <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> fields pertinent to research into questi<strong>on</strong>s<br />

in ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling in c<strong>on</strong>servati<strong>on</strong> biology. These lectures were augmented<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> computati<strong>on</strong>al exercises, in multiple s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware platforms, giving students<br />

hands-<strong>on</strong> experience and coded examples to build <strong>on</strong>. Students from <str<strong>on</strong>g>th</str<strong>on</strong>g>e US<br />

and ten African countries from <str<strong>on</strong>g>th</str<strong>on</strong>g>e fields <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, ecology, c<strong>on</strong>servati<strong>on</strong> biology,<br />

and wildlife and natural resource management came toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er for an intense<br />

week <str<strong>on</strong>g>of</str<strong>on</strong>g> training, reinforced and implemented in group projects.<br />

Projects were formulated, c<strong>on</strong>ceived and chosen by <str<strong>on</strong>g>th</str<strong>on</strong>g>e students, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> guidance<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e mentors. They included: agent-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> anti-poaching strategies<br />

am<strong>on</strong>gst villages wi<str<strong>on</strong>g>th</str<strong>on</strong>g> human-elephant c<strong>on</strong>flict, modifying epidemiological models<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> bovine tuberculosis in African buffalo to understand directed culling efforts in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

face <str<strong>on</strong>g>of</str<strong>on</strong>g> different transmissi<strong>on</strong> scenarios, modeling populati<strong>on</strong> viability and management<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> impacts <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e flamingoes in Lake Nakuru, spatial modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> landscape<br />

fragmentati<strong>on</strong> and elephant movement corridors in Kenya, to name a few. Projects<br />

were initiated at <str<strong>on</strong>g>th</str<strong>on</strong>g>e institutes, and plans for c<strong>on</strong>tinuing work, <str<strong>on</strong>g>th</str<strong>on</strong>g>rough email and<br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>er means <str<strong>on</strong>g>of</str<strong>on</strong>g> communicati<strong>on</strong>s were formalized and approved by faculty mentors.<br />

This mini-symposium is a product <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e initiative <str<strong>on</strong>g>th</str<strong>on</strong>g>at was not part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

original prospectus for funding. The initiative funded a follow-up institute to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

originally planned single combined institute and workshop. Faculty who would<br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>erwise not have met each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er have been inspired to collaboratively apply for<br />

funding to c<strong>on</strong>tinue teaching <str<strong>on</strong>g>th</str<strong>on</strong>g>ese institutes, and to c<strong>on</strong>duct joint research in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

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future. A minimum <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree publicati<strong>on</strong>s and 5 talks are resulting from student<br />

projects formed at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese institutes, so far, and established c<strong>on</strong>necti<strong>on</strong>s to <str<strong>on</strong>g>th</str<strong>on</strong>g>e Sou<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

African Wildlife College (SAWC) and Kenya Wildlife Services Training Institute<br />

(KWSTI) at Naivasha are spawning new ideas and project bases.<br />

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Turing !! Turing?? <strong>on</strong> morphogenesis via experimental and <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical<br />

approaches; Wednesday, June 29, 17:00<br />

Eam<strong>on</strong>n A. Gaffney<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: gaffney@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.oxa.c.uk<br />

Aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> Turing’s Pattern Formati<strong>on</strong> Mechanism On<br />

Growing Domains<br />

The prospect <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g range signalling by diffusible morphogens initiating large<br />

scale pattern formati<strong>on</strong> has been c<strong>on</strong>templated since <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial work <str<strong>on</strong>g>of</str<strong>on</strong>g> Turing<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e 1950s and has been explored <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretically and experimentally in numerous<br />

developmental settings. However, Turing ′ s pattern formati<strong>on</strong> mechanism exhibits<br />

sensitivity to <str<strong>on</strong>g>th</str<strong>on</strong>g>e details <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial c<strong>on</strong>diti<strong>on</strong>s suggesting <str<strong>on</strong>g>th</str<strong>on</strong>g>at, in isolati<strong>on</strong>, it cannot<br />

robustly generate pattern wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in noisy biological envir<strong>on</strong>ments. Aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> developmental<br />

self-organisati<strong>on</strong>, in particular a growing domain, have been suggested<br />

as a mechanism for robustly inducing a sequential cascade <str<strong>on</strong>g>of</str<strong>on</strong>g> self-organisati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>us<br />

circumventing <str<strong>on</strong>g>th</str<strong>on</strong>g>e difficulties <str<strong>on</strong>g>of</str<strong>on</strong>g> sensitivity. This propositi<strong>on</strong> is explored in detail<br />

for generalisati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Turing’s model which include fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er biological aspects, for<br />

example, <str<strong>on</strong>g>th</str<strong>on</strong>g>e inclusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong> dynamics or intrinsic noise.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Przemyslaw Gagat<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Genomics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Biotechnology, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Wroclaw, ul. Przybyszewskiego 63/77, 51-148 Wroclaw, Poland<br />

e-mail: gagat@smorfland.uni.wroc.pl<br />

Paweł Mackiewicz<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Genomics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Biotechnology, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Wroclaw, ul. Przybyszewskiego 63/77, 51-148 Wroclaw, Poland<br />

Andrzej Bodyl<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biodiversity and Evoluti<strong>on</strong>ary Tax<strong>on</strong>omy, Zoological<br />

Institute, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Wroclaw, ul. Przybyszewskiego 63/77, 51-148<br />

Wroclaw, Poland<br />

Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> protein targeting via endomembrane system to<br />

primary plastids<br />

Before 1.5 billi<strong>on</strong> years ago a heterotrophic eukaryotic ancestor <str<strong>on</strong>g>of</str<strong>on</strong>g> glaucophytes, red<br />

algae, and green plants engulfed cyanobacteria, which <str<strong>on</strong>g>th</str<strong>on</strong>g>en were transformed into<br />

primary plastids wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two envelope membranes. Gene transfer from <str<strong>on</strong>g>th</str<strong>on</strong>g>e cyanobacterial<br />

genome to <str<strong>on</strong>g>th</str<strong>on</strong>g>e host nucleus fostered <str<strong>on</strong>g>th</str<strong>on</strong>g>e integrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e endosymbi<strong>on</strong>t<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e host but it is still not clear how protein products <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transferred genes<br />

were initially transported back into <str<strong>on</strong>g>th</str<strong>on</strong>g>e ancestral primary plastid. At present, almost<br />

all proteins encoded by <str<strong>on</strong>g>th</str<strong>on</strong>g>e host nucleus are imported into primary plastids<br />

post-translati<strong>on</strong>ally using N-terminal transit peptides and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Toc and Tic transloc<strong>on</strong>s.<br />

Because <str<strong>on</strong>g>th</str<strong>on</strong>g>ese transloc<strong>on</strong>s c<strong>on</strong>sist <str<strong>on</strong>g>of</str<strong>on</strong>g> many specialized protein subunits, it is<br />

hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esized <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein import into <str<strong>on</strong>g>th</str<strong>on</strong>g>e ancestral plastid proceeded by a simpler<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e host endomembrane system involving <str<strong>on</strong>g>th</str<strong>on</strong>g>e endoplasmic<br />

reticulum (ER) and/or <str<strong>on</strong>g>th</str<strong>on</strong>g>e Golgi apparatus (GA). In accordance wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis,<br />

five known proteins wi<str<strong>on</strong>g>th</str<strong>on</strong>g> N-terminal signal peptides, which are directed to<br />

primary plastids in vesicles derived from <str<strong>on</strong>g>th</str<strong>on</strong>g>e endomembrane system, could be c<strong>on</strong>sidered<br />

relics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is primordial import pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way. To test if it is true, we performed<br />

phylogenetic analyses as well as applied o<str<strong>on</strong>g>th</str<strong>on</strong>g>er bioinformatics tools specialized in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> N-terminal targeting signals. Our analyses show <str<strong>on</strong>g>th</str<strong>on</strong>g>at all nuclearencoded<br />

plastid-targeted proteins wi<str<strong>on</strong>g>th</str<strong>on</strong>g> signal peptides are <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e eukaryotic (not<br />

cyanobacterial) origin and <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>eir homologs are equipped wi<str<strong>on</strong>g>th</str<strong>on</strong>g> signal peptides<br />

resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir co-translati<strong>on</strong>al import to <str<strong>on</strong>g>th</str<strong>on</strong>g>e ER. This indicates <str<strong>on</strong>g>th</str<strong>on</strong>g>at <strong>on</strong>ly a<br />

limited subset <str<strong>on</strong>g>of</str<strong>on</strong>g> host proteins, normally targeted to different secretory compartments,<br />

exploited <str<strong>on</strong>g>th</str<strong>on</strong>g>eir signal peptides to reach higher plant primary plastids via<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e endomembrane system. Thus, currently known plastid proteins wi<str<strong>on</strong>g>th</str<strong>on</strong>g> signal<br />

peptides cannot be c<strong>on</strong>sidered a relic <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e primordial plastid vesicular trafficking.<br />

The protein import into primary plastids was dominated right from <str<strong>on</strong>g>th</str<strong>on</strong>g>e beginning<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e gradually evolving Toc-Tic-based pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way while <str<strong>on</strong>g>th</str<strong>on</strong>g>e vesicular trafficking<br />

to primary plastids evolved sec<strong>on</strong>darily l<strong>on</strong>g after <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary endosymbiosis and<br />

probably <strong>on</strong>ly in <str<strong>on</strong>g>th</str<strong>on</strong>g>e land plant lineage.<br />

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Statistical Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Signals II; Saturday, July 2, 11:00<br />

Elżbieta Gajecka-Mirek<br />

State Higher Vocati<strong>on</strong>al School in Nowy Sącz<br />

e-mail: egajecka@pwsz-ns.edu.pl<br />

AR-Sieve Bootstrap Me<str<strong>on</strong>g>th</str<strong>on</strong>g>od and Its Applicati<strong>on</strong> in<br />

Biological Time Series<br />

The problem <str<strong>on</strong>g>of</str<strong>on</strong>g> estimating characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> time series is c<strong>on</strong>sidered. The<br />

bootstrap procedure, introduced by Bühlmann (1997), based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

autoregressive process sieve is used. AR(p(n)) model is fitted to <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed data<br />

and a bootstrap sample is generated by resampling from <str<strong>on</strong>g>th</str<strong>on</strong>g>e centered residuals.<br />

The autoregressive sieve bootstrap is alternative me<str<strong>on</strong>g>th</str<strong>on</strong>g>od to <str<strong>on</strong>g>th</str<strong>on</strong>g>e approach based <strong>on</strong><br />

asymptotic <str<strong>on</strong>g>th</str<strong>on</strong>g>eory. The AR-sieve bootstrap me<str<strong>on</strong>g>th</str<strong>on</strong>g>od was applied to medical data:<br />

Heart Rate time series.<br />

References.<br />

[1] P.J. Brockwell, R.A. Davis, Time Series: Theory and Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods Springer-Verlag, 1987.<br />

[2] P. Bülman, Botstrap for Time Series Statistical Science 2002, Vol. 17, No. 1 52–72.<br />

[3] P. Bülman, Sieve bootstrap for time series Bernoulli 3(2), 1997,123-148.<br />

[4] S.N. Lahiri, Resampling Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for Dependent Data Springer, 2003.<br />

[5] R.H. Shumway, D.S. St<str<strong>on</strong>g>of</str<strong>on</strong>g>fer Time Series Analysis and Its Applicati<strong>on</strong>sSpringer, 2006.<br />

[6] http://physi<strong>on</strong>et.org<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> physiological processes in patients <strong>on</strong> dialysis;<br />

Saturday, July 2, 11:00<br />

Magda Galach<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biocybernetics and Biomedical Engineering, PAS<br />

e-mail: mgalach@ibib.waw.pl<br />

Jacek Waniewski<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biocybernetics and Biomedical Engineering, PAS, Warsaw,<br />

Poland<br />

Ol<str<strong>on</strong>g>of</str<strong>on</strong>g> Heimburger<br />

Divisi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Baxter Novum and Renal Medicine, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Clinical<br />

Science, Interventi<strong>on</strong> and Technology, Karolinska Institutet,<br />

Stockholm, Sweden<br />

Daniel Schneditz<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physiology, Medical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Graz, Graz, Austria<br />

Andrzej Werynski<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biocybernetics and Biomedical Engineering, PAS<br />

Bengt Lindholm<br />

Divisi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Baxter Novum and Renal Medicine, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Clinical<br />

Science, Interventi<strong>on</strong> and Technology, Karolinska Institutet,<br />

Stockholm, Sweden.<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose-insulin system in patients <strong>on</strong> dialysis<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most comm<strong>on</strong> causes <str<strong>on</strong>g>of</str<strong>on</strong>g> end-stage renal disease (ESRD) worldwide is diabetes<br />

mellitus. According to <str<strong>on</strong>g>th</str<strong>on</strong>g>e US Renal Data System in 2005 above 44% <str<strong>on</strong>g>of</str<strong>on</strong>g> new<br />

ESRD patients were diabetics. The process <str<strong>on</strong>g>of</str<strong>on</strong>g> regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose c<strong>on</strong>centrati<strong>on</strong><br />

in blood is complicated and can be substantially affected by uremia and dialysis,<br />

which bo<str<strong>on</strong>g>th</str<strong>on</strong>g> may have an impact <strong>on</strong> secreti<strong>on</strong> and clearance <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose and insulin,<br />

and <strong>on</strong> insulin resistance leading to hypo- or hyperglycemia. Low levels <str<strong>on</strong>g>of</str<strong>on</strong>g> blood<br />

glucose may cause shock and dea<str<strong>on</strong>g>th</str<strong>on</strong>g>, while too high levels are toxic. Thus, it is<br />

essential <str<strong>on</strong>g>th</str<strong>on</strong>g>at glucose levels must be tightly regulated and an analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> dialysis (perit<strong>on</strong>eal dialysis wi<str<strong>on</strong>g>th</str<strong>on</strong>g> glucose-based soluti<strong>on</strong> and hemodialysis) <strong>on</strong><br />

plasma glucose and insulin c<strong>on</strong>centrati<strong>on</strong> is <str<strong>on</strong>g>of</str<strong>on</strong>g> great importance. A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model describing glucose-insulin regulati<strong>on</strong> was based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e models proposed by<br />

Stolwijk and Hardy (1974) and Tolic et al (2000). Two different sources <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose<br />

were taken into account: hepatic glucose producti<strong>on</strong> and an external source (e.g.<br />

food digesti<strong>on</strong>, intravenous glucose infusi<strong>on</strong> or transport between dialysis fluid in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e perit<strong>on</strong>eal cavity and blood). There are <str<strong>on</strong>g>th</str<strong>on</strong>g>ree types <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose utilizati<strong>on</strong>: 1)<br />

glucose leaves blood to enter most cells <str<strong>on</strong>g>th</str<strong>on</strong>g>rough facilitated diffusi<strong>on</strong> (insulin independent<br />

glucose utilizati<strong>on</strong>), 2) in certain types <str<strong>on</strong>g>of</str<strong>on</strong>g> cells (e.g. muscle and adipose<br />

tissue) insulin helps to stimulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e facilitated diffusi<strong>on</strong> process (insulin dependent<br />

glucose utilizati<strong>on</strong>), 3) glucose can be also excreted by <str<strong>on</strong>g>th</str<strong>on</strong>g>e kidneys. As regards insulin,<br />

two sources are taken into account: pancreatic insulin producti<strong>on</strong> c<strong>on</strong>trolled<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e glucose c<strong>on</strong>centrati<strong>on</strong> and external source <str<strong>on</strong>g>of</str<strong>on</strong>g> insulin (e.g. injecti<strong>on</strong>). Insulin<br />

is degradated <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a reacti<strong>on</strong> involving <str<strong>on</strong>g>th</str<strong>on</strong>g>e insulinase at a rate proporti<strong>on</strong>al to<br />

insulin c<strong>on</strong>centrati<strong>on</strong> in blood. All <str<strong>on</strong>g>th</str<strong>on</strong>g>ese assumpti<strong>on</strong>s are used in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mass balance<br />

equati<strong>on</strong> describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood c<strong>on</strong>centrati<strong>on</strong> changes <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose and insulin during<br />

dialysis (perit<strong>on</strong>eal dialysis and hemodialysis). The clinical parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

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glucose-insulin system, insulin sensitivity index and glucose effectiveness at basal<br />

and zero insulin (GEZI) were also estimated using clinical data from: 1) six hour<br />

perit<strong>on</strong>eal dialysis dwells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> glucose 3.86% soluti<strong>on</strong> performed in 13 stable, fasting,<br />

n<strong>on</strong>-diabetic patients, and 2) hemodialysis wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a bolus <str<strong>on</strong>g>of</str<strong>on</strong>g> 33% glucose infused<br />

into blood in 8 stable, n<strong>on</strong>-diabetic maintenance hemodialysis patients during <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

regular dialysis treatment. Computer simulati<strong>on</strong>s based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model were performed<br />

for each patient and each dialysis sessi<strong>on</strong> to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e model parameters.<br />

The mean values and standard deviati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters were calculated and<br />

compared for bo<str<strong>on</strong>g>th</str<strong>on</strong>g> studies. There were statistically significant differences between<br />

hemodialysis and perit<strong>on</strong>eal dialysis patients especially in <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters describing<br />

insulin regulati<strong>on</strong> such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e insulin catabolism rate and <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximal level <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

insulin generati<strong>on</strong>. Clinical and modeling results dem<strong>on</strong>strated high interpatient<br />

variability in glucose and insulin c<strong>on</strong>centrati<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles during a perit<strong>on</strong>eal dwell<br />

and during hemodialysis, and in <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter values <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e glucose-insulin system.<br />

The proposed model was able to adequately reproduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e clinical data <strong>on</strong><br />

glucose and insulin transport and plasma levels and to distinguish patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

and wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out abnormalities in glucose regulati<strong>on</strong>.<br />

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Jill Gallaher<br />

e-mail: jill.gallaher@m<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt.org<br />

Alexander R. A. Anders<strong>on</strong><br />

e-mail: alexander.anders<strong>on</strong>@m<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt.org<br />

Integrated Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Oncology,<br />

M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center,<br />

12902 Magnolia Dr., Tampa, FL 33612.<br />

Cancer; Saturday, July 2, 14:30<br />

Phenotypic inheritance transforms heterogeneity in tumor<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Cell-to-cell variati<strong>on</strong> is seen in almost all aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer from initiati<strong>on</strong> to<br />

invasi<strong>on</strong> and subsequent metastasis. Our current understanding at <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic scale<br />

gives little informati<strong>on</strong> <strong>on</strong> translating to actual changes in cell behavior, which<br />

will ultimately dictate tumor aggressiveness and treatability. Cell behavior can be<br />

described in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> phenotypic traits, e.g., proliferati<strong>on</strong>, migrati<strong>on</strong>, and apoptosis<br />

rates. Because <str<strong>on</strong>g>th</str<strong>on</strong>g>ese traits vary across a tumor populati<strong>on</strong> a useful way to represent<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>em is in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> distributi<strong>on</strong>s. How traits are passed <strong>on</strong> as cells divide and<br />

compete for space and resources affects how <str<strong>on</strong>g>th</str<strong>on</strong>g>e trait distributi<strong>on</strong>s evolve.<br />

An <str<strong>on</strong>g>of</str<strong>on</strong>g>f-lattice cellular automata model is built where cells are ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er initiated as<br />

a tight cluster, to simulate a growing tumor mass, or as a dispersed populati<strong>on</strong>, to<br />

represent a cell culture experiment. These initial spatial distributi<strong>on</strong>s give different<br />

outcomes and lead us to questi<strong>on</strong> how heterogeneity in vitro can be translated in<br />

vivo. We combine <str<strong>on</strong>g>th</str<strong>on</strong>g>e model’s trait distributi<strong>on</strong>s, repopulati<strong>on</strong> times, and morphological<br />

features wi<str<strong>on</strong>g>th</str<strong>on</strong>g> biological data to analyze how treatment resistance emerges<br />

and how it might be regulated.<br />

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Bioinformatics and System Biology; Wednesday, June 29, 14:30<br />

Joerg Galle<br />

Interdisciplinary Centre for Bioinformatics, University Leipzig<br />

e-mail: galle@izbi.uni-leipzig.de<br />

Lydia Steiner<br />

Interdisciplinary Centre for Bioinformatics, University Leipzig<br />

Hans Binder<br />

nterdisciplinary Centre for Bioinformatics, University Leipzig<br />

Transcripti<strong>on</strong>al regulati<strong>on</strong> by hist<strong>on</strong>e modificati<strong>on</strong>s<br />

Transcripti<strong>on</strong>al regulati<strong>on</strong> in cells makes use <str<strong>on</strong>g>of</str<strong>on</strong>g> diverse mechanisms to ensure <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

functi<strong>on</strong>al states can be maintained and adapted to variable envir<strong>on</strong>ments. Am<strong>on</strong>g<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese mechanisms are cis-regulatory modules and chromatin modificati<strong>on</strong>s. Unraveling<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e hierarchy <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese different layers <str<strong>on</strong>g>of</str<strong>on</strong>g> regulati<strong>on</strong> represents a challenge <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Molecular Systems Biology. We here introduce a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> genomewide<br />

transcripti<strong>on</strong>al regulati<strong>on</strong> governed by hist<strong>on</strong>e modificati<strong>on</strong>s. This model describes<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e binding <str<strong>on</strong>g>of</str<strong>on</strong>g> protein complexes to DNA which are capable <str<strong>on</strong>g>of</str<strong>on</strong>g> reading and<br />

writing hist<strong>on</strong>e marks. Cooperative molecular interacti<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein<br />

complexes, <str<strong>on</strong>g>th</str<strong>on</strong>g>e DNA and <str<strong>on</strong>g>th</str<strong>on</strong>g>e modified hist<strong>on</strong>es create a regulatory memory and<br />

allow for switch-like changes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e expressi<strong>on</strong> state <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e genome. We provide<br />

analytical results <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulatory states <strong>on</strong> i) <str<strong>on</strong>g>th</str<strong>on</strong>g>e (de-) modificati<strong>on</strong><br />

activity <str<strong>on</strong>g>of</str<strong>on</strong>g> hist<strong>on</strong>e (de-)me<str<strong>on</strong>g>th</str<strong>on</strong>g>ylases, ii) <str<strong>on</strong>g>th</str<strong>on</strong>g>e accessibility <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e DNA-binding<br />

regi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein complexes and iii) <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> hist<strong>on</strong>es <str<strong>on</strong>g>th</str<strong>on</strong>g>at act cooperatively;<br />

and discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular envir<strong>on</strong>ment <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese properties. We<br />

dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at according to our model proliferati<strong>on</strong> activity per se can switch<br />

expressi<strong>on</strong> states <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e genome as a c<strong>on</strong>sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> suppressed inheritance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

hist<strong>on</strong>e marks. We apply our model to transcripti<strong>on</strong>al regulati<strong>on</strong> by trxG- and<br />

PcG-binding to DNA. By analysing ChIP-seq data <str<strong>on</strong>g>of</str<strong>on</strong>g> mouse ESC we provide evidence<br />

for cooperative modes <str<strong>on</strong>g>of</str<strong>on</strong>g> hist<strong>on</strong>e modificati<strong>on</strong>s. Thereby, our data suggest a<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>reshold leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cooperative chromatin regi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> about 10kb which agrees<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e loop leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> an un-interrupted chromatin fibre. Our results provide new<br />

insights into genome-wide transcripti<strong>on</strong>al regulati<strong>on</strong> by hist<strong>on</strong>e modificati<strong>on</strong>s and<br />

represent a first step towards simulati<strong>on</strong> studies <strong>on</strong> changes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epigenome during<br />

ageing and disease.<br />

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Medical Physiology; Tuesday, June 28, 11:00<br />

Martina Gallenberger ∗<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Biometry, Helmholtz Zentrum München,<br />

Germany<br />

e-mail: martina.gallenberger@helmholtz-muenchen.de<br />

Burkhard A. Hense<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Biometry, Helmholtz Zentrum München,<br />

Germany<br />

Christina Kuttler<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Technical University Munich, Germany<br />

A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for glucose and insulin dynamics<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> direct c<strong>on</strong>necti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e β-cell cycle<br />

The term diabetes mellitus describes a group <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic diseases wi<str<strong>on</strong>g>th</str<strong>on</strong>g> persisting<br />

hyperglycemia as <str<strong>on</strong>g>th</str<strong>on</strong>g>e main symptom. Interest is increasingly focused <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e understanding<br />

and treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease because <str<strong>on</strong>g>of</str<strong>on</strong>g> its rising prevalence and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

variety <str<strong>on</strong>g>of</str<strong>on</strong>g> severe complicati<strong>on</strong>s. Recent experimental results indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>e relevance<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e β-cell cycle for <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> diabetes mellitus.<br />

We investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose, insulin and <str<strong>on</strong>g>th</str<strong>on</strong>g>e β-cell cycle<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary differential equati<strong>on</strong>s. The basis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

system is built by <str<strong>on</strong>g>th</str<strong>on</strong>g>ree different models. To analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> insulin <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

work <str<strong>on</strong>g>of</str<strong>on</strong>g> Grodsky [1] introducing a packet hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis for insulin storage has been<br />

modified. This has been c<strong>on</strong>nected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose (Topp et al. [2])<br />

and a model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e β-cell cycle based <strong>on</strong> Daukste et al. [3]. The advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

system c<strong>on</strong>sists in its explicit incorporati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e β-cell cycle wi<str<strong>on</strong>g>th</str<strong>on</strong>g> insulin directly<br />

enhancing <str<strong>on</strong>g>th</str<strong>on</strong>g>e replicati<strong>on</strong> rate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e presentati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model and its development will be introduced as well as its<br />

capability <str<strong>on</strong>g>of</str<strong>on</strong>g> accounting for metabolic failures in <str<strong>on</strong>g>th</str<strong>on</strong>g>e progressi<strong>on</strong> to diabetes.<br />

References.<br />

[1] Grodsky, G.M., A <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold distributi<strong>on</strong> hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis for packet storage <str<strong>on</strong>g>of</str<strong>on</strong>g> insulin and its ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

modeling, The Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Clinical Investigati<strong>on</strong> 51 (1972), 2047-2059<br />

[2] Topp, B., Promislow, K., De Vries, G., Miura, R.M., Finegood, D.T., A model <str<strong>on</strong>g>of</str<strong>on</strong>g> β-cell mass,<br />

insulin and glucose kinetics: pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways to diabetes, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology 206 (2000),<br />

605-619<br />

[3] Daukste, L., Basse, B., Bagueley, B.C., Wall, D.J.N., Using a stem cell and progeny model to<br />

illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship between cell cycle times <str<strong>on</strong>g>of</str<strong>on</strong>g> in vivo human tumour cell tissue populati<strong>on</strong>s,<br />

in vitro primary cultures and <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell lines derived from <str<strong>on</strong>g>th</str<strong>on</strong>g>em, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical<br />

Biology (2009), 1-9<br />

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Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

II; Tuesday, June 28, 14:30<br />

Alberto Gandolfi<br />

Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti" - CNR,<br />

Rome, Italy<br />

e-mail: alberto.gandolfi@iasi.cnr.it<br />

Alberto d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Oncology, Milan, Italy<br />

Vascularizati<strong>on</strong> and chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy: inferences from a simple<br />

model<br />

Most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e models <str<strong>on</strong>g>of</str<strong>on</strong>g> chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy are currently developed making <strong>on</strong>ly reference<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells. We propose to model chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy taking<br />

into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutual interacti<strong>on</strong> between tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e development<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tumor vasculature. By adopting a simple model for <str<strong>on</strong>g>th</str<strong>on</strong>g>is interacti<strong>on</strong>, and assuming<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficacy <str<strong>on</strong>g>of</str<strong>on</strong>g> a drug can be modulated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e vessel density, we studied<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>stant c<strong>on</strong>tinuous and bolus-based chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, and combined <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies in<br />

which a chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic drug is associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an antiangiogenic agent [1]. The<br />

model allows to represent <str<strong>on</strong>g>th</str<strong>on</strong>g>e vessel-disrupting activity <str<strong>on</strong>g>of</str<strong>on</strong>g> some standard chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic<br />

drugs, and shows, in case <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>stant c<strong>on</strong>tinuous drug administrati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

possibility <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple stable equilibria. The multistability suggests an explanati<strong>on</strong><br />

for some sudden losses <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trol observed during <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, and for <str<strong>on</strong>g>th</str<strong>on</strong>g>e beneficial<br />

effect <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular “pruning” exherted by antiangiogenic agents in combined <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy.<br />

References.<br />

[1] A. d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio and A. Gandolfi: Chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy <str<strong>on</strong>g>of</str<strong>on</strong>g> vascularised tumours: role <str<strong>on</strong>g>of</str<strong>on</strong>g> vessel density<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular "pruning", J. Theor. Biol. 2010, 264, 253-265.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Immunology; Wednesday, June 29, 17:00<br />

José A. García<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Preventive and Social Medicine, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Otago,<br />

PO Box 913, Dunedin 9054, New Zealand<br />

e-mail: jose.garcia@otago.ac.nz<br />

Aidin Jalilzadeh<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Otago, Dunedin<br />

9054, New Zealand<br />

e-mail: aidin_jalilzadeh@yahoo.com<br />

Boris Baeumer<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Otago, PO<br />

Box 913, Dunedin 9054, New Zealand<br />

e-mail: bbaeumer@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.otago.ac.nz<br />

A reinforced random walk model for studying <str<strong>on</strong>g>th</str<strong>on</strong>g>e acute<br />

inflammatory resp<strong>on</strong>se<br />

The <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> reinforced random walks (RRWs) provides a natural framework<br />

for modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e movement <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals. RRWs are in particular suitable for<br />

modelling cell motility in resp<strong>on</strong>se to <strong>on</strong>e or more c<strong>on</strong>trol substances [1]. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

past RRWs have been used to model angiogenesis and solid tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and<br />

metastasis [2, 3].<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we have developed a spatio-temporal ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model c<strong>on</strong>sisting<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a system <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong>-advecti<strong>on</strong>-reacti<strong>on</strong> equati<strong>on</strong>s, to capture some aspects<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tissue inflammatory resp<strong>on</strong>se. Two sorts <str<strong>on</strong>g>of</str<strong>on</strong>g> cell movement mechanisms are c<strong>on</strong>sidered:<br />

1. Chemotactic as <str<strong>on</strong>g>th</str<strong>on</strong>g>e major physiological effect <str<strong>on</strong>g>th</str<strong>on</strong>g>at leads <str<strong>on</strong>g>th</str<strong>on</strong>g>e movement<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> leukocytes towards <str<strong>on</strong>g>th</str<strong>on</strong>g>e site <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong>/inflammati<strong>on</strong>, 2. Leukocytes’ random<br />

motility described via diffusi<strong>on</strong> process. The proposed model accounts for (1) antigen<br />

recogniti<strong>on</strong>, (2) <str<strong>on</strong>g>th</str<strong>on</strong>g>e effector functi<strong>on</strong> (activati<strong>on</strong>/inhibiti<strong>on</strong>), (3) innate immune<br />

resp<strong>on</strong>se, (4) eliminati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> antigen and resoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong> and (5) returning<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e immune cells back to a steady state. In case <str<strong>on</strong>g>of</str<strong>on</strong>g> a persistent source <str<strong>on</strong>g>of</str<strong>on</strong>g> antigen,<br />

i.e. chr<strong>on</strong>ic infecti<strong>on</strong>, it is observed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune resp<strong>on</strong>se reaches an equilibrium<br />

level. 2-D Matlab simulati<strong>on</strong>s have enabled us to visualise <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e immune cells and chemicals.<br />

Our simulati<strong>on</strong>s could provide insights for better understanding complex diseases<br />

associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> chr<strong>on</strong>ic inflammati<strong>on</strong> like cancer and autoimmunity.<br />

References.<br />

[1] EA Codling, et al, Random walk models in biology J R Soc Interface (2008) 5 813–834.<br />

[2] MJ Plank and BD Sleeman, A reinforced random walk model <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour angiogenesis and<br />

anti-angiogenic strategies Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Med Biol (2003) 20 135–181.<br />

[3] ARA Anders<strong>on</strong>, et al, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour invasi<strong>on</strong> and metastasis Comp Ma<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g> Med (2000) 2 129–154.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Diana Garcia Lopez<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Manchester<br />

e-mail: diana.garcia@manchester.ac.uk<br />

Sam Brown<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Edinburgh<br />

Ben Quigley<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

Alan McKane<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Manchester<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Specialist-v-generalist host-parasite interacti<strong>on</strong>s: influence<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> bacteria-phage infecti<strong>on</strong><br />

The main models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetics underlying host-parasite infecti<strong>on</strong>s are <str<strong>on</strong>g>th</str<strong>on</strong>g>e matchingalleles<br />

(MA) and <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene-for-gene (GFG) models. These can be interpreted as two<br />

extremes <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>tinuum <str<strong>on</strong>g>th</str<strong>on</strong>g>at ranges from <strong>on</strong>e-to-<strong>on</strong>e specific matching in all hostparasite<br />

pairs (MA) to many-to-<strong>on</strong>e generalist interacti<strong>on</strong>s in some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese (GFG).<br />

We have incorporated <str<strong>on</strong>g>th</str<strong>on</strong>g>is variable degree <str<strong>on</strong>g>of</str<strong>on</strong>g> generalism into a simple epidemiological<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> bacteria by lytic phages, adopting a fully stochastic<br />

descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> dynamics and analyzing <str<strong>on</strong>g>th</str<strong>on</strong>g>e different dynamical<br />

regimes <str<strong>on</strong>g>th</str<strong>on</strong>g>at appear al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e MA-to-GFG c<strong>on</strong>tinuum.<br />

335

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Tuesday, June 28, 11:00<br />

Astrid Gasselhuber<br />

Medical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina; Vienna University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: astrid.gs@gmail.com<br />

Dieter Haemmerich<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Pediatric Cardiology, Medical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina,<br />

Charlest<strong>on</strong>, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina, USA; Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioengineering,<br />

Clems<strong>on</strong> University, Clems<strong>on</strong>, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina, USA<br />

Computati<strong>on</strong>al Model <str<strong>on</strong>g>of</str<strong>on</strong>g> Targeted Drug Delivery via<br />

Low-Temperature Sensitive Liposomes and image-guided<br />

focused ultrasound<br />

The chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic agent doxorubicin (DOX) is comm<strong>on</strong>ly used in cancer treatment,<br />

but causes dose limiting side effects. Various liposomal drug carriers were<br />

developed to overcome short plasma half-life and negative side effects <str<strong>on</strong>g>of</str<strong>on</strong>g> chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic<br />

agents. Low temperature sensitive liposomes (LTSL) release <str<strong>on</strong>g>th</str<strong>on</strong>g>eir c<strong>on</strong>tent<br />

<strong>on</strong>ly if exposed to a temperature above approximately 40 C and in c<strong>on</strong>trast release<br />

a relatively small amount <str<strong>on</strong>g>of</str<strong>on</strong>g> drug at normal body temperature. The combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

LTSL wi<str<strong>on</strong>g>th</str<strong>on</strong>g> local heat generated by image-guided focused ultrasound enables n<strong>on</strong>invasively<br />

targeted drug delivery. We developed an axial symmetric computati<strong>on</strong>al<br />

model to simulate temperature, blood perfusi<strong>on</strong>, and drug c<strong>on</strong>centrati<strong>on</strong>s in different<br />

compartments <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model. The model describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e release <str<strong>on</strong>g>of</str<strong>on</strong>g> drug from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e liposomes, transport mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug between different compartments<br />

and spatio-temporal drug and liposome c<strong>on</strong>centrati<strong>on</strong>s. We compared two cases:<br />

Tissue heated to hyper<str<strong>on</strong>g>th</str<strong>on</strong>g>ermic temperatures wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a target temperature <str<strong>on</strong>g>of</str<strong>on</strong>g> 43C, and<br />

hyper<str<strong>on</strong>g>th</str<strong>on</strong>g>ermia followed by a short high temperature exposure wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a target temperature<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> 68 C <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same regi<strong>on</strong>. Blood perfusi<strong>on</strong> was reduced <str<strong>on</strong>g>of</str<strong>on</strong>g> 7% <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e baseline<br />

value wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e heated area after hyper<str<strong>on</strong>g>th</str<strong>on</strong>g>ermia, whereas it was completely eliminated<br />

inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e target regi<strong>on</strong> in case <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e high-temperature exposure. Due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

eliminated blood flow drug is facilitated to remain trapped wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue. The<br />

plasma c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> DOX reached a peak value <str<strong>on</strong>g>of</str<strong>on</strong>g> 12.1 g/g at t=3 min in bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

cases. The intracellular c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> DOX during hyper<str<strong>on</strong>g>th</str<strong>on</strong>g>ermia followed by<br />

short high temperature exposure was almost two times higher <str<strong>on</strong>g>th</str<strong>on</strong>g>an hyper<str<strong>on</strong>g>th</str<strong>on</strong>g>ermia<br />

al<strong>on</strong>e wi<str<strong>on</strong>g>th</str<strong>on</strong>g> peak values <str<strong>on</strong>g>of</str<strong>on</strong>g> 18 g/g and 10 g/g, respectively. The complex interacti<strong>on</strong><br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>ermal cancer treatments and locally induced chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy agents,<br />

require a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship between heat exposure<br />

and pharmacokinetics in order to optimize drug delivery.<br />

336

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> gene regulati<strong>on</strong>; Tuesday, June 28, 11:00<br />

Tomas Gede<strong>on</strong><br />

M<strong>on</strong>tana State University<br />

e-mail: gede<strong>on</strong>@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.m<strong>on</strong>tana.edu<br />

Lisa Davis<br />

M<strong>on</strong>tana State University<br />

Modelling delays induced by transcripti<strong>on</strong> and translati<strong>on</strong><br />

Delays are always present In gene regulati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are increasingly finding <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

way into models <str<strong>on</strong>g>of</str<strong>on</strong>g> gene networks . In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I will discuss sources <str<strong>on</strong>g>of</str<strong>on</strong>g> delays in<br />

gene regulati<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>en c<strong>on</strong>centrate <strong>on</strong> our recent attempts to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e processes<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong> and translati<strong>on</strong>. The resulting models closely resemble old linear<br />

and n<strong>on</strong>linear traffic models.<br />

337

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Eva Gehrmann<br />

Technische Universität Darmstadt<br />

Institut für Festkörperphysik<br />

Hochschulstr. 6, 64289 Darmstadt<br />

e-mail: evachr@fkp.tu-darmstadt.de<br />

Barbara Drossel<br />

Technische Universität Darmstadt<br />

Institut für Festkörperphysik<br />

Hochschulstr. 6, 64289 Darmstadt<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Boolean versus c<strong>on</strong>tinuous dynamics <strong>on</strong> simple two-gene<br />

modules<br />

We investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> simple modules composed <str<strong>on</strong>g>of</str<strong>on</strong>g> two<br />

genes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two or <str<strong>on</strong>g>th</str<strong>on</strong>g>ree regulating c<strong>on</strong>necti<strong>on</strong>s. C<strong>on</strong>tinuous dynamics for mRNA<br />

and protein c<strong>on</strong>centrati<strong>on</strong>s is compared to a Boolean model for gene activity. Using<br />

a generalized me<str<strong>on</strong>g>th</str<strong>on</strong>g>od, we study wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a single framework different c<strong>on</strong>tinuous<br />

models and different types <str<strong>on</strong>g>of</str<strong>on</strong>g> regulatory functi<strong>on</strong>s, and establish c<strong>on</strong>diti<strong>on</strong>s under<br />

which <str<strong>on</strong>g>th</str<strong>on</strong>g>e system can display stable oscillati<strong>on</strong>s. These c<strong>on</strong>diti<strong>on</strong>s depend <strong>on</strong>ly <strong>on</strong><br />

general features such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relevant time scales, <str<strong>on</strong>g>th</str<strong>on</strong>g>e degree <str<strong>on</strong>g>of</str<strong>on</strong>g> cooperativity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulating interacti<strong>on</strong>s, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e logical structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s.<br />

Our results combine and generalize <str<strong>on</strong>g>th</str<strong>on</strong>g>e findings <str<strong>on</strong>g>of</str<strong>on</strong>g> several disc<strong>on</strong>nected previous<br />

studies.<br />

References.<br />

[1] Gross, Thilo and Feudel, Ulrike, Generalized models as a universal approach to <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear dynamical systems Physical Review E 73 (1) (2006).<br />

[2] Gehrmann, Eva and Drossel, Barbara, Boolean versus c<strong>on</strong>tinuous dynamics <strong>on</strong> simple twogene<br />

modules Physical Review E 82 (4) (2010).<br />

338

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Biological Systems; Tuesday, June 28, 17:00<br />

Richard Gejji<br />

Postdoc<br />

e-mail: rgejji@mbi.osu.edu<br />

Macroscopic model <str<strong>on</strong>g>of</str<strong>on</strong>g> reversing self-propelled bacteria<br />

Periodic reversals in systems <str<strong>on</strong>g>of</str<strong>on</strong>g> self-propelled rod shaped bacteria enable <str<strong>on</strong>g>th</str<strong>on</strong>g>em to<br />

effectively resolve traffic jams formed during swarming and maximize <str<strong>on</strong>g>th</str<strong>on</strong>g>eir swarming<br />

rate. A c<strong>on</strong>necti<strong>on</strong> is shown between a microscopic <strong>on</strong>e dimensi<strong>on</strong>al cell-based<br />

stochastic model <str<strong>on</strong>g>of</str<strong>on</strong>g> reversing n<strong>on</strong>-overlapping bacteria and a macroscopic n<strong>on</strong>-linear<br />

diffusi<strong>on</strong> equati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular density. Boltzmann-Matano analysis<br />

is used to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>linear diffusi<strong>on</strong> equati<strong>on</strong> corresp<strong>on</strong>ding to <str<strong>on</strong>g>th</str<strong>on</strong>g>e specific<br />

reversal frequency. A combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> microscopic and macroscopic models are used<br />

for studying swarming rates <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> bacteria reversing at different frequencies.<br />

Cell populati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high reversal frequencies are able to spread out<br />

effectively at high densities. If <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells rarely reverse, <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are able to spread<br />

out at lower densities but are less efficient at spreading out at higher densities.<br />

339

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Cell and Tissue Biophysics; Saturday, July 2, 11:00<br />

Uduak George<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sussex, Bright<strong>on</strong>, BN1 9QH,<br />

UK<br />

e-mail: ude20@sussex.ac.uk<br />

Angélique Stéphanou<br />

IN3S, Faculté de Médecine de Grenoble, 38706 La Tr<strong>on</strong>che cedex,<br />

France<br />

e-mail: angelique.stephanou@imag.fr<br />

Anotida Madzvamuse<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sussex, Bright<strong>on</strong>, BN1 9QH,<br />

UK<br />

e-mail: a.madzvamuse@sussex.ac.uk<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and numerical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> cell membrane<br />

deformati<strong>on</strong>s as a c<strong>on</strong>sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> actin dynamics<br />

Actin is a molecule <str<strong>on</strong>g>th</str<strong>on</strong>g>at exists in two different forms which can be m<strong>on</strong>omeric as<br />

globular actin (G-actin) or assembled into <str<strong>on</strong>g>th</str<strong>on</strong>g>e polar filamentous form (F-actin).<br />

It resides in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell cytoskelet<strong>on</strong> and plays an important role in c<strong>on</strong>trolling cell<br />

motility and maintaining cell shape [3]. Cell motility c<strong>on</strong>sist <str<strong>on</strong>g>of</str<strong>on</strong>g> numerous highly<br />

coordinated events which involve a combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chemical kinetics and physical<br />

forces, transport and movements <str<strong>on</strong>g>of</str<strong>on</strong>g> a polymer protein network interacting wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a<br />

vast number <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er proteins. These events can be treated ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically by combining<br />

models <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tinuum mechanics and biochemical kinetics [2]. These models<br />

have proven to be useful for decoding cell motility processes [1]. The model we c<strong>on</strong>sider<br />

is a system <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> a force balance equati<strong>on</strong> and a reacti<strong>on</strong>-diffusi<strong>on</strong><br />

equati<strong>on</strong> describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical properties and biochemical kinetic <str<strong>on</strong>g>of</str<strong>on</strong>g> actin respectively.<br />

We solve <str<strong>on</strong>g>th</str<strong>on</strong>g>e model equati<strong>on</strong>s by use <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e moving grid finite element<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>od whose key advantage is in its ability to treat moving boundary problems<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> pr<strong>on</strong>ounced curvature and is very beneficial in <str<strong>on</strong>g>th</str<strong>on</strong>g>e accurate representati<strong>on</strong><br />

and approximati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e shape <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. Assuming slow domain evoluti<strong>on</strong> we<br />

validate <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical results by comparing <str<strong>on</strong>g>th</str<strong>on</strong>g>e finite element soluti<strong>on</strong>s to <str<strong>on</strong>g>th</str<strong>on</strong>g>ose<br />

predicted by linear stability <str<strong>on</strong>g>th</str<strong>on</strong>g>eory. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical scheme computes<br />

spatially inhomogeneous steady state soluti<strong>on</strong>s which coincides wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ose predicted<br />

by linear stability <str<strong>on</strong>g>th</str<strong>on</strong>g>eory close to bifurcati<strong>on</strong> points [4].<br />

Far away from instability, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is model is able to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular<br />

actin dynamics and <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting shapes and movements <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane.<br />

In particular, by varying <str<strong>on</strong>g>th</str<strong>on</strong>g>e pressure coefficient and <str<strong>on</strong>g>th</str<strong>on</strong>g>e measure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tractile<br />

t<strong>on</strong>icity parameter, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model behaviour gives uniform expansi<strong>on</strong>s, c<strong>on</strong>tracti<strong>on</strong>s<br />

and irregular deformati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell membrane wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell centre staying mostly<br />

unchanged in <str<strong>on</strong>g>th</str<strong>on</strong>g>e majority <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cases c<strong>on</strong>sidered. The model also allow us to<br />

compare <str<strong>on</strong>g>th</str<strong>on</strong>g>e actin distributi<strong>on</strong> at <str<strong>on</strong>g>th</str<strong>on</strong>g>e vicinity where large deformati<strong>on</strong>s occur and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e results we obtain are found to be c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ose observed experimentally.<br />

References.<br />

[1] C. Franco, T. Tzvetkova-Chevolleau and A. Stéphanou, On <str<strong>on</strong>g>th</str<strong>on</strong>g>e Influence <str<strong>on</strong>g>of</str<strong>on</strong>g> Discrete Adhesive<br />

Patterns for Cell Shape and Motility: A Computati<strong>on</strong>al Approach Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Model. Nat. Phenom.<br />

(2010), 5(1):56-83.<br />

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[2] Alex Mogilner, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics <str<strong>on</strong>g>of</str<strong>on</strong>g> cell motility: have we got its number? J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. (2009),<br />

58:105-134.<br />

[3] Ville O. Paavilainen, Enni Bertling, Sandra Falck and Pekka Lappalainen, Regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cytoskeletal<br />

dynamics by actin-m<strong>on</strong>omer-binding proteins Trends in Cell Biology (2004), 14(7):<br />

386-394.<br />

[4] Uduak George, Angélique Stéphanou and Anotida Madzvamuse, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling and<br />

Numerical Simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Actin Dynamics in an Eukaryotic cell. In preparati<strong>on</strong>.<br />

341

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Immunology; Wednesday, June 29, 14:30<br />

Sebastian Gerdes<br />

Institute for Medical Informatics and Biometry, Medical Faculty Carl<br />

Gustav Carus, Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: sebastian.gerdes@tu-dresden.de<br />

Ingmar Glauche<br />

Institute for Medical Informatics and Biometry, Medical Faculty Carl<br />

Gustav Carus, Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: ingmar.glauche@tu-dresden.de<br />

Ingo Roeder<br />

Institute for Medical Informatics and Biometry, Medical Faculty Carl<br />

Gustav Carus, Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: ingo.roeder@tu-dresden.de<br />

Can polycl<strong>on</strong>ality prevent <str<strong>on</strong>g>th</str<strong>on</strong>g>e outbreak <str<strong>on</strong>g>of</str<strong>on</strong>g> leukemia?<br />

T cell receptor (TCR) polycl<strong>on</strong>al mature T cells are surprisingly resistant to<br />

<strong>on</strong>cogenic transformati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough retroviral inducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> T cell <strong>on</strong>cogenes. It has<br />

been shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at leukemia/lymphoma did not occur up<strong>on</strong> transplantati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> polycl<strong>on</strong>al<br />

T cells into RAG1-1-deficient recipients, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e T-cells were transduced<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high copy numbers <str<strong>on</strong>g>of</str<strong>on</strong>g> gammaretroviral vectors encoding potent T cell <strong>on</strong>cogenes<br />

[1]. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er studies dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e transplantati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> T cells from<br />

TCR m<strong>on</strong>ocl<strong>on</strong>al OT1 mice <str<strong>on</strong>g>th</str<strong>on</strong>g>at were transduced wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same protocol resulted<br />

in leukemia/lymphoma. The underlying mechanisms <str<strong>on</strong>g>th</str<strong>on</strong>g>at prevent <strong>on</strong>cogenesis in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e polycl<strong>on</strong>al situati<strong>on</strong> and endorse <str<strong>on</strong>g>th</str<strong>on</strong>g>e outbreak <str<strong>on</strong>g>of</str<strong>on</strong>g> leukemia in <str<strong>on</strong>g>th</str<strong>on</strong>g>e m<strong>on</strong>ocl<strong>on</strong>al<br />

situati<strong>on</strong> are currently unclear.<br />

Using a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling approach, we challenge <str<strong>on</strong>g>th</str<strong>on</strong>g>e arising hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at polycl<strong>on</strong>ality induces competiti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e T cell repertoire, which in turn<br />

suppresses <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> a leukemic cl<strong>on</strong>e. As a starting point, we developed a<br />

simple model <str<strong>on</strong>g>of</str<strong>on</strong>g> T cell homeostasis emphasizing <str<strong>on</strong>g>th</str<strong>on</strong>g>e analogy <str<strong>on</strong>g>of</str<strong>on</strong>g> T cell homeostasis<br />

to species coexisting in ecological niches. The key assumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

T cell survival is critically dependent <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cl<strong>on</strong>e-specific TCR<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> self-peptide-MHC-complexes (corresp<strong>on</strong>ding to envir<strong>on</strong>mental niches).<br />

Based <strong>on</strong> our modelling results, we speculate about <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

leukemic cl<strong>on</strong>e. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in our model framework, we are able to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed<br />

phenomena under <str<strong>on</strong>g>th</str<strong>on</strong>g>e following two assumpti<strong>on</strong>s about <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

leukemic cl<strong>on</strong>e: (i) The leukemic cl<strong>on</strong>e is less competent <str<strong>on</strong>g>th</str<strong>on</strong>g>an o<str<strong>on</strong>g>th</str<strong>on</strong>g>er T cell cl<strong>on</strong>es in<br />

acquiring survival stimuli from niches. (ii) Proliferati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e leukemic cl<strong>on</strong>e is less<br />

dependent <strong>on</strong> niche interacti<strong>on</strong>. This is a plausible assumpti<strong>on</strong> as <str<strong>on</strong>g>th</str<strong>on</strong>g>e transgenes<br />

are potent <strong>on</strong>cogenes capable <str<strong>on</strong>g>of</str<strong>on</strong>g> activating mitotic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways.<br />

From our results we c<strong>on</strong>clude, <str<strong>on</strong>g>th</str<strong>on</strong>g>at cl<strong>on</strong>al competiti<strong>on</strong> is a possible mechanism<br />

to counterbalance cl<strong>on</strong>al dominance. Our modeling results allow us to foster <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

design <str<strong>on</strong>g>of</str<strong>on</strong>g> fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er biological experiments. A future goal is to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e minimum<br />

cl<strong>on</strong>al complexity <str<strong>on</strong>g>th</str<strong>on</strong>g>at is needed in order to c<strong>on</strong>trol <str<strong>on</strong>g>th</str<strong>on</strong>g>e leukemic cl<strong>on</strong>e under <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

given circumstances.<br />

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References.<br />

[1] Newrzela S, Cornils K et al. Resistance <str<strong>on</strong>g>of</str<strong>on</strong>g> mature T cells to <strong>on</strong>cogene transformati<strong>on</strong>. Blood.<br />

2008;112(6):2278–2286.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

III; Tuesday, June 28, 17:00<br />

C. Gerin1 , M. Badoual1 , C. Deroulers1 , B. Grammaticos1 , J. Pallud2,3 ,<br />

E. Mand<strong>on</strong>net4 1IMNC, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Paris VII-Paris XI, CNRS, UMR 8165, Orsay,<br />

France<br />

2Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Neurosurgery, Sainte-Anne Hospital, Paris, France<br />

3University René Descartes Paris-V, Paris, France<br />

4Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Neurosurgery, Lariboisière Hospital, Paris, France<br />

e-mail: gerin@imnc.in2p3.fr<br />

When do a low-grade glioma appear?<br />

Gliomas are <str<strong>on</strong>g>th</str<strong>on</strong>g>e most comm<strong>on</strong> tumour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e brain. The problem <str<strong>on</strong>g>of</str<strong>on</strong>g> WHO grade<br />

II and higher gliomas is <str<strong>on</strong>g>th</str<strong>on</strong>g>e infiltrati<strong>on</strong>: it is not possible to see <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole tumour<br />

<strong>on</strong> a MRI examinati<strong>on</strong> because a part <str<strong>on</strong>g>of</str<strong>on</strong>g> it is underside <str<strong>on</strong>g>th</str<strong>on</strong>g>e detecti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold [1].<br />

Inevitably an anaplastic transformati<strong>on</strong> occurs, <str<strong>on</strong>g>th</str<strong>on</strong>g>at rapidly causes <str<strong>on</strong>g>th</str<strong>on</strong>g>e demise <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e patient.<br />

A recent clinical study showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> low-grade gliomas appears<br />

linear, at roughly 2 mm/yr [2]. Is it possible to assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at it is always true ?<br />

Using <str<strong>on</strong>g>th</str<strong>on</strong>g>is property, can we extrapolate <str<strong>on</strong>g>th</str<strong>on</strong>g>e date <str<strong>on</strong>g>of</str<strong>on</strong>g> bir<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> gliomas ? To answer<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is questi<strong>on</strong>s, we use a diffusi<strong>on</strong>-proliferati<strong>on</strong> model, employed wi<str<strong>on</strong>g>th</str<strong>on</strong>g> success for<br />

high-grade gliomas [3]. It is a simple model (few parameters) <str<strong>on</strong>g>th</str<strong>on</strong>g>at can explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

c<strong>on</strong>stant velocity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fr<strong>on</strong>t visible wi<str<strong>on</strong>g>th</str<strong>on</strong>g> MRI at large times.<br />

This model is based <strong>on</strong> a partial differential equati<strong>on</strong> where <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tumour cells is determined by <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong> and by <str<strong>on</strong>g>th</str<strong>on</strong>g>e proliferati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells.<br />

We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour is symmetric and begins wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a single cell.<br />

The model predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> a "silent period": <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour is growing,<br />

but remains under <str<strong>on</strong>g>th</str<strong>on</strong>g>e detecti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold and <str<strong>on</strong>g>th</str<strong>on</strong>g>us it is not visible. A c<strong>on</strong>sequence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is phase is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e extrapolati<strong>on</strong> always underestimates <str<strong>on</strong>g>th</str<strong>on</strong>g>e age <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour<br />

predicted by <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong>-proliferati<strong>on</strong> model.<br />

We analyse data <strong>on</strong> real-life patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model. We estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e age <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour at <str<strong>on</strong>g>th</str<strong>on</strong>g>e time <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e first MRI examinati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e age <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e patient at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

<strong>on</strong>set <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour and <str<strong>on</strong>g>th</str<strong>on</strong>g>e coefficients <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong> and proliferati<strong>on</strong>.<br />

We also apply <str<strong>on</strong>g>th</str<strong>on</strong>g>e model to patients who do not present symptoms, and we<br />

find, as expected, <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour age at time <str<strong>on</strong>g>of</str<strong>on</strong>g> MRI is smaller <str<strong>on</strong>g>th</str<strong>on</strong>g>an in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> symptomatic patients.<br />

References.<br />

[1] J. Pallud, P. Varlet,B. Devaux, S. Geha, M. Badoual, C. Deroulers, P. Page, E. Dezamis, C.<br />

Daumas-Duport, and F.-X. Roux Diffuse low-grade oligodendrogliomas extend bey<strong>on</strong>d MRIdefined<br />

abnormalities Neurology 74 1724-1731,2010.<br />

[2] E. Mand<strong>on</strong>net, J. Y. Delattre, M. L. Tanguy, K. R. Swans<strong>on</strong>, A. F. Carpentier, H. Duffau, P.<br />

Cornu, R. Van Effenterre, E. C. Jr. Alvord and L. Capelle C<strong>on</strong>tinuous grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> mean tumor<br />

diameter in a subset <str<strong>on</strong>g>of</str<strong>on</strong>g> grade II gliomas Annals <str<strong>on</strong>g>of</str<strong>on</strong>g> Neurology 53 524–528 2003.<br />

[3] K. R. Swans<strong>on</strong>, E. C. Alvord, and J. D. Murray. A quantitative model for differential motility<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> gliomas in grey and white matter Cell Prolif 33(5) 317–329 2000.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Saturday, July 2, 14:30<br />

Philip Gerlee<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg<br />

e-mail: philip.gerlee@gu.se<br />

Sven Nelander<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg<br />

e-mail: sven.nelander@gu.se<br />

The impact <str<strong>on</strong>g>of</str<strong>on</strong>g> phenotypic switching <strong>on</strong> glioma grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is c<strong>on</strong>tingent <strong>on</strong> numerous intra-cellular and extra-cellular processes,<br />

such as an elevated rate <str<strong>on</strong>g>of</str<strong>on</strong>g> proliferati<strong>on</strong>, evasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> apoptosis and angiogenesis<br />

[1]. Out <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese, proliferati<strong>on</strong> has traditi<strong>on</strong>ally been singled out as <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

most important, and has generally been <str<strong>on</strong>g>th</str<strong>on</strong>g>e target <str<strong>on</strong>g>of</str<strong>on</strong>g> anti-cancer <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies. Recently,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ere has been a growing interest in <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cell motility, and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is is especially true in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> glioblastoma, which generally exhibit diffuse<br />

morphologies stemming from <str<strong>on</strong>g>th</str<strong>on</strong>g>e high motility <str<strong>on</strong>g>of</str<strong>on</strong>g> individual glioma cells.<br />

In order to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>is phenomen<strong>on</strong>, we propose a 3-dimensi<strong>on</strong>al cellular<br />

automat<strong>on</strong> model, which describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> a glioma c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> up 10 6<br />

cells. In accordance wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e go or grow hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis [2] each cell can be ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er in a<br />

proliferating or motile state. The switching between <str<strong>on</strong>g>th</str<strong>on</strong>g>e states is achieved by means<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a two-state Markov chain wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in each cell, characterised by two parameters pm,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>of</str<strong>on</strong>g> remaining in <str<strong>on</strong>g>th</str<strong>on</strong>g>e motile state, and pp <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding parameter<br />

for proliferati<strong>on</strong>. Simulating <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular automat<strong>on</strong> and by sweeping <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter<br />

space <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e phenotypic switching model we find <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e most invasive tumours<br />

(i.e. wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e highest grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate) occur at (pm, pp) ≈ (0.9, 0.9), i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are<br />

characterised by bo<str<strong>on</strong>g>th</str<strong>on</strong>g> proliferative and motile behaviour, and by a high degree <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

phenotypic persistence. We also find <str<strong>on</strong>g>th</str<strong>on</strong>g>at for each pp ∈ [0, 1] <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a pm = 0 such<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate is maximised.<br />

These observati<strong>on</strong>s are in agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental results, where glioma<br />

cell lines wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a lower proliferative capacity have been observed to rise to larger<br />

tumours when implanted in mice [3]. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er it suggest cancer cell motility as a<br />

potential target for <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy.<br />

References.<br />

[1] Hanahan, D., Weinberg, R., 2000. The hallmarks <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer. Cell 100:57–70.<br />

[2] A. Giese, R. Bjerkvig, M.E. Berens and M Westphal, 2003. Cost <str<strong>on</strong>g>of</str<strong>on</strong>g> migrati<strong>on</strong>: invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

malignant gliomas and implicati<strong>on</strong>s for treatment. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Clinical Oncology 8:1624–1636.<br />

[3] R. Chen et al. 2010. A Hierarchy <str<strong>on</strong>g>of</str<strong>on</strong>g> Self-Renewing Tumor-Initiating Cell Types in Glioblastoma.<br />

Cancer Cell 17:362–375.<br />

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Epidemiology, Eco-Epidemiology and Evoluti<strong>on</strong>; Saturday, July 2, 11:00<br />

Philip Gerrish<br />

CMAF, Lisb<strong>on</strong> University<br />

e-mail: pgerrish@unm.edu<br />

Genomic mutati<strong>on</strong> rates <str<strong>on</strong>g>th</str<strong>on</strong>g>at cause extincti<strong>on</strong>: general<br />

evoluti<strong>on</strong>ary predicti<strong>on</strong>s<br />

When mutati<strong>on</strong> rates are low, increasing <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutati<strong>on</strong> rate can give rise to an increase<br />

in adaptati<strong>on</strong> rate. If mutati<strong>on</strong> rate is increased fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er, however, a point<br />

may be reached at which fitness declines despite c<strong>on</strong>tinued adaptive and/or compensatory<br />

evoluti<strong>on</strong>. If fitness decline persists, it intuitively culminates in populati<strong>on</strong><br />

extincti<strong>on</strong>. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical formalizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is criteri<strong>on</strong> for extincti<strong>on</strong> gives rise to<br />

a simple relati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at puts a dynamic upper limit <strong>on</strong> viable mutati<strong>on</strong> rates. The<br />

particular ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical guise <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is relati<strong>on</strong> suggests encompassing generality,<br />

which we c<strong>on</strong>firm using individual-based simulati<strong>on</strong>s. Additi<strong>on</strong>ally, we re-derive<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e classical "error <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold" formula and show, by proxy, <str<strong>on</strong>g>th</str<strong>on</strong>g>at it is similarly general<br />

when used dynamically an attribute not previously recognized. Finally, we<br />

dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>e utility <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e insights gained from <str<strong>on</strong>g>th</str<strong>on</strong>g>ese developments wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an<br />

example applicati<strong>on</strong> to immunology.<br />

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Stochastic models in computati<strong>on</strong>al neuroscience I; Wednesday, June 29, 14:30<br />

Wulfram Gerstner<br />

Richard Naud<br />

Skander Mensi<br />

Christian Pozzorini<br />

EPFL Lausanne<br />

e-mail: wulfram.gerstner@epfl.ch<br />

Predicting acti<strong>on</strong> potentials and membrane potential <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

neur<strong>on</strong>s<br />

If neur<strong>on</strong>s receive a current <str<strong>on</strong>g>th</str<strong>on</strong>g>at is generated by a filtered point process, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey fire<br />

spikes at specific moments in time, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> little variati<strong>on</strong> from <strong>on</strong>e trial to <str<strong>on</strong>g>th</str<strong>on</strong>g>e next.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talks I will discuss<br />

(i) how to compare spike trains and measure reliability<br />

(ii) how to extract adaptative currents from <str<strong>on</strong>g>th</str<strong>on</strong>g>e data<br />

(iii) how to systematicaly c<strong>on</strong>struct neur<strong>on</strong> models from simple models to more<br />

complex <strong>on</strong>es.<br />

347

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Delay Differential Equati<strong>on</strong>s and Applicati<strong>on</strong>s I; Friday, July 1, 14:30<br />

Philipp Getto<br />

BCAM Basque Center For Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

e-mail: phgetto@yahoo.com<br />

A differential equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> state-dependent delay from cell<br />

populati<strong>on</strong> dynamics<br />

The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is research is an analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e maturati<strong>on</strong> process <str<strong>on</strong>g>of</str<strong>on</strong>g> stem cell populati<strong>on</strong>s.<br />

The regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is process leads to a descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong><br />

dynamics as a differential equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> state-dependent delay, i.e., an object <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

great ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical challenge. We show for <str<strong>on</strong>g>th</str<strong>on</strong>g>is system well-posedness and give<br />

some results <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> equilibria.<br />

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Populati<strong>on</strong> Dynamics; Tuesday, June 28, 17:00<br />

Wayne M. Getz<br />

Dept. Envir<strong>on</strong>mental Science, Policy and Management<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> California at Berkeley, CA 94720-3114, USA<br />

e-mail: getz@nature.berkeley.edu<br />

A Biomass Flow Approach to Populati<strong>on</strong> Models and Food<br />

Webs<br />

The dominant differential equati<strong>on</strong> paradigm for modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> species interacting in <str<strong>on</strong>g>th</str<strong>on</strong>g>e framework <str<strong>on</strong>g>of</str<strong>on</strong>g> a food web retains at its core<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e basic prey-predator and competiti<strong>on</strong> models formulati<strong>on</strong> by Alfred J. Lotka<br />

(1880-1945) and Vito Volterra (1860-1940) nearly nine decades ago. This framework<br />

lacks a trophic-level-independent formulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> leading<br />

to ambiguities in how to treat populati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at are simultaneously bo<str<strong>on</strong>g>th</str<strong>on</strong>g> prey and<br />

predator. Also, it does not fundamentally include inertial processes needed to account<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong>s to fluctuating resource envir<strong>on</strong>ments. Here I<br />

present an approach <str<strong>on</strong>g>th</str<strong>on</strong>g>at corrects bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese deficits and provides a unified framework<br />

for accounting for biomass transformati<strong>on</strong> in food webs <str<strong>on</strong>g>th</str<strong>on</strong>g>at include bo<str<strong>on</strong>g>th</str<strong>on</strong>g> live<br />

and dead comp<strong>on</strong>ents <str<strong>on</strong>g>of</str<strong>on</strong>g> all species in <str<strong>on</strong>g>th</str<strong>on</strong>g>e system. This biomass transformati<strong>on</strong><br />

formulati<strong>on</strong> (BTW) allows for a unified treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> webs <str<strong>on</strong>g>th</str<strong>on</strong>g>at include c<strong>on</strong>sumers<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> live and dead material—bo<str<strong>on</strong>g>th</str<strong>on</strong>g> carnivores and carcassivores, herbivores and<br />

detrivores—and incorporates scavengers, parasites, and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er neglected food web<br />

c<strong>on</strong>sumpti<strong>on</strong> categories in a coherent manner. I trace how BTW is an outgrow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e metaphysiological grow<str<strong>on</strong>g>th</str<strong>on</strong>g> modeling paradigm and provide a general compact<br />

formulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> BTW in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> a live/dead/deficit-stress <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-variable differential<br />

equati<strong>on</strong> formulati<strong>on</strong> for each species in <str<strong>on</strong>g>th</str<strong>on</strong>g>e food web. I <str<strong>on</strong>g>th</str<strong>on</strong>g>en illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is new paradigm to provide insights into two-species competiti<strong>on</strong><br />

in variable envir<strong>on</strong>ments and discuss applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> BTW to food webs <str<strong>on</strong>g>th</str<strong>on</strong>g>at incorporate<br />

parasites and pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Atiyo Ghosh<br />

Leiden University<br />

e-mail: ghosh@cml.leidenuniv.nl<br />

Populati<strong>on</strong> Dynamics; Saturday, July 2, 11:00<br />

Quantifying Stochastic Introgressi<strong>on</strong> Processes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Hazard<br />

Rates<br />

Introgressi<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>e permanent incorporati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genes from <strong>on</strong>e populati<strong>on</strong> into<br />

ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er. It has become <str<strong>on</strong>g>of</str<strong>on</strong>g> particular c<strong>on</strong>cern wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e advent <str<strong>on</strong>g>of</str<strong>on</strong>g> genetically modified<br />

crops, since <str<strong>on</strong>g>th</str<strong>on</strong>g>e introgressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genetically modified crop genes into <str<strong>on</strong>g>th</str<strong>on</strong>g>eir wild<br />

relatives could have adverse effects <strong>on</strong> local biodiversity. Modeling introgressi<strong>on</strong><br />

can become a difficult task, compounded by stochasticity <strong>on</strong> several levels, from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> certain plants, to different wea<str<strong>on</strong>g>th</str<strong>on</strong>g>er patterns. This talk<br />

outlines how a branching process based approach can be used to derive a measure<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> risk <str<strong>on</strong>g>of</str<strong>on</strong>g> introgressi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e hazard rate, which is <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability per generati<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at introgressi<strong>on</strong> occurs given it hasn’t occurred before. Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to calculate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

hazard rate wi<str<strong>on</strong>g>th</str<strong>on</strong>g> randomness <strong>on</strong> different levels, from individual to envir<strong>on</strong>mental,<br />

form <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e talk.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Heart rate dynamics: models and measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity (part I);<br />

Wednesday, June 29, 14:30<br />

J. Gierałtowski<br />

Cardiovascular Physics Group, Physics <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Systems Divisi<strong>on</strong>,<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, Warsaw University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: gieraltowski@if.pw.edu.pl<br />

J. J. Żebrowski<br />

Cardiovascular Physics Group, Physics <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Systems Divisi<strong>on</strong>,<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, Warsaw University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

R. Baranowski<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Cardiology, Warsaw<br />

Generalized multifractal analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> heart rate variability<br />

recordings wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a large number <str<strong>on</strong>g>of</str<strong>on</strong>g> arrhy<str<strong>on</strong>g>th</str<strong>on</strong>g>mia<br />

The regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> human heart rate is <str<strong>on</strong>g>th</str<strong>on</strong>g>e result <str<strong>on</strong>g>of</str<strong>on</strong>g> many inputs e.g. <str<strong>on</strong>g>th</str<strong>on</strong>g>e activity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sympa<str<strong>on</strong>g>th</str<strong>on</strong>g>etic and parasympa<str<strong>on</strong>g>th</str<strong>on</strong>g>etic nervous system, respirati<strong>on</strong> and its c<strong>on</strong>trol<br />

or such pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologies as ectopic activity or delayed c<strong>on</strong>ducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cardiac tissue - each<br />

having its own characteristic time scale and magnitude. The MF-DFA (MultiFractal<br />

Detrended Fluctuati<strong>on</strong> Analysis) me<str<strong>on</strong>g>th</str<strong>on</strong>g>od used by us allows to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e different c<strong>on</strong>trols systems and pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologies. Because it requires stati<strong>on</strong>arity <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is applied in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature to heart rate variability recordings wi<str<strong>on</strong>g>th</str<strong>on</strong>g> less <str<strong>on</strong>g>th</str<strong>on</strong>g>an<br />

5% <str<strong>on</strong>g>of</str<strong>on</strong>g> arrhy<str<strong>on</strong>g>th</str<strong>on</strong>g>mia.<br />

We analyzed <str<strong>on</strong>g>th</str<strong>on</strong>g>e published MF-DFA me<str<strong>on</strong>g>th</str<strong>on</strong>g>od, using syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic data and chosen<br />

RR intervals series. We developed an original, generalized versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e MF-DFA<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>od - multiscale multifractal analysis MMA. We found <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e calculati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e f(α) curve is a major source <str<strong>on</strong>g>of</str<strong>on</strong>g> artifacts. We <str<strong>on</strong>g>th</str<strong>on</strong>g>us focused <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e local Hurst exp<strong>on</strong>ent h <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e multifractal parameter q: h(q) and we allowed<br />

it to depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e scale s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard MF-DFA <str<strong>on</strong>g>th</str<strong>on</strong>g>e time scale s is fixed,<br />

somewhat arbitrarily (usually from 50 intervals up to 500). Thus, we obtained <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

h(q, s) dependence - a surface - <str<strong>on</strong>g>th</str<strong>on</strong>g>e shape <str<strong>on</strong>g>of</str<strong>on</strong>g> which tells us what is <str<strong>on</strong>g>th</str<strong>on</strong>g>e magnitude <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e fluctuati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>e RR intervals have in different time scales (different frequency<br />

bands). MMA was found to be immune to noise c<strong>on</strong>taminati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e data (we<br />

tested up to 50% <str<strong>on</strong>g>of</str<strong>on</strong>g> noise). It also allows to study heart rate variability wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an<br />

arbitrary level <str<strong>on</strong>g>of</str<strong>on</strong>g> arrhy<str<strong>on</strong>g>th</str<strong>on</strong>g>mia required for clinical applicati<strong>on</strong>s.<br />

We analyzed 51 24-hour recordings <str<strong>on</strong>g>of</str<strong>on</strong>g> heart rate variability (36 males age 16-64,<br />

15 females age 11-57: 42 heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y pers<strong>on</strong>s, 9 cardiac arrest cases including 5 wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out<br />

organic heart disease). We did not remove arrhy<str<strong>on</strong>g>th</str<strong>on</strong>g>mia from <str<strong>on</strong>g>th</str<strong>on</strong>g>e recordings. We<br />

limited <str<strong>on</strong>g>th</str<strong>on</strong>g>e study to <str<strong>on</strong>g>th</str<strong>on</strong>g>e night hours to avoid arbitrary daytime activity. Our<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical criteri<strong>on</strong> was able to distinguish, in a blind test, heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y subjects<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e high risk cardiac arrest cases including <str<strong>on</strong>g>th</str<strong>on</strong>g>ose wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out organic disease.<br />

The different peculiarities <str<strong>on</strong>g>of</str<strong>on</strong>g> each recording have a unique effect <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e results <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e multiscale MF-DFA analysis e.g. <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> arrhy<str<strong>on</strong>g>th</str<strong>on</strong>g>mia may readily be<br />

identified from <str<strong>on</strong>g>th</str<strong>on</strong>g>e results. Thus, <str<strong>on</strong>g>th</str<strong>on</strong>g>e new me<str<strong>on</strong>g>th</str<strong>on</strong>g>od allows to recognize and assign<br />

a complexity measure to features <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart rate variability which hi<str<strong>on</strong>g>th</str<strong>on</strong>g>erto went<br />

unnoticed when using standard, linear diagnostic me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods and MF-DFA.<br />

References.<br />

351

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[1] J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, H. E. Stanley,<br />

Multifractal detrended fluctuati<strong>on</strong> analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>stati<strong>on</strong>ary time series Physica A 316 87.<br />

[2] A. Saichev, D. Sornette, Generic multifractality in exp<strong>on</strong>entials <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g memory processes<br />

Physical Review E 74 011111.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cell and Tissue Biophysics; Thursday, June 30, 11:30<br />

Kyriaki Giorgakoudi<br />

Institute for Animal Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, Pirbright Laboratory, Ash Road,<br />

Surrey, GU24 0NF, UK<br />

e-mail: Kyriaki.Giorgakoudi@bbsrc.ac.uk, K.Giorgakoudi@lboro.ac.uk<br />

Sim<strong>on</strong> Gubbins<br />

Institute for Animal Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, Pirbright Laboratory, Ash Road,<br />

Surrey, GU24 0NF, UK<br />

e-mail: Sim<strong>on</strong>.Gubbins@bbsrc.ac.uk<br />

John Ward<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Loughborough University,<br />

Leicestershire, LE11 3TU, UK<br />

e-mail: John.Ward@lboro.ac.uk<br />

Zhid<strong>on</strong>g Zhang<br />

Nati<strong>on</strong>al Centre for Foreign Animal Disease, Canadian Food<br />

Inspecti<strong>on</strong> Agency, 1015 Arlingt<strong>on</strong> Street, Winnipeg, MB, R3E 3M4,<br />

Canada<br />

e-mail: Zhid<strong>on</strong>g.Zhang@inspecti<strong>on</strong>.gc.ca<br />

David Schley<br />

Institute for Animal Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, Pirbright Laboratory, Ash Road,<br />

Surrey, GU24 0NF, UK<br />

e-mail: David.Schley@bbsrc.ac.uk<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> foot-and-mou<str<strong>on</strong>g>th</str<strong>on</strong>g> disease virus<br />

infecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> bovine epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells.<br />

Foot-and-mou<str<strong>on</strong>g>th</str<strong>on</strong>g> disease (FMD) is a highly infectious animal disease <str<strong>on</strong>g>th</str<strong>on</strong>g>at affects<br />

cloven ho<str<strong>on</strong>g>of</str<strong>on</strong>g>ed animals (including cattle, sheep and pigs) and causes acute clinical<br />

signs such as vesicular lesi<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e foot and mou<str<strong>on</strong>g>th</str<strong>on</strong>g>, lameness, fever and pain; in<br />

more severe cases it can lead to dea<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> young livestock. In areas where FMD is<br />

endemic, it is c<strong>on</strong>sidered to be <str<strong>on</strong>g>th</str<strong>on</strong>g>e main <str<strong>on</strong>g>th</str<strong>on</strong>g>reat to animal heal<str<strong>on</strong>g>th</str<strong>on</strong>g> and ec<strong>on</strong>omic development,<br />

while an outbreak <str<strong>on</strong>g>of</str<strong>on</strong>g> FMD in 2001 in <str<strong>on</strong>g>th</str<strong>on</strong>g>e United Kingdom, a disease-free<br />

country, resulted in 6.5 milli<strong>on</strong> animals being slaughtered and losses <str<strong>on</strong>g>of</str<strong>on</strong>g> £6 billi<strong>on</strong>.<br />

Persistence <str<strong>on</strong>g>of</str<strong>on</strong>g> FMD virus (FMDV) occurs in previously infected but apparently<br />

recovered animals, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e pharyngeal area, specifically in <str<strong>on</strong>g>th</str<strong>on</strong>g>e dorsal s<str<strong>on</strong>g>of</str<strong>on</strong>g>t palate [1].<br />

These carrier animals are a possible source <str<strong>on</strong>g>of</str<strong>on</strong>g> virus transmissi<strong>on</strong>, and potentially<br />

facilitate viral mutati<strong>on</strong>s. In additi<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e persistence <str<strong>on</strong>g>of</str<strong>on</strong>g> FMDV, <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus appears<br />

not to cause lysis in <str<strong>on</strong>g>th</str<strong>on</strong>g>e dorsal s<str<strong>on</strong>g>of</str<strong>on</strong>g>t palate, even <str<strong>on</strong>g>th</str<strong>on</strong>g>ough lesi<strong>on</strong>s appears <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e t<strong>on</strong>gue and cor<strong>on</strong>ary band.<br />

Presented in <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk is a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model which aims to test <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at it is <str<strong>on</strong>g>th</str<strong>on</strong>g>e different structure <str<strong>on</strong>g>of</str<strong>on</strong>g> epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells, ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e intrinsic properties<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e t<strong>on</strong>gue and dorsal s<str<strong>on</strong>g>of</str<strong>on</strong>g>t palate <str<strong>on</strong>g>th</str<strong>on</strong>g>at determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e extent <str<strong>on</strong>g>of</str<strong>on</strong>g> FMDV lysis. A<br />

simple ODE compartmental model <str<strong>on</strong>g>of</str<strong>on</strong>g> Schley et al (2010) [2] c<strong>on</strong>sidered static live<br />

cells and indicated <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e dimensi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial tissues in <str<strong>on</strong>g>th</str<strong>on</strong>g>e t<strong>on</strong>gue and<br />

dorsal s<str<strong>on</strong>g>of</str<strong>on</strong>g>t palate are important for cell lysis and FMDV persistence. Here, <str<strong>on</strong>g>th</str<strong>on</strong>g>is has<br />

been extended to a spatially explicit system <str<strong>on</strong>g>of</str<strong>on</strong>g> partial differential equati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

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describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral dynamics in <str<strong>on</strong>g>th</str<strong>on</strong>g>e epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial layers <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> tissue types. The model<br />

accounts for <str<strong>on</strong>g>th</str<strong>on</strong>g>e movement <str<strong>on</strong>g>of</str<strong>on</strong>g> cells <str<strong>on</strong>g>th</str<strong>on</strong>g>rough grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, and includes heterogeneity <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cell layers which form <str<strong>on</strong>g>th</str<strong>on</strong>g>e epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elium. New experimental data, required to fit<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e model, has been collected and applied, toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> existing results from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

literature. We will present numerical results from a limit <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, relevant<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e timescale <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e early infecti<strong>on</strong> stages before <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune resp<strong>on</strong>se becomes<br />

effective and discuss key insights. A full active system which accounts for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> lesi<strong>on</strong>s is work in progress.<br />

References.<br />

[1] S. Alexandersen, Z. Zhang, A. I. D<strong>on</strong>alds<strong>on</strong>, and A. J. M. Garland, The pa<str<strong>on</strong>g>th</str<strong>on</strong>g>o- genesis and<br />

diagnosis <str<strong>on</strong>g>of</str<strong>on</strong>g> foot-and-mou<str<strong>on</strong>g>th</str<strong>on</strong>g> disease. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Comparative Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology 129 1–36.<br />

[2] D. Schley, J. Ward, and Z. Zhang, Modelling foot-and-mou<str<strong>on</strong>g>th</str<strong>on</strong>g> disease virus dynamics in<br />

oral epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elium to help identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e determinants <str<strong>on</strong>g>of</str<strong>on</strong>g> lysis. Bulletin <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology<br />

http://dx.doi.org/10.1007/s11538-010-9576-6 11–26.<br />

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Modeling and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor invasi<strong>on</strong> II; Tuesday, June 28, 14:30<br />

Chiara Giverso<br />

Politecnico di Torino<br />

e-mail: chiara.giverso@polito.it<br />

Modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> cell aggregates and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> meso<str<strong>on</strong>g>th</str<strong>on</strong>g>elial linings.<br />

The transmigrati<strong>on</strong> across <str<strong>on</strong>g>th</str<strong>on</strong>g>e meso<str<strong>on</strong>g>th</str<strong>on</strong>g>elial lining is a fundamental step in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

process <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer invasi<strong>on</strong> and formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> metastasis. We reproduce in vitro transmeso<str<strong>on</strong>g>th</str<strong>on</strong>g>elial<br />

migrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ovarian cancer cells, <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

integrates: (a) an Extended Cellular Potts Model (CPM), <str<strong>on</strong>g>th</str<strong>on</strong>g>at captures mechanisms<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cellular adhesi<strong>on</strong>, shape c<strong>on</strong>straints, moti<strong>on</strong> in resp<strong>on</strong>se to chemo-attractants and<br />

degradati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> extracellular matrix (ECM); (b) a c<strong>on</strong>tinuous model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong><br />

and uptake <str<strong>on</strong>g>of</str<strong>on</strong>g> chemo-attractants, and for <str<strong>on</strong>g>th</str<strong>on</strong>g>e release <str<strong>on</strong>g>of</str<strong>on</strong>g> matrix metalloproteinases<br />

(MMPs). Simulati<strong>on</strong>s are in good agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> biological experiments (provided<br />

by N. Lo Bu<strong>on</strong>o and A. Funaro, Laboratory <str<strong>on</strong>g>of</str<strong>on</strong>g> Immunogenetics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Molinette<br />

Hospital in Turin), showing <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall process is str<strong>on</strong>gly regulated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

activity <str<strong>on</strong>g>of</str<strong>on</strong>g> matrix metalloproteinases (MMPs) and by <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay <str<strong>on</strong>g>of</str<strong>on</strong>g> adhesive<br />

properties between cells. In particular in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular aggregates <str<strong>on</strong>g>th</str<strong>on</strong>g>e process<br />

is more destructive.<br />

Indeed <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability <str<strong>on</strong>g>of</str<strong>on</strong>g> cells to form aggregates is fundamental in many biological<br />

processes and it seems promising to study spheroid mechanical behavior, because<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> s<str<strong>on</strong>g>of</str<strong>on</strong>g>t biological tissues may serve as a parameter in <str<strong>on</strong>g>th</str<strong>on</strong>g>e diagnosis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tumor metastatic potential. We study <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> multicellular<br />

aggregates, treated as porous materials, composed <str<strong>on</strong>g>of</str<strong>on</strong>g> cells and filled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> water,<br />

to derive an elasto-visco-plastic model. The cellular c<strong>on</strong>stituent is resp<strong>on</strong>sible for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e elastic and <str<strong>on</strong>g>th</str<strong>on</strong>g>e plastic behavior (due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e rearrangement <str<strong>on</strong>g>of</str<strong>on</strong>g> adhesive b<strong>on</strong>ds<br />

between cells). On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, <str<strong>on</strong>g>th</str<strong>on</strong>g>e liquid c<strong>on</strong>stituent is resp<strong>on</strong>sible <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

viscous-like resp<strong>on</strong>se during deformati<strong>on</strong>. The model is used to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e uniaxial<br />

homogeneous compressi<strong>on</strong> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> when a c<strong>on</strong>stant load is applied and when<br />

a fixed deformati<strong>on</strong> is imposed and subsequently released. Results are compared<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics observed in mechanical experiments found in literature.<br />

References.<br />

[1] C. Giverso, M. Scianna, L. Preziosi, N. Lo Bu<strong>on</strong>o and A. Funaro. Individual cell-based model<br />

for in-vitro meso<str<strong>on</strong>g>th</str<strong>on</strong>g>elial invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ovarian cancer. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> Natural Phenomena,<br />

Vol. 5, 2010, pp. 203–223.<br />

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Vector-borne diseases; Tuesday, June 28, 14:30<br />

Erida Gjini<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Glasgow, University<br />

Gardens, Glasgow G12 8QW, UK<br />

e-mail: egjini@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.gla.ac.uk<br />

Christina A. Cobbold<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Glasgow, University<br />

Gardens, Glasgow G12 8QW, UK<br />

Daniel T. Hayd<strong>on</strong><br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biodiversity, Animal Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> and Comparative Medicine,<br />

College <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine, Veterinary & Life Sciences, Graham Kerr Building,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Glasgow, Glasgow, G12 8QQ<br />

J. D. Barry<br />

Glasgow Biomedical Research Centre, Wellcome Trust Centre for<br />

Molecular Parasitology, 120 University Place, Glasgow G12 8TA,<br />

Scotland, UK<br />

Optimizing pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen fitness: <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e antigenic<br />

archive for African Trypanosomes<br />

Antigenic variati<strong>on</strong> processes play a central role in vector-borne infectious diseases<br />

and are likely to resp<strong>on</strong>d to host immune mechanisms and epidemiological characteristics.<br />

A key priority in disease c<strong>on</strong>trol and understanding pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen evoluti<strong>on</strong><br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>e investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanisms by which pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens regulate antigenic diversity<br />

and how <str<strong>on</strong>g>th</str<strong>on</strong>g>ese affect larger-scale populati<strong>on</strong> processes. While <str<strong>on</strong>g>th</str<strong>on</strong>g>e wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-host populati<strong>on</strong><br />

ecology <str<strong>on</strong>g>of</str<strong>on</strong>g> antigen switching pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens is not a new topic, increasing access<br />

to genetic data provides us wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a rapidly widening opportunity to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

evoluti<strong>on</strong>ary ecology <str<strong>on</strong>g>of</str<strong>on</strong>g> antigenic variati<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, we study <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure and functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e antigenic archive <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e African Trypanosome,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e parasite resp<strong>on</strong>sible for sleeping sickness. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic<br />

architecture <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e archive has important c<strong>on</strong>sequences for pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen fitness wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in<br />

and between hosts. The optimality criteria we find for <str<strong>on</strong>g>th</str<strong>on</strong>g>e antigenic archive arise<br />

as a result <str<strong>on</strong>g>of</str<strong>on</strong>g> typical trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>fs between transmissi<strong>on</strong> and virulence. Our analysis<br />

suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at different traits <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e host populati<strong>on</strong> can select for different aspects<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e antigenic archive, reinforcing <strong>on</strong>ce more <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> host heterogeneity<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> parasites.<br />

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From <strong>on</strong>e to many: Cell-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective, emergent behaviors<br />

in biology -I; Tuesday, June 28, 11:00<br />

James Glazier<br />

Indiana University<br />

e-mail: glazier@indiana.edu<br />

Abbas Shirinifard<br />

Indiana University<br />

Multi-scale, Multi-cell Computati<strong>on</strong>al Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Choroidal<br />

Neovascularizati<strong>on</strong> in Age-Related Macular Degenerati<strong>on</strong><br />

Choroidal neovascularizati<strong>on</strong> (CNV) <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e macular area <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e retina is <str<strong>on</strong>g>th</str<strong>on</strong>g>e major<br />

cause <str<strong>on</strong>g>of</str<strong>on</strong>g> severe visi<strong>on</strong> loss in patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> age-related macular degenerati<strong>on</strong> (AMD)<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e major cause <str<strong>on</strong>g>of</str<strong>on</strong>g> visi<strong>on</strong> loss in adults in <str<strong>on</strong>g>th</str<strong>on</strong>g>e developed world. In CNV, after<br />

choriocapillaries initially penetrate Bruch’s Membrane (BrM), <str<strong>on</strong>g>th</str<strong>on</strong>g>e invading vessels<br />

may regress or expand (CNV initiati<strong>on</strong>). After initiati<strong>on</strong>, during early and late<br />

CNV, <str<strong>on</strong>g>th</str<strong>on</strong>g>e expanding vasculature usually spreads in <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree distinct patterns:<br />

in a layer between BrM and <str<strong>on</strong>g>th</str<strong>on</strong>g>e retinal pigment epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elium (sub-RPE, occult or<br />

Type 1 CNV), in a layer between <str<strong>on</strong>g>th</str<strong>on</strong>g>e RPE and <str<strong>on</strong>g>th</str<strong>on</strong>g>e photoreceptors (subretinal,<br />

classic or Type 2 CNV) or in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> loci simultaneously (combined pattern or Type<br />

3 CNV). The factors determining bo<str<strong>on</strong>g>th</str<strong>on</strong>g> CNV initiati<strong>on</strong> and progressi<strong>on</strong> are poorly<br />

understood. While most previous studies <str<strong>on</strong>g>of</str<strong>on</strong>g> CNV have assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at it is primarily<br />

related to grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factor effects or to local holes in BrM, our simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ree-dimensi<strong>on</strong>al (3D) multi-cell model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e maculae <str<strong>on</strong>g>of</str<strong>on</strong>g> normal and pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ological<br />

retinas successfully recapitulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ree clinically observed types <str<strong>on</strong>g>of</str<strong>on</strong>g> CNV, under<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at initiati<strong>on</strong> and early and late CNV result from combinati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

impairment <str<strong>on</strong>g>of</str<strong>on</strong>g>: 1) RPE-RPE epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial juncti<strong>on</strong>s (i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e outer blood-retinal barrier),<br />

2) <str<strong>on</strong>g>th</str<strong>on</strong>g>e adhesi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basement membrane <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e RPE (BaM) to BrM, and 3)<br />

adhesi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e RPE to <str<strong>on</strong>g>th</str<strong>on</strong>g>e photoreceptor outer segments (POS). Our key findings<br />

are <str<strong>on</strong>g>th</str<strong>on</strong>g>at when an endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial tip cell or immune cell penetrate BrM: 1) RPE wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

normal epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial juncti<strong>on</strong>s and basal attachment to BrM and apical attachment to<br />

POS resists CNV, showing <str<strong>on</strong>g>th</str<strong>on</strong>g>at higher rates <str<strong>on</strong>g>of</str<strong>on</strong>g> EC activati<strong>on</strong> due to excess vascular<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factors by <str<strong>on</strong>g>th</str<strong>on</strong>g>emselves are insufficient to produce CNV. 2) Similarly small<br />

holes in BrM do not, by <str<strong>on</strong>g>th</str<strong>on</strong>g>emselves, initiate CNV. 3) RPE wi<str<strong>on</strong>g>th</str<strong>on</strong>g> normal epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial<br />

juncti<strong>on</strong>s and normal apical RPE-POS adhesi<strong>on</strong>, but weak adhesi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> BaM<br />

to BrM (e.g. due to lipid accumulati<strong>on</strong> in BrM) initially results in Type 1 CNV.<br />

4) Normal adhesi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> BaM to BrM, but reduced apical RPE-POS and epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial<br />

RPE-RPE binding (e.g. due to inflammati<strong>on</strong>) initially results in Type 2 CNV. 5)<br />

Simultaneous reducti<strong>on</strong> in RPE-RPE epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial binding and BaM-BrM adhesi<strong>on</strong><br />

results in early Type 1 or 2 CNV which <str<strong>on</strong>g>of</str<strong>on</strong>g>ten progresses to Type 3 CNV as neovascularizati<strong>on</strong><br />

fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er perturbs RPE-RPE adhesi<strong>on</strong> and BaM-BrM attachment.<br />

These findings suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at previously neglected changes in adhesi<strong>on</strong> ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e more <str<strong>on</strong>g>of</str<strong>on</strong>g>ten hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esized excess producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factors dominate<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> CNV initiati<strong>on</strong> and progressi<strong>on</strong>.<br />

357

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Tilmann Glimm<br />

Western Washingt<strong>on</strong> University<br />

e-mail: glimmt@wwu.edu<br />

Developmental Biology; Friday, July 1, 14:30<br />

Pattern formati<strong>on</strong> in reacti<strong>on</strong>-diffusi<strong>on</strong> systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an<br />

external morphogen gradient<br />

Gradients <str<strong>on</strong>g>of</str<strong>on</strong>g> signalling molecules are abundant in <str<strong>on</strong>g>th</str<strong>on</strong>g>e early embryo. They are central<br />

to early development. The Turing mechanism in reacti<strong>on</strong>-diffusi<strong>on</strong> systems<br />

is a paradigm for pattern formati<strong>on</strong> which has been proposed as an explanati<strong>on</strong><br />

for many developmental phenomena. We propose a generic model <str<strong>on</strong>g>of</str<strong>on</strong>g> a reacti<strong>on</strong>diffusi<strong>on</strong><br />

system c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> an activator and an inhibitor molecule in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a linear morphogen gradient. We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is morphogen gradient is established<br />

independently <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong>-diffusi<strong>on</strong> system. Hence it is referred to as<br />

an "external" morphogen. It acts by increasing <str<strong>on</strong>g>th</str<strong>on</strong>g>e producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e activator<br />

proporti<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e morphogen c<strong>on</strong>centrati<strong>on</strong>. The model is motivated by several<br />

existing models in developmental biology in which a Turing patterning mechanism<br />

is proposed and various chemical gradients are known to be important for development.<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically, <str<strong>on</strong>g>th</str<strong>on</strong>g>is leads to reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> explicit<br />

spatial dependence. We investigate how <str<strong>on</strong>g>th</str<strong>on</strong>g>e Turing pattern is affected, if it exists.<br />

We also show <str<strong>on</strong>g>th</str<strong>on</strong>g>at in <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter range where a Turing pattern is not possible,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e system may never<str<strong>on</strong>g>th</str<strong>on</strong>g>eless produce “Turing-like” patterns. We also apply our<br />

general findings to a model <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e pattern formati<strong>on</strong> in vertebrate limbs and show<br />

how <str<strong>on</strong>g>th</str<strong>on</strong>g>ey may shed light <strong>on</strong> some experimental findings c<strong>on</strong>cerning <str<strong>on</strong>g>th</str<strong>on</strong>g>e acti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e protein S<strong>on</strong>ic Hedgehog.<br />

References.<br />

[1] T. Glimm, J. Zhang and Y.-Q. Shen Interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Turing patterns wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an external linear<br />

morphogen gradient N<strong>on</strong>linearity 22 10, 2541-2560 (2009).<br />

[2] T. Glimm, J. Zhang, Y.-Q. Shen and S. A. Newman Reacti<strong>on</strong>-diffusi<strong>on</strong> systems and external<br />

morphogen gradients: The two-dimensi<strong>on</strong>al case, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an applicati<strong>on</strong> to skeletal pattern<br />

formati<strong>on</strong> submitted (2010).<br />

[3] M. Alber, T. Glimm, H.G.E. Hentschel, B. Kazmierczak, Y.-T. Zhang, J. Zhu and S. A.<br />

Newman The morphostatic limit for a model <str<strong>on</strong>g>of</str<strong>on</strong>g> skeletal pattern formati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e vertebrate<br />

limb Bull. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. 70 460–483 (2008).<br />

358

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Wojciech Goch<br />

Uniwersytet Warszawski<br />

e-mail: Wojciech_Goch@wp.pl<br />

Wojciech Bal<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemistry and Biophysics Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Science<br />

The range <str<strong>on</strong>g>of</str<strong>on</strong>g> fluctuati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> number <str<strong>on</strong>g>of</str<strong>on</strong>g> zinc i<strong>on</strong>s depends <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e ligand binding reacti<strong>on</strong> rate c<strong>on</strong>stant and <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial<br />

c<strong>on</strong>centrati<strong>on</strong><br />

The range <str<strong>on</strong>g>of</str<strong>on</strong>g> fluctuati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> number <str<strong>on</strong>g>of</str<strong>on</strong>g> zinc i<strong>on</strong>s depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ligand binding<br />

reacti<strong>on</strong> rate c<strong>on</strong>stant and <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial c<strong>on</strong>centrati<strong>on</strong> Wojciech Goch a), and Wojciech<br />

Bal b)<br />

a) student <str<strong>on</strong>g>of</str<strong>on</strong>g> Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics and Mechanics at Warsaw<br />

University b) Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemistry and Biophysics, Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences,<br />

Warsaw<br />

We present <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependency <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> fluctuati<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a reversible chemical associati<strong>on</strong> reacti<strong>on</strong> in an equilibrium state. We derived <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

infinite system <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e central moments from a set <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s<br />

called Chemical Master Equati<strong>on</strong>. Next, we performed a series <str<strong>on</strong>g>of</str<strong>on</strong>g> numerical simulati<strong>on</strong>s<br />

in order to find appropriate assumpti<strong>on</strong>s in our model. Finally, by placing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese assumpti<strong>on</strong>s into <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong>s, we derived <str<strong>on</strong>g>th</str<strong>on</strong>g>e explicit formulas <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e first<br />

two central moments. The sec<strong>on</strong>d central moment determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> fluctuati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>e partner <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>us, we are able to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e probability factor <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system. We compared <str<strong>on</strong>g>th</str<strong>on</strong>g>e obtained results<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> numerical simulati<strong>on</strong>s. The essential result is <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical formula<br />

describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependency <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> fluctuati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting<br />

molecules <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong> rate c<strong>on</strong>stants and <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial c<strong>on</strong>centrati<strong>on</strong>s. The ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model, as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e approximati<strong>on</strong>, could be expanded to<br />

much more complicated systems. The me<str<strong>on</strong>g>th</str<strong>on</strong>g>od was tested <strong>on</strong> several experimental<br />

data available in literature for interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Zn(II) i<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> biomolecules, including<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a zinc finger complex, for which K_d = k_<str<strong>on</strong>g>of</str<strong>on</strong>g>f/k_<strong>on</strong><br />

= 50 pM. For <str<strong>on</strong>g>th</str<strong>on</strong>g>is particular example, <str<strong>on</strong>g>th</str<strong>on</strong>g>e volume, in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e virtual experiment<br />

was performed, was V = 0.5 pL, initial c<strong>on</strong>centrati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> reagents were: [Zn] _Free<br />

=50 pM, [ZnP] = 50 M, [P] = 50 M and, as a result, <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> fluctuati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

zinc i<strong>on</strong>s was estimated to be ca. 26%, translating into <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluctuati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Kd<br />

value in <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> 59% 190%.<br />

359

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Julia Gog<br />

DAMTP, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cambridge<br />

e-mail: jrg20@cam.ac.uk<br />

Adam Kucharski<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cambridge<br />

Strain dynamics and influenza drift<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most exciting current areas in infectious disease modelling is in bringing<br />

toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic and evoluti<strong>on</strong>ary dynamics. Influenza drift is perhaps <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

most striking example <str<strong>on</strong>g>of</str<strong>on</strong>g> where <str<strong>on</strong>g>th</str<strong>on</strong>g>e two processes must be c<strong>on</strong>sidered toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er:<br />

epidemics give rise to new strains, which in turn permit new epidemics.<br />

We will begin wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a general introducti<strong>on</strong> to models <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple strains, and<br />

some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir challenges, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> technical and in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> capturing observed biological<br />

phenomena. In most populati<strong>on</strong>-based models <str<strong>on</strong>g>of</str<strong>on</strong>g> strain dynamics, <str<strong>on</strong>g>th</str<strong>on</strong>g>e number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> variables grows exp<strong>on</strong>entially wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> strains. We present two items<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> our recent work, each <str<strong>on</strong>g>of</str<strong>on</strong>g> which avoids <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem in <strong>on</strong>e way or ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er:<br />

1) The impact <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary c<strong>on</strong>straints <strong>on</strong> influenza drift: standard drift<br />

models assume influenza is free to mutate to escape host immunity. In practice,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ere may be some functi<strong>on</strong>al cost associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese mutati<strong>on</strong>s, and <str<strong>on</strong>g>th</str<strong>on</strong>g>is can<br />

be incorporated into a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model. In c<strong>on</strong>trast to unc<strong>on</strong>strained drift<br />

models, <str<strong>on</strong>g>th</str<strong>on</strong>g>is system is bistable, exhibiting bo<str<strong>on</strong>g>th</str<strong>on</strong>g> drift-like patterns and single strain<br />

dynamics for <str<strong>on</strong>g>th</str<strong>on</strong>g>e same parameter values. This raises some important questi<strong>on</strong>s for<br />

vaccinati<strong>on</strong> strategies.<br />

2) Age-structure and immune history: al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough relatively simple assumpti<strong>on</strong>s<br />

about <str<strong>on</strong>g>th</str<strong>on</strong>g>e acquisiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> immunity capture well <str<strong>on</strong>g>th</str<strong>on</strong>g>e general dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> influenza<br />

drift, recent outbreaks have highlighted <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>sidering <str<strong>on</strong>g>th</str<strong>on</strong>g>e details<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> precisely how immunity is acquired by an individual over <str<strong>on</strong>g>th</str<strong>on</strong>g>eir lifetime. In<br />

particular, strains <str<strong>on</strong>g>th</str<strong>on</strong>g>at infect us when we are young may be disproporti<strong>on</strong>ately<br />

important (e.g. <str<strong>on</strong>g>th</str<strong>on</strong>g>rough original antigenic sin), and <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune resp<strong>on</strong>se may be<br />

weakened in <str<strong>on</strong>g>th</str<strong>on</strong>g>e elderly.<br />

360<br />

;

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Game <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical modelling and optimizati<strong>on</strong> in evoluti<strong>on</strong> and ecology II;<br />

Tuesday, June 28, 14:30<br />

Chaitanya S. Gokhale and Arne Traulsen<br />

Research Group for Evoluti<strong>on</strong>ary Theory, Max-Planck-Institute for<br />

Evoluti<strong>on</strong>ary Biology, August-Thienemann-Str. 2, 24306 Plön, Germany<br />

e-mail: gokhale@evolbio.mpg.de<br />

Multiplayer evoluti<strong>on</strong>ary games: from selecti<strong>on</strong> to mutati<strong>on</strong><br />

Evoluti<strong>on</strong>ary game <str<strong>on</strong>g>th</str<strong>on</strong>g>eory is an abstract and simple, but very powerful way to<br />

model evoluti<strong>on</strong>ary dynamics. Even complex biological phenomena can sometimes<br />

be abstracted to simple two player games. But <str<strong>on</strong>g>of</str<strong>on</strong>g>ten, <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> between<br />

several parties determines evoluti<strong>on</strong>ary success. In <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cases, <strong>on</strong>e can resort to<br />

multiplayer games. Public goods games are a special class <str<strong>on</strong>g>of</str<strong>on</strong>g> multiplayer games<br />

which have been studied in great detail. A general approach to multiplayer games<br />

has al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough has remained limited [3]. We extend <str<strong>on</strong>g>th</str<strong>on</strong>g>e replicator analysis to general<br />

d player games wi<str<strong>on</strong>g>th</str<strong>on</strong>g> n strategies and comment <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximum number <str<strong>on</strong>g>of</str<strong>on</strong>g> equilibria<br />

possible. Moving <strong>on</strong> to finite populati<strong>on</strong>s we provide general c<strong>on</strong>diti<strong>on</strong>s for a<br />

strategy to be favoured by natural selecti<strong>on</strong> in a d player game wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two strategies<br />

[4]. Ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er important evoluti<strong>on</strong>ary force is mutati<strong>on</strong>s, which has <strong>on</strong>ly recently<br />

yielded to analytical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods [1, 2]. We derive <str<strong>on</strong>g>th</str<strong>on</strong>g>e compositi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a d player, n<br />

strategy system in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutati<strong>on</strong>-selecti<strong>on</strong> equilibrium [5]. The average frequencies<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e strategies at <str<strong>on</strong>g>th</str<strong>on</strong>g>is equilibrium are obtained via recursi<strong>on</strong>s using coalescence<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eory [6]. Multiplayer multi strategy games <str<strong>on</strong>g>of</str<strong>on</strong>g>fer <str<strong>on</strong>g>th</str<strong>on</strong>g>e generality which helps us to<br />

apply <str<strong>on</strong>g>th</str<strong>on</strong>g>em to diverse entities like from alleles to behavioural strategies.<br />

References.<br />

[1] T. Antal, H. Ohtsuki, J. Wakeley, P. D. Taylor, and M. A. Nowak. Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cooperati<strong>on</strong><br />

by phenotypic similarity. Proc. Natl. Acad. Sci. USA, 106:8597–8600, 2009a.<br />

[2] T. Antal, A. Traulsen, H. Ohtsuki, C. E. Tarnita, and M. A. Nowak. Mutati<strong>on</strong>-selecti<strong>on</strong><br />

equilibrium in games wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multiple strategies. J. Theor. Biol., 258:614–622, 2009b.<br />

[3] M. Broom. The use <str<strong>on</strong>g>of</str<strong>on</strong>g> multiplayer game <str<strong>on</strong>g>th</str<strong>on</strong>g>eory in <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological populati<strong>on</strong>s.<br />

Comments <strong>on</strong> Theoretical Biology, 8:103–123, 2003.<br />

[4] C. S. Gokhale and A. Traulsen. Evoluti<strong>on</strong>ary games in <str<strong>on</strong>g>th</str<strong>on</strong>g>e multiverse. Proc. Natl. Acad. Sci.<br />

U.S.A., 107(12):5500–5504, 2010.<br />

[5] C. S. Gokhale and A. Traulsen. Mutati<strong>on</strong>-selecti<strong>on</strong> equilibrium in evoluti<strong>on</strong>ary games wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

multiple players and multiple strategies. Submitted, 2011.<br />

[6] J. F. C. Kingman. Origins <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e coalescent. 1974-1982. Genetics, 156(4):1461–1463, 2000.<br />

ISSN 0016-6731 (Print).<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Meltem Gölgeli<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Biometry, Helmholtz Zentrum München,<br />

Germany<br />

e-mail: meltem.goelgeli@helmholtz-muenchen.de<br />

Burkhard A. Hense<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Biometry, Helmholtz Zentrum München,<br />

Germany<br />

Christina Kuttler<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Technical University Munich, Germany<br />

Johannes Müller<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Technical University Munich, Germany<br />

A stochastic modelling approache for bacterial cell-cell<br />

communicati<strong>on</strong><br />

Quorum sensing is a form <str<strong>on</strong>g>of</str<strong>on</strong>g> microbial communicati<strong>on</strong> via so-called autoinducers<br />

which regulates many bacterial processes. In an experiment, bacteria (Pseudom<strong>on</strong>as<br />

putida) were attached in a flow chamber. There, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey grow in small microcol<strong>on</strong>ies;<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e state <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bacteria (ON or OFF, influenced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e present autoinducer c<strong>on</strong>centrati<strong>on</strong>)<br />

can be observed via Gfp (a fluorescence protein) by c<strong>on</strong>focal laser scanning<br />

microscopy. We developed stochastic modelling approaches which allow to quantify<br />

e.g. rates <str<strong>on</strong>g>of</str<strong>on</strong>g> cell divisi<strong>on</strong>, activati<strong>on</strong> or detachment <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bacteria. The autoinducer<br />

producti<strong>on</strong> can also be c<strong>on</strong>sidered in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model and depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>e bacterial<br />

states in <str<strong>on</strong>g>th</str<strong>on</strong>g>e microcol<strong>on</strong>y. The model (a kind <str<strong>on</strong>g>of</str<strong>on</strong>g> extended bir<str<strong>on</strong>g>th</str<strong>on</strong>g>-dea<str<strong>on</strong>g>th</str<strong>on</strong>g> process) can<br />

be adapted numerically to data <str<strong>on</strong>g>of</str<strong>on</strong>g> quite different situati<strong>on</strong>s: e.g. flow versus n<strong>on</strong>flow,<br />

and by <str<strong>on</strong>g>th</str<strong>on</strong>g>at helps to understand better <str<strong>on</strong>g>th</str<strong>on</strong>g>e steps <str<strong>on</strong>g>of</str<strong>on</strong>g> cell activati<strong>on</strong> and how<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ey can be influenced.<br />

References.<br />

[1] Thomas, J.W., Numerical Partial Differential Equati<strong>on</strong>s, Springer Verlag (1995)<br />

[2] Holden, H., Oksendal, B., Uboe, J., Zhang, T., Stochastic Partial Differential Equati<strong>on</strong>s,<br />

Birkhäuser (1996)<br />

[3] Müller, J., Kuttler, C., Hense, Burkhard A., Zeiser, S., Liebscher,V. Transcripti<strong>on</strong>, intercellular<br />

variability and correlated random walk,Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences 216(2008), 30-39<br />

[4] Czupp<strong>on</strong>, P., Stochastische Modelliereung v<strong>on</strong> Zell-Zell Kommunikati<strong>on</strong>, TUM Bachelor-<br />

Arbeit (2010).<br />

362

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious agents;<br />

Tuesday, June 28, 17:00<br />

Gabriela Gomes<br />

Instituto Gulbenkian de Ciencia, Oeias, Portugal<br />

e-mail: ggomes@igc.gulbenkian.pt<br />

Andrea Parisi<br />

Departamento de Fisica, Faculdade de Ciencias, Universidade de Lisboa<br />

Ana Nunes<br />

Departamento de Fisica, Faculdade de Ciencias, Universidade de Lisboa<br />

Heterogeneity in antibody range is required for <str<strong>on</strong>g>th</str<strong>on</strong>g>e antigenic<br />

drift <str<strong>on</strong>g>of</str<strong>on</strong>g> influenza A viruses<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper we explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sequences for <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a rapidly mutating<br />

virus <str<strong>on</strong>g>of</str<strong>on</strong>g> a heterogeneous immune resp<strong>on</strong>se in <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong>. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at several<br />

features <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e incidence and phylogenetic patterns typical <str<strong>on</strong>g>of</str<strong>on</strong>g> influenza A may be<br />

understood in <str<strong>on</strong>g>th</str<strong>on</strong>g>is framework. Limited diversity and rapid drift <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e circulating<br />

viral strains result from <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay <str<strong>on</strong>g>of</str<strong>on</strong>g> two interacting subpopulati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two<br />

different types <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>se, narrow or broad, up<strong>on</strong> infecti<strong>on</strong>. The subpopulati<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e narrow immune resp<strong>on</strong>se acts as a reservoir where c<strong>on</strong>secutive<br />

neutral mutati<strong>on</strong>s escape immunity and can persist. Strains wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a number <str<strong>on</strong>g>of</str<strong>on</strong>g> accumulated<br />

mutati<strong>on</strong>s escape immunity in <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er subpopulati<strong>on</strong> as well, causing<br />

larger epidemic peaks in <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole populati<strong>on</strong>, and reducing strain diversity. These<br />

recurrent larger epidemics have been identified in <str<strong>on</strong>g>th</str<strong>on</strong>g>e data and associated in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

modelling literature wi<str<strong>on</strong>g>th</str<strong>on</strong>g> "cluster jumps", or mutati<strong>on</strong>s whose antigenic effect is<br />

larger and generate strains for which <str<strong>on</strong>g>th</str<strong>on</strong>g>e pool <str<strong>on</strong>g>of</str<strong>on</strong>g> susceptibles in <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> is<br />

also larger. Our model reproduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed epidemic peak height variati<strong>on</strong> and<br />

antigenic drift patterns wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out any assumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> punctuated antigenic evoluti<strong>on</strong>.<br />

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Didier G<strong>on</strong>ze<br />

Université Libre de Bruxelles<br />

e-mail: dg<strong>on</strong>ze@ulb.ac.be<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Modeling circadian clocks as coupled damped oscillators<br />

Circadian rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms represent <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e more c<strong>on</strong>spicuous examples <str<strong>on</strong>g>of</str<strong>on</strong>g> biological<br />

rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms. Manifested at <str<strong>on</strong>g>th</str<strong>on</strong>g>e physiological, behavioral, and cellular levels, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese 24hour<br />

rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms originate at <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular level, <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a complex gene regulatory<br />

network. In mammals, <str<strong>on</strong>g>th</str<strong>on</strong>g>e circadian pacemaker is located in <str<strong>on</strong>g>th</str<strong>on</strong>g>e suprachiasmatic<br />

nuclei <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>alamus (SCN). We have developed deterministic models using<br />

n<strong>on</strong>-linear ordinary differential equati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at account for <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> aut<strong>on</strong>omous<br />

circadian oscillati<strong>on</strong>s in single cells, for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir entrainment by light-dark<br />

cycles, and for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir phase shifting by light pulses. The model can be used to unravel<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e links between molecular alterati<strong>on</strong>s (e.g. mutati<strong>on</strong>s in clock genes) and<br />

clock-related physiological pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologies (such as sleep phase disorders). We have<br />

investigated <str<strong>on</strong>g>th</str<strong>on</strong>g>e coupling between <str<strong>on</strong>g>th</str<strong>on</strong>g>e SCN cells and proposed a synchr<strong>on</strong>izati<strong>on</strong><br />

mechanism based <strong>on</strong> neurotransmitter release. Numerical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>at (1) efficient synchr<strong>on</strong>izati<strong>on</strong> is achieved when <str<strong>on</strong>g>th</str<strong>on</strong>g>e average neurotransmitter<br />

c<strong>on</strong>centrati<strong>on</strong> dampens individual oscillators and (2) phases <str<strong>on</strong>g>of</str<strong>on</strong>g> individual<br />

cells are governed by <str<strong>on</strong>g>th</str<strong>on</strong>g>eir intrinsic periods. These results illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e possible interplay<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e single-cell oscillator and <str<strong>on</strong>g>th</str<strong>on</strong>g>e inter-cellular coupling mechanisms.<br />

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Regulatory Networks; Tuesday, June 28, 17:00<br />

Madalena Chaves<br />

Project-team COMORE, INRIA, 06902 Sophia Antipolis, France<br />

e-mail: madalena.chaves@inria.fr<br />

Jean-Luc Gouzé<br />

Project-team COMORE, INRIA, 06902 Sophia Antipolis, France<br />

e-mail: gouze@sophia.inria.fr<br />

Qualitative C<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> a Bistable Genetic Network<br />

The c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> a generic model for a genetic network is studied using piecewise<br />

affine differential systems. The system is <str<strong>on</strong>g>th</str<strong>on</strong>g>e well-known bistable switch wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two<br />

genes and proteins x1, x2:<br />

˙x1 = uκ1s − (x2, θ2) − γ1x1<br />

˙x2 = uκ2s − (x1, θ1) − γ2x2.<br />

where κi denote producti<strong>on</strong> rates, γi denote <str<strong>on</strong>g>th</str<strong>on</strong>g>e degradati<strong>on</strong> rate c<strong>on</strong>stants, and<br />

θi <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold c<strong>on</strong>centrati<strong>on</strong>s. The step functi<strong>on</strong> represents <str<strong>on</strong>g>th</str<strong>on</strong>g>e inhibiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> each gene by <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er.<br />

s − (r, θ) =<br />

1, r < θ<br />

0, r > θ.<br />

This class <str<strong>on</strong>g>of</str<strong>on</strong>g> piecewise affine systems (PWA) was first introduced by [1], and is<br />

widely used for modeling genetic regulatory networks [2]. It is assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

state measurements <str<strong>on</strong>g>of</str<strong>on</strong>g> x1, x2 are qualitative (each variable is at high or low c<strong>on</strong>centrati<strong>on</strong>)<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e possible input values <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol u are also qualitative<br />

(no c<strong>on</strong>trol, high value or low value). The advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach is to obtain<br />

c<strong>on</strong>trol laws which can be implemented in <str<strong>on</strong>g>th</str<strong>on</strong>g>e laboratory, using <strong>on</strong>ly qualitative<br />

knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system’s variables. Soluti<strong>on</strong>s are given for <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trolling<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e bistable switch to ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>of</str<strong>on</strong>g> its <str<strong>on</strong>g>th</str<strong>on</strong>g>ree steady states [3].<br />

References.<br />

[1] L. Glass and S.A. Kauffman. The logical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tinuous, n<strong>on</strong>linear biochemical c<strong>on</strong>trol<br />

networks. J. Theor. Biol., 39:103–129, 1973.<br />

[2] R. Casey, H. de J<strong>on</strong>g, and J.L. Gouzé. Piecewise-linear models <str<strong>on</strong>g>of</str<strong>on</strong>g> genetic regulatory networks:<br />

equilibria and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir stability. J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol., 52:27–56, 2006.<br />

[3] M. Chaves and J.L. Gouzé. Qualitative C<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> Genetic Networks: <str<strong>on</strong>g>th</str<strong>on</strong>g>e Bistable Switch<br />

Example. Technical Report, INRIA, 2010, http://hal.inria.fr/<br />

365

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: from physical tools to<br />

applicati<strong>on</strong>s in cancer modeling II; Saturday, July 2, 11:00<br />

Isabell Graf<br />

Universität Augsburg<br />

e-mail: grafisab@googlemail.com<br />

Homogenizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a reacti<strong>on</strong>-diusi<strong>on</strong> system modeling<br />

carcino- gens inside a human cell<br />

We use a reacti<strong>on</strong>-diusi<strong>on</strong> model to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> potentially cancercausing<br />

chemicals inside a human cell. We show how periodic homogenizati<strong>on</strong> can<br />

be used to upscale rigorously <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong>-diusi<strong>on</strong> equati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytosol as well<br />

as <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e surface <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e endoplasmic reticulum. The resulting macromodel is also<br />

suitable for direct implementati<strong>on</strong>. Results <str<strong>on</strong>g>of</str<strong>on</strong>g> numerical simulati<strong>on</strong>s will be shown.<br />

366

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Heart rate dynamics: models and measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity (part I);<br />

Wednesday, June 29, 14:30<br />

Beata Graff<br />

Hypertensi<strong>on</strong> Unit, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Hypertensi<strong>on</strong> and Diabetology,<br />

Medical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Gdańsk, Poland<br />

e-mail: bgraff@gumed.edu.pl<br />

Grzegorz Graff<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Physics and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Gdańsk University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Technology, Poland<br />

e-mail: graff@mif.pg.gda.pl<br />

Agnieszka Kaczkowska<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Physics and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Gdańsk University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Technology, Poland<br />

e-mail: kaczkowska.agnieszka@gmail.com<br />

Entropy-based measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity in <str<strong>on</strong>g>th</str<strong>on</strong>g>e assessment <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

heart rate variability: a clinical approach<br />

N<strong>on</strong>-linear dynamics is a powerful approach to understanding physiological data but<br />

n<strong>on</strong>-linear me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods usually require l<strong>on</strong>g data sets. In 1991, Pincus et al. introduced<br />

Approximate Entropy, a measure <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity which can be applied to short and<br />

noisy time series <str<strong>on</strong>g>of</str<strong>on</strong>g> clinical data [1]. Subsequently, o<str<strong>on</strong>g>th</str<strong>on</strong>g>er entropy-based me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some improvements were added and presently <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are many examples <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

successful applicati<strong>on</strong> in medicine. An overview <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most promising applicati<strong>on</strong>s<br />

in heart rate variability assessment will be presented. Advantages and limitati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods from <str<strong>on</strong>g>th</str<strong>on</strong>g>e physician’s point <str<strong>on</strong>g>of</str<strong>on</strong>g> view will be discussed based <strong>on</strong><br />

recently published papers and our own results.<br />

References.<br />

[1] S. Pincus, Approximate entropy as a measure <str<strong>on</strong>g>of</str<strong>on</strong>g> system complexity Proc Nati Acad Sci. USA<br />

88 (6) 2297–2301.<br />

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Immunology; Saturday, July 2, 08:30<br />

Galina Gramotnev<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Physics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Queensland, St.<br />

Lucia, QLD 4072, Australia<br />

e-mail: d.gramotnev@centre-pst.com<br />

Dmitri K. Gramotnev<br />

Centre for Psychosomatic Treatment, GPO Box 1272, Aspley, QLD<br />

4034, Australia<br />

Generalised Stress: A unifying model for psychological stress<br />

and psychosomatic treatment<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e impacts <str<strong>on</strong>g>of</str<strong>on</strong>g> psychological stress and psychosomatic<br />

treatment <strong>on</strong> patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> serious immune-related diseases and c<strong>on</strong>diti<strong>on</strong>s is bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

challenging and important for <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> new quantifiable and effective<br />

treatment approaches for a range <str<strong>on</strong>g>of</str<strong>on</strong>g> diseases and c<strong>on</strong>diti<strong>on</strong>s, including cancers [1],<br />

myeloproliferative blood diseases [2], etc. The development <str<strong>on</strong>g>of</str<strong>on</strong>g> such quantitative<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models is impeded by <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e characterisati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> psychological<br />

stress and psychosomatic treatment is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten based up<strong>on</strong> subjective percepti<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e involved human subjects (including preservative cogniti<strong>on</strong>). In <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

paper, we introduce and justify a new model based <strong>on</strong> a c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> generalised<br />

stress <str<strong>on</strong>g>th</str<strong>on</strong>g>at ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically unifies psychological stress and psychosomatic (hypnotic)<br />

treatment. This model correlates <str<strong>on</strong>g>th</str<strong>on</strong>g>e two independently and subjectively<br />

reported levels <str<strong>on</strong>g>of</str<strong>on</strong>g> psychological stress and psychosomatic treatment <strong>on</strong> two different<br />

arbitrary scales to an objectively measured physiological parameter platelet<br />

count. As a result, <str<strong>on</strong>g>th</str<strong>on</strong>g>e two subjectively reported quantities are reduced to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

same unit scale and ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically unified into <strong>on</strong>e new quantity called generalised<br />

stress. Excellent applicability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model is dem<strong>on</strong>strated <strong>on</strong> an example<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a 3.5 years l<strong>on</strong>gitudinal study <str<strong>on</strong>g>of</str<strong>on</strong>g> blood parameters in a patient wi<str<strong>on</strong>g>th</str<strong>on</strong>g> myel<str<strong>on</strong>g>of</str<strong>on</strong>g>ibrosis,<br />

who was subjected to severe work-related psychological stress and psychosomatic<br />

(hypnotic) treatment. The stress and treatment were statistically shown to have a<br />

major (dominant) impact <strong>on</strong> blood platelet counts well described by an exp<strong>on</strong>ential<br />

dependence <strong>on</strong> cumulative levels <str<strong>on</strong>g>of</str<strong>on</strong>g> generalized stress. Only 12 % <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e total<br />

variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> platelet counts could be attributed to factors o<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an psychological<br />

stress and psychosomatic treatment. The developed model will be instrumental for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e quantified analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e impacts <str<strong>on</strong>g>of</str<strong>on</strong>g> psychological stress and psychosomatic<br />

treatment for patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> immune and blood disorders. It also dem<strong>on</strong>strates a<br />

unique role <str<strong>on</strong>g>of</str<strong>on</strong>g> platelets for neuroimmunological pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways for psychological stress<br />

and psychosomatic treatment.<br />

References.<br />

[1] B. L. Andersen, et al, Biobehavioral, immune, and heal<str<strong>on</strong>g>th</str<strong>on</strong>g> benefits following recurrence for<br />

psychological interventi<strong>on</strong> participants, Clinical Cancer Res, 16, 270-278, 2010.<br />

[2] D. K. Gramotnev, G. Gramotnev, Psychological stress and psychosomatic treatment: Major<br />

impact <strong>on</strong> serious blood disorders?, NeuroImmunoModulati<strong>on</strong>, 18, 171-183, 2011.<br />

368

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J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an Greenman<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling, UK<br />

e-mail: j.v.greenman@stir.ac.uk<br />

Virginia Pasour<br />

US Army Research Office<br />

Ecosystems Dynamics; Tuesday, June 28, 14:30<br />

Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen exclusi<strong>on</strong> in eco-epidemiological models<br />

It is well known <str<strong>on</strong>g>th</str<strong>on</strong>g>at external forcing (whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er periodic or stochastic) can alter <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

c<strong>on</strong>diti<strong>on</strong>s under which a populati<strong>on</strong> is excluded from or can establish itself wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in<br />

an ecological system. This phenomen<strong>on</strong> is largely understood when <str<strong>on</strong>g>th</str<strong>on</strong>g>e forcing<br />

<strong>on</strong>ly has <strong>on</strong>e comp<strong>on</strong>ent but less so when <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are multiple comp<strong>on</strong>ents, especially<br />

when some are envir<strong>on</strong>mental while o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers are c<strong>on</strong>trols imposed by management to<br />

achieve its objectives. The problem <str<strong>on</strong>g>of</str<strong>on</strong>g> how to exercise <str<strong>on</strong>g>th</str<strong>on</strong>g>ese c<strong>on</strong>trols is <str<strong>on</strong>g>of</str<strong>on</strong>g> importance<br />

in eco-epidemiological systems where <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen is to be excluded, particularly<br />

so in wildlife systems <str<strong>on</strong>g>th</str<strong>on</strong>g>at impinge <strong>on</strong> human heal<str<strong>on</strong>g>th</str<strong>on</strong>g> and livelihood. Much <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e work in <str<strong>on</strong>g>th</str<strong>on</strong>g>is area has focused <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying unforced<br />

and unmanaged system but progress has also been made <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> specific<br />

c<strong>on</strong>trols (e.g. culling, vaccinati<strong>on</strong>) in systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> periodic envir<strong>on</strong>mental forcing<br />

(e.g. <strong>on</strong> bir<str<strong>on</strong>g>th</str<strong>on</strong>g> rate, infecti<strong>on</strong> transmissi<strong>on</strong>). In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper we wish to add to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

literature by taking an algebraic approach based <strong>on</strong> a quadratic approximati<strong>on</strong> in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e forcing streng<str<strong>on</strong>g>th</str<strong>on</strong>g>, linking directly to <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen exclusi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold <str<strong>on</strong>g>th</str<strong>on</strong>g>rough<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e rare invader approximati<strong>on</strong>. This approach generates explicit formulae for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

distorti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold when <str<strong>on</strong>g>th</str<strong>on</strong>g>e forcing is <str<strong>on</strong>g>of</str<strong>on</strong>g> moderate streng<str<strong>on</strong>g>th</str<strong>on</strong>g>. We<br />

can <str<strong>on</strong>g>th</str<strong>on</strong>g>en efficiently explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> specific eco-epidemiological models<br />

and to make general statements about <str<strong>on</strong>g>th</str<strong>on</strong>g>eir behaviour. The algebraic analysis<br />

provides a sound basis to extend <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis to large streng<str<strong>on</strong>g>th</str<strong>on</strong>g> forcing by numerical<br />

simulati<strong>on</strong>, <str<strong>on</strong>g>of</str<strong>on</strong>g> importance when <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold reflects res<strong>on</strong>ance in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

resident subsystem and <str<strong>on</strong>g>th</str<strong>on</strong>g>e subharm<strong>on</strong>ics and chaos <str<strong>on</strong>g>th</str<strong>on</strong>g>at increased forcing can<br />

create. Applicati<strong>on</strong>s include <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> added structure<br />

in epidemiological models and <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> forcing <strong>on</strong> coexistence in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> apparent competiti<strong>on</strong> mediated by pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen or predator.<br />

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Stochastic models in computati<strong>on</strong>al neuroscience I; Wednesday, June 29, 14:30<br />

Priscilla Greenwood<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> British Columbia<br />

e-mail: pgreenw@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.asu.edu<br />

Priscilla Greenwood<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> British Columbia, Vancouver<br />

Peter Rowat<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> California, San Diego<br />

C<strong>on</strong>tinuity across bifurcati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic Morris Lecar<br />

output distributi<strong>on</strong>s<br />

Using <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic Morris Lecar model neur<strong>on</strong>, type II, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> i<strong>on</strong> channel noise,we<br />

investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e inter-spike interval distributi<strong>on</strong> as increasing levels <str<strong>on</strong>g>of</str<strong>on</strong>g> applied current<br />

drive <str<strong>on</strong>g>th</str<strong>on</strong>g>e model <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a sub-critical Hopf bifurcati<strong>on</strong>. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e exp<strong>on</strong>ential tail <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ISI distributi<strong>on</strong> is c<strong>on</strong>tinuous over <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire range<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> plausible applied current, regardless <str<strong>on</strong>g>of</str<strong>on</strong>g> disc<strong>on</strong>tinuities in <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase-portrait <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e model. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e seldom-c<strong>on</strong>sidered distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> number <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

c<strong>on</strong>secutive spikes is geometric wi<str<strong>on</strong>g>th</str<strong>on</strong>g> associated parameter similarly c<strong>on</strong>tinuous as<br />

a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> applied current over <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire input range.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Fabio Grizzi<br />

IRCCS Istituto Clinico Humanitas, Rozzano, Milan, Italy.<br />

e-mail: fabio.grizzi@humanitasresearch.it<br />

Irene Guaraldo<br />

Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Rome La Sapienza, Rome, Italy.<br />

Fractal Geometry: a helpful way for looking cancer<br />

complexity<br />

Cancer research has underg<strong>on</strong>e radical changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e past few years. Amount <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong><br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> at <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic and clinical levels is no l<strong>on</strong>ger <str<strong>on</strong>g>th</str<strong>on</strong>g>e issue. Ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er, how to<br />

handle <str<strong>on</strong>g>th</str<strong>on</strong>g>is informati<strong>on</strong> has become <str<strong>on</strong>g>th</str<strong>on</strong>g>e major obstacle to progress. System biology<br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>e latest fashi<strong>on</strong> in cancer biology, driven by advances in technology <str<strong>on</strong>g>th</str<strong>on</strong>g>at have<br />

provided us wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a suite <str<strong>on</strong>g>of</str<strong>on</strong>g> omics techniques. It can be seen as a c<strong>on</strong>ceptual approach<br />

to biological research <str<strong>on</strong>g>th</str<strong>on</strong>g>at combines reducti<strong>on</strong>ist (parts) and integrati<strong>on</strong>ist<br />

(interacti<strong>on</strong>s) research, to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e nature and maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> entities. In<br />

geometrical terms, cancerous lesi<strong>on</strong>s can be depicted as fractal entities mainly characterized<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>eir irregular shape, self-similar structure, scaling relati<strong>on</strong>ship and<br />

n<strong>on</strong>-integer or fractal dimensi<strong>on</strong>. It is indubitable <str<strong>on</strong>g>th</str<strong>on</strong>g>at The Fractal Geometry <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Nature has provided an innovative paradigm, a novel epistemological approach for<br />

interpreting <str<strong>on</strong>g>th</str<strong>on</strong>g>e anatomical world. It is also known <str<strong>on</strong>g>th</str<strong>on</strong>g>at ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir derivatives have proved to be possible and practical in <strong>on</strong>cology. Viewing<br />

cancer as a system <str<strong>on</strong>g>th</str<strong>on</strong>g>at is dynamically complex in time and space will probably<br />

reveal more about its underlying behavioural characteristics. It is encouraging <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematicians, biologists and clinicians c<strong>on</strong>tribute toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er towards a comm<strong>on</strong><br />

quantitative understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer complexity.<br />

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Game <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical modelling and optimizati<strong>on</strong> in evoluti<strong>on</strong> and ecology I;<br />

Tuesday, June 28, 11:00<br />

Andrei R. Akhmetzhanov<br />

INRIA Sophia-Antipolis, Project Biocore (France) &<br />

McMaster University, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology (Canada)<br />

e-mail: akhmetzhanov@gmail.com<br />

Pierre Bernhard<br />

INRIA Sophia-Antipolis, Project Biocore (France)<br />

e-mail: Pierre.Bernhard@inria.fr<br />

Frédéric Grognard<br />

INRIA Sophia-Antipolis, Project Biocore (France)<br />

e-mail: Frederic.Grognard@inria.fr<br />

Ludovic Mailleret<br />

INRA Sophia-Antipolis, UR880 (France)<br />

e-mail: Ludovic.Mailleret@sophia.inra.fr<br />

Dynamic game for optimal resource allocati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

annual plants and grazing c<strong>on</strong>sumers<br />

In [1] au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors have formulated a model <str<strong>on</strong>g>of</str<strong>on</strong>g> optimal resource allocati<strong>on</strong> in annual<br />

plants wi<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>stant grazing pressure al<strong>on</strong>g a seas<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> fixed leng<str<strong>on</strong>g>th</str<strong>on</strong>g>. The plant has<br />

two choices: ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er to invest nutrients in <str<strong>on</strong>g>th</str<strong>on</strong>g>e vegetative part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e plant or in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

reproductive part. This kind <str<strong>on</strong>g>of</str<strong>on</strong>g> problem has been stated and solved as a problem<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> optimal c<strong>on</strong>trol using P<strong>on</strong>tryagin’s maximum principle.<br />

In our work we c<strong>on</strong>sider a similar model but we take into account <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

grazing pressure <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e plant varies in time and occurs due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

c<strong>on</strong>sumers in <str<strong>on</strong>g>th</str<strong>on</strong>g>e system. C<strong>on</strong>sumers are also faced wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an allocati<strong>on</strong> dilemma<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e investment <str<strong>on</strong>g>of</str<strong>on</strong>g> time in increasing <str<strong>on</strong>g>th</str<strong>on</strong>g>eir internal energy <str<strong>on</strong>g>th</str<strong>on</strong>g>rough grazing<br />

or in reproducti<strong>on</strong> (see for details [2]). Hence we are dealing here wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a dynamic<br />

game <str<strong>on</strong>g>of</str<strong>on</strong>g> two players which are known to be fairly advanced ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical objects<br />

[3]. Its resoluti<strong>on</strong> address interesting questi<strong>on</strong>s such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> an adaptive,<br />

ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an fixed, grazing pressure <strong>on</strong> plants phenology.<br />

References.<br />

[1] N. Yamamura, N. Fujita, M. Hayashi, Y. Nakamura, A. Yamauchi, Optimal phenology <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

annual plants under grazing pressure Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology 246 530–537, 2007<br />

[2] A.R. Akhmetzhanov, F. Grognard, L. Mailleret, Optimal life-history strategies in seas<strong>on</strong>al<br />

c<strong>on</strong>sumer-resource dynamics In revisi<strong>on</strong> for Evoluti<strong>on</strong><br />

[3] T. Basar, G.J. Olsder Dynamic N<strong>on</strong>-Cooperative Game Theory, 2nd ed., SIAM, Philadelphia,<br />

1999<br />

372

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Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

IV; Wednesday, June 29, 08:30<br />

C. M. Groh and B. D. Sleeman<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Leeds, Leeds, LS2<br />

9JT, UK<br />

e-mail: c.m.groh@leeds.ac.uk<br />

M. E. Hubbard<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Computing, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Leeds, Leeds, LS2 9JT, UK<br />

e-mail: m.e.hubbard@leeds.ac.uk<br />

P. F. J<strong>on</strong>es<br />

Leeds Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular Medicine, Leeds, LS9 7TF, UK<br />

e-mail: p.j<strong>on</strong>es@leeds.ac.uk<br />

P. M. Loadman, N. Periasamy and R. M. Phillips<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Cancer Therapeutics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bradford, BD7 1DP,<br />

UK<br />

e-mail: p.m.loadman@bradford.ac.uk<br />

S. W. Smye<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Physics, Leeds Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Genetics, Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> and<br />

Therapeutics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Leeds, LS2 9JT, UK<br />

e-mail: s.w.smye@leeds.ac.uk<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Model <str<strong>on</strong>g>of</str<strong>on</strong>g> Doxorubicin Transport wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in Solid<br />

Tumours<br />

The efficacy <str<strong>on</strong>g>of</str<strong>on</strong>g> treating tumours wi<str<strong>on</strong>g>th</str<strong>on</strong>g> chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic agents, such as doxorubicin,<br />

is dependent <strong>on</strong> how much drug reaches <str<strong>on</strong>g>th</str<strong>on</strong>g>e regi<strong>on</strong>s most distant from<br />

drug supply in sufficient c<strong>on</strong>centrati<strong>on</strong>s. Primerau et al. [1] show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> doxorubicin decreases exp<strong>on</strong>entially wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e distance from <str<strong>on</strong>g>th</str<strong>on</strong>g>e nearest<br />

blood vessel. It is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore important to understand how drug penetrates <str<strong>on</strong>g>th</str<strong>on</strong>g>rough<br />

cancerous tissue and how <str<strong>on</strong>g>th</str<strong>on</strong>g>e penetrati<strong>on</strong> depends <strong>on</strong> treatment c<strong>on</strong>straints, such<br />

as <str<strong>on</strong>g>th</str<strong>on</strong>g>e pharmacokinetic pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile or <str<strong>on</strong>g>th</str<strong>on</strong>g>e dose <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e injecti<strong>on</strong>.<br />

Evans et al. [2] develop a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug penetrati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough<br />

a multicellular layer, incorporating <str<strong>on</strong>g>th</str<strong>on</strong>g>e “flip-flop” mechanism as a form <str<strong>on</strong>g>of</str<strong>on</strong>g> transport<br />

to and from cells and a Pgp-pump mechanism, which is <str<strong>on</strong>g>th</str<strong>on</strong>g>ought to be <str<strong>on</strong>g>th</str<strong>on</strong>g>e leading<br />

mechanism for <str<strong>on</strong>g>th</str<strong>on</strong>g>e increased drug resistance <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells. Because <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is<br />

bespoke to a transwell geometry, it has been successfully validated by experiments<br />

and important transport rates have been estimated.<br />

Building <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e work <str<strong>on</strong>g>of</str<strong>on</strong>g> Evans et al. [2], a model is presented for a geometry<br />

closer to <str<strong>on</strong>g>th</str<strong>on</strong>g>at encountered in-vivo: a cylindrical blood vessel surrounded by multiple<br />

layers <str<strong>on</strong>g>of</str<strong>on</strong>g> cancerous cells. Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>e limited amount <str<strong>on</strong>g>of</str<strong>on</strong>g> membrane proteins<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at facilitate <str<strong>on</strong>g>th</str<strong>on</strong>g>e transport <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug is incorporated into <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, leading to<br />

Michaelis-Menten transport terms. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>is model, <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> different pharmacokinetic<br />

pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles representing bolus injecti<strong>on</strong>s, repeated bolus injecti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> lower<br />

c<strong>on</strong>centrati<strong>on</strong> and infusi<strong>on</strong>s over several hours are assessed for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir ability to deliver<br />

drug to <str<strong>on</strong>g>th</str<strong>on</strong>g>e outer layers in <str<strong>on</strong>g>th</str<strong>on</strong>g>e most efficacious manner.<br />

References.<br />

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[1] A. J. Primeau, A. Rend<strong>on</strong>, D. Hedley, L. Lilge, and I. F. Tannock, The distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e anticancer<br />

drug doxorubicin in relati<strong>on</strong> to blood vessels in solid tumors, Clinical Cancer Research<br />

11 8782–8788.<br />

[2] C. J. Evans, R. M. Phillips, P. F. J<strong>on</strong>es, P. M. Loadman, B. D. Sleeman, C. J. Twelves and<br />

S. W. Smye, A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> doxorubicin penetrati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough multicellular layers,<br />

Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology 257 598–608.<br />

374

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Statistical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in computati<strong>on</strong>al neuroscience II; Wednesday, June 29,<br />

17:00<br />

S<strong>on</strong>ja Grün<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Neuroscience and Medicine (INM-6), Research Center<br />

Jülich, Jülich, Germany & RWTH Aachen University, Aachen, Germany<br />

e-mail: s.gruen@fz-juelich.de<br />

Scales <str<strong>on</strong>g>of</str<strong>on</strong>g> Neur<strong>on</strong>al Data and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Problem <str<strong>on</strong>g>of</str<strong>on</strong>g> Interacti<strong>on</strong><br />

Cortical informati<strong>on</strong> processing was suggested to be performed via functi<strong>on</strong>al<br />

groups <str<strong>on</strong>g>of</str<strong>on</strong>g> cells, called cell assemblies [1]. Theoretical work supported <str<strong>on</strong>g>th</str<strong>on</strong>g>is idea by<br />

indicating <str<strong>on</strong>g>th</str<strong>on</strong>g>at synchr<strong>on</strong>ous input to a neur<strong>on</strong> is much more effective in emitting<br />

a spike <str<strong>on</strong>g>th</str<strong>on</strong>g>an uncorrelated input. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>is coding scheme was c<strong>on</strong>troversially<br />

discussed, first supporting indicati<strong>on</strong>s for spike synchr<strong>on</strong>y were published, so<strong>on</strong> after<br />

techniques became available to simultaneously record from more <str<strong>on</strong>g>th</str<strong>on</strong>g>an a single<br />

neur<strong>on</strong>. Presence <str<strong>on</strong>g>of</str<strong>on</strong>g> excess spike synchr<strong>on</strong>y was found to be dynamic and related<br />

to behaviorally relevant instances in time. As expressed by different recording<br />

techniques (e.g. acti<strong>on</strong> potentials, local field potential (LFP)), <str<strong>on</strong>g>th</str<strong>on</strong>g>e brain exhibits<br />

interesting phenomena <strong>on</strong> several spatial and temporal scales. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e various measures <str<strong>on</strong>g>of</str<strong>on</strong>g> cortical activity now experimentally available is<br />

largely unknown. The characterizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint signature <str<strong>on</strong>g>of</str<strong>on</strong>g> cortical processing<br />

in functi<strong>on</strong>ally meaningful c<strong>on</strong>texts provides insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e relevant scales and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

potentially hierarchical organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> brain processes.<br />

The mechanisms underlying neur<strong>on</strong>al coding and in particular <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> temporal<br />

spike coordinati<strong>on</strong> are hotly debated. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>is debate is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten c<strong>on</strong>founded<br />

by an implicit discussi<strong>on</strong> about <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> appropriate analysis me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods.<br />

To avoid wr<strong>on</strong>g interpretati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> data, <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> simultaneous spike trains<br />

for correlati<strong>on</strong> needs to be properly adjusted to <str<strong>on</strong>g>th</str<strong>on</strong>g>e features <str<strong>on</strong>g>of</str<strong>on</strong>g> experimental spike<br />

trains. Neur<strong>on</strong>al spiking activity is typically not stati<strong>on</strong>ary in time, but neur<strong>on</strong>s<br />

’resp<strong>on</strong>d’ by changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir firing rates to external stimuli or behavioral c<strong>on</strong>texts.<br />

Also, data are not stati<strong>on</strong>ary across trials, but <str<strong>on</strong>g>th</str<strong>on</strong>g>e statistical features may change<br />

during <str<strong>on</strong>g>th</str<strong>on</strong>g>e experiment. Parametric approaches may be applied to experimental<br />

data to account for <str<strong>on</strong>g>th</str<strong>on</strong>g>ese aspects, however, <str<strong>on</strong>g>th</str<strong>on</strong>g>e data may also c<strong>on</strong>tain features (e.g.<br />

deviati<strong>on</strong> from Poiss<strong>on</strong>) <str<strong>on</strong>g>th</str<strong>on</strong>g>at do not allow an analytical treatment or parametric<br />

testing. Ignorance <str<strong>on</strong>g>of</str<strong>on</strong>g> such features present in parallel spike trains are potent generators<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> false positives, but can be avoided by including <str<strong>on</strong>g>th</str<strong>on</strong>g>ose features in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

null-hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e significance test. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>text <str<strong>on</strong>g>th</str<strong>on</strong>g>e usage <str<strong>on</strong>g>of</str<strong>on</strong>g> surrogate data<br />

becomes increasingly important to deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> such complex data [2].<br />

The assembly hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis implies <str<strong>on</strong>g>th</str<strong>on</strong>g>at entities <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ought or percepti<strong>on</strong> are represented<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e coordinated activity <str<strong>on</strong>g>of</str<strong>on</strong>g> (large) neur<strong>on</strong>al groups. However, whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

or not <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamic formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell assemblies c<strong>on</strong>stitutes a fundamental principle<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cortical informati<strong>on</strong> processing remains a c<strong>on</strong>troversial issue <str<strong>on</strong>g>of</str<strong>on</strong>g> current research.<br />

While initially mainly technical problems limited <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental surge for support<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e assembly hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis, <str<strong>on</strong>g>th</str<strong>on</strong>g>e recent advent <str<strong>on</strong>g>of</str<strong>on</strong>g> multi-electrode arrays reveals<br />

fundamental shortcomings <str<strong>on</strong>g>of</str<strong>on</strong>g> available analysis tools. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough larger samplings <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

simultaneous recordings from <str<strong>on</strong>g>th</str<strong>on</strong>g>e cortical tissue are expected to ease <str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> assembly activity, it implies <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand an increase in <str<strong>on</strong>g>th</str<strong>on</strong>g>e number<br />

375

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> parameters to be estimated. It is usually infeasible to simply extend existing<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to such massively parallel data due to a combinatorial explosi<strong>on</strong> and a<br />

lack <str<strong>on</strong>g>of</str<strong>on</strong>g> reliable statistics if individual spike patterns are c<strong>on</strong>sidered. Due to limitati<strong>on</strong>s<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> experimental data, in particular in respect to stati<strong>on</strong>arity,<br />

all parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e full system cannot be estimated. Thus new c<strong>on</strong>cepts need<br />

to be developed and I will give a short review <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods we developed <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

allow <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> massively parallel (hundred or more) spike trains for correlated<br />

activities [3].<br />

Alternatively, <strong>on</strong>e may directly observe a measure <str<strong>on</strong>g>th</str<strong>on</strong>g>at reflects <str<strong>on</strong>g>th</str<strong>on</strong>g>e activity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>s, as does <str<strong>on</strong>g>th</str<strong>on</strong>g>e local field potential (LFP). It has been<br />

c<strong>on</strong>jectured <str<strong>on</strong>g>th</str<strong>on</strong>g>at LFP oscillati<strong>on</strong>s may represent an alternative network-averaged<br />

signature <str<strong>on</strong>g>of</str<strong>on</strong>g> assembly activati<strong>on</strong>s. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e aim to test <str<strong>on</strong>g>th</str<strong>on</strong>g>is hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis we study<br />

and found <str<strong>on</strong>g>th</str<strong>on</strong>g>at in different species and brain areas spikes are locked to <str<strong>on</strong>g>th</str<strong>on</strong>g>e LFP and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e locking may even increase wi<str<strong>on</strong>g>th</str<strong>on</strong>g> learning. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we found <str<strong>on</strong>g>th</str<strong>on</strong>g>at excess<br />

spike synchr<strong>on</strong>y is much better locked to <str<strong>on</strong>g>th</str<strong>on</strong>g>e LFP <str<strong>on</strong>g>th</str<strong>on</strong>g>an chance synchr<strong>on</strong>ous events<br />

or individual spikes clearly indicating <str<strong>on</strong>g>th</str<strong>on</strong>g>at significant excess spike synchr<strong>on</strong>y reflects<br />

coordinated network activity <strong>on</strong> larger scales as expressed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e LFP [4].<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is presentati<strong>on</strong> I will give an overview <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential obstacles in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

correlati<strong>on</strong> analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> parallel neur<strong>on</strong>al data and possible routes to overcome <str<strong>on</strong>g>th</str<strong>on</strong>g>em.<br />

References.<br />

[1] Hebb. The organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> behavior. John Wiley, 1949<br />

[2] Grün (2009) Data-driven significance estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> precise spike correlati<strong>on</strong>. J Neurophysiol,<br />

101, 1126-1140<br />

[3] Grün & Rotter (eds) Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> parallel spike trains. Springer, 2010<br />

[4] Denker, Roux, Lindén, Diesmann, Riehle, Grün (2011) Local field potentials reflects surplus<br />

spike synchr<strong>on</strong>y. Cerebral Cortex (in press)<br />

376

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cell and Tissue Biophysics; Saturday, July 2, 11:00<br />

Z.J. Grzywna<br />

P. Borys<br />

M. Krasowska<br />

P. Pawełek<br />

Secti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Chemical Physics and Biophysics, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Physical<br />

Chemistry and Technology <str<strong>on</strong>g>of</str<strong>on</strong>g> Polymers, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Chemistry, Silesian<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Gliwice, Poland<br />

e-mail: Zbigniew.Grzywna@polsl.pl<br />

Role and activity <str<strong>on</strong>g>of</str<strong>on</strong>g> some chosen voltage-gated K+ and Na+<br />

channels ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical descripti<strong>on</strong> and analyses.<br />

I<strong>on</strong> channels play crucial role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>ducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> electrical impulses,<br />

particularly in nerve and muscle cells. Channels are integral proteins immersed in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cells lipid bilayer, which itself has usually poor i<strong>on</strong>ic permeati<strong>on</strong>. Channels<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ird order structure creates a transmembrane pore a passage for i<strong>on</strong>s. As comes<br />

out from experiments, permeability <str<strong>on</strong>g>of</str<strong>on</strong>g> i<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>rough channels fluctuates in time, and<br />

is determine by varying structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e channel. Modulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> i<strong>on</strong>ic flux is called<br />

gating, which may be driven by different stimuli like chemical species or variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

electric potential. It is interesting <str<strong>on</strong>g>th</str<strong>on</strong>g>at even if channel is subjected to <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>stant,<br />

positive transmembrane voltage <str<strong>on</strong>g>th</str<strong>on</strong>g>at should keep it open, its permeability decreases<br />

after short time channel inactivati<strong>on</strong>. It is <str<strong>on</strong>g>th</str<strong>on</strong>g>an clear <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e voltage gating is not<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>ly <strong>on</strong>e mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> gating present in i<strong>on</strong> channels. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper we will discuss,<br />

so called ball and chain model <str<strong>on</strong>g>of</str<strong>on</strong>g> inactivati<strong>on</strong> addressed to potassium Shaker<br />

channel [1-3]. Polypeptide ball a part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e channels protein <str<strong>on</strong>g>th</str<strong>on</strong>g>at is resp<strong>on</strong>sible<br />

for inactivati<strong>on</strong>, is treaded as a Brownian particle te<str<strong>on</strong>g>th</str<strong>on</strong>g>ered <strong>on</strong> polypeptide chain.<br />

Its wandering was described by means <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong> (parabolic and hyperbolic operators)<br />

[4,5]. First passage time <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ball was calculated and compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

experimental data [2]. Sec<strong>on</strong>d part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e paper is devoted to <str<strong>on</strong>g>th</str<strong>on</strong>g>e sodium channel<br />

activity in rat prostate cancer cells as well as human breast cancer cells. Fractal<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods were used to analyze quantitative differences in secretory membrane activities<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> two rat prostate cancer cell lines (Mat-LyLu and AT-2) <str<strong>on</strong>g>of</str<strong>on</strong>g> str<strong>on</strong>g and weak<br />

metastatic potential, respectively [6]. Each cells endocytic activity was determined<br />

by horseradish peroxidase uptake. Digital images <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> vesicular staining<br />

were evaluated by multifractal analyses: generalized fractal dimensi<strong>on</strong> (Dq)<br />

and its Legendre transform f(a), as well as partiti<strong>on</strong>ed iterated functi<strong>on</strong> system<br />

semifractal (PIFS-SF) analysis. These approaches revealed c<strong>on</strong>sistently <str<strong>on</strong>g>th</str<strong>on</strong>g>at, under<br />

c<strong>on</strong>trol c<strong>on</strong>diti<strong>on</strong>s, all multifractal parameters and PIFS-SF codes determined<br />

had values greater for Mat-LyLu compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g> AT-2 cells. This would agree generally<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e endocytic/vesicular activity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e str<strong>on</strong>gly metastatic Mat-LyLu<br />

cells being more developed <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding weakly metastatic AT-2 cells.<br />

All <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters studied were sensitive to tetrodotoxin (TTX) pre-treatment <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cells, which blocked voltage-gated Na+ channels (VGSCs). Some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters<br />

had a simple dependence <strong>on</strong> VGSC activity, whereby pre-treatment wi<str<strong>on</strong>g>th</str<strong>on</strong>g> TTX<br />

reduced <str<strong>on</strong>g>th</str<strong>on</strong>g>e values for <str<strong>on</strong>g>th</str<strong>on</strong>g>e MAT-LyLu cells and eliminated <str<strong>on</strong>g>th</str<strong>on</strong>g>e differences between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e two cell lines. For o<str<strong>on</strong>g>th</str<strong>on</strong>g>er parameters, however, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere was a complex dependence<br />

377

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

<strong>on</strong> VGSC activity. The possible physical/physiological meaning <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

parameters studied and <str<strong>on</strong>g>th</str<strong>on</strong>g>e nature <str<strong>on</strong>g>of</str<strong>on</strong>g> involvement <str<strong>on</strong>g>of</str<strong>on</strong>g> VGSC activity in c<strong>on</strong>trol<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> endocytosis/ secreti<strong>on</strong> are discussed. Basically, <str<strong>on</strong>g>th</str<strong>on</strong>g>e same sort <str<strong>on</strong>g>of</str<strong>on</strong>g> approach had<br />

been used to analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e endocytic membrane activities <str<strong>on</strong>g>of</str<strong>on</strong>g> two human breast cancer<br />

cell lines (MDA-MB-231 and MCF-7) <str<strong>on</strong>g>of</str<strong>on</strong>g> str<strong>on</strong>g and weak metastatic potential,<br />

respectively, were studied in a comparative approach [7]. Uptake <str<strong>on</strong>g>of</str<strong>on</strong>g> horseradish<br />

peroxidase was used to follow endocytosis. Dependence <strong>on</strong> i<strong>on</strong>ic c<strong>on</strong>diti<strong>on</strong>s and<br />

voltage-gated sodium channel (VGSC) activity were characterized. Fractal me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

were used to analyze quantitative differences in vesicular patterning. Digital<br />

quantificati<strong>on</strong> showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at MDA-MB-231 cells took up more tracer (i.e., were more<br />

endocytic) <str<strong>on</strong>g>th</str<strong>on</strong>g>an MCF-7 cells. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e former, uptake was totally dependent <strong>on</strong><br />

extracellular Na+ and partially dependent <strong>on</strong> extracellular and intracellular Ca2+<br />

and protein kinase activity. Analyzing <str<strong>on</strong>g>th</str<strong>on</strong>g>e generalized fractal dimensi<strong>on</strong> (D(q )) and<br />

its Legendre transform f(alpha) revealed <str<strong>on</strong>g>th</str<strong>on</strong>g>at under c<strong>on</strong>trol c<strong>on</strong>diti<strong>on</strong>s, all multifractal<br />

parameters determined had values greater for MDA-MB-231 compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

MCF-7 cells, c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> endocytic/vesicular activity being more developed in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e str<strong>on</strong>gly metastatic cells. All fractal parameters studied were sensitive to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

VGSC blocker tetrodotoxin (TTX). Some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters had a "simple" dependence<br />

<strong>on</strong> VGSC activity, if present, whereby pretreatment wi<str<strong>on</strong>g>th</str<strong>on</strong>g> TTX reduced <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

values for <str<strong>on</strong>g>th</str<strong>on</strong>g>e MDA-MB-231 cells and eliminated <str<strong>on</strong>g>th</str<strong>on</strong>g>e differences between <str<strong>on</strong>g>th</str<strong>on</strong>g>e two<br />

cell lines. For o<str<strong>on</strong>g>th</str<strong>on</strong>g>er parameters, however, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere was a "complex" dependence <strong>on</strong><br />

VGSC activity. The possible physical/physiological meaning <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

parameters studied and <str<strong>on</strong>g>th</str<strong>on</strong>g>e nature <str<strong>on</strong>g>of</str<strong>on</strong>g> involvement <str<strong>on</strong>g>of</str<strong>on</strong>g> VGSC activity in c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

endocytosis/secreti<strong>on</strong> are discussed.<br />

References.<br />

[1] K.Małysiak, P.Borys, Z.J.Grzywna, On <str<strong>on</strong>g>th</str<strong>on</strong>g>e ball and chain model by simple and hyperbolic<br />

diffusi<strong>on</strong> - an analytical approach, Acta Physica Pol<strong>on</strong>ica B, 5, (2007)<br />

[2] K.Małysiak, Z.J.Grzywna, On <str<strong>on</strong>g>th</str<strong>on</strong>g>e possible me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ball and chain model <str<strong>on</strong>g>of</str<strong>on</strong>g> i<strong>on</strong> channel inactivati<strong>on</strong>, Cellular and Molecular Biology Letters, 13,<br />

535 - 552 (2008)<br />

[3] K. Małysiak, Z. J. Grzywna, Electrostatic interacti<strong>on</strong>s during Kv1.2 N-type inactivati<strong>on</strong>: random<br />

walk simulati<strong>on</strong>, <str<strong>on</strong>g>European</str<strong>on</strong>g> Biophysics Journal 38, 1003 (2009)<br />

[4] P. Borys, Z. J. Grzywna, On <str<strong>on</strong>g>th</str<strong>on</strong>g>e recovery from inactivati<strong>on</strong> by <str<strong>on</strong>g>th</str<strong>on</strong>g>e chain in <str<strong>on</strong>g>th</str<strong>on</strong>g>e ball and chain<br />

model, Cellular and Molecular Biology Letters, 13, 526-534 (2008)<br />

[5] A. Wawrzkiewicz, K.Pawelek, P.Borys, B. Dworakowska, Z.J. Grzywna, On <str<strong>on</strong>g>th</str<strong>on</strong>g>e random walk<br />

model s<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e BK i<strong>on</strong> channel kinetics, Physical Biology -submitted<br />

[6] M. Krasowska, Z.J. Grzywna, M.E. Mycielska, M.B.A. Djamgoz, Patterning <str<strong>on</strong>g>of</str<strong>on</strong>g> endocytic vesicles<br />

and its c<strong>on</strong>trol by voltage - gated Na+ channel activity in rat prostate cancer cells: fractal<br />

analyses , Eur.Biophys. J., 33, 535, (2004)<br />

[7] M. Krasowska, Z. J. Grzywna, M. E. Mycielska, M. B. A. Djamgoz, Fractal analysis and i<strong>on</strong>ic<br />

dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> endocytic membrane activity <str<strong>on</strong>g>of</str<strong>on</strong>g> human breast cancer cells. <str<strong>on</strong>g>European</str<strong>on</strong>g> Biophysics<br />

Journal, 38, 1115 (2009)<br />

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Modeling viral hepatitis dynamics in-vivo and in-vitro in <str<strong>on</strong>g>th</str<strong>on</strong>g>e era <str<strong>on</strong>g>of</str<strong>on</strong>g> direct<br />

anti-viral agents I; Tuesday, June 28, 17:00<br />

Jeremie Guedj<br />

Los Alamos Nati<strong>on</strong>al Laboratory<br />

e-mail: guedj@lanl.gov<br />

Harel Dahari<br />

Uni <str<strong>on</strong>g>of</str<strong>on</strong>g> Illinois at Chicago<br />

Alan Perels<strong>on</strong><br />

Los Alamos Nati<strong>on</strong>al Laboratory, NM, USA<br />

Determinants <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e early hepatitis C viral decline after<br />

treatment initiati<strong>on</strong><br />

The standard model <str<strong>on</strong>g>of</str<strong>on</strong>g> HCV infecti<strong>on</strong> and treatment (Neumann et al., 1998, Science<br />

282(5386):103-107) has played an important role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> HCV RNA<br />

decay after <str<strong>on</strong>g>th</str<strong>on</strong>g>e initiati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> interfer<strong>on</strong> (IFN)-based <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>is model and<br />

assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>at IFN rapidly reduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e average rate <str<strong>on</strong>g>of</str<strong>on</strong>g> viri<strong>on</strong> producti<strong>on</strong>, it has been<br />

possible to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e antiviral effectiveness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, as well as to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

rate <str<strong>on</strong>g>of</str<strong>on</strong>g> HCV clearance rate. However it will be shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is model cannot predict<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e early viral decline observed wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some new direct-acting antiviral (DAA) agents<br />

if <strong>on</strong>e uses <str<strong>on</strong>g>th</str<strong>on</strong>g>e HCV clearance rate estimated during IFN-based <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, which hints<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e determinants <str<strong>on</strong>g>of</str<strong>on</strong>g> HCV decline under treatment may not be fully understood.<br />

Indeed <strong>on</strong>e limitati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard model is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular viral replicati<strong>on</strong>,<br />

which is directly targeted by DAA agents, is not taken into account. In<br />

order to provide a more comprehensive understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e determinants <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

early viral decline after treatment initiati<strong>on</strong>, a new multi-scale model <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>siders<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> intra- and extra-cellular level <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong> will be introduced. Simulati<strong>on</strong><br />

studies will show <str<strong>on</strong>g>th</str<strong>on</strong>g>at in <str<strong>on</strong>g>th</str<strong>on</strong>g>e framework <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model, <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> HCV RNA<br />

decay allows to <strong>on</strong>e to dissect <str<strong>on</strong>g>th</str<strong>on</strong>g>e antiviral effectiveness in blocking different stages<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> viral replicati<strong>on</strong>. Based <strong>on</strong> data from several clinical trials, HCV kinetics under<br />

different classes <str<strong>on</strong>g>of</str<strong>on</strong>g> DAAs will be compared and <str<strong>on</strong>g>th</str<strong>on</strong>g>e implicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is new<br />

approach for <str<strong>on</strong>g>th</str<strong>on</strong>g>e estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e HCV clearance rate will be discussed.<br />

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Modeling and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor invasi<strong>on</strong> I; Tuesday, June 28, 11:00<br />

Caterina Guiot<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Torino, Italia<br />

e-mail: caterina.guiot@unito.it<br />

Ant<strong>on</strong>io S. Gliozzi<br />

Politecnico di Torino, Italia<br />

Pier Paolo Delsanto<br />

Politecnico di Torino, Italia<br />

Lumped models for tumor progressi<strong>on</strong><br />

(Primary)tumors have been described mainly as localized entities which grow by<br />

mitotic duplicati<strong>on</strong> (wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a given intrinsic maximal grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate) in restricted c<strong>on</strong>diti<strong>on</strong>s.<br />

Such restricti<strong>on</strong>s will slow tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate until a proper value <str<strong>on</strong>g>of</str<strong>on</strong>g> carrying<br />

capacity is reached.<br />

Some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most popular scenarios, reflecting tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in specific phases<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> development ( avascular phase, ’multipassage’syngenic transplant in mice, development<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e necrotic core, angiogenesis, invasive phase,..)can be satisfactorily<br />

described by means <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Phenomenological Universality (PUN) me<str<strong>on</strong>g>th</str<strong>on</strong>g>od, which<br />

assumes <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor volume V depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate c(t), whose effective<br />

time derivative can be approximated by a series expansi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e variable c(t) itself:<br />

dV/dt = c(t) V; dc/dt = -alpha c - beta c2 +...<br />

Retaining <strong>on</strong>ly <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>stant term we get <str<strong>on</strong>g>th</str<strong>on</strong>g>e unlimited grow<str<strong>on</strong>g>th</str<strong>on</strong>g> U(0), while by<br />

c<strong>on</strong>sidering <str<strong>on</strong>g>th</str<strong>on</strong>g>e linear term <str<strong>on</strong>g>th</str<strong>on</strong>g>e Gompertz law U(1) is obtained, accounting for a<br />

time-varying grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate and a c<strong>on</strong>stant carrying capacity.U(2), which is <str<strong>on</strong>g>th</str<strong>on</strong>g>e following<br />

term, corresp<strong>on</strong>ds to <str<strong>on</strong>g>th</str<strong>on</strong>g>e so called West law, whose main characteristics is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>of</str<strong>on</strong>g> accounting for tumor vascularizati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough an ’optimal’ fractal network.<br />

As a matter <str<strong>on</strong>g>of</str<strong>on</strong>g> fact, U(2) entails a variati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall tumor carrying capacity,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at in a more general sense becomes not <strong>on</strong>ly dependent from <str<strong>on</strong>g>th</str<strong>on</strong>g>e limiting volume<br />

for tumor development, but <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s, including<br />

nutrients availability, switch to different metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways, horm<strong>on</strong>al influences<br />

and so <strong>on</strong>.<br />

Provided <str<strong>on</strong>g>th</str<strong>on</strong>g>e two main parameters, i.e. grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate and carrying capacity, are<br />

modulated in time to properly account for <str<strong>on</strong>g>th</str<strong>on</strong>g>e internal metabolism and <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor and its envir<strong>on</strong>ment respectively, a full descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

’natural history’ <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor can finally be obtained. Comparis<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> available<br />

data and clinical descripti<strong>on</strong> ( e.g. for <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> prostate cancer) will help in finely<br />

modulating <str<strong>on</strong>g>th</str<strong>on</strong>g>e model parameters. Even more interestingly, such a general model is<br />

suitable for ’<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical’ validati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic efficiency. The effect <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

t(t), whose functi<strong>on</strong>al form can be expressed in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor radiosensitivity,<br />

drug resistance, etc., can be incorporated into Eqn. 1 by substituting c(t) wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e difference c(t) - t(t). Spatially inhomogeneous tumor patterns can be included<br />

provided different ’cl<strong>on</strong>es’ <str<strong>on</strong>g>of</str<strong>on</strong>g> cells are accounted for.<br />

In c<strong>on</strong>clusi<strong>on</strong>, by retaining <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor biological complexity in <str<strong>on</strong>g>th</str<strong>on</strong>g>e progressively<br />

changing values <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate and carrying capacity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor-host system,<br />

a easy-to-handle lumped-model can be worked out, which can prove useful to fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

stimulate and improve cooperati<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>eoreticians and clinicians.<br />

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Epidemiology, Eco-Epidemiology and Evoluti<strong>on</strong>; Saturday, July 2, 11:00<br />

Caterina Guiot1 , Ilaria Stura2 , Ezio Venturino2 , Lorenzo Priano1,3 , Alessandro<br />

Mauro1,3 1Dipartimento di Neuroscienze<br />

Università di Torino, Italy.<br />

2Dipartimento di Matematica “Giuseppe Peano”,<br />

Università di Torino, Italy.<br />

Email: ezio.venturino@unito.it<br />

1Dipartimento di Neurologia e Neuroriabilitazi<strong>on</strong>e,<br />

IRCCS Ist. Auxologico Italiano, Piancavallo (VB), Italy.<br />

Multi-scale modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> human sleep<br />

Sleep is a complex dynamic process, regulated bo<str<strong>on</strong>g>th</str<strong>on</strong>g> by “l<strong>on</strong>g time” circadian<br />

and homeostatic rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms and <str<strong>on</strong>g>th</str<strong>on</strong>g>e alternance between Rapid Eyes Movement (REM)<br />

and n<strong>on</strong> REM (NREM) sleep and by <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> peculiar “short-time” transient<br />

Electro Encephalo Graphics (EEG) events, namely Transient Synchr<strong>on</strong>ized<br />

EEG Patterns (TSEP), which are <str<strong>on</strong>g>th</str<strong>on</strong>g>ought to be expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> synchr<strong>on</strong>ous cortical<br />

neur<strong>on</strong> discharges and are supposed to play <str<strong>on</strong>g>th</str<strong>on</strong>g>e main role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e building-up <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

NREM sleep and flexible adaptati<strong>on</strong> against perturbati<strong>on</strong>s. Our study aims at collecting,<br />

analyzing and modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e time series <str<strong>on</strong>g>of</str<strong>on</strong>g> TSEP related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e achievement,<br />

maintenance and interrupti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> NREM sleep, in physiological c<strong>on</strong>diti<strong>on</strong>s.<br />

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Semigroups <str<strong>on</strong>g>of</str<strong>on</strong>g> Operators in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology I; Wednesday, June 29, 08:30<br />

Piotr Gwiazda<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw,<br />

Banacha 2, 02-097 Warszawa<br />

e-mail: pgwiazda@mimuw.edu.pl<br />

Split-up algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m in <str<strong>on</strong>g>th</str<strong>on</strong>g>e metric space for <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

structured populati<strong>on</strong> dynamics<br />

The talk is based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint research wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Jose Carillo, Rinaldo Colombo,<br />

Anna Marciniak-Czochra and Agnieszka Ulikowska. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e example <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e structured<br />

populati<strong>on</strong> equati<strong>on</strong>s we mean <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> so-called age-structured model<br />

(transport equati<strong>on</strong> in a half space wi<str<strong>on</strong>g>th</str<strong>on</strong>g> n<strong>on</strong>-local boundary c<strong>on</strong>diti<strong>on</strong>s) or size<br />

structured model (transport equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an integral term in space <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e right<br />

hand side), see for more details B. Per<str<strong>on</strong>g>th</str<strong>on</strong>g>ame "Transport equati<strong>on</strong>s in ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

biology" 2007. From <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological reas<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a need for using initial data in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e space <str<strong>on</strong>g>of</str<strong>on</strong>g> Rad<strong>on</strong> measures. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>e Lipschitz-bounded distance (flat metric)<br />

we prove Lipschitz dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong>s to linear and n<strong>on</strong>linear system w.r.t.<br />

initial data and coefficients <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s. Significant simplificati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e calculati<strong>on</strong>s<br />

is d<strong>on</strong>e by using <str<strong>on</strong>g>th</str<strong>on</strong>g>e split-up algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m, dealing separately wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a semigroup<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> transport and a semigroup <str<strong>on</strong>g>of</str<strong>on</strong>g> an integral kernel operator.<br />

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Applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>negative Rad<strong>on</strong> measure spaces wi<str<strong>on</strong>g>th</str<strong>on</strong>g> metric structure<br />

to populati<strong>on</strong> dynamic models; Wednesday, June 29, 17:00<br />

Piotr Gwiazda<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw,<br />

Banacha 2, 02-097 Warszawa<br />

e-mail: pgwiazda@mimuw.edu.pl<br />

Mertics <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e space <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e measures and transport equati<strong>on</strong><br />

The talk will be a short introducti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e issue <str<strong>on</strong>g>of</str<strong>on</strong>g> abstract me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> Wasserstein<br />

and related metrics in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eir applicati<strong>on</strong>s to soluti<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

space <str<strong>on</strong>g>of</str<strong>on</strong>g> Rad<strong>on</strong> measures for linear and n<strong>on</strong>linear PDEs. However <str<strong>on</strong>g>th</str<strong>on</strong>g>e topic was<br />

studied in many aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> PDEs coming from ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical physics, but in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical biology it is not very well understood. As an introductory<br />

talk to <str<strong>on</strong>g>th</str<strong>on</strong>g>e mini-symposium we will give some survey <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most important facts,<br />

to give some general feeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e topic.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Game <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical modelling and optimizati<strong>on</strong> in evoluti<strong>on</strong> and ecology II;<br />

Tuesday, June 28, 14:30<br />

Christ<str<strong>on</strong>g>of</str<strong>on</strong>g>oros Hadjichrysan<str<strong>on</strong>g>th</str<strong>on</strong>g>ou<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Science, City University, L<strong>on</strong>d<strong>on</strong> EC1V 0HB,<br />

UK<br />

e-mail: Christ<str<strong>on</strong>g>of</str<strong>on</strong>g>oros.Hadjichrysan<str<strong>on</strong>g>th</str<strong>on</strong>g>ou.1@city.ac.uk<br />

Mark Broom<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Science, City University, L<strong>on</strong>d<strong>on</strong> EC1V 0HB,<br />

UK<br />

e-mail: Mark.Broom.1@city.ac.uk<br />

Jan Rychtar<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nor<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Carolina at Greensboro, Greensboro NC27402, USA<br />

e-mail: rychtar@uncg.edu<br />

Evoluti<strong>on</strong>ary games <strong>on</strong> graphs<br />

Evoluti<strong>on</strong>ary game dynamics models have been mainly studied <strong>on</strong> homogeneous<br />

infinite populati<strong>on</strong>s. However, real populati<strong>on</strong>s are nei<str<strong>on</strong>g>th</str<strong>on</strong>g>er homogeneously mixed<br />

nor infinite. This study investigates <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic evoluti<strong>on</strong>ary game dynamics in<br />

structured populati<strong>on</strong>s as represented by graphs. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, we c<strong>on</strong>sider analytically<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e fixati<strong>on</strong> probability and <str<strong>on</strong>g>th</str<strong>on</strong>g>e speed <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary process (absorpti<strong>on</strong><br />

time) when a single mutant individual invades into <str<strong>on</strong>g>th</str<strong>on</strong>g>ree simple graphs <str<strong>on</strong>g>of</str<strong>on</strong>g> finite<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> vertices: <str<strong>on</strong>g>th</str<strong>on</strong>g>e star, <str<strong>on</strong>g>th</str<strong>on</strong>g>e circle and <str<strong>on</strong>g>th</str<strong>on</strong>g>e complete graph. Applying <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

obtained results, it is <str<strong>on</strong>g>th</str<strong>on</strong>g>en shown <str<strong>on</strong>g>th</str<strong>on</strong>g>e significant impact <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

populati<strong>on</strong> might have <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary process. As a specific example, we c<strong>on</strong>sider<br />

a Hawk-Dove type game. Finally, it is dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e update<br />

rule (evoluti<strong>on</strong>ary dynamics) <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary process does not significantly affect<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e invader mutants in homogeneous populati<strong>on</strong>s, it might<br />

cause significant changes in populati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a n<strong>on</strong>-homogeneous structure.<br />

References.<br />

[1] Broom, M., Hadjichrysan<str<strong>on</strong>g>th</str<strong>on</strong>g>ou, C., Rychtar, J. (2010), Evoluti<strong>on</strong>ary games <strong>on</strong> graphs and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

speed <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary process Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Royal Society A 466 1327–1346.<br />

[2] Broom, M., Hadjichrysan<str<strong>on</strong>g>th</str<strong>on</strong>g>ou, C., Rychtar, J. (2011), Evoluti<strong>on</strong>ary games <strong>on</strong> star graphs<br />

under various updating rules Dynamic Games and Applicati<strong>on</strong>s (submitted).<br />

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Stem cells and cancer; Wednesday, June 29, 14:30<br />

Hiroshi Haeno<br />

Dana-Farber Cancer Institute/ Harvard School <str<strong>on</strong>g>of</str<strong>on</strong>g> Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

e-mail: hiroshi@jimmy.harvard.edu<br />

Ross L. Levine<br />

Memorial Sloan-Kettering Cancer Center<br />

D. Gary Gilliland<br />

Merck Research Laboratories<br />

Franziska Michor<br />

Dana-Farber Cancer Institute/ Harvard School <str<strong>on</strong>g>of</str<strong>on</strong>g> Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

A progenitor cell origin <str<strong>on</strong>g>of</str<strong>on</strong>g> myeloid malignancies<br />

All cancers rely <strong>on</strong> cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at have properties <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g-term self-renewal or stemness<br />

to maintain and propagate <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor, but <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell <str<strong>on</strong>g>of</str<strong>on</strong>g> origin <str<strong>on</strong>g>of</str<strong>on</strong>g> most cancers<br />

is still unknown. Here, we design a stochastic ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> hematopoietic<br />

stem and progenitor cells to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer initiati<strong>on</strong>.<br />

We c<strong>on</strong>sider different evoluti<strong>on</strong>ary pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways leading to cancer-initiating cells<br />

in JAK2V617F-positive myeloproliferative neoplasms (MPN): (i) <str<strong>on</strong>g>th</str<strong>on</strong>g>e JAK2V617F<br />

mutati<strong>on</strong> may arise in a stem cell; (ii) a progenitor cell may first acquire a mutati<strong>on</strong><br />

c<strong>on</strong>ferring self-renewal, followed by acquisiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e JAK2V617F mutati<strong>on</strong>;<br />

(iii) <str<strong>on</strong>g>th</str<strong>on</strong>g>e JAK2V617F mutati<strong>on</strong> may first emerge in a progenitor cell, followed by<br />

a mutati<strong>on</strong> c<strong>on</strong>ferring self-renewal; and (iv) a mutati<strong>on</strong> c<strong>on</strong>ferring self-renewal to<br />

progenitors may arise in <str<strong>on</strong>g>th</str<strong>on</strong>g>e stem cell populati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out causing a change in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

stem cell’s phenotype, followed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e JAK2V617F mutati<strong>on</strong> emerging in a progenitor<br />

cell. We find ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical evidence <str<strong>on</strong>g>th</str<strong>on</strong>g>at a progenitor is <str<strong>on</strong>g>th</str<strong>on</strong>g>e most likely cell <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

origin <str<strong>on</strong>g>of</str<strong>on</strong>g> JAK2V617F-mutant MPN. These results may also have relevance to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

tumor types arising in tissues <str<strong>on</strong>g>th</str<strong>on</strong>g>at are organized as a differentiati<strong>on</strong> hierarchy.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Saliha Hamdous<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Tizi-Ouzou, Algeria<br />

e-mail: hamdoussaliha2002@yahoo.fr<br />

Hisao Fujita Yashima<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Turin, Italy<br />

e-mail: hisao.fujitayashima@unito.it<br />

Luigi Manca<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Marne la Vally, France<br />

e-mail: Luigi.Manca@univ-mlv.fr<br />

Populati<strong>on</strong> Dynamics; Wednesday, June 29, 08:30<br />

Invariant Measure for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Stochastic Models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Populati<strong>on</strong> Dynamics wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Spatial Diffusi<strong>on</strong><br />

We c<strong>on</strong>sider a stochastic equati<strong>on</strong>s system modeling populati<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> competiti<strong>on</strong><br />

and prey-predator type wi<str<strong>on</strong>g>th</str<strong>on</strong>g> diffusi<strong>on</strong> in a territorial domain. We prove<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> an invariant measure for <str<strong>on</strong>g>th</str<strong>on</strong>g>e competiti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e prey-predator<br />

stochastic models. To dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>ese results, we apply <str<strong>on</strong>g>th</str<strong>on</strong>g>e Krylov-Bogoliubov’s<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eorem, who requires an estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic equati<strong>on</strong>s<br />

system.<br />

To obtain <str<strong>on</strong>g>th</str<strong>on</strong>g>e appropriate estimates we apply <str<strong>on</strong>g>th</str<strong>on</strong>g>e Itô’s formula in infinite dimensi<strong>on</strong><br />

space to an adequate functi<strong>on</strong>.<br />

References.<br />

[1] S. Hamdous, H. Fujita Yashima: Mesure invariante pour le système d’équati<strong>on</strong>s stochastiques<br />

du modèle de compétiti<strong>on</strong> avec diffusi<strong>on</strong> spatiale. Rend. Sem. Mat. Padova, vol 122 (2009)<br />

p.p. 85-98.<br />

[2] S. Hamdous, L. Manca, H. Fujita Yashima: Mesure invariante pour le système d’équati<strong>on</strong>s<br />

stochastiques du modèle de proie-prédateur avec diffusi<strong>on</strong> spatiale. Rend. Sem. Mat. Padova,<br />

vol 124 (2010) p.p. 57-75.<br />

[3] R. Rudnicki: L<strong>on</strong>g-time behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> a stochastic prey-predator model. Stoch. Proc. Appl.,<br />

vol. 108 (2003), pp. 93-107.<br />

[4] E. Tornatore: Stochastic equati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> dynamic wi<str<strong>on</strong>g>th</str<strong>on</strong>g> diffusi<strong>on</strong> <strong>on</strong> a domain. Rend.<br />

Circ. Mat. Palermo, Serie II, Tomo 52 (2003), pp. 15-29.<br />

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Fluid-structure interacti<strong>on</strong> problems in biomechanics; Saturday, July 2, 08:30<br />

Christina Hamlet<br />

e-mail: chamlet@email.unc.edu<br />

Laura A. Miller<br />

e-mail: lam9@email.unc.edu<br />

Austin Baird<br />

e-mail: abaird@email.unc.edu<br />

Terry Rodriguez<br />

e-mail: tjrodrig@email.unc.edu<br />

Excitable tissues in fluids<br />

A wide range <str<strong>on</strong>g>of</str<strong>on</strong>g> numerical, analytical, and experimental work in recent years has<br />

focused <strong>on</strong> understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> between fluids and elastic structures in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> cardiovascular flows, animal swimming and flying, cellular flows, and<br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>er biological problems. While great progress has been made in understanding<br />

such systems, less is known about how <str<strong>on</strong>g>th</str<strong>on</strong>g>ese excitable tissues modulate <str<strong>on</strong>g>th</str<strong>on</strong>g>eir mechanical<br />

properties in resp<strong>on</strong>se to fluid forces and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er envir<strong>on</strong>mental cues. The<br />

broad goal <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is to develop a framework to integrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>ducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

acti<strong>on</strong> potentials wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> muscles, to <str<strong>on</strong>g>th</str<strong>on</strong>g>e movement <str<strong>on</strong>g>of</str<strong>on</strong>g> organs and<br />

organisms, to <str<strong>on</strong>g>th</str<strong>on</strong>g>e moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluid, and back to <str<strong>on</strong>g>th</str<strong>on</strong>g>e nervous system <str<strong>on</strong>g>th</str<strong>on</strong>g>rough envir<strong>on</strong>mental<br />

cues. Such coupled models can <str<strong>on</strong>g>th</str<strong>on</strong>g>en be used to understand how small<br />

changes in tissue physics can result in large changes in performance at <str<strong>on</strong>g>th</str<strong>on</strong>g>e organ<br />

and organism level. Two examples will be discussed in <str<strong>on</strong>g>th</str<strong>on</strong>g>is presentati<strong>on</strong>. The first<br />

example c<strong>on</strong>siders how active c<strong>on</strong>tracti<strong>on</strong>s generated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiac c<strong>on</strong>ducti<strong>on</strong> system<br />

can enhance flows in tubular hearts, particularly at low Reynolds numbers. The<br />

sec<strong>on</strong>d example c<strong>on</strong>siders how <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s between pacemakers in <str<strong>on</strong>g>th</str<strong>on</strong>g>e upside<br />

down jellyfish can alter feeding currents generated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e bell pulsati<strong>on</strong>s. In bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

cases, <str<strong>on</strong>g>th</str<strong>on</strong>g>e ultimate goal is to simulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e electropotentials in <str<strong>on</strong>g>th</str<strong>on</strong>g>e nervous system<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at trigger mechanical changes in 1D fibers representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e muscular bands. The<br />

muscular c<strong>on</strong>tracti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>en apply forces to <str<strong>on</strong>g>th</str<strong>on</strong>g>e boundaries <str<strong>on</strong>g>th</str<strong>on</strong>g>at interacts wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

fluid modeled by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Navier-Stokes equati<strong>on</strong>s. The computati<strong>on</strong>al framework used<br />

to solve <str<strong>on</strong>g>th</str<strong>on</strong>g>ese problems is <str<strong>on</strong>g>th</str<strong>on</strong>g>e immersed boundary me<str<strong>on</strong>g>th</str<strong>on</strong>g>od originally developed by<br />

Charles Peskin.<br />

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Bioinformatics and System Biology; Wednesday, June 29, 14:30<br />

Samuel Handelman<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences Institute, The Ohio State University, Columbus<br />

OH<br />

e-mail: shandelman@mbi.osu.edu<br />

J. S. Verducci<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Statistics, The Ohio State University, Columbus OH<br />

J. J. Kwiek<br />

The Center for Microbial Interface Biology, Ohio State University<br />

College <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine, Columbus OH<br />

S. B. Kumar<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Veterinary Biosciences, The Ohio State University,<br />

Columbus OH<br />

D. A. Janies<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biomedical Informatics, Ohio State University College<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine, Columbus OH<br />

GENPHEN: Genotype/Phenotype Associati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Reference to Phylogeny<br />

When genome sequences are obtained from organisms wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different associated phenotypes,<br />

it should be possible to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>ose sequence properties which c<strong>on</strong>fer a<br />

given phenotype. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary relati<strong>on</strong>ships between organisms lead<br />

to n<strong>on</strong>-independence between <str<strong>on</strong>g>th</str<strong>on</strong>g>e sequence properties. For example, <str<strong>on</strong>g>th</str<strong>on</strong>g>e HIV-1<br />

virus has a populati<strong>on</strong> structure reflecting bo<str<strong>on</strong>g>th</str<strong>on</strong>g> transmissi<strong>on</strong> between individuals<br />

and evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e HIV-1 quasispecies wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in each patient. This n<strong>on</strong>-independence<br />

can introduce interdependence between unrelated mutati<strong>on</strong>s giving a false appearance<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> causati<strong>on</strong>. These evoluti<strong>on</strong>ary relati<strong>on</strong>ships are an issue even in HIV-1<br />

where recombinati<strong>on</strong> is rapid, and are pervasive in humans, where linkage disequilibrium<br />

is extensive. In human disease studies, <str<strong>on</strong>g>th</str<strong>on</strong>g>is can sometimes be overcome by<br />

comparing siblings: alleles comm<strong>on</strong> <strong>on</strong>ly in sick siblings are likely true causative alleles.<br />

GENPHEN identifies, in a phylogenetic rec<strong>on</strong>structi<strong>on</strong>, sibling lineages where<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e phenotype varies. Then, GENPHEN uses modified proporti<strong>on</strong>al hazard models<br />

to identify causal polymorphisms. GENPHENs advantages include: speed practical<br />

for high-<str<strong>on</strong>g>th</str<strong>on</strong>g>roughput sequence data, estimates <str<strong>on</strong>g>of</str<strong>on</strong>g> relative streng<str<strong>on</strong>g>th</str<strong>on</strong>g> or speed <str<strong>on</strong>g>of</str<strong>on</strong>g> different<br />

effects, and improved precisi<strong>on</strong> even vs. o<str<strong>on</strong>g>th</str<strong>on</strong>g>er tree-based me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: 50%-300%<br />

improvement in precisi<strong>on</strong> at same recall, ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er to predict experimental correlati<strong>on</strong>s<br />

(obtained from STRING: http://string-db.org/) or in simulati<strong>on</strong>s under biologically<br />

reas<strong>on</strong>able parameters <strong>on</strong> HIV quasispecies sequence trees.<br />

388

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

IV; Wednesday, June 29, 08:30<br />

Le<strong>on</strong>id Hanin<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Idaho State University, USA<br />

e-mail: hanin@isu.edu<br />

The End <str<strong>on</strong>g>of</str<strong>on</strong>g> Linear-Quadratic Era in Radiati<strong>on</strong> Biology<br />

We review ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and biological grounds for <str<strong>on</strong>g>th</str<strong>on</strong>g>e linear-quadratic (LQ) model<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> irradiated cell survival. The LQ model was a tool <str<strong>on</strong>g>of</str<strong>on</strong>g> choice in quantitative<br />

radiati<strong>on</strong> biology for more <str<strong>on</strong>g>th</str<strong>on</strong>g>an 60 years. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e premises <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

LQ model are unrealistic, especially for intermediate and high doses <str<strong>on</strong>g>of</str<strong>on</strong>g> radiati<strong>on</strong>.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we develop a more realistic cell survival model based <strong>on</strong> rigorous<br />

accounting for microdosimetric effects [1]. The new model is applicable to low,<br />

intermediate, and high acute doses <str<strong>on</strong>g>of</str<strong>on</strong>g> radiati<strong>on</strong>, and unlike <str<strong>on</strong>g>th</str<strong>on</strong>g>e LQ model, it does<br />

not assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> primary lesi<strong>on</strong>s is Poiss<strong>on</strong>. For<br />

small doses, <str<strong>on</strong>g>th</str<strong>on</strong>g>e new model can be approximated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e LQ model. However, for<br />

high doses, <str<strong>on</strong>g>th</str<strong>on</strong>g>e best fitting LQ model grossly underestimates cell survival. The<br />

same is also true for <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>venti<strong>on</strong>al LQ model, <strong>on</strong>ly more so. It is shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at for<br />

high doses, <str<strong>on</strong>g>th</str<strong>on</strong>g>e microdosimetric distributi<strong>on</strong> can be approximated by a Gaussian<br />

distributi<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding cell survival probabilities are compared.<br />

This is a joint work wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Dr. Marco Zaider from <str<strong>on</strong>g>th</str<strong>on</strong>g>e Memorial Sloan-Kettering<br />

Cancer Center, New York.<br />

References.<br />

[1] L.G. Hanin and M. Zaider (2010), Cell-survival probability at large doses: an alternative to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e linear-quadratic model, Physics in Medicine and Biology, v. 55, pp. 4687-4702.<br />

389

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Hea<str<strong>on</strong>g>th</str<strong>on</strong>g>er Hardway<br />

Bost<strong>on</strong> University<br />

e-mail: hhardway@bu.edu<br />

Tasso Kaper<br />

Bost<strong>on</strong> University<br />

Cyn<str<strong>on</strong>g>th</str<strong>on</strong>g>ia Bradham<br />

Bost<strong>on</strong> University<br />

Developmental Biology; Wednesday, June 29, 17:00<br />

Dorsal-ventral patterning in sea urchin and Drosophila<br />

embryos<br />

The dorsal-ventral axis in Drosophila is specified by gradients <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e morphogenetic<br />

proteins (BMPs). While initially secreted in a broad regi<strong>on</strong>, later c<strong>on</strong>centrate<br />

into a narrow band, designating <str<strong>on</strong>g>th</str<strong>on</strong>g>e dorsal-most 10% <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e embryo. Modeling<br />

papers have focused <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics seen in Drosophila, but <str<strong>on</strong>g>th</str<strong>on</strong>g>e same mechanism<br />

specifies <str<strong>on</strong>g>th</str<strong>on</strong>g>e sea urchin axis. Yet in urchins, <str<strong>on</strong>g>th</str<strong>on</strong>g>e BMP secreti<strong>on</strong> and expressi<strong>on</strong><br />

domains are complementary. Reacti<strong>on</strong>-diffusi<strong>on</strong> models are c<strong>on</strong>sidered for <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterning<br />

seen in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> organisms, but are limited in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir capabilities to reproduce<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e sharp curvature seen in <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological data. While positive feedback is likely<br />

resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>e fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er c<strong>on</strong>centrating <str<strong>on</strong>g>th</str<strong>on</strong>g>e BMP gradient, we c<strong>on</strong>sider alternative<br />

types <str<strong>on</strong>g>th</str<strong>on</strong>g>at could account for <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterning seen in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> organisms.<br />

390

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Statistical Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Signals I; Saturday, July 2, 08:30<br />

Modeling mass spectrometry proteomics data using<br />

n<strong>on</strong>parametric regressi<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

Jaroslaw Harezlak<br />

Indiana University School <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine, Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Biostatistics,<br />

410 W 10<str<strong>on</strong>g>th</str<strong>on</strong>g> St., Suite 3000, Indianapolis, IN 46202, USA<br />

e-mail: harezlak@iupui.edu<br />

The amount and complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e data collected from <str<strong>on</strong>g>th</str<strong>on</strong>g>e mass spectrometry<br />

instruments has outpaced <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>odological developments in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir processing.<br />

We propose a number <str<strong>on</strong>g>of</str<strong>on</strong>g> approaches to address <str<strong>on</strong>g>th</str<strong>on</strong>g>e issues arising in modeling such<br />

data. The me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods used include local polynomial kernel regressi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> adaptive<br />

bandwid<str<strong>on</strong>g>th</str<strong>on</strong>g> selecti<strong>on</strong> and wavelet me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods. We address <str<strong>on</strong>g>th</str<strong>on</strong>g>e issues <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-stati<strong>on</strong>arity<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e variance process and correlated errors. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, we provide <str<strong>on</strong>g>th</str<strong>on</strong>g>e results <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

preliminary simulati<strong>on</strong> studies and apply <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to a lung cancer SELDI-TOF<br />

MS data set.<br />

391

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Mechanics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> and cortical actin at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular level;<br />

Saturday, July 2, 08:30<br />

Andrew Harris<br />

L<strong>on</strong>d<strong>on</strong> Centre for Nanotechnology<br />

e-mail: uccaarh@ucl.ac.uk<br />

Measuring <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> cell m<strong>on</strong>olayers<br />

Cell m<strong>on</strong>olayers are c<strong>on</strong>tinuously exposed to mechanical stresses in development<br />

and normal physiological functi<strong>on</strong>. Mutati<strong>on</strong>s in cytoskeletal and cell-cell adhesi<strong>on</strong><br />

proteins lead to patient symptoms associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> increased tissue fragility, however<br />

a me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for characterizing m<strong>on</strong>olayer mechanics is lacking. We have developed<br />

a novel system for tensile testing <str<strong>on</strong>g>of</str<strong>on</strong>g> m<strong>on</strong>olayers which are suspended between two<br />

test rods. One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e rods is rigid acting as a reference whilst <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er is flexible<br />

to allow for force measurement. Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> stress-strain curves during m<strong>on</strong>olayer<br />

extensi<strong>on</strong> enables <str<strong>on</strong>g>th</str<strong>on</strong>g>e determinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a m<strong>on</strong>olayer in plane elastic modulus. The<br />

c<strong>on</strong>tributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> different cytoskeletal filaments to m<strong>on</strong>olayer elasticity is ascertained<br />

by treatment wi<str<strong>on</strong>g>th</str<strong>on</strong>g> inhibitors. By depolymerising <str<strong>on</strong>g>th</str<strong>on</strong>g>e actin cytoskelet<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Latrunculin<br />

B a substantial decrease in <str<strong>on</strong>g>th</str<strong>on</strong>g>e elastic modulus can be observed.<br />

392

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Eleanor Harris<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Ba<str<strong>on</strong>g>th</str<strong>on</strong>g>, UK<br />

e-mail: E.M.Harris<strong>on</strong>@ba<str<strong>on</strong>g>th</str<strong>on</strong>g>.ac.uk<br />

Ben Adams<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Ba<str<strong>on</strong>g>th</str<strong>on</strong>g>, UK<br />

e-mail: B.Adams@ba<str<strong>on</strong>g>th</str<strong>on</strong>g>.ac.uk<br />

Epidemics; Tuesday, June 28, 11:00<br />

Epidemic Models for Leishmaniasis: Elucidati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Key<br />

Processes and Parameters<br />

Leishmaniasis is a vector-borne Neglected Tropical Disease. It is caused by Leishmania<br />

protozoa transmitted between humans by infected female sandflies. Previously<br />

associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e impoverished in Africa, Leishmaniasis is now c<strong>on</strong>sidered to be<br />

an emerging disease as it spreads across a range <str<strong>on</strong>g>of</str<strong>on</strong>g> locati<strong>on</strong>s from Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> America to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Mediterranean Basin. We present a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemiology<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Leishmaniasis. We use a range <str<strong>on</strong>g>of</str<strong>on</strong>g> techniques including elasticity analysis to make<br />

a comprehensive assessment <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> various processes and parameters<br />

in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e igniti<strong>on</strong> and maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> disease spread. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e vector<br />

populati<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>e critical link when determining whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er an infecti<strong>on</strong> can become<br />

established in a naive populati<strong>on</strong>, but <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e host populati<strong>on</strong> is key in <str<strong>on</strong>g>th</str<strong>on</strong>g>e perpetuati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> endemic infecti<strong>on</strong>. We c<strong>on</strong>clude by discussing <str<strong>on</strong>g>th</str<strong>on</strong>g>e implicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> our<br />

analysis for <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> Leishmaniasis in different parts <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e world.<br />

393

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Saturday, July 2, 08:30<br />

S.Naser Hashemi<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer<br />

Science, Amirkabir University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology,Tehran, Iran<br />

e-mail: nhashemi@aut.ac.ir<br />

Fazeleh S.M.Salehi<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer<br />

Science, Amirkabir University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology,Tehran, Iran<br />

"Modeling C<strong>on</strong>trol Strategies for Influenza Epidemic wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Emergence and Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Drug Resistance"<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most important problems in preventing influenza outbreak is <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> drug resistance during disease infecti<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is study, we model an influenza<br />

epidemic c<strong>on</strong>sidering emergence and evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> drug resistance. Since antiviral<br />

treatment is not effective <strong>on</strong> resistant infecteds, we implement <str<strong>on</strong>g>th</str<strong>on</strong>g>e quarantine c<strong>on</strong>trol<br />

strategy to mitigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e final size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic. In additi<strong>on</strong>, prophylaxis and<br />

treatment strategies are c<strong>on</strong>sidered in our model. A system <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary differential<br />

equati<strong>on</strong> is formulated for a SIQR influenza epidemic model. The influences <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese <str<strong>on</strong>g>th</str<strong>on</strong>g>ree main c<strong>on</strong>trol strategies are investigated <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e final size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic.<br />

Numerical simulati<strong>on</strong>s show <str<strong>on</strong>g>th</str<strong>on</strong>g>at implementati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> optimal quarantine and treatment<br />

toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er leads to outbreak c<strong>on</strong>tainment. The basic reproducti<strong>on</strong> numbers and<br />

c<strong>on</strong>trol reproducti<strong>on</strong> numbers are calculated for sensitive and resistant strains.<br />

394

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Crowd Dynamics: Modeling, Analysis and Simulati<strong>on</strong> (Part 1); Wednesday,<br />

June 29, 11:00<br />

Jan Haskovec<br />

RICAM, Austrian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

e-mail: jan.haskovec@oeaw.ac.at<br />

Massimo Fornasier<br />

RICAM, Austrian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

Jan Vybiral<br />

RICAM, Austrian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

Particle systems and kinetic equati<strong>on</strong>s modelling interacting<br />

agents in high dimensi<strong>on</strong><br />

We explore how c<strong>on</strong>cepts <str<strong>on</strong>g>of</str<strong>on</strong>g> high-dimensi<strong>on</strong>al data compressi<strong>on</strong> via random projecti<strong>on</strong>s<br />

<strong>on</strong>to lower-dimensi<strong>on</strong>al spaces can be applied for tractable simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

certain dynamical systems modeling complex interacti<strong>on</strong>s. In such systems, <strong>on</strong>e<br />

has to deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a large number <str<strong>on</strong>g>of</str<strong>on</strong>g> agents (typically milli<strong>on</strong>s) in spaces <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters<br />

describing each agent <str<strong>on</strong>g>of</str<strong>on</strong>g> high-dimensi<strong>on</strong> (<str<strong>on</strong>g>th</str<strong>on</strong>g>ousands or more). Even wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

todays powerful computers, numerical simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> such systems are prohibitively<br />

expensive. We propose an approach for <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamical systems governed<br />

by functi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> adjacency matrices in high-dimensi<strong>on</strong>, by random projecti<strong>on</strong>s<br />

via Johns<strong>on</strong>-Lindenstrauss embeddings, and recovery by compressed sensing techniques.<br />

395

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Moving Organisms: From Individuals to Populati<strong>on</strong>s; Wednesday, June 29, 17:00<br />

Jan Haskovec<br />

RICAM, Austrian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

e-mail: jan.haskovec@oeaw.ac.at<br />

Radek Erban<br />

OCCAM, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

From individual to collective behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled velocity<br />

jump processes: a locust example<br />

A class <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic individual-based models, written in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled velocity<br />

jump processes, is presented and analysed. This modelling approach incorporates<br />

recent experimental findings <strong>on</strong> behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> locusts. It exhibits n<strong>on</strong>trivial dynamics<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a phase change behaviour and recovers <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed group directi<strong>on</strong>al<br />

switching. Estimates <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e expected switching times, in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> number <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals<br />

and values <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model coefficients, are obtained using <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding<br />

Fokker-Planck equati<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e limit <str<strong>on</strong>g>of</str<strong>on</strong>g> large populati<strong>on</strong>s, a system <str<strong>on</strong>g>of</str<strong>on</strong>g> two kinetic<br />

equati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> n<strong>on</strong>local and n<strong>on</strong>linear right hand side is derived and analyzed. The<br />

existence <str<strong>on</strong>g>of</str<strong>on</strong>g> its soluti<strong>on</strong>s is proven and <str<strong>on</strong>g>th</str<strong>on</strong>g>e systems l<strong>on</strong>g-time behaviour is investigated.<br />

Finally, a first step towards <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean field limit <str<strong>on</strong>g>of</str<strong>on</strong>g> topological interacti<strong>on</strong>s<br />

is made by studying <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> shrinking <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> radius in <str<strong>on</strong>g>th</str<strong>on</strong>g>e individualbased<br />

model in <str<strong>on</strong>g>th</str<strong>on</strong>g>e large populati<strong>on</strong> limit.<br />

396

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling III; Wednesday, June 29,<br />

17:00<br />

Beata Hat-Plewinska, Bogdan Kazmierczak and Tomasz Lipniacki<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research, Warsaw, Poland<br />

e-mail: bhat@ippt.gov.pl<br />

e-mail: bkazmier@ippt.gov.pl<br />

e-mail: tlipnia@ippt.gov.pl<br />

B cell activati<strong>on</strong> triggered by <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e small receptor cluster: a computati<strong>on</strong>al study<br />

B cells are activated in resp<strong>on</strong>se to <str<strong>on</strong>g>th</str<strong>on</strong>g>e binding <str<strong>on</strong>g>of</str<strong>on</strong>g> polyvalent ligands, which<br />

induces <str<strong>on</strong>g>th</str<strong>on</strong>g>e aggregati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> B cell receptors. The formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> even small clusters<br />

c<strong>on</strong>taining less <str<strong>on</strong>g>th</str<strong>on</strong>g>an 1% <str<strong>on</strong>g>of</str<strong>on</strong>g> all <str<strong>on</strong>g>th</str<strong>on</strong>g>e receptors is sufficient for activati<strong>on</strong>. This observati<strong>on</strong><br />

led us to <str<strong>on</strong>g>th</str<strong>on</strong>g>e model in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e receptor cluster serves <strong>on</strong>ly as a switch<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at turns <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e activati<strong>on</strong> process, involving also <str<strong>on</strong>g>th</str<strong>on</strong>g>e remaining receptors. We<br />

have proposed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e system is bistable, and <str<strong>on</strong>g>th</str<strong>on</strong>g>us its local activati<strong>on</strong> may start<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e propagati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a traveling wave, which spreads activati<strong>on</strong> over <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire mebrane.<br />

We found <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e minimal size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e activatory cluster decreases wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ickness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoplasm and kinase diffusi<strong>on</strong> coefficient. It is particularly small<br />

when kinases are restricted to <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane. These findings are c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e properties <str<strong>on</strong>g>of</str<strong>on</strong>g> B cells, which have extremely <str<strong>on</strong>g>th</str<strong>on</strong>g>in cytoplasmic layer and in which<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e receptor interacting Src family kinases are te<str<strong>on</strong>g>th</str<strong>on</strong>g>ered to <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane.<br />

397

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor invasi<strong>on</strong> I; Tuesday, June 28, 11:00<br />

Haralampos Hatzikirou<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> New Mexico<br />

e-mail: hhatzikirou@salud.unm.edu<br />

Mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> glioma tumor invasi<strong>on</strong><br />

Invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> malignant glioma tumors is typically very aggressive and a highly complex<br />

phenomen<strong>on</strong> involving molecular and cellular processes at various spatiotemporal<br />

scales, whose precise interplay is still not fully understood. By means <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling, we compare <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical results to <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental data<br />

and deduce microscopic interacti<strong>on</strong>s (cellular mechanisms) from microscopic and<br />

macroscopic observables (experimental data). In particular, using multicellular<br />

spheroid data, we exhibit <str<strong>on</strong>g>th</str<strong>on</strong>g>e key role <str<strong>on</strong>g>of</str<strong>on</strong>g> migrati<strong>on</strong>/proliferati<strong>on</strong> in tumor invasi<strong>on</strong><br />

dynamics. Finally, we study <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> vascularizati<strong>on</strong> <strong>on</strong> tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e help <str<strong>on</strong>g>of</str<strong>on</strong>g> a combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> in vivo data from implanted xenografts <str<strong>on</strong>g>of</str<strong>on</strong>g> U87 MG in<br />

nude mice brain and a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model.<br />

398

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Delay Differential Equati<strong>on</strong>s and Applicati<strong>on</strong>s II; Saturday, July 2, 08:30<br />

M.L. Hbid<br />

LMDP, UMI - UMMISCO (IRD -UPMC). Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics,<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, University Cadi Ayyad, BP 2390, Marrakech, Morocco.<br />

Unité Associée au CNRST (URAC02), Unité Associée au CNERS<br />

e-mail: hassan.hbid@gmail.com<br />

Delay in Structured Populati<strong>on</strong> Models.<br />

The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is to put in evidence <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>set <str<strong>on</strong>g>of</str<strong>on</strong>g> delays, distributed delays<br />

and state-dependent delays in models, especialy in <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold models for structured<br />

populati<strong>on</strong> dynamics. A unified approach to <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models is provided, based <strong>on</strong><br />

solving <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding balance law (hyperbolic P.D.E.) al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristic<br />

lines and showing <str<strong>on</strong>g>th</str<strong>on</strong>g>e comm<strong>on</strong> underlying ideas. Size and age-structured models<br />

in different fields are presented: fish populati<strong>on</strong>s, insect populati<strong>on</strong>s, cell proliferati<strong>on</strong><br />

and epidemics. Existence and uniqueness results related to such models will<br />

be discussed as well as some results <str<strong>on</strong>g>of</str<strong>on</strong>g> semigroup’s properties , <str<strong>on</strong>g>of</str<strong>on</strong>g> stability, and<br />

bifurcati<strong>on</strong> results.<br />

399

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Turing !! Turing?? <strong>on</strong> morphogenesis via experimental and <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical<br />

approaches; Wednesday, June 29, 17:00<br />

Denis Head<strong>on</strong><br />

The Roslin Institute, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Edinburgh<br />

e-mail: denis.head<strong>on</strong>@roslin.ed.ac.uk<br />

Kevin Painter<br />

Heriot Watt University<br />

Chunyan Mou<br />

The Roslin Institute, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Edinburgh<br />

Periodic patterning across heterogeneous fields: insights<br />

from embry<strong>on</strong>ic fea<str<strong>on</strong>g>th</str<strong>on</strong>g>er development<br />

Vertebrate skin is characterized by its patterned array <str<strong>on</strong>g>of</str<strong>on</strong>g> pigments and structural<br />

appendages such as fea<str<strong>on</strong>g>th</str<strong>on</strong>g>ers, hairs and scales. A number <str<strong>on</strong>g>of</str<strong>on</strong>g> lines <str<strong>on</strong>g>of</str<strong>on</strong>g> evidence point to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e acti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a Turing type mechanism in laying out <str<strong>on</strong>g>th</str<strong>on</strong>g>e periodic pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> fea<str<strong>on</strong>g>th</str<strong>on</strong>g>ers<br />

and hairs in <str<strong>on</strong>g>th</str<strong>on</strong>g>e developing skin. Several candidate Activator and Inhibitor<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways which act during <str<strong>on</strong>g>th</str<strong>on</strong>g>is process have been identified, <str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e full set<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> interacti<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>em remains to be defined. B<strong>on</strong>e morphogenetic proteins<br />

(BMPs) act as key Inhibitors during fea<str<strong>on</strong>g>th</str<strong>on</strong>g>er formati<strong>on</strong>, and we have uncovered different<br />

sensitivities to <str<strong>on</strong>g>th</str<strong>on</strong>g>is Inhibitor in different regi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e skin. We <str<strong>on</strong>g>th</str<strong>on</strong>g>en focused<br />

<strong>on</strong> combining ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and experimental approaches to explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

pattern outcomes and propensity for pattern change arising from <str<strong>on</strong>g>th</str<strong>on</strong>g>e operati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a Turing type system across a field wi<str<strong>on</strong>g>th</str<strong>on</strong>g> unequal Inhibitor sensitivities.<br />

400

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cellular Systems Biology; Tuesday, June 28, 14:30<br />

Robert Heise and Zoran Nikoloski<br />

Systems Biology and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling group, Max-Planck Institute<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular Plant Physiology, Postdam, Germany<br />

e-mail: heise@mpimp-golm.mpg.de<br />

e-mail: nikoloski@mpimp-golm.mpg.de<br />

Extensi<strong>on</strong>s to Kinetic Flux Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iling to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> fluxes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e central carb<strong>on</strong> metabolism <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Arabidopsis <str<strong>on</strong>g>th</str<strong>on</strong>g>aliana<br />

Determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e stati<strong>on</strong>ary and transient behaviors <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic networks is<br />

tightly coupled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> quantitative descripti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic states, characterized by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong> fluxes and metabolite c<strong>on</strong>centrati<strong>on</strong>s. Despite recent<br />

progress in me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for estimating <str<strong>on</strong>g>th</str<strong>on</strong>g>e flux distributi<strong>on</strong>s in a metabolic network<br />

based <strong>on</strong> 13 C labeled metabolomics data, <str<strong>on</strong>g>th</str<strong>on</strong>g>e existing approaches ultimately rely <strong>on</strong><br />

precise stoichiometry, atomic mappings, and availability <str<strong>on</strong>g>of</str<strong>on</strong>g> data for all metabolites<br />

participating <str<strong>on</strong>g>th</str<strong>on</strong>g>e analyzed biochemical reacti<strong>on</strong>s. Kinetic Flux Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iling (KPF) is<br />

a recently proposed me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for determining reacti<strong>on</strong> fluxes based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e washout<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e unlabeled fracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a metabolite pool and is described mass-acti<strong>on</strong>-like<br />

differential equati<strong>on</strong> model [1,2]. However, wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out substantial assumpti<strong>on</strong>s, KPF<br />

is applicable <strong>on</strong>ly to linear pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways.<br />

Here we propose an extensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> KPF based <strong>on</strong> simulated annealing <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows<br />

analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> branched and circular pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways. Our approach does not rely <strong>on</strong> atomic<br />

maps, and can efficiently utilize <str<strong>on</strong>g>th</str<strong>on</strong>g>e time-resolved distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> isotopomers to<br />

determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluxes in an experimentally studied metabolic network. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

proposed approach, we quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e flux distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e central carb<strong>on</strong> metabolism<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Arabidopsis <str<strong>on</strong>g>th</str<strong>on</strong>g>aliana based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e time-resolved isotopomoer data over<br />

60 minutes for 16 metabolites toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> informati<strong>on</strong> about <str<strong>on</strong>g>th</str<strong>on</strong>g>eir subcellular<br />

localizati<strong>on</strong>. We investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e robustness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e findings due to partial data inclusi<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to bo<str<strong>on</strong>g>th</str<strong>on</strong>g> metabolites and different time scales. In additi<strong>on</strong>,<br />

we dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at our me<str<strong>on</strong>g>th</str<strong>on</strong>g>od toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e employed data can be used to<br />

discriminate between different models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying metabolic network.<br />

References.<br />

[1] J. Yuan, W.U. Fowler, E. Kimball, W. Lu, J.D. Rabinowitz (2006) Kinetic flux pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iling <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

nitrogen assimilati<strong>on</strong> in Escherichia coli Nat. Chem. Biol. 2 529–530.<br />

[2] J. Yuan, B.D. Bennett, J.D. Rabinowitz (2008) Kinetic flux pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iling for quantificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cellular metabolic fluxes Nat. Prot. 1 1328–1340.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biomechanical regulati<strong>on</strong> in b<strong>on</strong>e tissue (Sessi<strong>on</strong><br />

I); Wednesday, June 29, 08:30<br />

Christian Hellmich<br />

Vienna University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: christian.hellmich@tuwien.ac.at<br />

B<strong>on</strong>e fibrillogenesis and mineralizati<strong>on</strong>: Quantitative<br />

analysis and implicati<strong>on</strong>s for tissue elasticity<br />

Data from b<strong>on</strong>e drying, demineralizati<strong>on</strong>, and deorganificati<strong>on</strong> tests, collected over<br />

a time span <str<strong>on</strong>g>of</str<strong>on</strong>g> more <str<strong>on</strong>g>th</str<strong>on</strong>g>an eighty years, evidence a myriad <str<strong>on</strong>g>of</str<strong>on</strong>g> different chemical compositi<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> different b<strong>on</strong>e materials. However, careful analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e data, as to<br />

extract <str<strong>on</strong>g>th</str<strong>on</strong>g>e chemical c<strong>on</strong>centrati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> hydroxyapatite, <str<strong>on</strong>g>of</str<strong>on</strong>g> water, and <str<strong>on</strong>g>of</str<strong>on</strong>g> organic material<br />

(mainly collagen) in <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular b<strong>on</strong>e matrix, reveals an ast<strong>on</strong>ishing fact:<br />

it appears <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere exists a unique bilinear relati<strong>on</strong>ship between organic c<strong>on</strong>centrati<strong>on</strong><br />

and mineral c<strong>on</strong>centrati<strong>on</strong>, across different species, organs, and age groups,<br />

from early childhood to senility: During organ grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mineral c<strong>on</strong>centrati<strong>on</strong><br />

increases linearly wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e organic c<strong>on</strong>centrati<strong>on</strong> (which increases during fibrillogenesis),<br />

while from adul<str<strong>on</strong>g>th</str<strong>on</strong>g>ood <strong>on</strong>, fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er increase <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mineral c<strong>on</strong>centrati<strong>on</strong><br />

is accompanied by a decrease in organic c<strong>on</strong>centrati<strong>on</strong>. These relati<strong>on</strong>ships imply<br />

unique mass density-c<strong>on</strong>centrati<strong>on</strong> laws for fibrillogenesis and mineralizati<strong>on</strong>, which<br />

- in combinati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> micromechanical models - deliver ’universal’ mass densityelasticity<br />

relati<strong>on</strong>ships in extracellular b<strong>on</strong>e matrix - valid across different species,<br />

organs, and ages. They turn out as quantitative reflecti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e well-instrumented<br />

interplay <str<strong>on</strong>g>of</str<strong>on</strong>g> osteoblasts, osteoclasts, osteocytes, and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir precursors, c<strong>on</strong>trolling,<br />

in a fine-tuned fashi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e chemical genesis and c<strong>on</strong>tinuous transformati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

extracellular b<strong>on</strong>e matrix. C<strong>on</strong>siderati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e aformenti<strong>on</strong>ed rules may str<strong>on</strong>gly<br />

affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential success <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue engineering strategies, in particular when translating,<br />

via micromechanics, <str<strong>on</strong>g>th</str<strong>on</strong>g>e aformenti<strong>on</strong>ed grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and mineralizati<strong>on</strong> characteristics<br />

into tissue-specific elastic properties.<br />

402

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Dorota Herman<br />

Center for Systems Biology, School <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Birmingham, Edgbast<strong>on</strong>, Birmingham B15 2TT, UK<br />

e-mail: dxh885@bham.ac.uk<br />

Christopher M. Thomas<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Birmingham, Edgbast<strong>on</strong>, Birmingham<br />

B15 2TT, UK<br />

Dov J. Stekel<br />

Integrative Systems Biology, School <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Nottingham, LE12 5RD, UK<br />

Evoluti<strong>on</strong>ary optimizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> negative and co-operative<br />

autoregulati<strong>on</strong> in RK2 plasmids<br />

The central c<strong>on</strong>trol oper<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e RK2 plasmid is negatively and co-operatively<br />

autoregulated by dimers <str<strong>on</strong>g>of</str<strong>on</strong>g> two global plasmid regulators, KorA and KorB. Several<br />

roles for negative feedbacks in biosystems have been proposed by many researchers,<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>ese roles include reducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> noise, increased robustness, speeding <str<strong>on</strong>g>of</str<strong>on</strong>g> resp<strong>on</strong>se<br />

time and reducing burden <strong>on</strong> host. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, we seek to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary<br />

adaptati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e RK2 central c<strong>on</strong>trol oper<strong>on</strong> in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese proposed roles, using<br />

comparative analyses <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e wild type system wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a progressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> simpler systems.<br />

We used a stochastic, multi-scale model <str<strong>on</strong>g>th</str<strong>on</strong>g>at includes negative and co-operative<br />

gene autoregulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e central c<strong>on</strong>trol oper<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e plasmid, plasmid replicati<strong>on</strong><br />

and host cell grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and divisi<strong>on</strong>. Keeping track <str<strong>on</strong>g>of</str<strong>on</strong>g> an RK2 plasmid line, we can<br />

observe <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> protein abundance from entry <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e plasmid into a naive<br />

host <str<strong>on</strong>g>th</str<strong>on</strong>g>rough to steady state. The comparative analyses between <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong> in<br />

models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e wild type central c<strong>on</strong>trol oper<strong>on</strong> and models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> simpler, adequate<br />

architectures show a speed up <str<strong>on</strong>g>of</str<strong>on</strong>g> resp<strong>on</strong>se time and a decrease in burden for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

host, indicated by a decrease in <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> produced mRNAs. In comparis<strong>on</strong>,<br />

minimal increased robustness and reducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> internal noise in steady state <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

bacterial grow<str<strong>on</strong>g>th</str<strong>on</strong>g> phase were observed in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese anayses. We c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at possible<br />

reas<strong>on</strong>s for evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex negative feedback regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e RK2 central<br />

c<strong>on</strong>trol oper<strong>on</strong> are <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> fast resp<strong>on</strong>se times and reduced burden to<br />

host, and <str<strong>on</strong>g>th</str<strong>on</strong>g>at it is unlikely <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is regulatory system has evolved to reduced noise<br />

or increase robustness.<br />

403

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Joachim Hermiss<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Vienna<br />

e-mail: joachim.hermiss<strong>on</strong>@univie.ac.at<br />

Speciati<strong>on</strong>; Wednesday, June 29, 08:30<br />

Dobshansky-Muller incompatibilities in parapatry<br />

The accumulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Dobshansky-Muller incompatibilities is a widely accepted<br />

mechanism for speciati<strong>on</strong> in allopatric populati<strong>on</strong>s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is presentati<strong>on</strong>, we analyze<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e scope and limits <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is mechanism if <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong>s are not fully separated.<br />

We use classical migrati<strong>on</strong>-selecti<strong>on</strong> models to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e limiting rates<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> gene-flow <str<strong>on</strong>g>th</str<strong>on</strong>g>at allow i) for <str<strong>on</strong>g>th</str<strong>on</strong>g>e origin and ii) for <str<strong>on</strong>g>th</str<strong>on</strong>g>e maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> a single<br />

Dobshansky-Muller incompatibility in parapatry. We use our results to discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

importance <str<strong>on</strong>g>of</str<strong>on</strong>g> ecological and genetic factors (such as recombinati<strong>on</strong> rate, streng<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e incompatibility, level <str<strong>on</strong>g>of</str<strong>on</strong>g> local adaptati<strong>on</strong>) for <str<strong>on</strong>g>th</str<strong>on</strong>g>e speciati<strong>on</strong> process in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

presence <str<strong>on</strong>g>of</str<strong>on</strong>g> gene-flow.<br />

404

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Ana Hernandez<br />

Centro de investigación y de estudios avanzados del instituto politecnico<br />

naci<strong>on</strong>al CINVESTAV-IPN Unidad Mérida<br />

e-mail: ahernandezh@mda.cinvestav.mx<br />

Rodrigo Huerta Quintanilla<br />

Centro de investigación y de estudios avanzados del instituto politecnico<br />

naci<strong>on</strong>al CINVESTAV-IPN Unidad Mérida<br />

Body mass variati<strong>on</strong> in a two-dimensi<strong>on</strong>al regular network<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we study <str<strong>on</strong>g>th</str<strong>on</strong>g>e mass variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e human body using <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Chow and Hall[1]. We implement <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at provide a framework to<br />

c<strong>on</strong>sider a model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e single pers<strong>on</strong> mass dynamics, as well as a network in<br />

which agents can interact am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>em. We use as a comp<strong>on</strong>ents <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e total energy expenditure per day (E) and <str<strong>on</strong>g>th</str<strong>on</strong>g>e daily energy intake (I). We feed<br />

our model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> data obtained from <str<strong>on</strong>g>th</str<strong>on</strong>g>e FAO and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er references[2]. We compare<br />

our results wi<str<strong>on</strong>g>th</str<strong>on</strong>g> data from mexican tables for pers<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different ages. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

case <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network we took a two-dimensi<strong>on</strong>al regular lattice wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 400 agents,<br />

each agent have a initial mass (Mo), initial intake (Io), and an initial total energy<br />

expenditure (Eo).In order to fit our model we proposed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e intake equati<strong>on</strong><br />

changes like I(t)=Io(deltaM)gamma, where deltaM=M(t)/Mo. We c<strong>on</strong>sider ages<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e agents between 19 and 65 years.We could see how <str<strong>on</strong>g>th</str<strong>on</strong>g>e change <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial<br />

energy c<strong>on</strong>diti<strong>on</strong>s produced large changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e average mass <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network and<br />

in some cases <str<strong>on</strong>g>th</str<strong>on</strong>g>e agent’s mass can big very large and also can have low values, ie,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a large spread in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mass values. Also we studied how <str<strong>on</strong>g>th</str<strong>on</strong>g>e average mass<br />

changes when <str<strong>on</strong>g>th</str<strong>on</strong>g>e agents have different numbers <str<strong>on</strong>g>of</str<strong>on</strong>g> links. We have implemnted <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

model to cover ages between 0 and 18 years old, as well.<br />

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Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part I;<br />

Tuesday, June 28, 11:00<br />

Miguel A. Herrero<br />

IMI and Departamento de Matematica Aplicada, Universidad Complutense,<br />

Madrid, Spain<br />

e-mail: Miguel_Herrero@mat.ucm.es<br />

A. Fasano<br />

Dipartimento di Matematica, Università di Firenze, Viale Morgagni<br />

67A, 50134 Firenze, Italy.<br />

e-mail: fasano@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.unifi.it<br />

M. R. Rodrigo<br />

Departamento Académico de Matemáticas, Instituto Tecnológico aut<strong>on</strong>omo<br />

de México, Rio H<strong>on</strong>do 1, San Angel, México.<br />

Wave propagati<strong>on</strong> and tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Travelling waves (TWs), a particular type <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Reacti<strong>on</strong>-Diffusi<strong>on</strong> systems<br />

which move wi<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>stant speed, have been widely employed to model various aspects<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tumour invasi<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is lecture, I shall deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some TWs <str<strong>on</strong>g>th</str<strong>on</strong>g>at have been<br />

recently used to describe particular types <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. More precisely, <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

capability to reproduce some observed morphological features will be addressed,<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>eir dynamical properties and <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying biological<br />

processes will be discussed.<br />

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Modeling and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor invasi<strong>on</strong> II; Tuesday, June 28, 14:30<br />

Miguel A. Herrero<br />

IMI and Departamento de Matematica Aplicada, Universidad Complutense<br />

, Madrid, Spain<br />

e-mail: Miguel_Herrero@mat.ucm.es<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>e determinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal radiati<strong>on</strong> dose <strong>on</strong> a<br />

target tissue volume<br />

A key problem in radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy c<strong>on</strong>sists in determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e appropriate dose to be<br />

delivered to a clinical target in order to achieve maximum efficiency over malignant<br />

tissue <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>e hand, while at <str<strong>on</strong>g>th</str<strong>on</strong>g>e same time sparing heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y tissue and organs<br />

at risk as much as possible. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is lecture a model problem will be presented and<br />

discussed to address <str<strong>on</strong>g>th</str<strong>on</strong>g>at issue , and a number <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding soluti<strong>on</strong>s will be discussed<br />

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Modeling viral hepatitis dynamics in-vivo and in-vitro in <str<strong>on</strong>g>th</str<strong>on</strong>g>e era <str<strong>on</strong>g>of</str<strong>on</strong>g> direct<br />

anti-viral agents I; Tuesday, June 28, 17:00<br />

Eva Herrmann<br />

Goe<str<strong>on</strong>g>th</str<strong>on</strong>g>e University Frankfurt<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biostatistics and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling<br />

60590 Frankfurt (Main), Germany<br />

e-mail: herrmann@uni-frankfurt.de<br />

PK-PD Models for viral kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> combinati<strong>on</strong> treatments<br />

in viral hepatitis<br />

Even in <str<strong>on</strong>g>th</str<strong>on</strong>g>e era <str<strong>on</strong>g>of</str<strong>on</strong>g> direct anti-viral agents, interfer<strong>on</strong>-based combinati<strong>on</strong> treatments<br />

are very important. It is well known <str<strong>on</strong>g>th</str<strong>on</strong>g>at serum levels <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g-acting interfer<strong>on</strong>s can<br />

vary c<strong>on</strong>siderably and <str<strong>on</strong>g>th</str<strong>on</strong>g>at PK <str<strong>on</strong>g>of</str<strong>on</strong>g> interfer<strong>on</strong> has an observable influence <strong>on</strong> viral<br />

kinetics also in combinati<strong>on</strong> treatment. Therefore, reliable viral kinetic modeling<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> interfer<strong>on</strong>-based treatments should deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> n<strong>on</strong>-c<strong>on</strong>stant treatment efficacies<br />

based <strong>on</strong> PK-PD models.<br />

The first topic <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e talk will focus <strong>on</strong> modeling results which analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> different PK and treatment schedules <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g-acting interfer<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment<br />

efficacy and <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance. Overall, high or low peak-to-trough<br />

levels <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e PK <str<strong>on</strong>g>of</str<strong>on</strong>g> interfer<strong>on</strong> has <strong>on</strong>ly minor influence <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance<br />

as l<strong>on</strong>g as <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall interfer<strong>on</strong> efficacy is not changed.<br />

Sec<strong>on</strong>dly, we will illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>at modeling PK <str<strong>on</strong>g>of</str<strong>on</strong>g> direct antivirals can be quite<br />

challenging and simple open <strong>on</strong>e-compartment models may be too simplistic to obtain<br />

reliable modeling results which fit wi<str<strong>on</strong>g>th</str<strong>on</strong>g> observed PK pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles.<br />

Besides some <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical background and illustrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> simulati<strong>on</strong> results, we<br />

will also show some clinical data analysis where a full PK-PD approach can give<br />

some indicati<strong>on</strong>s how to optimize treatments.<br />

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Neurosciences; Thursday, June 30, 11:30<br />

Joanna Tyrcha<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Statistics, Stockholm University<br />

e-mail: joanna@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.su.se<br />

John Hertz<br />

Niels Bohr Institute, Copenhagen; Nordita, Stockholm<br />

e-mail: hertz@nbi.dk<br />

Yasser Roudi<br />

Kavli Institute, NTNU, Tr<strong>on</strong>dheim; Nordita, Stockholm<br />

e-mail: yasserroudi@gmail.com<br />

Network rec<strong>on</strong>structi<strong>on</strong> from n<strong>on</strong>stati<strong>on</strong>ary spike trains<br />

Existing approaches to <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> extracting neur<strong>on</strong>al c<strong>on</strong>nectivity from spike<br />

data [1,2] assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e network is in a stati<strong>on</strong>ary state, which it is not in many<br />

experiments. Here we describe a me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for inferring bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network c<strong>on</strong>nectivity<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e time-dependent external drive <str<strong>on</strong>g>th</str<strong>on</strong>g>at causes <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>stati<strong>on</strong>arity.<br />

C<strong>on</strong>sider an experiment in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e neur<strong>on</strong>s recorded are subjected repeatedly<br />

to a potentially unknown external input (such as would arise from sensory<br />

stimulati<strong>on</strong>). The spikes are assumed to be binned in time and represented by a<br />

binary array: Si(t, r) = 1 indicates a spike and Si(t, r) = −1 indicates no spike<br />

by neur<strong>on</strong> i in time bin t <str<strong>on</strong>g>of</str<strong>on</strong>g> repetiti<strong>on</strong> r <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e measurement. We fit <str<strong>on</strong>g>th</str<strong>on</strong>g>ese data to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e simplest kind <str<strong>on</strong>g>of</str<strong>on</strong>g> binary stochastic model: At time step t <str<strong>on</strong>g>of</str<strong>on</strong>g> repetiti<strong>on</strong> r, each<br />

formal neur<strong>on</strong> receives a net input, Hi(t, r) = hi(t)+ <br />

j JijSj(t, r), and it takes <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

value +1 at <str<strong>on</strong>g>th</str<strong>on</strong>g>e next step wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a probability given by a logistic sigmoidal functi<strong>on</strong><br />

1/[1 + exp(−Hi(t, r))] <str<strong>on</strong>g>of</str<strong>on</strong>g> Hi(t, r). Maximizing <str<strong>on</strong>g>th</str<strong>on</strong>g>e likelihood <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e data leads to<br />

learning rules<br />

(1)<br />

(2)<br />

δhi(t) = ηh {〈Si(t + 1, r)〉r − 〈tanh[Hi(t, r))]〉r]}<br />

δJij = ηJ {〈Si(t + 1, r)Sj(t, r)〉rt − 〈tanh[Hi(t, r)]Sj(t, r)〉rt}<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e model parameters – <str<strong>on</strong>g>th</str<strong>on</strong>g>e couplings Jij and external inputs hi(t). For weak<br />

coupling or densely c<strong>on</strong>nected networks, faster alternative algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms are possible<br />

[3], based <strong>on</strong> expanding (1) and (2) around mean-field and TAP [4] equati<strong>on</strong>s for<br />

mi(t) = 〈Si(r, t)〉r.<br />

Here we present results <str<strong>on</strong>g>of</str<strong>on</strong>g> applying bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is and me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods assuming stati<strong>on</strong>arity<br />

to (1) data generated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic model itself (<str<strong>on</strong>g>th</str<strong>on</strong>g>e realizable case), (2)<br />

data from a realistic computati<strong>on</strong>al model <str<strong>on</strong>g>of</str<strong>on</strong>g> a small cortical network, and (3)<br />

data recorded from salamander retina under visual stimulati<strong>on</strong>. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at, in<br />

all <str<strong>on</strong>g>th</str<strong>on</strong>g>ree cases, performing <str<strong>on</strong>g>th</str<strong>on</strong>g>e rec<strong>on</strong>structi<strong>on</strong> assuming stati<strong>on</strong>arity systematically<br />

overestimates <str<strong>on</strong>g>th</str<strong>on</strong>g>e couplings in <str<strong>on</strong>g>th</str<strong>on</strong>g>e network: <str<strong>on</strong>g>th</str<strong>on</strong>g>e algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms effectively invent fictitious<br />

couplings to explain stimulus-induced correlati<strong>on</strong>s. The n<strong>on</strong>stati<strong>on</strong>ary treatment<br />

outlined above enables us to find, for sufficient data, <str<strong>on</strong>g>th</str<strong>on</strong>g>e correct (weaker)<br />

couplings and to extract <str<strong>on</strong>g>th</str<strong>on</strong>g>e time-dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e external input.<br />

References.<br />

[1] E Schneidman, M Berry, R Segev and W Bialek, Weak pairwise correlati<strong>on</strong>s imply str<strong>on</strong>gly<br />

correlated networks states in a neural populati<strong>on</strong>, Nature 440 1007-1012 (2006).<br />

[2] Y Roudi, J Tyrcha and J Hertz, Ising model for neural data: Model quality and approximate<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for exctracting functi<strong>on</strong>al c<strong>on</strong>nectivity, Phys Rev E 79 051915 (2009).<br />

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[3] Y Roudi and J Hertz, Mean Field Theory for N<strong>on</strong>equilibrium Network Rec<strong>on</strong>structi<strong>on</strong>, Phys<br />

Rev Lett 106 048702 (2011).<br />

[4] D Thouless et al, Soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ‘solvable model <str<strong>on</strong>g>of</str<strong>on</strong>g> a spin glass’, Phil Mag 35 593-601 (1977).<br />

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Epidemics; Tuesday, June 28, 17:00<br />

R.I. Hicks<strong>on</strong><br />

Nati<strong>on</strong>al Centre for Epidemiology and Populati<strong>on</strong> Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, Australian<br />

Nati<strong>on</strong>al University, Canberra, ACT 0200, AUSTRALIA<br />

e-mail: Roslyn.Hicks<strong>on</strong>@anu.edu.au<br />

G.N. Mercer<br />

Nati<strong>on</strong>al Centre for Epidemiology and Populati<strong>on</strong> Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, Australian<br />

Nati<strong>on</strong>al University, Canberra, ACT 0200, AUSTRALIA<br />

e-mail: Ge<str<strong>on</strong>g>of</str<strong>on</strong>g>f.Mercer@anu.edu.au<br />

K.M. Lokuge<br />

Nati<strong>on</strong>al Centre for Epidemiology and Populati<strong>on</strong> Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, Australian<br />

Nati<strong>on</strong>al University, Canberra, ACT 0200, AUSTRALIA<br />

e-mail: Kamalini.Lokuge@anu.edu.au<br />

H. Nguyen<br />

Crawford School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ec<strong>on</strong>omics & Government, Australian Nati<strong>on</strong>al<br />

University, Canberra, ACT 0200, AUSTRALIA<br />

e-mail: Hoa.Nguyen@anu.edu.au<br />

Evaluating c<strong>on</strong>trol strategies for TB in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Torres Strait<br />

Island regi<strong>on</strong><br />

There is a high prevalence <str<strong>on</strong>g>of</str<strong>on</strong>g> tuberculosis (TB) in Papua New Guinea (PNG),<br />

which is exacerbated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> drug-resistant TB strains and HIV infecti<strong>on</strong>.<br />

This is an important public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> issue not <strong>on</strong>ly locally wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in PNG, but also in<br />

Australia due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e high cross-border traffic in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Torres Strait Island–Western<br />

Province (PNG) treaty regi<strong>on</strong>. We use a metapopulati<strong>on</strong> model to evaluate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

effect <str<strong>on</strong>g>of</str<strong>on</strong>g> varying c<strong>on</strong>trol strategies in <str<strong>on</strong>g>th</str<strong>on</strong>g>e regi<strong>on</strong>, and perform a sensitivity analysis<br />

to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e most important parameters.<br />

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Moving Organisms: From Individuals to Populati<strong>on</strong>s; Wednesday, June 29, 17:00<br />

Danielle Hilhorst<br />

Laboratoire de Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ématiques, Université de Paris-Sud 11<br />

e-mail: Danielle.Hilhorst@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.u-psud.fr<br />

Masayasu Mimura<br />

Institute for Advanced Study <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Meiji University,<br />

1-1 Higashi Mita, Tama-ku, Kawasaki, 214-8571 Japan<br />

A n<strong>on</strong>linear parabolic-hyperbolic PDE model for c<strong>on</strong>tact<br />

inhibiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell-grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

We c<strong>on</strong>sider a parabolic-hyperbolic system <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear partial differential equati<strong>on</strong>s<br />

which describes a simplified model for c<strong>on</strong>tact inhibiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> two cell<br />

populati<strong>on</strong>s. In <strong>on</strong>e space dimensi<strong>on</strong> it is known <str<strong>on</strong>g>th</str<strong>on</strong>g>at global soluti<strong>on</strong>s exist and <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ey satisfy <str<strong>on</strong>g>th</str<strong>on</strong>g>e segregati<strong>on</strong> property which reflects <str<strong>on</strong>g>th</str<strong>on</strong>g>e inhibiti<strong>on</strong> mechanism: if <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

two populati<strong>on</strong>s are initially segregated - in ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical terms <str<strong>on</strong>g>th</str<strong>on</strong>g>is is translated<br />

into disjoint spatial supports <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir densities - <str<strong>on</strong>g>th</str<strong>on</strong>g>is property remains valid for<br />

all later times. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, we use recent results <strong>on</strong> transport equati<strong>on</strong>s and<br />

Lagrangian flows to obtain similar results in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> arbitrary space dimensi<strong>on</strong>s.<br />

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Reports from US - African BioMa<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Initiative: C<strong>on</strong>servati<strong>on</strong><br />

Biology; Saturday, July 2, 14:30<br />

Gina Himes Boor<br />

M<strong>on</strong>tana State University<br />

e-mail: gkhimesboor@m<strong>on</strong>tana.edu<br />

Shar<strong>on</strong> Baruch-Mordo<br />

Using individual-based movement models to investigate<br />

mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> emergent herding behavior in African buffalo<br />

Ungulate species worldwide have been observed to aggregate into variable-sized<br />

temporary or permanent herds. One important <str<strong>on</strong>g>th</str<strong>on</strong>g>read <str<strong>on</strong>g>of</str<strong>on</strong>g> research in ecology has<br />

been to try to understand why such aggregati<strong>on</strong>s occur, and what mechanisms<br />

c<strong>on</strong>trol <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> herding. Most research to date has focused <strong>on</strong> populati<strong>on</strong>level<br />

herding dynamics, and evidence exists for bo<str<strong>on</strong>g>th</str<strong>on</strong>g> bottom-up c<strong>on</strong>trol, wherein<br />

herds form as a result <str<strong>on</strong>g>of</str<strong>on</strong>g> patchy resource distributi<strong>on</strong>, and top-down c<strong>on</strong>trol, in<br />

which predator avoidance c<strong>on</strong>trols aggregati<strong>on</strong> dynamics. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is study we used<br />

an individual-based model (IBM) to test whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er populati<strong>on</strong>-level herding patterns<br />

emerge from individual-level movement decisi<strong>on</strong>s, and to examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

bottom-up mechanisms <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is emergent phenomen<strong>on</strong>. We used African buffalo<br />

(Syncerus caffer) in Kruger Nati<strong>on</strong>al Park, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Africa as our focal populati<strong>on</strong>,<br />

and simulated individual movement based <strong>on</strong> rules in which each buffalo attempts<br />

to meet its daily resource requirements. Our model did not incorporate bir<str<strong>on</strong>g>th</str<strong>on</strong>g> or<br />

dea<str<strong>on</strong>g>th</str<strong>on</strong>g> processes but focused solely <strong>on</strong> spatial dynamics. To validate our model we<br />

compared herd size distributi<strong>on</strong> observed in our IBM to herd size distributi<strong>on</strong>s observed<br />

in Kruger Nati<strong>on</strong>al Park between 1985 and 2001. Using IBM we found <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

herding behavior was an emergent property. We were able to emulate empirical<br />

herd size distributi<strong>on</strong>s when resources were available at low levels in large parts<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e study area but abundant in small scattered areas. Our study dem<strong>on</strong>strates<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at empirically-based patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> herding behavior can emerge from bottom-up<br />

mechanisms al<strong>on</strong>e. Our c<strong>on</strong>tinued research will attempt to elucidate whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er predator<br />

avoidance behavior can produce similar empirically-validated herding patterns<br />

and how a combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> top-down and bottom-up mechanisms might change<br />

populati<strong>on</strong>-level herding dynamics.<br />

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Populati<strong>on</strong> Dynamics; Friday, July 1, 14:30<br />

Erwan Hingant<br />

Institut Camille Jordan, Ly<strong>on</strong>, France.<br />

e-mail: hingant@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.univ-ly<strong>on</strong>1.fr<br />

Pascaline F<strong>on</strong>tes<br />

Centre CECEMA, M<strong>on</strong>tpellier, France.<br />

Teresa Alvarez-Martinez<br />

Institut Fédératif de Biologie de M<strong>on</strong>tpellier, M<strong>on</strong>tpellier, France.<br />

Jacques-Damien Arnaud<br />

Institut Fédératif de Biologie de M<strong>on</strong>tpellier, M<strong>on</strong>tpellier, France.<br />

Jean-Pierre Liautard<br />

Centre de Recherche sur les Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogènes et Biologie pour la Santé,<br />

M<strong>on</strong>tpellier, France<br />

Laurent Pujo-Menjouet<br />

Institut Camille Jordan, Ly<strong>on</strong>, France.<br />

An <strong>on</strong>-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way step explains <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinetic <str<strong>on</strong>g>of</str<strong>on</strong>g> pri<strong>on</strong> amyloid<br />

formati<strong>on</strong><br />

The pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenic process <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissible sp<strong>on</strong>giform encephalopa<str<strong>on</strong>g>th</str<strong>on</strong>g>ies diseases,<br />

is typically associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>formati<strong>on</strong>al c<strong>on</strong>versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e so-called pri<strong>on</strong><br />

protein (PrP). The protein-<strong>on</strong>ly model asserts <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e misfolded is<str<strong>on</strong>g>of</str<strong>on</strong>g>orm represents<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e infectious pri<strong>on</strong> agent, self-propagating by binding to <str<strong>on</strong>g>th</str<strong>on</strong>g>e normal PrP<br />

and inducing its c<strong>on</strong>versi<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e abnormal form [6]. This scenario was quantitatively<br />

described as a nucleati<strong>on</strong>-dependent amyloid polymerizati<strong>on</strong> [4]. However,<br />

we obtained experimental results inc<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is <str<strong>on</strong>g>th</str<strong>on</strong>g>eory. Indeed al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> polymerizati<strong>on</strong> resemble a simple nucleus-dependent fibrillogenesis, nei<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e initial c<strong>on</strong>centrati<strong>on</strong> dependence nor <str<strong>on</strong>g>of</str<strong>on</strong>g>f-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis fit completely<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental results when submitted to <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical models [1], comparable<br />

discrepancies were obtained by o<str<strong>on</strong>g>th</str<strong>on</strong>g>er [2,3,4,5]. We <str<strong>on</strong>g>th</str<strong>on</strong>g>us hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esise <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> an <strong>on</strong>-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way before nucleati<strong>on</strong> associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a c<strong>on</strong>formati<strong>on</strong>al change <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

generates intermediate c<strong>on</strong>formati<strong>on</strong>s compatible wi<str<strong>on</strong>g>th</str<strong>on</strong>g> nucleati<strong>on</strong> and polymerizati<strong>on</strong>.<br />

Using electr<strong>on</strong> microscopy analysis, we observed odd-structures <str<strong>on</strong>g>th</str<strong>on</strong>g>at behaved<br />

as precursor <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e amyloid formati<strong>on</strong>. We have developed a quantitative model<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an explicit descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> microscopic processes <str<strong>on</strong>g>th</str<strong>on</strong>g>at takes into account our<br />

observati<strong>on</strong>s. Then, we c<strong>on</strong>fr<strong>on</strong>ted, under several c<strong>on</strong>diti<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model predicti<strong>on</strong>s<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental data. It appears <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are in a good agreement. Several<br />

c<strong>on</strong>clusi<strong>on</strong>s can be drawn from <str<strong>on</strong>g>th</str<strong>on</strong>g>is model <str<strong>on</strong>g>th</str<strong>on</strong>g>at better explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e nucleati<strong>on</strong> kinetic<br />

barrier and pri<strong>on</strong> misfolding. We discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model in <str<strong>on</strong>g>th</str<strong>on</strong>g>e light<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e in vivo phenomen<strong>on</strong>.<br />

References.<br />

[1] Alvarez-Martinez, M. T., et al., Dynamic <str<strong>on</strong>g>of</str<strong>on</strong>g> polymerizati<strong>on</strong> shed light <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

lead to multiple amyloid structures <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pri<strong>on</strong> protein. Submit (2010).<br />

[2] Baskakov, I. V. & Bochora, 0. V., In vitro c<strong>on</strong>verti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> mammalian pri<strong>on</strong> protein into amyloid<br />

fibrils displays unusual features. Biochemistry 44, 2339–2348 (2005).<br />

[3] Collins, S. R., Douglass, A., Vae, R. D. & Weissmann, J. S., Mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> pri<strong>on</strong> propagati<strong>on</strong>:<br />

Amyloid grow<str<strong>on</strong>g>th</str<strong>on</strong>g> occurs by m<strong>on</strong>omer additi<strong>on</strong>. PLOS Biol. 2, e321 (2004).<br />

414

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[4] Come, J. H., Fraser, P. E. & Landsbury, P. T. A kinetic model for amyloid formati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

pri<strong>on</strong> diseases: Importance <str<strong>on</strong>g>of</str<strong>on</strong>g> seeding. Proc. Natl. Acad. Sci. U S A 90, 5959–5963 (1993).<br />

[5] Masel, J., Jansen, V. A. A. & Nowak, M. A., Quantifying <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinetic parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> pri<strong>on</strong><br />

replicati<strong>on</strong>. Biophys. Chem. 77, 139–152 (1999).<br />

[6] Prusiner, S. B., Novel proteinaceous infectious particles cause scrapie. Science 216, 136–144<br />

(1982).<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Semigroups <str<strong>on</strong>g>of</str<strong>on</strong>g> Operators in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology II; Saturday, July 2, 11:00<br />

, Peter<br />

József Z. Farkas<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Computing Science and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Stirling, Stirling, FK9 4LA, United Kingdom<br />

Peter Hinow<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Wisc<strong>on</strong>sin - Milwaukee,<br />

P.O. Box 413, Milwaukee, WI 53201, USA<br />

e-mail: hinow@uwm.edu<br />

Structured and unstructured c<strong>on</strong>tinuous models for<br />

Wolbachia infecti<strong>on</strong>s<br />

Wolbachia is a maternally transmitted bacterium <str<strong>on</strong>g>th</str<strong>on</strong>g>at lives in symbiosis wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

many ar<str<strong>on</strong>g>th</str<strong>on</strong>g>ropod species. We introduce and investigate a series <str<strong>on</strong>g>of</str<strong>on</strong>g> models for an infecti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a diplodiploid host species by Wolbachia. The c<strong>on</strong>tinuous models are characterized<br />

by partial vertical transmissi<strong>on</strong>, cytoplasmic incompatibility and fitness<br />

costs associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong>. A particular aspect <str<strong>on</strong>g>of</str<strong>on</strong>g> interest is competiti<strong>on</strong>s<br />

between mutually incompatible strains. We fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er introduce an age-structured<br />

model <str<strong>on</strong>g>th</str<strong>on</strong>g>at takes into account different fertility and mortality rates at different<br />

stages <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e life cycle <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e individuals. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <strong>on</strong>ly a few parameters, <str<strong>on</strong>g>th</str<strong>on</strong>g>e ordinary<br />

differential equati<strong>on</strong> models exhibit already interesting dynamics and can be used<br />

to predict criteria under which a strain <str<strong>on</strong>g>of</str<strong>on</strong>g> bacteria is able to invade a populati<strong>on</strong>.<br />

Interestingly, but not surprisingly, <str<strong>on</strong>g>th</str<strong>on</strong>g>e age-structured model shows significant differences<br />

c<strong>on</strong>cerning <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence and stability <str<strong>on</strong>g>of</str<strong>on</strong>g> equilibrium soluti<strong>on</strong>s compared<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e unstructured model.<br />

Keywords: Wolbachia, endosymbiosis, cytoplasmic incompatibility<br />

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J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an E. Hiorns<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham<br />

e-mail: pmxjh1@nottingham.ac.uk<br />

B.S. Brook, I. Hall, O.E. Jensen<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham<br />

Medical Physiology; Tuesday, June 28, 11:00<br />

A biomechanical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e as<str<strong>on</strong>g>th</str<strong>on</strong>g>matic airway<br />

When as<str<strong>on</strong>g>th</str<strong>on</strong>g>matics come in c<strong>on</strong>tact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> ag<strong>on</strong>ists (e.g. cold air, chemicals or dust),<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> muscle in <str<strong>on</strong>g>th</str<strong>on</strong>g>e walls <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir lung airways c<strong>on</strong>tracts, causing wheezing<br />

and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er brea<str<strong>on</strong>g>th</str<strong>on</strong>g>ing difficulties. Over l<strong>on</strong>g periods <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is also substantial <str<strong>on</strong>g>th</str<strong>on</strong>g>ickening<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e muscular airway wall. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling has significant potential<br />

to <str<strong>on</strong>g>of</str<strong>on</strong>g>fer insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>e signalling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways <str<strong>on</strong>g>th</str<strong>on</strong>g>at initiate<br />

smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> muscle c<strong>on</strong>tracti<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical acti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cross-bridges wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in smoo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

muscle <str<strong>on</strong>g>th</str<strong>on</strong>g>at leads to c<strong>on</strong>tracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e airway and surrounding tissue, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

l<strong>on</strong>ger-term impact <str<strong>on</strong>g>of</str<strong>on</strong>g> wall remodelling <strong>on</strong> airway functi<strong>on</strong>. Here we address some<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem by modelling an airway as a two-layer<br />

annulus in plane strain. The inner layer, representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e airway wall, is modelled<br />

as a n<strong>on</strong>linear incompressible fibre-reinforced material. The outer layer, representing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding parenchyma, is modelled as a linear compressible viscoelastic<br />

material. Airway deformati<strong>on</strong>s are induced ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er by imposing external stresses or<br />

via active forces generated in <str<strong>on</strong>g>th</str<strong>on</strong>g>e inner muscular layer. When passively inflated,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e airway wall exhibits strain-stiffening and creep. The model reveals differences in<br />

patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> deformati<strong>on</strong> depending <strong>on</strong> whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er inflati<strong>on</strong> is driven by stresses <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

inner or outer boundary (reflecting differences between artificial and natural ventilati<strong>on</strong>).<br />

The model also shows significant stress gradients across <str<strong>on</strong>g>th</str<strong>on</strong>g>ickened airway<br />

walls. Initial results coupling wall and muscle mechanics will also be discussed.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bar<str<strong>on</strong>g>th</str<strong>on</strong>g>olomäus Hirt<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham<br />

e-mail: pmxbvh@nottingham.ac.uk<br />

Bioinformatics and System Biology; Wednesday, June 29, 08:30<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical investigati<strong>on</strong> into <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e anti-cancer<br />

compound RHPS4 <strong>on</strong> cell-cycle dynamics<br />

The pentacyclic acridinium salt RHPS4 displays anti-tumour properties in vitro<br />

as well as in vivo and is potentially cell-cycle specific. We have collected experimental<br />

data and formulated a compartmental model using ordinary differential<br />

equati<strong>on</strong>s to investigate how <str<strong>on</strong>g>th</str<strong>on</strong>g>e compound affects cells in each stage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell<br />

cycle. The eukaryotic cell cycle primarily c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> five phases, namely a resting<br />

state, G0, and four cycling phases: G1, S, G2 and M phase wi<str<strong>on</strong>g>th</str<strong>on</strong>g> cells progressing<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>is order and <str<strong>on</strong>g>th</str<strong>on</strong>g>en dividing into two cells back in G1. Understanding how a<br />

drug affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell cycle could give insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug’s mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> acti<strong>on</strong><br />

and may assist research into potential treatment strategies.<br />

We treated colorectal cancer cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree different c<strong>on</strong>centrati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

drug and fitted simulati<strong>on</strong>s from our models to experimental observati<strong>on</strong>s. We<br />

found <str<strong>on</strong>g>th</str<strong>on</strong>g>at RHPS4 caused a c<strong>on</strong>centrati<strong>on</strong>-dependent, marked cell dea<str<strong>on</strong>g>th</str<strong>on</strong>g> in treated<br />

cells, which is best modelled by allowing rate parameters in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell cycle to be<br />

time-dependent functi<strong>on</strong>s. Our compartmental models fit data from c<strong>on</strong>trol cells<br />

and cells treated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> lower c<strong>on</strong>centrati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> RHPS4 particularly well. We have<br />

also shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is “identifiable", meaning <str<strong>on</strong>g>th</str<strong>on</strong>g>at, at least in principle,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter values can be determined from observable quantities. Our fitting<br />

procedure generates informati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sensitivity <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model.<br />

We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at at low c<strong>on</strong>centrati<strong>on</strong>s RHPS4 primarily affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells’ behaviour<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e G2/M phase, and <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug has a delayed effect wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e delay decreasing<br />

at larger doses. Since <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug diffuses into <str<strong>on</strong>g>th</str<strong>on</strong>g>e nucleus, <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed delayed effect<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e compound is unexpected and is a novel finding <str<strong>on</strong>g>of</str<strong>on</strong>g> our research into <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

compound. We propose <str<strong>on</strong>g>th</str<strong>on</strong>g>at sec<strong>on</strong>dary effects lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e inducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> observed<br />

cell dea<str<strong>on</strong>g>th</str<strong>on</strong>g> and <str<strong>on</strong>g>th</str<strong>on</strong>g>at changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>-coding DNA<br />

sequences at chromosome ends, called telomeres, might be a precursor <str<strong>on</strong>g>of</str<strong>on</strong>g> delayed<br />

cell dea<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics <str<strong>on</strong>g>of</str<strong>on</strong>g> liver: bridging molecular systems biology to<br />

virtual physiological human scale; Wednesday, June 29, 11:00<br />

Stefan Hoehme<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Leipzig, Germany<br />

e-mail: hoehme@uni-leipzig.de<br />

Dirk Drasdo<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Leipzig, INRIA Paris<br />

Jan Hengstler<br />

IfADo Dortmund<br />

Regenerati<strong>on</strong> after partial hepatectomy: from cell to organ<br />

scale<br />

The liver is a vital organ wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a wide range <str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong>s. It plays a key role in<br />

detoxificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood and is essential for most metabolic functi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e body.<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e outstanding features <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver is its capacity to regenerate a loss <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

large parts <str<strong>on</strong>g>of</str<strong>on</strong>g> its mass wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in days. This rapid regenerati<strong>on</strong> is <str<strong>on</strong>g>of</str<strong>on</strong>g> utmost importance<br />

for patient survival for example after partial hepatectomy, a process where parts<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver are surgically removed for example during liver transplantati<strong>on</strong> or <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> liver cancer. In liver, functi<strong>on</strong> and architecture are tightly coupled.<br />

Therefore, a deep understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> liver regenerati<strong>on</strong> requires an understanding<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> how functi<strong>on</strong>al comp<strong>on</strong>ents like hepatocytes or blood vessels and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir spatial<br />

organizati<strong>on</strong> toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e regenerati<strong>on</strong> process. In order to study regenerati<strong>on</strong><br />

after partial hepatectomy, we advanced <str<strong>on</strong>g>th</str<strong>on</strong>g>e single-cell based spatial-temporal model<br />

in 3D established in [1]. The model is c<strong>on</strong>structed based <strong>on</strong> experimental data, in<br />

particular c<strong>on</strong>focal laser scans and whole slide scans, <str<strong>on</strong>g>th</str<strong>on</strong>g>at were quantified by a novel<br />

image processing and analysis chain. It now spans from cellular scale up to organ<br />

scale.<br />

The talk introduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e model al<strong>on</strong>g wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods developed to c<strong>on</strong>struct<br />

it and presents first results obtained by model simulati<strong>on</strong>s.<br />

References.<br />

[1] Hoehme, S., Brulport, M., Bauer, A., Bedawy, E., Schormann, W., Gebhardt, R., Zellmer,<br />

S., Schwarz, M., Bockamp, E., Timmel, T., G. Hengstler, J.G., and Drasdo, D. (2010). Predicti<strong>on</strong><br />

and validati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell alignment al<strong>on</strong>g microvessels as order principle to restore tissue<br />

architecture in liver regenerati<strong>on</strong>. Proc. Natl. Acad. Sci. (USA), 107(23), 10371-10376.<br />

419

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Nadine Hohmann<br />

Centre for Informati<strong>on</strong> Services and High Performance Computing,<br />

TU Dresden<br />

e-mail: nadine.hohmann@tu-dresden.de<br />

Anja Voß-Böhme<br />

Centre for Informati<strong>on</strong> Services and High Performance Computing,<br />

TU Dresden<br />

Andreas Deutsch<br />

Centre for Informati<strong>on</strong> Services and High Performance Computing,<br />

TU Dresden<br />

Mechanisms for liver size regulati<strong>on</strong><br />

The liver is a multi-functi<strong>on</strong>al organ <str<strong>on</strong>g>th</str<strong>on</strong>g>at participates in major physiological processes<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>at possesses a remarkable regenerati<strong>on</strong> capacity. After loss <str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong>al<br />

liver mass <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver regrows to its original, individual-dependent size. A<br />

transplanted liver adjusts its size to <str<strong>on</strong>g>th</str<strong>on</strong>g>e host organism by increasing in size when<br />

small-for-size or decreasing in size when large-for-size. Yet, how does <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver<br />

"know" when it has achieved its correct size?<br />

The mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> organ size c<strong>on</strong>trol are still not well understood. Intracellular<br />

signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trol cell size regulati<strong>on</strong>, cell proliferati<strong>on</strong> and apoptosis<br />

have already been studied in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature. However, organ size c<strong>on</strong>trol is <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

collective result <str<strong>on</strong>g>of</str<strong>on</strong>g> decentralized, individual cell decisi<strong>on</strong>s. It is proposed in several<br />

works <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is collective behavior might be guided by n<strong>on</strong>local interacti<strong>on</strong>s mediated<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough morphogen gradients. Here, we pose <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong>, whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er organ size<br />

c<strong>on</strong>trol can also be accomplished by a mechanism solely based <strong>on</strong> local intercellular<br />

interacti<strong>on</strong>s.<br />

Based <strong>on</strong> a careful review <str<strong>on</strong>g>of</str<strong>on</strong>g> currently debated mechanisms and recent experiments<br />

for organ size regulati<strong>on</strong> we will develop and analyze several model prototypes.<br />

We will focus <strong>on</strong> an Interacting Cell System Model to study especially<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e implicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> local intercellular interacti<strong>on</strong>s as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulatory role <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

organ-intrinsic grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factors and organ-extrinsic grow<str<strong>on</strong>g>th</str<strong>on</strong>g> regulators. The study is<br />

part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Virtual Liver project funded by <str<strong>on</strong>g>th</str<strong>on</strong>g>e German BMBF.<br />

420

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Symmetry Breaking and Cellular Polarizati<strong>on</strong> in Motile Cells<br />

William Holmes<br />

e-mail: wrholmes@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ubc.ca<br />

Chemotaxis is <str<strong>on</strong>g>th</str<strong>on</strong>g>e process by which cells undergo directed moti<strong>on</strong> toward an external<br />

signal. In Eukaryotic cells, a precurser to such moti<strong>on</strong> is a symmetry breaking<br />

event where proteins resp<strong>on</strong>sible for cytoskeletal remodelling and motility self organize<br />

to form a fr<strong>on</strong>t and back. A model developed in collaborati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an experimental<br />

group <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese regulatory proteins and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir associated kinetics is presented.<br />

It is shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is model accounts for observed characteristics not found in o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

models and provides new insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e physiologically resp<strong>on</strong>sible processes.<br />

Novel psuedo-analytic me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for analysing such models will be briefly discussed<br />

and c<strong>on</strong>necti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental observati<strong>on</strong>s will be highlighted.<br />

421

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Statistical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in computati<strong>on</strong>al neuroscience II; Wednesday, June 29,<br />

17:00<br />

Klaus Kähler Holst<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biostatistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Copenhagen<br />

e-mail: k.k.holst@biostat.ku.dk<br />

A Latent Variable Model for brain serot<strong>on</strong>in levels as<br />

measured by cerebral serot<strong>on</strong>in transporter and 5-HT2A<br />

receptor binding in vivo<br />

Today, it is not possible to n<strong>on</strong>-invasively measure <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular levels <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

serot<strong>on</strong>in (5-HT) in vivo. However, indirect measurements can be obtained by<br />

positr<strong>on</strong> emissi<strong>on</strong> tomography (PET) techniques. A n<strong>on</strong>-linear structural equati<strong>on</strong><br />

model is proposed for describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e associati<strong>on</strong> between 5-HT2A receptor binding<br />

and serot<strong>on</strong>in (5-HT) transporter binding as measured by PET imaging. The<br />

approach is based <strong>on</strong> a biological model where <str<strong>on</strong>g>th</str<strong>on</strong>g>e 5-HT2A receptor and serot<strong>on</strong>in<br />

transporter measurements are expressed n<strong>on</strong>-linearly by a comm<strong>on</strong> regulator, e.g.<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e raphe serot<strong>on</strong>ergic output. The proposed model makes it possible to study<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e associati<strong>on</strong> between latent brain 5-HT levels and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er end-points, for instance<br />

development <str<strong>on</strong>g>of</str<strong>on</strong>g> mood disorders.<br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for obtaining approximate maximum likelihood estimates are discussed<br />

and new model diagnostic me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods based <strong>on</strong> cumulative residuals are presented.<br />

422

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Bi<str<strong>on</strong>g>of</str<strong>on</strong>g>luids, Solute Transport, and Hemodynamics; Wednesday, June 29, 11:00<br />

Niels-Henrik Holstein-Ra<str<strong>on</strong>g>th</str<strong>on</strong>g>lou<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biomedical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Copenhagen, Denmark<br />

e-mail: nhhr@sund.ku.dk<br />

Olga Sosnovtseva<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biomedical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Copenhagen, Denmark<br />

e-mail: olga@sund.ku.dk<br />

D<strong>on</strong>ald J. Marsh<br />

Brown University, Providence, RI, USA<br />

e-mail: marsh@ash.biomed.brown.edu<br />

Synchr<strong>on</strong>izati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> nephr<strong>on</strong>s in vascular networks<br />

Tubuloglomerular feedback (TGF) has an important role in autoregulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> renal<br />

blood flow and glomerular filtrati<strong>on</strong> rate (GFR). Because <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

signal transmissi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e feedback loop, <str<strong>on</strong>g>th</str<strong>on</strong>g>e TGF undergoes self sustained oscillati<strong>on</strong>s<br />

in single nephr<strong>on</strong> blood flow, GFR and tubular pressure and flow. Nephr<strong>on</strong>s<br />

interact by exchanging electrical signals c<strong>on</strong>ducted electrot<strong>on</strong>ically <str<strong>on</strong>g>th</str<strong>on</strong>g>rough cells <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e vascular wall, leading to synchr<strong>on</strong>izati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e TGF mediated oscillati<strong>on</strong>s. To<br />

study <str<strong>on</strong>g>th</str<strong>on</strong>g>e extent <str<strong>on</strong>g>of</str<strong>on</strong>g> synchr<strong>on</strong>izati<strong>on</strong> we have used laser speckle c<strong>on</strong>trast imaging<br />

to measure <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood flow dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> 50 – 100 nephr<strong>on</strong>s simultaneously <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

renal surface <str<strong>on</strong>g>of</str<strong>on</strong>g> anes<str<strong>on</strong>g>th</str<strong>on</strong>g>etized rats. Synchr<strong>on</strong>ized TGF oscillati<strong>on</strong>s were detected in<br />

pairs or triplets <str<strong>on</strong>g>of</str<strong>on</strong>g> nephr<strong>on</strong>s. The amplitude and <str<strong>on</strong>g>th</str<strong>on</strong>g>e frequency <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e oscillati<strong>on</strong>s<br />

changed wi<str<strong>on</strong>g>th</str<strong>on</strong>g> time, as did <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> synchr<strong>on</strong>izati<strong>on</strong>. Synchr<strong>on</strong>izati<strong>on</strong> may<br />

take place am<strong>on</strong>g nephr<strong>on</strong>s not immediately adjacent <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e surface <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e kidney.<br />

Nephr<strong>on</strong>s are organized in a vascular network, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>em<br />

takes place across <str<strong>on</strong>g>th</str<strong>on</strong>g>e network. To investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e significance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network structure,<br />

we modeled two alternative network c<strong>on</strong>figurati<strong>on</strong>s: a linear serial network,<br />

and a branching fractal structure. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough synchr<strong>on</strong>izati<strong>on</strong> am<strong>on</strong>g nephr<strong>on</strong>s was<br />

observed in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>figurati<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e tendency was for in phase synchr<strong>on</strong>izati<strong>on</strong><br />

am<strong>on</strong>g nephr<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e linear, serial network; whereas more complex in- and out<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> phase patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> synchr<strong>on</strong>izati<strong>on</strong> was observed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e branching model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

vascular network.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics <str<strong>on</strong>g>of</str<strong>on</strong>g> liver: bridging molecular systems biology to<br />

virtual physiological human scale; Wednesday, June 29, 11:00<br />

Hermann-Georg Holzhuetter<br />

Charité - Universitaetsmedizin Berlin, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemistry<br />

e-mail: hermann-georg.holzhuetter@charite.de<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> liver metabolism — do we need a<br />

multi-scale approach?<br />

The liver is <str<strong>on</strong>g>th</str<strong>on</strong>g>e central metabolic organ <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e human organism au<str<strong>on</strong>g>th</str<strong>on</strong>g>oritatively<br />

involved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e detoxificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> xenobiotics (drugs), <str<strong>on</strong>g>th</str<strong>on</strong>g>e homeostasis <str<strong>on</strong>g>of</str<strong>on</strong>g> numerous<br />

blood compounds and producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> anti-inflammatory agents. Most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

metabolic functi<strong>on</strong>s are accomplished by hepatocytes comprising about two <str<strong>on</strong>g>th</str<strong>on</strong>g>irds<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> liver cells. Therefore, ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> liver metabolism hi<str<strong>on</strong>g>th</str<strong>on</strong>g>erto has<br />

widely focused <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e single hepatocytes. However, hepatocytes arranged al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

same supporting vessel have different access to oxygen, nutrients and horm<strong>on</strong>es in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e blood and <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore differ in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir functi<strong>on</strong>al capacities. Irregularities <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vascular<br />

tree and regi<strong>on</strong>al partial occlusi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> blood vessels (e.g. caused by swollen<br />

cells due to lipid accumulati<strong>on</strong>) may entail <str<strong>on</strong>g>th</str<strong>on</strong>g>at wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e organ normoxic and<br />

partly ischemic regi<strong>on</strong>s coexist. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular processes underlying<br />

complex physiological liver functi<strong>on</strong>s proceed at different time scales: Sec<strong>on</strong>ds for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e horm<strong>on</strong>al initiati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> glycogen degradati<strong>on</strong>, some weeks for liver regenerati<strong>on</strong><br />

after partial hepatectomy and several m<strong>on</strong><str<strong>on</strong>g>th</str<strong>on</strong>g>s or even years for <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a n<strong>on</strong>-alcoholic fatty liver. Finally, <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolic state <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatocytes is affected<br />

by cellular c<strong>on</strong>tacts wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er and signals received from o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hepatic cells,<br />

e.g. endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells or macrophages. These are aspects <str<strong>on</strong>g>th</str<strong>on</strong>g>at necessitate to study<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolism <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> a multi-scale model <str<strong>on</strong>g>th</str<strong>on</strong>g>at covers different<br />

spatial and temporal scales. This talk outlines <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic structure <str<strong>on</strong>g>of</str<strong>on</strong>g> such a liver<br />

model and presents some first results.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part I;<br />

Tuesday, June 28, 11:00<br />

Mary Ann Horn<br />

Program in Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics & Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Nati<strong>on</strong>al Science Foundati<strong>on</strong>, Arlingt<strong>on</strong>, USA<br />

e-mail: mhorn@nsf.gov<br />

Hannah L.<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Portland, and H. Alex Brown and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Brown Laboratory<br />

at Vanderbilt University, Nashville, USA<br />

Using ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling to understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

diacylglycerol (DAG) as a sec<strong>on</strong>d messenger<br />

Diacylgylcerol (DAG) plays a key role in cellular signaling as a sec<strong>on</strong>d messenger.<br />

In particular, it regulates a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular processes and <str<strong>on</strong>g>th</str<strong>on</strong>g>e breakdown <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way <str<strong>on</strong>g>th</str<strong>on</strong>g>at involves DAG c<strong>on</strong>tributes to <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> a variety<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> diseases, including cancer. We present a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e G-protein<br />

signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way in RAW 264.7 macrophages downstream <str<strong>on</strong>g>of</str<strong>on</strong>g> P2Y6 activati<strong>on</strong> by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e ubiquitous signaling nucleotide uridine 5’-diphosphate. Our primary goal is<br />

to better understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> diacylglycerol in <str<strong>on</strong>g>th</str<strong>on</strong>g>e signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

underlying biological dynamics <str<strong>on</strong>g>th</str<strong>on</strong>g>at cannot always be easily measured experimentally.<br />

The model is based <strong>on</strong> time-course measurements <str<strong>on</strong>g>of</str<strong>on</strong>g> P2Y6 surface receptors,<br />

inositol trisphosphate, cytosolic calcium, and wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a particular focus <strong>on</strong> differential<br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple species <str<strong>on</strong>g>of</str<strong>on</strong>g> diacylglycerol. When using <str<strong>on</strong>g>th</str<strong>on</strong>g>e can<strong>on</strong>ical representati<strong>on</strong>,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e model predicted <str<strong>on</strong>g>th</str<strong>on</strong>g>at key interacti<strong>on</strong>s were missing from <str<strong>on</strong>g>th</str<strong>on</strong>g>e current<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way structure. Indeed, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>at to accurately depict experimental<br />

observati<strong>on</strong>s, an additi<strong>on</strong>al branch to <str<strong>on</strong>g>th</str<strong>on</strong>g>e signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way was needed,<br />

whereby an intracellular pool <str<strong>on</strong>g>of</str<strong>on</strong>g> diacylglycerol is immediately phosphorylated up<strong>on</strong><br />

stimulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an extracellular receptor for uridine 5’-diphosphate and subsequently<br />

used to aid replenishment <str<strong>on</strong>g>of</str<strong>on</strong>g> phosphatidylinositol. As a result <str<strong>on</strong>g>of</str<strong>on</strong>g> sensitivity analysis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model parameters, key predicti<strong>on</strong>s can be made regarding which <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese parameters<br />

are <str<strong>on</strong>g>th</str<strong>on</strong>g>e most sensitive to perturbati<strong>on</strong>s and are <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore most resp<strong>on</strong>sible<br />

for output uncertainty.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Recent developments in <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> Lotka-Volterra and Kolmogorov<br />

systems; Saturday, July 2, 14:30<br />

Zhanyuan Hou<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Computing, L<strong>on</strong>d<strong>on</strong> Metropolitan University, L<strong>on</strong>d<strong>on</strong>, UK<br />

e-mail: z.hou@l<strong>on</strong>d<strong>on</strong>met.ac.uk<br />

Stephen Baigent<br />

Demartment <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, UCL<br />

Heteroclinic limit cycles in Lotka-Volterra systems<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, we are c<strong>on</strong>cerned wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e global, ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an local, attracti<strong>on</strong> (repulsi<strong>on</strong>)<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a heteroclinic limit cycle in competitive Lotka-Volterra systems. C<strong>on</strong>diti<strong>on</strong>s<br />

will be explored for omiga (alpha) limit sets to be a single heteroclinic cycle for almost<br />

all interior initial points in <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>negative c<strong>on</strong>e.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemic models: Networks and stochasticity I; Wednesday, June 29, 14:30<br />

Thomas House<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warwick<br />

e-mail: T.A.House@warwick.ac.uk<br />

István Kiss<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sussex<br />

e-mail: I.Z.Kiss@sussex.ac.uk<br />

Overview <str<strong>on</strong>g>of</str<strong>on</strong>g> Networks and Stochasticity in Epidemic Models<br />

Two areas <str<strong>on</strong>g>of</str<strong>on</strong>g> much recent work in modelling epidemics are c<strong>on</strong>tact networks<br />

and populati<strong>on</strong> stochasticity. These c<strong>on</strong>cepts are closely related, since <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a small, finite neighbourhood <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tacts around each individual (or simple demographic<br />

stochasticity) make chance events important at <str<strong>on</strong>g>th</str<strong>on</strong>g>e local level, which<br />

can <str<strong>on</strong>g>th</str<strong>on</strong>g>en scale up to significant populati<strong>on</strong>-level effects.<br />

This talk will introduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cepts <str<strong>on</strong>g>of</str<strong>on</strong>g> network structure and stochasticity, and<br />

by focusing <strong>on</strong> network models, will provide an overview <str<strong>on</strong>g>of</str<strong>on</strong>g> different ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical,<br />

computati<strong>on</strong>al and empirical tools used to address <str<strong>on</strong>g>th</str<strong>on</strong>g>ese issues. In particular, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

relati<strong>on</strong>ship between exact models, approximati<strong>on</strong>s based <strong>on</strong> heuristic arguments,<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e results <str<strong>on</strong>g>of</str<strong>on</strong>g> M<strong>on</strong>te Carlo simulati<strong>on</strong> will be discussed.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis II; Wednesday, June<br />

29, 11:00<br />

N. André<br />

Pediatric <strong>on</strong>cology, La Tim<strong>on</strong>e hospital. Marseille, France.<br />

e-mail: nicolas.andre@ap-hm.fr<br />

D. Barbolosi<br />

Laboratoire de Toxicocinétique et Pharmacocinétique. Marseille,<br />

France.<br />

e-mail: dominique.barbolosi@univ-cezanne.fr<br />

A. Benabdallah<br />

LATP , Université de Provence Marseille, France.<br />

e-mail: assia@cmi.univ-mrs.fr<br />

S. Benzekry<br />

LATP & Laboratoire de Toxicocinétique et Pharmacocinétique.<br />

Marseille, France.<br />

e-mail: benzekry@phare.normalesup.org<br />

F. Hubert<br />

LATP , Université de Provence, Marseille, France.<br />

e-mail: fhubert@cmi.univ-mrs.fr<br />

A model for anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

Since <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposal by J. Folkman in <str<strong>on</strong>g>th</str<strong>on</strong>g>e 70’s to use tumoral neo-angiogenesis<br />

as a <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic target, important efforts lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> various antiangiogenic<br />

drugs now used in <str<strong>on</strong>g>th</str<strong>on</strong>g>e clinic. Though, <str<strong>on</strong>g>th</str<strong>on</strong>g>e practical results obtained by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese so-called "targeted <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies" are quite poor up to now and anti-angiogenic<br />

drugs are far from replacing <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical, very toxic, chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapies. In some cases,<br />

angiogenic drugs can even exhibit paroxystic effects such as metastatic accelerati<strong>on</strong><br />

[3]. It seems <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e way <str<strong>on</strong>g>of</str<strong>on</strong>g> administering <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug, its scheduling is <str<strong>on</strong>g>of</str<strong>on</strong>g> fundamental<br />

importance and determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e best schedules for anti-angiogenic drugs al<strong>on</strong>e or<br />

in combinati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> cytotoxic drugs is a clinical open questi<strong>on</strong>.<br />

In order to give insights <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese questi<strong>on</strong>s, we developed <str<strong>on</strong>g>th</str<strong>on</strong>g>e model <str<strong>on</strong>g>of</str<strong>on</strong>g> [2] and<br />

included a module to incorporate <str<strong>on</strong>g>th</str<strong>on</strong>g>e metastases [1]. We will present interesting<br />

simulati<strong>on</strong>s studying and optimizing efficient temporal administrati<strong>on</strong> protocols,<br />

and describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e paradoxal effect observed in [3].<br />

In particular, we can give answers in an emerging area <str<strong>on</strong>g>of</str<strong>on</strong>g> clinical <strong>on</strong>cology named<br />

metr<strong>on</strong>omic chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy (or anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy) [4]. It c<strong>on</strong>sists in delivering<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy at doses below <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximum tolerated doses, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a frequent<br />

schedule and is based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e assumpti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at such a schedule would have an antiangiogenic<br />

effect.<br />

References.<br />

[1] Benzekry, S. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and numerical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> a model for anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy in<br />

metastatic cancers, submitted.<br />

[2] Hahnfeldt, P. and Panigraphy, D. and Folkman, J. and Hlatky, L., Tumor development under<br />

angiogenic signaling : a dynamical <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, treatment, resp<strong>on</strong>se and postvascular<br />

dormancy, Cancer Research., 59, 4770–4775, 1999.<br />

428

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[3] J. ML Ebos, C. R. Lee, W. Cruz-Munoz, G. A. Bjarnas<strong>on</strong>, J. G. Christensen and R. S.<br />

Kerbel, Accelerated metastasis after short-term treatment wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a potent inhibitor <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor<br />

angiogenesis. Cancer Cell 15 (2009) 232-239.<br />

[4] Kerbel RS, Kamen BA. The anti-angiogenic basis <str<strong>on</strong>g>of</str<strong>on</strong>g> metr<strong>on</strong>omic chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy. Nat. Rev.<br />

Cancer 4 (2004) 423-436.<br />

429

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

From <strong>on</strong>e to many: Cell-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective, emergent behaviors<br />

in biology -I; Tuesday, June 28, 11:00<br />

C. An<str<strong>on</strong>g>th</str<strong>on</strong>g><strong>on</strong>y Hunt<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioengineering and Therapeutic Sciences, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> California, San Francisco<br />

e-mail: a.hunt@ucsf.edu<br />

Shahab Sheikh-Bahaei<br />

Program in Bioengineering , University <str<strong>on</strong>g>of</str<strong>on</strong>g> California, San Francisco<br />

Emergent patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatic z<strong>on</strong>ati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> xenobiotic<br />

clearance and hepatotoxicity: a plausible role for cell<br />

learning<br />

Hepatic z<strong>on</strong>ati<strong>on</strong> is c<strong>on</strong>spicuous periportal (afferent) to perivenous (efferent) attribute<br />

gradients wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in lobules. Z<strong>on</strong>al differences occur in <str<strong>on</strong>g>th</str<strong>on</strong>g>e clearance <str<strong>on</strong>g>of</str<strong>on</strong>g> a variety<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> endogenous compounds and xenobiotics, and are evident for a number <str<strong>on</strong>g>of</str<strong>on</strong>g> normal<br />

hepatic functi<strong>on</strong>s. However, no c<strong>on</strong>crete, causal, mechanistic <str<strong>on</strong>g>th</str<strong>on</strong>g>eory is available to<br />

explain how, for example, different hepatic z<strong>on</strong>ati<strong>on</strong> patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> P450 isozyme levels<br />

and hepatotoxicity emerge following dosing wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different compounds. We used <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g> modeling and simulati<strong>on</strong> to discover, explore, and experimentally<br />

challenge c<strong>on</strong>crete mechanisms <str<strong>on</strong>g>th</str<strong>on</strong>g>at show how and why biomimetic z<strong>on</strong>ati<strong>on</strong><br />

patterns emerge and change wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in agent-based analogues. Syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods enable<br />

teasing apart complex systems in c<strong>on</strong>trast to inductive me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods, which target<br />

predicti<strong>on</strong>. Following an iterative Refinement Protocol enabled c<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> real<br />

(not c<strong>on</strong>ceptual), strictly defined, biomimetic mechanisms while also accounting for<br />

c<strong>on</strong>siderable uncertainty. Even <str<strong>on</strong>g>th</str<strong>on</strong>g>ough abstract, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir spatial<br />

c<strong>on</strong>text are flexible and sufficiently c<strong>on</strong>crete to instantiate mechanistic hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses<br />

and test <str<strong>on</strong>g>th</str<strong>on</strong>g>eir plausibility experimentally. Our working hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis was <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ose<br />

mechanisms have counterparts in rats. Mobile objects map to compounds. One<br />

analogue is comprised <str<strong>on</strong>g>of</str<strong>on</strong>g> 460 identical, quasi-aut<strong>on</strong>omous functi<strong>on</strong>al units called sinusoidal<br />

segments (SSs). SSs detect and resp<strong>on</strong>d to compound-generated resp<strong>on</strong>se<br />

signals and <str<strong>on</strong>g>th</str<strong>on</strong>g>e local level <str<strong>on</strong>g>of</str<strong>on</strong>g> an endogenous gradient. Each SS used a learning algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m<br />

to adapt to new informati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e objective <str<strong>on</strong>g>of</str<strong>on</strong>g> improving efficiency. Up<strong>on</strong><br />

compound exposure, analogues developed a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> patterns <str<strong>on</strong>g>th</str<strong>on</strong>g>at were strikingly<br />

similar to <str<strong>on</strong>g>th</str<strong>on</strong>g>ose reported in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature. A degree <str<strong>on</strong>g>of</str<strong>on</strong>g> quantitative validati<strong>on</strong> was<br />

achieved against data <strong>on</strong> hepatic z<strong>on</strong>ati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> CYP1A2 mRNA expressi<strong>on</strong> caused by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ree different doses <str<strong>on</strong>g>of</str<strong>on</strong>g> TCDD (2,3,7,8-tetracholorodibenzo-p-diox<strong>on</strong>e).<br />

430

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics <str<strong>on</strong>g>of</str<strong>on</strong>g> liver: bridging molecular systems biology to<br />

virtual physiological human scale; Wednesday, June 29, 11:00<br />

Peter Hunter<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Auckland, New Zealand<br />

e-mail: p.hunter@auckland.ac.nz<br />

Modelling infrastructure for <str<strong>on</strong>g>th</str<strong>on</strong>g>e VPH/Physiome project<br />

This talk will describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e model and data encoding standards and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir associated<br />

databases and tools <str<strong>on</strong>g>th</str<strong>on</strong>g>at are being developed as part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e VPH/Physiome project.<br />

431

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Biological Systems; Tuesday, June 28, 17:00<br />

Paul Hurtado<br />

Center for Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Cornell University<br />

e-mail: ph62@cornell.edu<br />

In-Host Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Mycoplasma Infecti<strong>on</strong>s: C<strong>on</strong>junctivitis<br />

in Wild Passerine Birds<br />

The host-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen interacti<strong>on</strong> is at <str<strong>on</strong>g>th</str<strong>on</strong>g>e core <str<strong>on</strong>g>of</str<strong>on</strong>g> every infectious disease system,<br />

and provides an important foundati<strong>on</strong> from which to study infectious disease at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e individual, populati<strong>on</strong> and community levels. This work uses tools from applied<br />

dynamical systems and bifurcati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eory to investigate how different aspects<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e host immune resp<strong>on</strong>se affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e progressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a localized bacterial infecti<strong>on</strong><br />

caused by small, persistent bacteria known as mycoplasmas. The goal is to<br />

better understand observed variati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in and between host species in <str<strong>on</strong>g>th</str<strong>on</strong>g>e motivating<br />

biological system: infectious c<strong>on</strong>junctivitis in <str<strong>on</strong>g>th</str<strong>on</strong>g>e house finch (Carpodacus<br />

mexicanus) and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er passerine birds caused by <str<strong>on</strong>g>th</str<strong>on</strong>g>e novel pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen Mycoplasma<br />

gallisepticum.<br />

432

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Populati<strong>on</strong> Genetics; Wednesday, June 29, 14:30<br />

Thiemo Hustedt<br />

Universität Bielefeld, Technische Fakultät, Bielefeld<br />

e-mail: <str<strong>on</strong>g>th</str<strong>on</strong>g>ustedt@techfak.uni-bielefeld.de<br />

Moment closure in a Moran model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> recombinati<strong>on</strong><br />

The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> processes <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> genetics is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten well understood in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e limit <str<strong>on</strong>g>of</str<strong>on</strong>g> infinite populati<strong>on</strong> size where a law <str<strong>on</strong>g>of</str<strong>on</strong>g> large numbers leads to a deterministic<br />

descripti<strong>on</strong>. Great challenges arise in models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> finite populati<strong>on</strong>s<br />

and interacting individuals. In <str<strong>on</strong>g>th</str<strong>on</strong>g>ese n<strong>on</strong>linear models even <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e expectati<strong>on</strong><br />

is difficult. Its dynamics does, usually, not <strong>on</strong>ly depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e current<br />

expectati<strong>on</strong> but <strong>on</strong> higher moments, and <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is no moment closure.<br />

In my talk, I will present an excepti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>is rule. I will c<strong>on</strong>sider a c<strong>on</strong>tinuoustime<br />

Moran model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> arbitrary recombinati<strong>on</strong> and mutati<strong>on</strong>, but wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out resampling<br />

(i.e., genetic drift). In <str<strong>on</strong>g>th</str<strong>on</strong>g>is case <str<strong>on</strong>g>th</str<strong>on</strong>g>e expectati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> products <str<strong>on</strong>g>of</str<strong>on</strong>g> marginal processes<br />

defined via partiti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> sites form a closed hierarchy, which is exhaustively<br />

described by a finite system <str<strong>on</strong>g>of</str<strong>on</strong>g> differential equati<strong>on</strong>s. One <str<strong>on</strong>g>th</str<strong>on</strong>g>us has <str<strong>on</strong>g>th</str<strong>on</strong>g>e excepti<strong>on</strong>al<br />

situati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> moment closure in a n<strong>on</strong>linear system. Surprisingly, <str<strong>on</strong>g>th</str<strong>on</strong>g>is property is<br />

lost when resampling is included.<br />

References.<br />

[1] E. Baake, and T. Hustedt, Moment closure in a Moran model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> recombinati<strong>on</strong>, submitted.<br />

433

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> gene regulati<strong>on</strong>; Tuesday, June 28, 11:00<br />

Dagmar Iber<br />

ETH Zurich<br />

e-mail: dagmar.iber@bsse.e<str<strong>on</strong>g>th</str<strong>on</strong>g>z.ch<br />

From Gene Networks to Tissue Engineering: Computati<strong>on</strong>al<br />

Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Pattern Formati<strong>on</strong><br />

Limb bud development has l<strong>on</strong>g served as a paradigm <str<strong>on</strong>g>of</str<strong>on</strong>g> organogenesis and pattern<br />

formati<strong>on</strong>. Decades <str<strong>on</strong>g>of</str<strong>on</strong>g> genetic and biochemical studies provide us wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a weal<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

informati<strong>on</strong> about <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular circuits <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trol cell expansi<strong>on</strong> and positi<strong>on</strong>dependent<br />

cell differentiati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e developing limb bud. In spite <str<strong>on</strong>g>of</str<strong>on</strong>g> much detailed<br />

biological knowledge and much <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical work a detailed mechanistic understanding<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> how <str<strong>on</strong>g>th</str<strong>on</strong>g>e genes and regulatory circuits interact to c<strong>on</strong>trol limb organogenesis<br />

is still lacking. In collaborati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Zeller group at <str<strong>on</strong>g>th</str<strong>on</strong>g>e Department <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Biomedicine <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e University <str<strong>on</strong>g>of</str<strong>on</strong>g> Basel we are developing detailed computati<strong>on</strong>al<br />

models for limb development in mice. By combining ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

experimentati<strong>on</strong> we seek to understand how key processes at <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic level<br />

interact to give rise to patterning at <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic level.<br />

The signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways (Fgf, Shh, Bmp, Gremlin) <str<strong>on</strong>g>th</str<strong>on</strong>g>at regulate limb bud development<br />

are strikingly similar to <str<strong>on</strong>g>th</str<strong>on</strong>g>ose <str<strong>on</strong>g>th</str<strong>on</strong>g>at regulate lung morphogenesis. Based<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model for limb development we have also developed a mechanistic model for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e regulatory network <str<strong>on</strong>g>th</str<strong>on</strong>g>at governs lung branching. The branching <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e br<strong>on</strong>chi<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lungs is highly stereotyped and results from a highly regulated process <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

restricts <str<strong>on</strong>g>th</str<strong>on</strong>g>e types and sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> branching modes.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g run we seek to use our mechanistic insights in <str<strong>on</strong>g>th</str<strong>on</strong>g>e engineering <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

tissue and b<strong>on</strong>e.<br />

434

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Satomi Iino, Masanori Kohda, Satoshi Takahashi<br />

Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Humanities and Sciences, Nara Women’s University,<br />

Nara, Japan<br />

e-mail: sato0504@ics.nara-wu.ac.jp<br />

Masanori Kohda<br />

Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Osaka City University, Osaka, Japan<br />

e-mail: maskohda@sci.osaka-cu.ac.jp<br />

Satoshi Takahashi<br />

Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Humanities and Sciences, Nara Women’s University,<br />

Nara, Japan<br />

e-mail: takahasi@lisboa.ics.nara-wu.ac.jp<br />

Model <str<strong>on</strong>g>of</str<strong>on</strong>g> coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> fish by mating territory<br />

The feeding territories <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree species (P. polyod<strong>on</strong>, P. trewavasae, P. famula )<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> genus Petrochromis in Lake Tanganyika in Africa are distributed in a mosaic<br />

pattern. The feeding territories rarely overlap wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>specific<br />

and c<strong>on</strong>generic individuals invading in <str<strong>on</strong>g>th</str<strong>on</strong>g>e feeding territory are driven out as <str<strong>on</strong>g>th</str<strong>on</strong>g>ey<br />

competes food resource. Males <str<strong>on</strong>g>of</str<strong>on</strong>g> P. polyod<strong>on</strong>, P. trewavasae, P. famula have<br />

feeding territory <str<strong>on</strong>g>th</str<strong>on</strong>g>at is 1 m apart from <str<strong>on</strong>g>th</str<strong>on</strong>g>ose <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>specific males. Their distances<br />

are caused by mating territory where c<strong>on</strong>specific males are driven out.<br />

To examine if <str<strong>on</strong>g>th</str<strong>on</strong>g>e mating territory promote <str<strong>on</strong>g>th</str<strong>on</strong>g>e species coexistence we c<strong>on</strong>struted<br />

total leng<str<strong>on</strong>g>th</str<strong>on</strong>g> dependent rank model. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, <str<strong>on</strong>g>th</str<strong>on</strong>g>e territory arranged in<br />

c<strong>on</strong>tinuous space and feeding territory radius is decided from its species and total<br />

leng<str<strong>on</strong>g>th</str<strong>on</strong>g>. If territory overlap, smaller individual shift its territory for <strong>on</strong>ce, so <str<strong>on</strong>g>th</str<strong>on</strong>g>at its<br />

territory does not overlap. Dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals <str<strong>on</strong>g>of</str<strong>on</strong>g> each species<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> species mating territory to <str<strong>on</strong>g>th</str<strong>on</strong>g>e radius <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e male <str<strong>on</strong>g>of</str<strong>on</strong>g> P. polyod<strong>on</strong>,<br />

P. trewavasae, P. famula are examined. Moreover, <strong>on</strong>e fictitious species is added,<br />

to examined whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er coexistence species number is limited. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e total leng<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

dependent rank model, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mating territory does not promote <str<strong>on</strong>g>th</str<strong>on</strong>g>e coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

species.<br />

We c<strong>on</strong>structed ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er model where <str<strong>on</strong>g>th</str<strong>on</strong>g>e time c<strong>on</strong>cept is introduced. It deals<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e dea<str<strong>on</strong>g>th</str<strong>on</strong>g>, and breeding. When two territories overlap, <str<strong>on</strong>g>th</str<strong>on</strong>g>e overlapped<br />

regi<strong>on</strong> is divided by <str<strong>on</strong>g>th</str<strong>on</strong>g>e line <str<strong>on</strong>g>of</str<strong>on</strong>g> equal influemce. We caluculate <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

difference between <str<strong>on</strong>g>th</str<strong>on</strong>g>e feeding territory radius and <str<strong>on</strong>g>th</str<strong>on</strong>g>e distance from <str<strong>on</strong>g>th</str<strong>on</strong>g>e center. For<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is model, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mating territory <str<strong>on</strong>g>of</str<strong>on</strong>g> intermediate radius promotes <str<strong>on</strong>g>th</str<strong>on</strong>g>e coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

species.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> Macromolecules and Molecular Aggregates;<br />

Saturday, July 2, 14:30<br />

Giuliana Indelicato<br />

York Centre for Complex Systems Analysis - The University <str<strong>on</strong>g>of</str<strong>on</strong>g> York<br />

- UK<br />

e-mail: giuliana.indelicato@york.ac.uk<br />

The dynamic behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> viral capsids under structural<br />

transiti<strong>on</strong>s important for infecti<strong>on</strong><br />

We present a general me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for <str<strong>on</strong>g>th</str<strong>on</strong>g>e investigati<strong>on</strong> and predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> likely transiti<strong>on</strong><br />

mechanisms for capsids <str<strong>on</strong>g>of</str<strong>on</strong>g> icosahedral viruses. C<strong>on</strong>cepts from <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-dimensi<strong>on</strong>al (3D) quasicrystals, and from <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> structural phase<br />

transformati<strong>on</strong>s in 3D crystalline solids, are combined to give a framework for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

study <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese structural transformati<strong>on</strong>s. Applicati<strong>on</strong>s to a number <str<strong>on</strong>g>of</str<strong>on</strong>g> viruses will<br />

be discussed.<br />

436

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Dynamics; Tuesday, June 28, 14:30<br />

Jaime Iranzo<br />

Centro de Astrobiología (INTA-CSIC), Madrid, Spain<br />

e-mail: iranzosj@cab.inta-csic.es<br />

Celia Perales<br />

Centro de Biología Molecular “Severo Ochoa” (CSIC-UAM), Madrid,<br />

Spain<br />

e-mail: cperales@cbm.uam.es<br />

Esteban Domingo<br />

Centro de Biología Molecular “Severo Ochoa” (CSIC-UAM), Madrid,<br />

Spain<br />

e-mail: edomingo@cbm.uam.es<br />

Susanna C. Manrubia<br />

Centro de Astrobiología (INTA-CSIC), Madrid, Spain<br />

e-mail: scmanrubia@cab.inta-csic.es<br />

Tempo and mode <str<strong>on</strong>g>of</str<strong>on</strong>g> inhibitor-mutagen <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies: a<br />

multidisciplinary approach<br />

The c<strong>on</strong>tinuous emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> drug-resistant viruses is a major obstacle for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

successful treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> viral infecti<strong>on</strong>s, and is steadily spurring <str<strong>on</strong>g>th</str<strong>on</strong>g>e design <str<strong>on</strong>g>of</str<strong>on</strong>g> new<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic strategies [1]. Corresp<strong>on</strong>dingly, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a pressing need to understand<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical effect <str<strong>on</strong>g>of</str<strong>on</strong>g> antiviral <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies <strong>on</strong> complex, diverse and fast mutating<br />

viral populati<strong>on</strong>s. Indeed, <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> viral populati<strong>on</strong>s is at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

basis <str<strong>on</strong>g>of</str<strong>on</strong>g> some recently suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic strategies, such as le<str<strong>on</strong>g>th</str<strong>on</strong>g>al mutagenesis<br />

and le<str<strong>on</strong>g>th</str<strong>on</strong>g>al defecti<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>at use mutagenic agents to induce viral extincti<strong>on</strong> [2,3].<br />

Despite bo<str<strong>on</strong>g>th</str<strong>on</strong>g> procedures have proved to be effective in vitro, <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> high doses<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> mutagen in vivo could involve severe side effects. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, low doses<br />

allow <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus to get adapted <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e rapid appearance <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance mutants.<br />

Hence, research <strong>on</strong> combinati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies arises as a step towards reducing doses<br />

while keeping low <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus becomes resistant to <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug<br />

cocktail.<br />

Here we discuss combinati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies involving two dissimilar drugs: <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutagen<br />

ribavirin, and an inhibitor <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral replicati<strong>on</strong>, guanidine. These drugs<br />

were used in vitro to analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>e performance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir sequential versus simultaneous<br />

administrati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong>s by foot-and-mou<str<strong>on</strong>g>th</str<strong>on</strong>g> disease virus [4].<br />

C<strong>on</strong>trary to <str<strong>on</strong>g>th</str<strong>on</strong>g>e well known case when two inhibitors are used, it was found <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

sequential administrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e inhibitor followed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutagen is more effective<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>an simultaneous treatment. In order to explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e reas<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>is behavior we<br />

designed a simple computati<strong>on</strong>al model representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

viral populati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e two drugs. It shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e two-edged role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutagen,<br />

reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e viable <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus but also favouring <str<strong>on</strong>g>th</str<strong>on</strong>g>e appearance<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> resistant mutants, causes an interacti<strong>on</strong> between inhibitor and mutagen <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficience <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy. In agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical predicti<strong>on</strong>s,<br />

laboratory experiments c<strong>on</strong>firm in particular cases <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e suitability <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

simultaneous or sequential administrati<strong>on</strong> depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e administered dose. The<br />

model predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamic resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral populati<strong>on</strong> for any dose combinati<strong>on</strong><br />

and, in particular, determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount <str<strong>on</strong>g>of</str<strong>on</strong>g> inhibitor and mutagen required<br />

437

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

to minimise <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>of</str<strong>on</strong>g> appearance <str<strong>on</strong>g>of</str<strong>on</strong>g> resistant mutants. Knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

relevant model parameters is obtainable by means <str<strong>on</strong>g>of</str<strong>on</strong>g> few, simple experiments, such<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at our predicti<strong>on</strong>s could be extended to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er viral systems.<br />

References.<br />

[1] E. Domingo, A. Grande-Pérez & V. Martín, Future prospects for <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> rapidly<br />

evolving viral pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens: insights from evoluti<strong>on</strong>ary biology Expert Opin. Biol. Ther. 8 1455–<br />

1460 (2008).<br />

[2] M. Eigen, Error catastrophe and antiviral strategy Proc. Natl. Acad. Sci. USA 99 13374–13376<br />

(2002).<br />

[3] A. Grande-Pérez, E. Lázaro, P. Lowenstein, E. Domingo & S. C. Manrubia, Suppresi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

viral infectivity <str<strong>on</strong>g>th</str<strong>on</strong>g>rough le<str<strong>on</strong>g>th</str<strong>on</strong>g>al defecti<strong>on</strong> Proc. Natl. Acad. Sci. USA 102 4448–4452 (2005).<br />

[4] C. Perales, R. Agudo, H. Tejero, S. C. Manrubia & E. Domingo, Potential benefits <str<strong>on</strong>g>of</str<strong>on</strong>g> sequential<br />

inhibitor-mutagen treatments <str<strong>on</strong>g>of</str<strong>on</strong>g> RNA virus infecti<strong>on</strong>s PLoS Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>. 5 e1000658 (2009).<br />

438

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Shingo Iwami<br />

Japan Science and Technology Agency<br />

e-mail: siwami@ms.u-tokyo.ac.jp<br />

Ca<str<strong>on</strong>g>th</str<strong>on</strong>g>erine Beauchemin<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, Ryers<strong>on</strong> University<br />

Tetsuko Tada<br />

Institute for Virus Research, Kyoto University<br />

Tatsuhiko Igarashi<br />

Institute for Virus Research, Kyoto University<br />

Tomoyuki Miura<br />

Institute for Virus Research, Kyoto University<br />

Immunology; Wednesday, June 29, 14:30<br />

Quantificati<strong>on</strong> system <str<strong>on</strong>g>of</str<strong>on</strong>g> viral dynamics in vitro - <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> SHIV <strong>on</strong> HSC-F -<br />

What we want to obtain and analyze are quantitative time-course experimental<br />

data but not qualitative snap-shot experimental data for <str<strong>on</strong>g>th</str<strong>on</strong>g>e purpose <str<strong>on</strong>g>of</str<strong>on</strong>g> getting<br />

dynamical informati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> viral infecti<strong>on</strong> such as half-life <str<strong>on</strong>g>of</str<strong>on</strong>g> infected cells, <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

viri<strong>on</strong>s, burst-size <str<strong>on</strong>g>of</str<strong>on</strong>g> virus, basic reproductive number <str<strong>on</strong>g>of</str<strong>on</strong>g> infected cell and so <strong>on</strong>.<br />

Today, I am going to show our recent studies about "Quantificati<strong>on</strong> system <str<strong>on</strong>g>of</str<strong>on</strong>g> viral<br />

dynamics in vitro", in which we can quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e above dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> SHIV <strong>on</strong> HSC-F<br />

cell line.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling I; Tuesday, June 28, 17:00<br />

Marta Iwanaszko<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Poland<br />

e-mail: marta.iwanaszko@polsl.pl<br />

The dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> NF-B dependent genes:<br />

Statistics and evoluti<strong>on</strong>ary c<strong>on</strong>servati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trol sequences<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e promoter and in <str<strong>on</strong>g>th</str<strong>on</strong>g>e 3 UTR<br />

Background: NF-B family plays a prominent role in innate (early) immune resp<strong>on</strong>se<br />

and has impact <strong>on</strong> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er processes such as cell cycle activati<strong>on</strong> or cell apoptosis.<br />

Up<strong>on</strong> stimulati<strong>on</strong> by pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens such as viral RNA a kinase cascade is activated,<br />

which eventually strips <str<strong>on</strong>g>th</str<strong>on</strong>g>e NF-B <str<strong>on</strong>g>of</str<strong>on</strong>g> its inhibitor IB molecule and allows it to<br />

translocate into <str<strong>on</strong>g>th</str<strong>on</strong>g>e nucleus. Once in <str<strong>on</strong>g>th</str<strong>on</strong>g>e nucleus, it activates transcripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

approximately 90 genes, some <str<strong>on</strong>g>of</str<strong>on</strong>g> which trigger fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er stages <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune resp<strong>on</strong>se.<br />

NF-B-dependent genes can be categorized, based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e timing <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

activati<strong>on</strong> counted from NF-B translocati<strong>on</strong> into <str<strong>on</strong>g>th</str<strong>on</strong>g>e nucleus, as Early, Middle and<br />

Late genes. It is not obvious what mechanism is resp<strong>on</strong>sible for segregati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

genes timing <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong>al resp<strong>on</strong>se. Results: It is likely <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e differences<br />

in timing are reflected in differences in <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure <str<strong>on</strong>g>of</str<strong>on</strong>g> promoter regi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> genes<br />

in different categories. Specifically, <str<strong>on</strong>g>th</str<strong>on</strong>g>is might c<strong>on</strong>cern differences in number and<br />

type <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong> factor binding motifs, required for NF-B itself as well as for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e putative c<str<strong>on</strong>g>of</str<strong>on</strong>g>actors. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach we analyzed if genes assignment to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Early, Middle or Late group based <strong>on</strong> expressi<strong>on</strong> pattern, is c<strong>on</strong>nected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> special<br />

features in promoter structure. This c<strong>on</strong>necti<strong>on</strong> may be <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms<br />

underlying <str<strong>on</strong>g>th</str<strong>on</strong>g>e different patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong> c<strong>on</strong>trol. This issue is best c<strong>on</strong>sidered<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary framework, first, since functi<strong>on</strong>al binding sites are likely<br />

to be c<strong>on</strong>served in evoluti<strong>on</strong> and sec<strong>on</strong>d, since <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary change<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> promoter regi<strong>on</strong>s are not very well-known and are <str<strong>on</strong>g>of</str<strong>on</strong>g> serious interest. Ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

c<strong>on</strong>trol sequences are AU - rich elements (ARE) located in 3UTR. AREs target<br />

mRNA for rapid degradati<strong>on</strong> and inflict mRNA instability. Latest studies show<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at genes transcribed wi<str<strong>on</strong>g>th</str<strong>on</strong>g> unstable mRNA have different transcripti<strong>on</strong> dynamic.<br />

We have found <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are significant differences between <str<strong>on</strong>g>th</str<strong>on</strong>g>e Early and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Late<br />

genes promoter and 3UTR regi<strong>on</strong>s and many similarities are observed am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Early genes even between distant species, while <str<strong>on</strong>g>th</str<strong>on</strong>g>e Late genes promoter regi<strong>on</strong>s are<br />

much more diversified. C<strong>on</strong>clusi<strong>on</strong>s: Wider phylogenetic analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> NF-B dependent<br />

genes provides insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e degree <str<strong>on</strong>g>of</str<strong>on</strong>g> cross species similarity found in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Early genes, opposed to many differences in promoter structure <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be found<br />

am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e Late genes. This suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at activati<strong>on</strong> and expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Late<br />

genes is much more species specific <str<strong>on</strong>g>th</str<strong>on</strong>g>an in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Early genes. Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e promoter<br />

structure and ARE c<strong>on</strong>tent Middle genes can be divided into two subgroups: Early<br />

like and Late like.<br />

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Bioinformatics and System Biology; Wednesday, June 29, 11:00<br />

Sara Jabbari<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, UK<br />

e-mail: sara.jabbari@nottingham.ac.uk<br />

Systems biology <str<strong>on</strong>g>of</str<strong>on</strong>g> Clostridium acetobutylicum<br />

A renewed interest in <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> bi<str<strong>on</strong>g>of</str<strong>on</strong>g>uels has emerged in recent years,<br />

principally due to dwindling crude oil reserves and c<strong>on</strong>cerns over <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>mental<br />

impact <str<strong>on</strong>g>of</str<strong>on</strong>g> fossil fuels. Bacterial fermentati<strong>on</strong> is a possible soluti<strong>on</strong> to questi<strong>on</strong>s over<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e source <str<strong>on</strong>g>of</str<strong>on</strong>g> future bi<str<strong>on</strong>g>of</str<strong>on</strong>g>uels.<br />

Clostridium acetobutylicum is an anaerobic, n<strong>on</strong>-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenic, Gram-positive<br />

bacterium capable <str<strong>on</strong>g>of</str<strong>on</strong>g> producing <str<strong>on</strong>g>th</str<strong>on</strong>g>e solvents acet<strong>on</strong>e, butanol and e<str<strong>on</strong>g>th</str<strong>on</strong>g>anol. Though<br />

each <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese can be used as a bi<str<strong>on</strong>g>of</str<strong>on</strong>g>uel, <str<strong>on</strong>g>th</str<strong>on</strong>g>e properties <str<strong>on</strong>g>of</str<strong>on</strong>g> butanol make it <str<strong>on</strong>g>th</str<strong>on</strong>g>e most<br />

promising energy source <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ree. For butanol producti<strong>on</strong> by C. acetobutylicum<br />

to be exploited <strong>on</strong> an industrial scale, however, genetically-engineered strains must<br />

be designed which can produce butanol at much higher levels <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>ose achieved<br />

by wild-type strains.<br />

The SysMO and SysMO2 programmes COSMIC (Clostridium acetobutylicum<br />

Systems Microbiology) were established to apply a systems approach to understanding<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e complex mechanisms behind solvent producti<strong>on</strong> by C. acetobutylicum and to<br />

establish <str<strong>on</strong>g>th</str<strong>on</strong>g>is bacterium as <str<strong>on</strong>g>th</str<strong>on</strong>g>e paradigm for clostridial systems biology. An iterative<br />

approach is adopted whereby experimental work is designed to complement ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

models <str<strong>on</strong>g>of</str<strong>on</strong>g> solventogenesis which in turn generate experimentally-testable<br />

hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses. Notably, <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene regulati<strong>on</strong> networks governing solvent producti<strong>on</strong><br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>nected process <str<strong>on</strong>g>of</str<strong>on</strong>g> sporulati<strong>on</strong> are modelled and parametrised according<br />

to experimental data. Systematic in silico alterati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong> for each<br />

comp<strong>on</strong>ent <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e networks enables identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ose genes most crucial for<br />

butanol producti<strong>on</strong> and will elucidate <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal genetic engineering strategies for<br />

maximising butanol yield.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Jędrzej Jabłoński<br />

Uniwersytet Warszawski; Wydział Matematyki, Informatyki i Mechaniki<br />

e-mail: jjabłoński@mimuw.edu.pl<br />

Size-structured populati<strong>on</strong> model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> disc<strong>on</strong>tinuous grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

rate<br />

Modelling size-structured populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> copepods demands allowing grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate to<br />

be disc<strong>on</strong>tinuous. This is <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e moulting process, which ocures<br />

rapidly after a l<strong>on</strong>g period <str<strong>on</strong>g>of</str<strong>on</strong>g> stagnati<strong>on</strong>. Introducing size structure simplifies modelling<br />

predator-dependent mortality. This leads to McKendrick equati<strong>on</strong> system<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> n<strong>on</strong>local bir<str<strong>on</strong>g>th</str<strong>on</strong>g> rate and mortality and disc<strong>on</strong>tinuous grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate. It can be<br />

shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere exists a soluti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem and c<strong>on</strong>tinuity <str<strong>on</strong>g>of</str<strong>on</strong>g> it (in weak*<br />

topology wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to time) can be proven. Moreover a stable numerical scheme<br />

which is weakly c<strong>on</strong>vergent is presented.<br />

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Systems Biology <str<strong>on</strong>g>of</str<strong>on</strong>g> Development; Saturday, July 2, 14:30<br />

Johannes Jaeger<br />

EMBL/CRG Research Unit in Systems Biology, Centre de Regulació<br />

Genòmica (CRG), Barcel<strong>on</strong>a, Spain<br />

e-mail: yogi.jaeger@crg.es<br />

Reverse-Engineering <str<strong>on</strong>g>th</str<strong>on</strong>g>e Evoluti<strong>on</strong>ary and Developmental<br />

Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Gap Gene Network<br />

Evoluti<strong>on</strong>ary developmental biology tries to close <str<strong>on</strong>g>th</str<strong>on</strong>g>e gap between molecular evoluti<strong>on</strong><br />

and phenotypic change. This requires a quantitative systems-level understanding<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene networks underlying development across multiple levels from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular to <str<strong>on</strong>g>th</str<strong>on</strong>g>e organismic. Obtaining such an understanding is challenging<br />

due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e large number <str<strong>on</strong>g>of</str<strong>on</strong>g> factors involved. We depend <strong>on</strong> computati<strong>on</strong>al models<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>is task. I present a reverse-engineering approach, where gene regulatory<br />

interacti<strong>on</strong>s are inferred from quantitative expressi<strong>on</strong> data, using data-driven ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

models (called gene circuits). Gene circuit models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e gap gene network<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Drosophila reproduce observed gene expressi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high precisi<strong>on</strong> and temporal<br />

resoluti<strong>on</strong> and reveal a dynamic mechanism for <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> positi<strong>on</strong>al informati<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough shifts <str<strong>on</strong>g>of</str<strong>on</strong>g> gap gene expressi<strong>on</strong> domains. We are extending <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach to<br />

a comparative study <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e gap gene network between different species <str<strong>on</strong>g>of</str<strong>on</strong>g> dipterans<br />

(flies, midges and mosquitoes). I present preliminary results <strong>on</strong> data quantificati<strong>on</strong><br />

and modeling for gap genes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e scuttle fly Megaselia abdita, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e mo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

midge Clogmia albipunctata. Our approach yields predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> how changes <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

gene regulatory feedback affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e timing and positi<strong>on</strong>ing <str<strong>on</strong>g>of</str<strong>on</strong>g> expressi<strong>on</strong> domains.<br />

These predicti<strong>on</strong>s will be tested experimentally using RNA interference in all <str<strong>on</strong>g>th</str<strong>on</strong>g>ree<br />

species. No such quantitative systems-level analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> an evolving gene regulatory<br />

network has been achieved to date.<br />

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Cellular Systems Biology; Saturday, July 2, 11:00<br />

Mehrdad Jafari-Mamaghani<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosciences & Nutriti<strong>on</strong>, Karolinska Institutet<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Stockholm University<br />

e-mail: mjm@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.su.se<br />

Staffan Strömblad<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosciences & Nutriti<strong>on</strong>, Karolinska Institutet<br />

e-mail: Staffan.Stromblad@ki.se<br />

John Lock<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosciences & Nutriti<strong>on</strong>, Karolinska Institutet<br />

e-mail: John.Lock@ki.se<br />

Joanna Tyrcha<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Stockholm University<br />

e-mail: joanna@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.su.se<br />

Olivia Erikss<strong>on</strong><br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Stockholm University<br />

e-mail: olivia@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.su.se<br />

Employing Statistics in Systems Microscopy<br />

As <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> metastasis is fundamental in <str<strong>on</strong>g>th</str<strong>on</strong>g>e progressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> breast cancer, it is<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> paramount significance to study cell adhesi<strong>on</strong> and cell migrati<strong>on</strong>, mechanisms<br />

tightly related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e machinery <str<strong>on</strong>g>of</str<strong>on</strong>g> metastasis, in closer details. Yet, cell adhesi<strong>on</strong><br />

and cell migrati<strong>on</strong> result from a series <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamic procedures in space <strong>on</strong> a subcellular<br />

level, namely <str<strong>on</strong>g>th</str<strong>on</strong>g>e organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell-matrix adhesi<strong>on</strong> complexes (CMACs)<br />

[1].<br />

Using techniques <str<strong>on</strong>g>of</str<strong>on</strong>g> high-<str<strong>on</strong>g>th</str<strong>on</strong>g>roughput microscopy and post-acquisiti<strong>on</strong> image quantificati<strong>on</strong>,<br />

large sets <str<strong>on</strong>g>of</str<strong>on</strong>g> data representing cell and CMAC properties are made available<br />

for statistical analysis. Such analysis is an essential comp<strong>on</strong>ent <str<strong>on</strong>g>of</str<strong>on</strong>g> what is<br />

now termed as Systems Microscopy: systems biology analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> living cells using<br />

a coaliti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> automated microscopy, image quantificati<strong>on</strong>, data mining and statistical<br />

analysis [2].<br />

The nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e statistical analysis in Systems Microscopy includes unsupervised<br />

as well as supervised statistical learning. The unsupervised learning approaches are<br />

employed for purposes such as visualizati<strong>on</strong> using dimensi<strong>on</strong> reducti<strong>on</strong>, and detecti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> sub-populti<strong>on</strong>s using mixture models. The focus <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e supervised learning<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>odologies is <strong>on</strong> between-populati<strong>on</strong> tests, spatial point pattern analysis, and<br />

predictive modeling using various techniques <str<strong>on</strong>g>of</str<strong>on</strong>g> classificati<strong>on</strong>. Naturally, given <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e self-organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> living cells is a spatio-temporal process, all <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e aforementi<strong>on</strong>ed<br />

statistical procedures are intended to interrogate static as well as dynamic<br />

(time-series) data.<br />

Thus, by employing <str<strong>on</strong>g>th</str<strong>on</strong>g>e necessary data and various statistical me<str<strong>on</strong>g>th</str<strong>on</strong>g>odologies, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

processes <str<strong>on</strong>g>of</str<strong>on</strong>g> cell adhesi<strong>on</strong> and cell migrati<strong>on</strong> may receive fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er eluciati<strong>on</strong> and<br />

potentially advance our understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying causes as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e progressi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> metastasis.<br />

The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk is to give a brief descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e employed me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e statistical analysis.<br />

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References.<br />

[1] John G. Lock, Bernhard Wehrle-Haller and Staffan Strömblad, Cell–matrix adhesi<strong>on</strong> complexes:<br />

Master c<strong>on</strong>trol machinery <str<strong>on</strong>g>of</str<strong>on</strong>g> cell migrati<strong>on</strong> Seminars in Cancer Biology, Volume 18,<br />

Issue 1, February 2008, Pages 65-76.<br />

[2] John G. Lock and Staffan Strömblad, Systems microscopy: An emerging strategy for <str<strong>on</strong>g>th</str<strong>on</strong>g>e life<br />

sciences Experimental Cell Research, Volume 316, Issue 8, 1 May 2010, Pages 1438-1444.<br />

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Peter Jagers<br />

Chalmers and U. <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg<br />

e-mail: jagers@chalmers.se<br />

Populati<strong>on</strong> Dynamics; Tuesday, June 28, 17:00<br />

Finite Populati<strong>on</strong>s Regulated by a Carrying Capacity<br />

A populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> independently reproducing individuals in a stable envir<strong>on</strong>ment will<br />

die out, if reproducti<strong>on</strong> is critical or subcritical. If it is supercritical, <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong><br />

may escape extincti<strong>on</strong>. But <str<strong>on</strong>g>th</str<strong>on</strong>g>en it must grow exp<strong>on</strong>entially bey<strong>on</strong>d all limits,<br />

which is <str<strong>on</strong>g>of</str<strong>on</strong>g> course a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical artifact, unrealisabkle in a finite world. But<br />

what happens in reality, where <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a bound to grow<str<strong>on</strong>g>th</str<strong>on</strong>g>? A carrying capacity<br />

such <str<strong>on</strong>g>th</str<strong>on</strong>g>at individuals reproduce in a supercritical manner while populati<strong>on</strong> size<br />

is below it, reproducti<strong>on</strong> however turning subcritical as so<strong>on</strong> as <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> is<br />

larger <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e habitat carrying capacity?<br />

These questi<strong>on</strong>s are answered in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> general branching processes, i.e. populati<strong>on</strong>s<br />

where individuals have arbitrarily distributed life-spans and may give bir<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

according to an arbitrary pattern, and individual reproductive behaviour is influenced<br />

by populati<strong>on</strong> size in <str<strong>on</strong>g>th</str<strong>on</strong>g>e manner described.<br />

References.<br />

[1] Jagers, P. and Harding, K., Viability <str<strong>on</strong>g>of</str<strong>on</strong>g> small populati<strong>on</strong>s experiencing recurring catastrophes.<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Pop. Studies 16 177–188 (2009).<br />

[2] Klebaner, F. C., Sagitov, S., Vatutin, V., Haccou, P., and Jagers, P., Stochasticity in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

adaptive dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>: <str<strong>on</strong>g>th</str<strong>on</strong>g>e bare b<strong>on</strong>es. J. Biol. Dyn. 5 147–162 (2011).<br />

[3] Jagers, P. and Klebaner, F. Populati<strong>on</strong> size dependent, age structured branching processes<br />

linger around <str<strong>on</strong>g>th</str<strong>on</strong>g>eir carrying capacity. J. Appl. Prob. 48A, to appear (2011).<br />

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Populati<strong>on</strong> Dynamics; Wednesday, June 29, 14:30<br />

Nick Jagiella<br />

INRIA Rocquencourt, Paris, France<br />

e-mail: nick.jagiella@inria.fr<br />

Benedikt Müller 1 , Irene Vign<strong>on</strong>-Clementel 2 , Margareta Müller 1 , Dirk<br />

Drasdo 2<br />

1 DKFZ, Heidelberg, Germany, 2 INRIA Rocquencourt, Paris, France<br />

From Data Analysis to Model Parameterizati<strong>on</strong> &<br />

Predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Tumor Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and Therapy<br />

In order to establish a predictive model for in-vivo tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy a<br />

multi-scale model has to be set-up and calibrated individually in a stepwise process<br />

to a targeted cell type. As a pro<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> principle we will present <str<strong>on</strong>g>th</str<strong>on</strong>g>e process chain<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> model c<strong>on</strong>structi<strong>on</strong> and parameterizati<strong>on</strong> from different data sources for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

EMT6/Ro and <str<strong>on</strong>g>th</str<strong>on</strong>g>e SK-MES-1 cell line.<br />

In a first step <str<strong>on</strong>g>th</str<strong>on</strong>g>e model has been built up and validated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> EMT6/Ro mouse<br />

mammary carcinoma multi-cellular cell spheroid data from literature. For <str<strong>on</strong>g>th</str<strong>on</strong>g>is cell<br />

line it predicted <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> kinetics to be c<strong>on</strong>trolled by spatial restrains over a wide<br />

range <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen and glucose medium c<strong>on</strong>centrati<strong>on</strong>s. Only if bo<str<strong>on</strong>g>th</str<strong>on</strong>g>, oxygen and<br />

glucose are very limiting saturati<strong>on</strong> was observed which <str<strong>on</strong>g>th</str<strong>on</strong>g>e model could explain<br />

by cells switching from aerobic to anaerobic glycolysis.<br />

In a sec<strong>on</strong>de step <str<strong>on</strong>g>th</str<strong>on</strong>g>e model was adapted to <str<strong>on</strong>g>th</str<strong>on</strong>g>e SK-MES-1 cell line. The<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> kinetics was calibrated quantitatively in comparis<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> curves<br />

and qualitatively by image analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> spheroid cryosecti<strong>on</strong>s stained for apoptosis<br />

and proliferati<strong>on</strong>.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Harsh Jain<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences Institute, Ohio State University<br />

e-mail: hjain@mbi.osu.edu<br />

Helen Byrne<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham<br />

Nicanor Moldovan<br />

Biomedical Engineering, Ohio State University<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Validati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a Novel Implantable Oxygen<br />

Sensor<br />

N<strong>on</strong>-vascularized tissue engineering c<strong>on</strong>structs and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er solid implants wi<str<strong>on</strong>g>th</str<strong>on</strong>g> biomedical<br />

applicati<strong>on</strong>s, such as encapsulated live cells or glucose sensors, need oxygen (O2)<br />

for proper functi<strong>on</strong>ing. To better understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e availability <str<strong>on</strong>g>of</str<strong>on</strong>g> O2 to implants, a<br />

novel sensor has been developed by researchers at <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ohio State University, <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

can n<strong>on</strong>-invasively record, after implantati<strong>on</strong> in mice, <str<strong>on</strong>g>th</str<strong>on</strong>g>e signal provided by local<br />

pO2. This has subsequently been used to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> neovascularizati<strong>on</strong><br />

and foreign body reacti<strong>on</strong> in resp<strong>on</strong>se to an implanted device. Briefly, b<strong>on</strong>e marrow<br />

progenitor cells embedded in a Matrigel plug were implanted next to <str<strong>on</strong>g>th</str<strong>on</strong>g>e sensor, or<br />

gel al<strong>on</strong>e used as c<strong>on</strong>trol, and weekly O2 readings noted. In order to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

readings, we have developed a partial differential equati<strong>on</strong> model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental<br />

system. The model anticipates <str<strong>on</strong>g>th</str<strong>on</strong>g>at pO2 in implant follows a parabolic pattern,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e descending side <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e curve being indicative <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>se to normalizati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic demands <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue which requires a lower pO2. The model is sensitive<br />

to angiogenic stimulati<strong>on</strong>, predicting a rapid raise in pO2 and a slower reducti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e signal. These results can <str<strong>on</strong>g>th</str<strong>on</strong>g>us be used to predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e various stages <str<strong>on</strong>g>of</str<strong>on</strong>g> foreign<br />

body reacti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at occurs in resp<strong>on</strong>se to <str<strong>on</strong>g>th</str<strong>on</strong>g>e implants, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect stem-cell<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy has <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is. A 2D illustrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is is also simulated.<br />

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Bridging <str<strong>on</strong>g>th</str<strong>on</strong>g>e Divide: Cancer Models in Clinical Practice; Thursday, June 30,<br />

11:30<br />

Harsh Jain<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences Institute, Ohio State University<br />

e-mail: hjain@mbi.osu.edu<br />

Avner Friedman<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences Institute, Ohio State University<br />

Steven Clint<strong>on</strong><br />

Comprehensive Cancer Center, Ohio State University<br />

Arvinder Bhinder<br />

Comprehensive Cancer Center, Ohio State University<br />

The Impact <str<strong>on</strong>g>of</str<strong>on</strong>g> Androgen Ablati<strong>on</strong> <strong>on</strong> Mutati<strong>on</strong> Acquisiti<strong>on</strong><br />

in Prostate Cancer<br />

Prostate cancer (CaP) is <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d most comm<strong>on</strong> cancer in American men. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e majority <str<strong>on</strong>g>of</str<strong>on</strong>g> patients diagnosed wi<str<strong>on</strong>g>th</str<strong>on</strong>g> CaP are cured wi<str<strong>on</strong>g>th</str<strong>on</strong>g> primary treatment,<br />

it remains <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d lead cause behind <strong>on</strong>ly lung cancer, <str<strong>on</strong>g>of</str<strong>on</strong>g> male cancerrelated<br />

dea<str<strong>on</strong>g>th</str<strong>on</strong>g>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e western world. A few features set it apart from o<str<strong>on</strong>g>th</str<strong>on</strong>g>er cancers;<br />

it develops slowly over a period <str<strong>on</strong>g>of</str<strong>on</strong>g> years; CaP cells are dependent <strong>on</strong> male sex horm<strong>on</strong>es<br />

for grow<str<strong>on</strong>g>th</str<strong>on</strong>g>; treatment in <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tinuous androgen ablati<strong>on</strong> fails due<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> castrate-resistant CaP cells. Therefore, it has been proposed<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at intermittent androgen ablati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy might be a better strategy for treating<br />

CaP. I present a model <str<strong>on</strong>g>of</str<strong>on</strong>g> prostate grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in humans, which can simulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>set<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> CaP, as well as explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance in resp<strong>on</strong>se to <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy. Our<br />

model shall incorporate a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> cell types such as heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y and CaP cells, as<br />

well as detailed biochemical pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways crucial to <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cells. Fits to<br />

individual patient data will also be presented. By being able to distinguish between<br />

various drug acti<strong>on</strong>s, and being fitted to individual patient data, we hope to develop<br />

a truly prescriptive tool to aid physicians in treatment choices for CaP patients.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Roman Jaksik<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: roman.jaksik@polsl.pl<br />

Michał Marczyk<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Automatic C<strong>on</strong>trol, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Joanna Polańska<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Automatic C<strong>on</strong>trol, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

MicroImage as a tool for microarray image artifacts<br />

correcti<strong>on</strong><br />

Olig<strong>on</strong>ucleotide single color microarrays are <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most popular platforms<br />

used to characterize transcripti<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile changes induced by various chemical or<br />

physical factors. This me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is based <strong>on</strong> hundreds <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ousands unique 25-mer<br />

olig<strong>on</strong>ucleotide probes grouped into gene specific sets. Single probes attach labeled<br />

transcripts <str<strong>on</strong>g>of</str<strong>on</strong>g> specific genes which quantity is proporti<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluorescence intensity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e probe, accessed wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a laser scanner. Microarray surface images obtained<br />

in such experiment <str<strong>on</strong>g>of</str<strong>on</strong>g>ten c<strong>on</strong>tain artifacts <str<strong>on</strong>g>of</str<strong>on</strong>g> various shape and size caused by ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

defects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e manufacturing process or impurities wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in target genomic material.<br />

Data processing me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g>ten fail to exclude outlying signal values resulting from<br />

such defects which leads to artificially increased variati<strong>on</strong> between replicate experiments,<br />

decreasing statistical significance <str<strong>on</strong>g>of</str<strong>on</strong>g> inter sample studies, or to reduced<br />

accuracy <str<strong>on</strong>g>of</str<strong>on</strong>g> sample classificati<strong>on</strong> if <str<strong>on</strong>g>th</str<strong>on</strong>g>e experiment aims to search for factor induced<br />

genetic resp<strong>on</strong>se signature.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we present different kinds <str<strong>on</strong>g>of</str<strong>on</strong>g> artifacts and propose a novel detecti<strong>on</strong><br />

and correcti<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od based <strong>on</strong> signal intensities <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er, unaffected replicate<br />

probes. The me<str<strong>on</strong>g>th</str<strong>on</strong>g>od was implemented as a standal<strong>on</strong>e windows applicati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

a very easy to use graphical interface allowing to process hundreds <str<strong>on</strong>g>of</str<strong>on</strong>g> microarray<br />

images wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in few minutes and visualize <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <strong>on</strong> various complexity steps.<br />

The usefulness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is me<str<strong>on</strong>g>th</str<strong>on</strong>g>od was evaluated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> breast cancer microarray<br />

dataset, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> marked patients radiosensitivity and technical replicate data<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> simulated artificial noise objects.<br />

Using comm<strong>on</strong> statistical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods inter-group correlati<strong>on</strong>, inter-gene variance<br />

and discriminative gene analysis were performed. The overall impact <str<strong>on</strong>g>of</str<strong>on</strong>g> artifacts<br />

processing <strong>on</strong> sample classificati<strong>on</strong> accuracy was also evaluated. The results show<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at image artifacts correcti<strong>on</strong> increases dataset integrity, proving <str<strong>on</strong>g>th</str<strong>on</strong>g>at it is possible<br />

to separate image defects from inter sample variati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> biological origin and<br />

specific features <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microarray chip achieving higher quality <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e analyzed<br />

data.<br />

ACKNOWLEDGMENT:<br />

The au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors would like to <str<strong>on</strong>g>th</str<strong>on</strong>g>ank <str<strong>on</strong>g>th</str<strong>on</strong>g>e teams <str<strong>on</strong>g>of</str<strong>on</strong>g> Peter O’Neill from <str<strong>on</strong>g>th</str<strong>on</strong>g>e Medical<br />

Research Council Radiati<strong>on</strong> & Genome Stability Unit in Harwell, Michael B<strong>on</strong>in<br />

from University <str<strong>on</strong>g>of</str<strong>on</strong>g> Tuebingen, Micheline Giphart-Gassler from Leiden University<br />

Medical Center and John Yarnold from The Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Cancer Research in Sutt<strong>on</strong><br />

for useful comments and for providing <str<strong>on</strong>g>th</str<strong>on</strong>g>e microarray data.<br />

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This work was supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>European</str<strong>on</strong>g> Program FP6 - 036452, GENEPIlowRT<br />

and Ministry <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Higher Educati<strong>on</strong> grant no N N519 647840.<br />

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Applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>negative Rad<strong>on</strong> measure spaces wi<str<strong>on</strong>g>th</str<strong>on</strong>g> metric structure<br />

to populati<strong>on</strong> dynamic models; Wednesday, June 29, 17:00<br />

Grzegorz Jamróz<br />

Uniwersytet Warszawski<br />

e-mail: jamroz@mimuw.edu.pl<br />

Measure-transmissi<strong>on</strong> c<strong>on</strong>diti<strong>on</strong>s - a powerful tool in<br />

modeling bimodal dynamics<br />

Differentiati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells may be subject to two paradigms. Ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er a cell is in a<br />

state <str<strong>on</strong>g>of</str<strong>on</strong>g> inevitable alterati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> its characteristics or <str<strong>on</strong>g>th</str<strong>on</strong>g>e state is quasi-stati<strong>on</strong>ary,<br />

meaning <str<strong>on</strong>g>th</str<strong>on</strong>g>at for a certain period <str<strong>on</strong>g>of</str<strong>on</strong>g> time <str<strong>on</strong>g>th</str<strong>on</strong>g>e biochemical characteristics remain <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

same. A cell in <str<strong>on</strong>g>th</str<strong>on</strong>g>e former, transient state usually originated in and heads towards<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e latter, reaching it in a finite time. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, a cell in a quasi-stati<strong>on</strong>ary<br />

state may stay <str<strong>on</strong>g>th</str<strong>on</strong>g>ere arbitrarily l<strong>on</strong>g and is typically capable <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> self-renewal<br />

(by divisi<strong>on</strong>) and differentiati<strong>on</strong> (wi<str<strong>on</strong>g>th</str<strong>on</strong>g> or wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out divisi<strong>on</strong>). Incidentally, all <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

scenarios may coincide in a single system, as e.g. in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> neurogenesis, and<br />

lead to interesting bimodal dynamics. These two types <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamics can be modeled<br />

by transport equati<strong>on</strong>s or (a system <str<strong>on</strong>g>of</str<strong>on</strong>g>) ordinary differential equati<strong>on</strong>s, respectively.<br />

N<strong>on</strong>e<str<strong>on</strong>g>th</str<strong>on</strong>g>eless, <str<strong>on</strong>g>th</str<strong>on</strong>g>e two approaches can be unified in a purely c<strong>on</strong>tinuous setting <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

measure-valued soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transport equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> additi<strong>on</strong>al transmissi<strong>on</strong><br />

c<strong>on</strong>diti<strong>on</strong>s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e simplest case, <str<strong>on</strong>g>th</str<strong>on</strong>g>is leads to <str<strong>on</strong>g>th</str<strong>on</strong>g>e following problem ([1]):<br />

∂tµ(t) + ∂x(g(v(t)1x=xi (x)µ(t)) = p(v(t), x)µ(t),<br />

g(v(t)) dµ(t)<br />

<br />

(x+<br />

dL1 i ) = ci(v(t)) dµ(t), i = 0, . . . , N,<br />

µ(0) = µ0,<br />

<br />

v(t) =<br />

{xN }<br />

{xi}<br />

dµ(t).<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e talk, we present <str<strong>on</strong>g>th</str<strong>on</strong>g>is new setting and discuss how it allows to capture in<br />

an elegant way a weal<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> effects, promising interesting applicati<strong>on</strong>s well bey<strong>on</strong>d<br />

its original motivati<strong>on</strong>.<br />

References.<br />

[1] Piotr Gwiazda, Grzegorz Jamróz, Anna Marciniak-Czochra, Models <str<strong>on</strong>g>of</str<strong>on</strong>g> discrete and c<strong>on</strong>tinuous<br />

cell differentiati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e framework <str<strong>on</strong>g>of</str<strong>on</strong>g> transport equati<strong>on</strong>. Submitted.<br />

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Populati<strong>on</strong> Dynamics; Saturday, July 2, 14:30<br />

Joanna Jaroszewska<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics, and Mechanics; University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Warsaw<br />

e-mail: jar@mimuw.edu.pl<br />

Chaotic properties <str<strong>on</strong>g>of</str<strong>on</strong>g> some partial differential equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

a random delay describing cellular replicati<strong>on</strong><br />

We study some model <str<strong>on</strong>g>of</str<strong>on</strong>g> a cell populati<strong>on</strong>, which is based <strong>on</strong> a model proposed<br />

by Mackey and Rudnicki in [1]. Our model is described by a partial differential<br />

equati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a transport-type wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a random delay. We c<strong>on</strong>sider a random dynamical<br />

system generated by <str<strong>on</strong>g>th</str<strong>on</strong>g>is equati<strong>on</strong> and describe its chaotic behaviour.<br />

References.<br />

[1] M. C. Mackey and R. Rudnicki, Global stability in a delayed partial differential equati<strong>on</strong><br />

describing cellular replicati<strong>on</strong>, J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol., 33, 89–109.<br />

453

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling II; Wednesday, June 29,<br />

14:30<br />

Joanna Jaruszewicz<br />

IPPT PAN<br />

e-mail: jjarusz@ippt.gov.pl<br />

Pawel Zuk<br />

IPPT PAN<br />

Tomasz Lipniacki<br />

IPPT PAN<br />

Type <str<strong>on</strong>g>of</str<strong>on</strong>g> noise defines <str<strong>on</strong>g>th</str<strong>on</strong>g>e most stable attractor in bistable<br />

gene expressi<strong>on</strong> model<br />

We c<strong>on</strong>sider simplified stochastic model <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>linear positive<br />

feedback. It is assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene may be in <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two states: active<br />

or inactive. Protein molecules are produced directly from <str<strong>on</strong>g>th</str<strong>on</strong>g>e active gene. We focus<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e case in which in <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic approximati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system has two stable<br />

steady state soluti<strong>on</strong>s. Two types <str<strong>on</strong>g>of</str<strong>on</strong>g> noise are c<strong>on</strong>sidered; transcripti<strong>on</strong>al (characteristic<br />

for bacteria) - due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e limited number <str<strong>on</strong>g>of</str<strong>on</strong>g> protein molecules, and gene<br />

switching noise (important in Eukaryotes) - due to gene activati<strong>on</strong> and inactivati<strong>on</strong><br />

transiti<strong>on</strong>s. We explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>dence between <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic system and its<br />

deterministic approximati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e limit <str<strong>on</strong>g>of</str<strong>on</strong>g> low noise. Analytical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> two<br />

approximati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic system, each wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <strong>on</strong>ly <strong>on</strong>e type <str<strong>on</strong>g>of</str<strong>on</strong>g> noise included,<br />

showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at when noise decreases to zero (I) <str<strong>on</strong>g>th</str<strong>on</strong>g>e stati<strong>on</strong>ary probability density<br />

(SPD) c<strong>on</strong>verges to Dirac delta in <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> two stable steady states, (II) in a broad<br />

range <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters <str<strong>on</strong>g>th</str<strong>on</strong>g>e SPD <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system wi<str<strong>on</strong>g>th</str<strong>on</strong>g> transcripti<strong>on</strong>al noise c<strong>on</strong>verges to<br />

Dirac delta in a different steady state <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e SPD <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system wi<str<strong>on</strong>g>th</str<strong>on</strong>g> gene switching<br />

noise. This suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transcripti<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene-switching<br />

noise dictates in which state <str<strong>on</strong>g>th</str<strong>on</strong>g>e SPD c<strong>on</strong>centrates. We verified <str<strong>on</strong>g>th</str<strong>on</strong>g>is hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis by<br />

M<strong>on</strong>te Carlo simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact model. This finding has <str<strong>on</strong>g>th</str<strong>on</strong>g>e following <str<strong>on</strong>g>th</str<strong>on</strong>g>ermodynamic<br />

interpretati<strong>on</strong>. The n<strong>on</strong> interacting molecules diffusing in <str<strong>on</strong>g>th</str<strong>on</strong>g>e uniform<br />

temperature field settle in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lowest potential well as temperature tends to zero.<br />

However when <str<strong>on</strong>g>th</str<strong>on</strong>g>e temperature field is not uniform temperature pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile dictates in<br />

which well molecules c<strong>on</strong>centrate. Apparently, <str<strong>on</strong>g>th</str<strong>on</strong>g>e two types <str<strong>on</strong>g>of</str<strong>on</strong>g> noise specific for<br />

gene expressi<strong>on</strong> are c<strong>on</strong>nected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two different temperature fields and <str<strong>on</strong>g>th</str<strong>on</strong>g>us favors<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e different attractors.<br />

Our study dem<strong>on</strong>strates <str<strong>on</strong>g>th</str<strong>on</strong>g>at in systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying bistability, like genetic<br />

switches, <str<strong>on</strong>g>th</str<strong>on</strong>g>e noise characteristic c<strong>on</strong>trols in which <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epigenetic attractors<br />

cell populati<strong>on</strong> will settle.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Fractals and Complexity I; Wednesday, June 29, 14:30<br />

Herbert Jelinek<br />

Charles Sturt University<br />

e-mail: hjelinek@csu.edu.au<br />

Audrey Karperien<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Community Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, Charles Sturt University<br />

Nebojsa Milosevic<br />

Biophysics Department, Belgrade University<br />

Lacunarity analysis and classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> microglia in<br />

neuroscience<br />

Fractal analysis in <str<strong>on</strong>g>th</str<strong>on</strong>g>e neurosciences has advanced over <str<strong>on</strong>g>th</str<strong>on</strong>g>e last twenty years<br />

to include measures such as lacunarity. Lacunarity assesses heterogeneity or translati<strong>on</strong>al<br />

and rotati<strong>on</strong>al invariance in an image. In general, measures <str<strong>on</strong>g>of</str<strong>on</strong>g> lacunarity<br />

corresp<strong>on</strong>d to visual impressi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> uniformity, where low lacunarity c<strong>on</strong>venti<strong>on</strong>ally<br />

implies homogeneity and high lacunarity heterogeneity. It is now necessary to<br />

review some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e new permutati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is analysis technique and what it can<br />

tell <str<strong>on</strong>g>th</str<strong>on</strong>g>e neuroscientist. This paper outlines me<str<strong>on</strong>g>th</str<strong>on</strong>g>odological c<strong>on</strong>siderati<strong>on</strong>s associated<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree different types <str<strong>on</strong>g>of</str<strong>on</strong>g> lacunarity analysis applied to <str<strong>on</strong>g>th</str<strong>on</strong>g>e classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

microglial cells.<br />

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W<strong>on</strong>ju Je<strong>on</strong><br />

Nati<strong>on</strong>al Institute for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences<br />

e-mail: wje<strong>on</strong>@nims.re.kr<br />

Sang-Hee Lee<br />

Nati<strong>on</strong>al Institute for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences<br />

Ecosystems Dynamics; Tuesday, June 28, 11:00<br />

Exploring Algal Blooms <str<strong>on</strong>g>th</str<strong>on</strong>g>rough Plankt<strong>on</strong>s Interacti<strong>on</strong>s<br />

Using Trophic Model<br />

We developed two-level trophic model to systematically understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e algal blooming<br />

in aquatic systems. The model combined two ecological processes: <strong>on</strong>e is <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

predator (zooplankt<strong>on</strong>)-prey (phytoplankt<strong>on</strong>) interacti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er is <str<strong>on</strong>g>th</str<strong>on</strong>g>e advecti<strong>on</strong><br />

and diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluid. By using <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, we computati<strong>on</strong>ally revealed<br />

how <str<strong>on</strong>g>th</str<strong>on</strong>g>e combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biological and envir<strong>on</strong>mental factors causes <str<strong>on</strong>g>th</str<strong>on</strong>g>e algal bloom<br />

in relati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e turbulent mixing <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e plankt<strong>on</strong>s. We showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e turbulent<br />

mixing is likely to str<strong>on</strong>gly affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e blooming <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e surface<br />

plankt<strong>on</strong>. In additi<strong>on</strong>, we briefly discussed <str<strong>on</strong>g>th</str<strong>on</strong>g>e competiti<strong>on</strong> strategy between <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

plankt<strong>on</strong>s to increase <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir survival in c<strong>on</strong>necti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e blooming.<br />

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From <strong>on</strong>e to many: Cell-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective, emergent behaviors<br />

in biology -II; Tuesday, June 28, 14:30<br />

Yi Jiang<br />

Los Alamos Nati<strong>on</strong>al Laboratory<br />

e-mail: jiang@lanl.gov<br />

Yilin Wu<br />

Harvard<br />

Mark Alber<br />

Notre Dame<br />

Dale Kaiser<br />

Stanford<br />

Bacterial behavioral principles: Learning from Myxobacteria<br />

Many bacteria are able to spread rapidly over surfaces by <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> swarming.<br />

Bacterial swarms are model systems for <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> multicellularity and biological<br />

self-organizati<strong>on</strong>. Swarming bacteria have rod-shaped cells, and are observed to<br />

move smoo<str<strong>on</strong>g>th</str<strong>on</strong>g>ly even when <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are packed toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er at high density. Why d<strong>on</strong>t<br />

swarming cells interfere wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers movements? Using a cell-based biomechanical<br />

model, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at periodic reversals <str<strong>on</strong>g>of</str<strong>on</strong>g> moving directi<strong>on</strong> in populati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> rod-shaped bacteria can lead to extensive ordering <str<strong>on</strong>g>of</str<strong>on</strong>g> cells, <str<strong>on</strong>g>th</str<strong>on</strong>g>us enabling <str<strong>on</strong>g>th</str<strong>on</strong>g>em<br />

to effectively resolve traffic jams formed during swarming. We also show <str<strong>on</strong>g>th</str<strong>on</strong>g>at an<br />

optimal reversal period and an optimal cell leng<str<strong>on</strong>g>th</str<strong>on</strong>g> exist for producing such order.<br />

The optimal reversal period and <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal cell leng<str<strong>on</strong>g>th</str<strong>on</strong>g> are c<strong>on</strong>nected by a simple<br />

relati<strong>on</strong>. We suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at basic behavioral principles exist for bacterial swarming<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at are independent <str<strong>on</strong>g>of</str<strong>on</strong>g> detailed motility mechanisms.<br />

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Mechanics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> and cortical actin at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular level;<br />

Saturday, July 2, 08:30<br />

Jean-François Joanny<br />

Physico-Chimie Curie Institut Curie<br />

e-mail: jean-francois.joanny@curie.fr<br />

Cortical actin and cell instabilities<br />

Cortical actin and cell instabilities. JF Joanny, J. Prost, G. Salbreux<br />

We present a review <str<strong>on</strong>g>of</str<strong>on</strong>g> our work <strong>on</strong> cortical actin and <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e instabilities <str<strong>on</strong>g>of</str<strong>on</strong>g> cells<br />

induced by cortical actin. We first show how we can apply our active gel <str<strong>on</strong>g>th</str<strong>on</strong>g>eory<br />

to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e acti-myosin cortex in a cell. We <str<strong>on</strong>g>th</str<strong>on</strong>g>en discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cortical actin layer. The results are applied to <str<strong>on</strong>g>th</str<strong>on</strong>g>ree problems: <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> belbs to discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimetns <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e group <str<strong>on</strong>g>of</str<strong>on</strong>g> E. Paluch in Dresden<br />

where <str<strong>on</strong>g>th</str<strong>on</strong>g>e blebs are induced by photoablati<strong>on</strong>; oscillati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong> adhering cells to<br />

discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e experiments <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e group <str<strong>on</strong>g>of</str<strong>on</strong>g> P. Pullarkat in Bangalore; and <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tractile rings. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is last case, we discuss bo<str<strong>on</strong>g>th</str<strong>on</strong>g> wound healing formati<strong>on</strong> in<br />

a xenopus embryo and <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>tractile ring during cytokinesis<br />

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H.C. Johns<strong>on</strong>*<br />

L<strong>on</strong>d<strong>on</strong> School <str<strong>on</strong>g>of</str<strong>on</strong>g> Hygiene and Tropical Medicine<br />

e-mail: Helen.Johns<strong>on</strong>@lshtm.ac.uk<br />

W.J. Edmunds<br />

L<strong>on</strong>d<strong>on</strong> School <str<strong>on</strong>g>of</str<strong>on</strong>g> Hygiene and Tropical Medicine<br />

e-mail: John.Edmunds@lshtm.ac.uk<br />

R.G. White<br />

L<strong>on</strong>d<strong>on</strong> School <str<strong>on</strong>g>of</str<strong>on</strong>g> Hygiene and Tropical Medicine<br />

e-mail: Richard.White@lshtm.ac.uk<br />

Epidemics; Saturday, July 2, 08:30<br />

Novel ABC - Bayesian Emulati<strong>on</strong> Hybrid Algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m For<br />

Complex Model Calibrati<strong>on</strong>: The First Waves<br />

Introducti<strong>on</strong>. The complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical systems underlying epidemics<br />

has led to <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> large-scale stochastic models for predicti<strong>on</strong> purposes. However,<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for robustly calibrating and analysing <str<strong>on</strong>g>th</str<strong>on</strong>g>ese simulators can be prohibitively<br />

inefficient. We propose an algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m for fitting complex models <str<strong>on</strong>g>th</str<strong>on</strong>g>at incorporates<br />

elements <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> Approximate Bayesian Computati<strong>on</strong> (ABC) and Bayesian Emulati<strong>on</strong>.<br />

ABC enables inference about model parameters wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out <str<strong>on</strong>g>th</str<strong>on</strong>g>e need for calculating<br />

a likelihood functi<strong>on</strong>, by generating approximati<strong>on</strong>s from repeated model<br />

runs. However, each complex model run might take hours. Emulati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are<br />

being developed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e fields <str<strong>on</strong>g>of</str<strong>on</strong>g> cosmology, oceanography and meteorological modelling.<br />

The complex model functi<strong>on</strong> is summarised as an ‘emulator’: a stochastic<br />

functi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at represents <str<strong>on</strong>g>th</str<strong>on</strong>g>e global behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex model functi<strong>on</strong> as a<br />

linear regressi<strong>on</strong> model and local deviati<strong>on</strong>s from <str<strong>on</strong>g>th</str<strong>on</strong>g>is behaviour as Gaussian processes.<br />

The emulator <str<strong>on</strong>g>th</str<strong>on</strong>g>en becomes a cheap proxy for <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex model, allowing<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> calibrati<strong>on</strong> and probabilistic sensitivity analysis to be c<strong>on</strong>ducted in a fracti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong>al time.<br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods. We report <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an emulati<strong>on</strong>-based calibrati<strong>on</strong><br />

algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m to an individual-based stochastic model <str<strong>on</strong>g>of</str<strong>on</strong>g> STI transmissi<strong>on</strong> in Uganda.<br />

Starting wi<str<strong>on</strong>g>th</str<strong>on</strong>g> uninformative priors for 19 behavioural and biological input parameters,<br />

we ‘trained’ an emulator wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 200 sampled parameter sets and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir corresp<strong>on</strong>ding<br />

complex model output (point estimates <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV prevalence). Sampling a<br />

fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er 10,000 parameter sets from <str<strong>on</strong>g>th</str<strong>on</strong>g>e priors, we used <str<strong>on</strong>g>th</str<strong>on</strong>g>e emulator to make output<br />

predicti<strong>on</strong>s over a large area <str<strong>on</strong>g>of</str<strong>on</strong>g> input parameter space. Weighting each parameter<br />

set according to goodness <str<strong>on</strong>g>of</str<strong>on</strong>g> fit to observed data, we identified promising areas <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

parameter space to evaluate using <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex model. A more accurate emulator<br />

was <str<strong>on</strong>g>th</str<strong>on</strong>g>en trained, incorporating <str<strong>on</strong>g>th</str<strong>on</strong>g>is additi<strong>on</strong>al complex model output. This process<br />

was repeated in ‘waves’ as per sequential ABC me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods.<br />

Results. The use <str<strong>on</strong>g>of</str<strong>on</strong>g> emulators allowed an evaluati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> large areas <str<strong>on</strong>g>of</str<strong>on</strong>g> parameter<br />

space due to increased computati<strong>on</strong>al efficiency. Processing time for <strong>on</strong>e<br />

prevalence point estimate was reduced from over 15 minutes <strong>on</strong> an HPC cluster to<br />

less <str<strong>on</strong>g>th</str<strong>on</strong>g>an 0.1 sec<strong>on</strong>d <strong>on</strong> a PC. Even <str<strong>on</strong>g>th</str<strong>on</strong>g>e first two waves <str<strong>on</strong>g>of</str<strong>on</strong>g> such an algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m provided<br />

helpful insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e most influential parameters and identified promising<br />

regi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> parameter space.<br />

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C<strong>on</strong>clusi<strong>on</strong>s. The development <str<strong>on</strong>g>of</str<strong>on</strong>g> an ABC - Bayesian Emulati<strong>on</strong> hybrid approach<br />

to complex model calibrati<strong>on</strong> is promising, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> emulators <str<strong>on</strong>g>of</str<strong>on</strong>g>fering large<br />

advantages in computati<strong>on</strong>al efficiency. However, fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er research is needed regarding<br />

weighting, tolerance levels and covariance.<br />

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Cell and Tissue Biophysics; Saturday, July 2, 11:00<br />

Z<str<strong>on</strong>g>of</str<strong>on</strong>g>ia J<strong>on</strong>es<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, Nottingham, NG7<br />

2RD, UK<br />

e-mail: pmxzj1@nottingham.ac.uk<br />

Helfrich Energy Model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Phagocytosis <str<strong>on</strong>g>of</str<strong>on</strong>g> a Fibre<br />

CNTs are a form <str<strong>on</strong>g>of</str<strong>on</strong>g> High Aspect Ratio Nanoparticles (HARN). Their radius is<br />

typically <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>ly a few nanometres (10 −9 ) while <str<strong>on</strong>g>th</str<strong>on</strong>g>eir leng<str<strong>on</strong>g>th</str<strong>on</strong>g> can be <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e micr<strong>on</strong><br />

scale (10 −6 ). Their shape has been found to make <str<strong>on</strong>g>th</str<strong>on</strong>g>eir removal from <str<strong>on</strong>g>th</str<strong>on</strong>g>e lung<br />

surface <strong>on</strong> inhalati<strong>on</strong> by macrophages especially difficult. This is widely regarded<br />

as a key mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> toxicity [1] [2]. Frustrated phagocytosis leads to scarring<br />

and granuloma formati<strong>on</strong> which impairs <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lung.<br />

Following <str<strong>on</strong>g>th</str<strong>on</strong>g>e precendent set by Helfrich and Deuling [3] [4], <str<strong>on</strong>g>th</str<strong>on</strong>g>e free energy <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a cell membrane is taken to be given by<br />

<br />

<br />

F = ∆p + λ + (mean curvature − c0)<br />

V<br />

<br />

S<br />

<br />

S<br />

Volume Energy Surface Energy<br />

2<br />

<br />

Helfrich Energy<br />

The Helfrich energy was introduced in [3] to quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e energy associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a<br />

cell membrane <str<strong>on</strong>g>of</str<strong>on</strong>g> a particular shape. It is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten referred to as <str<strong>on</strong>g>th</str<strong>on</strong>g>e bending energy.<br />

The sp<strong>on</strong>taneous curvature c0 takes into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e natural curvature <str<strong>on</strong>g>of</str<strong>on</strong>g> a cell<br />

membrane due to proteins in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lipid bilayer and <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong>.<br />

For a given set <str<strong>on</strong>g>of</str<strong>on</strong>g> boundary c<strong>on</strong>diti<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e shape <str<strong>on</strong>g>of</str<strong>on</strong>g> a <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell membrane is<br />

found by solving <str<strong>on</strong>g>th</str<strong>on</strong>g>e associated Euler-Lagrange equati<strong>on</strong>s. The topology <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

surface is restricted to <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>of</str<strong>on</strong>g> a surface <str<strong>on</strong>g>of</str<strong>on</strong>g> rotati<strong>on</strong> around an axis which is taken<br />

to be <str<strong>on</strong>g>th</str<strong>on</strong>g>e axis <str<strong>on</strong>g>of</str<strong>on</strong>g> a fibre. Due to singularities in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese Euler-Lagrange equati<strong>on</strong>s,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e problem is a boundary value problem ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an an initial value problem.<br />

The soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is energy minimisati<strong>on</strong> problem in [4] corresp<strong>on</strong>d to soluti<strong>on</strong>s<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e limit <str<strong>on</strong>g>of</str<strong>on</strong>g> a vanishing radius <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell <strong>on</strong> a fibre problem. Boundary c<strong>on</strong>diti<strong>on</strong>s<br />

specific to <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell <strong>on</strong> a fibre problem are introduced. These boundary c<strong>on</strong>diti<strong>on</strong>s<br />

can be chosen to ensure <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e boundary terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e first variati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e free<br />

energy are set to zero. They can also be chosen to fix <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tact angle <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell<br />

membrane wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fibre surface.<br />

It is assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e shape <str<strong>on</strong>g>of</str<strong>on</strong>g> a lipid membrane which has successfully engulfed<br />

a particle will be energetically stable, in order to c<strong>on</strong>serve <str<strong>on</strong>g>th</str<strong>on</strong>g>e limited resources <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a macrophage. This does not take into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e energy required to remodel<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell to reach <str<strong>on</strong>g>th</str<strong>on</strong>g>is shape. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e bending energy<br />

associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> cell membranes <str<strong>on</strong>g>of</str<strong>on</strong>g> increasing leng<str<strong>on</strong>g>th</str<strong>on</strong>g> can be used to suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

amount <str<strong>on</strong>g>of</str<strong>on</strong>g> energy required in <str<strong>on</strong>g>th</str<strong>on</strong>g>is dynamical process.<br />

References.<br />

[1] G. Oberdörster, V. St<strong>on</strong>e and K. D<strong>on</strong>alds<strong>on</strong>, Toxicology <str<strong>on</strong>g>of</str<strong>on</strong>g> nanoparticles: A historical perspective<br />

Nanotoxicology 1 2–25, 2007.<br />

[2] K. D<strong>on</strong>alds<strong>on</strong> et al, Carb<strong>on</strong> nanotubes: A review <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir properties in relati<strong>on</strong> to pulm<strong>on</strong>ary<br />

toxicology and workplace safety Toxicological Sciences 92 5–22,2006.<br />

[3] W. Helfrich, Elastic properties <str<strong>on</strong>g>of</str<strong>on</strong>g> lipid bilayers: Theory and possible experiments, 28 Z. Naturforsch<br />

693–703, 1973.<br />

461

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[4] H.J. Deuling and W. Helfrich, The curvature elasticity <str<strong>on</strong>g>of</str<strong>on</strong>g> fluid membranes: A catalogue <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

vesicle shapes J. Phys. France 37 1335-1345, 1976<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Undergraduate Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Educati<strong>on</strong> Bey<strong>on</strong>d BIO 2010 (Part I);<br />

Wednesday, June 29, 14:30<br />

Winfried Just<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Ohio University<br />

A<str<strong>on</strong>g>th</str<strong>on</strong>g>ens, OH 45701, USA<br />

e-mail: ma<str<strong>on</strong>g>th</str<strong>on</strong>g>just@gmail.com<br />

Discrete vs. indiscrete models <str<strong>on</strong>g>of</str<strong>on</strong>g> network dynamics<br />

A key step in modeling biological network dynamics is <str<strong>on</strong>g>th</str<strong>on</strong>g>e decisi<strong>on</strong> whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er to<br />

use a stochastic process, a system <str<strong>on</strong>g>of</str<strong>on</strong>g> differential equati<strong>on</strong>s, or a discrete dynamical<br />

system. This step in <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling process poses bo<str<strong>on</strong>g>th</str<strong>on</strong>g> special challenges and special<br />

opportunities for undergraduate teaching. The challenge is <str<strong>on</strong>g>th</str<strong>on</strong>g>at performing <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

step requires familiarity wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a number <str<strong>on</strong>g>of</str<strong>on</strong>g> different areas <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, which<br />

cannot be taken for granted in undergraduate teaching. Moreover, undergraduates<br />

tend to view ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics as neatly compartmentalized into subdisciplines, each<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir own set <str<strong>on</strong>g>of</str<strong>on</strong>g> standard word problems. The opportunity is for leading students<br />

bey<strong>on</strong>d <str<strong>on</strong>g>th</str<strong>on</strong>g>is view and giving <str<strong>on</strong>g>th</str<strong>on</strong>g>em a taste <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>a fide ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling<br />

where <str<strong>on</strong>g>th</str<strong>on</strong>g>e tools need to be chosen depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system and available computati<strong>on</strong>al<br />

resources. Moreover, <strong>on</strong>e can introduce quite sophisticated ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

c<strong>on</strong>cepts from a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> areas <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e way.<br />

This presentati<strong>on</strong> will illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach based <strong>on</strong> ODE<br />

and discrete models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> finite state spaces for certain networks. We will investigate<br />

c<strong>on</strong>diti<strong>on</strong>s under which <str<strong>on</strong>g>th</str<strong>on</strong>g>e coarse-graining via discrete models is a valid<br />

modeling approach and give examples <str<strong>on</strong>g>of</str<strong>on</strong>g> open problems <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be explored as<br />

undergraduate research projects.<br />

463

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Winfried Just<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Ohio University<br />

A<str<strong>on</strong>g>th</str<strong>on</strong>g>ens, OH 45701, USA<br />

e-mail: ma<str<strong>on</strong>g>th</str<strong>on</strong>g>just@gmail.com<br />

Benjamin Elbert<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Ohio University<br />

A<str<strong>on</strong>g>th</str<strong>on</strong>g>ens, OH 45701, USA<br />

e-mail: be173805@ohio.edu<br />

Mas<strong>on</strong> Korb<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Ohio University<br />

A<str<strong>on</strong>g>th</str<strong>on</strong>g>ens, OH 45701, USA<br />

e-mail: mk367807@ohio.edu<br />

Bismark Oduro<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Ohio University<br />

A<str<strong>on</strong>g>th</str<strong>on</strong>g>ens, OH 45701, USA<br />

e-mail: bo613809@ohio.edu<br />

Todd R. Young<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Ohio University<br />

A<str<strong>on</strong>g>th</str<strong>on</strong>g>ens, OH 45701, USA<br />

e-mail: youngt@ohio.edu<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Boolean dynamics vs. ODE dynamics<br />

The corresp<strong>on</strong>dence between systems <str<strong>on</strong>g>of</str<strong>on</strong>g> piecewise linear ODE’s and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir Boolean<br />

idealizati<strong>on</strong>s has been extensively studied by Le<strong>on</strong> Glass and his collaborators.<br />

These types <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamical systems have been proposed as frameworks for studying<br />

biological processes such as gene regulati<strong>on</strong>.<br />

We c<strong>on</strong>sider a different class <str<strong>on</strong>g>of</str<strong>on</strong>g> ODE systems <str<strong>on</strong>g>th</str<strong>on</strong>g>at naturally admit Boolean<br />

idealizati<strong>on</strong>s. The ODEs in <str<strong>on</strong>g>th</str<strong>on</strong>g>is class have Lipschitz-c<strong>on</strong>tinuous right-hand sides,<br />

and our class is ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er broad. We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e variables can be grouped into<br />

agents <str<strong>on</strong>g>of</str<strong>on</strong>g> sorts, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> individual agents having a certain bifurcati<strong>on</strong> structure and<br />

inputs from o<str<strong>on</strong>g>th</str<strong>on</strong>g>er agents acting as changing bifurcati<strong>on</strong> parameters.<br />

This talk will present bo<str<strong>on</strong>g>th</str<strong>on</strong>g> simulati<strong>on</strong>s and analytical results <str<strong>on</strong>g>th</str<strong>on</strong>g>at show how<br />

structural properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e systems influence <str<strong>on</strong>g>th</str<strong>on</strong>g>e degree <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>sistency between <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ODE dynamics and its Boolean idealizati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> synchr<strong>on</strong>ous or asynchr<strong>on</strong>ous<br />

updating. In particular, we explore to what extent features <str<strong>on</strong>g>of</str<strong>on</strong>g> chaotic dynamics<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Boolean idealizati<strong>on</strong> corresp<strong>on</strong>d to <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> chaos in <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying<br />

ODE system.<br />

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Heart rate dynamics: models and measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity (part I);<br />

Wednesday, June 29, 14:30<br />

Agnieszka Kaczkowska<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Physics and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Gdańsk University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Technology, Poland<br />

e-mail: kaczkowska.agnieszka@gmail.com<br />

Grzegorz Graff<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Physics and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Gdańsk University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Technology, Poland<br />

e-mail: graff@mif.pg.gda.pl<br />

Beata Graff<br />

Hypertensi<strong>on</strong> Unit, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Hypertensi<strong>on</strong> and Diabetology,<br />

Medical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Gdańsk, Poland<br />

e-mail: bgraff@gumed.edu.pl<br />

Entropy-based measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity in <str<strong>on</strong>g>th</str<strong>on</strong>g>e assessment <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

heart rate variability: a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical approach<br />

Recently, in a study <str<strong>on</strong>g>of</str<strong>on</strong>g> heart rate variability and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er physiological data, growing<br />

attenti<strong>on</strong> has been paid to entropy-based complexity measures, am<strong>on</strong>g which<br />

are Approximate Entropy, Sample Entropy, Fuzzy Entropy, local entropies and<br />

some o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical comp<strong>on</strong>ents <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir definiti<strong>on</strong>s will be presented wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e stress <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e problems <str<strong>on</strong>g>of</str<strong>on</strong>g> vulnerability to noise, loss <str<strong>on</strong>g>of</str<strong>on</strong>g> data, relative c<strong>on</strong>sistency,<br />

dependence <strong>on</strong> sample leng<str<strong>on</strong>g>th</str<strong>on</strong>g> and sensitivity to <str<strong>on</strong>g>th</str<strong>on</strong>g>e input parameters. The<br />

usefulness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e above me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to distinguish time series wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

irregularity and unpredictability will be discussed and tested <strong>on</strong> various kinds <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

stochastic, n<strong>on</strong>linear and physiological data.<br />

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Cellular Systems Biology; Tuesday, June 28, 14:30<br />

Maik Kschischo<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Sciences Koblenz, RheinAhrCampus, Remagen,<br />

Germany, D-53424<br />

e-mail: kschischo@rheinahrcampus.de<br />

Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ias Kahm<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Sciences Koblenz, RheinAhrCampus, Remagen,<br />

Germany, D-53424<br />

e-mail: kahm@rheinahrcampus.de<br />

Clara Navarrete<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enborg, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Cell- and Molecular Biology,<br />

Medicinaregatan 9C, Box 462 SE 405 30, Sweden<br />

e-mail: b92naroc@uco.es<br />

José Ramos<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cordoba, Avenida Menendes Pidal, 14071 Cordoba, Spain<br />

e-mail: mi1raruj@uco.es<br />

Actuators <str<strong>on</strong>g>of</str<strong>on</strong>g> yeast potassium homeostasis<br />

Potassium is <str<strong>on</strong>g>th</str<strong>on</strong>g>e most abundant cati<strong>on</strong> in living cells and is involved in a variety<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> essential cellular processes including translati<strong>on</strong>, endocytosis and even cell<br />

cycle regulati<strong>on</strong>. Changes <str<strong>on</strong>g>of</str<strong>on</strong>g> external and internal K + c<strong>on</strong>centrati<strong>on</strong>s change <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

membrane potential required for <str<strong>on</strong>g>th</str<strong>on</strong>g>e transport <str<strong>on</strong>g>of</str<strong>on</strong>g> molecules across <str<strong>on</strong>g>th</str<strong>on</strong>g>e plasma membrane,<br />

affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e pH and osmolarity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytosol and induce changes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell<br />

volume [1]. Metabolic decarboxylati<strong>on</strong> processes release CO2, which affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

pH, <str<strong>on</strong>g>th</str<strong>on</strong>g>e bicarb<strong>on</strong>ate c<strong>on</strong>centrati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e prot<strong>on</strong> buffer capacity and <str<strong>on</strong>g>th</str<strong>on</strong>g>e potassium<br />

transport [2].<br />

To gain a deeper understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex interplay between <str<strong>on</strong>g>th</str<strong>on</strong>g>ese variables<br />

we developed an ordinary differential equati<strong>on</strong> model <str<strong>on</strong>g>of</str<strong>on</strong>g> potassium c<strong>on</strong>trol in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e yeast Saccharomyces cerevisiae. The basic model covers <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ermodynamic<br />

c<strong>on</strong>straints <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e operati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e major potassium transport systems and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

prot<strong>on</strong> ATPase Pma1. Regulati<strong>on</strong> mechanisms where <strong>on</strong>ly partly included as many<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em are ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er unknown or not sufficiently characterized. This basic model<br />

qualitatively reproduces known aspects such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e hyperpolarisati<strong>on</strong> in trk1,2∆<br />

mutants and potassium starved cells, as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e potassium uptake energized by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Pma1 driven prot<strong>on</strong> extrusi<strong>on</strong>.<br />

To make quantitative predicti<strong>on</strong>s we calibrated <str<strong>on</strong>g>th</str<strong>on</strong>g>e model to potassium starvati<strong>on</strong><br />

experiments given in [3]. For cells grown in a medium wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high K + and shifted<br />

to K + free medium, a decrease <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular K + c<strong>on</strong>tent and cell volume was<br />

measured. While <str<strong>on</strong>g>th</str<strong>on</strong>g>e external potassium drop occurs in minutes, <str<strong>on</strong>g>th</str<strong>on</strong>g>e internal K +<br />

is slowly reduced during several hours.<br />

The regulatory c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e various transport systems under potassium starvati<strong>on</strong><br />

c<strong>on</strong>diti<strong>on</strong>s is not well understood. To identify potential c<strong>on</strong>trol mechanisms<br />

and points <str<strong>on</strong>g>of</str<strong>on</strong>g> applicati<strong>on</strong>s we regarded <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental time course K +<br />

data (t) as a<br />

signal which has to be tracked by <str<strong>on</strong>g>th</str<strong>on</strong>g>e model K +<br />

sim (t). More precisely, we determined<br />

a time dependent input functi<strong>on</strong> p(t) <str<strong>on</strong>g>th</str<strong>on</strong>g>at solves <str<strong>on</strong>g>th</str<strong>on</strong>g>e minimizati<strong>on</strong> problem<br />

(1)<br />

466<br />

|| K +<br />

sim (p(t), θ, t) − K+<br />

data (t) || = Min .

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Each transport protein or any o<str<strong>on</strong>g>th</str<strong>on</strong>g>er comp<strong>on</strong>ent <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model for which such an<br />

input functi<strong>on</strong> exists was regarded as a potential actuator for potassium c<strong>on</strong>trol.<br />

We found <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e (i) <str<strong>on</strong>g>th</str<strong>on</strong>g>e prot<strong>on</strong> pump Pma1 and <str<strong>on</strong>g>th</str<strong>on</strong>g>e (ii) <str<strong>on</strong>g>th</str<strong>on</strong>g>e CO2 system are <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

most likely actuators <str<strong>on</strong>g>of</str<strong>on</strong>g> potassium homeostasis. In additi<strong>on</strong>, we found evidence <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

yeast cells sense external potassium ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an internal potassium, what is also<br />

supported experimentally. To dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sistency <str<strong>on</strong>g>of</str<strong>on</strong>g> our predicti<strong>on</strong>s we<br />

successfully designed a modified PI-c<strong>on</strong>troller which reproduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental<br />

time courses <str<strong>on</strong>g>of</str<strong>on</strong>g> internal potassium. This PI c<strong>on</strong>troller mimics <str<strong>on</strong>g>th</str<strong>on</strong>g>e unknown details <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

signalling and gene expressi<strong>on</strong> changes required for <str<strong>on</strong>g>th</str<strong>on</strong>g>e maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> homeostasis.<br />

In summary, we present a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model which provides testable predicti<strong>on</strong>s<br />

about unknown regulatory mechanisms necessary for homeostatic c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

potassium in S. cerevisiae. We also believe <str<strong>on</strong>g>th</str<strong>on</strong>g>at our tracking approach to ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

modeling has general applicability. It is a versatile strategy to detect<br />

unmodeled dynamics and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir points <str<strong>on</strong>g>of</str<strong>on</strong>g> applicati<strong>on</strong>.<br />

References.<br />

[1] J. Ariño, J. Ramos, H. Sychrová, Alkali metal cati<strong>on</strong> transport and homeostasis in yeasts<br />

FEMS Yeast Research 74 95–120.<br />

[2] R. Lopéz, E. Enríquez, A. Peña, Effects <str<strong>on</strong>g>of</str<strong>on</strong>g> weak acids <strong>on</strong> cati<strong>on</strong> accumulati<strong>on</strong>, ∆pH and ∆ψ<br />

in yeast YEAST, 15 553–562.<br />

[3] C. Navarrete et al., Lack <str<strong>on</strong>g>of</str<strong>on</strong>g> main K + uptake systems in Saccharomyces cerevisiae cells affects<br />

yeast performance in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> potassium-sufficient and potassium-limiting c<strong>on</strong>diti<strong>on</strong> FEMS Yeast<br />

Research 10 508–517.<br />

467

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Yannis Kalaidzidis<br />

MPI-CBG<br />

e-mail: kalaidzi@mpi-cbg.de<br />

Claudio Collinet<br />

MPI-CBG<br />

Akhila Chandrashaker<br />

MPI-CBG<br />

Thierry Galvez<br />

MPI-CBG<br />

Rachel Meyers<br />

Alnylam Pharm. Inc.<br />

Marino Zerial<br />

MPI-CBG<br />

Bioimaging; Tuesday, June 28, 11:00<br />

Quantitative Multiparametric Image Analysis for Estimati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> siRNA Induced Off-target Effect<br />

Small Interfering RNA (siRNA) and automated high-<str<strong>on</strong>g>th</str<strong>on</strong>g>roughput high-resoluti<strong>on</strong><br />

microscopy provides technological platform for systematic genome-wide survey <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

individual gene knockdown phenotype. Quantitative multi-parametric descripti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> knockdown phenotype can be used for gene functi<strong>on</strong>s elucidati<strong>on</strong> and establishing<br />

mechanistic models <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular processes in which genes participate. However,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e large degree <str<strong>on</strong>g>of</str<strong>on</strong>g> morphological variati<strong>on</strong> between cells in repetiti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> biological<br />

experiment as well as variati<strong>on</strong> between phenotypes <str<strong>on</strong>g>of</str<strong>on</strong>g> different siRNAs, which are<br />

targeting <str<strong>on</strong>g>th</str<strong>on</strong>g>e same gene, represents a major challenge to <str<strong>on</strong>g>th</str<strong>on</strong>g>e reliable identificati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> gene silencing phenotypes. We have developed a system for <str<strong>on</strong>g>th</str<strong>on</strong>g>e high c<strong>on</strong>tent<br />

analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> automatically acquired high-resoluti<strong>on</strong> images, which describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e endosomal<br />

organelles in quantitative terms (gene silencing pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile) (Collinet et al, Nature<br />

2010). The stability <str<strong>on</strong>g>of</str<strong>on</strong>g> individual parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> phenotypic pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles between<br />

different imaging sessi<strong>on</strong>s and experimental replicates were tested. The analysis<br />

showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at different parameters reveal a wide variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> stabilities which dependent<br />

<strong>on</strong> biological variability, typical automatic imaging problems and parameter<br />

calculati<strong>on</strong> details. Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> multi-parametric phenotype pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles produced by<br />

independent siRNAs, which are targeting <str<strong>on</strong>g>th</str<strong>on</strong>g>e same gene, reveals <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean level <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g>f-target effect, its dependence <strong>on</strong> siRNA c<strong>on</strong>centrati<strong>on</strong> and chemical modificati<strong>on</strong>.<br />

The estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e minimum number <str<strong>on</strong>g>of</str<strong>on</strong>g> independent siRNAs which are required<br />

to infer <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene knockdown phenotype wi<str<strong>on</strong>g>th</str<strong>on</strong>g> given c<strong>on</strong>fidence was d<strong>on</strong>e. Quantitative<br />

estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g>f-target effect gives an objective feedback for no <str<strong>on</strong>g>of</str<strong>on</strong>g>f-target<br />

siRNA selecti<strong>on</strong>, for <str<strong>on</strong>g>th</str<strong>on</strong>g>e new generati<strong>on</strong> siRNA development and could provide<br />

insight for deeper understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> siRNA-mediated gene silencing mechanism.<br />

468

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Structure and Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemical Reacti<strong>on</strong> Networks II; Tuesday, June<br />

28, 17:00<br />

Hiroko Kamei<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee, U.K.<br />

e-mail: hiroko@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.dundee.ac.uk<br />

Classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> networks for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir synchr<strong>on</strong>ous dynamics<br />

Small subnetworks, such as network motifs, and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir modularity have been c<strong>on</strong>sidered<br />

to play an important role in large complex networks. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>text, a major<br />

topic is <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay between network structures and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir corresp<strong>on</strong>ding dynamics.<br />

We c<strong>on</strong>sider <strong>on</strong>e form dynamics, synchr<strong>on</strong>y-breaking in a network. This can<br />

be interpreted as speciati<strong>on</strong>, differentiati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells, or clustering <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong><br />

patterns. For any network we c<strong>on</strong>struct a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical structure, a lattice, which<br />

results from <str<strong>on</strong>g>th</str<strong>on</strong>g>e eigenvalues and eigenvectors <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network’s adjacency matrix.<br />

Many networks have <str<strong>on</strong>g>th</str<strong>on</strong>g>e same lattice, allowing a large number <str<strong>on</strong>g>of</str<strong>on</strong>g> networks to be<br />

classified into a smaller number <str<strong>on</strong>g>of</str<strong>on</strong>g> lattice structures. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, by looking at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e lattice structure we can identify networks wi<str<strong>on</strong>g>th</str<strong>on</strong>g> similar synchr<strong>on</strong>ous dynamics.<br />

References.<br />

[1] C<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> lattices <str<strong>on</strong>g>of</str<strong>on</strong>g> balanced equivalence relati<strong>on</strong>s for regular homogeneous networks<br />

using lattice generators and lattice indices, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 19<br />

(2009)<br />

[2] The existence and classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> synchr<strong>on</strong>y-breaking bifurcati<strong>on</strong>s in regular homogeneous<br />

networks using lattice structures, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 19 (2009)<br />

469

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biomechanical regulati<strong>on</strong> in b<strong>on</strong>e tissue (Sessi<strong>on</strong><br />

II); Wednesday, June 29, 11:00<br />

Yoshitaka Kameo<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Mechanical Engineering and Science, Graduate School<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Engineering, Kyoto University<br />

e-mail: y.kameo@t02.mbox.media.kyoto-u.ac.jp<br />

Taiji Adachi<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biomechanics, Research Center for Nano Medical Engineering,<br />

Institute for Fr<strong>on</strong>tier Medical Sciences, Kyoto University<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> trabecular b<strong>on</strong>e remodeling<br />

induced by osteocytic resp<strong>on</strong>se to interstitial fluid flow<br />

B<strong>on</strong>e is a load-bearing tissue <str<strong>on</strong>g>th</str<strong>on</strong>g>at can adapt its internal structure and outer shape<br />

by remodeling to a changing mechanical envir<strong>on</strong>ment. The morphological changes<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e trabecular microstructure are realized by <str<strong>on</strong>g>th</str<strong>on</strong>g>e coupling <str<strong>on</strong>g>of</str<strong>on</strong>g> osteoclastic b<strong>on</strong>e<br />

resorpti<strong>on</strong> and osteoblastic b<strong>on</strong>e formati<strong>on</strong>. It is widely believed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolic<br />

activities <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese executive cells are regulated by a mechanosensory system<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> osteocytes buried in <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular b<strong>on</strong>e matrix, forming a <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-dimensi<strong>on</strong>al<br />

intercellular network <str<strong>on</strong>g>th</str<strong>on</strong>g>rough cellular processes in lacuno-canalicular porosity [1].<br />

The small space surrounding <str<strong>on</strong>g>th</str<strong>on</strong>g>e osteocytes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e porosity is filled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> interstitial<br />

fluid. When <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e is subjected to dynamic loading, b<strong>on</strong>e matrix deformati<strong>on</strong><br />

induces an interstitial fluid flow [2]. The fluid flow in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lacuno-canalicular porosity<br />

seems to mechanically activate <str<strong>on</strong>g>th</str<strong>on</strong>g>e osteocytes and serve as <str<strong>on</strong>g>th</str<strong>on</strong>g>e prime mover<br />

for b<strong>on</strong>e remodeling, as well as transport cell signaling molecules [3]. To understand<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e functi<strong>on</strong>al adaptati<strong>on</strong>, it will be useful to propose<br />

a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical framework <str<strong>on</strong>g>of</str<strong>on</strong>g> trabecular b<strong>on</strong>e remodeling <str<strong>on</strong>g>th</str<strong>on</strong>g>at interc<strong>on</strong>nects <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic<br />

cellular activities to <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic morphological changes <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

mechanical hierarchy. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is study, first, we c<strong>on</strong>structed a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for<br />

trabecular b<strong>on</strong>e remodeling, taking cellular mechanosensing and intercellular communicati<strong>on</strong><br />

into c<strong>on</strong>siderati<strong>on</strong> [4]. This model assumes <str<strong>on</strong>g>th</str<strong>on</strong>g>at osteocytes resp<strong>on</strong>d to<br />

fluid-induced shear stress and deliver <str<strong>on</strong>g>th</str<strong>on</strong>g>eir mechanical signals to <str<strong>on</strong>g>th</str<strong>on</strong>g>e surface cells by<br />

intercellular communicati<strong>on</strong>. The mechanical behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> a trabecula wi<str<strong>on</strong>g>th</str<strong>on</strong>g> lacunocanalicular<br />

porosity is modeled as a poroelastic material to evaluate <str<strong>on</strong>g>th</str<strong>on</strong>g>e interstitial<br />

fluid flow under mechanical loading. Sec<strong>on</strong>d, <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model, we simulated morphological changes in a single trabecula under<br />

cyclic uniaxial loading wi<str<strong>on</strong>g>th</str<strong>on</strong>g> various frequencies, which is <str<strong>on</strong>g>th</str<strong>on</strong>g>ought to be a significant<br />

mechanical factor in b<strong>on</strong>e remodeling. The results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> show <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

trabecula reoriented to <str<strong>on</strong>g>th</str<strong>on</strong>g>e loading directi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e progress <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e remodeling.<br />

As <str<strong>on</strong>g>th</str<strong>on</strong>g>e imposed loading frequency increased, <str<strong>on</strong>g>th</str<strong>on</strong>g>e diameter <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e trabecula in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

equilibrium state was enlarged by remodeling. Finally, we c<strong>on</strong>ducted a remodeling<br />

simulati<strong>on</strong> for a cancellous b<strong>on</strong>e cube under m<strong>on</strong>ot<strong>on</strong>ously increasing compressive<br />

loading, where all <str<strong>on</strong>g>th</str<strong>on</strong>g>e trabeculae are randomly-oriented in <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial geometry.<br />

As a result, <str<strong>on</strong>g>th</str<strong>on</strong>g>e degree <str<strong>on</strong>g>of</str<strong>on</strong>g> trabecular c<strong>on</strong>nectivity was gradually decreased and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

trabeculae in cancellous b<strong>on</strong>e aligned al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e loading directi<strong>on</strong>. These results<br />

indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>at our remodeling simulati<strong>on</strong> model can successfully express <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic<br />

changes in trabecular morphology from <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic cellular activities.<br />

470

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

References.<br />

[1] Burger, E.H., Klein-Nulend, J., 1999. Mechanotransducti<strong>on</strong> in b<strong>on</strong>e - Role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lacunocanalicular<br />

network. FASEB J. 13, S101-S112.<br />

[2] Cowin, S.C., 1999. B<strong>on</strong>e poroelasticity. J. Biomech. 32, 217-238.<br />

[3] Weinbaum, S., Cowin, S.C., Zeng, Y., 1994. A model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e excitati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> osteocytes by<br />

mechanical loading-induced b<strong>on</strong>e fluid shear stresses. J. Biomech. 27, 339-360.<br />

[4] Adachi, T., Kameo, Y., Hojo, M., 2010. Trabecular b<strong>on</strong>e remodeling simulati<strong>on</strong> c<strong>on</strong>sidering<br />

osteocytic resp<strong>on</strong>se to fluid-induced shear stress. Phil. Trans. R. Soc. A 368, 2669-2682.<br />

471

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Atsushi Kamimura<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Industrial Science, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Tokyo<br />

e-mail: kamimura@sat.t.u-tokyo.ac.jp<br />

Tetsuya J. Kobayashi<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Industrial Science, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Tokyo<br />

PRESTO, Japan Science and technilogy Agency<br />

Trade<str<strong>on</strong>g>of</str<strong>on</strong>g>f <str<strong>on</strong>g>of</str<strong>on</strong>g> Informati<strong>on</strong> Transmissi<strong>on</strong> and Decoding wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Intracellular Kinetics<br />

A variety <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular processes functi<strong>on</strong>s reliably by intracellular reacti<strong>on</strong>s even<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ough substantial noise is inevitable. In particular, detecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> relevant informati<strong>on</strong><br />

from envir<strong>on</strong>ment is crucial for <str<strong>on</strong>g>th</str<strong>on</strong>g>e fate <str<strong>on</strong>g>of</str<strong>on</strong>g> cells.<br />

From <str<strong>on</strong>g>th</str<strong>on</strong>g>e viewpoint <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eory, such informati<strong>on</strong> processing is composed<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree parts: encoding, transmissi<strong>on</strong> and decoding. Here, for a simple setup<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> biochemical reacti<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e roles <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ree parts can be played<br />

by envir<strong>on</strong>ment, receptors <strong>on</strong> membranes, and intracellular reacti<strong>on</strong>s, respectively.<br />

In engineering, much efforts have been generally made to reduce noise in encoding<br />

and transmissi<strong>on</strong> parts. By c<strong>on</strong>trast, decoding may also play equally important<br />

role in biological systems, which is suggested by <str<strong>on</strong>g>th</str<strong>on</strong>g>e substantial noise in microscopic<br />

cellular systems.<br />

While decoding is to extract as much informati<strong>on</strong> as possible from <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmitted<br />

signals, such processing, in reality, should be implemented in <str<strong>on</strong>g>th</str<strong>on</strong>g>e chemical reacti<strong>on</strong>s.<br />

For example, kinetics wi<str<strong>on</strong>g>th</str<strong>on</strong>g> dual positive feedback structure can implement a<br />

dynamic Bayesian inference, which gives <str<strong>on</strong>g>th</str<strong>on</strong>g>e statistical limit for <str<strong>on</strong>g>th</str<strong>on</strong>g>e decoding[1][2].<br />

However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> decoding would be limited by physical c<strong>on</strong>straints such<br />

as amount <str<strong>on</strong>g>of</str<strong>on</strong>g> available energetic cost. We still lack a general framework to quantify<br />

how <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> and decoding work.<br />

Here, we c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem by calculating mutual informati<strong>on</strong> am<strong>on</strong>g encoding,<br />

transmissi<strong>on</strong>, and decoding parts <str<strong>on</strong>g>of</str<strong>on</strong>g> simple models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> several intracellular<br />

reacti<strong>on</strong>s. By <str<strong>on</strong>g>th</str<strong>on</strong>g>e quantificati<strong>on</strong>, we clarify <str<strong>on</strong>g>th</str<strong>on</strong>g>e trade<str<strong>on</strong>g>of</str<strong>on</strong>g>f <str<strong>on</strong>g>of</str<strong>on</strong>g> transmissi<strong>on</strong> and<br />

decoding. When <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> part carries a large amount <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong>, decoding<br />

need not necessarily work effectively, since it is clear from <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmitted<br />

informati<strong>on</strong> to detect <str<strong>on</strong>g>th</str<strong>on</strong>g>e state <str<strong>on</strong>g>of</str<strong>on</strong>g> envir<strong>on</strong>ment. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, decoding by<br />

intracellular reacti<strong>on</strong>s becomes essential to obtain informati<strong>on</strong> when detecting from<br />

transmitted informati<strong>on</strong> is not straightforward.<br />

References.<br />

[1] T. J. Kobayashi, Implementati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Dynamic Bayesian Decisi<strong>on</strong> Making by Intracellular Kinetics,<br />

Phys. Rev. Lett. 104 228104(2010).<br />

[2] T. J. Kobayashi and A. Kamimura, Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Intracellular Informati<strong>on</strong> Decoding, submitted<br />

Physical Biology (2011).<br />

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Epidemic models: Networks and stochasticity II; Thursday, June 30, 11:30<br />

Christel Kamp<br />

Paul-Ehrlich-Institut<br />

e-mail: christel.kamp@pei.de<br />

Following epidemic spread: how epidemics travel and trim<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir network <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious c<strong>on</strong>tacts<br />

Epidemics <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases are ubiquitous, however, <str<strong>on</strong>g>th</str<strong>on</strong>g>eir patterns vary depending<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e course <str<strong>on</strong>g>of</str<strong>on</strong>g> disease and <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> network established by infectious<br />

c<strong>on</strong>tacts. Therefore, strategies to maintain public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> cannot be applied<br />

uniformly but have to be adjusted to <str<strong>on</strong>g>th</str<strong>on</strong>g>e specific epidemic scenario. Network models<br />

have proven to be a helpful tool to infer time scales <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemic expansi<strong>on</strong> and<br />

prevalence from <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure and dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying transmissi<strong>on</strong> network.<br />

We extend <str<strong>on</strong>g>th</str<strong>on</strong>g>e existing ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical framework to also quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e reverse<br />

effect: epidemics impact <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e way c<strong>on</strong>tacts are made am<strong>on</strong>g susceptible and infected<br />

hosts. A set <str<strong>on</strong>g>of</str<strong>on</strong>g> partial differential equati<strong>on</strong>s links <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure and dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> network to <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic process. It allows to study epidemics<br />

<strong>on</strong> dynamic transmissi<strong>on</strong> networks wi<str<strong>on</strong>g>th</str<strong>on</strong>g> arbitrary degree distributi<strong>on</strong>s and under<br />

demographic change [1,2]. The framework will be used in epidemic case studies<br />

including multi-staged HIV epidemics. These studies show how epidemics do not<br />

<strong>on</strong>ly travel but also trim <str<strong>on</strong>g>th</str<strong>on</strong>g>eir transmissi<strong>on</strong> networks and allow for an explorati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> interventi<strong>on</strong> strategies.<br />

References.<br />

[1] C. Kamp Untangling <str<strong>on</strong>g>th</str<strong>on</strong>g>e Interplay between Epidemic Spread and Transmissi<strong>on</strong> Network Dynamics<br />

PLoS Comput Biol 6(11): e1000984.<br />

[2] C. Kamp Demographic and behavioural change during epidemics Proc Comp Sci 1: 2247–2253.<br />

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Modeling physiological systems: model validati<strong>on</strong> and experimental design<br />

issues; Wednesday, June 29, 11:00<br />

Franz Kappel<br />

Institute for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Scientific Computing<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Graz<br />

e-mail: franz.kappel@uni-graz.at<br />

H. T. Banks<br />

Center for Research in Scientific Computati<strong>on</strong><br />

Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina State University<br />

e-mail: htbanks@ncsu.edu<br />

M. Munir<br />

Abbottabad, Pakistan<br />

e-mail: muhammad m2k4@yahoo.com<br />

Parameter selecti<strong>on</strong> in multi-output systems<br />

We present me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for a priori selecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters to be estimated in inverse<br />

problem formulati<strong>on</strong>s for models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multiple measurable outputs. Since in many<br />

modeling processes we have to deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> dynamical systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> numerous state<br />

variables and an even larger number <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters, but wi<str<strong>on</strong>g>th</str<strong>on</strong>g> limited availability <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

data, we cannot expect to estimate all parameters wi<str<strong>on</strong>g>th</str<strong>on</strong>g> sufficient accuracy. Therefore<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e type indicated above are becoming increasingly important. In<br />

situati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multiple measurable outputs we are also interested to know if <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

possibility to measure additi<strong>on</strong>al outputs would improve parameter estimates. Such<br />

questi<strong>on</strong>s become important if <str<strong>on</strong>g>th</str<strong>on</strong>g>ese additi<strong>on</strong>al measurements involve high costs,<br />

for instance. We illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e results for a model for insulin-glucose dynamics [2]<br />

and a model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiovascular system to an ergometric workload<br />

[1].<br />

References.<br />

[1] F. Kappel and R. O. Peer, A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for fundamental regulati<strong>on</strong> processes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cardiovascular system, J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biology 31 (1993), 611 – 631.<br />

[2] M. Munir, Generalized Sensitivity Functi<strong>on</strong>s in Physiological Modelling, PhD-Thesis, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Graz, April 2010.<br />

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Game <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical modelling and optimizati<strong>on</strong> in evoluti<strong>on</strong> and ecology II;<br />

Tuesday, June 28, 14:30<br />

Irina Kareva<br />

Ariz<strong>on</strong>a State University<br />

e-mail: ikareva@asu.edu<br />

Faina Berezovskaya<br />

Howard University, Washingt<strong>on</strong>, DC<br />

Georgy Karev<br />

Nati<strong>on</strong>al Institutes <str<strong>on</strong>g>of</str<strong>on</strong>g> Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, Be<str<strong>on</strong>g>th</str<strong>on</strong>g>esda, MD<br />

Mixed Strategies, Evoluti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Tragedy <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Comm<strong>on</strong>s in Heterogeneous Populati<strong>on</strong>s<br />

The questi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> sustainability and preventi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tragedy <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e comm<strong>on</strong>s, also<br />

known as evoluti<strong>on</strong>ary suicide, which occurs when extremely efficient c<strong>on</strong>sumers<br />

exhaust <str<strong>on</strong>g>th</str<strong>on</strong>g>e comm<strong>on</strong> resource and eventually harm <str<strong>on</strong>g>th</str<strong>on</strong>g>emselves, is becoming <str<strong>on</strong>g>of</str<strong>on</strong>g> vital<br />

importance in <str<strong>on</strong>g>th</str<strong>on</strong>g>e modern world. In order to investigate it we c<strong>on</strong>sider a situati<strong>on</strong>,<br />

when c<strong>on</strong>sumers can choose different strategies for resource c<strong>on</strong>sumpti<strong>on</strong> in different<br />

proporti<strong>on</strong>, investing primarily in c<strong>on</strong>sumpti<strong>on</strong> or in sustaining <str<strong>on</strong>g>th</str<strong>on</strong>g>e resource.<br />

This is modeled by an infinitely-dimensi<strong>on</strong>al system <str<strong>on</strong>g>of</str<strong>on</strong>g> ODEs, which is <str<strong>on</strong>g>th</str<strong>on</strong>g>en reduced<br />

to a finitely-dimensi<strong>on</strong>al system using parameter distributi<strong>on</strong>. The populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

c<strong>on</strong>sumers is <str<strong>on</strong>g>th</str<strong>on</strong>g>en allowed to evolve over time, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e frequency <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

different strategies are tracked <str<strong>on</strong>g>th</str<strong>on</strong>g>rough changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e expected value <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e choice <str<strong>on</strong>g>of</str<strong>on</strong>g> a strategy. We dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at under different<br />

parameter values different strategies predominate, leading to ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er sustained interacti<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resources, or to populati<strong>on</strong> extincti<strong>on</strong>, which occurs after a series<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> transiti<strong>on</strong>al regimes.<br />

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Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 08:30<br />

Arseny S. Karkach<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Numerical Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Russian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

e-mail: arseny@mail.ru<br />

Alexei A. Romanyukha<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Numerical Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Russian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

e-mail: eburg@inm.ras.ru<br />

Adaptive trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f between reproducti<strong>on</strong> and survival in<br />

Mediterranean fruit flies induced by changing dietary<br />

c<strong>on</strong>diti<strong>on</strong>s<br />

The c<strong>on</strong>cepti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cost <str<strong>on</strong>g>of</str<strong>on</strong>g> reproducti<strong>on</strong> provides an important insight <strong>on</strong><br />

c<strong>on</strong>necti<strong>on</strong> between fertility and life span in living organisms. Despite substantial<br />

progress in understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>necti<strong>on</strong> many important features <str<strong>on</strong>g>of</str<strong>on</strong>g> fertilityl<strong>on</strong>gevity<br />

trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f are masked by c<strong>on</strong>founding factors, and remain poorly understood.<br />

We performed reanalysis <str<strong>on</strong>g>of</str<strong>on</strong>g> data from experimental study <str<strong>on</strong>g>of</str<strong>on</strong>g> fertility and<br />

l<strong>on</strong>gevity resp<strong>on</strong>se to different diets in females <str<strong>on</strong>g>of</str<strong>on</strong>g> Mediterranean fruit fly C. capitata<br />

[1, 2]. A negative dependence between average fertility and l<strong>on</strong>gevity was observed<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g lived part <str<strong>on</strong>g>of</str<strong>on</strong>g> experimental cohorts as <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein c<strong>on</strong>tent <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e diet<br />

changed. In order to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed phenomen<strong>on</strong> we suggest a mechanistic<br />

resource allocati<strong>on</strong> model. The model is fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resource allocati<strong>on</strong><br />

model proposed in [3]. The presence <str<strong>on</strong>g>of</str<strong>on</strong>g> a fertility-l<strong>on</strong>gevity trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f suggests<br />

a possibility <str<strong>on</strong>g>of</str<strong>on</strong>g> existence <str<strong>on</strong>g>of</str<strong>on</strong>g> some resource used bo<str<strong>on</strong>g>th</str<strong>on</strong>g> by reproducti<strong>on</strong> and somatic<br />

maintenance in a fly. The trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f may be a manifestati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic machinery,<br />

processes and genetically determined laws <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trol which define balance between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e processes <str<strong>on</strong>g>of</str<strong>on</strong>g> reproducti<strong>on</strong> and regenerati<strong>on</strong>. We propose and discuss a principle<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> dynamic resource allocati<strong>on</strong> which explains fertility-l<strong>on</strong>gevity data for <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g-,<br />

intermediate- and short-lived flies. Adaptive allocati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er resources<br />

allows flies to tailor <str<strong>on</strong>g>th</str<strong>on</strong>g>eir life history parameters to <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment. Due to<br />

limitati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e physiological adaptati<strong>on</strong> a significant share <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> may<br />

be genetically “preadapted” to different envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>us c<strong>on</strong>tributing<br />

to populati<strong>on</strong> stability and heterogeneity. This may be observed even in relatively<br />

homogeneous populati<strong>on</strong>s, such as experimental fly cohorts.<br />

References.<br />

[1] J.R.Carey, P.Liedo, L.Harshman, X.Liu, H.-G.Muller, L.Partridge, J.-L.Wang. Food pulses<br />

increase l<strong>on</strong>gevity and induce cyclical egg producti<strong>on</strong> in Mediterranean fruit flies, Functi<strong>on</strong>al<br />

Ecology 16 313–325 2002.<br />

[2] J.R.Carey, P.Liedo, H.-G.Muller, J.-L.Wang, J.W.Vaupel. Dual Modes <str<strong>on</strong>g>of</str<strong>on</strong>g> Aging in Mediterranean<br />

Fruit Fly Females, Science, 281 996–998 1998.<br />

[3] A.A.Romanyukha, J.R.Carey, A.S.Karkach, A.I.Yashin. The impact <str<strong>on</strong>g>of</str<strong>on</strong>g> diet switching <strong>on</strong> resource<br />

allocati<strong>on</strong> to reproducti<strong>on</strong> and l<strong>on</strong>gevity in Mediterranean fruitflies, Proc. R. Soc. L<strong>on</strong>d.<br />

B. 271 1319–1324 2004.<br />

476

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ilmari Kar<strong>on</strong>en<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Helsinki<br />

e-mail: ilmari.kar<strong>on</strong>en@helsinki.fi<br />

Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 11:00<br />

Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> polymorphism <strong>on</strong> a heterogeneous landscape<br />

The effect <str<strong>on</strong>g>of</str<strong>on</strong>g> spatial heterogeneity and habitat boundaries <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

multiple competing strains has been <str<strong>on</strong>g>of</str<strong>on</strong>g> recent interest as a novel mechanism for<br />

maintaining diversity above <str<strong>on</strong>g>th</str<strong>on</strong>g>e level predicted by <str<strong>on</strong>g>th</str<strong>on</strong>g>e competitive exclusi<strong>on</strong> principle.<br />

Given <str<strong>on</strong>g>th</str<strong>on</strong>g>at limited dispersal in heterogeneous landscapes can indeed enable<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e stable coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> more competitors <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are resources, a natural next<br />

step is to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence and stability <str<strong>on</strong>g>of</str<strong>on</strong>g> such diversity under evoluti<strong>on</strong>.<br />

I present some results from individual-based simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> evolving populati<strong>on</strong>s<br />

<strong>on</strong> a heterogeneous lattice landscape, and c<strong>on</strong>trast <str<strong>on</strong>g>th</str<strong>on</strong>g>ese wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some semi-analytical<br />

approximati<strong>on</strong>s, showing <str<strong>on</strong>g>th</str<strong>on</strong>g>at evoluti<strong>on</strong> in such systems can indeed lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> polymorphism and stabilize it against local extincti<strong>on</strong> due to demographic<br />

stochasticity.<br />

477

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

III; Tuesday, June 28, 17:00<br />

Khalid Kassara<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science,<br />

University Hassan II Casablanca, Morocco<br />

e-mail: kassarak@ams.org<br />

Amine Moustafid<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science,<br />

University Hassan II Casablanca, Morocco<br />

e-mail: moustafid_amine@yahoo.fr<br />

A c<strong>on</strong>trol approach for ODE cancer models<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, we investigate cancer by using a c<strong>on</strong>trol approach based <strong>on</strong> setvalued<br />

analysis and viability <str<strong>on</strong>g>th</str<strong>on</strong>g>eory, given a class <str<strong>on</strong>g>of</str<strong>on</strong>g> ODE tumor dynamics. We<br />

show how adequate selecti<strong>on</strong> procedures can lead to feedback protocols wi<str<strong>on</strong>g>th</str<strong>on</strong>g> which<br />

cancer cells are eradicated. In c<strong>on</strong>trast to <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal c<strong>on</strong>trol approach, our setvalued<br />

framework allows <str<strong>on</strong>g>of</str<strong>on</strong>g> highlighting <str<strong>on</strong>g>th</str<strong>on</strong>g>e well known c<strong>on</strong>necti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

initial cancer stage and its curability, as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e minimality and smoo<str<strong>on</strong>g>th</str<strong>on</strong>g>ness<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a protocol and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir impact <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e patient quality <str<strong>on</strong>g>of</str<strong>on</strong>g> life. Examples from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

literature are studied in order to illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e approach.<br />

References.<br />

[1] De Pillis, L. G., Gu, W., Fister, K. R., Head, T., Maples, K., Murugan, A., Neal, T., Yoshida,<br />

K., Chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy for tumors: an analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics and a study <str<strong>on</strong>g>of</str<strong>on</strong>g> quadratic and linear<br />

optimal c<strong>on</strong>trols, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci. 209(1), 292-315.<br />

[2] Hahndfeldt, P., Panigrahy, D., Folkman, J., Hlatky, L., Tumor development under angiogenic<br />

signaling: a dynamical <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, treatment resp<strong>on</strong>se, and postvascular<br />

dormancy, Cancer Res. 59(1999), 4770-4775.<br />

[3] K. Kassara, A Unified Set-valued Approach to C<strong>on</strong>trol Immuno<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, SIAM Journal <strong>on</strong><br />

C<strong>on</strong>trol and Optimizati<strong>on</strong>, 48(2009) 909-924.<br />

[4] K. Kassara, A. Moustafid, Feedback Protocol Laws for Immuno<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics, 7(2008), 2120033.<br />

[5] K. Kassara, A. Moustafid, Angiogenesis inhibiti<strong>on</strong> and tumor-immune interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy by a c<strong>on</strong>trol set-valued me<str<strong>on</strong>g>th</str<strong>on</strong>g>od, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences, to appear.<br />

478

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Joanna Kawka<br />

Bioquant, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Heidelberg, Heidelberg Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

and Humanities<br />

e-mail: joanna.kawka@bioquant.uni-heidelberg.de<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> β-catenin signaling in Medulloblastoma<br />

Medulloblastoma is a brain tumor <str<strong>on</strong>g>th</str<strong>on</strong>g>at mainly affects children and is caused by several<br />

mutati<strong>on</strong>s. Our research is devoted to understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> m<strong>on</strong>osomy<br />

and trisomy <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e 6 chromosome. Each perturbati<strong>on</strong> is characterized by extremely<br />

different prognosis. Trisomy is found to have a very bad prognosis and m<strong>on</strong>osomy<br />

surprisingly good after medical treatment. 6q loss and 6q gain are related wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

difference in expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cMyc, SGK1, which are target genes <str<strong>on</strong>g>of</str<strong>on</strong>g> β-catenin signaling<br />

in mutated cells. Our observati<strong>on</strong>s suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at disrupti<strong>on</strong> in chromosome<br />

balance str<strong>on</strong>gly affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e menti<strong>on</strong>ed signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanism<br />

is still not explained. We can <strong>on</strong>ly see c<strong>on</strong>sequences which result in different mRNA<br />

levels <str<strong>on</strong>g>of</str<strong>on</strong>g> cMyc and SGK1. It is also not well understood how <str<strong>on</strong>g>th</str<strong>on</strong>g>ese differences influence<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e prognosis. Thus investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> particular interacti<strong>on</strong>s between proteins<br />

is so interesting. We propose an ODE model describing complicated dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

chosen genes, c<strong>on</strong>cerning transcripti<strong>on</strong>, translati<strong>on</strong> as well as transport between<br />

cytoplasm and nucleus. We calibrate models based <strong>on</strong> clinical data for bo<str<strong>on</strong>g>th</str<strong>on</strong>g> types<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> medulloblastoma. Simulati<strong>on</strong>s lead to a better understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e process. In<br />

particularly, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model indicates <str<strong>on</strong>g>th</str<strong>on</strong>g>e important role <str<strong>on</strong>g>of</str<strong>on</strong>g> SGK1 gene in <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<strong>on</strong>cogene cMyc producti<strong>on</strong> leading to cancer relapse.<br />

479

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Toshiya Kazama<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Life Sciences, Hiroshima University<br />

e-mail: toshiya-kazama@hiroshima-u.ac.jp<br />

Takuya Okuno<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Life Sciences, Hiroshima University<br />

Kentaro Ito<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Life Sciences, Hiroshima University<br />

Toshiyuki Nakagaki<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex and Intelligent Systems, Future University<br />

Hakodate<br />

Ryo Kobayashi<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Life Sciences, Hiroshima University<br />

A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e mode transiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> locomoti<strong>on</strong><br />

in Amoeba proteus<br />

In amoeba locomoti<strong>on</strong>, pseudopods extend toward <str<strong>on</strong>g>th</str<strong>on</strong>g>e directi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> moti<strong>on</strong> [1]. Recently,<br />

we found <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e pseudopod <str<strong>on</strong>g>of</str<strong>on</strong>g> Amoeba proteus shows <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristic<br />

extensi<strong>on</strong> modes depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tail speed <str<strong>on</strong>g>of</str<strong>on</strong>g> amoeba. When <str<strong>on</strong>g>th</str<strong>on</strong>g>e tail speed is<br />

high, <str<strong>on</strong>g>th</str<strong>on</strong>g>e pseudopod extends at almost c<strong>on</strong>stant speed (Smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> mode.) On <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, when <str<strong>on</strong>g>th</str<strong>on</strong>g>e tail speed is low, <str<strong>on</strong>g>th</str<strong>on</strong>g>e pseudopod extends and stopps alternately<br />

(Oscillatory mode.) Namely, <str<strong>on</strong>g>th</str<strong>on</strong>g>e extensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pseudopod shows <str<strong>on</strong>g>th</str<strong>on</strong>g>e mode<br />

transiti<strong>on</strong> from <str<strong>on</strong>g>th</str<strong>on</strong>g>e smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> mode to <str<strong>on</strong>g>th</str<strong>on</strong>g>e oscillatory mode as <str<strong>on</strong>g>th</str<strong>on</strong>g>e tail speed decreases.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>venti<strong>on</strong>al understanding, <str<strong>on</strong>g>th</str<strong>on</strong>g>e tail c<strong>on</strong>tracti<strong>on</strong> was c<strong>on</strong>sidered to be <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

origin <str<strong>on</strong>g>of</str<strong>on</strong>g> motile force <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e locomoti<strong>on</strong> in Amoeba proteus [2]. Our finding suggests<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tail c<strong>on</strong>tracti<strong>on</strong> also c<strong>on</strong>tributes <str<strong>on</strong>g>th</str<strong>on</strong>g>e pseudopodial extensi<strong>on</strong> patterns which<br />

exhibit <str<strong>on</strong>g>th</str<strong>on</strong>g>e mode transiti<strong>on</strong>.<br />

To understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanism, we c<strong>on</strong>struct a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model. In our<br />

model, <str<strong>on</strong>g>th</str<strong>on</strong>g>e amoeba is described as an elastic tube in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e protoplasmic sol is<br />

c<strong>on</strong>fined. The locomoti<strong>on</strong> is driven by <str<strong>on</strong>g>th</str<strong>on</strong>g>e tail c<strong>on</strong>tracti<strong>on</strong>. The head is extended<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e inner pressure, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e velocity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e head is c<strong>on</strong>trolled by <str<strong>on</strong>g>th</str<strong>on</strong>g>e s<str<strong>on</strong>g>of</str<strong>on</strong>g>tness <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e head. Our model successfully represented <str<strong>on</strong>g>th</str<strong>on</strong>g>e mode transiti<strong>on</strong> from <str<strong>on</strong>g>th</str<strong>on</strong>g>e smoo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

mode to <str<strong>on</strong>g>th</str<strong>on</strong>g>e oscillatory mode as <str<strong>on</strong>g>th</str<strong>on</strong>g>e tail speed decreases.<br />

References.<br />

[1] McNeill, A. R., Exploring biomechanics: Animals in moti<strong>on</strong> W.H.Freeman and Company,<br />

New York, 1992.<br />

[2] S<strong>on</strong>obe, S., and Nishihara, E. Cell biology <str<strong>on</strong>g>of</str<strong>on</strong>g> Amoeba proteus. Jpn J Protozool, 37 159–167,<br />

2003.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling V; Saturday, July 2, 11:00<br />

Bogdan Kazmierczak<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research, Polish Academy<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

e-mail: bkazmier@ippt.gov.pl<br />

(1)<br />

Buffered calcium waves wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mechano-chemical effects<br />

We analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e following system <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s:<br />

∂c<br />

∂t<br />

∂2<br />

= D c + g(c) +<br />

∂x2 n<br />

Gi(c, vi) + R(c, θ, J1, J2)<br />

∂vi ∂<br />

= Di<br />

∂t 2<br />

∂x2 vi − Gi(c, vi), i = 1, . . . , n,<br />

(2)<br />

<br />

E<br />

0 = ∇ · ε +<br />

1 + ν<br />

ν<br />

1 − 2ν θI<br />

<br />

<br />

∂ε ∂θ<br />

+ µ1 + µ2 I + τ(c)I − ϑu.<br />

∂t ∂t<br />

i=1<br />

where c denotes <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> free cytosolic calcium i<strong>on</strong>s, vi <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e i-<str<strong>on</strong>g>th</str<strong>on</strong>g> buffer, ε <str<strong>on</strong>g>th</str<strong>on</strong>g>e strain tensor, u displacement field, τ active c<strong>on</strong>centrati<strong>on</strong><br />

stress resulting from <str<strong>on</strong>g>th</str<strong>on</strong>g>e actomyosin tracti<strong>on</strong> τ(c). We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e ratio<br />

(µ1 + µ2)/E is sufficiently small. We prove <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> travelling waves to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e above system, analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> viscosity <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e speed <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e wave and<br />

give <str<strong>on</strong>g>th</str<strong>on</strong>g>e explicit formulae for some specific soluti<strong>on</strong>s. We c<strong>on</strong>fine ourselves to <str<strong>on</strong>g>th</str<strong>on</strong>g>ree<br />

geometrical cases: bulk medium (large in every directi<strong>on</strong>), infinite plane layer <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

sufficiently small wid<str<strong>on</strong>g>th</str<strong>on</strong>g> and l<strong>on</strong>g cylinder <str<strong>on</strong>g>of</str<strong>on</strong>g> sufficiently small radius.<br />

This study was supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Polish Ministry <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Higher Educati<strong>on</strong><br />

grant N N 201548738 and Foundati<strong>on</strong> for Polish Science grant TEAM/2009-<br />

3/6.<br />

481

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> Macromolecules and Molecular Aggregates;<br />

Saturday, July 2, 14:30<br />

T. Keef<br />

e-mail: tk506@york.ac.uk<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> York<br />

D. Sal<str<strong>on</strong>g>th</str<strong>on</strong>g>ouse<br />

e-mail: dgs504@york.ac.uk<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> York<br />

R. Twarock<br />

e-mail: rt507@york.ac.uk<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> York, York YO10 5DD, U.K.<br />

Penrose-like tilings as geometric c<strong>on</strong>straints <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

structures <str<strong>on</strong>g>of</str<strong>on</strong>g> protein assemblies.<br />

N<strong>on</strong>-crystallographic symmetry is comm<strong>on</strong> in protein assemblies, from icosahedral<br />

symmetry in viral capsids to five-fold and seven-fold axial symmetry in<br />

C-reactive proteins and chaper<strong>on</strong>in molecules, respectively. We have shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e overall organisati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> such structures can be predicted using affine extensi<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-crystallographic symmetry. In particular, important insights can be gained<br />

not <strong>on</strong>ly into <str<strong>on</strong>g>th</str<strong>on</strong>g>e outer surfaces <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese clusters, but also in how symmetry is correlated<br />

at different radial levels. For example, in applicati<strong>on</strong>s to viruses, <str<strong>on</strong>g>th</str<strong>on</strong>g>is has<br />

led to <str<strong>on</strong>g>th</str<strong>on</strong>g>e discovery <str<strong>on</strong>g>of</str<strong>on</strong>g> a molecular scaling principle between different viral comp<strong>on</strong>ents.<br />

Here I will show <str<strong>on</strong>g>th</str<strong>on</strong>g>at Penrose-like n<strong>on</strong>-crystallographic tilings derived from<br />

higher dimensi<strong>on</strong>al lattices can be used to provide bounding boxes for proteins in<br />

n<strong>on</strong>-crystallographic assemblies.<br />

482

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Moving Organisms: From Individuals to Populati<strong>on</strong>s; Wednesday, June 29, 17:00<br />

Jan Kelkel<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stuttgart<br />

e-mail: Jan.Kelkel@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematik.uni-stuttgart.de<br />

Integrin mediated Cell Migrati<strong>on</strong>: Multiscale Models,<br />

Analysis and Numerics<br />

Invasi<strong>on</strong> is a key property <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells, whereby <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding<br />

tissue bo<str<strong>on</strong>g>th</str<strong>on</strong>g> enables <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells to move al<strong>on</strong>g tissue fibers and stimulates <str<strong>on</strong>g>th</str<strong>on</strong>g>e producti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> proteolytic enzymes <str<strong>on</strong>g>th</str<strong>on</strong>g>at destroy <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue network, <str<strong>on</strong>g>th</str<strong>on</strong>g>us enhancing cell<br />

migrati<strong>on</strong>. The product <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue degradati<strong>on</strong> is seen as a chemotactic signal<br />

influencing <str<strong>on</strong>g>th</str<strong>on</strong>g>e movement directi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells.<br />

Existing models for <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cells deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment but do not account for biochemical processes<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell or <strong>on</strong> its surface. This processes are however very important, since <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> receptors <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell surface and <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> structure are decisive<br />

in determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e speed <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e secreti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> proteolytic enzymes.<br />

We present a model incorporating <str<strong>on</strong>g>th</str<strong>on</strong>g>is subcellular mechanisms in a kinetic<br />

equati<strong>on</strong> for cell movement, which is <str<strong>on</strong>g>th</str<strong>on</strong>g>en supplemented by a reacti<strong>on</strong>-diffusi<strong>on</strong><br />

equati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e chemoattractant al<strong>on</strong>g wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an integro-differential equati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

tissue fibers. We <str<strong>on</strong>g>th</str<strong>on</strong>g>en address <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> existence and uniqueness <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>is str<strong>on</strong>gly coupled system <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s.<br />

This str<strong>on</strong>gly coupled and high dimensi<strong>on</strong>al model presents a real challenge<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e design <str<strong>on</strong>g>of</str<strong>on</strong>g> a suitable simulati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology. Selected simulati<strong>on</strong> results<br />

illustrate important phenomena <str<strong>on</strong>g>th</str<strong>on</strong>g>at arise in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model.<br />

483

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

David Kelly<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bristol<br />

e-mail: dk3531@bristol.ac.uk<br />

Karoline Wiesner<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bristol<br />

Mark Dillilngham<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bristol<br />

Andrew Huds<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Leicester<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to model (and quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity <str<strong>on</strong>g>of</str<strong>on</strong>g>)<br />

bio-molecular c<strong>on</strong>formati<strong>on</strong>al dynamics<br />

We present me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for inferring hidden Markov models from c<strong>on</strong>tinuous data clustered<br />

around discrete values wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out <str<strong>on</strong>g>th</str<strong>on</strong>g>e necessity <str<strong>on</strong>g>of</str<strong>on</strong>g> assuming a model architecture<br />

and as such are capable <str<strong>on</strong>g>of</str<strong>on</strong>g> inferring <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> degenerate states (states wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e same distributi<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e observable variable but different transiti<strong>on</strong> probabilities).<br />

The models inferred in <str<strong>on</strong>g>th</str<strong>on</strong>g>is way are provably optimal and minimal statistical<br />

predictors <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e data. Additi<strong>on</strong>ally, informati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretic measures applied to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

inferred model quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e data.<br />

The me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods have been dem<strong>on</strong>strated <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>formati<strong>on</strong>al dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Holliday<br />

(4 way DNA) juncti<strong>on</strong>s (under review - http://arxiv.org/abs/1011.2969) as<br />

investigated by fluorescence res<strong>on</strong>ance energy transfer spectroscopy. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are applicable to any data meeting certain criteria and as such may be<br />

applicable to many dynamical systems.<br />

484

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Harald Kempf<br />

Frankfurt Institute for Advanced Studies, Frankfurt, Germany<br />

e-mail: kempf@fias.uni-frankfurt.de<br />

Michael Meyer-Hermann<br />

Helmholtz Centre for Infecti<strong>on</strong> Research, Braunschweig, Germany<br />

e-mail: michael.meyer-hermann@helmholtz-hzi.de<br />

Optimising chemo- and radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic treatment protocols<br />

using synergy and tumour synchr<strong>on</strong>isati<strong>on</strong><br />

We present an agent-based approach to <str<strong>on</strong>g>th</str<strong>on</strong>g>e modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular dynamics wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in<br />

tumour spheroids under <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> combined chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy and radiati<strong>on</strong> treatment.<br />

Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in our agent-based approach cells are represented as instances <str<strong>on</strong>g>of</str<strong>on</strong>g> a C++<br />

cell-class which advance <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a realistic cell cycle in resp<strong>on</strong>se to external and<br />

internal stimuli such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> nutrients and <str<strong>on</strong>g>th</str<strong>on</strong>g>e pressure up<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cell by neighbouring cells. The model makes use <str<strong>on</strong>g>of</str<strong>on</strong>g> a dynamic Delaunay triangulati<strong>on</strong><br />

in order to derive <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell neighbourhood topology while its dual, a Vor<strong>on</strong>oi<br />

tessellati<strong>on</strong>, is employed in order to calculate <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tact surfaces between adjacent<br />

cells. Our model employs <str<strong>on</strong>g>th</str<strong>on</strong>g>e well-known linear quadratic model for irradiati<strong>on</strong><br />

damage in combinati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a stochastic model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell’s dynamic reacti<strong>on</strong> to<br />

damage.<br />

We can study <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour spheroids up to a volume <str<strong>on</strong>g>of</str<strong>on</strong>g> about 1mm 3<br />

which show a high degree <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity and can <str<strong>on</strong>g>th</str<strong>on</strong>g>us be used as a model system<br />

for larger amounts <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour tissue as <str<strong>on</strong>g>th</str<strong>on</strong>g>ey possess all properties which are present<br />

in large-scale tumours (hypoxic regi<strong>on</strong>s, necrosis, c<strong>on</strong>centrati<strong>on</strong> gradients). As a<br />

results <str<strong>on</strong>g>of</str<strong>on</strong>g> irradiati<strong>on</strong> treatment a dynamic reacti<strong>on</strong> is triggered in <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour system<br />

which can be studied in detail. Reoxygenati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour volume and a<br />

decrease in pressure due to cell necrosis lead to excessive regrow<str<strong>on</strong>g>th</str<strong>on</strong>g> after irradiati<strong>on</strong><br />

as previously quiescent cells are reactivated. A distinct resynchr<strong>on</strong>isati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell<br />

cycle is observed which can be exploited wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in fracti<strong>on</strong>ated irradiati<strong>on</strong> treatment<br />

or <str<strong>on</strong>g>th</str<strong>on</strong>g>e timed delivery <str<strong>on</strong>g>of</str<strong>on</strong>g> drugs.<br />

Using measured survival curves for single cell cycle phases we can show <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e amount <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour killing will str<strong>on</strong>gly depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e activati<strong>on</strong> status <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

tumour. A radiati<strong>on</strong>- or drug-induced synchr<strong>on</strong>isati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell cycle can be<br />

exploited to target <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour in an optimal state where <str<strong>on</strong>g>th</str<strong>on</strong>g>e sensitivity to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

planed treatment is maximal. Thus we can calculate treatment protocols which<br />

will result in a greatly enhanced amount <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour killing for <str<strong>on</strong>g>th</str<strong>on</strong>g>e same dose <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

radiati<strong>on</strong> or drug.<br />

Combining medicati<strong>on</strong> and radiati<strong>on</strong> treatment in our simulati<strong>on</strong> we can show<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour can be optimally prepared to increase <str<strong>on</strong>g>th</str<strong>on</strong>g>e radiosensitivity during<br />

following treatments. Vice versa <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are optimal points to employ chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

after irradiati<strong>on</strong> sessi<strong>on</strong>s.<br />

References.<br />

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[1] H. Kempf and M. Bleicher and M. Meyer-Hermann, Spatio-temporal cell dynamics in tumour<br />

spheroid irradiati<strong>on</strong> <str<strong>on</strong>g>European</str<strong>on</strong>g> Physical Journal D 60 177–193 (2010).<br />

[2] G. Schaller and M. Meyer-Hermann, Multicellular Tumor Spheroid in an <str<strong>on</strong>g>of</str<strong>on</strong>g>f-lattice<br />

Vor<strong>on</strong>oi/Delaunay cell model Physical Review E 71 51910–16 (2005).<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> Macromolecules and Molecular Aggregates;<br />

Saturday, July 2, 14:30<br />

Richard Kerner<br />

University Pierre et Marie Curie (Paris-VI), Paris, France<br />

e-mail: richard.kerner@upmc.fr<br />

Discrete groups and internal symmetries <str<strong>on</strong>g>of</str<strong>on</strong>g> icosahedral<br />

capsids.<br />

The Caspar-Klug classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> icosahedral capsids [1] takes into account <strong>on</strong>ly<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir size, given by <str<strong>on</strong>g>th</str<strong>on</strong>g>e triangular number T = p + pq + q. It can also note <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

difference between chiral and n<strong>on</strong>-chiral capsids. But it does not take into account<br />

more subtle differences resulting from <str<strong>on</strong>g>th</str<strong>on</strong>g>e differentiati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> coat proteins serving as<br />

elementary blocks from which capsids are assembled by agglomerati<strong>on</strong>. [2], [3]. We<br />

develop fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> icosahedral capsids introduced a few years ago<br />

[4], [5], using <str<strong>on</strong>g>th</str<strong>on</strong>g>e symmetry group acti<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e elementary triangles<br />

We analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e differentiati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> coat proteins forming an icosahedral viral<br />

capsid wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a given triangular number T. A typical icosahedral capsid can be subdivided<br />

into twelve pentag<strong>on</strong>s and 10(T-1) hexag<strong>on</strong>s, which can be realized ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

as genuine hexamers, or as a combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dimers or trimers.We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

pentamers, which are found in twelve vertices <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e capsid, display five identical<br />

sides. This is usually <str<strong>on</strong>g>th</str<strong>on</strong>g>e case, except for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Papovaviridae family in which all pentamers<br />

are maximally differentiated, displaying five different sides (abcde) instead<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> five identical <strong>on</strong>es (aaaaa).<br />

Hexamers can display various degrees <str<strong>on</strong>g>of</str<strong>on</strong>g> differentiati<strong>on</strong>. The symmetry imposes<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>eir sides can be ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>of</str<strong>on</strong>g> two types, or <str<strong>on</strong>g>th</str<strong>on</strong>g>ree types, or six different<br />

types: (ababab), (abcabc) or (abcdef), respectively, because 6 is divisible by 2, 3<br />

and 6. These cases have been discussed in our previous work, and enabled us to<br />

introduce four internal symmetry classes in capsid viruses, according to <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence<br />

or absence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e aforementi<strong>on</strong>ed hexamer types. The full informati<strong>on</strong> about<br />

a given icosahedral capsid structure can be read from <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e twenty identical<br />

triangular faces. The first hexamer type, (ababab) is fouund <strong>on</strong>ly in triangles’s<br />

centers, because <str<strong>on</strong>g>of</str<strong>on</strong>g> its <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-fold symmetry; <str<strong>on</strong>g>th</str<strong>on</strong>g>e type (abcabc) can be found at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

edges <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e triangular face, and maximally differentiated hexamers (abcdef) can<br />

be found in any positi<strong>on</strong>.<br />

However, a more subtle analysis can be made if o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hexamer types are taken<br />

into account. The partiti<strong>on</strong> into 2, 3 or 6 different sides must be maintained,<br />

but <str<strong>on</strong>g>th</str<strong>on</strong>g>e two (ab) and <str<strong>on</strong>g>th</str<strong>on</strong>g>ree (abc) proteins can be placed differently in a hexamer,<br />

e.g. like (aaabbb) instead <str<strong>on</strong>g>of</str<strong>on</strong>g> (ababab), or (aabbab); <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ree different proteins<br />

(abc) can be displayed as (abccba) instead <str<strong>on</strong>g>of</str<strong>on</strong>g> (abcabc), generating even instead<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> chiral symmetry around <str<strong>on</strong>g>th</str<strong>on</strong>g>e edge. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese new c<strong>on</strong>figurati<strong>on</strong>s included, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> icosahedral capsids becomes more complete.<br />

We also show how <str<strong>on</strong>g>th</str<strong>on</strong>g>e capsids agglomerate in a way <str<strong>on</strong>g>th</str<strong>on</strong>g>at always minimizes <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> different proteins needed for <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>structi<strong>on</strong>. This is being illustrated <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e examples provided by <str<strong>on</strong>g>th</str<strong>on</strong>g>e herpesvirus (T=16) and human adenovirus (T=25).<br />

Our classificati<strong>on</strong> gives some extra hints c<strong>on</strong>cerning genetic proximity <str<strong>on</strong>g>of</str<strong>on</strong>g> viruses<br />

displaying similar classes <str<strong>on</strong>g>of</str<strong>on</strong>g> capsid symmetries.<br />

487

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

References.<br />

[1] Caspar, D.L.D., Klug A., 1962, Symp. Quant. Biol. bf 27, 1.<br />

[2] Zlotnick, A. 1994, J. Mol. Biology bf 241, pp. 59-67<br />

[3] R. Kerner, Models <str<strong>on</strong>g>of</str<strong>on</strong>g> agglomerati<strong>on</strong> and glass transiti<strong>on</strong>, Imperial College Press, (2007)<br />

[4] R. Kerner, it Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Medicine, Vol. 6 (2), p.95-97 (2005)<br />

[5] R. Kerner, it Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Medicine, Vol. 9 (3,4), p.175-181 (2008)<br />

488

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Helen Kettle<br />

Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics Scotland<br />

e-mail: helen@bioss.ac.uk<br />

Petra Louis<br />

Rowett Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Nutriti<strong>on</strong> and Heal<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Harry Flint<br />

Rowett Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Nutriti<strong>on</strong> and Heal<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Ruairi D<strong>on</strong>nelly<br />

Heriot Watt University<br />

Grietje Holtrop<br />

Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics Scotland<br />

Glenn Mari<strong>on</strong><br />

Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics Scotland<br />

Ecosystems Dynamics; Tuesday, June 28, 14:30<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e Emergent Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Microbial<br />

Communities in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Human Col<strong>on</strong><br />

Modelling microbial ecosystem dynamics in <str<strong>on</strong>g>th</str<strong>on</strong>g>e human col<strong>on</strong> is challenging due to<br />

large variati<strong>on</strong>s between individuals and limited amounts <str<strong>on</strong>g>of</str<strong>on</strong>g> data. In an attempt to<br />

overcome <str<strong>on</strong>g>th</str<strong>on</strong>g>ese issues we take a complex adaptive systems (CAS) approach to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

problem. Thus a model is developed in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e dominant bacterial strains are not<br />

defined a priori but are allowed to ’emerge’ from a stochastically generated bacterial<br />

populati<strong>on</strong>. To do <str<strong>on</strong>g>th</str<strong>on</strong>g>is we begin by assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>at every bacterial strain falls into<br />

<strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> ten bacterial functi<strong>on</strong>al groups (BFGs) which are distinguished by <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir preferred pH ranges. The metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways form<br />

a network which determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e dietary substrates each BFG grows <strong>on</strong> and which<br />

metabolites it may c<strong>on</strong>sume or produce. The parameters c<strong>on</strong>trolling <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact rates<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> transfer al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>ese pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e preferred pH ranges are <str<strong>on</strong>g>th</str<strong>on</strong>g>en generated<br />

stochastically, wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in appropriate limits, for a populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> 300 bacterial strains.<br />

The rates <str<strong>on</strong>g>of</str<strong>on</strong>g> change <str<strong>on</strong>g>of</str<strong>on</strong>g> mass <str<strong>on</strong>g>of</str<strong>on</strong>g> each strain, resource and metabolite are computed<br />

by solving a system <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary differential equati<strong>on</strong>s. Due to competiti<strong>on</strong> for<br />

resources, and interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolic network, some strains will flourish<br />

and some will disappear, such <str<strong>on</strong>g>th</str<strong>on</strong>g>at over time a viable community for <str<strong>on</strong>g>th</str<strong>on</strong>g>e given<br />

envir<strong>on</strong>ment emerges. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong>s governing <str<strong>on</strong>g>th</str<strong>on</strong>g>e model are described<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e model results are compared to data from a fermentor study which examines<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> pH <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microbial community. We <str<strong>on</strong>g>th</str<strong>on</strong>g>en dem<strong>on</strong>strate how <str<strong>on</strong>g>th</str<strong>on</strong>g>is CAS<br />

modelling approach allows <str<strong>on</strong>g>th</str<strong>on</strong>g>e system to adapt to its envir<strong>on</strong>ment <str<strong>on</strong>g>th</str<strong>on</strong>g>rough species<br />

successi<strong>on</strong> and investigate different mechanisms for avoiding competitive exclusi<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e BFGs.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Evgeniy Khain<br />

Oakland University<br />

e-mail: khain@oakland.edu<br />

Y. T. Lin<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Michigan<br />

L. M. Sander<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Michigan<br />

Populati<strong>on</strong> Dynamics; Wednesday, June 29, 08:30<br />

Role <str<strong>on</strong>g>of</str<strong>on</strong>g> fluctuati<strong>on</strong>s in fr<strong>on</strong>t propagati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e insect outbreak<br />

model<br />

Propagating fr<strong>on</strong>ts arising from bistable reacti<strong>on</strong> diffusi<strong>on</strong> equati<strong>on</strong>s are a purely<br />

deterministic effect. Stochastic reacti<strong>on</strong> diffusi<strong>on</strong> processes also show fr<strong>on</strong>t propagati<strong>on</strong><br />

which coincides wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic effect in <str<strong>on</strong>g>th</str<strong>on</strong>g>e limit <str<strong>on</strong>g>of</str<strong>on</strong>g> small fluctuati<strong>on</strong>s<br />

(usually, large populati<strong>on</strong>s). However, for larger fluctuati<strong>on</strong>s propagati<strong>on</strong> can be<br />

affected. We give an example, based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e classic spruce-budworm model, where<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e directi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> wave propagati<strong>on</strong>, i.e., <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative stability <str<strong>on</strong>g>of</str<strong>on</strong>g> two phases, can be<br />

reversed by fluctuati<strong>on</strong>s.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

C<strong>on</strong>necting microscale and macroscale models <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular migrati<strong>on</strong>;<br />

Tuesday, June 28, 17:00<br />

Evgeniy Khain<br />

Oakland University<br />

e-mail: khain@oakland.edu<br />

Le<strong>on</strong>ard Sander<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Michigan<br />

Fr<strong>on</strong>ts <str<strong>on</strong>g>of</str<strong>on</strong>g> cells invading a wound: from discrete stochastic<br />

approach to c<strong>on</strong>tinuum descripti<strong>on</strong><br />

We present a stochastic model <str<strong>on</strong>g>th</str<strong>on</strong>g>at describes fr<strong>on</strong>ts <str<strong>on</strong>g>of</str<strong>on</strong>g> cells invading a wound. In<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e model, cells can migrate, proliferate, and experience cell-cell adhesi<strong>on</strong>. We find<br />

several qualitatively different regimes <str<strong>on</strong>g>of</str<strong>on</strong>g> fr<strong>on</strong>t moti<strong>on</strong> and analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e transiti<strong>on</strong>s<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>em. Above a critical value <str<strong>on</strong>g>of</str<strong>on</strong>g> adhesi<strong>on</strong> and for small proliferati<strong>on</strong>, large<br />

isolated clusters are formed ahead <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fr<strong>on</strong>t. This is mapped <strong>on</strong>to <str<strong>on</strong>g>th</str<strong>on</strong>g>e well-known<br />

ferromagnetic phase transiti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ising model. The results are compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

experiments, and possible directi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> future work are proposed. We also focus <strong>on</strong> a<br />

c<strong>on</strong>tinuum descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is phenomen<strong>on</strong> by means <str<strong>on</strong>g>of</str<strong>on</strong>g> a generalized Cahn-Hilliard<br />

equati<strong>on</strong> (GCH) wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a proliferati<strong>on</strong> term. As in <str<strong>on</strong>g>th</str<strong>on</strong>g>e discrete model, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are two<br />

interesting regimes. For subcritical adhesi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are propagating "pulled" fr<strong>on</strong>ts,<br />

similarly to <str<strong>on</strong>g>th</str<strong>on</strong>g>ose <str<strong>on</strong>g>of</str<strong>on</strong>g> Fisher-Kolmogorov equati<strong>on</strong>. The problem <str<strong>on</strong>g>of</str<strong>on</strong>g> fr<strong>on</strong>t velocity<br />

selecti<strong>on</strong> is examined, and our <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical predicti<strong>on</strong>s are in a good agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

a numerical soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e GCH equati<strong>on</strong>. For supercritical adhesi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a<br />

n<strong>on</strong>trivial transient behavior, where density pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile exhibits a sec<strong>on</strong>dary peak. The<br />

results <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tinuum and discrete models are in a good agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e different regimes we analyzed.<br />

491

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Afifa Iftikhar, Mudassar Imran, Adnan Khan<br />

Lahore University <str<strong>on</strong>g>of</str<strong>on</strong>g> Management Sciences, Lahore, Pakistan<br />

A Stochastic Model for Calcium Regulati<strong>on</strong> in Spines<br />

The study <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium signals in dendritic spines is <str<strong>on</strong>g>of</str<strong>on</strong>g> great interest, as <str<strong>on</strong>g>th</str<strong>on</strong>g>ese by ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

acti<strong>on</strong> potential or by synaptic activity play a crucial role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e synaptic plasticity<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in an individual spine. Because <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e small size <str<strong>on</strong>g>of</str<strong>on</strong>g> spine and <str<strong>on</strong>g>th</str<strong>on</strong>g>e indicators<br />

comm<strong>on</strong>ly used to measure spine calcium activity, calcium functi<strong>on</strong> can be severely<br />

disrupted. Therefore, it is very difficult to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact relati<strong>on</strong>ship between<br />

spine geometry and spine calcium dynamics. Recently, it has been suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e medium range <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium which induces l<strong>on</strong>g term potentiati<strong>on</strong> leads to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

structural stability stage <str<strong>on</strong>g>of</str<strong>on</strong>g> spines, while very low or very high amount <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium<br />

leads to <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g term depressi<strong>on</strong> stage which results in shortening and eventually<br />

pruning <str<strong>on</strong>g>of</str<strong>on</strong>g> spines. We discuss a stochastic model to examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms <str<strong>on</strong>g>th</str<strong>on</strong>g>at govern its regulati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e spine morphology.<br />

492

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Saturday, July 2, 08:30<br />

Amjad Khan<br />

Nati<strong>on</strong>al University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences and Technology (NUST), School <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Civil and envir<strong>on</strong>mental Engineering (SCEE), NUST Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Civil<br />

Engineering (NICE), Sector H-12, Islamabad, Pakistan.<br />

e-mail: za ¯ amjad@yahoo.com<br />

Rahmat Ali Khan<br />

Centre for Advanced Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Physics, Nati<strong>on</strong>al University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences and Technology(NUST), Sector H-12, Islamabad, Pakistan<br />

e-mail: rahmat ¯ alipk@yahoo.com<br />

Takenori Takada<br />

Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Envir<strong>on</strong>mental Ear<str<strong>on</strong>g>th</str<strong>on</strong>g> Science, Hokkaido University,<br />

Kita-ku, Sapporo 060-0810, Japan.<br />

e-mail: takada@ees.hokudai.ac.jp<br />

Homotopy perturbati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for traveling wave soluti<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> system <str<strong>on</strong>g>of</str<strong>on</strong>g> biological reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong>s<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper, we apply a technique which is called homotopy perturbati<strong>on</strong><br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>od (HPM) for obtaining analytical approximate traveling wave soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

system <str<strong>on</strong>g>of</str<strong>on</strong>g> biological reacti<strong>on</strong> diffusi<strong>on</strong> equati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e type<br />

(1)<br />

St = εSxx − νSx − f(S)P,<br />

Pt = Pxx − νPx + [f(S) − K]P.<br />

Biological reacti<strong>on</strong> diffusi<strong>on</strong> equati<strong>on</strong>s are used as ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for several<br />

problems in biology and chemistry. For example (1) was used as a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model for microbial grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and competiti<strong>on</strong> in a flow reactor. The <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

reacti<strong>on</strong>-diffusi<strong>on</strong> waves started in <str<strong>on</strong>g>th</str<strong>on</strong>g>e 1930s, initial works was carried out in populati<strong>on</strong><br />

dynamics, combusti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eory and chemical kinetics. Nowadays, it is a well<br />

developed area <str<strong>on</strong>g>of</str<strong>on</strong>g> research. This includes qualitative properties <str<strong>on</strong>g>of</str<strong>on</strong>g> traveling waves<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e scalar reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong> and for system <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s, complex n<strong>on</strong>linear<br />

dynamics, numerous applicati<strong>on</strong>s in physics, chemistry, biology and medicine.<br />

Existence <str<strong>on</strong>g>of</str<strong>on</strong>g> traveling waves reflects <str<strong>on</strong>g>th</str<strong>on</strong>g>e important phenomena <str<strong>on</strong>g>of</str<strong>on</strong>g> wave propagati<strong>on</strong><br />

and has extensively studied by many au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors. The homotopy perturbati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od<br />

(HPM) proposed by Ji-Huan He in 1998 is a me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for finding approximate soluti<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-linear differential and integral equati<strong>on</strong>s. This me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is popular<br />

am<strong>on</strong>gst n<strong>on</strong>-ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematician and engineers because HPM decomposes a complex<br />

problem under study to a series <str<strong>on</strong>g>of</str<strong>on</strong>g> simple problems <str<strong>on</strong>g>th</str<strong>on</strong>g>at are easy to be solved. The<br />

results obtained reveal <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e homotopy perturbati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is effective and<br />

simple. Some plots are presented to c<strong>on</strong>firm <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical results.<br />

493

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Nino Khatiashvili<br />

Iv. Javakhishvili Tbilisi State University<br />

e-mail: ninakhat@yahoo.com<br />

Christina Pirumova<br />

Iv. Javakhishvili Tbilisi State University<br />

e-mail: chr4mk@gmail.com<br />

Vladimer Akhobadze<br />

Iv. Javakhishvili Tbilisi State University<br />

e-mail: vakhobadze@gmail.com<br />

Cancer; Wednesday, June 29, 08:30<br />

The n<strong>on</strong>-linear ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> tumors <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

different forms<br />

The ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is c<strong>on</strong>structed taking into <str<strong>on</strong>g>th</str<strong>on</strong>g>e account<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e competiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> normal and tumor cells for <str<strong>on</strong>g>th</str<strong>on</strong>g>e nutrients supply and new vessels<br />

formati<strong>on</strong> under oxygenal stress. The character <str<strong>on</strong>g>of</str<strong>on</strong>g> different geometry <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is c<strong>on</strong>sidered (such as cylindrical and spherical). The system <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-linear<br />

differential equati<strong>on</strong>s is obtained<br />

dx<br />

2<br />

= g1x 3 − ν1y,<br />

dt<br />

dy<br />

dt = g2y α − ν2y,<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial c<strong>on</strong>diti<strong>on</strong>s<br />

x(0) = x0, y(0) = y0,<br />

where x(t) is <str<strong>on</strong>g>th</str<strong>on</strong>g>e volume <str<strong>on</strong>g>of</str<strong>on</strong>g> normal cells, y(t)- is <str<strong>on</strong>g>th</str<strong>on</strong>g>e volume <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cells, which<br />

depends <strong>on</strong> time t, a and b are <str<strong>on</strong>g>th</str<strong>on</strong>g>e nutrients c<strong>on</strong>sumpti<strong>on</strong> rates, g1, g2 are <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> velocity <str<strong>on</strong>g>of</str<strong>on</strong>g> x(t) and y(t) c<strong>on</strong>sequently, ν1 and ν2 reflects a necrotic factors,<br />

α is a geometric characteristic <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor volume.<br />

The system is investigated numerically, computer simulati<strong>on</strong>s are given.<br />

The designated project has been fulfilled by financial support <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Georgia<br />

Rustaveli Foundati<strong>on</strong> (Grant #GNSF/ST08/3-395). Any idea in <str<strong>on</strong>g>th</str<strong>on</strong>g>is publicati<strong>on</strong><br />

is possessed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e au<str<strong>on</strong>g>th</str<strong>on</strong>g>or and may not represent <str<strong>on</strong>g>th</str<strong>on</strong>g>e opini<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Foundati<strong>on</strong><br />

itself.<br />

494

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biomechanical regulati<strong>on</strong> in b<strong>on</strong>e tissue (Sessi<strong>on</strong><br />

II); Wednesday, June 29, 11:00<br />

Hanifeh Khayyeri<br />

Trinity Centre for Bioengineering, School <str<strong>on</strong>g>of</str<strong>on</strong>g> Engineering, Trinity<br />

College Dublin, Dublin, Ireland<br />

e-mail: khayyerh@tcd.ie<br />

Patrick J. Prendergast<br />

Trinity Centre for Bioengineering, School <str<strong>on</strong>g>of</str<strong>on</strong>g> Engineering, Trinity<br />

College Dublin, Dublin, Ireland<br />

e-mail: pprender@tcd.ie<br />

Evoluti<strong>on</strong>ary simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

mechano-regulated endoch<strong>on</strong>dral healing process<br />

The ability <str<strong>on</strong>g>of</str<strong>on</strong>g> tissues to adapt to <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical envir<strong>on</strong>ment is a remarkable<br />

feature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e skelet<strong>on</strong>. Several mechano-regulati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eories have been proposed<br />

for describing how <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical envir<strong>on</strong>ment modulates mesenchymal stem cell<br />

differentiati<strong>on</strong> into b<strong>on</strong>e, cartilage and fibrous tissue. Despite <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological complexity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e process, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese <str<strong>on</strong>g>th</str<strong>on</strong>g>eories have <str<strong>on</strong>g>of</str<strong>on</strong>g>ten been able to predict osseous healing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough bo<str<strong>on</strong>g>th</str<strong>on</strong>g> membraneous and ch<strong>on</strong>dral healing, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> reas<strong>on</strong>able success [1,2].<br />

It is intriguing to w<strong>on</strong>der about <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese healing processes, in<br />

particular <str<strong>on</strong>g>th</str<strong>on</strong>g>e endoch<strong>on</strong>dral ossificati<strong>on</strong> process, in evoluti<strong>on</strong> and whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> mechano-regulati<strong>on</strong> has been involved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> new healing processes<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough natural selecti<strong>on</strong>. Early vertebrates, like cartilaginous fishes, could<br />

modulate <str<strong>on</strong>g>th</str<strong>on</strong>g>eir tissues to <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical envir<strong>on</strong>ment and it is likely <str<strong>on</strong>g>th</str<strong>on</strong>g>at evoluti<strong>on</strong><br />

worked wi<str<strong>on</strong>g>th</str<strong>on</strong>g> adapting <str<strong>on</strong>g>th</str<strong>on</strong>g>e skeletal tissues to <str<strong>on</strong>g>th</str<strong>on</strong>g>e local c<strong>on</strong>diti<strong>on</strong>s ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an<br />

involving major changes in cells or tissue types [3].<br />

This study shows how <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechano-regulated endoch<strong>on</strong>dral ossificati<strong>on</strong> process<br />

could have emerged in evoluti<strong>on</strong> by being favoured in natural selecti<strong>on</strong>. The<br />

combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a mechano-regulated tissue differentiati<strong>on</strong> model [4] and a genetic<br />

algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m for simulating evoluti<strong>on</strong>ary change [5], used in <str<strong>on</strong>g>th</str<strong>on</strong>g>is investigati<strong>on</strong>, was<br />

fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er able to capture inter-populati<strong>on</strong> variability in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechano-regulated resp<strong>on</strong>se<br />

and arrived at results <str<strong>on</strong>g>th</str<strong>on</strong>g>at are in agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental studies <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

mechano-regulated differentiati<strong>on</strong> and maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e [6,7].<br />

References.<br />

[1] H. Isakss<strong>on</strong> et al., 2006 Corroborati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanoregulatory algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms for tissue differentiati<strong>on</strong><br />

during fracture healing: Comparis<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> in vivo results J. Or<str<strong>on</strong>g>th</str<strong>on</strong>g>op Res. 24 898–907.<br />

[2] H. Khayyeri et al., 2009,Corroborati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanobiological simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue differentiati<strong>on</strong><br />

in an in vivo b<strong>on</strong>e chamber using a lattice-modeling approach J. Or<str<strong>on</strong>g>th</str<strong>on</strong>g>op Res. 27<br />

1659–1666.<br />

[3] B. K. Hall, 2005, B<strong>on</strong>es and cartilage: developmental and evoluti<strong>on</strong>ary skeletal biology San<br />

Diego, Elsevier Academic Press.<br />

[4] P. J. Prendergast et al., 1997, Biophysical stimuli <strong>on</strong> cells during tissue differentiati<strong>on</strong> at<br />

implant interfaces J. Biomech. 30 539–548.<br />

[5] N. Nowlan and P. J. Prendergast, 2005, Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanoregulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> will<br />

lead to n<strong>on</strong>-optimal b<strong>on</strong>e phenotypes J. Theor. Biol. 235 408–418.<br />

[6] E. F. Morgan et al., 2010, Correlati<strong>on</strong>s between local strains and tissue phenotypes in an<br />

experimental model <str<strong>on</strong>g>of</str<strong>on</strong>g> skeletal healing] J. Biomech. 43 2418–2424.<br />

[7] U. Meyer et al., 2001, Tissue differentiati<strong>on</strong> and cytokine syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis during strain-related b<strong>on</strong>e<br />

formati<strong>on</strong> in distracti<strong>on</strong> osteogenesis Br. J. Oral Maxill<str<strong>on</strong>g>of</str<strong>on</strong>g>ac. Surg. 39 22–29.<br />

495

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Eunjung Kim<br />

e-mail: Eunjung.Kim@m<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt.org<br />

David Basanta<br />

e-mail: david@basanta.org.es<br />

Keiran S. Smalley<br />

e-mail: Keiran.Smalley@m<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt.org<br />

Alexander R. A. Anders<strong>on</strong><br />

e-mail: Alexander.Anders<strong>on</strong>@m<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt.org<br />

Integrated Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Oncology,<br />

M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center,<br />

12902 Magnolia Dr., Tampa, FL 33612.<br />

Cancer; Wednesday, June 29, 08:30<br />

Getting old and misbehaving:<br />

Can stromal aging drive melanoma initiati<strong>on</strong>?<br />

We have implemented a hybrid cellular automata model <str<strong>on</strong>g>of</str<strong>on</strong>g> skin <str<strong>on</strong>g>th</str<strong>on</strong>g>at focuses<br />

<strong>on</strong> key variables implicated in <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> normal homeostatic skin functi<strong>on</strong><br />

and its disrupti<strong>on</strong> in melanoma initiati<strong>on</strong> and progressi<strong>on</strong>. The model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> discrete cellular species such as melanocytes, transformed melanocytes, keratinocytes,<br />

and fibroblasts, and c<strong>on</strong>tinuous microenvir<strong>on</strong>mental variables such as<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factors and extracellular matrix. The behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> each <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e discrete cell<br />

species is defined using life cycle flowcharts. Based <strong>on</strong> experimental observati<strong>on</strong>s,<br />

we know <str<strong>on</strong>g>th</str<strong>on</strong>g>at when fibroblasts age <str<strong>on</strong>g>th</str<strong>on</strong>g>ey can become senescent and start producing<br />

factors <str<strong>on</strong>g>th</str<strong>on</strong>g>at may disrupt <str<strong>on</strong>g>th</str<strong>on</strong>g>e very homeostasis <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey should maintain. We incorporate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese phenotypic changes as fibroblasts age and use our model to examine<br />

how <str<strong>on</strong>g>th</str<strong>on</strong>g>ese changes affect skin functi<strong>on</strong>.<br />

Specifically, we examined <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> disrupting interacti<strong>on</strong>s between melanocytes,<br />

keratinocytes, fibroblasts and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir microenvir<strong>on</strong>ment and <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> aged fibroblasts<br />

in driving melanoma initiati<strong>on</strong>. Model simulati<strong>on</strong>s provide a series <str<strong>on</strong>g>of</str<strong>on</strong>g> virtual<br />

skin pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologies <str<strong>on</strong>g>th</str<strong>on</strong>g>at readily recapitulate a spectrum <str<strong>on</strong>g>of</str<strong>on</strong>g> true aberrant clinical<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologies. Direct comparis<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>ese pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologies allowed us to find <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

critical perturbati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at drive melanoma initiati<strong>on</strong> and progressi<strong>on</strong>. We also utilize<br />

an in vitro 3D organotypic skin model to fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er investigate some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

predicti<strong>on</strong>s.<br />

496

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Multiscale modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: from physical tools to<br />

applicati<strong>on</strong>s in cancer modeling I; Saturday, July 2, 08:30<br />

Yangjin Kim<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Michigan<br />

e-mail: yangjink@umd.umich.edu<br />

The role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microenvir<strong>on</strong>ment in an early development<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> breast cancer: a hybrid (multiscale) model.<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and computati<strong>on</strong>al analysis are essential for understanding<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex gene networks <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trol normal development<br />

and homeostasis, and can help to understand how circumventi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trol<br />

leads to abnormal outcomes such as cancer. Tumor microenvir<strong>on</strong>ment (TME) is<br />

comprised <str<strong>on</strong>g>of</str<strong>on</strong>g> various signaling molecules, cell types and <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular matrix.<br />

We investigate how <str<strong>on</strong>g>th</str<strong>on</strong>g>e local biochemical and mechanical microenvir<strong>on</strong>ment can affect<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e progressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> potentially-cancerous cells in an early development <str<strong>on</strong>g>of</str<strong>on</strong>g> breast<br />

cancer. The model deals wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microenvir<strong>on</strong>ment<br />

<strong>on</strong> tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, and we report results from a multi-scale model<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways and <str<strong>on</strong>g>th</str<strong>on</strong>g>e TME. The results emphasize <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexities <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e TME and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir effect <strong>on</strong> tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, and show <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

tumor progressi<strong>on</strong> is not solely determined by <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> a cl<strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> mutated<br />

immortal cells, but ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>at it is communityc<strong>on</strong>trolled.<br />

497

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Mechanical Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Movement and Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cells and Tissues I;<br />

Wednesday, June 29, 14:30<br />

Yangjin Kim<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Michigan<br />

e-mail: yangjink@umd.umich.edu<br />

The role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microenvir<strong>on</strong>ment in tumor invasi<strong>on</strong>: a<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model<br />

Glioma cells tend to migrate from <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary tumor into <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding tissue.<br />

We develop a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model which includes <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> adhesi<strong>on</strong> and mechanical<br />

interacti<strong>on</strong> between glioma cells and collagen network. Simulati<strong>on</strong> results show<br />

cell migrati<strong>on</strong> behavior <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular matrix using informati<strong>on</strong> from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e complex fibrous structure. We also take into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular signals<br />

at each cell site for <str<strong>on</strong>g>th</str<strong>on</strong>g>is cell migrati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e ECM. We c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e detailed<br />

mechanical interacti<strong>on</strong>s between cells and between a cell and <str<strong>on</strong>g>th</str<strong>on</strong>g>e collagen fibers in<br />

additi<strong>on</strong> to reacti<strong>on</strong>-diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> molecules.<br />

498

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Modeling physiological systems: model validati<strong>on</strong> and experimental design<br />

issues; Wednesday, June 29, 11:00<br />

Julian King<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e University <str<strong>on</strong>g>of</str<strong>on</strong>g> Vienna and<br />

Brea<str<strong>on</strong>g>th</str<strong>on</strong>g> Research Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Austrian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

Nordbergstr. 15, A-1090 Wien, Austria<br />

e-mail: julian.king@oeaw.ac.at<br />

Karl Unterk<str<strong>on</strong>g>of</str<strong>on</strong>g>ler<br />

Vorarlberg University <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Sciences and<br />

Brea<str<strong>on</strong>g>th</str<strong>on</strong>g> Research Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Austrian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

Hochschulstr. 1, A-6850 Dornbirn, Austria<br />

e-mail: karl.unterk<str<strong>on</strong>g>of</str<strong>on</strong>g>ler@fhv.at<br />

Helin Koç<br />

Vorarlberg University <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Sciences<br />

Hochschulstr. 1, A-6850 Dornbirn, Austria<br />

e-mail: helin.koc@fhv.at<br />

Gerald Teschl<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e University <str<strong>on</strong>g>of</str<strong>on</strong>g> Vienna<br />

Nordbergstr. 15, A-1090 Wien, Austria<br />

e-mail: gerald.teschl@univie.ac.at<br />

Susanne Teschl<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Sciences Technikum Wien<br />

Höchstädtplatz 5, A-1200 Wien, Austria<br />

e-mail: susanne.teschl@esi.ac.at<br />

Ant<strong>on</strong> Amann<br />

Univ.-Clinic for Anes<str<strong>on</strong>g>th</str<strong>on</strong>g>esia <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Innsbruck Medical University and<br />

Brea<str<strong>on</strong>g>th</str<strong>on</strong>g> Research Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Austrian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

Anichstr. 35, A-6020 Innsbruck, Austria<br />

e-mail: ant<strong>on</strong>.amann@i-med.ac.at<br />

Physiological modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> trace gas exhalati<strong>on</strong> kinetics:<br />

a n<strong>on</strong>-invasive window to <str<strong>on</strong>g>th</str<strong>on</strong>g>e body<br />

Exhaled brea<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>tains a ple<str<strong>on</strong>g>th</str<strong>on</strong>g>ora <str<strong>on</strong>g>of</str<strong>on</strong>g> volatile organic compounds (VOCs),<br />

resulting from normal metabolic activity as well as from specific pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ological disorders.<br />

These trace gases can be detected and quantified at c<strong>on</strong>centrati<strong>on</strong>s down<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e parts-per-billi<strong>on</strong> (ppb) level and hold great promise for medical diagnosis,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic m<strong>on</strong>itoring, and general assessments <str<strong>on</strong>g>of</str<strong>on</strong>g> physiological functi<strong>on</strong>. In particular,<br />

exhaled brea<str<strong>on</strong>g>th</str<strong>on</strong>g> can nowadays be measured <strong>on</strong>-line, <str<strong>on</strong>g>th</str<strong>on</strong>g>us rendering VOC<br />

analysis as an optimal choice for gaining c<strong>on</strong>tinuous and n<strong>on</strong>-invasive informati<strong>on</strong><br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e current metabolic and physiological state <str<strong>on</strong>g>of</str<strong>on</strong>g> an individual.<br />

The success <str<strong>on</strong>g>of</str<strong>on</strong>g> using brea<str<strong>on</strong>g>th</str<strong>on</strong>g> VOC c<strong>on</strong>centrati<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles for estimating endogenous<br />

processes will mainly hinge <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e availability <str<strong>on</strong>g>of</str<strong>on</strong>g> valid mechanistic descripti<strong>on</strong>s<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e observable exhalati<strong>on</strong> kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e compound under scrutiny. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

c<strong>on</strong>text, we focus <strong>on</strong> real-time measurements <str<strong>on</strong>g>of</str<strong>on</strong>g> VOCs during distinct physiological<br />

states, e.g., rest, exercise, and sleep [1,2].<br />

499

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

An experimental setup for correlating brea<str<strong>on</strong>g>th</str<strong>on</strong>g>-by-brea<str<strong>on</strong>g>th</str<strong>on</strong>g> analyses using prot<strong>on</strong><br />

transfer reacti<strong>on</strong> mass spectrometry (PTR-MS) wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> major hemodynamic<br />

and respiratory variables will be presented. Building <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e phenomenological<br />

findings from studies <str<strong>on</strong>g>of</str<strong>on</strong>g> normal volunteers, a novel compartmental modeling<br />

framework capturing <str<strong>on</strong>g>th</str<strong>on</strong>g>e physiological flow <str<strong>on</strong>g>of</str<strong>on</strong>g> two prototypic VOCs, isoprene and<br />

acet<strong>on</strong>e, is developed and validated [3,4].<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, several powerful c<strong>on</strong>cepts for system and parameter identificati<strong>on</strong><br />

will be outlined, including qualitative system analysis, a priori identifiability, and<br />

numerical schemes based <strong>on</strong> multiple shooting.<br />

The results discussed are intended as a first step towards employing brea<str<strong>on</strong>g>th</str<strong>on</strong>g> gas<br />

analysis as a tool for examining exhalati<strong>on</strong>, storage, transport, and biotransformati<strong>on</strong><br />

processes associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> volatile organic compounds in vivo.<br />

References.<br />

[1] J. King, A. Kupfer<str<strong>on</strong>g>th</str<strong>on</strong>g>aler, K. Unterk<str<strong>on</strong>g>of</str<strong>on</strong>g>ler, H. Koc, S. Teschl, G. Teschl, W. Miekisch, J. Schubert,<br />

H. Hinterhuber, and A. Amann. Isoprene and acet<strong>on</strong>e c<strong>on</strong>centrati<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles during<br />

exercise <strong>on</strong> an ergometer. J. Brea<str<strong>on</strong>g>th</str<strong>on</strong>g> Res. 3 027006 (16pp).<br />

[2] J. King, P. Mochalski, A. Kupfer<str<strong>on</strong>g>th</str<strong>on</strong>g>aler, K. Unterk<str<strong>on</strong>g>of</str<strong>on</strong>g>ler, H. Koc, W. Filipiak, S. Teschl, H. Hinterhuber,<br />

and A. Amann. Dynamic pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles <str<strong>on</strong>g>of</str<strong>on</strong>g> volatile organic compounds in exhaled brea<str<strong>on</strong>g>th</str<strong>on</strong>g> as<br />

determined by a coupled PTR-MS/GC-MS study. Physiol. Meas. 31 1169–1184.<br />

[3] J. King, H. Koc, K. Unterk<str<strong>on</strong>g>of</str<strong>on</strong>g>ler, P. Mochalski, A. Kupfer<str<strong>on</strong>g>th</str<strong>on</strong>g>aler, G. Teschl, S. Teschl, H. Hinterhuber,<br />

and A. Amann. Physiological modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> isoprene dynamics in exhaled brea<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

J. Theor. Biol. 267 626–637.<br />

[4] J. King, K. Unterk<str<strong>on</strong>g>of</str<strong>on</strong>g>ler, G. Teschl, S. Teschl, H. Koc, H. Hinterhuber, and A. Amann. A<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for brea<str<strong>on</strong>g>th</str<strong>on</strong>g> gas analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> volatile organic compounds wi<str<strong>on</strong>g>th</str<strong>on</strong>g> special emphasis<br />

<strong>on</strong> acet<strong>on</strong>e. J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. DOI 10.1007/s00285-010-0398-9.<br />

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Ecology and evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases; Friday, July 1, 14:30<br />

Eva Kisdi<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Helsinki<br />

e-mail: eva.kisdi@helsinki.fi<br />

Barbara Boldin<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Primorska<br />

The curse <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pharaoh hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis revisited: Evoluti<strong>on</strong>ary<br />

coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> parasite strains<br />

Several pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens produce free-living stages <str<strong>on</strong>g>th</str<strong>on</strong>g>at allow <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong> to spread from<br />

<strong>on</strong>e host to <str<strong>on</strong>g>th</str<strong>on</strong>g>e next indirectly, via an outside envir<strong>on</strong>ment. Since <str<strong>on</strong>g>th</str<strong>on</strong>g>e reproductive<br />

success <str<strong>on</strong>g>of</str<strong>on</strong>g> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens wi<str<strong>on</strong>g>th</str<strong>on</strong>g> l<strong>on</strong>g-lived spores depends less <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e host’s survival,<br />

it has been hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esized <str<strong>on</strong>g>th</str<strong>on</strong>g>at such pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens can afford to exploit <str<strong>on</strong>g>th</str<strong>on</strong>g>eir hosts<br />

more recklessly and <str<strong>on</strong>g>th</str<strong>on</strong>g>us evolve higher virulence. We revisit <str<strong>on</strong>g>th</str<strong>on</strong>g>e so called ‘curse<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pharaoh’ hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis and study <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> virulence in pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

can transmit directly as well as indirectly, via free-living stages. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e two transmissi<strong>on</strong> routes introduce two envir<strong>on</strong>mental feedback variables, which<br />

allows for coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> two parasite strains <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two specializes to some<br />

extent <strong>on</strong> direct transmissi<strong>on</strong>, while <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er makes better use <str<strong>on</strong>g>of</str<strong>on</strong>g> indirect route<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> transmissi<strong>on</strong>. We give general c<strong>on</strong>diti<strong>on</strong>s for coexistence in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> incidence<br />

in host-to-host and host-propagule-host transmissi<strong>on</strong>, and discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s<br />

for evoluti<strong>on</strong>ary branching leading to coexisting strains in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e shape <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f functi<strong>on</strong>s.<br />

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Informati<strong>on</strong>, human behaviour and disease; Saturday, July 2, 11:00<br />

Istvan Kiss<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Physical Sciences, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sussex, UK<br />

e-mail: i.z.kiss@sussex.ac.uk<br />

Vasilis Hatzopoulos<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sussex, UK<br />

Michael Taylor<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sussex, UK<br />

Peter L. Sim<strong>on</strong><br />

Eotvos Lorand University, Hungary<br />

Multiple sources and routes <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> transmissi<strong>on</strong>:<br />

implicati<strong>on</strong>s for epidemic dynamics<br />

In a recent paper [1], we proposed and analyzed a compartmental ODE-based model<br />

describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> an infectious disease where <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen<br />

also triggers <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> about <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper, we extend<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is previous work by presenting results based <strong>on</strong> pairwise and simulati<strong>on</strong> models<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at are better suited for capturing <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> c<strong>on</strong>tact structure at a local level.<br />

We use <str<strong>on</strong>g>th</str<strong>on</strong>g>e pairwise model to examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential <str<strong>on</strong>g>of</str<strong>on</strong>g> different informati<strong>on</strong> generating<br />

mechanisms and routes <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> transmissi<strong>on</strong> to stop disease spread<br />

or to minimize <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic. The individual-based simulati<strong>on</strong> is used<br />

to better differentiate between <str<strong>on</strong>g>th</str<strong>on</strong>g>e networks <str<strong>on</strong>g>of</str<strong>on</strong>g> disease and informati<strong>on</strong> transmissi<strong>on</strong><br />

and to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> different basic network topologies and network<br />

overlap <strong>on</strong> epidemic dynamics. The paper c<strong>on</strong>cludes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an individual-based semianalytic<br />

calculati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> R0 at <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>-trivial disease free equilibrium.<br />

References.<br />

[1] I.Z. Kiss, J. Cassell, M. Recker, and P.L. Sim<strong>on</strong>. (2010) The effect <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> transmissi<strong>on</strong><br />

<strong>on</strong> epidemic outbreaks. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci. 225, 1-10.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Agnieszka Kitlas<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Informatics, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Białystok, Sosnowa 64, 15-887 Białystok, Poland<br />

e-mail: akitlas@ii.uwb.edu.pl<br />

Edward Oczeretko<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Mechanical Engineering, Białystok University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology,<br />

Wiejska 45C, 15-351 Białystok, Poland<br />

e-mail: e.oczeretko@pb.edu.pl<br />

Tadeusz Laudański<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Perinatology, M. Skłodowskiej-Curie 24A, 15-276 Białystok,<br />

Poland<br />

e-mail: laudan@umwb.edu.pl<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e uterine c<strong>on</strong>tractility: wavelet<br />

cross-correlati<strong>on</strong> functi<strong>on</strong> and wavelet coherence measure<br />

Evaluati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> uterine c<strong>on</strong>tracti<strong>on</strong> activity is an important element in physiological<br />

menstrual cycle and diagnostics <str<strong>on</strong>g>of</str<strong>on</strong>g> labor. Changes in synchr<strong>on</strong>izati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> two<br />

simultaneously recorded uterine c<strong>on</strong>tractility signals accompany various kinds <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

gynecology disorders and obstetric pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologies, e.g. endometriosis, fibromyomas,<br />

preterm bir<str<strong>on</strong>g>th</str<strong>on</strong>g> and tumors. The purpose <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is study is to analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>ese signals<br />

using wavelet cross-correlati<strong>on</strong> functi<strong>on</strong> and wavelet coherence measure.<br />

Sp<strong>on</strong>taneous uterine c<strong>on</strong>tracti<strong>on</strong>s were recorded directly by a dual micro-tip<br />

ca<str<strong>on</strong>g>th</str<strong>on</strong>g>eter (Millar Instruments, Inc.). The device c<strong>on</strong>sisted <str<strong>on</strong>g>of</str<strong>on</strong>g> two ultra-miniature<br />

pressure sensors. The distance between <str<strong>on</strong>g>th</str<strong>on</strong>g>e sensors was 30mm (<strong>on</strong>e sensor was<br />

placed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e fundus and <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cervix). The sensors produced electrical<br />

signals, which varied in direct proporti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e magnitude <str<strong>on</strong>g>of</str<strong>on</strong>g> measured pressure.<br />

We have analyzed <str<strong>on</strong>g>th</str<strong>on</strong>g>e signals obtained during examinati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> women suffering<br />

from primary dysmenorrhea (28 examinati<strong>on</strong>s), endometriosis (11 examinati<strong>on</strong>s),<br />

uterine myomas (9 examinati<strong>on</strong>s), and 1 examinati<strong>on</strong> from heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y woman. The<br />

Bioe<str<strong>on</strong>g>th</str<strong>on</strong>g>ics Committee <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Białystok approved <str<strong>on</strong>g>th</str<strong>on</strong>g>e study. This<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is invasive <str<strong>on</strong>g>th</str<strong>on</strong>g>us <str<strong>on</strong>g>th</str<strong>on</strong>g>ere was no c<strong>on</strong>trol group.<br />

Wavelet cross-correlati<strong>on</strong> functi<strong>on</strong> describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependency <str<strong>on</strong>g>of</str<strong>on</strong>g> correlati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

two signals <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e shift between <str<strong>on</strong>g>th</str<strong>on</strong>g>em. Locati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> maximum or minimum <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is functi<strong>on</strong> informs us about <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative time delay <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese signals. Signals<br />

are c<strong>on</strong>sidered similar if <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximum is close to 1 or minimum is close to −1<br />

(inverted signal). We have used multiresoluti<strong>on</strong> analysis from wavelet analysis to<br />

create wavelet cross-correlati<strong>on</strong> functi<strong>on</strong>. We have chosen suitable frequency level,<br />

where energy is transferred, as <str<strong>on</strong>g>th</str<strong>on</strong>g>e base for computati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> wavelet cross-correlati<strong>on</strong><br />

functi<strong>on</strong>. Wavelet coherence measure was calculated by multiresoluti<strong>on</strong> wavelet<br />

analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e uterine c<strong>on</strong>tracti<strong>on</strong> signals and a coherence analysis by means <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Welch me<str<strong>on</strong>g>th</str<strong>on</strong>g>od in selected frequency band c<strong>on</strong>taining <str<strong>on</strong>g>th</str<strong>on</strong>g>e dominant frequency. By<br />

computati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> wavelet coherence functi<strong>on</strong> we have obtained <str<strong>on</strong>g>th</str<strong>on</strong>g>e informati<strong>on</strong> what<br />

are <str<strong>on</strong>g>th</str<strong>on</strong>g>e comm<strong>on</strong> frequencies and when <str<strong>on</strong>g>th</str<strong>on</strong>g>ey appear. We were also able to estimate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e similarity <str<strong>on</strong>g>of</str<strong>on</strong>g> two signals.<br />

Negative shifts computed by means <str<strong>on</strong>g>of</str<strong>on</strong>g> wavelet cross-correlati<strong>on</strong> functi<strong>on</strong> indicate<br />

improper propagati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tracti<strong>on</strong>s (wr<strong>on</strong>g directi<strong>on</strong>) in unheal<str<strong>on</strong>g>th</str<strong>on</strong>g>y women.<br />

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Using graphs <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese functi<strong>on</strong>s <strong>on</strong>e can distinguish visually <str<strong>on</strong>g>th</str<strong>on</strong>g>e signals obtained<br />

from heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y woman from signals obtained from unheal<str<strong>on</strong>g>th</str<strong>on</strong>g>y women. Comm<strong>on</strong> frequency<br />

for signals from uterine fundus and uterine cervix computed by means <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

wavelet coherence functi<strong>on</strong> is about 0.05Hz. The lowest similarity (synchr<strong>on</strong>izati<strong>on</strong>)<br />

between signals from uterine fundus and uterine cervix has been observed for<br />

signals from women suffering from primary dysmenorrhea.<br />

We c<strong>on</strong>cluded <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods may be useful tools in analyzing synchr<strong>on</strong>izati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> two simultaneously recorded uterine c<strong>on</strong>tracti<strong>on</strong> signals.<br />

References.<br />

[1] A. Kitlas, E. Oczeretko, J. Świątecka, M. Borowska, T. Laudański, Uterine c<strong>on</strong>tracti<strong>on</strong> signals<br />

— applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e linear synchr<strong>on</strong>izati<strong>on</strong> measures <str<strong>on</strong>g>European</str<strong>on</strong>g> Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Obstetrics &<br />

Gynecology and Reproductive Biology 144S 2009 S61–S64.<br />

[2] J. P. Lachaux, A. Lutz, D. Rudrauf, D. Cosmelli, M. le van Quyen, J. Martinerie, F. Varela,<br />

Estimating <str<strong>on</strong>g>th</str<strong>on</strong>g>e time-course <str<strong>on</strong>g>of</str<strong>on</strong>g> coherence between single-trial brain signals: an introducti<strong>on</strong> to<br />

wavelet coherence Neurophysiologie Clinique (Clinical Neurophysiology) 32 2002 157–174.<br />

[3] S. Gigola, C. E. D’Attellis, S. Kochen, Wavelet coherence in EEG signals Clinical Neurophysiology<br />

119 2008 e142–e143.<br />

[4] Y. Mizuno-Matsumoto, G. K. Motamedi, W. R. S. Webber, R. Ishii, S. Ukai, T. Kaishima, K.<br />

Shinosaki, R. P. Lesser, Wavelet-cross correlati<strong>on</strong> analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> electrocorticography recordings<br />

from epilepsyInternati<strong>on</strong>al C<strong>on</strong>gress Series 1278 2005 411–414.<br />

[5] Y. Mizuno-Matsumoto, K. Okazaki, A. Kato, T. Yoshimine, Y. Sato, S. Tamura, T. Hayakawa,<br />

Visualizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> epileptogenic phenomena using cross-correlati<strong>on</strong> analysis: localizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

epileptic foci and propagati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> epileptiform discharges IEEE Transacti<strong>on</strong>s <strong>on</strong> Biomedical<br />

Engineering 46(3) 1999 271–279.<br />

[6] G. de Michele, S. Sello, M. C. Carb<strong>on</strong>cini, B. Rossi, S. K. Strambi, Cross-correlati<strong>on</strong> timefrequency<br />

analysis for multiple EMG signals in Parkins<strong>on</strong>’s disease: a wavelet approach Medical<br />

Engineering & Physics 25 2003 361–369.<br />

[7] E. Oczeretko, J. Świątecka, A. Kitlas, T. Laudański and P. Pierzyński, Visualizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> synchr<strong>on</strong>izati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e uterine c<strong>on</strong>tracti<strong>on</strong> signals: Running cross-correlati<strong>on</strong> and wavelet running<br />

cross-correlati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods Medical Engineering & Physics 28 2006 75–81.<br />

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Epidemic models: Networks and stochasticity II; Thursday, June 30, 11:30<br />

Adam Kleczkowski<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Natural Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling, Stirling FK9 4LA,<br />

United Kingdom<br />

e-mail: ak@cs.stir.ac.uk<br />

Savi Maharaj<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Natural Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling, Stirling FK9 4LA,<br />

United Kingdom<br />

e-mail: savi@cs.stir.ac.uk<br />

C<strong>on</strong>trolling epidemic spread by resp<strong>on</strong>ding to risk: Do it<br />

well or not at all<br />

Disease outbreaks change people behaviour. This change can be used to c<strong>on</strong>trol<br />

epidemics but it comes at a cost. We describe results from using simulati<strong>on</strong> to<br />

study <str<strong>on</strong>g>th</str<strong>on</strong>g>e costs and benefits <str<strong>on</strong>g>of</str<strong>on</strong>g> using social distancing as a form <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trol. Our<br />

model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> a standard SIR model superimposed <strong>on</strong> a simple spatial network.<br />

Disease spread is c<strong>on</strong>trolled by allowing susceptible individuals to temporarily reduce<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir social c<strong>on</strong>tacts in resp<strong>on</strong>se to <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir local<br />

neighbourhood. We ascribe an ec<strong>on</strong>omic cost to <str<strong>on</strong>g>th</str<strong>on</strong>g>e loss <str<strong>on</strong>g>of</str<strong>on</strong>g> social c<strong>on</strong>tacts, and<br />

weigh <str<strong>on</strong>g>th</str<strong>on</strong>g>is against <str<strong>on</strong>g>th</str<strong>on</strong>g>e ec<strong>on</strong>omic benefit gained by reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e attack rate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

epidemic. Our first result is <str<strong>on</strong>g>th</str<strong>on</strong>g>at, depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic<br />

and <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative ec<strong>on</strong>omic importance <str<strong>on</strong>g>of</str<strong>on</strong>g> making c<strong>on</strong>tacts versus avoiding infecti<strong>on</strong>,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal c<strong>on</strong>trol is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> two extremes: ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er to panic, <str<strong>on</strong>g>th</str<strong>on</strong>g>at is, to adopt<br />

a highly cautious c<strong>on</strong>trol, <str<strong>on</strong>g>th</str<strong>on</strong>g>ereby suppressing <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic quickly by drastically<br />

reducing c<strong>on</strong>tacts as so<strong>on</strong> as disease is detected; or else to relax by forgoing c<strong>on</strong>trol<br />

and allowing <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic to run its course. The worst outcome arises when c<strong>on</strong>trol<br />

is attempted, but not cautiously enough to cause <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic to be suppressed.<br />

Our sec<strong>on</strong>d result comes from comparing <str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e neighbourhood <str<strong>on</strong>g>of</str<strong>on</strong>g> which<br />

individuals are aware to <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e neighbourhood wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in which transmissi<strong>on</strong> can<br />

occur. We see <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trol works best when <str<strong>on</strong>g>th</str<strong>on</strong>g>ese sizes match, and <str<strong>on</strong>g>th</str<strong>on</strong>g>at it is particularly<br />

ineffective when <str<strong>on</strong>g>th</str<strong>on</strong>g>e awareness neighbourhood is smaller <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong><br />

neighbourhood. These results have implicati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e design <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trol strategies<br />

using social distancing. An important message is <str<strong>on</strong>g>th</str<strong>on</strong>g>at a weak c<strong>on</strong>trol, or <strong>on</strong>e based<br />

up<strong>on</strong> inaccurate knowledge, may give a worse outcome <str<strong>on</strong>g>th</str<strong>on</strong>g>an doing no<str<strong>on</strong>g>th</str<strong>on</strong>g>ing.<br />

References.<br />

[1] A. Au<str<strong>on</strong>g>th</str<strong>on</strong>g>or, Title <str<strong>on</strong>g>of</str<strong>on</strong>g> paper Journal Name 1 1–10.<br />

505

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bioinformatics and System Biology; Wednesday, June 29, 11:00<br />

Sabrina Kleessen<br />

Max Planck Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular Plant Physiology, Potsdam, Germany<br />

e-mail: kleessen@mpimp-golm.mpg.de<br />

Zoran Nikoloski<br />

Max Planck Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular Plant Physiology and Institute<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemistry and Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Potsdam, Potsdam, Germany<br />

e-mail: nikoloski@mpimp-golm.mpg.de<br />

Dynamic regulatory <strong>on</strong>/<str<strong>on</strong>g>of</str<strong>on</strong>g>f minimizati<strong>on</strong> infers key<br />

regulators <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Calvin cycle under internal temporal<br />

perturbati<strong>on</strong>s<br />

Flux balance analysis (FBA) toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> its dynamic extensi<strong>on</strong>, DFBA, have<br />

proven instrumental for analyzing <str<strong>on</strong>g>th</str<strong>on</strong>g>e robustness <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic networks. Under <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

assumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> minimizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic adjustment, DFBA has recently been employed<br />

to analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e transiti<strong>on</strong> between metabolic states at systemic level. Here we<br />

propose a suite <str<strong>on</strong>g>of</str<strong>on</strong>g> novel me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for analyzing <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> perturbed metabolic<br />

networks and quantifying <str<strong>on</strong>g>th</str<strong>on</strong>g>eir robustness wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> kinetic parameters.<br />

Following <str<strong>on</strong>g>th</str<strong>on</strong>g>e biochemically meaningful premise <str<strong>on</strong>g>th</str<strong>on</strong>g>at metabolite c<strong>on</strong>centrati<strong>on</strong>s exhibit<br />

smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> temporal changes, <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods rely <strong>on</strong> minimizing <str<strong>on</strong>g>th</str<strong>on</strong>g>e significant<br />

fluctuati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles to predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e time-resolved metabolic<br />

state characterized by bo<str<strong>on</strong>g>th</str<strong>on</strong>g> fluxes and c<strong>on</strong>centrati<strong>on</strong>s. On a model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Calvin<br />

cycle, we dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e principle <str<strong>on</strong>g>of</str<strong>on</strong>g> regulatory <strong>on</strong>/<str<strong>on</strong>g>of</str<strong>on</strong>g>f minimizati<strong>on</strong> (ROOM)<br />

coupled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> DFBA can accurately predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e changes in metabolic states. Our<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods outperform <str<strong>on</strong>g>th</str<strong>on</strong>g>e existing DFBA-based modeling alternatives, and help in<br />

revealing <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms for maintaining robustness <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamic processes in metabolic<br />

networks over time.<br />

506

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biomechanical regulati<strong>on</strong> in b<strong>on</strong>e tissue (Sessi<strong>on</strong><br />

II); Wednesday, June 29, 11:00<br />

Václav Klika<br />

FNSPE, Czech Technical University in Prague and Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Thermomechanics,<br />

AS CR<br />

e-mail: klika@it.cas.cz<br />

František Maršík<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Thermomechanics, AS CR<br />

e-mail: marsik@it.cas.cz<br />

Tissue adaptati<strong>on</strong> driven by chemo-mechanical coupling wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

applicati<strong>on</strong> to b<strong>on</strong>e<br />

Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e current knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e remodelling process, a biochemical<br />

model is proposed which describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e essential interacti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at governs <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole<br />

b<strong>on</strong>e remodelling process. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er, <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanical stimulati<strong>on</strong> <strong>on</strong> b<strong>on</strong>e<br />

tissue is well known. C<strong>on</strong>siderati<strong>on</strong>s from n<strong>on</strong>-equilibrium <str<strong>on</strong>g>th</str<strong>on</strong>g>ermodynamics are<br />

used to quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>is effect and moreover to stress <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamic<br />

character <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e loading. Particularly, <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> what c<strong>on</strong>stitutes a mechanical<br />

stimulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biochemical reacti<strong>on</strong>s in general will be addressed and fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er to<br />

compare <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two possible mechanical stimulati<strong>on</strong>s: shear rate<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> volume variati<strong>on</strong>. C<strong>on</strong>sequently, a modified form <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Law <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Mass Acti<strong>on</strong> is derived which includes also <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechano-chemical coupling and<br />

not <strong>on</strong>ly <str<strong>on</strong>g>th</str<strong>on</strong>g>e affinity <str<strong>on</strong>g>of</str<strong>on</strong>g> interacti<strong>on</strong> based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e difference in chemical potentials.<br />

This ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er different approach from <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical <strong>on</strong>es can predict b<strong>on</strong>e density<br />

distributi<strong>on</strong> as will be shown <strong>on</strong> some examples including <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> stem inserti<strong>on</strong><br />

or osteoporosis.<br />

Acknowledgement. This research has been supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Czech Science<br />

Foundati<strong>on</strong> project no. 106/08/0557.<br />

References.<br />

[1] Klika, V., Maršík, F., 2009. Coupling effect between mechanical loading and chemical reacti<strong>on</strong>s.<br />

Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Physical Chemistry B 113, 14689–14697.<br />

[2] Klika, V., 2010. Comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Effects <str<strong>on</strong>g>of</str<strong>on</strong>g> Possible Mechanical Stimuli <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Rate <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Biochemical Reacti<strong>on</strong>s. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Physical Chemistry B 114(32), 10567—10572.<br />

[3] Klika, V., Maršík, F., 2010. A Thermodynamic Model <str<strong>on</strong>g>of</str<strong>on</strong>g> B<strong>on</strong>e Remodelling: The Influence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Dynamic Loading Toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Biochemical C<strong>on</strong>trol. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Musculoskeletal and Neur<strong>on</strong>al<br />

Interacti<strong>on</strong>s 10(3), 210–220.<br />

507

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Fractals and Complexity II; Wednesday, June 29, 17:00<br />

Wlodzimierz Kl<strong>on</strong>owski<br />

Nalecz Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biocybernetics and Biomedica Engineering, Polish<br />

Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences Warsaw, POLAND<br />

e-mail: wkl<strong>on</strong>@ibib.waw.pl<br />

Michal Pierzchalski<br />

Nalecz Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biocybernetics and Biomedica Engineering, Polish<br />

Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences Warsaw, POLAND<br />

Pawel Stepien<br />

Nalecz Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biocybernetics and Biomedica Engineering, Polish<br />

Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences Warsaw, POLAND<br />

Robert Stepien<br />

Nalecz Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biocybernetics and Biomedica Engineering, Polish<br />

Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences Warsaw, POLAND<br />

Applying Fractal Dimensi<strong>on</strong> in Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosignals and <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Medical Images<br />

We present applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> fractal analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> EEG and HRV signals, as well as <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

medical images, for supporting medical diagnosis and for assessment <str<strong>on</strong>g>of</str<strong>on</strong>g> influence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

chemical and physical agents <strong>on</strong> living systems. We will show examples <str<strong>on</strong>g>of</str<strong>on</strong>g> stress assessment,<br />

sleep analysis, measuring <str<strong>on</strong>g>th</str<strong>on</strong>g>e dep<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> anes<str<strong>on</strong>g>th</str<strong>on</strong>g>esia, classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tumors<br />

based <strong>on</strong> Higuchis fractal dimensi<strong>on</strong>.<br />

508

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Sandra Klu<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Bielefeld University<br />

e-mail: sandra.klu<str<strong>on</strong>g>th</str<strong>on</strong>g>@uni-bielefeld.de<br />

Populati<strong>on</strong> Genetics; Wednesday, June 29, 17:00<br />

The stati<strong>on</strong>ary distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ancestral types in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Moran model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mutati<strong>on</strong> and selecti<strong>on</strong><br />

We c<strong>on</strong>sider a stochastic model <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> genetics, namely, <str<strong>on</strong>g>th</str<strong>on</strong>g>e Moran model<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mutati<strong>on</strong> and selecti<strong>on</strong>. We use it to trace back <str<strong>on</strong>g>th</str<strong>on</strong>g>e ancestral lines <str<strong>on</strong>g>of</str<strong>on</strong>g> single<br />

individuals, and are interested in <str<strong>on</strong>g>th</str<strong>on</strong>g>e stati<strong>on</strong>ary distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding<br />

ancestral types. Two approaches to <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem are already available: The <strong>on</strong>e by<br />

Fearnhead (2002), which is based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ancestral selecti<strong>on</strong> graph (Kr<strong>on</strong>e/Neuhauser<br />

1997), and <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>e by Taylor (2007), which relies <strong>on</strong> a descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e full populati<strong>on</strong><br />

backward in time by means <str<strong>on</strong>g>of</str<strong>on</strong>g> a diffusi<strong>on</strong> equati<strong>on</strong>.<br />

In bo<str<strong>on</strong>g>th</str<strong>on</strong>g> approaches, <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting expressi<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e stati<strong>on</strong>ary distributi<strong>on</strong> does<br />

not have an obvious interpretati<strong>on</strong> in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e graphical representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

model (i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e representati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at makes individual lineages and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir interacti<strong>on</strong>s<br />

explicit). In <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>tributi<strong>on</strong> (which is joint work wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Ellen Baake), we use <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

graphical representati<strong>on</strong> to derive equati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e fixati<strong>on</strong> probabilities <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> all ‘fit’ individuals (regardless <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring’s type). In <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong><br />

limit, <str<strong>on</strong>g>th</str<strong>on</strong>g>is yields Taylor’s differential equati<strong>on</strong> - but now wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a plausible interpretati<strong>on</strong><br />

attached to it. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, <str<strong>on</strong>g>th</str<strong>on</strong>g>is also points <str<strong>on</strong>g>th</str<strong>on</strong>g>e way towards a better<br />

understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e coefficients <str<strong>on</strong>g>th</str<strong>on</strong>g>at define <str<strong>on</strong>g>th</str<strong>on</strong>g>e stati<strong>on</strong>ary distributi<strong>on</strong>.<br />

509

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Statistical Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Signals I; Saturday, July 2, 08:30<br />

Markus P. Knappitsch<br />

Theoretical Biology Group<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> B<strong>on</strong>n<br />

Kirschallee 1-3<br />

53115 B<strong>on</strong>n<br />

e-mail: markus.knappitsch@gmx.net<br />

Dynamic Informati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Meaning <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Signs<br />

The communicati<strong>on</strong> between cooperating and adversary organisms is central to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> biological ecosystems. Comm<strong>on</strong>ly, <str<strong>on</strong>g>th</str<strong>on</strong>g>is communicati<strong>on</strong> is formalized<br />

in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> Claude E. Shann<strong>on</strong>’s Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Theory <str<strong>on</strong>g>of</str<strong>on</strong>g> Communicati<strong>on</strong> [4].<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is <str<strong>on</strong>g>th</str<strong>on</strong>g>eory, informati<strong>on</strong> is represented as a measurable quantity arising from<br />

statistics <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying vocabulary. There have been several works addressing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Shann<strong>on</strong> informati<strong>on</strong> to biological systems [1,3,5].<br />

Here, I argue <str<strong>on</strong>g>th</str<strong>on</strong>g>at Shann<strong>on</strong> informati<strong>on</strong> encompasses significant shortcomings,<br />

which limit <str<strong>on</strong>g>th</str<strong>on</strong>g>e applicability to communicati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e life sciences. Since Shann<strong>on</strong><br />

informati<strong>on</strong> is a purely statistical quantity, it treats <strong>on</strong>ly syntactic aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

communicati<strong>on</strong> process. In c<strong>on</strong>trast, <str<strong>on</strong>g>th</str<strong>on</strong>g>e levels <str<strong>on</strong>g>of</str<strong>on</strong>g> semantics, pragmatics, and dynamics<br />

[1] are not under c<strong>on</strong>siderati<strong>on</strong>. Clearly, a message has always an impact<br />

<strong>on</strong> living systems, because it leads to a certain adaptive resp<strong>on</strong>se. Yet <str<strong>on</strong>g>th</str<strong>on</strong>g>is active<br />

resp<strong>on</strong>se is part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pragmatic-dynamic level and integral part <str<strong>on</strong>g>of</str<strong>on</strong>g> biological<br />

communicati<strong>on</strong>.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, I present an alternative c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> [2]. The so-called<br />

Dynamic Informati<strong>on</strong> rates incoming signals wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a relative importance depending<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e internal state <str<strong>on</strong>g>of</str<strong>on</strong>g> an agent [1,2]. The bigger <str<strong>on</strong>g>th</str<strong>on</strong>g>e induced change in <str<strong>on</strong>g>th</str<strong>on</strong>g>e agent’s<br />

behavior, <str<strong>on</strong>g>th</str<strong>on</strong>g>e bigger are relative importance and <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting dynamic informati<strong>on</strong>.<br />

First, I introduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical framework modeling elementary biological<br />

communicati<strong>on</strong> by means <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamical systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> input and output. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

approach, agents are represented by n<strong>on</strong>linear coupled systems <str<strong>on</strong>g>of</str<strong>on</strong>g> ODEs wi<str<strong>on</strong>g>th</str<strong>on</strong>g> input<br />

terms. Next, <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamic informati<strong>on</strong> is developed as a bridge between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamical systems and Shann<strong>on</strong>s’s <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> communicati<strong>on</strong>. Finally,<br />

I apply <str<strong>on</strong>g>th</str<strong>on</strong>g>e developed framework to task allocati<strong>on</strong> in ant col<strong>on</strong>ies.<br />

References.<br />

[1] Hermann Haken. Informati<strong>on</strong> and Self-Organisati<strong>on</strong>. Springer, Berlin, 2006<br />

[2] Markus P. Knappitsch, K<strong>on</strong>strukti<strong>on</strong> und Simulati<strong>on</strong> eines ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematischen Rahmenmodells<br />

biologischer Kommunikati<strong>on</strong> mittels dynamischer Systeme, B<strong>on</strong>ner Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematische Schriften,<br />

402, 1-126<br />

[3] Drew Rendall, M. J. Owren, M. J.Ryan. What do animal signs mean?, Animal Behaviour, 78,<br />

233-240<br />

[4] Claude E. Shann<strong>on</strong>, A Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Theory <str<strong>on</strong>g>of</str<strong>on</strong>g> Communicati<strong>on</strong>, Bell System Technical Journal,<br />

27, 379-423<br />

[5] Robert M. Seyfar<str<strong>on</strong>g>th</str<strong>on</strong>g>, Doro<str<strong>on</strong>g>th</str<strong>on</strong>g>y L. Cheney, Thore Bergman, Julia Fischer, Klaus Zuberbühler,<br />

Kurt Hammerschmidt. The central importance <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> in studies <str<strong>on</strong>g>of</str<strong>on</strong>g> animal communicati<strong>on</strong>,<br />

Animal Behaviour, 80, 3-8<br />

510

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Regulatory Networks; Friday, July 1, 14:30<br />

Michael Knudsen<br />

Bioinformatics Research Centre, Aarhus University, Denmark<br />

e-mail: micknudsen@gmail.com<br />

Elisenda Feliu<br />

Bioinformatics Research Centre, Aarhus University, Denmark<br />

e-mail: efeliu@birc.au.dk<br />

Carsten Wiuf<br />

Bioinformatics Research Centre, Aarhus University, Denmark<br />

e-mail: wiuf@birc.au.dk<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Phosphorelay Dynamics<br />

Phosphorylati<strong>on</strong> is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most prevalent forms <str<strong>on</strong>g>of</str<strong>on</strong>g> post-translati<strong>on</strong>al modificati<strong>on</strong>s<br />

by which signals are transmitted in living cells. A type <str<strong>on</strong>g>of</str<strong>on</strong>g> signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way<br />

prevalent in bacteria is <str<strong>on</strong>g>th</str<strong>on</strong>g>e two-comp<strong>on</strong>ent system (TCS), in which a signal is transferred<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough a series <str<strong>on</strong>g>of</str<strong>on</strong>g> phosphate group transfers moving <str<strong>on</strong>g>th</str<strong>on</strong>g>e phosphate group<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e sensor domain <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>e protein to <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulator domain <str<strong>on</strong>g>of</str<strong>on</strong>g> ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er protein.<br />

Similar pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways involving more <str<strong>on</strong>g>th</str<strong>on</strong>g>an two proteins exist, and toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> TCSs<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese are known as phosphorelays.<br />

We present a rigorous ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> phosphorelays assuming <strong>on</strong>ly<br />

mass-acti<strong>on</strong> kinetics. By combining an algebraic approach, previously applied to<br />

linear signaling cascades [1], wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eory for m<strong>on</strong>ot<strong>on</strong>e systems, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at phosphorelays<br />

c<strong>on</strong>verge to unique stable steady states given initial total substrate c<strong>on</strong>centrati<strong>on</strong>s.<br />

The pro<str<strong>on</strong>g>of</str<strong>on</strong>g> relies <strong>on</strong> graph <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e species-reacti<strong>on</strong><br />

Petri net (SR-net) and an analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e phosphorelay system in reacti<strong>on</strong> coordinates.<br />

Using reacti<strong>on</strong> coordinates, <str<strong>on</strong>g>th</str<strong>on</strong>g>e system exhibits a special kind <str<strong>on</strong>g>of</str<strong>on</strong>g> m<strong>on</strong>ot<strong>on</strong>icity<br />

(<str<strong>on</strong>g>th</str<strong>on</strong>g>e system is cooperative).<br />

For <str<strong>on</strong>g>th</str<strong>on</strong>g>e TCS, algebraic manipulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e steady state equati<strong>on</strong> lead to fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e system dynamics, for example in relati<strong>on</strong> to stimulus-resp<strong>on</strong>se<br />

curves. We obtain a polynomial equati<strong>on</strong> relating stimulus and resp<strong>on</strong>se, <strong>on</strong>ly depending<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate c<strong>on</strong>stants and <str<strong>on</strong>g>th</str<strong>on</strong>g>e total substrate c<strong>on</strong>centrati<strong>on</strong>s. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

relati<strong>on</strong>ship we are able to investigate, wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out restoring to simulati<strong>on</strong> or fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

approximati<strong>on</strong>, how <str<strong>on</strong>g>th</str<strong>on</strong>g>e stimulus depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number phosphorylati<strong>on</strong> sites <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

each protein.<br />

Algebraic approaches to phosphorylati<strong>on</strong> networks have been <str<strong>on</strong>g>th</str<strong>on</strong>g>e topic <str<strong>on</strong>g>of</str<strong>on</strong>g> many<br />

recent publicati<strong>on</strong>s, see [1,2] and references <str<strong>on</strong>g>th</str<strong>on</strong>g>erein, and we believe <str<strong>on</strong>g>th</str<strong>on</strong>g>at such approaches<br />

will be helpful for understanding many different types <str<strong>on</strong>g>of</str<strong>on</strong>g> systems.<br />

References.<br />

[1] E. Feliu, M. Knudsen, L.N. Andersen, C. Wiuf: An Algebraic Approach to Signaling Cascades<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> n Layers, arXiv:1008.0431 (2010).<br />

[2] E. Feliu, L.N. Andersen, M. Knudsen, C. Wiuf: A General Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Framework Suitable<br />

for Studying Signaling Cascades, arXiv:1008.0427 (2010).<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Statistical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in computati<strong>on</strong>al neuroscience II; Wednesday, June 29,<br />

17:00<br />

Ryota Kobayashi<br />

Ristumeikan University<br />

e-mail: kobayashi@cns.ci.ritsumei.ac.jp<br />

Yasuhiro Tsubo<br />

RIKEN Brain Science Institute<br />

e-mail: tsubo@brain.riken.jp<br />

Shigeru Shinomoto<br />

Kyoto University<br />

e-mail: shinomoto@scphys.kyoto-u.ac.jp<br />

Made-to-Order spiking neur<strong>on</strong> model for a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> cortical<br />

neur<strong>on</strong>s<br />

Informati<strong>on</strong> is transmitted wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e brain <str<strong>on</strong>g>th</str<strong>on</strong>g>rough various types <str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>s<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at resp<strong>on</strong>d differently to <str<strong>on</strong>g>th</str<strong>on</strong>g>e same input. The Hodgkin−Huxley model has been<br />

revised by including i<strong>on</strong>ic channels <str<strong>on</strong>g>th</str<strong>on</strong>g>at account for typical neur<strong>on</strong>al firing phenomena.<br />

However, estimating parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Hodgkin−Huxley models from<br />

experimental data is a notoriously difficult. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong>al costs<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models are high, which hinders performing a simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> massively interc<strong>on</strong>nected<br />

neural networks.<br />

Here we introduce a computati<strong>on</strong>ally fast spiking neur<strong>on</strong> model [1] <str<strong>on</strong>g>th</str<strong>on</strong>g>at is capable<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> accurately predicting a rich variety <str<strong>on</strong>g>of</str<strong>on</strong>g> spike resp<strong>on</strong>ses. We also developed<br />

a procedure for optimizing model parameters. The key features <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e new model<br />

are a n<strong>on</strong>-resetting leaky integrator and an adaptive <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold equipped wi<str<strong>on</strong>g>th</str<strong>on</strong>g> fast<br />

(10 ms) and slow (200 ms) time c<strong>on</strong>stants. The model can be easily tailored to various<br />

cortical neur<strong>on</strong>s, including regular-spiking, intrinsic-bursting, and fast-spiking<br />

neur<strong>on</strong>s, by simply adjusting <str<strong>on</strong>g>th</str<strong>on</strong>g>ree parameters. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e high flexibility and low<br />

computati<strong>on</strong>al cost would help to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e real brain reliably and examine how<br />

network properties may be influenced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributed characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> comp<strong>on</strong>ent<br />

neur<strong>on</strong>s.<br />

References.<br />

[1] R. Kobayashi, Y. Tsubo, S. Shinomoto, Made-to-order spiking neur<strong>on</strong> model equipped wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a<br />

multi-timescale adaptive <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold. Fr<strong>on</strong>t. Comput. Neurosci. 3 9.<br />

512

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cellular Systems Biology; Tuesday, June 28, 17:00<br />

Tetsuya J. Kobayashi<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Industrial Science, <str<strong>on</strong>g>th</str<strong>on</strong>g>e University <str<strong>on</strong>g>of</str<strong>on</strong>g> Tokyo.<br />

e-mail: tetsuya@mail.crmind.net<br />

Noise-Induced Symmetry-Breaking Underlies Reliable and<br />

Flexible Cellular Decisi<strong>on</strong>-Making<br />

All-or-n<strong>on</strong>e decisi<strong>on</strong>-making by a cell such as differentiati<strong>on</strong> and apoptosis is tightly<br />

linked to symmetry-breaking in intracellular networks. The underlying mechanism<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> such symmetry-breaking has been c<strong>on</strong>sidered to be <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic bifurcati<strong>on</strong><br />

generated by positive feedback loops. By c<strong>on</strong>trolling <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>set <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bifurcati<strong>on</strong><br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bifurcated attractors by external inputs, it can also implement<br />

various cellular functi<strong>on</strong>s such as hysteresis, irreversibility, and historydependent<br />

memory. Waddingt<strong>on</strong> expressed its importance for development in a<br />

metaphor <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e famous epigenetic landscape, in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e fate <str<strong>on</strong>g>of</str<strong>on</strong>g> each cell is<br />

gradually determined in <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>e landscape <str<strong>on</strong>g>of</str<strong>on</strong>g> potential whose complexity increases<br />

during development. While <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic bifurcati<strong>on</strong> has already been accepted<br />

as <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimentally observed symmetry-breaking, it<br />

has rarely been proven experimentally because <str<strong>on</strong>g>th</str<strong>on</strong>g>e bistability is <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic<br />

c<strong>on</strong>cept and we cannot completely eliminate noise from biological systems. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e bistable attractor lacks <str<strong>on</strong>g>th</str<strong>on</strong>g>e property to flexibly produce <str<strong>on</strong>g>th</str<strong>on</strong>g>e distinctive<br />

outputs according to <str<strong>on</strong>g>th</str<strong>on</strong>g>e subtle external guidance signal. This indicates <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

bistable attractor is not <str<strong>on</strong>g>th</str<strong>on</strong>g>e best dynamical behavior to implement <str<strong>on</strong>g>th</str<strong>on</strong>g>e flexible<br />

decisi<strong>on</strong>-making while it is better to reinforce and memorize <str<strong>on</strong>g>th</str<strong>on</strong>g>e determined decisi<strong>on</strong>.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, I reveal <str<strong>on</strong>g>th</str<strong>on</strong>g>at a noise-induced symmetry-breaking, ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er mechanism<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> symmetry-breaking in a noisy system, can also produce <str<strong>on</strong>g>th</str<strong>on</strong>g>e distinctive outputs<br />

required for cellular decisi<strong>on</strong>-making. Such noise-induced property is shown<br />

to have <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong> to flexibly resp<strong>on</strong>d to <str<strong>on</strong>g>th</str<strong>on</strong>g>e external guidance signal even wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

substantial noise in <str<strong>on</strong>g>th</str<strong>on</strong>g>e signal. The underlying logic <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is flexibility is revealed to<br />

be <str<strong>on</strong>g>th</str<strong>on</strong>g>e Bayesian informati<strong>on</strong> decoding <str<strong>on</strong>g>th</str<strong>on</strong>g>at optimally extracts <str<strong>on</strong>g>th</str<strong>on</strong>g>e informati<strong>on</strong> from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e noisy signal. The biological validity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e noise-induced symmetry-breaking<br />

and Bayesian informati<strong>on</strong> decoding will be dem<strong>on</strong>strated by using various cellular<br />

phenomena such as signal transducti<strong>on</strong>, immune-resp<strong>on</strong>se and polarity formati<strong>on</strong>.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, I propose an experimental procedure to discriminate <str<strong>on</strong>g>th</str<strong>on</strong>g>e noiseinduced<br />

symmetry-breaking from <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic bifurcati<strong>on</strong> by using single-cell<br />

time-lapse measurement. This result will serve to experimentally investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

noise-induced symmetry-breaking and <str<strong>on</strong>g>th</str<strong>on</strong>g>e related Bayesian informati<strong>on</strong> processing<br />

by a cell.<br />

References.<br />

[1] T.J. Kobayashi, Implementati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Dynamic Bayesian Decisi<strong>on</strong> Making by Intracellular Kinetics<br />

Physical Review Letters 104, 228104, 2010.<br />

[2] T.J. Kobayashi & A. Kamimura, Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Intracellular Informati<strong>on</strong> Decoding submitted,<br />

2011.<br />

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B and T cell immune resp<strong>on</strong>ses; Wednesday, June 29, 11:00<br />

Marek Kochańczyk<br />

Jagiell<strong>on</strong>ian University, Krakow, Poland<br />

e-mail: marek.kochanczyk@uj.edu.pl<br />

Tomasz Lipniacki<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research, Warsaw, Poland<br />

e-mail: tlipnia@ippt.gov.pl<br />

A spatially extended model <str<strong>on</strong>g>of</str<strong>on</strong>g> B cell<br />

receptor cluster signaling<br />

The process <str<strong>on</strong>g>of</str<strong>on</strong>g> B cell activati<strong>on</strong> is initiated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e clustering <str<strong>on</strong>g>of</str<strong>on</strong>g> B cell receptors<br />

(BCR) up<strong>on</strong> specific engagement and cross-linking wi<str<strong>on</strong>g>th</str<strong>on</strong>g> antigens (Ag). A BCR-Ag<br />

microcluster must comprise a minimum number <str<strong>on</strong>g>of</str<strong>on</strong>g> receptors (∼ 10-20) in order to<br />

create an immun<strong>on</strong> – <str<strong>on</strong>g>th</str<strong>on</strong>g>e smallest signaling unit capable <str<strong>on</strong>g>of</str<strong>on</strong>g> triggering intracellular<br />

signaling leading to <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> immunogenic resp<strong>on</strong>se.<br />

We have approached <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinetic simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> early signaling events wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in<br />

a two-dimensi<strong>on</strong>al cellular automat<strong>on</strong> in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e plane representing a regi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e B cell membrane is discretized using <str<strong>on</strong>g>th</str<strong>on</strong>g>e hexag<strong>on</strong>al tiling. Transmembrane<br />

molecules <str<strong>on</strong>g>of</str<strong>on</strong>g> BCR and membrane-te<str<strong>on</strong>g>th</str<strong>on</strong>g>ered Src-family kinases (represented in our<br />

study by single kinase Lyn) diffuse over <str<strong>on</strong>g>th</str<strong>on</strong>g>e tiles while Ag ligands are placed in<br />

trig<strong>on</strong>al cells <str<strong>on</strong>g>of</str<strong>on</strong>g> a dual lattice. We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e Y-shaped extracellular part<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e BCR (mIg) can bind up to two Ag, <str<strong>on</strong>g>th</str<strong>on</strong>g>at may have higher valency. Movements<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Ag-bound BCR are limited: singly linked BCR can move <strong>on</strong>ly to <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at are adjacent to Ag, and BCR is immobilized when bound twice. Lyn may<br />

bind to <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoplasmic part <str<strong>on</strong>g>of</str<strong>on</strong>g> BCR ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er by its unique domain (week binding)<br />

or by SH2 domain (str<strong>on</strong>g binding to phosphorylated BCR), resulting in <str<strong>on</strong>g>th</str<strong>on</strong>g>e creati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> complexes <str<strong>on</strong>g>th</str<strong>on</strong>g>at by c<strong>on</strong>venti<strong>on</strong> occupy a single hexag<strong>on</strong>al cell <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e plane.<br />

Associated Lyn can phosphorylate <str<strong>on</strong>g>th</str<strong>on</strong>g>e neighboring BCR or Lyn. Every binding<br />

reacti<strong>on</strong> is reversible and molecules undergo sp<strong>on</strong>taneous dephosphorylati<strong>on</strong>. The<br />

process is coded in s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware in <str<strong>on</strong>g>th</str<strong>on</strong>g>e way <str<strong>on</strong>g>th</str<strong>on</strong>g>at ensures <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact state-to-state dynamics:<br />

reacti<strong>on</strong> and diffusi<strong>on</strong> events are selected from <str<strong>on</strong>g>th</str<strong>on</strong>g>e catalog <str<strong>on</strong>g>of</str<strong>on</strong>g> possible events<br />

and are fired at random wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir propensities proporti<strong>on</strong>al to corresp<strong>on</strong>ding rate<br />

c<strong>on</strong>stants.<br />

We found <str<strong>on</strong>g>th</str<strong>on</strong>g>at when <str<strong>on</strong>g>th</str<strong>on</strong>g>e receptors are freely moving over <str<strong>on</strong>g>th</str<strong>on</strong>g>e surface (in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

absence <str<strong>on</strong>g>of</str<strong>on</strong>g> ligands) <str<strong>on</strong>g>th</str<strong>on</strong>g>e system exhibits <strong>on</strong>ly small basal activity – characteristic for<br />

unstimulated cells. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> ligands BCR form clusters which enhance<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e effective interacti<strong>on</strong> rate and triggers kinase activity. Trivalent ligands are<br />

much more effective <str<strong>on</strong>g>th</str<strong>on</strong>g>an bivalent <strong>on</strong>es in building dense, signaling-efficient, BCR<br />

clusters. Due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e positive feedback in mutual receptor and kinase activati<strong>on</strong><br />

(phosphorylati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> receptor stabilizes kinase binding and autophosphorylati<strong>on</strong>)<br />

clusters exhibit switch-like activati<strong>on</strong>. The cluster inactivati<strong>on</strong> propensity decreases<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cluster, and clusters <str<strong>on</strong>g>of</str<strong>on</strong>g> ten or more receptors activate<br />

virtually persistently.<br />

514

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This study was supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Polish Ministry <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Higher Educati<strong>on</strong><br />

grant N N501 132936 and Foundati<strong>on</strong> for Polish Science grant TEAM/2009-<br />

3/6.<br />

515

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling II; Wednesday, June 29,<br />

14:30<br />

Pawel Kocieniewski<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research - Polish Academy<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warsaw<br />

e-mail: pkocien@ippt.gov.pl<br />

Tomasz Lipniacki<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research - Polish Academy<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warsaw<br />

e-mail: tlipnia@ippt.gov.pl<br />

Dimerizati<strong>on</strong> Effects in MAPK cascade<br />

The MAPK (Mitogen-Activated Protein Kinase) cascades are am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e most important<br />

signal transducti<strong>on</strong> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways in eukaryotic cells. The core <str<strong>on</strong>g>of</str<strong>on</strong>g> a MAPK<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way comprises a series <str<strong>on</strong>g>of</str<strong>on</strong>g> sequentially activated kinases, generically referred to<br />

as MAP3Ks, MAP2Ks, and MAPKs. Of particular importance are Raf/MEK/ERK<br />

and MEKK/MEK/JNK cascades due to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir role in stress resp<strong>on</strong>se, proliferati<strong>on</strong>,<br />

differentiati<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer. C<strong>on</strong>sequently, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways have<br />

been extensively modeled. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e models developed so far ignore homo- and<br />

heterodimerizati<strong>on</strong> events occurring between kinases wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in each tier <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cascade.<br />

The significance <str<strong>on</strong>g>of</str<strong>on</strong>g> dimerizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Raf and MEK proteins is especially well documented.<br />

In particular, <str<strong>on</strong>g>th</str<strong>on</strong>g>e dimerizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> RAF proteins appears critical for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

activati<strong>on</strong> - its dysregulati<strong>on</strong> due to mutati<strong>on</strong>s or experimental chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic<br />

inhibitors can lead to <strong>on</strong>cogenesis [1] or paradoxical activati<strong>on</strong> [2], respectively. The<br />

dimerizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> MEK1 and MEK2, <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, introduces a novel regulatory<br />

mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trolling <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way’s output via feedback phosphorylati<strong>on</strong><br />

by ERK [3]. Lastly, <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-member scaffold proteins such as KSR, which assemble<br />

signalling complexes, have <str<strong>on</strong>g>th</str<strong>on</strong>g>emselves been shown to dimerize [4], potentially<br />

providing a platform for dimerizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er MAPK comp<strong>on</strong>ents. We have incorporated<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese effects to produce more realistic models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e MAPK cascade as<br />

well as to explore <str<strong>on</strong>g>th</str<strong>on</strong>g>eir possible role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way’s regulati<strong>on</strong> and dynamics.<br />

References.<br />

[1] P.T. Wan, M.J. Garnett, S.M. Roe, S. Lee, D. Niculescu-Duvaz, V.M. Good, C.M. J<strong>on</strong>es,<br />

C.J. Marshall, C.J. Springer, D. Barford, R. Marais; Cancer Genome Project, Mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e RAF-ERK signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way by <strong>on</strong>cogenic mutati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> B-RAF Cell. 116<br />

855–67.<br />

[2] P.I. Poulikakos, C. Zhang, G. Bollag, K.M. Shokat, N. Rosen, RAF inhibitors transactivate<br />

RAF dimers and ERK signalling in cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> wild-type BRAF Nature 464 427–430.<br />

[3] F. Catalanotti, G. Reyes, V. Jesenberger, G. Galabova-Kovacs, R. de Matos Simoes, O. Carugo,<br />

M. Baccarini, A Mek1-Mek2 heterodimer determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e streng<str<strong>on</strong>g>th</str<strong>on</strong>g> and durati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Erk<br />

signal Nat Struct Mol Biol. 16 294–303.<br />

[4] C. Chen, R.E. Lewis, M.A. White, IMP modulates KSR1-dependent multivalent complex formati<strong>on</strong><br />

to specify ERK1/2 pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way activati<strong>on</strong> and resp<strong>on</strong>se <str<strong>on</strong>g>th</str<strong>on</strong>g>resholds J Biol Chem. 283<br />

12789–96.<br />

516

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Regulatory Networks; Friday, July 1, 14:30<br />

M. Koetzing 1 , C. Kaleta 1 , S. Schuster 1<br />

1 Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioinformatics, Friedrich Schiller University Jena, Ernst-<br />

Abbe-Platz 2, D-07743 Jena, Germany<br />

e-mail: {martin.koetzing, christoph.kaleta, stefan.schu}@uni-jena.de<br />

M. Bartl 2<br />

2 Simulati<strong>on</strong> and Optimal Processes Group, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science<br />

and Automati<strong>on</strong>, Ilmenau University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Max-Planck-<br />

Ring 14, D-98693 Ilmenau, Germany<br />

Dynamic Optimizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Nitrogen Assimilati<strong>on</strong> in<br />

Chlamydom<strong>on</strong>as reinhardtii<br />

Optimizati<strong>on</strong> approaches are a useful tool to study principles behind dynamics<br />

observed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways [1]. While earlier studies c<strong>on</strong>sidered<br />

mostly steady-state systems [1, 2], <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamic regulati<strong>on</strong>, or just-in-time<br />

activati<strong>on</strong>, <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways has attracted increasing attenti<strong>on</strong> [3, 4] and was<br />

experimentally observed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e amino acid biosyn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>of</str<strong>on</strong>g> Escherichia coli [4]. Using<br />

dynamic optimizati<strong>on</strong> by solving a n<strong>on</strong>linear, dynamic optimal c<strong>on</strong>trol problem<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e quasi-sequential approach [5], we investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nitrogen<br />

assimilati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e nitrogen metabolism [6] by <str<strong>on</strong>g>th</str<strong>on</strong>g>e circadian clock [7] <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e green<br />

algae Chlamydom<strong>on</strong>as reinhardtii. The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> our analysis is to identify which enzymes<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a drastically simplified model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolism <str<strong>on</strong>g>of</str<strong>on</strong>g> C. reinhardtii need<br />

to be subjected to circadian c<strong>on</strong>trol in order to adapt <str<strong>on</strong>g>th</str<strong>on</strong>g>e organism to day-night<br />

rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms. Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>e physiological and envir<strong>on</strong>mental c<strong>on</strong>straints <str<strong>on</strong>g>th</str<strong>on</strong>g>at imply <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

necessity <str<strong>on</strong>g>of</str<strong>on</strong>g> circadian regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> different enzymes are investigated. Important<br />

comp<strong>on</strong>ents <str<strong>on</strong>g>of</str<strong>on</strong>g> such a model are appropriate kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> participating reacti<strong>on</strong>s as<br />

well as c<strong>on</strong>centrati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> enzymes and metabolites. We developed such a model<br />

focusing <strong>on</strong> nitrogen metabolism including assimilati<strong>on</strong>, transport and processing<br />

in C. reinhardtii. This model was analyzed under different envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s<br />

and provides first insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e cause <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolite and<br />

enzymes c<strong>on</strong>centrati<strong>on</strong>s observed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e course <str<strong>on</strong>g>of</str<strong>on</strong>g> a day.<br />

References.<br />

[1] Heinrich et al., Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> enzymic reacti<strong>on</strong> systems using optimizati<strong>on</strong> principles.<br />

Eur J Biochem 201 1–21. 1991.<br />

[2] Heinrich R. and Schuster S., The Regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cellular Systems New York: Chapman & Hall<br />

1996<br />

[3] Klipp et al., Predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> temporal gene expressi<strong>on</strong>. Metabolic opimizati<strong>on</strong> by re-distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> enzyme activities. Eur J Biochem 269 5406–5413. 2002.<br />

[4] Zaslaver et al., Just-in-time transcripti<strong>on</strong> program in metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways. Nat Genet 36 486–<br />

491. 2004.<br />

[5] H<strong>on</strong>g et al., A quasi-sequential approach to large-scale dynamic optimizati<strong>on</strong> problems AIChE<br />

Journal 52 255–268. 2006.<br />

[6] Fernandez E. and Galvan A., Inorganic nitrogen assimilati<strong>on</strong> in Chlamydom<strong>on</strong>as. J Exp Bot<br />

58 2279–2287. 2007.<br />

[7] Mittag et al., The circadian clock in Chlamydom<strong>on</strong>as reinhardtii. What is it for? What is it<br />

similar to? Plant Physiol 137 399–409, 2005.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Systems Biology <str<strong>on</strong>g>of</str<strong>on</strong>g> Development; Saturday, July 2, 14:30<br />

Alvaro Köhn-Luque<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and IMI<br />

Universidad Complutense de Madrid (Spain)<br />

e-mail: alvarokohn@mat.ucm.es<br />

Paracrine vs Autocrine Regulati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Early Vascular Patterning<br />

During embry<strong>on</strong>ic vasculogenesis, <str<strong>on</strong>g>th</str<strong>on</strong>g>e earliest mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> blood vessel morphogenesis,<br />

isolated vascular cell progenitors called angioblasts assemble into a characteristic<br />

network-like pattern. So far, however, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms underlying <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

coalescence and patterning <str<strong>on</strong>g>of</str<strong>on</strong>g> angioblasts remain unclear.<br />

We c<strong>on</strong>sider a hybrid cell-based approach similar to <str<strong>on</strong>g>th</str<strong>on</strong>g>at used for a similar in<br />

vitro process [1,2]. However, c<strong>on</strong>trary to previous ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>th</str<strong>on</strong>g>at assume<br />

chemotaxis towards an autocrine signal [1,2,3,4], we favour an alternative<br />

mechanism based <strong>on</strong> matrix-binding <str<strong>on</strong>g>of</str<strong>on</strong>g> paracrine signals. Detailed morphometric<br />

analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> simulated vascular networks and c<strong>on</strong>focal microscopy images obtained<br />

from in vivo quail embryos reveals our model can reproduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e vascular patterns<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high accuracy.<br />

The work to be reported has been made in collaborati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> W. de Back, J. Starruß<br />

and A. Deutsch (Center for High Performance Computing, Technische Universität<br />

Dresden), M. A. Herrero (Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and IMI, Universidad<br />

Complutense de Madrid) and A. Mattiotti and J. M. Pérez-Pomares (Laboratory<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Cardiovascular Development and Angiogenesis, Universidad de Málaga).<br />

References.<br />

[1] Merks RMH, Brodsky SV, Goligorksy MS, Newman SA and Glazier JA (2006) , Cell el<strong>on</strong>gati<strong>on</strong><br />

is key to in silico replicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> in vitro vasculogenesis and subsequent remodeling, Dev Biol<br />

289: 44-54.<br />

[2] Merks RMH, Perryn ED, Shirinifard A and Glazier JA (2008), C<strong>on</strong>tact-Inhibited Chemotaxis<br />

in De Novo and Sprouting Blood-Vessel Grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, PLoS Comput Biol 4(9): e1000163.<br />

[3] Serini G, Ambrosi D, Giraudo E, Gamba A, Preziosi L and Bussollino F (2003), Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

early stages <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular network assembly, EMBO J 22: 1771-1779.<br />

[4] Gamba A, Ambrosi D, C<strong>on</strong>iglio A, de Candia A, Di Talia et al (2003), Percolati<strong>on</strong>, Morphogenesis,<br />

and Burgers Dynamics in Blood Vessels Formati<strong>on</strong>, Phys Rev Lett 90, 11810:<br />

1-4.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Undergraduate Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Educati<strong>on</strong> Bey<strong>on</strong>d BIO 2010 (Part II);<br />

Saturday, July 2, 08:30<br />

Semen Koksal<br />

Florida Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: skoksal@fit.edu<br />

David Carroll<br />

Florida Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Robert van Woesik<br />

Florida Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Richard Sinden<br />

Florida Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Eugene Dshalalow<br />

Flroida Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Establishing an Undergraduate Program and Major in<br />

BioMa<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

To provide increased opportunity for students interested in <str<strong>on</strong>g>th</str<strong>on</strong>g>e intersecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology,<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science, an interdisciplinary degree-granting<br />

program in BioMa<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics was established at <str<strong>on</strong>g>th</str<strong>on</strong>g>e Florida Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

(FIT). This new major encompasses a program <str<strong>on</strong>g>th</str<strong>on</strong>g>at includes a significant undergraduate<br />

research comp<strong>on</strong>ent. The research students are supported by an NSF<br />

grant, UBM. Our emerging UBM program has already had a str<strong>on</strong>g impact <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e FIT campus, helping to create an atmosphere <str<strong>on</strong>g>of</str<strong>on</strong>g> excitement in undergraduates<br />

interested in exploring a new field and gaining novel research experience.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, <str<strong>on</strong>g>th</str<strong>on</strong>g>e positive aspects as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e difficulties in establishing <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

program at <str<strong>on</strong>g>th</str<strong>on</strong>g>e departmental and instituti<strong>on</strong>al level will be discussed. Sample <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

projects and <str<strong>on</strong>g>th</str<strong>on</strong>g>e newly established <str<strong>on</strong>g>th</str<strong>on</strong>g>ree bioma<str<strong>on</strong>g>th</str<strong>on</strong>g> courses will be presented.<br />

519

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Wednesday, June 29, 11:00<br />

Mikhail Kolev<br />

Warmia and Mazury University <str<strong>on</strong>g>of</str<strong>on</strong>g> Olsztyn, Poland<br />

e-mail: kolev@matman.uwm.edu.pl<br />

Barbara Zubik-Kowal<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Boise State University, USA<br />

e-mail: zubik@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.boisestate.edu<br />

Numerical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> a model <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor invasi<strong>on</strong><br />

We present a new algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m for <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model proposed by Chaplain and colleagues [1-3] describing tumor invasi<strong>on</strong> and<br />

metastasis. The model takes into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells to produce and<br />

secrete matrix degradative enzymes, which allow <str<strong>on</strong>g>th</str<strong>on</strong>g>e degradati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> extracellular<br />

matrix, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells due to diffusi<strong>on</strong> and haptotactic migrati<strong>on</strong>.<br />

For <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor cells and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding tissue, we apply numerical approximati<strong>on</strong>s, which are spectrally<br />

accurate and based <strong>on</strong> small amounts <str<strong>on</strong>g>of</str<strong>on</strong>g> grid-points. Our numerical experiments<br />

illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e metastatic ability <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cells.<br />

References.<br />

[1] M.A.J. Chaplain and A.R.A. Anders<strong>on</strong>, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue invasi<strong>on</strong>, in Cancer<br />

modelling and simulati<strong>on</strong>, L. Preziosi, ed., Chapman & Hall/CRC, Boca Rat<strong>on</strong>, FL, 269–297,<br />

2003.<br />

[2] M.A.J. Chaplain, G. Lolas, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cell invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue: The<br />

role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e urokinase plasminogen activati<strong>on</strong> system Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Models Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods Appl. Sci. 15<br />

1685–1734, 2005.<br />

[3] M.A.J. Chaplain, G. Lolas, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue: dynamic<br />

heterogeneity Netw. Heterog. Media 1 399–439, 2006.<br />

520

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Genetics and Genomics; Wednesday, June 29, 08:30<br />

Richard Kollár<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics,<br />

Physics and Informatics, Comenius University, Bratislava, Slovakia<br />

e-mail: kollar@fmph.uniba.sk<br />

Ľubomír Tomáška<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Genetics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Natural Sciences, Comenius University,<br />

Bratislava, Slovakia<br />

Jozef Nosek<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemistry, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Natural Sciences, Comenius<br />

University, Bratislava, Slovakia<br />

Katarína Boová<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, Comenius University,<br />

Bratislava, Slovakia<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> biophysical mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> telomere<br />

leng<str<strong>on</strong>g>th</str<strong>on</strong>g> maintenance in mitoch<strong>on</strong>drial DNA <str<strong>on</strong>g>of</str<strong>on</strong>g> C. parapsilosis<br />

The terminal structures <str<strong>on</strong>g>of</str<strong>on</strong>g> linear mitoch<strong>on</strong>drial DNA (mitoch<strong>on</strong>drial telomeres)<br />

in C. parapsilosis c<strong>on</strong>sist <str<strong>on</strong>g>of</str<strong>on</strong>g> repetitive l<strong>on</strong>g tandem units. Besides <str<strong>on</strong>g>th</str<strong>on</strong>g>ese linear<br />

telomeres o<str<strong>on</strong>g>th</str<strong>on</strong>g>er cyclic c<strong>on</strong>figurati<strong>on</strong>s as telomeric circles and telomeric loops were<br />

experimentally observed and are suspected to play an important role in telomere<br />

leng<str<strong>on</strong>g>th</str<strong>on</strong>g> maintenance. We c<strong>on</strong>struct a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>th</str<strong>on</strong>g>at captures biophysical<br />

interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> various telomeric structures <strong>on</strong> a short time scale and <str<strong>on</strong>g>th</str<strong>on</strong>g>at is able<br />

to reproduce experimental measurements in C. parapsilosis. Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

opens up a couple <str<strong>on</strong>g>of</str<strong>on</strong>g> interesting open ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical problems in quasi-steady state<br />

approximati<strong>on</strong> and discrete coagulati<strong>on</strong>-fragmentati<strong>on</strong> dynamical systems. This is<br />

a joint work wi<str<strong>on</strong>g>th</str<strong>on</strong>g> . Tomáška, J. Nosek and K. Boová.<br />

521

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Andrey V. Kolobov<br />

P. N. Lebedev Physical Institute, Moscow, Russia<br />

e-mail: kolobov@lpi.ru<br />

Vladimir V. Gubernov<br />

P. N. Lebedev Physical Institute, Moscow, Russia<br />

e-mail: gubernov@lpi.ru<br />

Andrey A. Polezhaev<br />

P. N. Lebedev Physical Institute, Moscow, Russia<br />

e-mail: apol@lpi.ru<br />

Cancer; Friday, July 1, 14:30<br />

Speed selecti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model <str<strong>on</strong>g>of</str<strong>on</strong>g> infiltrative tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> account <str<strong>on</strong>g>of</str<strong>on</strong>g> migrati<strong>on</strong>-proliferati<strong>on</strong> dichotomy<br />

A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> infiltrative tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g> taking into account transiti<strong>on</strong>s<br />

between two possible states <str<strong>on</strong>g>of</str<strong>on</strong>g> malignant cells: proliferating and migrating, is<br />

developed. These transiti<strong>on</strong>s are c<strong>on</strong>sidered to depend <strong>on</strong> oxygen level in a <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold<br />

manner: high oxygen c<strong>on</strong>centrati<strong>on</strong> allows cell proliferati<strong>on</strong>, while c<strong>on</strong>centrati<strong>on</strong><br />

below a certain critical value induces cell migrati<strong>on</strong>. Whenever a moving cell<br />

reaches <str<strong>on</strong>g>th</str<strong>on</strong>g>e domain wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high oxygen level it recruits into proliferati<strong>on</strong>, o<str<strong>on</strong>g>th</str<strong>on</strong>g>erwise<br />

it necrotizes.<br />

It is dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at model soluti<strong>on</strong> for localized initial tumour cell distributi<strong>on</strong><br />

tends to autowave soluti<strong>on</strong>. We investigate mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> autowave speed<br />

selecti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> migrati<strong>on</strong>-proliferati<strong>on</strong> dichotomy and compare results<br />

obtained wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>at for Kolmogorov-Petrovskii-Piskunov and Fisher (KPP-F) equati<strong>on</strong>s.<br />

It is known <str<strong>on</strong>g>th</str<strong>on</strong>g>at in KPP-F equati<strong>on</strong>s speed is defined by asymptotics at<br />

leading edge <str<strong>on</strong>g>of</str<strong>on</strong>g> autowave (pulled regime). It is dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

c<strong>on</strong>sidered autowave speed is determined by falling edge (pushed regime). The dependence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tumour spreading rate <strong>on</strong> model parameters is obtained. It is shown<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e spreading rate depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e oxygen level in tissue in a <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold manner.<br />

This work was supported by grants No. 10-01-00289 and 11-01-00392 from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Russian Foundati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Basic Research.<br />

522

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling IV; Saturday, July 2, 08:30<br />

Michał Komorowski<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular Biosciences, Imperial College L<strong>on</strong>d<strong>on</strong><br />

e-mail: M.Komorowski@imperial.ac.uk<br />

Quantificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> noise in signalling systems - importance <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

c<strong>on</strong>trolled signal degradati<strong>on</strong><br />

The phenomena <str<strong>on</strong>g>of</str<strong>on</strong>g> stochasticity in biochemical processes has been intriguing life<br />

scientists for <str<strong>on</strong>g>th</str<strong>on</strong>g>e last few decades. Studies revealed <str<strong>on</strong>g>th</str<strong>on</strong>g>at living cells take advantage<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> stochasticity in some cases and counterbalance stochastic effects in o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers. The<br />

intrinsic source <str<strong>on</strong>g>of</str<strong>on</strong>g> stochasticity in biomolecular systems has been identified wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

random timings <str<strong>on</strong>g>of</str<strong>on</strong>g> individual reacti<strong>on</strong>s, which in a cumulative effect lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

variability in outputs <str<strong>on</strong>g>of</str<strong>on</strong>g> such systems. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e presentati<strong>on</strong> I will dem<strong>on</strong>strate how<br />

stochasticity <str<strong>on</strong>g>of</str<strong>on</strong>g> individual reacti<strong>on</strong>s c<strong>on</strong>tributes to <str<strong>on</strong>g>th</str<strong>on</strong>g>e variability <str<strong>on</strong>g>of</str<strong>on</strong>g> system’s output;<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>at some reacti<strong>on</strong>s have dramatically different effect <strong>on</strong> noise <str<strong>on</strong>g>th</str<strong>on</strong>g>at o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers.<br />

Surprisingly, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e class <str<strong>on</strong>g>of</str<strong>on</strong>g> open c<strong>on</strong>versi<strong>on</strong> systems, <str<strong>on</strong>g>th</str<strong>on</strong>g>at serve as an approximati<strong>on</strong><br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> signal transducti<strong>on</strong>, degradati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an output c<strong>on</strong>tributes half <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

total noise. We also dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> degradati<strong>on</strong> in o<str<strong>on</strong>g>th</str<strong>on</strong>g>er relevant<br />

systems and propose a degradati<strong>on</strong> feedback c<strong>on</strong>trol mechanism <str<strong>on</strong>g>th</str<strong>on</strong>g>at have capability<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> effective noise suppressi<strong>on</strong>. Our me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology c<strong>on</strong>stitutes novel, intuitive and<br />

simple framework to investigate stochastic effects in biochemical networks allowing<br />

for unprecedented insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e origins <str<strong>on</strong>g>of</str<strong>on</strong>g> stochasticity.<br />

523

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ryusuke K<strong>on</strong><br />

e-mail: ryusuke.k<strong>on</strong>@gmail.com<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Permanence induced by life-cycle res<strong>on</strong>ances:<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e periodical cicada problem<br />

Periodical cicadas (Magicicada spp.) are known for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir unusually l<strong>on</strong>g life<br />

cycle for insects and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir prime periodicity <str<strong>on</strong>g>of</str<strong>on</strong>g> ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er 13 or 17 years. One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

explanati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e prime periodicity is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e prime periods are selected to<br />

prevent cicadas from res<strong>on</strong>ating wi<str<strong>on</strong>g>th</str<strong>on</strong>g> predators wi<str<strong>on</strong>g>th</str<strong>on</strong>g> submultiple periods (e.g., see<br />

[1,2]). Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is idea, Webb [3] c<strong>on</strong>structed ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models and gave a<br />

numerical example <str<strong>on</strong>g>th</str<strong>on</strong>g>at periodically oscillating predators wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 2- or 3-year period<br />

eliminate n<strong>on</strong>prime number periodical cicadas. However, in Webb’s model, <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong><br />

between well-timed cicada-cohorts and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir predators is ignored. In our<br />

study, we c<strong>on</strong>struct an age-structured model for dynamically interacting predator<br />

and prey populati<strong>on</strong>s and c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e predator-res<strong>on</strong>ance hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis.<br />

Our main result shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at preys are not necessarily eliminated by predators<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> submultiple periods since invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> preys is always facilitated by <str<strong>on</strong>g>th</str<strong>on</strong>g>eir welltimed<br />

cohorts. It is also shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at synchr<strong>on</strong>ized life-cycles between predator and<br />

prey populati<strong>on</strong>s can produce a permanent system, in which no cohorts are missing<br />

in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> populati<strong>on</strong>s. This c<strong>on</strong>trasts wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e result <str<strong>on</strong>g>th</str<strong>on</strong>g>at systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> asynchr<strong>on</strong>ous<br />

life-cycles cannot be permanent. These results suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at res<strong>on</strong>ances wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

predators are not always deleterious to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir preys.<br />

References.<br />

[1] M. Lloyd and H. S. Dybas: The periodical cicada problem. II. evoluti<strong>on</strong>, Evoluti<strong>on</strong>, (1966),<br />

20, pp.466–505.<br />

[2] S. J. Gould: Ever Since Darwin: Reflecti<strong>on</strong>s in Natural History, Nort<strong>on</strong>, New York, 1977.<br />

[3] G. F. Webb: The prime number periodical cicada problem, Discrete C<strong>on</strong>tin. Dyn. Syst. Ser.<br />

B, (2001), 1, pp.387–399.<br />

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Turing !! Turing?? <strong>on</strong> morphogenesis via experimental and <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical<br />

approaches; Wednesday, June 29, 17:00<br />

Shigeru K<strong>on</strong>do<br />

Osaka University<br />

e-mail: shigeruk<strong>on</strong>do@gmail.com<br />

How experiment and ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics can cooperate in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

study <str<strong>on</strong>g>of</str<strong>on</strong>g> Turing patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> real biological systems?<br />

It was 60 years ago <str<strong>on</strong>g>th</str<strong>on</strong>g>at Turing presented his outstanding idea about <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological<br />

pattern formati<strong>on</strong>. Since <str<strong>on</strong>g>th</str<strong>on</strong>g>en, many <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical studies have been suggesting <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

RD mechanism could be <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e principles <str<strong>on</strong>g>of</str<strong>on</strong>g> biological morphogenesis. Such<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical studies seem to be enough for <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematicians to believe <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological<br />

relevance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory. However, majority <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e developmental biologists still<br />

feel <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e idea <str<strong>on</strong>g>of</str<strong>on</strong>g> RD is not so much related to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir study in spite <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e several<br />

empirical evidences.<br />

We guess <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem comes from <str<strong>on</strong>g>th</str<strong>on</strong>g>e gap <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity between <str<strong>on</strong>g>th</str<strong>on</strong>g>e simple<br />

differential equati<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex real biological phenomena. Through <str<strong>on</strong>g>th</str<strong>on</strong>g>e 15<br />

years <str<strong>on</strong>g>of</str<strong>on</strong>g> experiment <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pigmentati<strong>on</strong> stripe <str<strong>on</strong>g>of</str<strong>on</strong>g> fish skin, we recently found <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

many kinds <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular events, migrati<strong>on</strong>, differentiati<strong>on</strong>, dendrite el<strong>on</strong>gati<strong>on</strong>, and<br />

gap juncti<strong>on</strong>s, are involved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e pigment pattern formati<strong>on</strong>. The whole system is<br />

not similar to any <str<strong>on</strong>g>of</str<strong>on</strong>g> simple model proposed before. After presenting our newest<br />

data, I would like to discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e possible way for <str<strong>on</strong>g>th</str<strong>on</strong>g>e cooperati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical and experimental sides.<br />

525

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Recent advances in infectious disease modelling II; Saturday, July 2, 14:30<br />

Bernhard K<strong>on</strong>rad<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> British Columbia<br />

e-mail: k<strong>on</strong>radbe@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ubc.ca<br />

Jessica M. C<strong>on</strong>way<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> British Columbia<br />

Alejandra Herrera<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> British Columbia<br />

Daniel Coombs<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> British Columbia<br />

Stochastic model-based predicti<strong>on</strong>s <strong>on</strong> post-exposure<br />

prophylaxis strategies for preventi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV infecti<strong>on</strong><br />

Antiretroviral treatment (ART) leads to a much lower viral load in HIV patients<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>us improves quality and leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> life. When used as a post-exposure prophylaxis<br />

(PEP) shortly after exposure to HIV, ARTs are also known to reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

risk <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong>. However, many aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e very early stages <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV infecti<strong>on</strong><br />

remain poorly understood because <str<strong>on</strong>g>th</str<strong>on</strong>g>e associated low viral loads are difficult to<br />

measure clinically. We present a c<strong>on</strong>tinuous-time branching process model <str<strong>on</strong>g>of</str<strong>on</strong>g> early<br />

HIV infecti<strong>on</strong> in order to capture dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e small number <str<strong>on</strong>g>of</str<strong>on</strong>g> virus particles.<br />

Using <str<strong>on</strong>g>th</str<strong>on</strong>g>e related Chapman-Kolmogorov differential equati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e associated<br />

probability generating functi<strong>on</strong> we derive an expressi<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus extincti<strong>on</strong><br />

probability which we solve numerically. This allows us to predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficacy <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

different PEP strategies, c<strong>on</strong>sidering initiati<strong>on</strong> time, durati<strong>on</strong>, and multi-drug regimens.<br />

We also evaluate <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk <str<strong>on</strong>g>of</str<strong>on</strong>g> emergent drug resistance in <str<strong>on</strong>g>th</str<strong>on</strong>g>e event <str<strong>on</strong>g>of</str<strong>on</strong>g> PEP<br />

failure and <str<strong>on</strong>g>th</str<strong>on</strong>g>en discuss how our results can be used to guide public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> decisi<strong>on</strong>s<br />

<strong>on</strong> optimal PEP strategies.<br />

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Plants, grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and transport processes I; Tuesday, June 28, 11:00<br />

Wilfried K<strong>on</strong>rad<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Tübingen, Institute for Geosciences, Sigwartstrasse 10,<br />

D-72070 Tübingen<br />

e-mail: wilfried.k<strong>on</strong>rad@uni-tuebingen.de<br />

Anita Ro<str<strong>on</strong>g>th</str<strong>on</strong>g>-Nebelsick<br />

State Museum <str<strong>on</strong>g>of</str<strong>on</strong>g> Natural History Stuttgart, Rosenstein 1, D-70191<br />

Stuttgart<br />

e-mail: anita.ro<str<strong>on</strong>g>th</str<strong>on</strong>g>nebelsick@smns-bw.de<br />

Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> plant water transport derived from applying an<br />

optimisati<strong>on</strong> scheme to Soil-Plant-Atmosphere-C<strong>on</strong>tinuum<br />

In Central Europe, plant transpirati<strong>on</strong> injects more <str<strong>on</strong>g>th</str<strong>on</strong>g>an 40% <str<strong>on</strong>g>of</str<strong>on</strong>g> precipitati<strong>on</strong><br />

back into <str<strong>on</strong>g>th</str<strong>on</strong>g>e atmosphere. Thus, plants play an important role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e exchange <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

water between soil and atmosphere.<br />

Plants can actively open and close <str<strong>on</strong>g>th</str<strong>on</strong>g>eir leaf openings (“stomata”), gateways<br />

for incoming carb<strong>on</strong> dioxide molecules to be processed by photosyn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis as well<br />

as for outgoing water vapour. Since bo<str<strong>on</strong>g>th</str<strong>on</strong>g> gas species use <str<strong>on</strong>g>th</str<strong>on</strong>g>e same pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

majority <str<strong>on</strong>g>of</str<strong>on</strong>g> terrestrial plants has to compromise between <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>flicting tasks <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

(i) minimising transpirati<strong>on</strong> (in order to avoid water stress and wilting) and (ii)<br />

maximising assimilati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> carbohydrates (which c<strong>on</strong>stitute bo<str<strong>on</strong>g>th</str<strong>on</strong>g> building material<br />

and energy source <str<strong>on</strong>g>of</str<strong>on</strong>g> plants).<br />

Plants deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>flict by regulating leaf gas exchange (via stomatal<br />

aperture) according to soil moisture and <str<strong>on</strong>g>th</str<strong>on</strong>g>e diurnal cycles <str<strong>on</strong>g>of</str<strong>on</strong>g> temperature, insolati<strong>on</strong><br />

and relative humidity. The (physiological) details <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is regulati<strong>on</strong> mechanism<br />

are largely unknown. N<strong>on</strong>e<str<strong>on</strong>g>th</str<strong>on</strong>g>eless, it is possible, to emulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e actual plant gas<br />

exchange by a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical optimisati<strong>on</strong> scheme ([1], [2], [3]): Optimum stomatal<br />

c<strong>on</strong>ductance as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> time is determined by requiring <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e assimilates<br />

assembled during <strong>on</strong>e day accumulate to a maximum, being subject to <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>straint<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e quantity <str<strong>on</strong>g>of</str<strong>on</strong>g> water transpired during <str<strong>on</strong>g>th</str<strong>on</strong>g>is time span equals a given<br />

amount. The diurnal variati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> temperature, insolati<strong>on</strong> and relative humidity<br />

have to be prescribed.<br />

The calculus <str<strong>on</strong>g>of</str<strong>on</strong>g> variati<strong>on</strong> subject to c<strong>on</strong>straints introduces a Lagrangian multiplier<br />

whose value cannot be determined in <str<strong>on</strong>g>th</str<strong>on</strong>g>e usual way, due to an intractable<br />

integral. Applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tinuity equati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e water current <str<strong>on</strong>g>th</str<strong>on</strong>g>rough soil,<br />

plant roots and xylem allows, however, to express <str<strong>on</strong>g>th</str<strong>on</strong>g>e Lagrangian multiplier in<br />

terms <str<strong>on</strong>g>of</str<strong>on</strong>g> soil properties, tree anatomy and tree physiologic restricti<strong>on</strong>s.<br />

Applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model encompass <str<strong>on</strong>g>th</str<strong>on</strong>g>e rec<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> palaeo-envir<strong>on</strong>ment<br />

from fossilised plant leaves and <str<strong>on</strong>g>th</str<strong>on</strong>g>e predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> changing atmospheric<br />

CO2-level <strong>on</strong> climate ([4]). Redistributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> precipitati<strong>on</strong> between soil<br />

(run-<str<strong>on</strong>g>of</str<strong>on</strong>g>f and ground water) and atmosphere (transpirati<strong>on</strong>) due to modified stomatal<br />

acti<strong>on</strong> caused by changing atmospheric CO2-c<strong>on</strong>tent can also be assessed.<br />

References.<br />

[1] Cowan, I.R., 1977. Stomatal behaviour and envir<strong>on</strong>ment. Adv. Bot. Res. 4, 117–228.<br />

527

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[2] Mäkelä , A., Berninger, F., Hari, P., 1996. Optimal c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> gas exchange during drought:<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical analysis. Ann. Bot. 77, 461–467.<br />

[3] W. K<strong>on</strong>rad, A. Ro<str<strong>on</strong>g>th</str<strong>on</strong>g>-Nebelsick and M. Grein, 2008. Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> stomatal density resp<strong>on</strong>se to<br />

atmospheric CO2 explained by a model. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology 253, 638–658.<br />

[4] Hugo Jan de Boer, Emmy I. Lammertsma, Friederike Wagner-Cremer, David L. Dilcher, Martin<br />

J. Wassen and Stefan C. Dekker, 2011. Climate forcing due to optimizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> maximal<br />

leaf c<strong>on</strong>ductance in subtropical vegetati<strong>on</strong> under rising CO2. PNAS Early Editi<strong>on</strong>,<br />

www.pnas.org/cgi/doi/10.1073/pnas.1100555108<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Lubomir Kostal<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physiology, AS CR, v.v.i., Videnska 1083, Praha 4, Czech<br />

Republic<br />

e-mail: kostal@biomed.cas.cz<br />

Petr Lansky<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physiology, AS CR, v.v.i., Videnska 1083, Praha 4, Czech<br />

Republic<br />

e-mail: lansky@biomed.cas.cz<br />

Ondrej Pokora<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physiology, AS CR, v.v.i., Videnska 1083, Praha 4, Czech<br />

Republic<br />

e-mail: pokora@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.muni.cz<br />

Entropy and Fisher informati<strong>on</strong> based measures <str<strong>on</strong>g>of</str<strong>on</strong>g> statistical<br />

dispersi<strong>on</strong><br />

We propose and discuss two informati<strong>on</strong>-based measures <str<strong>on</strong>g>of</str<strong>on</strong>g> statistical dispersi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> timing precisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>al firing: <str<strong>on</strong>g>th</str<strong>on</strong>g>e entropy-based dispersi<strong>on</strong> and Fisher<br />

informati<strong>on</strong>-based dispersi<strong>on</strong>, and compare <str<strong>on</strong>g>th</str<strong>on</strong>g>em wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard deviati<strong>on</strong>. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e standard deviati<strong>on</strong> is used routinely, we show, <str<strong>on</strong>g>th</str<strong>on</strong>g>at it is not well suited<br />

to quantify some aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> dispersi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten expected intuitively, such as<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e degree <str<strong>on</strong>g>of</str<strong>on</strong>g> randomness. The proposed dispersi<strong>on</strong> measures are not entirely independent,<br />

al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough each describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing regularity from a different point <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

view. We discuss relati<strong>on</strong>ships between <str<strong>on</strong>g>th</str<strong>on</strong>g>e measures and describe <str<strong>on</strong>g>th</str<strong>on</strong>g>eir extremal<br />

values. We also apply <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>od to real experimental data from sp<strong>on</strong>taneously<br />

active olfactory neur<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> rats. Our results and c<strong>on</strong>clusi<strong>on</strong>s are applicable to a<br />

wide range <str<strong>on</strong>g>of</str<strong>on</strong>g> situati<strong>on</strong>s where <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>tinuous positive random<br />

variable is <str<strong>on</strong>g>of</str<strong>on</strong>g> interest.<br />

References.<br />

[1] L. Kostal, P. Lansky, J-P. Rospars (2007) Review: Neur<strong>on</strong>al coding and spiking randomness<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Neuroscience 26 2693–2701<br />

[2] L. Kostal, P. Marsalek (2010) Neur<strong>on</strong>al jitter: can we measure <str<strong>on</strong>g>th</str<strong>on</strong>g>e spike timing dispersi<strong>on</strong><br />

differently? Chinese Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Physiology 53 454–464<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Tanya Kostova Vassilevska<br />

Nati<strong>on</strong>al Science Foundati<strong>on</strong><br />

e-mail: tvassile@nsf.gov<br />

Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 08:30<br />

A model <str<strong>on</strong>g>of</str<strong>on</strong>g> intracellular virus replicati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> implicati<strong>on</strong>s<br />

for virus evoluti<strong>on</strong><br />

Viruses are <str<strong>on</strong>g>th</str<strong>on</strong>g>e simplest living organisms. In order to survive, a virus has to successfully<br />

invade a host cell, overcome cellular degradati<strong>on</strong> mechanisms, produce progeny<br />

and export it to infect o<str<strong>on</strong>g>th</str<strong>on</strong>g>er cells; eventually evade immune resp<strong>on</strong>se and jump to<br />

a new host to start <str<strong>on</strong>g>th</str<strong>on</strong>g>e cycle again. The first challenge to virus survival is successful<br />

reproducti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e host cell. For RNA viruses, such reproducti<strong>on</strong> includes<br />

a balance between several competing processes: producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> RNA-derived RNA<br />

polymerase (RdRp), producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> viral protein, RNA replicati<strong>on</strong> by <str<strong>on</strong>g>th</str<strong>on</strong>g>e RdRp,<br />

formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> viri<strong>on</strong>s by combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genomic RNA and structural viral protein<br />

and degradati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese products. Here we design a model representing <str<strong>on</strong>g>th</str<strong>on</strong>g>ese processes<br />

for positive-sense single stranded viruses (such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e family <str<strong>on</strong>g>of</str<strong>on</strong>g> Picorna or<br />

Flavi viruses) as a system <str<strong>on</strong>g>of</str<strong>on</strong>g> ODEs derived from stoichiometric enzyme-substrate<br />

reacti<strong>on</strong>s and explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymptotic dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model. The possible regimes<br />

are (1) virus extincti<strong>on</strong>, (2) stable steady state and (3) a regime where RNA and<br />

RdRp are produced in excess (tend to infinity in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model) while <str<strong>on</strong>g>th</str<strong>on</strong>g>e structural<br />

protein is fully utilized (c<strong>on</strong>verges to 0). If <str<strong>on</strong>g>th</str<strong>on</strong>g>e net producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> viri<strong>on</strong>s is a measure<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> virus fitness (such a claim is supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e view <str<strong>on</strong>g>th</str<strong>on</strong>g>at larger virus populati<strong>on</strong>s<br />

can maintain higher diversity and <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore be more adaptable), <str<strong>on</strong>g>th</str<strong>on</strong>g>en we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

viruses <str<strong>on</strong>g>th</str<strong>on</strong>g>at have evolved to utilize scenario (3) have higher fitness <str<strong>on</strong>g>th</str<strong>on</strong>g>an viruses<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at establish equilibrium progeny producti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell.<br />

530

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bioimaging; Tuesday, June 28, 11:00<br />

Il<strong>on</strong>a Anna Kowalik-Urbaniak<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Waterloo, Waterloo, Ontario, Canada N2L 3G1<br />

e-mail: iakowali@uwaterloo.ca<br />

Edward R. Vrscay<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Waterloo, Waterloo, Ontario, Canada N2L 3G1<br />

e-mail: ervrscay@uwaterloo.ca<br />

Zhou Wang<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Electrical and Computer Engineering, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Engineering,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Waterloo, Waterloo, Ontario, Canada N2L<br />

3G1<br />

e-mail: zhouwang@ieee.org<br />

David K<str<strong>on</strong>g>of</str<strong>on</strong>g>f<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Diagnostic Imaging, Hamilt<strong>on</strong> Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Sciences, Department<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Radiology, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Sciences, McMaster University,<br />

Hamilt<strong>on</strong>, Ontario, Canada L8S4L8<br />

e-mail: k<str<strong>on</strong>g>of</str<strong>on</strong>g>f@hhsc.ca<br />

Objective quality assessment <str<strong>on</strong>g>of</str<strong>on</strong>g> JPEG- and JPEG2000compressed<br />

CT neuro images<br />

We have employed various objective image fidelity measures to evaluate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

quality <str<strong>on</strong>g>of</str<strong>on</strong>g> JPEG- and JPEG2000-compressed CT neuro images. Lossy compressi<strong>on</strong><br />

degrades image quality. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e compressi<strong>on</strong> ratio is increased, JPEG produces<br />

blocking and ringing artifacts whereas JPEG2000 introduces blurring and ringing<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e rec<strong>on</strong>structed images. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough subjective me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to evaluate quality <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

compressed medical images are complicated and difficult to c<strong>on</strong>duct, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

most accepted way for measuring diagnosis reliability. In order to overcome <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

problems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> subjective quality assessment and to automate <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> assessing<br />

degradati<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a need for reliable objective quality assessment <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

medical images. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is no generally accepted objective quality measure<br />

for medical images, Mean Squared Error (MSE) is widely used. It is, however, well<br />

known <str<strong>on</strong>g>th</str<strong>on</strong>g>at MSE does not corresp<strong>on</strong>d well wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e human visual system (HVS).<br />

We are <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore led to <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong>, “Which quality measures should be used <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

best corresp<strong>on</strong>d to visual and diagnostic quality?”<br />

The HVS is highly sensitive to structural informati<strong>on</strong> and distorti<strong>on</strong>s (e.g.<br />

JPEG blockiness, “salt-and-pepper” noise, ringing effect, blurring). The structural<br />

similarity (SSIM) index, introduced by Wang and Bovik [2], assumes <str<strong>on</strong>g>th</str<strong>on</strong>g>at images<br />

are highly structured and <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere exist str<strong>on</strong>g neighbouring dependencies am<strong>on</strong>g<br />

pixels. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese features are completely ignored by <str<strong>on</strong>g>th</str<strong>on</strong>g>e MSE.<br />

We also introduce ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er approach to measure <str<strong>on</strong>g>th</str<strong>on</strong>g>e quality <str<strong>on</strong>g>of</str<strong>on</strong>g> compressed CT<br />

images, <str<strong>on</strong>g>th</str<strong>on</strong>g>e so-called “Weberized L 2 ” me<str<strong>on</strong>g>th</str<strong>on</strong>g>od. It is a weighted versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e MSE<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at incorporates <str<strong>on</strong>g>th</str<strong>on</strong>g>e Weber model <str<strong>on</strong>g>of</str<strong>on</strong>g> percepti<strong>on</strong>.<br />

We analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e quality maps <str<strong>on</strong>g>of</str<strong>on</strong>g> compressed images associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e L 1 , L 2 ,<br />

Weberized L 2 and SSIM measures. Our investigati<strong>on</strong> supports <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>clusi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

an extensive subjective quality evaluati<strong>on</strong> study c<strong>on</strong>ducted by radiologists in K<str<strong>on</strong>g>of</str<strong>on</strong>g>f<br />

531

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

et al. [1] . The presence <str<strong>on</strong>g>of</str<strong>on</strong>g> edge artifacts introduced by JPEG2000 compressi<strong>on</strong><br />

is revealed <strong>on</strong>ly by <str<strong>on</strong>g>th</str<strong>on</strong>g>e SSIM quality map and may explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e results <str<strong>on</strong>g>of</str<strong>on</strong>g> K<str<strong>on</strong>g>of</str<strong>on</strong>g>f et<br />

al.. In c<strong>on</strong>clusi<strong>on</strong>, our study suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e SSIM measure and <str<strong>on</strong>g>th</str<strong>on</strong>g>e SSIM quality<br />

map provide <str<strong>on</strong>g>th</str<strong>on</strong>g>e most promising approach to predict subjective quality assessment<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> compressed brain CT images.<br />

References.<br />

[1] D. K<str<strong>on</strong>g>of</str<strong>on</strong>g>f, P. Bak and P. Brownrigg, D. Hosseinzadeh, A. Khademi, A. Kiss, L. Lepanto, T.<br />

Michalak, H. Shulman and A. Volkening. Pan-Canadian evaluati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> irreversible compressi<strong>on</strong><br />

ratios ("Lossy Compressi<strong>on</strong>") for development <str<strong>on</strong>g>of</str<strong>on</strong>g> nati<strong>on</strong>al guidelines J Digit Imaging. 2009<br />

Dec;22, 6, pp. 569-78. Oct 2008.<br />

[2] Z. Wang, A. C. Bovik, H. R. Sheikh, E. P. Sim<strong>on</strong>celli, Image quality assessment: From<br />

error visibility to structural similarity. IEEE Transacti<strong>on</strong>s <strong>on</strong> Image Processing, 13, no. 4, pp.<br />

600-612, Apr. 2004.<br />

532

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Statistical Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Signals I; Saturday, July 2, 08:30<br />

T. Kozubowski<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nevada, Reno<br />

e-mail: tkozubow@unr.edu<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Podgorski<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Statistics, Lund University,<br />

Sweden<br />

Skew Laplace Distributi<strong>on</strong>s: Theory and Some Applicati<strong>on</strong>s<br />

in Biology<br />

Skew Laplace distributi<strong>on</strong>s, which naturally arise in c<strong>on</strong>necti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> random summati<strong>on</strong><br />

and quantile regressi<strong>on</strong> settings, <str<strong>on</strong>g>of</str<strong>on</strong>g>fer an attractive and flexible alternative<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e normal (Gaussian) distributi<strong>on</strong> in a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> settings where <str<strong>on</strong>g>th</str<strong>on</strong>g>e assumpti<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> symmetry and short tail are too restrictive. In particular, <str<strong>on</strong>g>th</str<strong>on</strong>g>is model has<br />

been recently found useful for gene selecti<strong>on</strong> and classificati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in analysis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> microarray data sets. In ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er applicati<strong>on</strong>, it was observed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e Laplace<br />

distributi<strong>on</strong> adequately represents <str<strong>on</strong>g>th</str<strong>on</strong>g>e size distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> microbial cells. We shall<br />

present fundamental properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model, which give insight into its applicability<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese areas, and discuss its extensi<strong>on</strong>s to multivariate models, time series,<br />

and stochastic processes.<br />

533

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Models in Spatial Ecology; Tuesday, June 28, 17:00<br />

Roberto Kraenkel<br />

Institute for Theoretical Physics, São Paulo State University, Brazil<br />

e-mail: kraenkel@ift.unesp.br<br />

Diffusi<strong>on</strong> in fragmented landscapes: habitat split<br />

This talk gives an overview <str<strong>on</strong>g>of</str<strong>on</strong>g> some recent results c<strong>on</strong>cerning stage-structured<br />

species in fragmented habitats. It focus <strong>on</strong> amphibians, which need two distinct<br />

habitats in different life stages. We discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e particular case where <str<strong>on</strong>g>th</str<strong>on</strong>g>e habitat<br />

is split: <str<strong>on</strong>g>th</str<strong>on</strong>g>e terrestrial habitat <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e adults is separated from <str<strong>on</strong>g>th</str<strong>on</strong>g>e aquatic habitat<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e larvae. A central questi<strong>on</strong> is how <str<strong>on</strong>g>th</str<strong>on</strong>g>e distance between <str<strong>on</strong>g>th</str<strong>on</strong>g>e two required<br />

habitats affects populati<strong>on</strong> size and persistence in isolated fragment. We find a c<strong>on</strong>diti<strong>on</strong><br />

for persistence in a simple model based <strong>on</strong> diffusi<strong>on</strong> equati<strong>on</strong>s supplemented<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> boundary c<strong>on</strong>diti<strong>on</strong>s encompassing populati<strong>on</strong> regulati<strong>on</strong>. The habitat split<br />

model improves our understanding about spatially structured populati<strong>on</strong>s and has<br />

relevant implicati<strong>on</strong>s for landscape design for amphibian c<strong>on</strong>servati<strong>on</strong>.<br />

534

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics <str<strong>on</strong>g>of</str<strong>on</strong>g> Neglected Tropical Diseases; Wednesday, June 29, 11:00<br />

Roberto Kraenkel<br />

Institute for Theoretical Physics, São Paulo State University, Brazil<br />

e-mail: kraenkel@ift.unesp.br<br />

R. M. Coutinho<br />

Institute for Theoretical Physics, São Paulo State University, Brazil<br />

G. Z. Laporta<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, University <str<strong>on</strong>g>of</str<strong>on</strong>g> São Paulo, Brazil<br />

P. I. Prado<br />

Ecology Dept., Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> São Paulo,<br />

Brazil<br />

A model for malaria wi<str<strong>on</strong>g>th</str<strong>on</strong>g> ecological comp<strong>on</strong>ents<br />

We present a model for malaria epidemics which takes into account, besides humans<br />

and anopheles mosquitoes, <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er mosquitoes species which are not<br />

vectors for plasmodium but which create a competiti<strong>on</strong> effect <str<strong>on</strong>g>th</str<strong>on</strong>g>at can reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

basic reproductive number. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er, we c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er species<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at can provide blood meals for mosquitoes but are immune to malaria, creating a<br />

diluti<strong>on</strong> effect. These effects are meant to model observed situati<strong>on</strong>s in which almost<br />

no malaria cases are observed, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e anopheles mosquito is abundant.<br />

535

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Neurosciences; Wednesday, June 29, 08:30<br />

K.G. Kravchuk and A.K. Vidybida<br />

Bogolyubov Institute for Theoretical Physics,<br />

Metrololgichna str., 14-B, 03680 Kyiv, Ukraine<br />

e-mail: kgkravchuk@bitp.kiev.ua and vidybida@bitp.kiev.ua<br />

Delayed feedback results in n<strong>on</strong>-markovian statistics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>al firing<br />

The output inter-spike intervals (ISI) statistics <str<strong>on</strong>g>of</str<strong>on</strong>g> a single neur<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> delayed<br />

feedback is c<strong>on</strong>sidered. The c<strong>on</strong>structi<strong>on</strong> is driven externally wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Poiss<strong>on</strong> stream<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> excitatory impulses. Via <str<strong>on</strong>g>th</str<strong>on</strong>g>e feedback line, neur<strong>on</strong>’s output impulses are fed<br />

back to its input wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a fixed time delay. We c<strong>on</strong>sider cases <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> excitatory and<br />

inhibitory neur<strong>on</strong>. Namely, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e first case, <str<strong>on</strong>g>th</str<strong>on</strong>g>e neur<strong>on</strong> receives excitatory impulses<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> from <str<strong>on</strong>g>th</str<strong>on</strong>g>e driving Poiss<strong>on</strong> stream and from its own output stream <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

feedback line. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d case, apart from <str<strong>on</strong>g>th</str<strong>on</strong>g>e external Poiss<strong>on</strong> excitati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

delayed self-inhibiti<strong>on</strong> is present. For analytical derivati<strong>on</strong>, we take binding neur<strong>on</strong><br />

(BN) model [1].<br />

delayed feedback<br />

input stream<br />

✲<br />

✲<br />

Σ ≤ N0<br />

τ – memory ✲<br />

output stream<br />

<br />

t – ISI durati<strong>on</strong><br />

We obtain exact analytical expressi<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e single-ISI c<strong>on</strong>diti<strong>on</strong>al probability<br />

density P (t2 | t1), which gives <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability to obtain an output ISI <str<strong>on</strong>g>of</str<strong>on</strong>g> durati<strong>on</strong><br />

t2 provided <str<strong>on</strong>g>th</str<strong>on</strong>g>e previous ISI durati<strong>on</strong> was t1, and for <str<strong>on</strong>g>th</str<strong>on</strong>g>e double-ISI c<strong>on</strong>diti<strong>on</strong>al<br />

probability density P (t2 | t1, t0).<br />

It turns out, <str<strong>on</strong>g>th</str<strong>on</strong>g>at P (t2 | t1) does not reduce to <str<strong>on</strong>g>th</str<strong>on</strong>g>e output ISI probability density<br />

P (t2), found before. This means, <str<strong>on</strong>g>th</str<strong>on</strong>g>at firing statistics is n<strong>on</strong>-renewal <strong>on</strong>e even in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

simplest possible neur<strong>on</strong>al network. Moreover, we prove exactly, <str<strong>on</strong>g>th</str<strong>on</strong>g>at P (t2 | t1, t0)<br />

cannot be reduced to P (t2 | t1), <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence <strong>on</strong> t0 cannot be eliminated. This<br />

exactly means <str<strong>on</strong>g>th</str<strong>on</strong>g>at ISIs stream does not possess Markov property.<br />

Also, we introduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>al probability density P (tn+1 | tn, . . . , t1, t0). It<br />

is proven exactly, <str<strong>on</strong>g>th</str<strong>on</strong>g>at P (tn+1 | tn, . . . , t1, t0) does not reduce to P (tn+1 | tn, . . . , t1)<br />

for any n ≥ 0. This means <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e output ISIs stream cannot be represented as<br />

Markov chain <str<strong>on</strong>g>of</str<strong>on</strong>g> any finite order.<br />

We c<strong>on</strong>clude, <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e delayed feedback presence causes n<strong>on</strong>-markovian behavior<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>al firing statistics for bo<str<strong>on</strong>g>th</str<strong>on</strong>g> excitatory and inhibitory neur<strong>on</strong>s. We<br />

suggest, <str<strong>on</strong>g>th</str<strong>on</strong>g>at interpretati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> experimental records <str<strong>on</strong>g>of</str<strong>on</strong>g> spiking activity should take<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is fact into account.<br />

References.<br />

[1] A.K. Vidybida, Neur<strong>on</strong> as time coherence discriminator. Biol. Cybern. 74 539–544 (1996).<br />

[2] K.G. Kravchuk, A.K. Vidybida, Delayed feedback causes n<strong>on</strong>-Markovian behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>al<br />

firing statistics. arXiv:1012.6019v2.<br />

536<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Computati<strong>on</strong>al toxicology and pharmacology - in silico drug activity and<br />

safety assessment; Saturday, July 2, 11:00<br />

Axel Krinner, Markus Scholz<br />

IMISE, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Leipzig<br />

e-mail: krinner@izbi.uni-leipzig.de<br />

Ingo Roeder<br />

IMB, Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: ingo.roeder@tu-dresden.de<br />

Combining two model paradigms: How an agent-based<br />

hematopoietic stem cell model couples to an ordinary<br />

differential equati<strong>on</strong>s model <str<strong>on</strong>g>of</str<strong>on</strong>g> mature granulopoiesis and<br />

chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

To model <str<strong>on</strong>g>th</str<strong>on</strong>g>e organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> hematopoietic stem cells Roeder et al. have introduced<br />

an agent-based model which succeeded well in explaining several experimental<br />

data <str<strong>on</strong>g>of</str<strong>on</strong>g> cl<strong>on</strong>al competiti<strong>on</strong> and stem cell dynamics wi<str<strong>on</strong>g>th</str<strong>on</strong>g> clinically relevant<br />

applicati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e field <str<strong>on</strong>g>of</str<strong>on</strong>g> chr<strong>on</strong>ic myeloid leukemia [1]. The model assumes two<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g>-envir<strong>on</strong>ments and regulates stem cell activity by an intrinsic feedback <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

c<strong>on</strong>trols <str<strong>on</strong>g>th</str<strong>on</strong>g>e transiti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>ese envir<strong>on</strong>ments.<br />

In order to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy and grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factor applicati<strong>on</strong>s<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> mature granulocytes, a compartment-based ordinary differential<br />

equati<strong>on</strong>s (ODE) model <str<strong>on</strong>g>of</str<strong>on</strong>g> granulopoiesis has been introduced by Scholz et al. [2].<br />

Here <str<strong>on</strong>g>th</str<strong>on</strong>g>e stem cell compartment is represented in a very simplified fashi<strong>on</strong>.<br />

To overcome <str<strong>on</strong>g>th</str<strong>on</strong>g>is simplificati<strong>on</strong> and to take advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e established model<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> hematopoietic stem cells we replaced <str<strong>on</strong>g>th</str<strong>on</strong>g>e ODE stem cell compartment wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a difference<br />

equati<strong>on</strong> formulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e agent-based stem cell model [3]. Two feedback<br />

mechanisms for stem cell activati<strong>on</strong> were introduced for replacing <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> self-renewal probability and proliferative fracti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e stem cell compartments<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ODE model. Stem cell activati<strong>on</strong> was implemented firstly by increasing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

probability <str<strong>on</strong>g>of</str<strong>on</strong>g> exiting quiescent states and sec<strong>on</strong>dly by a general accelerati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

stem cell compartment.<br />

The resulting hybrid model was capable <str<strong>on</strong>g>of</str<strong>on</strong>g> reproducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental data<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy regime <str<strong>on</strong>g>of</str<strong>on</strong>g> Chop21. Interestingly, <str<strong>on</strong>g>th</str<strong>on</strong>g>e comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> feedback<br />

mechanisms for stem cell activati<strong>on</strong> showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e best agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e regenerati<strong>on</strong><br />

resp<strong>on</strong>se in <str<strong>on</strong>g>th</str<strong>on</strong>g>e clinical trials was achieved for <str<strong>on</strong>g>th</str<strong>on</strong>g>e intrinsic regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e agent-based model wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out additi<strong>on</strong>al activati<strong>on</strong>.<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e combined model, we aim to improve <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy effects <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hematopoietic system in <str<strong>on</strong>g>th</str<strong>on</strong>g>e future. In particular we<br />

expect fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> role <str<strong>on</strong>g>of</str<strong>on</strong>g> hematopoietic stem cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> a toxicity induced leukopoenia wi<str<strong>on</strong>g>th</str<strong>on</strong>g> subsequent regenerati<strong>on</strong><br />

References.<br />

[1] I. Roeder and M. Horn and I. Glauche and A. Hochhaus and M.C. Mueller and M. Loeffler,<br />

Dynamic modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> imatinib-treated chr<strong>on</strong>ic myeloid leukemia: functi<strong>on</strong>al insights and<br />

clinical implicati<strong>on</strong>s. Nat Med 12 1181–1184.<br />

[2] M. Scholz and C. Engel and M. Loeffler, Modeling human granulopoiesis under polychemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> G-CSF support J Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Biol 50 397–439.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[3] P.S. Kim, P.P. Lee and D. Levy, Modeling imatinib-treated chr<strong>on</strong>ic myelogenous leukemia:<br />

reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> agent-based models Bull Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Biol 70 728–744.<br />

538

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

J. Krishnan<br />

Imperial College L<strong>on</strong>d<strong>on</strong><br />

e-mail: krishnan@icex.imperial.ac.uk<br />

Aiman Alam-Nazki<br />

Imperial College L<strong>on</strong>d<strong>on</strong><br />

Cellular Systems Biology; Saturday, July 2, 11:00<br />

Modelling and elucidating design principles underlying<br />

attractive and repulsive gradient sensing<br />

Many cells, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> prokaryote and eukaryote exhibit <str<strong>on</strong>g>th</str<strong>on</strong>g>e feature <str<strong>on</strong>g>of</str<strong>on</strong>g> chemotaxis, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

directed moti<strong>on</strong> in resp<strong>on</strong>se to gradients <str<strong>on</strong>g>of</str<strong>on</strong>g> chemicals. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, many <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

cells exhibit bo<str<strong>on</strong>g>th</str<strong>on</strong>g> attractive and repulsive gradient sensing to ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e same or<br />

different chemicals. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, I will discuss two aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem.<br />

The first is <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanistic modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> a network postulated to describe<br />

chemorepulsi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model system Dictyostelium. The signalling network is complex<br />

since it is str<strong>on</strong>gly n<strong>on</strong>-linear incorporating a combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> feedforward and<br />

feedback loops wi<str<strong>on</strong>g>th</str<strong>on</strong>g> spatial signalling. A systematic mechanistic modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

work describes whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er and under which c<strong>on</strong>diti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network can exhibit <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

desired behaviour and makes clearcut predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e important features in <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

regard, resulting in very n<strong>on</strong>-trivial c<strong>on</strong>clusi<strong>on</strong>s.<br />

The sec<strong>on</strong>d aspect which I will discuss is how <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell signalling networks may<br />

be organized to give rise to bo<str<strong>on</strong>g>th</str<strong>on</strong>g> attractive and repulsive gradient sensing in a given<br />

cell, and how <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting behaviour depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e qualitative aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> signal<br />

transducti<strong>on</strong> (eg. adaptati<strong>on</strong>, sp<strong>on</strong>taneous polarizati<strong>on</strong>). Here a framework using<br />

qualitatively simplified models will be used to distill transparent insights. The<br />

relevance to individual systems will also be discussed.<br />

539

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Game <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical modelling and optimizati<strong>on</strong> in evoluti<strong>on</strong> and ecology II;<br />

Tuesday, June 28, 14:30<br />

Vlastimil Krivan<br />

Biology center AS CR and University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Bohemia, Ceske Budejovice,<br />

Czech Republic<br />

e-mail: vlastimil.krivan@gmail.com<br />

Ross Cressman<br />

Dept <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Wilfrid Laurier Univ., Waterloo, Ontario, N2L<br />

3C5, Canada<br />

On evoluti<strong>on</strong>ary stability in some populati<strong>on</strong> games<br />

The classical models <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> dynamics (e.g., <str<strong>on</strong>g>th</str<strong>on</strong>g>e Lotka-Volterra predator-prey<br />

model) assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at interacti<strong>on</strong> streng<str<strong>on</strong>g>th</str<strong>on</strong>g> is fixed and independent <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong><br />

densities. However, empirical evidence suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at bo<str<strong>on</strong>g>th</str<strong>on</strong>g> prey and/or predators<br />

change <str<strong>on</strong>g>th</str<strong>on</strong>g>eir behavior wi<str<strong>on</strong>g>th</str<strong>on</strong>g> changes in populati<strong>on</strong> numbers. For example, an increase<br />

in predator numbers <str<strong>on</strong>g>of</str<strong>on</strong>g>ten decreases prey activity. Such plasticity in animal<br />

behavior leads to variable interacti<strong>on</strong> streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>at can str<strong>on</strong>gly influence populati<strong>on</strong><br />

dynamics. As predators and prey <str<strong>on</strong>g>of</str<strong>on</strong>g>ten play avoidance game (i.e., prey try<br />

to avoid predators while predators try to find prey), to solve <str<strong>on</strong>g>th</str<strong>on</strong>g>is game me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>arily game <str<strong>on</strong>g>th</str<strong>on</strong>g>eory are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten used. In particular, it is assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

optimal soluti<strong>on</strong> to such a game corresp<strong>on</strong>ds to <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>arily stable strategy.<br />

By definiti<strong>on</strong>, such a strategy cannot be invaded by rare mutants, and from <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

respect it is <str<strong>on</strong>g>th</str<strong>on</strong>g>e ultimate outcome <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical <str<strong>on</strong>g>th</str<strong>on</strong>g>eory does<br />

not c<strong>on</strong>sider changes in populati<strong>on</strong> numbers and in such a dynamic setting it is not<br />

a priori clear, if evoluti<strong>on</strong>arily stable strategies can be invaded by rare behavioral<br />

mutants when populati<strong>on</strong> dynamics are c<strong>on</strong>sidered. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we will show <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is can happen, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough behavioral mutants cannot replace residents. However,<br />

a polymorphism can arise. Whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>is happens or not, depends <strong>on</strong> particular<br />

dynamics and food web topology.<br />

540

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Pawel Krupinski<br />

Computati<strong>on</strong>al Biology and Biological Physics Group, Department <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Theoretical Physics, Lund University, S-221 00 Lund, Sweden<br />

e-mail: pawel@<str<strong>on</strong>g>th</str<strong>on</strong>g>ep.lu.se<br />

Marcus Heisler<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> Molecular Biology Laboratory, Meyerh<str<strong>on</strong>g>of</str<strong>on</strong>g>strasse 1, D-69117<br />

Heidelberg, Germany<br />

e-mail: heisler@embl.de<br />

Olivier Hamant<br />

INRA, CNRS, ENS, Universite de Ly<strong>on</strong>, 46 Allee d Italie, 69364 Ly<strong>on</strong><br />

Cedex 07, France<br />

e-mail: Olivier.Hamant@ens-ly<strong>on</strong>.fr<br />

Magalie Uyttewaal<br />

INRA, CNRS, ENS, Universite de Ly<strong>on</strong>, 46 Allee d Italie, 69364 Ly<strong>on</strong><br />

Cedex 07, France<br />

e-mail: magalie.uyttewaal@ens-ly<strong>on</strong>.fr<br />

Arezki Boudaoud<br />

INRA, CNRS, ENS, Universite de Ly<strong>on</strong>, 46 Allee d Italie, 69364 Ly<strong>on</strong><br />

Cedex 07, France<br />

e-mail: arezki.boudaoud@ens-ly<strong>on</strong>.fr<br />

Carolyn Ohno<br />

<str<strong>on</strong>g>European</str<strong>on</strong>g> Molecular Biology Laboratory, Meyerh<str<strong>on</strong>g>of</str<strong>on</strong>g>strasse 1, D-69117<br />

Heidelberg, Germany<br />

e-mail: carolyn.ohno@embl.de<br />

Henrik J<strong>on</strong>ss<strong>on</strong><br />

Computati<strong>on</strong>al Biology and Biological Physics Group, Department <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Theoretical Physics, Lund University, S-221 00 Lund, Sweden<br />

e-mail: henrik@<str<strong>on</strong>g>th</str<strong>on</strong>g>ep.lu.se<br />

Jan Traas<br />

INRA, CNRS, ENS, Universite de Ly<strong>on</strong>, 46 Allee d Italie, 69364 Ly<strong>on</strong><br />

Cedex 07, France<br />

e-mail: Jan.Traas@ens-ly<strong>on</strong>.fr<br />

Elliot Meyerowitz<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology, California Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Pasadena,<br />

California 91125, USA<br />

e-mail: meyerow@caltech.edu<br />

Interplay <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanical and biochemical signals in plant<br />

morphogenesis<br />

The Shoot Apical Meristems (SAM) initiate grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> new aerial plant organs like<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e leaves and flowers. Formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e new primordia <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e surface <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e meristem<br />

involves complicated mechanical and biochemical interacti<strong>on</strong>s, yet meristem is<br />

able to achieve amazing regularity in repeating <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> outgrow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

new leaves and flowers for <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole lifetime <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e plant. From <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical<br />

point <str<strong>on</strong>g>of</str<strong>on</strong>g> view <str<strong>on</strong>g>th</str<strong>on</strong>g>is requires a precise regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount and directi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

541

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

cellular grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. The former is influenced by polarized transport <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e plant horm<strong>on</strong>e<br />

auxin, while <str<strong>on</strong>g>th</str<strong>on</strong>g>e latter is related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e directi<strong>on</strong>ality <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microtubule array.<br />

By using <str<strong>on</strong>g>th</str<strong>on</strong>g>e combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> experiments and modeling we have provided evidence<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at microtubules resp<strong>on</strong>d to mechanical stress and c<strong>on</strong>tribute to a feedback loop<br />

encompassing physical forces, microtubule orientati<strong>on</strong>, mechanical anisotropy and<br />

morphogenesis [1]. We have shown also <str<strong>on</strong>g>th</str<strong>on</strong>g>at auxin transport regulati<strong>on</strong> by PIN1<br />

can be explained by <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanism which uses <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical stresses in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell<br />

walls to c<strong>on</strong>vey informati<strong>on</strong> about auxin c<strong>on</strong>centrati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e neighboring cells. We<br />

presented a model <str<strong>on</strong>g>of</str<strong>on</strong>g> such interacti<strong>on</strong>s which is capable <str<strong>on</strong>g>of</str<strong>on</strong>g> creating phyllotactic<br />

patterns and is c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental results <str<strong>on</strong>g>of</str<strong>on</strong>g> cell ablati<strong>on</strong>s [2]. These results<br />

suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical signals are not <strong>on</strong>ly passively influenced by auxin<br />

patterning, but also actively direct transport <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin using mechanical stress as a<br />

comm<strong>on</strong> regulator <str<strong>on</strong>g>of</str<strong>on</strong>g> PIN1 localizati<strong>on</strong> and mechanical anisotropy c<strong>on</strong>tributing to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e phyllotactic patterns.<br />

References.<br />

[1] O. Hamant, M. Heisler, H. Jönss<strong>on</strong>, P. Krupinski, M. Uyttewaal, P. Bokov, F. Cors<strong>on</strong>, P.<br />

Sahlin, A. Boudaoud, E. M. Meyerowitz, Y. Couder, and J. Traas, Developmental patterning<br />

by mechanical signals in Arabidopsis Science 322, 1650–1655 (2008)<br />

[2] M. Heisler, O. Hamant, P. Krupinski, M. Uyttewaal, C. Ohno, H. Jönss<strong>on</strong>, J. Traas, E.<br />

Meyerowitz, Alignment between PIN1 Polarity and Microtubule Orientati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Shoot Apical<br />

Meristem Reveals a Tight Coupling between Morphogenesis and Auxin Transport PLoS<br />

Biology 8(10) :e1000516 (2010)<br />

542

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Pawel Krupinski<br />

Computati<strong>on</strong>al Biology and Biological Physics Group, Department <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Theoretical Physics, Lund University, S-221 00 Lund, Sweden<br />

e-mail: pawel@<str<strong>on</strong>g>th</str<strong>on</strong>g>ep.lu.se<br />

Vijay Chickarmane<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology, California Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Pasadena,<br />

California 91125, USA<br />

e-mail: vchickar@caltech.edu<br />

Carsten Peters<strong>on</strong><br />

Computati<strong>on</strong>al Biology and Biological Physics Group, Department <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Theoretical Physics, Lund University, S-221 00 Lund, Sweden<br />

e-mail: carsten@<str<strong>on</strong>g>th</str<strong>on</strong>g>ep.lu.se<br />

Molecular and mechanical interacti<strong>on</strong>s in early mammalian<br />

embryo<br />

Mammalian embryogenesis is a dynamic process involving gene expressi<strong>on</strong> and mechanical<br />

forces between proliferating cells. Despite a weal<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> research and identificati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e key genes c<strong>on</strong>tributing to <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e early embryo,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e precise nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese interacti<strong>on</strong>s is still elusive. We have developed a computati<strong>on</strong>al<br />

modeling framework by which we can analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> embryo<br />

development and differentiati<strong>on</strong> to specific tissues during its first 4.5 days [1]. We<br />

combine mechanical and biochemical interacti<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells to investigate<br />

how different mechanism c<strong>on</strong>tribute to <str<strong>on</strong>g>th</str<strong>on</strong>g>e specificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e trophectoderm, primitive<br />

endoderm and alignment <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e embryo axes. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e trophectoderm<br />

formati<strong>on</strong> we compare robustness <str<strong>on</strong>g>of</str<strong>on</strong>g> two models by which <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristic pattern<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Cdx2 and Oct4 transcripti<strong>on</strong> factors forms: gene expressi<strong>on</strong> is influenced by<br />

positi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell or bo<str<strong>on</strong>g>th</str<strong>on</strong>g> expressi<strong>on</strong> and positi<strong>on</strong> are regulated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e pattern <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

symmetric/asymmetric divisi<strong>on</strong>s depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Cdx2 levels. During endoderm<br />

formati<strong>on</strong> we examine influence <str<strong>on</strong>g>of</str<strong>on</strong>g> differential adhesi<strong>on</strong>, geometrical c<strong>on</strong>straints and<br />

stochastic active movement <str<strong>on</strong>g>of</str<strong>on</strong>g> cells <strong>on</strong> efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> endoderm layer specificati<strong>on</strong>.<br />

We dem<strong>on</strong>strate how purely mechanical factors can be resp<strong>on</strong>sible for alignment<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e animal-vegetal and embry<strong>on</strong>ic-abembry<strong>on</strong>ic axes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e embryo. This work<br />

by combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell-based spatial mechanical simulati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a genetic network<br />

approach hints <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two domains may be inseparably linked and <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

taking <str<strong>on</strong>g>th</str<strong>on</strong>g>eir interacti<strong>on</strong>s into account can be necessary for explaining mammalian<br />

embryogenesis.<br />

References.<br />

[1] P. Krupinski, V. Chickarmane and C. Peters<strong>on</strong>, Simulating <str<strong>on</strong>g>th</str<strong>on</strong>g>e mammalian blastocyst - molecular<br />

and mechanical interacti<strong>on</strong>s pattern <str<strong>on</strong>g>th</str<strong>on</strong>g>e embryo to appear in PloS Comp. Biology<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

IV; Wednesday, June 29, 08:30<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Bartoszek<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Chalmers University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg, Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg, Sweden<br />

e-mail: krzbar@chalmers.se<br />

Michał Krzemiński<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences 00-956 Warszawa,<br />

Poland<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Probability Theory and Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Technical Physics Gdańsk University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

80-233 Gdańsk, Poland<br />

e-mail: mkrzeminski@mif.pg.gda.pl<br />

Markov model <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer development – survival time<br />

predicti<strong>on</strong><br />

We will present a newly developed [1] Markov model <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer development. This<br />

is a compartmental model which allows <strong>on</strong>e to separately c<strong>on</strong>sider different stages<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease’s progress. The model assumes <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> waiting times<br />

between stages is exp<strong>on</strong>ential wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate depending linearly <strong>on</strong> an arbitrary number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> predictors. We apply <str<strong>on</strong>g>th</str<strong>on</strong>g>is model to a breast cancer data set <str<strong>on</strong>g>of</str<strong>on</strong>g> women from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Pomerania regi<strong>on</strong> (1987–1992) [2]. We use <str<strong>on</strong>g>th</str<strong>on</strong>g>e medical data in c<strong>on</strong>juncti<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a modified Bloom grading system to assign patients to different states <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Markov chain and explore what clinical predictors (which include am<strong>on</strong>gst o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers<br />

age, tumour size, number <str<strong>on</strong>g>of</str<strong>on</strong>g> infected nodes, presence <str<strong>on</strong>g>of</str<strong>on</strong>g> estrogen and proestrogen<br />

receptors) best describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e state dependent transiti<strong>on</strong> probabilities and whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ey have detrimental effects via a regressi<strong>on</strong> analysis. We also explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> survival time predicti<strong>on</strong> under <str<strong>on</strong>g>th</str<strong>on</strong>g>is Markov model <str<strong>on</strong>g>of</str<strong>on</strong>g> disease and c<strong>on</strong>sider<br />

extensi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e assumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> exp<strong>on</strong>entially distributed waiting times.<br />

References.<br />

[1] D. Faissol et. al. Bias in Markov models <str<strong>on</strong>g>of</str<strong>on</strong>g> disease Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences 220 143–156.<br />

[2] J. Skokowski Wartości rokownicze wybranych czynników klinicznych i patomorfologicznych w<br />

raku piersi PhD <str<strong>on</strong>g>th</str<strong>on</strong>g>esis Medical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Gdańsk 2001.<br />

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Computati<strong>on</strong>al toxicology and pharmacology - in silico drug activity and<br />

safety assessment; Saturday, July 2, 11:00<br />

Wojciech Krzyzanski<br />

University at Buffalo, Buffalo, New York, USA.<br />

e-mail: wk@buffalo.edu<br />

Hematopoietic cell populati<strong>on</strong>s as <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic targets<br />

Pharmacodynamics is a rapidly growing field wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a focus <strong>on</strong> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> drug effects. A very important class <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic/toxic effects is hematological<br />

cell populati<strong>on</strong>s, dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> which have been a well investigated subject <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

physiologically structured populati<strong>on</strong> models. However, <strong>on</strong>ly recently such models<br />

have incorporated drug effects <strong>on</strong> cell populati<strong>on</strong>s.<br />

This talk will introduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e pharmacodynamic models <str<strong>on</strong>g>of</str<strong>on</strong>g> drug effects <strong>on</strong> hematopoietic<br />

cell populati<strong>on</strong>s. It will also make a link to physiologically structured populati<strong>on</strong><br />

models <str<strong>on</strong>g>th</str<strong>on</strong>g>rough such structures as cell age and fluorescent label. The roles<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> physiological structures in describing <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic effects <str<strong>on</strong>g>of</str<strong>on</strong>g> various drugs will be<br />

emphasized.<br />

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Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

V; Wednesday, June 29, 11:00<br />

Akisato Kubo<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Sciences, Fujita Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Unicersity,<br />

Toyoake, Aichi 470-1192, Japan<br />

e-mail: akikubo@fujita-hu.ac.jp<br />

Existence and Asymptotic Behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> Soluti<strong>on</strong>s to<br />

N<strong>on</strong>linear Evoluti<strong>on</strong> Equati<strong>on</strong>s Arising in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e global existence in time and asymptotic pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear evoluti<strong>on</strong> equati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> str<strong>on</strong>g dissipati<strong>on</strong>. Applying<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e above result to some models <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical biology and medicine, we discuss<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em.<br />

For <str<strong>on</strong>g>th</str<strong>on</strong>g>is purpose we first show <str<strong>on</strong>g>th</str<strong>on</strong>g>e solvability and <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymptotic pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

soluti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e intial boundary value problem <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong> linear evoluti<strong>on</strong> equati<strong>on</strong>s:<br />

⎧<br />

utt = D∇2ut + ∇ · (χ(ut, e−u )e−u∇u) in Ω × (0, T ) (1.1)<br />

⎪⎨<br />

(NE)<br />

⎪⎩<br />

∂<br />

∂ν u | ∂Ω = 0 <strong>on</strong> ∂Ω × (0, T ) (1.2)<br />

u(x, 0) = u0(x), ut(x, 0) = u1(x) in Ω (1.3)<br />

where Ω is a bounded domain in Rn and ∂Ω is a smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> boundary <str<strong>on</strong>g>of</str<strong>on</strong>g> Ω and ν is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e outer unit normal vector and we denote<br />

∂ ∂<br />

= ∂t, = ∂xi, i = 1 · ··, n, ∇u = grad<br />

∂t ∂x<br />

xu = (∂x1u, · · ·, ∂xnu)<br />

i<br />

∇ 2 u = ∇ · ∇u = ∆u = ∂ 2 x1 u + · · · + ∂2 xn u.<br />

(1.1) includes <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>linear evoluti<strong>on</strong> equati<strong>on</strong>s c<strong>on</strong>sidered in [4]-[6] to show <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

global existence in time and <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymptotic pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models. We improve our ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical approach and obtain <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> (NE), which is in general form <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>e obtained in <str<strong>on</strong>g>th</str<strong>on</strong>g>em. Next we apply<br />

our result to ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, tumour induced angiogenesis<br />

and tumour invasi<strong>on</strong>, proposed by Chaplain and Anders<strong>on</strong>(see [1]-[3]).<br />

References.<br />

[1] Anders<strong>on</strong> and Chaplain, A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for capillary network formati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e absence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cell proliferati<strong>on</strong> Appl. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Lett., 11(3), 1998, 109–114.<br />

[2] Anders<strong>on</strong> and Chaplain, C<strong>on</strong>tinuous and discrete ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour-induced<br />

angiogenesis Bull. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol., 60, 1998, 857–899.<br />

[3] Anders<strong>on</strong>, Chaplain et al., Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour invasi<strong>on</strong> and metastasis J.<br />

Theor. Med., 2, 2000, 129–154.<br />

[4] Kubo and Suzuki, Asymptotic behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> to a parabolic ODE system modeling<br />

tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g> Differential and Integral Equati<strong>on</strong>s, 17(7-8), 2004, 721–736.<br />

[5] Kubo and Suzuki and Hoshino, Asymptotic behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> to a parabolic ODE system<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Sci. Appl., 22, 2005, 121–135.<br />

[6] Kubo and Suzuki, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour angiogenesis, J. Comp. Appl. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>., 204,<br />

2007, 48–55.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious agents;<br />

Tuesday, June 28, 17:00<br />

Adam Kucharski<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cambridge<br />

e-mail: A.Kucharski@damtp<br />

Julia Gog<br />

DAMTP, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cambridge<br />

e-mail: jrg20@cam.ac.uk<br />

Strain dynamics and influenza drift<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most exciting current areas in infectious disease modelling is in bringing<br />

toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic and evoluti<strong>on</strong>ary dynamics. Influenza drift is perhaps <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

most striking example <str<strong>on</strong>g>of</str<strong>on</strong>g> where <str<strong>on</strong>g>th</str<strong>on</strong>g>e two processes must be c<strong>on</strong>sidered toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er:<br />

epidemics give rise to new strains, which in turn permit new epidemics.<br />

We will begin wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a general introducti<strong>on</strong> to models <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple strains, and<br />

some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir challenges, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> technical and in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> capturing observed biological<br />

phenomena. In most populati<strong>on</strong>-based models <str<strong>on</strong>g>of</str<strong>on</strong>g> strain dynamics, <str<strong>on</strong>g>th</str<strong>on</strong>g>e number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> variables grows exp<strong>on</strong>entially wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> strains. We present two items<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> our recent work, each <str<strong>on</strong>g>of</str<strong>on</strong>g> which avoids <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem in <strong>on</strong>e way or ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er:<br />

1) The impact <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary c<strong>on</strong>straints <strong>on</strong> influenza drift: standard drift<br />

models assume influenza is free to mutate to escape host immunity. In practice,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ere may be some functi<strong>on</strong>al cost associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese mutati<strong>on</strong>s, and <str<strong>on</strong>g>th</str<strong>on</strong>g>is can<br />

be incorporated into a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model. In c<strong>on</strong>trast to unc<strong>on</strong>strained drift<br />

models, <str<strong>on</strong>g>th</str<strong>on</strong>g>is system is bistable, exhibiting bo<str<strong>on</strong>g>th</str<strong>on</strong>g> drift-like patterns and single strain<br />

dynamics for <str<strong>on</strong>g>th</str<strong>on</strong>g>e same parameter values. This raises some important questi<strong>on</strong>s for<br />

vaccinati<strong>on</strong> strategies.<br />

2) Age-structure and immune history: al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough relatively simple assumpti<strong>on</strong>s<br />

about <str<strong>on</strong>g>th</str<strong>on</strong>g>e acquisiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> immunity capture well <str<strong>on</strong>g>th</str<strong>on</strong>g>e general dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> influenza<br />

drift, recent outbreaks have highlighted <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>sidering <str<strong>on</strong>g>th</str<strong>on</strong>g>e details<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> precisely how immunity is acquired by an individual over <str<strong>on</strong>g>th</str<strong>on</strong>g>eir lifetime. In<br />

particular, strains <str<strong>on</strong>g>th</str<strong>on</strong>g>at infect us when we are young may be disproporti<strong>on</strong>ately<br />

important (e.g. <str<strong>on</strong>g>th</str<strong>on</strong>g>rough original antigenic sin), and <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune resp<strong>on</strong>se may be<br />

weakened in <str<strong>on</strong>g>th</str<strong>on</strong>g>e elderly.<br />

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Developmental Biology; Wednesday, June 29, 17:00<br />

Michael Kücken<br />

Max-Planck-Institute for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Physics <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Systems<br />

e-mail: kuecken@pks.mpg.de<br />

The role <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanical stress and Merkel cells in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> fingerprints<br />

In spite <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e great importance <str<strong>on</strong>g>of</str<strong>on</strong>g> fingerpint patterns in forensics and biometrics<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ere is still no generally accepted <str<strong>on</strong>g>th</str<strong>on</strong>g>eory how fingerprint patterns are formed in<br />

utero. Substantial evidence exists <str<strong>on</strong>g>th</str<strong>on</strong>g>at mechanical forces are decisive for determining<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e directi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ridges [1]. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er, it is well-supported <str<strong>on</strong>g>th</str<strong>on</strong>g>at a certain skin<br />

cell, <str<strong>on</strong>g>th</str<strong>on</strong>g>e Merkel cell, is <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary pattern forming agent [2]. However, until now<br />

no c<strong>on</strong>necti<strong>on</strong> has been established between <str<strong>on</strong>g>th</str<strong>on</strong>g>ese findings.<br />

In my talk I will present a model <str<strong>on</strong>g>th</str<strong>on</strong>g>at links stress distributi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e developing<br />

embry<strong>on</strong>al skin to <str<strong>on</strong>g>th</str<strong>on</strong>g>e Merkel cell. This model is an agent-based model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Merkel cells as agents <str<strong>on</strong>g>th</str<strong>on</strong>g>at are interacting wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er. As an outcome <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

model I will explain what factors in fingerprint formati<strong>on</strong> are genetically c<strong>on</strong>trolled<br />

and why indeed every fingerprint — even <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>es <str<strong>on</strong>g>of</str<strong>on</strong>g> identical twins — is unique.<br />

References.<br />

[1] M. Kücken and A.C. Newell, A model for fingerprint formati<strong>on</strong>, Europhys Lett, 68, 141–146<br />

[2] D.-K. Kim and K.A. Holbrook, The appearance, density and sistributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Merkel cells in<br />

human embry<strong>on</strong>ic and fetal skin: <str<strong>on</strong>g>th</str<strong>on</strong>g>eir relati<strong>on</strong> to sweat gland and hair follicle development,<br />

J Invest Dermat, 104, 411–416<br />

548

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Peter Kühl<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Basle, Switzerland<br />

e-mail: Peter-W.Kuehl@unibas.ch<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Stochastic time-time interacti<strong>on</strong>s in biocatalytic and<br />

signalling systems<br />

This c<strong>on</strong>tributi<strong>on</strong> deals in general terms wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic interplay <str<strong>on</strong>g>of</str<strong>on</strong>g> time points<br />

(P’s, durati<strong>on</strong>less events) and time intervals (I’s, eventless or eventful durati<strong>on</strong>s).<br />

P’s are visualized as <str<strong>on</strong>g>th</str<strong>on</strong>g>e heads or feet <str<strong>on</strong>g>of</str<strong>on</strong>g> time arrows (hitting or leaving an I). I’s are<br />

represented as simple linear segments <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e time axis or as 1-dimensi<strong>on</strong>al parts<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> more sophisticated geometries (time loops, composite time strings, time nets,<br />

zeitgestalten). The leng<str<strong>on</strong>g>th</str<strong>on</strong>g>s <str<strong>on</strong>g>of</str<strong>on</strong>g> I’s and <str<strong>on</strong>g>th</str<strong>on</strong>g>e placements <str<strong>on</strong>g>of</str<strong>on</strong>g> P’s wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in I’s are assumed<br />

to be describable by probability distributi<strong>on</strong>s (possessing positive, negative or no<br />

memory). Physical carriers <str<strong>on</strong>g>of</str<strong>on</strong>g> I’s are macromolecules, metabol<strong>on</strong>s, "signal<strong>on</strong>s" or<br />

whole cells. Physical examples <str<strong>on</strong>g>of</str<strong>on</strong>g> P’s are ligand arrivals at (or departures from)<br />

specific sites <strong>on</strong> macromolecules and - at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular level - nerve pulse arrivals at<br />

synapses. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e quantitative analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> P-I interacti<strong>on</strong>s we apply matrix-analytic<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods as used in Queueing Theory (cf. Kühl PW and Jobmann M (2006) J Rec<br />

Signal Transd 26, 1-34).<br />

Analogously to light-matter interacti<strong>on</strong>s, we distinguish <str<strong>on</strong>g>th</str<strong>on</strong>g>ree major ways how a<br />

P may interact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an I: (i) reflecti<strong>on</strong>, (ii) absorpti<strong>on</strong> and (iii) emissi<strong>on</strong>. Depending<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e degree <str<strong>on</strong>g>of</str<strong>on</strong>g> timing-sensitivity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e macromolecular or (sub)cellular structures<br />

and <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong>al shape <str<strong>on</strong>g>of</str<strong>on</strong>g> P’s and I’s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall performance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system<br />

may be optimal, suboptimal or pessimal. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e time patterns created<br />

by P’s and I’s may form - analogously to zeitgestalten in speech and music - a<br />

delicate mean <str<strong>on</strong>g>of</str<strong>on</strong>g> intra- and intercellular communicati<strong>on</strong> and informati<strong>on</strong> transfer.<br />

The above-described P-I interacti<strong>on</strong>s bel<strong>on</strong>g to <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> timing sensu latissimo,<br />

termed by us TIMETICS (Kühl PW (2007) FEBS J 274 (Suppl 1) 247);<br />

c<strong>on</strong>trary to kinetics, not rates but times and time patterns are <str<strong>on</strong>g>of</str<strong>on</strong>g> primary c<strong>on</strong>cern.<br />

TIMETICS (which also includes temporal logic and memory-based phenomena) is<br />

a vast field wi<str<strong>on</strong>g>th</str<strong>on</strong>g> applicati<strong>on</strong>s in biological as well as n<strong>on</strong>biological sciences.<br />

549

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cell migrati<strong>on</strong> during development: modelling and experiment; Saturday,<br />

July 2, 08:30<br />

Paul Kulesa<br />

Stowers Institute for Medical Research<br />

e-mail: pmk@stowers.org<br />

Rebecca McLennan<br />

Stowers Institute for Medical Research<br />

e-mail: rem@stowers.org<br />

Louise Dys<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: louise.dys<strong>on</strong>@balliol.ox.ac.uk<br />

Kate Pra<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

Stowers Institute for Medical Research<br />

e-mail: kjp@stowers.org<br />

Ru<str<strong>on</strong>g>th</str<strong>on</strong>g> Baker<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: ru<str<strong>on</strong>g>th</str<strong>on</strong>g>.baker@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

Philip Maini<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: maini@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

Experimental analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> neural crest migrati<strong>on</strong> during<br />

development<br />

Experimental analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> neural crest migrati<strong>on</strong> during development Cell migrati<strong>on</strong><br />

and cell fate decisi<strong>on</strong>s are str<strong>on</strong>gly influenced by microenvir<strong>on</strong>mental signals<br />

during embry<strong>on</strong>ic development and cancer. Yet, it is largely unclear how cells receive<br />

and interpret microenvir<strong>on</strong>mental signals <str<strong>on</strong>g>th</str<strong>on</strong>g>at influence <str<strong>on</strong>g>th</str<strong>on</strong>g>eir fate and choice<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> directi<strong>on</strong>. To address <str<strong>on</strong>g>th</str<strong>on</strong>g>ese questi<strong>on</strong>s, we use <str<strong>on</strong>g>th</str<strong>on</strong>g>e neural crest (NC) as our model<br />

system. NC cells are a highly invasive, multipotent embry<strong>on</strong>ic cell populati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

are sculpted into discrete migratory streams and patterned into multiple derivatives<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e microenvir<strong>on</strong>ments cells travel <str<strong>on</strong>g>th</str<strong>on</strong>g>rough. We have developed an in vivo<br />

imaging platform in chick <str<strong>on</strong>g>th</str<strong>on</strong>g>at permits single cell resoluti<strong>on</strong> and behavior analysis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> fluorescently labeled NC cells. By combining molecular interventi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> timelapse<br />

imaging, we have discovered a role for NC cell chemotaxis and how cells may<br />

resp<strong>on</strong>d to distinct microenvir<strong>on</strong>mental signals and navigate to precise locati<strong>on</strong>s.<br />

We will show recent tissue transplantati<strong>on</strong> and ablati<strong>on</strong> experiments <str<strong>on</strong>g>th</str<strong>on</strong>g>at alter <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

positi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> NC cells al<strong>on</strong>g a migratory route and discuss how cells resp<strong>on</strong>d to local<br />

microenvir<strong>on</strong>mental signals. These data provide <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis for close collaborati<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modellers and <str<strong>on</strong>g>of</str<strong>on</strong>g>fer insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

embry<strong>on</strong>ic pattern formati<strong>on</strong>.<br />

550

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Toshikazu Kuniya<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Tokyo<br />

e-mail: tkuniya@ms.u-tokyo.ac.jp<br />

Epidemics; Thursday, June 30, 11:30<br />

Global stability analysis wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a discretizati<strong>on</strong> approach for<br />

an age-structured SIR epidemic model<br />

The global stability analysis for each equilibrium <str<strong>on</strong>g>of</str<strong>on</strong>g> an age-structured SIR epidemic<br />

model is carried out. After discretizing <str<strong>on</strong>g>th</str<strong>on</strong>g>e model <str<strong>on</strong>g>th</str<strong>on</strong>g>at is a system <str<strong>on</strong>g>of</str<strong>on</strong>g> PDE wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>e age variable, we obtain a multigroup epidemic model <str<strong>on</strong>g>th</str<strong>on</strong>g>at is a system<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> ODE and can apply <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g> Lyapunov, a recently developed<br />

graph-<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretic approach and a m<strong>on</strong>ot<strong>on</strong>e iterative me<str<strong>on</strong>g>th</str<strong>on</strong>g>od in order to show <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

global asymptotic stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease-free equilibrium for R0 ≤ 1, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

global attractivity <str<strong>on</strong>g>of</str<strong>on</strong>g> an endemic equilibrium for R0 > 1, where R0 is <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic<br />

reproducti<strong>on</strong> number. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough for <str<strong>on</strong>g>th</str<strong>on</strong>g>e original PDE model <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility <str<strong>on</strong>g>of</str<strong>on</strong>g> local<br />

instability <str<strong>on</strong>g>of</str<strong>on</strong>g> an endemic equilibrium was shown even for R0 > 1, for <str<strong>on</strong>g>th</str<strong>on</strong>g>e discretized<br />

versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> it we can obtain <str<strong>on</strong>g>th</str<strong>on</strong>g>e aforementi<strong>on</strong>ed global attractivity result, and <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

implies <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility <str<strong>on</strong>g>of</str<strong>on</strong>g> periodic soluti<strong>on</strong>s might be ruled out from <str<strong>on</strong>g>th</str<strong>on</strong>g>e model,<br />

which has been discussed as an open questi<strong>on</strong> for more <str<strong>on</strong>g>th</str<strong>on</strong>g>an two decades. Numerical<br />

simulati<strong>on</strong> provides an example indicating <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two<br />

PDE and ODE systems become closer to each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er as <str<strong>on</strong>g>th</str<strong>on</strong>g>e step size <str<strong>on</strong>g>of</str<strong>on</strong>g> discretizati<strong>on</strong><br />

decreases.<br />

References.<br />

[1] S.N. Busenberg, M. Iannelli, H.R. Thieme, Global behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> an age-structured epidemic<br />

model SIAM J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Anal. 22 1065–1080.<br />

[2] H.R. Thieme, Stability change <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e endemic equilibrium in age-structured models for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

spread <str<strong>on</strong>g>of</str<strong>on</strong>g> S-I-R type infectious diseases in; S. Busenberg and M. Martelli (Eds.), Differential<br />

Equati<strong>on</strong>s Models in Biology, Epidemiology and Ecology, Springer-Verkag, Berlin, 1991, pp.<br />

139–158.<br />

551

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modelling bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms: from gene regulati<strong>on</strong> to large-scale structure and<br />

functi<strong>on</strong>; Wednesday, June 29, 17:00<br />

Christina Kuttler<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Technische Universität München, Boltzmannstraße<br />

3, 85747 Garching, Germany<br />

e-mail: kuttler@ma.tum.de<br />

Modelling approaches for Quorum sensing in Pseudom<strong>on</strong>as<br />

putida and its observati<strong>on</strong> in a bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm compartment<br />

More and more bacterial species are found to regulate gene expressi<strong>on</strong> via extracellular<br />

signals called autoinducers. By <str<strong>on</strong>g>th</str<strong>on</strong>g>at mechanism, usually called Quorum<br />

sensing (QS), <str<strong>on</strong>g>th</str<strong>on</strong>g>ey check for <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s as populati<strong>on</strong> density<br />

and diffusi<strong>on</strong> limitati<strong>on</strong>. Pseudom<strong>on</strong>as putida, a rhizosphere bacterium, has <strong>on</strong>e<br />

such QS regulati<strong>on</strong> system. Expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a fluorescence protein (GFP) allows for<br />

direct m<strong>on</strong>itoring <str<strong>on</strong>g>of</str<strong>on</strong>g> inducti<strong>on</strong> behaviour <strong>on</strong> single cell level, but uses as sec<strong>on</strong>d<br />

autoinducer receptor which perturbs <str<strong>on</strong>g>th</str<strong>on</strong>g>e original system to some extent. An ODE<br />

model allows to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>is perturbati<strong>on</strong> and helps to interpret <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed behaviour.<br />

In an experimental approach <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> upregulati<strong>on</strong> was observed under flow<br />

and n<strong>on</strong>-flow c<strong>on</strong>diti<strong>on</strong>s. A two compartment model was set up and fitted to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

experimental data. By <str<strong>on</strong>g>th</str<strong>on</strong>g>at, several hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses could be checked, giving a clear<br />

hint <strong>on</strong> a growing layer which is not directly accessible by <str<strong>on</strong>g>th</str<strong>on</strong>g>e flow compartment,<br />

probably a bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm.<br />

A sec<strong>on</strong>d interesting topic c<strong>on</strong>cerns an QS-induced (delayed) producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an<br />

autoinducer-degrading enzyme. We introduce a delay differential system, analyse<br />

its behaviour and compare it to simpler models. Transferred to a spatial model<br />

(as part <str<strong>on</strong>g>of</str<strong>on</strong>g> a reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong>) it allows to c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e ecological c<strong>on</strong>sequences<br />

for single bacteria in a bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm.<br />

552

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Julia Kzhyshkowska<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Heidelberg<br />

e-mail: julia.kzhyshkowska@umm.de<br />

Immunology; Wednesday, June 29, 14:30<br />

Perspectives <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling for understanding <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

intracellular signalling and vesicular trafficking in<br />

macrophages<br />

Perspectives <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling for understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> intracellular signalling<br />

and vesicular trafficking in macrophages<br />

Julia Kzhyshkowska, Anna Marciniak-Czochra, Alexei Gratchev University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Heidelberg, Germany.<br />

Macrophages are essential elements <str<strong>on</strong>g>of</str<strong>on</strong>g> immune system <str<strong>on</strong>g>th</str<strong>on</strong>g>at orchestrate activati<strong>on</strong><br />

and downregulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> inflammatory reacti<strong>on</strong>s, tissue remodelling, healing<br />

processes and tissue homeostasis. Macrophages have to resp<strong>on</strong>d to complex signals<br />

specific for homeostatic or pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologic c<strong>on</strong>diti<strong>on</strong>s. To retain sufficient accuracy<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong> macrophages make use <str<strong>on</strong>g>of</str<strong>on</strong>g> cooperative acti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple extracellular<br />

factors <str<strong>on</strong>g>th</str<strong>on</strong>g>at may amplify required activities and suppress undesired <strong>on</strong>es. This cooperativity<br />

is based <strong>on</strong> complex branching signalling networks coupled to positive<br />

and negative feedback loops; ligand uptake by scavenger receptors; intracellular<br />

sorting and multiple secretory pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways. Deregulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cooperativity leads to<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ological situati<strong>on</strong>s such as chr<strong>on</strong>ic inflammati<strong>on</strong>, allergy, tumour initiati<strong>on</strong> and<br />

progressi<strong>on</strong>. The complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system makes it impossible to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> every particular molecular event using classical molecular biological me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology.<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> signalling and membrane trafficking pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways<br />

using frameworks <str<strong>on</strong>g>of</str<strong>on</strong>g> differential equati<strong>on</strong>s will allow qualitative and quantitative<br />

descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> macrophage behaviour in c<strong>on</strong>diti<strong>on</strong>s simulating physiological situati<strong>on</strong>.<br />

Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e model c<strong>on</strong>structi<strong>on</strong> requires large amounts <str<strong>on</strong>g>of</str<strong>on</strong>g> quantitative<br />

experimental data, <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model using ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods enables<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e elements critical for <str<strong>on</strong>g>th</str<strong>on</strong>g>e system. Established models may<br />

be used to simulate behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> macrophages under different c<strong>on</strong>diti<strong>on</strong>s and to<br />

predict <str<strong>on</strong>g>th</str<strong>on</strong>g>eir reacti<strong>on</strong>s in vivo. Identified critical elements <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system will facilitate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e isolati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> predictive/diagnostic markers as well as potential <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic<br />

targets.<br />

553

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bioengineering; Tuesday, June 28, 14:30<br />

Paweł Lachor<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Informatics, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: pawel.lachor@polsl.pl<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Puszyński<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Automatic C<strong>on</strong>trol, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g>.puszynski@polsl.pl<br />

Andrzej Polański<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Informatics, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: andrzej.polanski@polsl.pl<br />

Accuracy indices for assessing performance <str<strong>on</strong>g>of</str<strong>on</strong>g> different<br />

versi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Gillespie Algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m for stochastic molecular<br />

simulati<strong>on</strong>s<br />

Dynamics in populati<strong>on</strong> models at <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular level are comm<strong>on</strong>ly described using<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic approach based <strong>on</strong> systems <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled first-order ordinary<br />

differential equati<strong>on</strong>s (ODEs). Deterministic approach al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough fast in calculati<strong>on</strong><br />

is not always accurate for systems c<strong>on</strong>taining low-rate reacti<strong>on</strong>s particularly for<br />

species occurring in small quantities. To account for random fluctuati<strong>on</strong>s in numbers<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> molecular species numerous variants <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic Gillespie Algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m has<br />

been introduced. There are already several survey studies comparing and summarizing<br />

different approaches in stochastic modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular mechanisms. In<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese studies <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> accuracy <str<strong>on</strong>g>of</str<strong>on</strong>g> modeling is addressed at <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> simplifying<br />

hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir verificati<strong>on</strong> [3], [4]. In our talk we critically discuss<br />

several possibilities <str<strong>on</strong>g>of</str<strong>on</strong>g> assessing accuracy <str<strong>on</strong>g>of</str<strong>on</strong>g> different strategies <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic molecular<br />

modeling. We also propose a new, direct and precise me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g> comparing<br />

different stochastic modeling strategies based <strong>on</strong> comparis<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> probability distributi<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> observed time instants <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular events. By using our me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

we compare several variants <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic simulati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods, direct, approximate<br />

and hybrid (numerical integrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ODEs and stochastic simulati<strong>on</strong>) [5], [6]. We<br />

grade accuracies <str<strong>on</strong>g>of</str<strong>on</strong>g> predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> different algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> differences betweeen<br />

c<strong>on</strong>diti<strong>on</strong>al distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> times <str<strong>on</strong>g>of</str<strong>on</strong>g> sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular events. In comparis<strong>on</strong>s<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e basic versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Gillespie algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m is c<strong>on</strong>sidered as an accurate<br />

<strong>on</strong>e, predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms are analyzed based <strong>on</strong> its comparis<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

basic versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Gillespie Algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m [1], [2]. Dedicated system written in C++<br />

is used as a computati<strong>on</strong>al platform for calculati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> models applying deferent approaches.<br />

Efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> system is also evaluated in comparis<strong>on</strong> to comm<strong>on</strong> soluti<strong>on</strong>s.<br />

Acknowledgment. This work was supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>European</str<strong>on</strong>g> Community from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>European</str<strong>on</strong>g> Social Fund.<br />

Acknowledgment. This work was financially supported by The Fundati<strong>on</strong> for<br />

Polish Science.<br />

554<br />

References.

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[1] D. T. Gillespie, Exact stochastic simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled chemical reacti<strong>on</strong>s The Journal <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Physical Chemistry 81 25.<br />

[2] D. T. Gillespie, Approximate accelerated stochastic simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chemically reacting systems<br />

Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Chemical Physics 115 4.<br />

[3] J. Pahle, Biochemical simulati<strong>on</strong>s: stochastic, approximate stochastic and hybrid approaches<br />

Briefings in Bioinformatics 10 53-64.<br />

[4] Mario Pineda-Krch, GillespieSSA: Implementing <str<strong>on</strong>g>th</str<strong>on</strong>g>e Gillespie Stochastic Simulati<strong>on</strong> Algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m<br />

in R Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Statistical S<str<strong>on</strong>g>of</str<strong>on</strong>g>tware 25 12.<br />

[5] E.L. Haseltine, J.B. Rawlings, Approximate simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled fast and slow reacti<strong>on</strong>s for<br />

stochastic chemical kinetics Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Chemical Physics 117 15.<br />

[6] K. Puszyński, R. Bertolusso, T. Lipniacki, Crosstalk between p53 and NF-kB systems: proand<br />

anti-apoptotic functi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> NF-kB IET System Biology 3 5.<br />

555

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Semigroups <str<strong>on</strong>g>of</str<strong>on</strong>g> Operators in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology II; Saturday, July 2, 11:00<br />

Mirosław Lachowicz<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics<br />

and Mechanics, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics<br />

e-mail: lachowic@mimuw.edu.pl<br />

Some Markov Jump Processes in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology<br />

The general approach <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows to c<strong>on</strong>struct <str<strong>on</strong>g>th</str<strong>on</strong>g>e Markov processes describing<br />

various processes in ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical biology (or in o<str<strong>on</strong>g>th</str<strong>on</strong>g>er applied sciences) is presented.<br />

The Markov processes are <str<strong>on</strong>g>of</str<strong>on</strong>g> a jump type and <str<strong>on</strong>g>th</str<strong>on</strong>g>e starting point is <str<strong>on</strong>g>th</str<strong>on</strong>g>e related linear<br />

equati<strong>on</strong>s. They describe at <str<strong>on</strong>g>th</str<strong>on</strong>g>e micro–scale level <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> a large number N<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> interacting entities (particles, agents, cells, individuals,...). The large entity limit<br />

("N → ∞") is studied and <str<strong>on</strong>g>th</str<strong>on</strong>g>e intermediate level (<str<strong>on</strong>g>th</str<strong>on</strong>g>e meso–scale level) is given<br />

in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear kinetic–type equati<strong>on</strong>s. Finally <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding systems<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear ODEs (or PDEs) at <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic level (in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> densities <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e interacting subpopulati<strong>on</strong>s) are obtained. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical relati<strong>on</strong>ships between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese <str<strong>on</strong>g>th</str<strong>on</strong>g>ree possible descripti<strong>on</strong>s are presented and explicit error estimates are given.<br />

The general framework is applied to propose <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic and mesoscopic models<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at corresp<strong>on</strong>d to well known systems <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear equati<strong>on</strong>s in bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics.<br />

556

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

IV; Wednesday, June 29, 08:30<br />

Mirosław Lachowicz<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics<br />

and Mechanics, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics<br />

e-mail: lachowic@mimuw.edu.pl<br />

Macroscopic limits <str<strong>on</strong>g>of</str<strong>on</strong>g> a model <str<strong>on</strong>g>of</str<strong>on</strong>g> alignment<br />

The macroscopic limits <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinetic model for interacting entities are studied.<br />

The kinetic model is <strong>on</strong>e–dimensi<strong>on</strong>al and entities are characterized by <str<strong>on</strong>g>th</str<strong>on</strong>g>eir positi<strong>on</strong><br />

and orientati<strong>on</strong> (+/-) wi<str<strong>on</strong>g>th</str<strong>on</strong>g> swarming interacti<strong>on</strong> c<strong>on</strong>trolled by <str<strong>on</strong>g>th</str<strong>on</strong>g>e sensitivity<br />

parameter. The macroscopic limits <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model are c<strong>on</strong>sidered for soluti<strong>on</strong>s close<br />

ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er to <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusive (isotropic) or to <str<strong>on</strong>g>th</str<strong>on</strong>g>e aligned (swarming) equilibrium states<br />

for various sensitivity parameters. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e former case <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical linear diffusi<strong>on</strong><br />

equati<strong>on</strong> results whereas in <str<strong>on</strong>g>th</str<strong>on</strong>g>e latter a traveling wave soluti<strong>on</strong> does bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

zero<str<strong>on</strong>g>th</str<strong>on</strong>g> ("Euler") and first ("Navier–Stokes") order <str<strong>on</strong>g>of</str<strong>on</strong>g> approximati<strong>on</strong>.<br />

557

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cellular Systems Biology; Tuesday, June 28, 17:00<br />

Tanny Lai<br />

Biophysics Team, Fluid Dynamics, A*STAR Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> High Performance<br />

Computing<br />

e-mail: laitl@ihpc.a-star.edu.sg<br />

Yukai Zeng<br />

Mechanical Engineering, Carnegie Mell<strong>on</strong> University<br />

Philip R. LeDuc<br />

Mechanical Engineering, Carnegie Mell<strong>on</strong> University<br />

K.-H. Chiam<br />

Biophysics Team, Fluid Dynamics, A*STAR Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> High Performance<br />

Computing<br />

Combined experimental and ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

circular dorsal ruffles<br />

Circular dorsal ruffles (CDRs) are transient actin-based structures <str<strong>on</strong>g>th</str<strong>on</strong>g>at are observed<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dorsal plasma membrane up<strong>on</strong> stimulati<strong>on</strong> by receptor-tyrosine-kinase<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factors such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e platelet-derived grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factor (PDGF). While <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> CDRs has not been elucidated, it has been suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are involved<br />

in cell migrati<strong>on</strong> and macropinocytosis. Here, we combine experiments wi<str<strong>on</strong>g>th</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

modeling to attempt to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> CDRs. Experimentally,<br />

we find <str<strong>on</strong>g>th</str<strong>on</strong>g>at lifetime <str<strong>on</strong>g>of</str<strong>on</strong>g> CDRs can be modified by varying <str<strong>on</strong>g>th</str<strong>on</strong>g>e substrate stiffness,<br />

whereas <str<strong>on</strong>g>th</str<strong>on</strong>g>eir sizes are independent <str<strong>on</strong>g>of</str<strong>on</strong>g> substrate stiffness. To understand <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

results, we c<strong>on</strong>struct a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways <str<strong>on</strong>g>th</str<strong>on</strong>g>at regulate<br />

CDRs. By coupling such reacti<strong>on</strong>s to protein diffusi<strong>on</strong>, we find <str<strong>on</strong>g>th</str<strong>on</strong>g>at our reacti<strong>on</strong>diffusi<strong>on</strong><br />

system <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s can reproduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e ring-like structure <str<strong>on</strong>g>of</str<strong>on</strong>g> CDRs, and<br />

how substrate stiffness modifies <str<strong>on</strong>g>th</str<strong>on</strong>g>eir lifetime via <str<strong>on</strong>g>th</str<strong>on</strong>g>e focal adhesi<strong>on</strong> kinase (FAK).<br />

We also show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e low diffusi<strong>on</strong> coefficient <str<strong>on</strong>g>of</str<strong>on</strong>g> membrane bound proteins relative<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e high diffusi<strong>on</strong> coefficient <str<strong>on</strong>g>of</str<strong>on</strong>g> cytosolic proteins is key to <str<strong>on</strong>g>th</str<strong>on</strong>g>e generati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> CDRs. Finally, we reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e model to a coupled two-species model involving<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e proteins Rac (which has been shown to result in <str<strong>on</strong>g>th</str<strong>on</strong>g>e generati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> actin filaments)<br />

and Rho (which has been shown to be involved in cell-substrate adhesi<strong>on</strong>),<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir antag<strong>on</strong>ism, and was able to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e CDRs as an<br />

excitable system. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>is reduced model, we study <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>is excitability<br />

to occur, and <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore make predicti<strong>on</strong>s <strong>on</strong> when and where CDRs will<br />

appear.<br />

558

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Christoph Landsberg<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Scientific Computing, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Natural<br />

Sciences, Technische Universität Dresden, Germany<br />

e-mail: Christoph.Landsberg@tu-dresden.de<br />

Sascha Heinemann<br />

Thomas Hanke<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Materials Science, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Mechanical Engineering,<br />

Technische Universität Dresden, Germany<br />

Modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> osteoblast-m<strong>on</strong>ocyte cocultures<br />

<strong>on</strong> calcium-modulating biomaterials<br />

We adapt and extend an existing model <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e remodeling [1] and simulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

populati<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> osteoblast-m<strong>on</strong>ocyte coculture <strong>on</strong> two different types <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

calcium-modulating biomaterials [2],[3], covered by m<strong>on</strong>olayers <str<strong>on</strong>g>of</str<strong>on</strong>g> hMSC-derived<br />

osteoblasts. From experimental findings it is known <str<strong>on</strong>g>th</str<strong>on</strong>g>at up<strong>on</strong> increased extracellular<br />

calcium c<strong>on</strong>centrati<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e activity <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e forming cells is greatly enhanced,<br />

while b<strong>on</strong>e resorpti<strong>on</strong> is reduced significantly [4], [5]. We include <str<strong>on</strong>g>th</str<strong>on</strong>g>ese observati<strong>on</strong>s<br />

by inserting a for<str<strong>on</strong>g>th</str<strong>on</strong>g> state variable and resp<strong>on</strong>se functi<strong>on</strong>s into <str<strong>on</strong>g>th</str<strong>on</strong>g>e original model, describing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular calcium c<strong>on</strong>centrati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium sorpti<strong>on</strong><br />

to or from <str<strong>on</strong>g>th</str<strong>on</strong>g>e biomaterial, respectively. Starting from different initial c<strong>on</strong>diti<strong>on</strong>s,<br />

we simulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> active osteoblasts and m<strong>on</strong>ocytes, reacting<br />

to different levels <str<strong>on</strong>g>of</str<strong>on</strong>g> extracellular calcium and different sorpti<strong>on</strong> properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

underlying scaffolds. As a result, we identify interesting parameter regimes for inducing<br />

transient changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e osteoblast/osteoclast ratio, indicating possible new<br />

approaches for tissue engineering applicati<strong>on</strong>s, e.g. in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e healing<br />

approaches for systemically diseased patients. In <strong>on</strong>going experiments, we develop<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to compare our results to bo<str<strong>on</strong>g>th</str<strong>on</strong>g> m<strong>on</strong>oculture and coculture experiments <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

osteoblasts and m<strong>on</strong>ocytes [6] <strong>on</strong> different resorbable biomaterials [2],[3] in vitro.<br />

References.<br />

[1] Vincent Lemaire et al. (2004), Modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s between osteoblast and osteoclast<br />

activities in b<strong>on</strong>e remodeling, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology, 229 (3), pp. 293-309.<br />

[2] Sascha Heinemann et al. (2007), A Novel Biomimetic Hybrid Material Made <str<strong>on</strong>g>of</str<strong>on</strong>g> Silicified Collagen:<br />

Perspectives for B<strong>on</strong>e Replacement, Advanced Engineering Materials, 9 (12), pp. 1061-<br />

1068.<br />

[3] Michael Gelinsky et al. (2008), Porous <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-dimensi<strong>on</strong>al scaffolds made <str<strong>on</strong>g>of</str<strong>on</strong>g> mineralised collagen:<br />

Preparati<strong>on</strong> and properties <str<strong>on</strong>g>of</str<strong>on</strong>g> a biomimetic nanocomposite material for tissue engineering<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e, Chemical Engineering Journal, 137 (1), pp. 84-96.<br />

[4] Yoichi Shirai et al. (1999), Effect <str<strong>on</strong>g>of</str<strong>on</strong>g> extracellular calcium c<strong>on</strong>centrati<strong>on</strong>s <strong>on</strong> osteoclast differentiati<strong>on</strong><br />

in vitro, Biochemical and Biophysical Research Communicati<strong>on</strong>s, 265, 2, pp. 484-488.<br />

[5] Melita M. Dvorak et al. (2004), Physiological changes in extracellular calcium c<strong>on</strong>centrati<strong>on</strong><br />

directly c<strong>on</strong>trol osteoblast functi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e absence <str<strong>on</strong>g>of</str<strong>on</strong>g> calciotropic horm<strong>on</strong>es, Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Nati<strong>on</strong>al Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e United States <str<strong>on</strong>g>of</str<strong>on</strong>g> America, 2004, 101 (14), pp. 5140-5145.<br />

[6] Christiane Heinemann et al. (2011), Development <str<strong>on</strong>g>of</str<strong>on</strong>g> an osteoblast/osteoclast co-culture derived<br />

by human b<strong>on</strong>e marrow stromal cells and human m<strong>on</strong>ocytes for biomaterials testing, <str<strong>on</strong>g>European</str<strong>on</strong>g><br />

Cells and Materials, 21, pp. 80-93.<br />

559

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models in Eco-epidemiology II; Wednesday, June 29, 11:00<br />

Michel Langlais<br />

Universite Bordeaux Segalen<br />

e-mail: michel.langlais@u-bordeaux2.fr<br />

E. Gillot-From<strong>on</strong>t<br />

VetAgro Sup, Campus Vétérinaire de Ly<strong>on</strong>, Ly<strong>on</strong> (France)<br />

M. Lélu<br />

VetAgro Sup, Campus Vétérinaire de Ly<strong>on</strong>, Ly<strong>on</strong> (France)<br />

Prey abundance, fragmented spatial structures and predator<br />

persistence in a predator-prey ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we develop a complex fragmented spatial model in which bo<str<strong>on</strong>g>th</str<strong>on</strong>g> dispersing<br />

well-fed and starving domestic cat populati<strong>on</strong>s are sharing a comm<strong>on</strong> multi-patch<br />

range occupied by n<strong>on</strong> dispersing prey. The overall dynamic is ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er intricate<br />

to decipher for Lotka-Volterra functi<strong>on</strong>al resp<strong>on</strong>ses to predati<strong>on</strong>. It becomes even<br />

quite complex when Holling type II functi<strong>on</strong>al resp<strong>on</strong>ses to predati<strong>on</strong> are c<strong>on</strong>sidered.<br />

Assuming dispersal occurs at a fast time scale while reproducti<strong>on</strong> and predati<strong>on</strong><br />

are much slower processes it is possible to transform our complex model into a<br />

simpler <strong>on</strong>e for which some (local) stability analysis is feasible. A toy model c<strong>on</strong>sists<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a spatial range made <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree patches wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two resident predators in <str<strong>on</strong>g>th</str<strong>on</strong>g>e first<br />

two patches, <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er a well-fed or a starving resident predator, and no<br />

predator at all in <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ird <strong>on</strong>e, predators traveling all over <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial range. For<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ree resulting toy models more (local) stability analysis results are available<br />

and illustrated by numerical simulati<strong>on</strong>s.<br />

560

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Petr Lansky<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physiology, Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Czech Republic<br />

e-mail: lansky@biomed.cas.cz<br />

Zbynek Pawlas<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Physics, Charles University<br />

Multiple neur<strong>on</strong>al spike trains observed in a short-time<br />

window<br />

Informati<strong>on</strong> obtained in experiments in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e spikes are recorded, usually from<br />

a single neur<strong>on</strong> or from quite limited number <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em, is fundamentally different<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>at which a neur<strong>on</strong> receives from <str<strong>on</strong>g>th</str<strong>on</strong>g>e network <str<strong>on</strong>g>of</str<strong>on</strong>g> interc<strong>on</strong>nected neur<strong>on</strong>s. In<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e experiments, a spike train is recorded for a relatively l<strong>on</strong>g period <str<strong>on</strong>g>of</str<strong>on</strong>g> time and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing are deduced. If <str<strong>on</strong>g>th</str<strong>on</strong>g>e type <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e investigated firing is<br />

transient, like in <str<strong>on</strong>g>th</str<strong>on</strong>g>e stimulated activity, <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>e extensive leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e record is<br />

replaced by repetiti<strong>on</strong>s assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese are identical and independent copies<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same phenomen<strong>on</strong>. In natural c<strong>on</strong>diti<strong>on</strong>s, neur<strong>on</strong> receives a large number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> spike trains, up to several <str<strong>on</strong>g>th</str<strong>on</strong>g>ousands, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e informati<strong>on</strong> has to be deduced in<br />

short-time intervals. This creates a discrepancy between what can be read from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

experiments and how real neur<strong>on</strong>s perform. To estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing frequency in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

parallel neur<strong>on</strong>al data is ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er simple task even if <str<strong>on</strong>g>th</str<strong>on</strong>g>e time window available for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong> is very short. In paper 1 we showed how to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e coefficient<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> interspike intervals under <str<strong>on</strong>g>th</str<strong>on</strong>g>e scenario wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e short-time window.<br />

Several n<strong>on</strong>parametric me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cumulative distributi<strong>on</strong> functi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interspike intervals under <str<strong>on</strong>g>th</str<strong>on</strong>g>e same restricti<strong>on</strong> posed <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong><br />

appear in our recent paper 2. The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e present c<strong>on</strong>tributi<strong>on</strong> is summarize<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e results and to show furter development in studying <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem.<br />

References.<br />

[1] Pawlas Z., Klebanov L.B., Prokop M., Lansky P. (2008) Parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> spike trains observed<br />

in a short time window. Neural Computati<strong>on</strong>, 20 1325-1343.<br />

[2] Pawlas Z., Lansky P. (2011) Distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> interspike intervals estimated from multiple spike<br />

trains observed in a short time window. Physical Review E, 83 Art. No. 011910.<br />

561

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

A. Lapin, M. Reuss<br />

Center Systems Biology, University Stuttgart, Germany<br />

e-mail: lapin@ibvt.uni-stuttgart.de<br />

Stirred Bioreactor Heating: Temperature Experience <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

Single Organism<br />

Rapid heating <str<strong>on</strong>g>of</str<strong>on</strong>g> bioreactors is extensively used for <str<strong>on</strong>g>th</str<strong>on</strong>g>e producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> recombinant<br />

proteins. Such temperature-induced expressi<strong>on</strong> systems show high levels <str<strong>on</strong>g>of</str<strong>on</strong>g> recombinant<br />

protein producti<strong>on</strong>s and present important and c<strong>on</strong>venient features for<br />

bioprocessing. The heating <str<strong>on</strong>g>of</str<strong>on</strong>g> a lab-scale stirred bioreactor is investigated, based<br />

<strong>on</strong> a two layer turbulence model. The wall temperature is assumed to be about 80<br />

degree Centigrade.<br />

We observed <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> a narrow high temperature layer near <str<strong>on</strong>g>th</str<strong>on</strong>g>e bioreactor<br />

wall. Bioorganisms entering <str<strong>on</strong>g>th</str<strong>on</strong>g>e viscous hot layer usually stay <str<strong>on</strong>g>th</str<strong>on</strong>g>ere for a<br />

l<strong>on</strong>g time and <str<strong>on</strong>g>th</str<strong>on</strong>g>is typically induces <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eir dea<str<strong>on</strong>g>th</str<strong>on</strong>g>. The simulati<strong>on</strong> results show<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at a c<strong>on</strong>siderable part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microorganism populati<strong>on</strong> is endangered by <str<strong>on</strong>g>th</str<strong>on</strong>g>e high<br />

temperature near <str<strong>on</strong>g>th</str<strong>on</strong>g>e bioreactor wall.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Anastasia Lavrova<br />

Physics Institute, Humboldt University at Berlin<br />

e-mail: aurebours@googlemail.com<br />

L. Schimansky-Geier<br />

Physics Institute, Humboldt University at Berlin<br />

Neurosciences; Thursday, June 30, 11:30<br />

Dynamical switching between network states in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

hippocampal circuit<br />

It is known <str<strong>on</strong>g>th</str<strong>on</strong>g>at hippocampus is a structure required for processes <str<strong>on</strong>g>of</str<strong>on</strong>g> learning and<br />

memory [1]. Gloveli et al. [2] reported <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong> network <str<strong>on</strong>g>of</str<strong>on</strong>g> CA3<br />

regi<strong>on</strong> exhibits some types <str<strong>on</strong>g>of</str<strong>on</strong>g> oscillati<strong>on</strong>s, so called gamma (30-80 Hz) and <str<strong>on</strong>g>th</str<strong>on</strong>g>eta(4-<br />

12 Hz) rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms. These oscillati<strong>on</strong>s are resp<strong>on</strong>sible for informati<strong>on</strong> transmissi<strong>on</strong>,<br />

storage, and spatial encoding [3]. Also, it have been shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at gamma and <str<strong>on</strong>g>th</str<strong>on</strong>g>eta<br />

rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms are generated by different types <str<strong>on</strong>g>of</str<strong>on</strong>g> cells in CA3 regi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> hippocampus.<br />

We have c<strong>on</strong>sidered a minimal network scheme, which describes c<strong>on</strong>necti<strong>on</strong>s<br />

between different types <str<strong>on</strong>g>of</str<strong>on</strong>g> cells. We have developed model based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is scheme<br />

which reproduces important physical characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e oscillati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> all cells<br />

types: <str<strong>on</strong>g>th</str<strong>on</strong>g>e period, amplitude and phase shift. The model allows us to analyze<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> synaptic streng<str<strong>on</strong>g>th</str<strong>on</strong>g>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network synchr<strong>on</strong>izati<strong>on</strong> and dynamical<br />

switching between <str<strong>on</strong>g>th</str<strong>on</strong>g>eta, gamma, and bursting regimes. In particular, we perform a<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>orough bifurcati<strong>on</strong> analysis and identify parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> synaptic c<strong>on</strong>necti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

can efficiently induce switches in <str<strong>on</strong>g>th</str<strong>on</strong>g>e network activity.<br />

References.<br />

[1] O’Keefe J.and Recce ML., Hippocampus, bf3 317-30, (1993)<br />

[2] Gloveli T., Dugladze T.,Rotstein H.,Traub R., M<strong>on</strong>yer H., Heinemann U., Whittingt<strong>on</strong> M.,<br />

Kopell N., PNAS, bf102 13295-300, (2005)<br />

[3] Harris KD, Csicsvari J., Hirase H., Dragoi G., Buzsaki G., Nature, bf424 552-56, (2003)<br />

[4] Tort A., Rotstein H., Dugladze T., Gloveli T., Kopell N., PNAS, bf104 13490-95, (2007)<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bi<str<strong>on</strong>g>of</str<strong>on</strong>g>luids, Solute Transport, and Hemodynamics; Wednesday, June 29, 11:00<br />

Anita Layt<strong>on</strong><br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Duke University<br />

e-mail: alayt<strong>on</strong>@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.duke.edu<br />

Myogenic Resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Afferent Arteriole<br />

We have formulated a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e rat afferent arteriole (AA). Our<br />

model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> a series <str<strong>on</strong>g>of</str<strong>on</strong>g> arteriolar smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> muscle cells, each <str<strong>on</strong>g>of</str<strong>on</strong>g> which represents<br />

i<strong>on</strong> transport, cell membrane potential, cellular c<strong>on</strong>tracti<strong>on</strong>, gap juncti<strong>on</strong> coupling,<br />

and wall mechanics. Blood flow <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e AA lumen is described by Poiseuille<br />

flow. Model results suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at interacting calcium and potassium fluxes, mediated<br />

by voltage-gated and voltage-calcium-gated channels, respectively, give rise<br />

to periodic oscillati<strong>on</strong>s in cytoplasmic calcium c<strong>on</strong>centrati<strong>on</strong>, myosin light chain<br />

phosphorylati<strong>on</strong>, and crossbridge formati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> attending muscle stress mediating<br />

vasomoti<strong>on</strong>. The AA model’s representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e myogenic resp<strong>on</strong>se is based<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e voltage dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium channel openings resp<strong>on</strong>ds<br />

to transmural pressure so <str<strong>on</strong>g>th</str<strong>on</strong>g>at vessel diameter decreases wi<str<strong>on</strong>g>th</str<strong>on</strong>g> increasing<br />

pressure. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>figurati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e AA model simulati<strong>on</strong>s agree<br />

well wi<str<strong>on</strong>g>th</str<strong>on</strong>g> findings in <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental literature, notably <str<strong>on</strong>g>th</str<strong>on</strong>g>ose <str<strong>on</strong>g>of</str<strong>on</strong>g> Steinhausen et<br />

al. (J Physiol 505:493, 1997), which indicated <str<strong>on</strong>g>th</str<strong>on</strong>g>at propagated vasoc<strong>on</strong>strictive resp<strong>on</strong>se<br />

induced by local electrical stimulati<strong>on</strong> decayed more rapidly in <str<strong>on</strong>g>th</str<strong>on</strong>g>e upstream<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>an in <str<strong>on</strong>g>th</str<strong>on</strong>g>e downstream flow directi<strong>on</strong>. The model can be incorporated into models<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> integrated renal hemodynamic regulati<strong>on</strong>. This research was supported in part<br />

by NIH grants DK-42091 and DK-89066, and by NSF grant DMS-0715021.<br />

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Bi<str<strong>on</strong>g>of</str<strong>on</strong>g>luids, Solute Transport, and Hemodynamics; Wednesday, June 29, 11:00<br />

Harold E. Layt<strong>on</strong><br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Duke University, Durham, NC 27708-0320,<br />

USA<br />

e-mail: layt<strong>on</strong>@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.duke.edu<br />

Anita T. Layt<strong>on</strong><br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Duke University, Durham, NC 27708-0320,<br />

USA<br />

e-mail: alayt<strong>on</strong>@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.duke.edu<br />

Countercurrent Multiplicati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Kidney: Is it Real?<br />

A fundamental functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mammalian kidney, when blood plasma osmolality<br />

is too high, is to produce a urine <str<strong>on</strong>g>th</str<strong>on</strong>g>at is more c<strong>on</strong>centrated <str<strong>on</strong>g>th</str<strong>on</strong>g>an blood plasma<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>ereby reduce blood plasma osmolality to a normal level. Urine is c<strong>on</strong>centrated<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e renal medulla by means <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>centrati<strong>on</strong> gradient <str<strong>on</strong>g>th</str<strong>on</strong>g>at promotes<br />

osmotic water wi<str<strong>on</strong>g>th</str<strong>on</strong>g>drawal from <str<strong>on</strong>g>th</str<strong>on</strong>g>e kidney’s collecting ducts. It has become widely<br />

accepted <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e osmolality gradient al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e cortico-medullary axis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mammalian<br />

outer medulla is generated and sustained by a process <str<strong>on</strong>g>of</str<strong>on</strong>g> countercurrent<br />

multiplicati<strong>on</strong>: active NaCl absorpti<strong>on</strong> from <str<strong>on</strong>g>th</str<strong>on</strong>g>ick ascending limbs is coupled wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

a counter-flow c<strong>on</strong>figurati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e descending and ascending limbs <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e loops <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Henle to generate <str<strong>on</strong>g>th</str<strong>on</strong>g>e axial gradient. However, aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> anatomic structure (e.g.,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e physical separati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e descending limbs <str<strong>on</strong>g>of</str<strong>on</strong>g> short loops <str<strong>on</strong>g>of</str<strong>on</strong>g> Henle from c<strong>on</strong>tiguous<br />

ascending limbs), recent physiologic experiments (e.g., <str<strong>on</strong>g>th</str<strong>on</strong>g>ose which suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>in descending limbs <str<strong>on</strong>g>of</str<strong>on</strong>g> short loops <str<strong>on</strong>g>of</str<strong>on</strong>g> Henle have a low water permeability),<br />

and ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling studies (e.g., <str<strong>on</strong>g>th</str<strong>on</strong>g>ose which predict <str<strong>on</strong>g>th</str<strong>on</strong>g>at water-permeable<br />

descending limbs <str<strong>on</strong>g>of</str<strong>on</strong>g> short loops are not required for <str<strong>on</strong>g>th</str<strong>on</strong>g>e generati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an axial osmolality<br />

gradient) suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at countercurrent multiplicati<strong>on</strong> may be an incomplete,<br />

or perhaps even err<strong>on</strong>eous, explanati<strong>on</strong>. We propose an alternative explanati<strong>on</strong> for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e axial osmolality gradient: we regard <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ick limbs as NaCl sources for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

surrounding interstitium, and we hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esize <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e increasing axial osmolality<br />

gradient al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e outer medulla is primarily sustained by an increasing ratio, as a<br />

functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> medullary dep<str<strong>on</strong>g>th</str<strong>on</strong>g>, <str<strong>on</strong>g>of</str<strong>on</strong>g> NaCl absorpti<strong>on</strong> from <str<strong>on</strong>g>th</str<strong>on</strong>g>ick ascending limbs to water<br />

absorpti<strong>on</strong> from <str<strong>on</strong>g>th</str<strong>on</strong>g>in descending limbs <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g loops <str<strong>on</strong>g>of</str<strong>on</strong>g> Henle and from collecting<br />

ducts.<br />

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Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

II; Tuesday, June 28, 14:30<br />

Urszula Ledzewicz<br />

Sou<str<strong>on</strong>g>th</str<strong>on</strong>g>ern Illinois University Edwardsville<br />

e-mail: uledzew@siue.edu<br />

Heinz Schaettler<br />

Washingt<strong>on</strong> University<br />

Optimal protocols for chemo- and immuno<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy in a<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor-immune interacti<strong>on</strong>s<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, a classical model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s between tumor and <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune<br />

system under treatment is c<strong>on</strong>sidered as an optimal c<strong>on</strong>trol problem wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multiple<br />

c<strong>on</strong>trols representing acti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cytotoxic drugs as well as <str<strong>on</strong>g>of</str<strong>on</strong>g> agents <str<strong>on</strong>g>th</str<strong>on</strong>g>at give a boost<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune system. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e objective, a weighted average <str<strong>on</strong>g>of</str<strong>on</strong>g> several quantities<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e effectiveness <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment is minimized. These terms include (i)<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells at <str<strong>on</strong>g>th</str<strong>on</strong>g>e terminal time, (ii) a measure for <str<strong>on</strong>g>th</str<strong>on</strong>g>e immunocompetent<br />

cell densities at <str<strong>on</strong>g>th</str<strong>on</strong>g>e terminal point (included as a negative term), (iii) a<br />

measure for <str<strong>on</strong>g>th</str<strong>on</strong>g>e side effects and cost <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment in form <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall amount <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

agents given and (iv) a small penalty <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e terminal time <str<strong>on</strong>g>th</str<strong>on</strong>g>at limits <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy horiz<strong>on</strong> which is assumed to be free. This last term is essential in obtaining<br />

a well-posed problem formulati<strong>on</strong>. The form <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e objective is motivated by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out treatment and models <str<strong>on</strong>g>th</str<strong>on</strong>g>e goal to move <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

state <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system from a regi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> malignant cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> into a benign regi<strong>on</strong>.<br />

Employing a Gompertzian grow<str<strong>on</strong>g>th</str<strong>on</strong>g> model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer cells, for various scenarios<br />

optimal c<strong>on</strong>trols and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir corresp<strong>on</strong>ding system resp<strong>on</strong>ses are calculated. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cases <str<strong>on</strong>g>of</str<strong>on</strong>g> m<strong>on</strong>o- and combinati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies will be c<strong>on</strong>sidered.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Chang Hye<strong>on</strong>g Lee<br />

Ulsan Nati<strong>on</strong>al Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Technology(UNIST), Ulsan,<br />

Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Korea<br />

e-mail: chlee@unist.ac.kr<br />

Recent Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for Computati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Reacti<strong>on</strong> Networks<br />

We c<strong>on</strong>sider reacti<strong>on</strong> networks where many biological or biochemical species<br />

interact <str<strong>on</strong>g>th</str<strong>on</strong>g>rough various reacti<strong>on</strong> channels. We introduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e background for analysis<br />

and computati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong> networks and we present recent results <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong>al me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong> networks. We also show<br />

numerical results obtained by simulating some motivating biological models.<br />

References.<br />

[1] Chang Hye<strong>on</strong>g Lee and Hans G. O<str<strong>on</strong>g>th</str<strong>on</strong>g>mer, A multi-time-scale analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> chemical reacti<strong>on</strong><br />

networks: I. Deterministic systems, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, Volume 60, 387-450<br />

(2010)<br />

[2] Chang Hye<strong>on</strong>g Lee and Roger Lui, A reducti<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for multiple time scale stochastic<br />

reacti<strong>on</strong> networks wi<str<strong>on</strong>g>th</str<strong>on</strong>g> n<strong>on</strong>-unique equilibrium probability,Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Chemistry<br />

Vol 47, 750-770(2010)<br />

[3] Chang Hye<strong>on</strong>g Lee, Kye<strong>on</strong>g-Hun Kim and Pilw<strong>on</strong> Kim, A moment closure me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for stochastic<br />

reacti<strong>on</strong> networks”, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Chemical Physics, vol 130, issue 13, 134107 (2009)<br />

[4] Chang Hye<strong>on</strong>g Lee and Roger Lui, “A reducti<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for multiple time scale stochastic<br />

reacti<strong>on</strong> networks”, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Chemistry Vol 46, 1292-1321(2009)<br />

567

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Junggul Lee<br />

K<strong>on</strong>kuk University<br />

e-mail: jack9872@k<strong>on</strong>kuk.ac.kr<br />

Eunok Jung<br />

K<strong>on</strong>kuk University<br />

e-mail: junge@k<strong>on</strong>kuk.ac.kr<br />

Do-Wan Kim<br />

Inha University<br />

e-mail: dokim@inha.ac.kr<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

An Open Tank System <str<strong>on</strong>g>of</str<strong>on</strong>g> Valveless Pumping<br />

We present a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> flows driven by periodic pumping wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out<br />

valves (valveless pumping) in an open tank system. The model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> a cylindrical<br />

elastic closed tube wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two open tanks under gravity. The two dimensi<strong>on</strong>al<br />

elastic tube is c<strong>on</strong>structed based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immersed boundary me<str<strong>on</strong>g>th</str<strong>on</strong>g>od and <str<strong>on</strong>g>th</str<strong>on</strong>g>e tank<br />

model is governed by a system <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary differential equati<strong>on</strong>s based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e law<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>servati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> energy. We have observed <str<strong>on</strong>g>th</str<strong>on</strong>g>e difference <str<strong>on</strong>g>of</str<strong>on</strong>g> fluid heights in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

tanks by <str<strong>on</strong>g>th</str<strong>on</strong>g>e periodic compress-and-release acti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at is applied to an asymmetric<br />

regi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e elastic tube. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e previous research <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e open systems <str<strong>on</strong>g>of</str<strong>on</strong>g> valveless<br />

pumping, we have also observed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e directi<strong>on</strong> and magnitude <str<strong>on</strong>g>of</str<strong>on</strong>g> a net flow in<br />

our open tank system are determined sensitively by <str<strong>on</strong>g>th</str<strong>on</strong>g>e driving frequency and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

compressi<strong>on</strong> durati<strong>on</strong>. We are able to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> local maximum<br />

or minimum mean flows (difference <str<strong>on</strong>g>of</str<strong>on</strong>g> tank heights) due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e res<strong>on</strong>ances <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

system.<br />

References.<br />

[1] Y. Kim, W. Lee, and E. Jung, An immersed boundary heart model coupled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a multicompartment<br />

lumped model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e circulatory system SIAM J. Sci. Comput. 32 1809–1831.<br />

[2] C. S. Peskin and B. F. Printz Improved volume c<strong>on</strong>servati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> flows wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

immersed elastic boundaries J. Comput. Phys. 105 33–46.<br />

[3] E. Jung and C.S. Peskin Two-dimensi<strong>on</strong>al simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> valveless pumping using <str<strong>on</strong>g>th</str<strong>on</strong>g>e immersed<br />

boundary me<str<strong>on</strong>g>th</str<strong>on</strong>g>od SIAM J. Sci. Comput. 23 19-–45.<br />

[4] K. M. Ar<str<strong>on</strong>g>th</str<strong>on</strong>g>urs, L. C. Moore, C. S. Peskin, E. B. Pitman and H. E. Layt<strong>on</strong> Modeling arteriolar<br />

flow and mass transport using <str<strong>on</strong>g>th</str<strong>on</strong>g>e immersed boundary me<str<strong>on</strong>g>th</str<strong>on</strong>g>od J. Comput. Phys. 147 402–440.<br />

[5] R. P. Beyer A computati<strong>on</strong>al model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cochlea using <str<strong>on</strong>g>th</str<strong>on</strong>g>e immersed boundary me<str<strong>on</strong>g>th</str<strong>on</strong>g>od J.<br />

Comput. Phys. 98 145—162.<br />

[6] D. M. McQueen, C. S. Peskin, and E. L. Yellin Fluid dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mitral valve: Physiological<br />

aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model Amer. J. Physiol. 242 H1095—H1110.<br />

[7] G. Liebau Die Bedeutung der Tragheitskrafte für die Dynamik des Blutkreislaufs Zs. Kreislaufforschung<br />

46 428—438.<br />

[8] J. S. Hansen and J. T. Ottesen Molecular dynamics simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> oscillatory flows in micr<str<strong>on</strong>g>of</str<strong>on</strong>g>luidic<br />

channels Micr<str<strong>on</strong>g>of</str<strong>on</strong>g>luid. Nan<str<strong>on</strong>g>of</str<strong>on</strong>g>luid. 2 301-–307.<br />

568

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Nam-Kyung Lee<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, Sej<strong>on</strong>g University<br />

e-mail: lee@sej<strong>on</strong>g.ac.kr<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Relaxati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> End-Grafted DNA Chains<br />

By spreading fr<strong>on</strong>t <str<strong>on</strong>g>of</str<strong>on</strong>g> a bioadhesive vesicle over stained end-grafted DNA molecules,<br />

DNA molecules are stapled into frozen c<strong>on</strong>finement pa<str<strong>on</strong>g>th</str<strong>on</strong>g>s. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>formati<strong>on</strong>al<br />

relaxati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> topologically trapped chain is very slow, it has been shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

stapled DNA gives access to <str<strong>on</strong>g>th</str<strong>on</strong>g>e local stretching values <str<strong>on</strong>g>of</str<strong>on</strong>g> individual DNA molecules<br />

and provides evidence <str<strong>on</strong>g>of</str<strong>on</strong>g> self-entanglements. By means <str<strong>on</strong>g>of</str<strong>on</strong>g> two dimensi<strong>on</strong>al computer<br />

simulati<strong>on</strong>s and scaling arguments, we study <str<strong>on</strong>g>th</str<strong>on</strong>g>e relaxati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> single grafted<br />

semiflexible chains freely rotating around <str<strong>on</strong>g>th</str<strong>on</strong>g>e grafting point. We provide <str<strong>on</strong>g>th</str<strong>on</strong>g>e autocorrelati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e end-to-end vector for <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole chain and for terminal secti<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> various leng<str<strong>on</strong>g>th</str<strong>on</strong>g>s.<br />

569

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Turing !! Turing?? <strong>on</strong> morphogenesis via experimental and <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical<br />

approaches; Wednesday, June 29, 17:00<br />

S. Seirin Lee<br />

Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Tokyo, Japan<br />

e-mail: seirin.lee@gmail.com; seirin@ms.u-tokyo.ac.jp<br />

Gene Expressi<strong>on</strong> Time Delays and Turing Pattern Formati<strong>on</strong><br />

There are numerous examples <str<strong>on</strong>g>of</str<strong>on</strong>g> morphogen gradients c<strong>on</strong>trolling l<strong>on</strong>g range<br />

signalling in developmental and cellular systems. The prospect <str<strong>on</strong>g>of</str<strong>on</strong>g> two such interacting<br />

morphogens instigating l<strong>on</strong>g range self-organisati<strong>on</strong> in biological systems via<br />

a Turing bifurcati<strong>on</strong> has been explored, postulated or implicated in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

numerous developmental processes. However, modelling investigati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular<br />

systems typically neglect <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong> <strong>on</strong> such dynamics, even<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ough transcripti<strong>on</strong> and translati<strong>on</strong> are observed to be important in morphogenetic<br />

systems.<br />

The investigati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> our study dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> Turing models<br />

pr<str<strong>on</strong>g>of</str<strong>on</strong>g>oundly changes <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e inclusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong> dynamics and is sensitive<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e sub-cellular details <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong>. These results also indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> Turing pattern formati<strong>on</strong> systems <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e inclusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong><br />

time delays may provide a means <str<strong>on</strong>g>of</str<strong>on</strong>g> distinguishing between possible forms <str<strong>on</strong>g>of</str<strong>on</strong>g> interacti<strong>on</strong><br />

kinetics, and also emphasises <str<strong>on</strong>g>th</str<strong>on</strong>g>at sub-cellular and gene expressi<strong>on</strong> dynamics<br />

should not be simply neglected in models <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g range biological pattern formati<strong>on</strong><br />

via morphogens. We present results mainly for Gierer-Meinhardt systems but our<br />

results are observed more universally in many Turing pattern formati<strong>on</strong> systems.<br />

Exploring <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese systems suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic Turing mechanism<br />

should be rec<strong>on</strong>sidered or would generally require a novel and extensive sec<strong>on</strong>dary<br />

mechanism to c<strong>on</strong>trol reacti<strong>on</strong> diffusi<strong>on</strong> patterning.<br />

*This work has already been extended in several papers. The works have been<br />

collaborated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> E.A. Gaffney (University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford), R.E. Baker (University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Oxford) and N.A.M. M<strong>on</strong>k (University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham). Papers related wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work<br />

are given in <str<strong>on</strong>g>th</str<strong>on</strong>g>e following References.<br />

References.<br />

[1] E.A. Gaffney, N.A.M. M<strong>on</strong>k, Gene expressi<strong>on</strong> time delays and Turing pattern formati<strong>on</strong> systems<br />

Bull.Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.Bio. (2006) 68: 99–130.<br />

[2] S. Seirin Lee, E.A. Gaffney, N.A.M. M<strong>on</strong>k, The Influence <str<strong>on</strong>g>of</str<strong>on</strong>g> Gene Expressi<strong>on</strong> Time Delays<br />

<strong>on</strong> Gierer-Meinhardt Pattern Formati<strong>on</strong> Systems Bull.Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.Bio. (2010) 72: 2139–2160.<br />

[3] S. Seirin Lee, E.A. Gaffney, Aberrant Behaviours <str<strong>on</strong>g>of</str<strong>on</strong>g> Reacti<strong>on</strong> Diffusi<strong>on</strong> Self-organisati<strong>on</strong> Models<br />

<strong>on</strong> Growing Domains in The Presence <str<strong>on</strong>g>of</str<strong>on</strong>g> Gene Expressi<strong>on</strong> Time Delays Bull.Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.Bio.<br />

(2010) 72: 2161–2179.<br />

570

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[4] S. Seirin Lee, E.A. Gaffney, R.E. Baker The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Turing patterns for morphogenregulated<br />

growing domains wi<str<strong>on</strong>g>th</str<strong>on</strong>g> cellular resp<strong>on</strong>se delays. (Submitted in Bull.Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.Bio.).<br />

[5] E.A. Gaffney, S. Seirin Lee, The Sensitivity <str<strong>on</strong>g>of</str<strong>on</strong>g> Turing Self-Organisati<strong>on</strong> to Biological Feedback<br />

Delays: 2D Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Zebrafish Pigmentati<strong>on</strong>. (Submitted in JTB).<br />

571

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Fluid-structure interacti<strong>on</strong> problems in biomechanics; Saturday, July 2, 08:30<br />

Karin Leiderman<br />

Duke University<br />

e-mail: karin@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.duke.edu<br />

A Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Model <str<strong>on</strong>g>of</str<strong>on</strong>g> Thrombus Formati<strong>on</strong> Under Flow<br />

To explore how blood flow affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>rombi (blood clots) and how <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

growing masses, in turn, feed back and affect flow, we have developed a spatialtemporal<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> platelet depositi<strong>on</strong> and coagulati<strong>on</strong> under flow. The<br />

model includes detailed descripti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> coagulati<strong>on</strong> biochemistry, chemical activati<strong>on</strong><br />

and depositi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> blood platelets, as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e two-way interacti<strong>on</strong> between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e fluid dynamics and <str<strong>on</strong>g>th</str<strong>on</strong>g>e growing platelet mass. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, I will present <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model and use it to explain what underlies <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold behavior<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an important enzyme wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e coagulati<strong>on</strong> system. I will<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>en show how <str<strong>on</strong>g>th</str<strong>on</strong>g>e wall shear rate <str<strong>on</strong>g>of</str<strong>on</strong>g> flow and a near-wall enhanced platelet c<strong>on</strong>centrati<strong>on</strong>s<br />

affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> growing <str<strong>on</strong>g>th</str<strong>on</strong>g>rombi. Since we account for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

porous nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>rombi, I am also able to dem<strong>on</strong>strate how advective and diffusive<br />

transport to and wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>rombi affects <str<strong>on</strong>g>th</str<strong>on</strong>g>eir grow<str<strong>on</strong>g>th</str<strong>on</strong>g> at different stages and spatial<br />

locati<strong>on</strong>s.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Felix Lenk<br />

TU Dresden / Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Food Technology and Bioprocess Engineering<br />

/ Chair <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioprocess Engineering<br />

e-mail: felix.lenk@tu-dresden.de<br />

Th. Bley<br />

TU Dresden / Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Food Technology and Bioprocess Engineering<br />

/ Chair <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioprocess Engineering<br />

J. Steingroewer<br />

TU Dresden / Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Food Technology and Bioprocess Engineering<br />

/ Chair <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioprocess Engineering<br />

A structured grow<str<strong>on</strong>g>th</str<strong>on</strong>g> model for hairy roots <str<strong>on</strong>g>of</str<strong>on</strong>g> beetroot (Beta<br />

vulgaris)<br />

Sec<strong>on</strong>dary metabolites produced by plant in vitro cultures such as Betanin (red-dye<br />

in beetroot) are nowadays in <str<strong>on</strong>g>th</str<strong>on</strong>g>e main focus wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e branch <str<strong>on</strong>g>of</str<strong>on</strong>g> White Biotechnology.<br />

Cells genetically altered using Agrobacterium rhizogenes form hairy roots<br />

which can be cultivated in horm<strong>on</strong>e free media in modern bioreactors.<br />

In order to improve <str<strong>on</strong>g>th</str<strong>on</strong>g>e cultivati<strong>on</strong> process (higher yield, shorter cultivati<strong>on</strong><br />

time) and <str<strong>on</strong>g>th</str<strong>on</strong>g>e bioreactor design (bubble column vs. stirred) a structured grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>sequent simulati<strong>on</strong>s and visualizati<strong>on</strong> is necessary. While <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese tissue cultures <strong>on</strong> agar plates, in shaking flasks or bioreactors for industrial<br />

use has been heavily investigated experimentally <strong>on</strong>ly limited <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical descripti<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> processes exist. The gained knowledge can be used by o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

scientists to improve <str<strong>on</strong>g>th</str<strong>on</strong>g>eir cultivati<strong>on</strong> protocols and to simulate grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir own<br />

cultures by amending <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model.<br />

The hairy roots <str<strong>on</strong>g>of</str<strong>on</strong>g> beetroot (Beta vulgaris) have been chosen for modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> morphology <str<strong>on</strong>g>of</str<strong>on</strong>g> hairy roots also wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> sec<strong>on</strong>dary<br />

metabolites such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e red dye Betanin. A matrix based approach is used for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed model which c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> a 2-dimensi<strong>on</strong>al model matrix for agar plates<br />

c<strong>on</strong>taining informati<strong>on</strong> about <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> each cell forming <str<strong>on</strong>g>th</str<strong>on</strong>g>e organ complex.<br />

C<strong>on</strong>diti<strong>on</strong>s are positi<strong>on</strong>, age, nutrient c<strong>on</strong>centrati<strong>on</strong> inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell as well as c<strong>on</strong>centrati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> sec<strong>on</strong>dary metabolites. A sec<strong>on</strong>d matrix c<strong>on</strong>tains nutrient c<strong>on</strong>centrati<strong>on</strong>s<br />

such as carb<strong>on</strong> source and oxygen in <str<strong>on</strong>g>th</str<strong>on</strong>g>e media.<br />

The simulati<strong>on</strong> process begins wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a given start state <str<strong>on</strong>g>of</str<strong>on</strong>g> a small organ complex<br />

which is recalculated recursively for a defined time step. The grow<str<strong>on</strong>g>th</str<strong>on</strong>g> processes involved<br />

such as el<strong>on</strong>gati<strong>on</strong> and branching <str<strong>on</strong>g>th</str<strong>on</strong>g>rough cell divisi<strong>on</strong> as well as sec<strong>on</strong>dary<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ickening <str<strong>on</strong>g>of</str<strong>on</strong>g> already existing cells are described using differential equati<strong>on</strong>s. After<br />

each grow<str<strong>on</strong>g>th</str<strong>on</strong>g> step <str<strong>on</strong>g>th</str<strong>on</strong>g>e organ matrix and <str<strong>on</strong>g>th</str<strong>on</strong>g>e nutrient matrix wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e involved<br />

diffusi<strong>on</strong> processes are calculated using partial differential equati<strong>on</strong>s (PDE). The<br />

newly formed matrices are used for <str<strong>on</strong>g>th</str<strong>on</strong>g>e next calculati<strong>on</strong> step. Experimental results<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cultivati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> B. vulgaris are compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e results <str<strong>on</strong>g>of</str<strong>on</strong>g> simulati<strong>on</strong>s.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Anne-Cécile Lesart<br />

UJF-Grenoble 1, CNRS, Laboratory TIMC-IMAG UMR 5525, DyCTiM<br />

research team, Grenoble, F-38041, France<br />

e-mail: aclesart@imag.fr<br />

Boudewijn van der Sanden<br />

INSERM U836, Grenoble Institut des Neurosciences,UJF-Grenoble,<br />

CHU Michall<strong>on</strong>, Grenoble, F-38042 France.<br />

François Esteve<br />

INSERM U836, Grenoble Institut des Neurosciences,UJF-Grenoble,<br />

CHU Michall<strong>on</strong>, Grenoble, F-38042 France.<br />

Angélique Stephanou<br />

UJF-Grenoble 1, CNRS, Laboratory TIMC-IMAG UMR 5525, DyCTiM<br />

research team, Grenoble, F-38041, France<br />

A Computati<strong>on</strong>al Model <str<strong>on</strong>g>of</str<strong>on</strong>g> Vascular Tumour Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> as<br />

Observed by Intravital Microscopy <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a Dorsal<br />

Skinfold Chamber <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Mouse<br />

A computati<strong>on</strong>al model is potentially a powerful tool to apprehend complex<br />

phenomena like solid tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, and to predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e outcome <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies in<br />

order to find <str<strong>on</strong>g>th</str<strong>on</strong>g>e best soluti<strong>on</strong> to fight <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease. To <str<strong>on</strong>g>th</str<strong>on</strong>g>at end, <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>fr<strong>on</strong>tati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> biological experiments is essential to validate <str<strong>on</strong>g>th</str<strong>on</strong>g>is tool.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is poster, we present a model specifically c<strong>on</strong>structed to match and interpret<br />

biological results obtained in vivo <strong>on</strong> mice by <str<strong>on</strong>g>th</str<strong>on</strong>g>e dorsal chamber me<str<strong>on</strong>g>th</str<strong>on</strong>g>od.<br />

We will focus especially <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vascular adaptati<strong>on</strong> and alterati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood<br />

rheology. In order to reproduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor evoluti<strong>on</strong>, interrelati<strong>on</strong> between vascular<br />

development and tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> are established <str<strong>on</strong>g>th</str<strong>on</strong>g>anks to oxygen diffusi<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

angiogenesis process. Indeed, oxygen is transported to <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor by <str<strong>on</strong>g>th</str<strong>on</strong>g>e vessels<br />

and hypoxia induces <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> new blood vessels via <str<strong>on</strong>g>th</str<strong>on</strong>g>e emissi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular<br />

endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factors by <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour cells. Vascular collapse in tumor is also<br />

taken into account as well as dilati<strong>on</strong> or c<strong>on</strong>stricti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vessels.<br />

Simulati<strong>on</strong>s based <strong>on</strong> existing vascular network and measured rheological parameters<br />

reproduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed tumour evoluti<strong>on</strong> including <str<strong>on</strong>g>th</str<strong>on</strong>g>e increased vascular<br />

density at <str<strong>on</strong>g>th</str<strong>on</strong>g>e periphery and <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a necrotic core. Biological results<br />

obtained by <str<strong>on</strong>g>th</str<strong>on</strong>g>e dorsal chamber me<str<strong>on</strong>g>th</str<strong>on</strong>g>od and numerical simulati<strong>on</strong> results are fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

compared to calibrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e model so as to use it as a predictive tool in order to<br />

fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er test and design new <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy protocols.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Statistical Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Signals II; Saturday, July 2, 11:00<br />

Jacek Leśkow<br />

The Polish-American Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Business WSB-NLU Nowy<br />

Sacz, Poland.<br />

e-mail: leskow@wsb-nlu.edu.pl<br />

Resampling wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Applicati<strong>on</strong>s to Neurophysiological Time<br />

Series<br />

Resampling wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Applicati<strong>on</strong>s to Neurophysiological Time Series<br />

Jacek Leskow Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Quantitative Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in Management The Polish-<br />

American Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Business WSB-NLU Nowy Sacz<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fundamental tools in <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> biosignals including functi<strong>on</strong>al<br />

magnetic res<strong>on</strong>ance imaging (fMRI) is a time series model and corresp<strong>on</strong>ding set<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> parameters. Such time series are known to exhibit temporal autocorrelati<strong>on</strong><br />

which is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fundamental characteristic for such fMRI observati<strong>on</strong>s (see e.g.<br />

Bullmore et al (2001)). In <str<strong>on</strong>g>th</str<strong>on</strong>g>e presentati<strong>on</strong>, a general survey <str<strong>on</strong>g>of</str<strong>on</strong>g> resampling me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

for time series will be presented and c<strong>on</strong>sistency issues will be addressed. The focus<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e presentati<strong>on</strong> will be applicati<strong>on</strong>-oriented toward fMRI signals <str<strong>on</strong>g>th</str<strong>on</strong>g>at exhibit<br />

n<strong>on</strong>-gaussian behavior and are n<strong>on</strong>-stati<strong>on</strong>ary. The statistical results presented e.g<br />

in Leskow et al (2008) will be accompanied by applicati<strong>on</strong>s to neurophysiological<br />

time series.<br />

References.<br />

[1] Bullmore E., L<strong>on</strong>g, C., Suckling, J. ,Fadili, J. Calvert, G., Zelaya. F., Carpenter, T.A, Brammer,<br />

M. (2001), Colored Noise and Computati<strong>on</strong>al Inference in Neurophysiological (fMRI)<br />

Time Series Analysis: Resampling Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in Time and Wavelet Domains. Human Brain<br />

Mapping, 12:61-78.<br />

[2] Leskow, J., Lenart, L and Synowiecki, R. (2008), Subsampling in testing autocovariance for<br />

periodically correlated time series, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Time Series Analysis, Vol. 29, No.6.<br />

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Sivan Leviyang<br />

Georgetown University<br />

e-mail: sr286@georgetown.edu<br />

Populati<strong>on</strong> Genetics; Wednesday, June 29, 17:00<br />

Sampling HIV intrahost genealogies based <strong>on</strong> a model <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

acute stage CTL resp<strong>on</strong>se<br />

Genealogy based me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods have become a comm<strong>on</strong> tool in analyzing intrahost HIV<br />

evoluti<strong>on</strong>. These me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods require a coalescent model which implicitly describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

role <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary forces in shaping HIV genealogies. Currently, HIV genealogies<br />

are c<strong>on</strong>structed assuming variants <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Kingman coalescent. The Kingman coalescent<br />

is a generic coalescent model <str<strong>on</strong>g>th</str<strong>on</strong>g>at does not explicitly account for <str<strong>on</strong>g>th</str<strong>on</strong>g>e special<br />

features <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV evoluti<strong>on</strong>. For example, <str<strong>on</strong>g>th</str<strong>on</strong>g>e Kingman coalescent does not account<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> CTL attack.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we introduce a coalescent model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e acute stage <str<strong>on</strong>g>th</str<strong>on</strong>g>at explicitly<br />

incorporates <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> early CTL attack. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>is coalescent model, we develop<br />

a computati<strong>on</strong>al me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows us to sample HIV genealogies shaped by CTL<br />

attack. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at such genealogies are different in form <str<strong>on</strong>g>th</str<strong>on</strong>g>an Kingman coalescent<br />

genealogies. We use our genealogy sampler to explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e type <str<strong>on</strong>g>of</str<strong>on</strong>g> CTL attack<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at is best at c<strong>on</strong>trolling HIV diversity. Our work is a first step in developing<br />

computati<strong>on</strong>al tools <str<strong>on</strong>g>th</str<strong>on</strong>g>at can use HIV genetic data to infer parameters describing<br />

CTL attack.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an F. Li<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> California at Irvine<br />

e-mail: j<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an.li@smes.org<br />

John Lowengrub<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> California at Irvine<br />

e-mail: lowengrb@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.uci.edu<br />

Cell and Tissue Biophysics; Saturday, July 2, 11:00<br />

Effects <str<strong>on</strong>g>of</str<strong>on</strong>g> Cell Compressibility, Motility and C<strong>on</strong>tact<br />

Inhibiti<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Tumor Cell Clusters<br />

We analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> cell migrati<strong>on</strong>, compressi<strong>on</strong>, and c<strong>on</strong>tact inhibiti<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cell clusters using <str<strong>on</strong>g>th</str<strong>on</strong>g>e Cellular Potts Model (CPM) in a m<strong>on</strong>olayer<br />

geometry. Cell proliferati<strong>on</strong>, motility, cell-to-cell adhesi<strong>on</strong>, c<strong>on</strong>tact inhibiti<strong>on</strong>, and<br />

cell compressibility are incorporated in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model. We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at increased motility<br />

has a direct effect <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate <str<strong>on</strong>g>of</str<strong>on</strong>g> clusters. Cell lines wi<str<strong>on</strong>g>th</str<strong>on</strong>g> greater motility<br />

overcome <str<strong>on</strong>g>th</str<strong>on</strong>g>e attractive forces <str<strong>on</strong>g>of</str<strong>on</strong>g> cell-to-cell adhesi<strong>on</strong> and have more space to proliferate.<br />

We analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay between cell motility and compressibility wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e CPM, and find <str<strong>on</strong>g>th</str<strong>on</strong>g>at more motile cells are generally smaller <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>eir more<br />

sedentary counterparts, which can lead to smaller clusters. We obtain an explicit<br />

inverse-relati<strong>on</strong>ship between <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell compressibility and motility parameters and<br />

use <str<strong>on</strong>g>th</str<strong>on</strong>g>is relati<strong>on</strong>ship to compensate for motility-induced cell compressi<strong>on</strong>. Clusters<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> motile cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at do not experience significant compressi<strong>on</strong> grow faster <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>ose<br />

composed <str<strong>on</strong>g>of</str<strong>on</strong>g> less motile cells. In additi<strong>on</strong>, c<strong>on</strong>tact inhibiti<strong>on</strong> amplifies <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

motility. Strict c<strong>on</strong>tact inhibiti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e CPM penalizes clumped cells by halting<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, giving motile cells a greater advantage. We have begun testing our<br />

model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> in vitro data obtained from a collaborator and our model is reflective<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e data.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Chelsea Liddell<br />

Dartmou<str<strong>on</strong>g>th</str<strong>on</strong>g> College, USA<br />

e-mail: Doro<str<strong>on</strong>g>th</str<strong>on</strong>g>y.Wallace@Dartmou<str<strong>on</strong>g>th</str<strong>on</strong>g>.edu<br />

Doro<str<strong>on</strong>g>th</str<strong>on</strong>g>y Wallace<br />

Dartmou<str<strong>on</strong>g>th</str<strong>on</strong>g> College<br />

Nicci Owusu-Brackett<br />

Dartmou<str<strong>on</strong>g>th</str<strong>on</strong>g> College<br />

Kristen Klepac<br />

Dartmou<str<strong>on</strong>g>th</str<strong>on</strong>g> College<br />

Evoluti<strong>on</strong>ary Ecology; Thursday, June 30, 11:30<br />

Persistence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Sickle Cell Genome in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Presence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Malaria<br />

It is believed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e sickle cell gene has persisted in <str<strong>on</strong>g>th</str<strong>on</strong>g>e human populati<strong>on</strong> due<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e partial resistance it c<strong>on</strong>fers <strong>on</strong> victims <str<strong>on</strong>g>of</str<strong>on</strong>g> malaria. We use a system <str<strong>on</strong>g>of</str<strong>on</strong>g> six<br />

equati<strong>on</strong>s tracking populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree genotypes and two age brackets to study<br />

what relative dea<str<strong>on</strong>g>th</str<strong>on</strong>g> rates for malaria and sickle cell are required in order for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

gene to persist, and what resulting proporti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> are expected to<br />

carry <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene under different assumpti<strong>on</strong>s about malarial dea<str<strong>on</strong>g>th</str<strong>on</strong>g> rates. The results<br />

can be compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g> current data to infer historical dea<str<strong>on</strong>g>th</str<strong>on</strong>g> rates for malaria. The<br />

model also allows estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> time it takes such a gene to reach<br />

equilibrium in a populati<strong>on</strong>, and how <str<strong>on</strong>g>th</str<strong>on</strong>g>is depends <strong>on</strong> assumed dea<str<strong>on</strong>g>th</str<strong>on</strong>g> rates.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bridging Time Scales in Biological Sciences; Saturday, July 2, 14:30<br />

Volkmar Liebscher<br />

Ernst-Moritz-Arndt-University Greifswald<br />

e-mail: volkmar.liebscher@uni-greifswald.de<br />

Stephan Thober<br />

Helmholtz-Centre for Envir<strong>on</strong>mental Research Leipzig<br />

The Quasi-steady state hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis for stochastic models <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

enzyme kinetics<br />

In a stochastic versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Briggs-Haldane equati<strong>on</strong>s, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical<br />

quasi-steady state hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis corresp<strong>on</strong>ds to a averaging principle or local ergodic<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eorem for <str<strong>on</strong>g>th</str<strong>on</strong>g>e fast enzymatic reacti<strong>on</strong>. This way, we obtain a more natural<br />

explanati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Michaelis Menten kinetics <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e slow time scale. Some more<br />

detailed estimates are presented, too.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Game <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical modelling and optimizati<strong>on</strong> in evoluti<strong>on</strong> and ecology I;<br />

Tuesday, June 28, 11:00<br />

Magnus Lindh<br />

UmeåUniversity, Sweden<br />

e-mail: magnus.lindh@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.umu.se<br />

Ulf Dieckmann<br />

Internati<strong>on</strong>al Institute for Applied Systems Analysis, Austria<br />

e-mail: dieckmann@iiasa.ac.at<br />

Åke Brännström<br />

UmeåUniversity, Sweden<br />

e-mail: ake.brannstrom@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.umu.se<br />

Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tree architecture<br />

The astounding biodiversity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ear<str<strong>on</strong>g>th</str<strong>on</strong>g>’s ecosystems is <str<strong>on</strong>g>th</str<strong>on</strong>g>e outcome <str<strong>on</strong>g>of</str<strong>on</strong>g> competiti<strong>on</strong>,<br />

cooperati<strong>on</strong>, and migrati<strong>on</strong> am<strong>on</strong>g species and wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-species varieties. The<br />

potential for frequency-dependent selecti<strong>on</strong> to shape <str<strong>on</strong>g>th</str<strong>on</strong>g>ese biodiversity patterns is<br />

easily appreciated in plants, where height-asymmetric competiti<strong>on</strong> for light has not<br />

<strong>on</strong>ly driven <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tall trees, but is also resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir coexistence<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> smaller plants. Less is known, however, <str<strong>on</strong>g>of</str<strong>on</strong>g> how frequency-dependent competiti<strong>on</strong><br />

for light has affected o<str<strong>on</strong>g>th</str<strong>on</strong>g>er salient aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> plant architecture. Here, we<br />

present a trait-, size-, and patch-structured model <str<strong>on</strong>g>of</str<strong>on</strong>g> vegetati<strong>on</strong> dynamics to study<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tree-crown architecture. Our study extends a related model by<br />

Falster et al. (2011), by incorporating self-shading wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in tree crowns and a more<br />

detailed representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biomass-allocati<strong>on</strong> to branches. Tree-crown architecture<br />

is described by two individual-level traits for crown shape and crown wid<str<strong>on</strong>g>th</str<strong>on</strong>g>. Three<br />

scenarios are investigated and c<strong>on</strong>trasted for different combinati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> sun angle,<br />

site productivity, and disturbance frequency. First, we c<strong>on</strong>sider optimal tree-crown<br />

architectures for solitary trees growing apart from competing trees. Sec<strong>on</strong>d, we ask<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e same questi<strong>on</strong> for a m<strong>on</strong>oculture <str<strong>on</strong>g>of</str<strong>on</strong>g> identical trees subject to density-dependent<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. Third, we investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e coevoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tree-crown shape and tree-crown<br />

wid<str<strong>on</strong>g>th</str<strong>on</strong>g> under competiti<strong>on</strong> and for potentially polymorphic traits, and determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

resultant evoluti<strong>on</strong>arily stable state. Finally, we critically reassess <str<strong>on</strong>g>th</str<strong>on</strong>g>e comm<strong>on</strong> belief<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at a low sun angle is a main force driving <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>ical tree-crown architectures<br />

observed in boreal forests.<br />

References.<br />

[1] Falster DS, Brännström Å, Dieckmann U, Westoby M. 2011. Influence <str<strong>on</strong>g>of</str<strong>on</strong>g> four major plant<br />

traits <strong>on</strong> average height, leaf-area cover, net primary productivity, and biomass density in<br />

single-species forests: a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical investigati<strong>on</strong>. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Ecology. 99, 148-164.<br />

[2] Shinozaki K, Yoda K, Hozumi K, Kira T. 1964. A quantitative analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> plant form - <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

pipe model <str<strong>on</strong>g>th</str<strong>on</strong>g>eory. I. Basic analyses. Japanese Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Ecology. 14, 97-105<br />

[3] Shinozaki K, Yoda K, Hozumi K, Kira T. 1964. A quantitative analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> plant form - <str<strong>on</strong>g>th</str<strong>on</strong>g>e pipe<br />

model <str<strong>on</strong>g>th</str<strong>on</strong>g>eory. II. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er evidence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory and its applicati<strong>on</strong> in forest ecology. Japanese<br />

Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Ecology. 14, 133-139<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective phenomena in biological systems; Saturday, July 2,<br />

08:30<br />

Pietro Lio<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cambridge<br />

e-mail: pl219@cam.ac.uk<br />

Nicola Paoletti<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Camerino<br />

Emanuela Merelli<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Camerino<br />

A combined process algebraic and a stochastic approaches to<br />

b<strong>on</strong>e remodeling<br />

In adult life <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e is being c<strong>on</strong>tinuously resorbed and replaced by new b<strong>on</strong>e. Here<br />

we present a stochastic model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e homeostatic nature <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e remodeling, where<br />

osteoclasts perform b<strong>on</strong>e resorpti<strong>on</strong> which is equally balanced by b<strong>on</strong>e formati<strong>on</strong><br />

performed by osteoblasts. The stochastic model is embedded in an algebraic process<br />

based <strong>on</strong> Shape calculus, which provides an effective multiscale descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e process. Our model c<strong>on</strong>siders increasing dimensi<strong>on</strong>ality from Rankl molecular<br />

signalling to osteoclast/osteoblast stochastic dynamics wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a basic multicellular<br />

units (BMU) to a b<strong>on</strong>e mass formati<strong>on</strong>. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at after a micr<str<strong>on</strong>g>of</str<strong>on</strong>g>racture <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

simulated b<strong>on</strong>e remodeling dynamics has timescale c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological<br />

process. Our combined me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology provides a first effective stochastic model <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

b<strong>on</strong>e remodeling framework which could be used to test heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y and pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ological<br />

c<strong>on</strong>diti<strong>on</strong>s.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling II; Wednesday, June 29,<br />

14:30<br />

Dipak Barua 1,2<br />

Wiliam Hlavacek 1,2,3<br />

Tomasz Lipniacki 4<br />

1 Theoretical Biology and Biophysics Group, Theoretical Divisi<strong>on</strong> and<br />

Center for N<strong>on</strong>linear Studies, Los Alamos Nati<strong>on</strong>al Laboratory, Los<br />

Alamos, New Mexico, USA<br />

2 Clinical Translati<strong>on</strong>al Research Divisi<strong>on</strong>, Translati<strong>on</strong>al Genomics<br />

Research Institute, Scottsdale, Ariz<strong>on</strong>a, USA<br />

3 Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> New Mexico, Albuquerque,<br />

New Mexico, USA<br />

4 Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research, Polish Academy<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warsaw, Poland, email: tlipnia@ippt.gov.pl<br />

A rule-based model for early events in B cell antigen<br />

receptor signaling<br />

B cell antigen receptor (BCR) signaling regulates <str<strong>on</strong>g>th</str<strong>on</strong>g>e activities and fates <str<strong>on</strong>g>of</str<strong>on</strong>g> B<br />

cells. Here, we present a rule-based model for early events in BCR signaling <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

encompasses membrane-proximal interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> BCR, two membrane-te<str<strong>on</strong>g>th</str<strong>on</strong>g>ered Srcfamily<br />

protein tyrosine kinases, Lyn and Fyn, <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptor protein PAG, and two<br />

cytosolic protein tyrosine kinases, Csk and Syk. The signaling is triggered by aggregati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e BCR by foreign antigens, which increase <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> BCR-Src<br />

kinases interacti<strong>on</strong>s. The interacti<strong>on</strong>s involve two feedback loops: a positive feedback<br />

loop acting <strong>on</strong> a short time scale and a negative feedback loop acting <strong>on</strong> a<br />

l<strong>on</strong>ger time scale. The positive feedback loop arises because <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e way <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e two<br />

Src-family kinases, Lyn and Fyn, interact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two signaling chains <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e BCR<br />

complex, Igα (CD79A) and Igβ (CD79B). Lyn and Fyn c<strong>on</strong>stitutively associate<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> BCR via low-affinity interacti<strong>on</strong>s and trans-phosphorylate tyrosine residues<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e immunoreceptor tyrosine-based activati<strong>on</strong> motifs (ITAMs) <str<strong>on</strong>g>of</str<strong>on</strong>g> Igα and Igβ<br />

in neighboring receptors wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in antigen-induced clusters <str<strong>on</strong>g>of</str<strong>on</strong>g> BCR. These sites <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

phosphorylati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>en serve as high-affinity docking sites for <str<strong>on</strong>g>th</str<strong>on</strong>g>e SH2 domains in<br />

Lyn and Fyn, which recruit more Lyn and Fyn to BCR clusters. Lyn and Fyn also<br />

undergo autophosphorylati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in antigen-induced clusters <str<strong>on</strong>g>of</str<strong>on</strong>g> BCR, which upregulates<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir kinase activities. The negative feedback loop is mediated by PAG,<br />

which associates wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Lyn and Fyn in a phosphorylati<strong>on</strong>-dependent manner. PAG<br />

serves as a docking site for Csk, which mediates <str<strong>on</strong>g>th</str<strong>on</strong>g>e phosphorylati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a C-terminal<br />

regulatory tyrosine residue found in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> Lyn and Fyn. Phosphorylati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

residue enables an intramolecular interacti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at downregulates Lyn/Fyn kinase<br />

activity. The model makes <str<strong>on</strong>g>th</str<strong>on</strong>g>e distincti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e two Src kinases, Lyn and<br />

Fyn. Whereas Lyn is allowed to phosphorylate PAG at all tyrosine residues, Fyn<br />

may not phosphorylate its own binding sites <strong>on</strong> PAG due to allosteric c<strong>on</strong>straints.<br />

This distinguishes Lyn as <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>ly Src kinase capable to induce <str<strong>on</strong>g>th</str<strong>on</strong>g>e negative feedback<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e system. A dynamical stability analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model reveals <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

BCR circuit can display two interesting behaviors. Bistability can be expected in<br />

PAG -/-, Csk -/-, and Lyn -/- cells, whereas oscillatory pulse-like resp<strong>on</strong>ses to BCR<br />

clustering can be expected in cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e negative feedback loop intact (wild-type<br />

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cells and Fyn -/- cells) under some c<strong>on</strong>diti<strong>on</strong>s. The qualitative behaviors predicted<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e model are c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e known behaviors <str<strong>on</strong>g>of</str<strong>on</strong>g> Lyn and Fyn deficient<br />

cells.<br />

This study was supported by Foundati<strong>on</strong> for Polish Science grant TEAM/2009-<br />

3/6 and Nati<strong>on</strong>al Institutes <str<strong>on</strong>g>of</str<strong>on</strong>g> Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> grants GM076570 and GM085273.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Bartosz Lisowski, Michał Świątek, Michał Żabicki and Ewa Gudowska-<br />

Nowak<br />

M. Smoluchowski Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics and M. Kac Complex Systems<br />

Research Center, Jagiell<strong>on</strong>ian University, Reym<strong>on</strong>ta 4, 30-059 Kraków,<br />

Poland<br />

e-mail: bartek.lisowski@uj.edu.pl<br />

Molecular Motor-Cargo systems: Modeling energetics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

kinesin wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different approaches<br />

Motor proteins, sometimes referred to as mechanoenzymes, are a group <str<strong>on</strong>g>of</str<strong>on</strong>g> proteins<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at maintain a large part <str<strong>on</strong>g>of</str<strong>on</strong>g> intracellular moti<strong>on</strong>. Being enzymes, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey undergo<br />

chemical reacti<strong>on</strong>s leading to energy c<strong>on</strong>versi<strong>on</strong> and changes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir c<strong>on</strong>formati<strong>on</strong>.<br />

Being mechano, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey use <str<strong>on</strong>g>th</str<strong>on</strong>g>e (chemical) energy to perform mechanical<br />

work, leading to <str<strong>on</strong>g>th</str<strong>on</strong>g>e phenomena <str<strong>on</strong>g>of</str<strong>on</strong>g> moti<strong>on</strong>. Series <str<strong>on</strong>g>of</str<strong>on</strong>g> novel experiments, e.g. single<br />

molecule observati<strong>on</strong>s, were performed to gain <str<strong>on</strong>g>th</str<strong>on</strong>g>e knowledge about <str<strong>on</strong>g>th</str<strong>on</strong>g>e performance<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> chemical states <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular motors as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>eir dynamics in<br />

presence or absence <str<strong>on</strong>g>of</str<strong>on</strong>g> an external force.<br />

At <str<strong>on</strong>g>th</str<strong>on</strong>g>e same time, many <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical models were proposed, <str<strong>on</strong>g>of</str<strong>on</strong>g>fering deeper<br />

insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e small-world (nanoworld) dynamics. They can be divided into <str<strong>on</strong>g>th</str<strong>on</strong>g>ree<br />

main categories: chemical models, ratchet models and molecular dynamics models.<br />

Chemical models focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Markovchain, kinetic descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong><br />

cycles resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical transiti<strong>on</strong>s. Ratchet models are mostly based<br />

<strong>on</strong> sets <str<strong>on</strong>g>of</str<strong>on</strong>g> Langevin equati<strong>on</strong>s and treat <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinesin dimer as two linked Brownian<br />

particles moving in a periodic potential. Molecular dynamics models approach<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e problem from <str<strong>on</strong>g>th</str<strong>on</strong>g>e low level dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> single or grouped molecules, based <strong>on</strong><br />

informati<strong>on</strong> obtained from crystallographical data.<br />

We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at by combining <str<strong>on</strong>g>th</str<strong>on</strong>g>ose complementary approaches <strong>on</strong>e can gain<br />

deeper understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics and chemistry <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e motor proteins. As a<br />

working example, we choose kinesin and dynein — motor proteins resp<strong>on</strong>sible for<br />

bidirecti<strong>on</strong>al transport <str<strong>on</strong>g>of</str<strong>on</strong>g> organelles and vesicles using microtubular tracts.<br />

References.<br />

[1] M. Żabicki, W. Ebeling, E. Gudowska-Nowak The <str<strong>on</strong>g>th</str<strong>on</strong>g>ermodynamic cycle <str<strong>on</strong>g>of</str<strong>on</strong>g> an entropy-driven<br />

stepper motor walking hand-over-hand Chem. Phys. 375 472–478 (2010)<br />

[2] B. Lisowski, M. Świątek and E. Gudowska-Nowak Understanding operating principles and<br />

processivity <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular motors work in progress.<br />

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Project operated wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Foundati<strong>on</strong> for Polish Science (Internati<strong>on</strong>al Ph.D.<br />

Projects Programme co-financed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>European</str<strong>on</strong>g> Regi<strong>on</strong>al Development Fund covering,<br />

under <str<strong>on</strong>g>th</str<strong>on</strong>g>e agreement No. MPD/2009/6; <str<strong>on</strong>g>th</str<strong>on</strong>g>e Jagiell<strong>on</strong>ian University Internati<strong>on</strong>al<br />

Ph.D. Studies in Physics <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Systems)<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Mosquito-Borne Diseases; Tuesday, June 28, 11:00<br />

Alun Lloyd<br />

Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Graduate Program, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Nor<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Carolina State University<br />

e-mail: alun_lloyd@ncsu.edu<br />

Modeling Wolbachia-Based Strategies for C<strong>on</strong>trolling<br />

Mosquito-Borne Diseases<br />

Mosquito borne infecti<strong>on</strong>s, most notably malaria and dengue, kill over a milli<strong>on</strong><br />

people every year. Traditi<strong>on</strong>al c<strong>on</strong>trol measures (such as insecticides) against <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

infecti<strong>on</strong>s in developing countries have had mixed success. A novel avenue <str<strong>on</strong>g>of</str<strong>on</strong>g> attack<br />

involves <str<strong>on</strong>g>th</str<strong>on</strong>g>e producti<strong>on</strong> and release <str<strong>on</strong>g>of</str<strong>on</strong>g> mosquitoes <str<strong>on</strong>g>th</str<strong>on</strong>g>at have been manipulated or<br />

genetically engineered to be less able, or even unable, to transmit infecti<strong>on</strong>.<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling is playing an important role in several large-scale<br />

projects <str<strong>on</strong>g>th</str<strong>on</strong>g>at are currently under way to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e feasibility <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese techniques. In<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I shall discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e biology <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>e approach <str<strong>on</strong>g>th</str<strong>on</strong>g>at uses <str<strong>on</strong>g>th</str<strong>on</strong>g>e bacterial symbi<strong>on</strong>t<br />

Wolbachia and <str<strong>on</strong>g>th</str<strong>on</strong>g>e accompanying modelling work, illustrating how a number <str<strong>on</strong>g>of</str<strong>on</strong>g> different<br />

models are being used as <str<strong>on</strong>g>th</str<strong>on</strong>g>e projects move al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g> from lab-based<br />

studies to field deployment.<br />

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Modeling and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor invasi<strong>on</strong> I; Tuesday, June 28, 11:00<br />

Georgios Lolas<br />

Nati<strong>on</strong>al Technical University <str<strong>on</strong>g>of</str<strong>on</strong>g> A<str<strong>on</strong>g>th</str<strong>on</strong>g>ens<br />

e-mail: glolas@yahoo.gr<br />

Avner Friedman<br />

Michael Pepper<br />

The Lymphatic Vascular System in Lymphangiogenesis,<br />

Invasi<strong>on</strong> and Metastasis: A Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Approach<br />

There are two distinct categories <str<strong>on</strong>g>of</str<strong>on</strong>g> tumors: benign and malignant. Benign tumors<br />

remain c<strong>on</strong>fined to <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue in which <str<strong>on</strong>g>th</str<strong>on</strong>g>ey arise and al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>ey may c<strong>on</strong>tinue<br />

to grow, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey do not spread to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er parts <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e body. Unlike benign tumors,<br />

malignant tumors grow rapidly, invade and destroy <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding tissues and,<br />

by exploiting <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood or <str<strong>on</strong>g>th</str<strong>on</strong>g>e lymphatic systems, establish new col<strong>on</strong>ies, a process<br />

called metastasis. Metastasis is <str<strong>on</strong>g>th</str<strong>on</strong>g>e predominant cause <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer dea<str<strong>on</strong>g>th</str<strong>on</strong>g>. There are<br />

four major routes <str<strong>on</strong>g>of</str<strong>on</strong>g> neoplastic disseminati<strong>on</strong>: (1) local invasi<strong>on</strong>; (2) direct seeding<br />

to body cavities; (3) hematogenous spread; and (4) lymphatic spread, preferentially<br />

to regi<strong>on</strong>al lymph nodes and later to distant sites.<br />

For a primary tumor to grow, it needs a supply <str<strong>on</strong>g>of</str<strong>on</strong>g> nutrients, delivered by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

blood. The tumor <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore secrets grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factors which induce <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

new blood vessels, sprouting <str<strong>on</strong>g>th</str<strong>on</strong>g>em from preexisting vessels and directing <str<strong>on</strong>g>th</str<strong>on</strong>g>em toward.<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor. This is <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor angiogenesis. Targeting angiogenesis,<br />

namely, cutting <str<strong>on</strong>g>of</str<strong>on</strong>g> blood supply, is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g>f <str<strong>on</strong>g>th</str<strong>on</strong>g>e strategies for blocking tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

and disseminati<strong>on</strong>.<br />

A similar, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough far less well studied process, also occurs in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lymphatic<br />

system and is referred to as lymphangiogenesis or lymphagenesis. Surprisingly,<br />

almost all <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e published literature focuses <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e correlati<strong>on</strong>s between angiogenesis,<br />

microvessel density, metastatic spread, and tumor prognosis, leaving a missed<br />

link between primary tumor and nodal metastases: <str<strong>on</strong>g>th</str<strong>on</strong>g>e lymphatic system.The lymphatic<br />

system comprises a vascular network <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>e-way, open-ended, <str<strong>on</strong>g>th</str<strong>on</strong>g>in-walled<br />

complex network <str<strong>on</strong>g>of</str<strong>on</strong>g> capillaries and larger vessels, collecting vessels, lymph nodes,<br />

trunks, and ducts <str<strong>on</strong>g>th</str<strong>on</strong>g>at transport lymph and cells from body tissues back to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

circulatory system.<br />

Various studies have shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at angiogenesis is important for solid tumour<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and, presumably, also in hematogenous metastasis. By c<strong>on</strong>trast, <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

lymphatic vessels and <str<strong>on</strong>g>th</str<strong>on</strong>g>e relevance <str<strong>on</strong>g>of</str<strong>on</strong>g> lymphangiogenesis to tumor pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology is less<br />

clear. Until recently <strong>on</strong>ly limited informati<strong>on</strong> c<strong>on</strong>cerning <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular mechanisms<br />

and pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways involved in tumor lymphangiogenesis and tumor lymphatic invasi<strong>on</strong><br />

have been obtained<br />

Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough intensive research in tumor angiogenesis has been going <strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

past four decades, experimental results in tumor lymphangiogenesis began to appear<br />

<strong>on</strong>ly in <str<strong>on</strong>g>th</str<strong>on</strong>g>e last five years. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper we propose <str<strong>on</strong>g>th</str<strong>on</strong>g>e first ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> lymphangiogenesis, and obtain numerical results <str<strong>on</strong>g>th</str<strong>on</strong>g>at qualitatively agree<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental results. In c<strong>on</strong>clusi<strong>on</strong>, we propose <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility to use <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model presented as a possible lymphangiogenesis assay for better<br />

understandingand preventing tumor invasi<strong>on</strong> and tumor lymphangiogenesis<br />

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Cancer; Tuesday, June 28, 11:00<br />

Juan Carlos López Alf<strong>on</strong>so<br />

Interdisciplinary Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Institute (IMI), Complutense University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Madrid, Spain<br />

e-mail: jc.atlantis@gmail.com<br />

Dr. Miguel A. Herrero<br />

Interdisciplinary Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Institute (IMI), Complutense University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Madrid, Spain<br />

Dr. Luis Nunez<br />

Radiophysics Department, Hospital Universitario Puerta de Hierro,<br />

Majadah<strong>on</strong>da, Spain<br />

Some Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Problems in Radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

Determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> radiati<strong>on</strong> over a target and selecting <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

best manner to deliver it are two key issues in radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is lecture, I shall<br />

describe recent results <strong>on</strong> optimizati<strong>on</strong>s me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods aimed at addressing <str<strong>on</strong>g>th</str<strong>on</strong>g>ese goals,<br />

and some examples <str<strong>on</strong>g>of</str<strong>on</strong>g> applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese techniques will be presented.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Tuesday, June 28, 14:30<br />

M. J. Lopez-Herrero<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Statistics, Complutense University <str<strong>on</strong>g>of</str<strong>on</strong>g> Madrid, 28040 Madrid,<br />

Spain<br />

e-mail: lherrero@estad.ucm.es<br />

The SIS and SIR stochastic epidemic models Leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> an<br />

outbreak and time to infecti<strong>on</strong><br />

We deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e SIS and SIR stochastic epidemic models. The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk is to<br />

present <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> some c<strong>on</strong>tinuous characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is sense,<br />

we first extend <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical study <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> an outbreak by investigating<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e whole probability distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e extincti<strong>on</strong> time via Laplace transforms.<br />

Moreover, we also study <str<strong>on</strong>g>th</str<strong>on</strong>g>e time until a n<strong>on</strong>-infected individual becomes infected.<br />

The obtained results are illustrated by numerical examples including an applicati<strong>on</strong><br />

to head lice infecti<strong>on</strong>s.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

O. Angulo<br />

Universidad de Valladolid, Valladolid, Spain<br />

e-mail: oscar@mat.uva.es<br />

J. C. López-Marcos<br />

Universidad de Valladolid, Valladolid, Spain<br />

e-mail: lopezmar@mac.uva.es<br />

M. A. López-Marcos<br />

Universidad de Valladolid, Valladolid, Spain<br />

e-mail: malm@mac.uva.es<br />

J. Martínez-Rodríguez<br />

Universidad de Valladolid, Valladolid, Spain<br />

e-mail: julia@eco.uva.es<br />

Populati<strong>on</strong> Dynamics; Thursday, June 30, 11:30<br />

Numerical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> a populati<strong>on</strong> model <str<strong>on</strong>g>of</str<strong>on</strong>g> marine<br />

invertebrates wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different life stages<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, we c<strong>on</strong>sider an age-structured populati<strong>on</strong> model <str<strong>on</strong>g>of</str<strong>on</strong>g> marine invertebrates<br />

whose life stage is composed <str<strong>on</strong>g>of</str<strong>on</strong>g> sessile adults and pelagic larvae, such as<br />

barnacles c<strong>on</strong>tained in a local habitat. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, proposed by Roughgarden and<br />

Iwasa and ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically analyzed by Kamioka, space is <str<strong>on</strong>g>th</str<strong>on</strong>g>e principal limiting resource.<br />

The l<strong>on</strong>g time simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is kind <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled systems is difficult. Here,<br />

we propose and analyze a numerical me<str<strong>on</strong>g>th</str<strong>on</strong>g>od in order to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymptotic<br />

behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong>s.<br />

References.<br />

[1] J. Roughgarden and Y. Iwasa, Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> a metapopulati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> space-limited subpopulati<strong>on</strong>,<br />

Theoretical Populati<strong>on</strong> Biology 29 (1986) 235–261.<br />

[2] K. Kamioka, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> an age-structured populati<strong>on</strong> model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> space-limited<br />

recruitment, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences 198 (2005) 27–56.<br />

[3] O. Angulo, L. M. Abia, J. C. López-Marcos and M. A. López-Marcos, L<strong>on</strong>g-time simulati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a size-structured populati<strong>on</strong> model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a dynamical resource, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Natural Phenomena 5 (2010) 1–21.<br />

[4] O. Angulo, J. C. López-Marcos, M. A. López-Marcos and J. Martínez-Rodríguez, Numerical<br />

investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e recruitment process in open marine populati<strong>on</strong> models, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Statistical<br />

Mechanics: Theory and Experiment (2011) doi: 10.1088/1742-5468/2011/01/P01003.<br />

.<br />

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Horacio Lopez-Menendez<br />

Zaragoza University<br />

e-mail: hlopez@unizar.es<br />

Manuel Doblare<br />

Zaragoza University<br />

Jose Felix Rodriguez<br />

Zaragoza University<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

The role <str<strong>on</strong>g>of</str<strong>on</strong>g> fluctuati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eorems in biological adhesi<strong>on</strong><br />

The catch-slip b<strong>on</strong>d mechanism are b<strong>on</strong>ds between ligands and receptors, <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

shows a counterintuitive effect. At low forces <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>d lifetime increase until a<br />

maximum value, wich is called <str<strong>on</strong>g>th</str<strong>on</strong>g>e catch b<strong>on</strong>d; after <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximun <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>d lifetime<br />

decrease as describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e Bell’s <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> adhesi<strong>on</strong>(Bell, 1978). In biology <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

effect can be observed in many ligand-receptor interacti<strong>on</strong>s such as Escherichia coli<br />

adhesi<strong>on</strong>, FimH and P-L selectins expressed in leukocytes, actin-myosin interacti<strong>on</strong>,<br />

or in integrins. But also <str<strong>on</strong>g>th</str<strong>on</strong>g>is effect can be useful in order to develop new nanotechnological<br />

applicati<strong>on</strong>s. From <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluctuati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>eorems during<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e late 90’s. These <str<strong>on</strong>g>th</str<strong>on</strong>g>eorems had shown be very usefull in order to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> small systems in biology, such as folding/unfolding cooperative effects.<br />

This systems operates away from equilibrium, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluctuati<strong>on</strong>s induce transiti<strong>on</strong>s<br />

between steady states. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we apply <str<strong>on</strong>g>th</str<strong>on</strong>g>e Crook’s fluctuati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eorem<br />

in order to derive an expressi<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>d lifetime, as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e applied<br />

elastic energy. The propossed model it is validated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er published works.<br />

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Multiscale modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong> kinetics in biology; Tuesday, June 28, 14:30<br />

Andreas Hellander, Stefan Hellander, Per Lötstedt<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Scientific Computing<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Informati<strong>on</strong> Technology<br />

Uppsala University<br />

P O Box 337, SE 75105 Uppsala, Sweden<br />

e-mail: andreas.hellander@it.uu.se, stefan.hellander@it.uu.se,<br />

perl@it.uu.se<br />

Stochastic simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong>-diffusi<strong>on</strong> processes in living<br />

cells <strong>on</strong> multiple scales<br />

The number <str<strong>on</strong>g>of</str<strong>on</strong>g> molecules <str<strong>on</strong>g>of</str<strong>on</strong>g> each chemical species in biological cells is small<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecules react wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a certain probability. A stochastic<br />

mesoscopic model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e chemical reacti<strong>on</strong>s is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore more accurate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>an a deterministic, macroscopic model based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong> rate equati<strong>on</strong>s.<br />

In a computer simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a trajectory <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system, <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

most computati<strong>on</strong>ally expensive part. The diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> different species are treated<br />

differently in [1] in order to reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong>al cost. Depending <strong>on</strong> if <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

copy number is high, intermediate or low <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> events are simulated macroscopically,<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tau leap me<str<strong>on</strong>g>th</str<strong>on</strong>g>od or wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic simulati<strong>on</strong> algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m<br />

(SSA) by Gillespie in an unstructured mesh covering <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. The reacti<strong>on</strong>s are<br />

handled by SSA. Sometimes <str<strong>on</strong>g>th</str<strong>on</strong>g>e mesoscopic model is not sufficiently accurate and<br />

a microscopic descripti<strong>on</strong> is necessary. In such a model, single reacting and diffusing<br />

molecules are tracked [2]. The molecules move in <str<strong>on</strong>g>th</str<strong>on</strong>g>e unstructured mesh by<br />

Brownian moti<strong>on</strong> and are coupled to <str<strong>on</strong>g>th</str<strong>on</strong>g>e mesoscopic model via <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong>s [3].<br />

Examples from molecular biology will be given.<br />

References.<br />

[1] L. Ferm, A. Hellander, P. Lötstedt, An adaptive algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m for simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic<br />

reacti<strong>on</strong>-diffusi<strong>on</strong> processes, J. Comput. Phys., 229 (2010), 343-360.<br />

[2] S. Hellander, P. Lötstedt, Flexible single molecule simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong>-diffusi<strong>on</strong> processes,<br />

J. Comput. Phys., to appear.<br />

[3] A. Hellander, S. Hellander, P. Lötstedt, Coupled mesoscopic and microscopic simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

stochastic reacti<strong>on</strong>–diffusi<strong>on</strong> processes in mixed dimensi<strong>on</strong>s, to appear.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Kavi<str<strong>on</strong>g>th</str<strong>on</strong>g>a Louis<br />

Periyar University, Tamil Nadu, India<br />

e-mail: kavi<str<strong>on</strong>g>th</str<strong>on</strong>g>alouis@yahoo.com<br />

A. Marlewski<br />

Pozna University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Pozna, Poland<br />

A. Muniyappan<br />

Periyar University, Tamil Nadu, India<br />

S. Zdravković<br />

Vinca Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Nuclear Sciences, Belgrade, Serbia<br />

D. Gopi<br />

Periyar University, Tamil Nadu, India<br />

Energy localizati<strong>on</strong> and shape changing solit<strong>on</strong>s in<br />

microtubules<br />

Microtubules are protein polymers made <str<strong>on</strong>g>of</str<strong>on</strong>g> / tubulin heterodimers <str<strong>on</strong>g>th</str<strong>on</strong>g>at form an<br />

essential part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> all eukaryotic cells. Besides giving structural<br />

stability and rigidity to a cell, microtubules play key roles in many physiological<br />

processes such as intracellular vesicle transport and chromosome separati<strong>on</strong> during<br />

mitosis. Nucleated MTs (e.g., as nucleated from <str<strong>on</strong>g>th</str<strong>on</strong>g>e centrosome during <str<strong>on</strong>g>th</str<strong>on</strong>g>e mitosis)<br />

are tightly attached to <str<strong>on</strong>g>th</str<strong>on</strong>g>e nucleated site by <str<strong>on</strong>g>th</str<strong>on</strong>g>eir minus ends and MTs exchange<br />

tubulin dimers between <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluble and polymer pools at <str<strong>on</strong>g>th</str<strong>on</strong>g>eir free plus ends using<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamic instability mechanism. Modulati<strong>on</strong>al instability (MI) is a universal<br />

process in which small phase and amplitude perturbati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at are always present<br />

in a wide input beam grow exp<strong>on</strong>entially during propagati<strong>on</strong> under <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay<br />

between dispersi<strong>on</strong> and n<strong>on</strong>linearity. The mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> depolymerizati<strong>on</strong> and repolymerizati<strong>on</strong><br />

provides c<strong>on</strong>tinual supply <str<strong>on</strong>g>of</str<strong>on</strong>g> energy into <str<strong>on</strong>g>th</str<strong>on</strong>g>e microtubule structures<br />

in a cell. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e tubulin heterodimers are polar, <str<strong>on</strong>g>th</str<strong>on</strong>g>e vibrati<strong>on</strong>s generate an oscillating<br />

electric field <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be excited by <str<strong>on</strong>g>th</str<strong>on</strong>g>e energy released from <str<strong>on</strong>g>th</str<strong>on</strong>g>e hydrolysis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e GTP. Also, we employ <str<strong>on</strong>g>th</str<strong>on</strong>g>e symbolic computati<strong>on</strong> and look for <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical<br />

equati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at supports solit<strong>on</strong> excitati<strong>on</strong>s. It was assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e anti-kink<br />

formati<strong>on</strong> is mainly due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e hydrolysis <str<strong>on</strong>g>of</str<strong>on</strong>g> GTP into GDP so <str<strong>on</strong>g>th</str<strong>on</strong>g>at <strong>on</strong>e can act<br />

as a hydrolyser which corresp<strong>on</strong>ds to <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>formati<strong>on</strong>al change resulting in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a solitary pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile. The propagati<strong>on</strong> will <str<strong>on</strong>g>th</str<strong>on</strong>g>en distribute <str<strong>on</strong>g>th</str<strong>on</strong>g>e energy <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

hydrolysis at a preferred end <str<strong>on</strong>g>of</str<strong>on</strong>g> MT. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, each solitary pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile can be<br />

viewed as a bit <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> whose propagati<strong>on</strong> can be c<strong>on</strong>trolled by an external<br />

electric field.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modelling dengue fever epidemiology; Saturday, July 2, 08:30<br />

José Lourenço<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Zoology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford, Oxford, UK.<br />

Instituto Gulbenkian de Ciência, Lisb<strong>on</strong>, Portugal.<br />

e-mail: lourenco.jml@gmail.com<br />

Mario Recker<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Zoology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford, Oxford, United Kingdom.<br />

e-mail: mario.recker@zoo.ox.ac.uk<br />

Determinants <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue virus phylodynamics.<br />

Dengue fever (DF) and <str<strong>on</strong>g>th</str<strong>on</strong>g>e more severe dengue haemorrhagic fever (DHF)<br />

are mosquito borne viral infecti<strong>on</strong>s which have seen a major increase in terms<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> global distributi<strong>on</strong> and total case numbers over <str<strong>on</strong>g>th</str<strong>on</strong>g>e last few decades. There<br />

are currently four antigenically distinct and potentially co-circulating dengue virus<br />

(DENV) serotypes and each <strong>on</strong>e shows substantial genetic diversity, organised into<br />

phylogenetically distinct lineages (genotypes). While <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is some evidence for<br />

positive selecti<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> DENV is supposed to be mostly dominated<br />

by purifying selecti<strong>on</strong> due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>straints imposed by its two-host lifecycle.<br />

Results from our previous work dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough small differences<br />

in viral fitness can explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e rapid expansi<strong>on</strong> and fixati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> novel genotypes, <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

fate is ultimately determined by <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemiological landscape in which <str<strong>on</strong>g>th</str<strong>on</strong>g>ey arise.<br />

Using a stochastic, spatially explicit model we revisit previous c<strong>on</strong>clusi<strong>on</strong>s and<br />

address <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> host and vector populati<strong>on</strong> structure <strong>on</strong> DENV molecular<br />

evoluti<strong>on</strong> and disease epidemiology.<br />

594

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Yoram Louzoun<br />

Bar Ilan University<br />

e-mail: louzouy@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.biu.ac.il<br />

Tal Vider<br />

Yaacov Maman<br />

Alexandra Agaranovich<br />

Lea Tsaban<br />

B and T cell immune resp<strong>on</strong>ses; Wednesday, June 29, 11:00<br />

Viruses selectively mutate <str<strong>on</strong>g>th</str<strong>on</strong>g>eir CD8+ T cell epitopes an<br />

optimizati<strong>on</strong> framework, a novel machine learning<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology and a large scale genetic analysis.<br />

The relati<strong>on</strong> between organisms and proteins complexity and between <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

evoluti<strong>on</strong> has been discussed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple generic models. The main<br />

robust claim from most such models is <str<strong>on</strong>g>th</str<strong>on</strong>g>e negative relati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e organism<br />

complexity and <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> mutati<strong>on</strong> accumulati<strong>on</strong>.<br />

We here validate <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>clusi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong> between viral gene leng<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir CD8 T cell epitope density. Viruses mutate <str<strong>on</strong>g>th</str<strong>on</strong>g>eir epitopes to avoid detecti<strong>on</strong><br />

by CD8 T cells and <str<strong>on</strong>g>th</str<strong>on</strong>g>e following destructi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir host cell. We propose a<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical model to show <str<strong>on</strong>g>th</str<strong>on</strong>g>at in viruses <str<strong>on</strong>g>th</str<strong>on</strong>g>e epitope density is negatively correlated<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> each protein and <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> proteins.<br />

In order to validate <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>clusi<strong>on</strong>, we developed a novel machine learning<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology to combine multiple modalities <str<strong>on</strong>g>of</str<strong>on</strong>g> peptide-protein docking measurement.<br />

We use <str<strong>on</strong>g>th</str<strong>on</strong>g>is me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology and large amount <str<strong>on</strong>g>of</str<strong>on</strong>g> genomic data to compute<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e epitope repertoire presented by over 1,300 viruses in many HLA alleles. We<br />

show <str<strong>on</strong>g>th</str<strong>on</strong>g>at such a negative correlati<strong>on</strong> is indeed observed.This negative correlati<strong>on</strong><br />

is specific to human viruses.<br />

The optimizati<strong>on</strong> framework also predicts a difference between human and n<strong>on</strong>human<br />

viruses, and an effect <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral life cycle <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epitope density. Proteins<br />

expressed early in <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral life cycle are expected to have a lower epitope density<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>an late proteins.<br />

We define <str<strong>on</strong>g>th</str<strong>on</strong>g>e "Size <str<strong>on</strong>g>of</str<strong>on</strong>g> Immune Repertoire (SIR) score," which represents <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ratio between <str<strong>on</strong>g>th</str<strong>on</strong>g>e epitope density wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a protein and <str<strong>on</strong>g>th</str<strong>on</strong>g>e expected density. This<br />

score is applied to all sequenced viruses to validate <str<strong>on</strong>g>th</str<strong>on</strong>g>e predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimizati<strong>on</strong><br />

model.<br />

The removal <str<strong>on</strong>g>of</str<strong>on</strong>g> early epitopes and <str<strong>on</strong>g>th</str<strong>on</strong>g>e targeting <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular immune resp<strong>on</strong>se<br />

to late viral proteins, allow <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus a time interval to propagate before its host<br />

cells are destroyed by T cells. Interestingly, such a selecti<strong>on</strong> is also observed in<br />

some bacterial proteins. We specifically discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e cases <str<strong>on</strong>g>of</str<strong>on</strong>g> Herpesviruses, HIV<br />

and HBV showing interesting selecti<strong>on</strong> biases.<br />

595

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

John Lowengrub<br />

UC Irvine<br />

e-mail: lowengrb@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.uci.edu<br />

Stem cells and cancer; Wednesday, June 29, 14:30<br />

Feedback, lineages and cancer<br />

We have developed a multispecies c<strong>on</strong>tinuum model to simulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cell lineages in solid tumors. The model accounts for spatiotemporally varying<br />

cell proliferati<strong>on</strong> and dea<str<strong>on</strong>g>th</str<strong>on</strong>g> mediated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e heterogeneous distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen<br />

and soluble proteins. Toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese regulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e rates <str<strong>on</strong>g>of</str<strong>on</strong>g> self-renewal and differentiati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lineages. Terminally differentiated cells release<br />

feedback factors <str<strong>on</strong>g>th</str<strong>on</strong>g>at promote differentiati<strong>on</strong> (e.g., from <str<strong>on</strong>g>th</str<strong>on</strong>g>e TGF superfamily <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

proteins) and decrease rates <str<strong>on</strong>g>of</str<strong>on</strong>g> proliferati<strong>on</strong> (and self-renewal) <str<strong>on</strong>g>of</str<strong>on</strong>g> less differentiated<br />

cells. Stem cells release a short-range feedback factor <str<strong>on</strong>g>th</str<strong>on</strong>g>at promotes self-renewal<br />

(e.g., representative <str<strong>on</strong>g>of</str<strong>on</strong>g> Wnt signaling factors), as well as a l<strong>on</strong>g-range inhibitor<br />

(e.g., representative <str<strong>on</strong>g>of</str<strong>on</strong>g> Wnt inhibitors such as Dkk) <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is factor. We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e progressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumors and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir resp<strong>on</strong>se to treatment is c<strong>on</strong>trolled by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

spatiotemporal dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e signaling processes. The model predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>e development<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> spatiotemporal heterogeneous distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e feedback factors (Wnt,<br />

Dkk and TGF) and tumor cell populati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> clusters <str<strong>on</strong>g>of</str<strong>on</strong>g> stem cells appearing<br />

at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor margin, cyes<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> recent experiments. The n<strong>on</strong>linear coupling<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e heterogeneous expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factors, <str<strong>on</strong>g>th</str<strong>on</strong>g>e heterogeneous<br />

distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell populati<strong>on</strong>s at different lineage stages and <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor shape may<br />

sufficiently depress feedback c<strong>on</strong>trol in parts <str<strong>on</strong>g>of</str<strong>on</strong>g> tumors to favor eventual escape from<br />

c<strong>on</strong>trol. This is shown to lead to invasive fingering, and enhanced aggressiveness<br />

after standard <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic interventi<strong>on</strong>s. We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at using a combinati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

involving differentiati<strong>on</strong> promoters and radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy is very effective in eradicating<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: from physical tools to<br />

applicati<strong>on</strong>s in cancer modeling II; Saturday, July 2, 11:00<br />

John Lowengrub<br />

UC Irvine<br />

e-mail: lowengrb@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.uci.edu<br />

Physical <strong>on</strong>cology<br />

Cancer models relating basic science to clinical care in <strong>on</strong>cology may fail to address<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e nuances <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor behavior and <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, as in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case, discussed herein, <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

complex multiscale dynamics leading to <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>of</str<strong>on</strong>g>ten-observed enhanced invasiveness,<br />

paradoxically induced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e very antiangiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy designed to destroy <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

tumor. Studies would benefit from approaches <str<strong>on</strong>g>th</str<strong>on</strong>g>at quantitatively link <str<strong>on</strong>g>th</str<strong>on</strong>g>e multiple<br />

physical and temporal scales from molecule to tissue in order to <str<strong>on</strong>g>of</str<strong>on</strong>g>fer outcome<br />

predicti<strong>on</strong>s for individual patients. Physical <strong>on</strong>cology is an approach <str<strong>on</strong>g>th</str<strong>on</strong>g>at applies<br />

fundamental principles from <str<strong>on</strong>g>th</str<strong>on</strong>g>e physical and biological sciences to explain certain<br />

cancer behaviors as observable characteristics arising from <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying physical<br />

and biochemical events. For example, <str<strong>on</strong>g>th</str<strong>on</strong>g>e transport <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen molecules <str<strong>on</strong>g>th</str<strong>on</strong>g>rough<br />

tissue affects phenotypic characteristics such as cell proliferati<strong>on</strong>, apoptosis, and<br />

adhesi<strong>on</strong>, which in turn underlie <str<strong>on</strong>g>th</str<strong>on</strong>g>e patient-scale tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and invasiveness.<br />

Here, we illustrate how tumor behavior and treatment resp<strong>on</strong>se may be a quantifiable<br />

functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> marginally stable molecular and/or cellular c<strong>on</strong>diti<strong>on</strong>s modulated<br />

by inhomogeneity. By incorporating patient-specific genomic, proteomic,<br />

metabolomic, and cellular data into multiscale physical models, physical <strong>on</strong>cology<br />

could complement current clinical practice <str<strong>on</strong>g>th</str<strong>on</strong>g>rough enhanced understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer<br />

behavior, <str<strong>on</strong>g>th</str<strong>on</strong>g>us potentially improving patient survival.<br />

597

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Developmental Biology; Thursday, June 30, 11:30<br />

Shar<strong>on</strong> Lubkin<br />

Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina State University<br />

e-mail: lubkin@eos.ncsu.edu<br />

Oswaldo Lozoya<br />

Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina State University/University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina-Chapel<br />

Hill<br />

Mechanical c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> spheroid grow<str<strong>on</strong>g>th</str<strong>on</strong>g>: distinct<br />

morphogenetic regimes<br />

We develop a model <str<strong>on</strong>g>of</str<strong>on</strong>g> transport and grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elio-mesenchymal interacti<strong>on</strong>s.<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> an avascular solid spheroid inside a passive mesenchyme<br />

or gel shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at sustained volumetric grow<str<strong>on</strong>g>th</str<strong>on</strong>g> requires four generic mechanisms:<br />

(1) grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factor, (2) protease, (3) c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> cellularity, and (4) swelling. The<br />

model reveals a bifurcati<strong>on</strong> delineating two distinct morphogenetic regimes: (A)<br />

steady grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, (B) grow<str<strong>on</strong>g>th</str<strong>on</strong>g> arrested by capsule formati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mesenchyme. In<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> morphogenetic regimes, grow<str<strong>on</strong>g>th</str<strong>on</strong>g> velocity is c<strong>on</strong>stant unless and until a complete<br />

capsule forms. Comprehensive explorati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e large parameter space reveals <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e bifurcati<strong>on</strong> is determined by just two ratios representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative streng<str<strong>on</strong>g>th</str<strong>on</strong>g>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and proteolytic activity. Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> velocity is determined <strong>on</strong>ly by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ratio governing grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, independent <str<strong>on</strong>g>of</str<strong>on</strong>g> proteolytic activity. There is a c<strong>on</strong>tinuum<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> interior versus surface grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> fastest grow<str<strong>on</strong>g>th</str<strong>on</strong>g> at <str<strong>on</strong>g>th</str<strong>on</strong>g>e surface. The model<br />

provides a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical basis for explaining observati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> arrest despite<br />

proteolysis <str<strong>on</strong>g>of</str<strong>on</strong>g> surrounding tissue, and gives a quantitative framework for <str<strong>on</strong>g>th</str<strong>on</strong>g>e design<br />

and interpretati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> experiments involving spheroids, and tissues which are locally<br />

equivalent to spheroids.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Developmental Biology; Friday, July 1, 14:30<br />

Torbjörn Lundh<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Chalmers and University <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg<br />

e-mail: torbjorn.lundh@chalmers.se<br />

Jun Udagawa<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Developmental Biology, Shimane University<br />

e-mail: jun@med.shimane-u.ac.jp<br />

Sven-Erik Hänel<br />

IFP Research AB, 431 22 Mölndal, Sweden<br />

e-mail: haenel@gotanet.com<br />

Hiroki Otani<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Developmental Biology, Shimane University<br />

e-mail: hotani@med.shimane-u.ac.jp<br />

Invariances <str<strong>on</strong>g>of</str<strong>on</strong>g> cross- and trippel-ratios <str<strong>on</strong>g>of</str<strong>on</strong>g> human limbs?<br />

Recall <str<strong>on</strong>g>th</str<strong>on</strong>g>at in <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex plain, four points, p, q, r, s, can be mapped to four<br />

, if and <strong>on</strong>ly if <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>er points, ˜p, ˜q, ˜r, ˜s, by a Möbius transformati<strong>on</strong>, z ↦→ az+b<br />

cz+d<br />

cross-ratio, (p−r)(q−s)<br />

(p−s)(q−r)<br />

, equals <str<strong>on</strong>g>th</str<strong>on</strong>g>e cross-ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> ˜p, ˜q, ˜r, ˜s. In [1], a bold and highly<br />

inspiring statement was given <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cross-ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>secutive joints <str<strong>on</strong>g>of</str<strong>on</strong>g> human<br />

limbs, are invariant, not <strong>on</strong>ly over time, but also between different limbs, and even<br />

different pers<strong>on</strong>s! In order to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>is intriguing statement, but also to<br />

develop new morphometric tools for development studies, we geometrically analyze<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e morphological development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e human body, and we examined <str<strong>on</strong>g>th</str<strong>on</strong>g>e crossratio<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree c<strong>on</strong>secutive body parts <str<strong>on</strong>g>th</str<strong>on</strong>g>at are segmented by four landmarks in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir c<strong>on</strong>figurati<strong>on</strong>. Moreover, we introduce an generalizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cross-ratio:<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e triple-ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> five landmarks <str<strong>on</strong>g>th</str<strong>on</strong>g>at segments four c<strong>on</strong>secutive parts (e.g. <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

shoulder, upper arm, forearm, and hand) and examined <str<strong>on</strong>g>th</str<strong>on</strong>g>eir grow<str<strong>on</strong>g>th</str<strong>on</strong>g> patterns. The<br />

triple-ratio was defined for five arbitrary points, p, q, r, s, and t as:<br />

κ(p, q, r, s, t) =<br />

|p − r||q − s||r − t|<br />

|q − r||r − s||p − t| .<br />

It is easy to show <str<strong>on</strong>g>th</str<strong>on</strong>g>at also <str<strong>on</strong>g>th</str<strong>on</strong>g>e trippel-ratio is invariant under Möbius transformati<strong>on</strong>s.<br />

The cross- and triple-ratios <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e upper limb and shoulder girdle in fetuses<br />

were c<strong>on</strong>stant when biomechanical landmarks were used al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e cross-ratio <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e upper limb varied when <str<strong>on</strong>g>th</str<strong>on</strong>g>e anatomical landmarks were used. The cross-ratios<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lower limbs, trunk, and pelvic girdles <str<strong>on</strong>g>of</str<strong>on</strong>g> fetuses differed from <str<strong>on</strong>g>th</str<strong>on</strong>g>eir corresp<strong>on</strong>ding<br />

cross-ratios in adults. These results suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>e Möbius grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

fetal upper limb and shoulder girdle, but not in <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er body parts we examined.<br />

However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> balance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ree c<strong>on</strong>tiguous body parts was represented by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e developmental change in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cross-ratio. Therefore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e cross- and triple-ratios<br />

may be applicable for <str<strong>on</strong>g>th</str<strong>on</strong>g>e assessment <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> balance or proporti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e body<br />

parts.<br />

References.<br />

[1] S.V. Petukhov N<strong>on</strong>-Euclidean geometries and algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms <str<strong>on</strong>g>of</str<strong>on</strong>g> living bodies Comput. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Appl.<br />

17:505–534.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Jamie Luo<br />

Centre for Complexity Science, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warwick<br />

e-mail: J.X.Luo@warwick.ac.uk<br />

Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ew Turner<br />

Centre for Complexity Science, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warwick<br />

Functi<strong>on</strong>ality and Speciati<strong>on</strong> in Boolean Networks<br />

Boolean Networks have been used to model Genetic Regulatory Networks since<br />

Stuart Kauffmann proposed <str<strong>on</strong>g>th</str<strong>on</strong>g>em as a model in <str<strong>on</strong>g>th</str<strong>on</strong>g>e 1960s. Early work focused<br />

<strong>on</strong> how <str<strong>on</strong>g>th</str<strong>on</strong>g>e topology <str<strong>on</strong>g>of</str<strong>on</strong>g> a network influenced its dynamics. We investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

inverse problem asking which network topologies satisfy a specified dynamic. In<br />

earlier work by A. Wagner a biological functi<strong>on</strong> or cell process was specified by<br />

an initial c<strong>on</strong>diti<strong>on</strong> v(0) and an end point v1 in <str<strong>on</strong>g>th</str<strong>on</strong>g>e expressi<strong>on</strong> state space. By<br />

so specifying a biological functi<strong>on</strong> <strong>on</strong>e can <str<strong>on</strong>g>th</str<strong>on</strong>g>en ask which networks perform <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

functi<strong>on</strong>. Our view is <str<strong>on</strong>g>th</str<strong>on</strong>g>at in many cases a more appropriate means for defining a<br />

biological functi<strong>on</strong> would be by specifying <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire pa<str<strong>on</strong>g>th</str<strong>on</strong>g> v(0), v(1), ... , v(T). We<br />

will report <strong>on</strong> how <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two c<strong>on</strong>trasting definiti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> biological functi<strong>on</strong>ality lead<br />

to divergent results for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir respective functi<strong>on</strong>al topologies, particularly regarding<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e implicati<strong>on</strong>s for neutral evoluti<strong>on</strong>, multi-functi<strong>on</strong>ality and speciati<strong>on</strong>.<br />

600

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting cell systems: from intercellular interacti<strong>on</strong><br />

to tissue-level traits I; Wednesday, June 29, 14:30<br />

Richard Gejji 1,2 , Pavel M. Lushnikov 3 and Mark Alber 1<br />

1 Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied and Computati<strong>on</strong>al Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Notre Dame, Notre Dame, IN 46656, USA<br />

2 Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences Institute, Ohio State University, 1735 Neil<br />

Avenue, Columbus, OH 43210<br />

3 Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> New Mexico,<br />

Albuquerque, NM 87131, USA<br />

e-mail: plushnik@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.unm.edu<br />

Macroscopic model <str<strong>on</strong>g>of</str<strong>on</strong>g> self-propelled bacteria swarming wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

regular reversals<br />

Periodic reversals <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e directi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> moti<strong>on</strong> in systems <str<strong>on</strong>g>of</str<strong>on</strong>g> self-propelled rod shaped<br />

bacteria enable <str<strong>on</strong>g>th</str<strong>on</strong>g>em to effectively resolve traffic jams formed during swarming and<br />

maximize <str<strong>on</strong>g>th</str<strong>on</strong>g>eir swarming rate. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper, a c<strong>on</strong>necti<strong>on</strong> is found between a microscopic<br />

<strong>on</strong>e dimensi<strong>on</strong>al cell-based stochastic model <str<strong>on</strong>g>of</str<strong>on</strong>g> reversing n<strong>on</strong>-overlapping<br />

bacteria and a macroscopic n<strong>on</strong>-linear diffusi<strong>on</strong> equati<strong>on</strong> describing dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular density. Boltzmann-Matano analysis is used to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>linear<br />

diffusi<strong>on</strong> equati<strong>on</strong> corresp<strong>on</strong>ding to <str<strong>on</strong>g>th</str<strong>on</strong>g>e specific reversal frequency. Macroscopically<br />

(ensemble-vise) averaged stochastic dynamics is shown to be in a very good<br />

agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>linear diffusi<strong>on</strong> equati<strong>on</strong>. Critical<br />

density p0 is obtained such <str<strong>on</strong>g>th</str<strong>on</strong>g>at n<strong>on</strong>linear diffusi<strong>on</strong> is str<strong>on</strong>gly suppressed for p < p0.<br />

An analytical approximati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pairwise collisi<strong>on</strong> time and semi-analytical fit<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e total jam time per reversal period are also obtained. It is shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

cell populati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high reversal frequencies are able to spread out effectively at<br />

high densities. If <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells rarely reverse <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are able to spread out at lower<br />

densities but are less efficient to spread out at higher densities.<br />

601

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Mosquito-Borne Diseases; Tuesday, June 28, 11:00<br />

Angelina Mageni Lutambi 1,2<br />

e-mail: angelina-m.lutambi@unibas.ch<br />

Nakul Chitnis 1<br />

Melissa Penny 1<br />

Tom Smi<str<strong>on</strong>g>th</str<strong>on</strong>g> 1<br />

1 Swiss Tropical and Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Institute, Socinstrasse 574002 BASEL,<br />

Switzerland<br />

2 Data Analysis Cluster, Ifakara Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Institute, Coordinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g>fice,<br />

Kiko Avenue, Mikocheni, PO Box 78373, Dar es Salaam, Tanzania<br />

Modelling mosquito dispersal in a heterogeneous<br />

envir<strong>on</strong>ment<br />

Mosquito foraging behaviour for hosts and ovipositi<strong>on</strong> sites/habitats is an important<br />

aspect for malaria c<strong>on</strong>trol. Recent studies have highlighted <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> habitats <strong>on</strong> mosquito search for ovipositi<strong>on</strong> sites. While o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers have<br />

highlighted <str<strong>on</strong>g>th</str<strong>on</strong>g>e significance <str<strong>on</strong>g>of</str<strong>on</strong>g> habitat eliminati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in certain distances from human<br />

habitati<strong>on</strong>s to prevent mosquitoes using human hosts for blood meals. While<br />

minimizing or eliminating <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> mosquitoes <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> malaria has<br />

been a c<strong>on</strong>cern <str<strong>on</strong>g>of</str<strong>on</strong>g> current malaria research, mosquito dynamics and mosquito spatial<br />

distributi<strong>on</strong> remain a challenge. The goal <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is to describe and understand<br />

mosquito populati<strong>on</strong> dynamics in relati<strong>on</strong> to dispersal in spatial envir<strong>on</strong>ments.<br />

A simple ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mosquito life cycle is formulated<br />

to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> mosquitoes. Dispersal <str<strong>on</strong>g>of</str<strong>on</strong>g> adult mosquitoes<br />

searching ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er for hosts or ovipositi<strong>on</strong> sites is also modelled and its effects incorporated<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> dynamics. The spatial aspect <str<strong>on</strong>g>of</str<strong>on</strong>g> mosquito dispersal is<br />

described by <str<strong>on</strong>g>th</str<strong>on</strong>g>eir movement between patches in a two-dimensi<strong>on</strong>al spatial envir<strong>on</strong>ment.<br />

A hexag<strong>on</strong>al grid wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each hexag<strong>on</strong> representing a patch is used where<br />

vital dynamics are allowed to occur. Numerical simulati<strong>on</strong>s are carried out to<br />

dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model.<br />

The modelled populati<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> each stage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mosquito life cycle in<br />

space are presented and <str<strong>on</strong>g>th</str<strong>on</strong>g>e links between factors influencing <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial dynamics<br />

are discussed.<br />

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Populati<strong>on</strong> Dynamics; Saturday, July 2, 11:00<br />

Wes Maciejewski<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Queen’s University, Canada<br />

e-mail: wes@mast.queensu.ca<br />

Resistance Distance and Relatedness <strong>on</strong> an Evoluti<strong>on</strong>ary<br />

Graph<br />

When investigating evoluti<strong>on</strong> in structured populati<strong>on</strong>s, it is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten c<strong>on</strong>venient to<br />

c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> as an evoluti<strong>on</strong>ary graph – individuals as nodes, and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

relati<strong>on</strong>s as edges. There has, in recent years, been a surge <str<strong>on</strong>g>of</str<strong>on</strong>g> interest in evoluti<strong>on</strong>ary<br />

graphs, especially in <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> social behaviors ([5],[6]). An<br />

inclusive fitness framework is best suited for <str<strong>on</strong>g>th</str<strong>on</strong>g>is type <str<strong>on</strong>g>of</str<strong>on</strong>g> study [2]. An expressi<strong>on</strong><br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic similarity between individuals residing <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e graph is required for<br />

inclusive fitness calculati<strong>on</strong>s. This has been a major hindrance for work in <str<strong>on</strong>g>th</str<strong>on</strong>g>is area<br />

as highly technical ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten required [1]. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is presentati<strong>on</strong>, I will<br />

derive a recent result [4] <str<strong>on</strong>g>th</str<strong>on</strong>g>at links genetic relatedness between haploid individuals<br />

<strong>on</strong> an evoluti<strong>on</strong>ary graph to <str<strong>on</strong>g>th</str<strong>on</strong>g>e resistance between vertices <strong>on</strong> a corresp<strong>on</strong>ding<br />

electrical network. Specifically, if Rij be <str<strong>on</strong>g>th</str<strong>on</strong>g>e relatedness and γij <str<strong>on</strong>g>th</str<strong>on</strong>g>e resistance<br />

distance [3] bo<str<strong>on</strong>g>th</str<strong>on</strong>g> between individuals i and j <strong>on</strong> a transitive graph G wi<str<strong>on</strong>g>th</str<strong>on</strong>g> N<br />

vertices each <str<strong>on</strong>g>of</str<strong>on</strong>g> degree k. Then,<br />

Rij = 1 − γij<br />

An example <str<strong>on</strong>g>th</str<strong>on</strong>g>at dem<strong>on</strong>strates <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is result over c<strong>on</strong>temporary<br />

approaches will be provided. I will discuss some new insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

relatedness c<strong>on</strong>cept brought about by <str<strong>on</strong>g>th</str<strong>on</strong>g>is result and menti<strong>on</strong> possible directi<strong>on</strong>s<br />

for future investigati<strong>on</strong>.<br />

References.<br />

[1] Grafen, A. (2007). An Inclusive Fitness Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Alrtuism <strong>on</strong> a Cyclical Network. Journal<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Evoluti<strong>on</strong>ary Biology, 20, pp. 2278-2283.<br />

[2] Hamilt<strong>on</strong>, W. D. (1964) The Genetical Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Social Behaviour I and II. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Theoretical Biology, 7, pp. 1–16, and 17-52.<br />

[3] Klein, D.J., Randić, M. (1993). Resistance Distance. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Chemistry, 12,<br />

pp. 81-95.<br />

[4] Maciejewski, W. (for<str<strong>on</strong>g>th</str<strong>on</strong>g>coming). Resistance Distance and Relatedness <strong>on</strong> an Evoluti<strong>on</strong>ary<br />

Graph.<br />

[5] Nowak, M.A. (2006). Evoluti<strong>on</strong>ary Dynamics. Cambridge, MA: Harvard University Press.<br />

[6] Taylor, P., Day, T., Wild, G. (2007). Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cooperati<strong>on</strong> in a Finite Homogeneous Graph.<br />

Nature, 447, pp. 469-472.<br />

γave<br />

.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Delay Differential Equati<strong>on</strong>s and Applicati<strong>on</strong>s I; Friday, July 1, 14:30<br />

Michael C. Mackey<br />

McGill University<br />

e-mail: michael.mackey@mcgill.ca<br />

Using ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling to tailor <str<strong>on</strong>g>th</str<strong>on</strong>g>e administrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy and G-CSF<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I will briefly describe recent work <str<strong>on</strong>g>th</str<strong>on</strong>g>at we have carried out using a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> human hematopoiesis to investigate optimal delivery<br />

strategies for granulocyte col<strong>on</strong>y stimulating factor (G-CSF) in <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> cyclical neutropenia, and to aid patients in <str<strong>on</strong>g>th</str<strong>on</strong>g>e post-chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

phase. Additi<strong>on</strong>ally I will discuss optimal ways to deliver chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy.<br />

604

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> gene regulati<strong>on</strong>; Tuesday, June 28, 11:00<br />

Michael C. Mackey<br />

McGill University<br />

e-mail: michael.mackey@mcgill.ca<br />

Marta Tyran-Kamińska<br />

Silesian University<br />

RomainYvinec<br />

Universite Ly<strong>on</strong> 1<br />

Molecular distributi<strong>on</strong>s in gene regulatory dynamics<br />

Extending <str<strong>on</strong>g>th</str<strong>on</strong>g>e work <str<strong>on</strong>g>of</str<strong>on</strong>g> Friedman et al.(2006), we study <str<strong>on</strong>g>th</str<strong>on</strong>g>e stati<strong>on</strong>ary density <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular c<strong>on</strong>stituents in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> noise arising from ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

bursting transcripti<strong>on</strong> or translati<strong>on</strong>, or noise in degradati<strong>on</strong> rates. We examine<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e global stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stati<strong>on</strong>ary density as well as its bifurcati<strong>on</strong> structure.<br />

We have compared our results wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same model systems<br />

(ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er inducible or repressible oper<strong>on</strong>s) in <str<strong>on</strong>g>th</str<strong>on</strong>g>e absence <str<strong>on</strong>g>of</str<strong>on</strong>g> any stochastic effects, and<br />

shown <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>dence between behaviour in <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic system and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

stochastic analogs. We have identified key dimensi<strong>on</strong>less parameters <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trol<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e appearance <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> two stable steady states in <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic case, or unimodal<br />

and bimodal densities in <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic systems, and detailed <str<strong>on</strong>g>th</str<strong>on</strong>g>e analytic<br />

requirements for <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> different behaviours. This approach provides, in<br />

some situati<strong>on</strong>s, an alternative to computati<strong>on</strong>ally intensive stochastic simulati<strong>on</strong>s.<br />

Our results indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>at, wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e simple models we have examined,<br />

bursting and degradati<strong>on</strong> noise cannot be distinguished analytically when<br />

present al<strong>on</strong>e.<br />

605

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Dorota Mackiewicz<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Genomics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Biotechnology, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Wroclaw, ul. Przybyszewskiego 63/77, 51-148 Wroclaw, Poland<br />

e-mail: dorota@smorfland.uni.wroc.pl<br />

Paulo Murilo Castro de Oliveira<br />

Instituto de Física, Universidade Federal Fluminense; Av. Litorânea<br />

s/n, Boa Viagem, Niterói 24210-340, RJ, Brazil<br />

Suzana Moss de Oliveira<br />

Instituto de Física, Universidade Federal Fluminense; Av. Litorânea<br />

s/n, Boa Viagem, Niterói 24210-340, RJ, Brazil<br />

Stanisław Cebrat<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Genomics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Biotechnology, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Wroclaw, ul. Przybyszewskiego 63/77, 51-148 Wroclaw, Poland<br />

Distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> recombinati<strong>on</strong> hotspots in human genome<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> computer simulati<strong>on</strong>s and real data<br />

Analyses <str<strong>on</strong>g>of</str<strong>on</strong>g> meiotic recombinati<strong>on</strong> between homologous human chromosomes revealed<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e uneven distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> recombinati<strong>on</strong> events al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e chromosomes.<br />

This phenomen<strong>on</strong> has been observed in different genomic scales. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e megabase<br />

scale, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean recombinati<strong>on</strong> rate is higher in <str<strong>on</strong>g>th</str<strong>on</strong>g>e sub-telomeric regi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>an in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

middle parts <str<strong>on</strong>g>of</str<strong>on</strong>g> chromosomes. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, at <str<strong>on</strong>g>th</str<strong>on</strong>g>e finer scale, recombinati<strong>on</strong><br />

events tend to cluster into narrow spans <str<strong>on</strong>g>of</str<strong>on</strong>g> a few kb in leng<str<strong>on</strong>g>th</str<strong>on</strong>g>, which are called recombinati<strong>on</strong><br />

hotspots. These short regi<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> very high recombinati<strong>on</strong> frequency<br />

occur also more frequently at <str<strong>on</strong>g>th</str<strong>on</strong>g>e ends <str<strong>on</strong>g>th</str<strong>on</strong>g>an in <str<strong>on</strong>g>th</str<strong>on</strong>g>e centre <str<strong>on</strong>g>of</str<strong>on</strong>g> chromosome. They<br />

were discovered based <strong>on</strong> high-resoluti<strong>on</strong> recombinati<strong>on</strong> maps which were inferred<br />

from high-density single-nucleotide polymorphism (SNP) data using linkage disequilibrium<br />

(LD) patterns. Recently, it has been reported a degenerate 13 bp l<strong>on</strong>g<br />

motif, CCNCCNTNNCCNC, which is overrepresented inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e human hotspots.<br />

Moreover, many experiments suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e zinc-finger protein PRDM9 binds to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is motif, which can indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> a comm<strong>on</strong> mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> recombinati<strong>on</strong><br />

regulati<strong>on</strong>. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, hotspot locati<strong>on</strong>s are not shared between human<br />

and chimpanzee, which suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>eir short lifespan. Understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

recombinati<strong>on</strong> hotspots can provide insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e linkage disequilibrium patterns<br />

and help create <str<strong>on</strong>g>th</str<strong>on</strong>g>e accurate linkage map for disease associati<strong>on</strong> studies. We have<br />

found <str<strong>on</strong>g>th</str<strong>on</strong>g>at many recombinati<strong>on</strong> properties, for example <str<strong>on</strong>g>th</str<strong>on</strong>g>e uneven distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

hotspots, can be predicted and explained by computer simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong><br />

evoluti<strong>on</strong>. Assuming spatial distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genes al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e chromosomes and finite<br />

size <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong>s, simulati<strong>on</strong>s render a perfect picture <str<strong>on</strong>g>of</str<strong>on</strong>g> recombinati<strong>on</strong> observed<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e human genome. The obtained results <str<strong>on</strong>g>of</str<strong>on</strong>g> simulati<strong>on</strong>s indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> crossing points are subjected to evoluti<strong>on</strong>. Therefore, it is expected <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e recombinati<strong>on</strong> motifs for <str<strong>on</strong>g>th</str<strong>on</strong>g>e hotspot regulati<strong>on</strong> should follow<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e uneven distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> recombinati<strong>on</strong> events. In order to test our hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis,<br />

we check <str<strong>on</strong>g>th</str<strong>on</strong>g>e locati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e motif al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e human chromosomes using bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

physical and <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic map. The analyses showed <str<strong>on</strong>g>th</str<strong>on</strong>g>e correlati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

frequency <str<strong>on</strong>g>of</str<strong>on</strong>g> recombinati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e locati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> motif. In additi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e examinati<strong>on</strong><br />

606

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e distances between motifs c<strong>on</strong>firmed <str<strong>on</strong>g>th</str<strong>on</strong>g>eir n<strong>on</strong> random distributi<strong>on</strong> al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

human chromosomes.<br />

607

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Paweł Mackiewicz<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Genomics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Biotechnology, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Wrocław, Przybyszewskiego 63/77, 51-148 Wrocław, Poland<br />

e-mail: pamac@smorfland.uni.wroc.pl<br />

Zuzanna Drulis-Kawa<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Genetics and Microbiology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Wrocław, Przybyszewskiego<br />

63/77, 51-148 Wrocław, Poland<br />

Ewa Maciaszczyk-Dziubinska<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Plant Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Wrocław, Kan<strong>on</strong>ia 6/8, 50-<br />

328 Wrocław Poland<br />

Andrew M. Kropinski<br />

Laboratory for Foodborne Zo<strong>on</strong>oses, Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Agency <str<strong>on</strong>g>of</str<strong>on</strong>g> Canada,<br />

110 St<strong>on</strong>e Road West, Guelph, ON, N1G 3W4, Canada<br />

Clustering and genomic analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> phages from Podoviridae<br />

family<br />

Phage genomes evolve, according to <str<strong>on</strong>g>th</str<strong>on</strong>g>e modular evoluti<strong>on</strong>, by <str<strong>on</strong>g>th</str<strong>on</strong>g>e exchange <str<strong>on</strong>g>of</str<strong>on</strong>g> interchangeable<br />

genetic elements. This causes <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard hierarchical branching<br />

phylogeny <str<strong>on</strong>g>of</str<strong>on</strong>g> phages and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir classificati<strong>on</strong> are unsatisfied and even impossible. To<br />

show relati<strong>on</strong>ships between <str<strong>on</strong>g>th</str<strong>on</strong>g>e phage genomes by an alternative approach, we applied<br />

CLANS s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware which uses a versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fruchterman–Reingold graph layout<br />

algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m to visualize pairwise sequence similarities in ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er two-dimensi<strong>on</strong>al<br />

or <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-dimensi<strong>on</strong>al space. The analyses were performed <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e 92 Podoviridae<br />

complete genome sequences using all-against-all TBLASTX searches <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e amino<br />

acid level. Additi<strong>on</strong>ally, we made <str<strong>on</strong>g>th</str<strong>on</strong>g>e pairwise comparis<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nucleotide level<br />

in BLASTN for 36 genome sequences from Autographivirinae subfamily to study<br />

relati<strong>on</strong>ships between <str<strong>on</strong>g>th</str<strong>on</strong>g>ese phages in detail. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e studies we also included <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

newly sequenced genome from Klebsiella pneum<strong>on</strong>iae KP34 phage. The analyses<br />

made possible to group <str<strong>on</strong>g>th</str<strong>on</strong>g>e phage genomes in clusters and proposed some modificati<strong>on</strong>s<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir current tax<strong>on</strong>omic classificati<strong>on</strong>. The applied me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is very sensitive<br />

and enabled to find a signal coming from horiz<strong>on</strong>tal gene transfer from some Picovirinae<br />

members to Lactococcus phage KSY1. Detailed comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genomes<br />

from phiKMV viruses revealed distinct gene c<strong>on</strong>tent and arrangement at <str<strong>on</strong>g>th</str<strong>on</strong>g>e 3’-end<br />

genomic regi<strong>on</strong> which may be resp<strong>on</strong>sible for differences in <str<strong>on</strong>g>th</str<strong>on</strong>g>e host recogniti<strong>on</strong> and<br />

infecti<strong>on</strong> mechanisms.<br />

608

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: from physical tools to<br />

applicati<strong>on</strong>s in cancer modeling I; Saturday, July 2, 08:30<br />

Paul Macklin<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee, United Kingdom<br />

e-mail: Paul.Macklin@Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>Cancer.org<br />

Mary E. Edgert<strong>on</strong><br />

Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, M.D. Anders<strong>on</strong> Cancer Center, USA<br />

Vittorio Cristini<br />

Depts. <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology & Chemical Engineering, U. <str<strong>on</strong>g>of</str<strong>on</strong>g> New Mexico, USA<br />

Lee B. Jordan, Colin A. Purdie<br />

NHS Tayside Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology / University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee, UK<br />

Andrew J. Evans, Alastair M. Thomps<strong>on</strong><br />

Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Surgical & Molecular Oncology, U. <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee, UK<br />

An illustrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> patient-specific cancer modelling: from<br />

microscopic data to macroscopic, quantitative predicti<strong>on</strong>s<br />

Ductal carcinoma in situ (DCIS)—a type <str<strong>on</strong>g>of</str<strong>on</strong>g> breast cancer whose grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is c<strong>on</strong>fined<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e duct lumen—is a significant precursor to invasive breast carcinoma.<br />

DCIS is comm<strong>on</strong>ly detected as a subtle pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> calcificati<strong>on</strong>s in mammograms.<br />

Mammograms are also used to plan surgical resecti<strong>on</strong> (lumpectomy) <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour,<br />

but multiple surgeries are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten required to fully eliminate DCIS. This highlights<br />

deficiencies in current surgical planning. Immunohistochemical measurements have<br />

been proposed to assess DCIS and plan treatment, but no standard has emerged<br />

to quantitatively predict a patient’s clinical progressi<strong>on</strong> (i.e., macroscopic measurements<br />

such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate) based up<strong>on</strong> such microscopic measurements.<br />

We present a mechanistic, agent-based model <str<strong>on</strong>g>of</str<strong>on</strong>g> solid-type DCIS wi<str<strong>on</strong>g>th</str<strong>on</strong>g> comed<strong>on</strong>ecrosis<br />

and calcificati<strong>on</strong> [1]. Each agent has a lattice-free positi<strong>on</strong> and phenotypic<br />

state. Cells move by exchanging biomechanical forces wi<str<strong>on</strong>g>th</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er cells and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e basement membrane. Each phenotypic state has a “submodel” <str<strong>on</strong>g>of</str<strong>on</strong>g> changes in<br />

cell volume and compositi<strong>on</strong>. Phenotypic transiti<strong>on</strong>s from <str<strong>on</strong>g>th</str<strong>on</strong>g>e quiescent state are<br />

regulated by proteomic- and microenvir<strong>on</strong>ment-dependent stochastic processes. We<br />

combine a model analysis, a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically-oriented literature search, and a new<br />

patient-specific calibrati<strong>on</strong> protocol to fully c<strong>on</strong>strain and calibrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e model to<br />

an individual patient’s immunohistochemical and morphometric data [3].<br />

The model predicts linear grow<str<strong>on</strong>g>th</str<strong>on</strong>g> at approximately 7–10 mm per year, c<strong>on</strong>sistent<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mammography [4]. It also predicts a linear correlati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e calcificati<strong>on</strong><br />

size (as in a mammogram) and <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour size (post-operative pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology<br />

measurement), in excellent quantitative agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 87 clinical data points [4].<br />

These results suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at hybrid multiscale models can be rigorously calibrated to<br />

molecular data by upscaling mechanistic cell-scale models. Such multiscale models<br />

can potentially bring ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics to <str<strong>on</strong>g>th</str<strong>on</strong>g>e clinic to improve patient care.<br />

References.<br />

[1] P. Macklin et al., Patient-calibrated agent-based modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> ductal carcinoma in situ (DCIS)<br />

I: Model formulati<strong>on</strong> and analysis, J. Theor. Biol. (2011, in review)<br />

[2] P. Macklin et al., Patient-calibrated agent-based modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> ductal carcinoma in situ (DCIS)<br />

II: From microscopic measurements to macroscopic predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> clinical progressi<strong>on</strong>, J.<br />

Theor. Biol. (2011, in review)<br />

609

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[3] J.Z. Thoms<strong>on</strong> et al., Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> ductal carcinoma in situ (DCIS): a retrospective<br />

analysis based <strong>on</strong> mammographic findings, Br. J. Canc., 85 225–7 (2001)<br />

[4] M.A.J. de Roos et al., Correlati<strong>on</strong> between imaging and pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology in ductal carcinoma in situ<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e breast, World J. Surg. Onco. 2 4 (2004)<br />

610

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Mechanical Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Movement and Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cells and Tissues II;<br />

Wednesday, June 29, 17:00<br />

Paul Macklin<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee, United Kingdom<br />

e-mail: Paul.Macklin@Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>Cancer.org<br />

Mary E. Edgert<strong>on</strong><br />

Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, M.D. Anders<strong>on</strong> Cancer Center, USA<br />

Vittorio Cristini<br />

Depts. <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology & Chemical Engineering, U. <str<strong>on</strong>g>of</str<strong>on</strong>g> New Mexico, USA<br />

Lee B. Jordan, Colin A. Purdie<br />

NHS Tayside Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology / University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee, UK<br />

Andrew J. Evans, Alastair M. Thomps<strong>on</strong><br />

Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Surgical & Molecular Oncology, U. <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee, UK<br />

Mechanistic cell-scale modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> ductal carcinoma in situ<br />

(DCIS): impact <str<strong>on</strong>g>of</str<strong>on</strong>g> biomechanics in comed<strong>on</strong>ecrosis<br />

Ductal carcinoma in situ (DCIS)—a type <str<strong>on</strong>g>of</str<strong>on</strong>g> breast cancer whose grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is c<strong>on</strong>fined<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e duct lumen—is a significant precursor to invasive breast carcinoma. The<br />

presence <str<strong>on</strong>g>of</str<strong>on</strong>g> a central necrotic core in <strong>on</strong>e or more affected ducts (comed<strong>on</strong>ecrosis) indicates<br />

poorer patient prognosis. Microcalcificati<strong>on</strong>s—calcium phosphate deposits<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at gradually replace necrotic cytoplasmic debris—are critically important to detecting<br />

DCIS by mammography. N<strong>on</strong>e<str<strong>on</strong>g>th</str<strong>on</strong>g>eless, most models <strong>on</strong>ly include necrosis as<br />

a simplistic volume loss term, and n<strong>on</strong>e have examined necrotic cell calcificati<strong>on</strong>.<br />

We present a mechanistic, agent-based model <str<strong>on</strong>g>of</str<strong>on</strong>g> solid-type DCIS wi<str<strong>on</strong>g>th</str<strong>on</strong>g> comed<strong>on</strong>ecrosis<br />

and calcificati<strong>on</strong> [1]. Each agent has a lattice-free positi<strong>on</strong> and phenotypic<br />

state. Cells move under <str<strong>on</strong>g>th</str<strong>on</strong>g>e balance <str<strong>on</strong>g>of</str<strong>on</strong>g> biomechanical forces <str<strong>on</strong>g>th</str<strong>on</strong>g>at are exchanged<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er cells and <str<strong>on</strong>g>th</str<strong>on</strong>g>e basement membrane. Each phenotypic state has<br />

a “submodel” <str<strong>on</strong>g>of</str<strong>on</strong>g> changes in cell volume and compositi<strong>on</strong>. Necrotic cells swell, lyse,<br />

and leak cytoplasmic fluid. Their nuclei degrade (pyknosis), and microcalcificati<strong>on</strong>s<br />

form in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir cytoplasm and deteriorate over l<strong>on</strong>g time scales [2]. Phenotypic transiti<strong>on</strong>s<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e quiescent state are regulated by proteomic- and microenvir<strong>on</strong>mentdependent<br />

stochastic processes. The model is fully calibrated to patient data [3].<br />

The model predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>at fast necrotic cell swelling and lysis account for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

mechanical separati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e viable rim and necrotic core seen in histopa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology—<br />

a feature <str<strong>on</strong>g>of</str<strong>on</strong>g>ten assumed to be an artifact <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue preparati<strong>on</strong>. Necrotic cell lysis is<br />

a major source <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanical relaxati<strong>on</strong>, directing proliferative cell flux towards <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

duct centre, ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e duct. Due to <str<strong>on</strong>g>th</str<strong>on</strong>g>is necrotic “flux absorbing” effect,<br />

DCIS grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is linear, and grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is slower in larger ducts, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a minimum grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

rate <str<strong>on</strong>g>of</str<strong>on</strong>g> 7.5 mm/year—in excellent agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mammography [4]. These results<br />

illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>at well-calibrated, mechanistic cell modelling can provide quantitative<br />

insight <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e biophysical phenomena <str<strong>on</strong>g>th</str<strong>on</strong>g>at drive cancer progressi<strong>on</strong>.<br />

References.<br />

[1] P. Macklin et al., Patient-calibrated agent-based modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> ductal carcinoma in situ (DCIS)<br />

I: Model formulati<strong>on</strong> and analysis, J. Theor. Biol. (2011, in review)<br />

[2] P. Macklin et al., An improved model <str<strong>on</strong>g>of</str<strong>on</strong>g> necrosis and calcificati<strong>on</strong>: quantitative comparis<strong>on</strong><br />

against ductal carcinoma in situ (DCIS) histopa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology and radiology, (2011, in preparati<strong>on</strong>)<br />

611

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[3] P. Macklin et al., Patient-calibrated agent-based modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> ductal carcinoma in situ (DCIS)<br />

II: From microscopic measurements to macroscopic predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> clinical progressi<strong>on</strong>, J.<br />

Theor. Biol. (2011, in review)<br />

[4] J.Z. Thoms<strong>on</strong> et al., Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> ductal carcinoma in situ (DCIS): a retrospective<br />

analysis based <strong>on</strong> mammographic findings, Br. J. Canc., 85 225–7 (2001)<br />

612

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Developmental Biology; Wednesday, June 29, 17:00<br />

Anotida Madzvamuse<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sussex, Bright<strong>on</strong>, BN1 9QH,<br />

UK<br />

e-mail: a.madzvamuse@sussex.ac.uk<br />

Raquel Barreira<br />

Escola Superior de Tecnologia do Barreiro/IPS, Rua Américo da Silva<br />

Marinho-Lavradio, 2839-001 Barreiro, Portugal<br />

e-mail: raquel.barreira@estbarreiro.ips.pt<br />

Charlie M. Elliott<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Institute and Centre for Scientific Computing, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Warwick, Coventry CV4 7AL, UK<br />

e-mail: C.M.Elliott@warwick.ac.uk<br />

The evolving surface finite element me<str<strong>on</strong>g>th</str<strong>on</strong>g>od (ESFEM) for<br />

pattern formati<strong>on</strong> <strong>on</strong> evolving biological surfaces<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we propose models and a numerical me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for pattern formati<strong>on</strong> <strong>on</strong><br />

evolving curved surfaces. We formulate reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong>s [4] <strong>on</strong> evolving<br />

surfaces using <str<strong>on</strong>g>th</str<strong>on</strong>g>e material transport formula, surface gradients and diffusive<br />

c<strong>on</strong>servati<strong>on</strong> laws [1]. The evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e surface is defined by a material surface<br />

velocity. The numerical me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evolving surface finite element<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>od (ESFEM) [2, 3]. The key idea is based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e approximati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Γ by a<br />

triangulated surface Γh c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> a uni<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> triangles wi<str<strong>on</strong>g>th</str<strong>on</strong>g> vertices <strong>on</strong> Γ. A<br />

finite element space <str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong>s is <str<strong>on</strong>g>th</str<strong>on</strong>g>en defined by taking <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tinuous functi<strong>on</strong>s<br />

<strong>on</strong> Γh which are linear affine <strong>on</strong> each simplex <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e polyg<strong>on</strong>al surface. To dem<strong>on</strong>strate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e capability, flexibility, versatility and generality <str<strong>on</strong>g>of</str<strong>on</strong>g> our me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology we<br />

present results for uniform isotropic grow<str<strong>on</strong>g>th</str<strong>on</strong>g> as well as anisotropic grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong><br />

surfaces and grow<str<strong>on</strong>g>th</str<strong>on</strong>g> coupled to <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong>-diffusi<strong>on</strong> system.<br />

The surface finite element me<str<strong>on</strong>g>th</str<strong>on</strong>g>od provides a robust numerical me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for solving<br />

partial differential systems <strong>on</strong> c<strong>on</strong>tinuously evolving domains and surfaces wi<str<strong>on</strong>g>th</str<strong>on</strong>g> numerous<br />

applicati<strong>on</strong>s in developmental biology, tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and cell movement<br />

and deformati<strong>on</strong>.<br />

References.<br />

[1] Barreira, R. Elliott, C.M. & Madzvamuse, A. (2011). The surface finite element me<str<strong>on</strong>g>th</str<strong>on</strong>g>od<br />

(SFEM) for pattern formati<strong>on</strong> <strong>on</strong> evolving biological surfaces. J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol., in press.<br />

[2] Dziuk, G. and Elliott, C.M. (2007) Finite elements <strong>on</strong> evolving surfaces. IMA J. Num. Anal.,<br />

27, 262-292.<br />

[3] Dziuk, G. and Elliott, C.M. (2007) Surface finite elements for parabolic equati<strong>on</strong>s. J. Comp.<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>., 25, 430-439.<br />

[4] Madzvamuse, A. Maini, P. K. and Wa<str<strong>on</strong>g>th</str<strong>on</strong>g>en, A. J. (2003). A moving grid finite element me<str<strong>on</strong>g>th</str<strong>on</strong>g>od<br />

applied to a model biological pattern generator. J. Comp. Phys. 190, 478-500.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Carsten Magnus<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Integrative Biology, ETH Zürich, Switzerland<br />

e-mail: carsten.magnus@env.e<str<strong>on</strong>g>th</str<strong>on</strong>g>z.ch<br />

Roland R. Regoes<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Integrative Biology, ETH Zürich, Switzerland<br />

e-mail: roland.regoes@env.e<str<strong>on</strong>g>th</str<strong>on</strong>g>z.ch<br />

Restricted Occupancy Models for Human Immunodeficiency<br />

Virus Neutralizati<strong>on</strong> by Antibodies<br />

Viruses are not able to replicate by <str<strong>on</strong>g>th</str<strong>on</strong>g>emselves. They need a host cell, which <str<strong>on</strong>g>th</str<strong>on</strong>g>ey<br />

manipulate to produce <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring according to <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic code <str<strong>on</strong>g>th</str<strong>on</strong>g>ey provide. To <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

end, <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus has to enter <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. The Human Immunodeficiency Virus (HIV) has<br />

spikes <strong>on</strong> its surface <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>sist <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree identical envelope proteins. These spikes<br />

attach to target cell receptors and induce <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell.<br />

To prevent <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune system elicits antibodies <str<strong>on</strong>g>th</str<strong>on</strong>g>at bind to specific<br />

structures <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e envelope proteins. If <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> spikes necessary for infecti<strong>on</strong><br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> antibodies binding to <strong>on</strong>e spike such <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e spike is rendered<br />

n<strong>on</strong>-functi<strong>on</strong>al are known, <strong>on</strong>e can estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> antibodies needed to<br />

neutralize <strong>on</strong>e viri<strong>on</strong> or a populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> viri<strong>on</strong>s.<br />

However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> spikes <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e viri<strong>on</strong>’s surface vary from viri<strong>on</strong> to viri<strong>on</strong> and<br />

antibodies can bind randomly to <str<strong>on</strong>g>th</str<strong>on</strong>g>e envelope proteins <str<strong>on</strong>g>of</str<strong>on</strong>g> different spikes. These<br />

effects make it impossible to directly determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> neutralizing antibodies.<br />

We present ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>th</str<strong>on</strong>g>at incorporate <str<strong>on</strong>g>th</str<strong>on</strong>g>ese random effects<br />

and allow to derive lower and upper bounds for <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> antibodies <str<strong>on</strong>g>th</str<strong>on</strong>g>at have<br />

to bind to neutralize a viri<strong>on</strong> or a viri<strong>on</strong> populati<strong>on</strong>. In additi<strong>on</strong>, by using restricted<br />

occupancy <str<strong>on</strong>g>th</str<strong>on</strong>g>eory, we are able to calculate <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean number <str<strong>on</strong>g>of</str<strong>on</strong>g> antibodies<br />

neutralizing <strong>on</strong>e viri<strong>on</strong> and a populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> viri<strong>on</strong>s.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Tuesday, June 28, 14:30<br />

, Mohammed Shuker<br />

Mohammed Shuker Mahmood<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Mechanical Engineering Faculty,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Žilina, 010 26 Žilina, Slovakia<br />

e-mail: mahmoodm@fstroj.uniza.sk<br />

Silvia Mahmood<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Biochemistry, Jessenius Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine, Comenius<br />

University, 037 54 Martin, Slovakia<br />

e-mail: mahmood@jfmed.uniba.sk<br />

Dušan Dobrota<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Biochemistry, Jessenius Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine, Comenius<br />

University, 037 54 Martin, Slovakia<br />

e-mail: dobrota@jfmed.uniba.sk<br />

Numerical simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>tinuum model for avascular<br />

tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Avascular grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is a benign stage <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer. Multicellular spheroids serve as<br />

powerful 3D experimental model system for <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is early stage <str<strong>on</strong>g>of</str<strong>on</strong>g> solid<br />

tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. We present results obtained from using a c<strong>on</strong>tinuum model <str<strong>on</strong>g>th</str<strong>on</strong>g>at we<br />

previously developed (Mahmood et al., 2010, 2011). The <str<strong>on</strong>g>th</str<strong>on</strong>g>ree cell types c<strong>on</strong>sidered<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model are: <str<strong>on</strong>g>th</str<strong>on</strong>g>e proliferating cells, able to grow and divide at intervals<br />

dependent up<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir size, envir<strong>on</strong>ment and regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell cycle; <str<strong>on</strong>g>th</str<strong>on</strong>g>e quiescent<br />

n<strong>on</strong>-dividing cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at may return to <str<strong>on</strong>g>th</str<strong>on</strong>g>e proliferative part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cycle ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er by<br />

an increase in nutrient c<strong>on</strong>centrati<strong>on</strong> or in resp<strong>on</strong>se to external stimuli such as<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factor; dead cells due to apoptosis or necrosis. We assume a different motile<br />

resp<strong>on</strong>se kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proliferating and quiescent cells to <str<strong>on</strong>g>th</str<strong>on</strong>g>e available nutrient<br />

gradient. Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model includes viable cell diffusi<strong>on</strong>, diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular<br />

material, viability inhibitor c<strong>on</strong>tributing to <str<strong>on</strong>g>th</str<strong>on</strong>g>e expansi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> necrotic centre and<br />

process <str<strong>on</strong>g>of</str<strong>on</strong>g> removal <str<strong>on</strong>g>of</str<strong>on</strong>g> dead cell. This means <str<strong>on</strong>g>th</str<strong>on</strong>g>at our model is a system <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> parabolic and hyperbolic types. The numerical simulati<strong>on</strong>s are performed using<br />

different sets <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters, including biologically realistic <strong>on</strong>es, to explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

effects <str<strong>on</strong>g>of</str<strong>on</strong>g> each <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese model parameters <strong>on</strong> reaching <str<strong>on</strong>g>th</str<strong>on</strong>g>e steady state reflecting<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> saturati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> viable cells, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e spheroid size.<br />

Acknowledgement: This work was supported by project "CENTER OF EXCEL-<br />

LENCY FOR RESEARCH IN PERSONALIZED THERAPY (CEVYPET)", code:<br />

26- 220120053, co-financed from EU sources and <str<strong>on</strong>g>European</str<strong>on</strong>g> Regi<strong>on</strong>al Development<br />

Fund and by project "CENTER OF TRANSLATIONAL MEDICINE" co-financed<br />

from EC sources and <str<strong>on</strong>g>European</str<strong>on</strong>g> Regi<strong>on</strong>al Development Fund, by Ministry <str<strong>on</strong>g>of</str<strong>on</strong>g> Heal<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Slovak Republic 2007/57-UK-17.<br />

References.<br />

[1] Mahmood, M. S., Mahmood, S., Dobrota, D., A numerical algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m for avascular tumour<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> model. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computers in Simulati<strong>on</strong>, Vol. 80 (6),(2010), pp. 1269-1277.<br />

[2] Mahmood, M. S., Mahmood, S., Dobrota, D., Formulati<strong>on</strong> and numerical simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

c<strong>on</strong>tinuum model <str<strong>on</strong>g>of</str<strong>on</strong>g> avascular tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. Accepted in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Bioscience.<br />

615

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ludovic Mailleret<br />

INRA, Sophia Antipolis, France<br />

e-mail: ludovic.mailleret@sophia.inra.fr<br />

Magda Castel<br />

INRA, Agrocampus Ouest, Rennes, France<br />

e-mail: castel@agrocampus-ouest.fr<br />

Frédéric Hamelin<br />

INRA, Agrocampus Ouest, Rennes, France<br />

e-mail: Frederic.hamelin@agrocampus-ouest.fr<br />

Epidemics; Tuesday, June 28, 11:00<br />

From elaborate to compact seas<strong>on</strong>al plant epidemic models<br />

Seas<strong>on</strong>ality, or periodic host absence, is a central feature in Plant Epidemiology.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is respect, seas<strong>on</strong>al plant epidemic models take into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e way <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

parasite overwinters and generate new infecti<strong>on</strong>s. The former are termed primary<br />

infecti<strong>on</strong>s while <str<strong>on</strong>g>th</str<strong>on</strong>g>e latter are sec<strong>on</strong>dary infecti<strong>on</strong>s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature, <strong>on</strong>e finds two<br />

classes <str<strong>on</strong>g>of</str<strong>on</strong>g> models: elaborate models, where primary infecti<strong>on</strong> dynamics are explicit<br />

[1, 2], and lower-dimensi<strong>on</strong>al, compact, models, where primary infecti<strong>on</strong> dynamics<br />

are implicit [3, 4]. The way compact models may derive from elaborate models has<br />

not been made explicit yet.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>tributi<strong>on</strong>, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at approximating primary infecti<strong>on</strong> dynamics<br />

as a fast process compared to sec<strong>on</strong>dary infecti<strong>on</strong>s in two elaborate models translate<br />

into two compact forms. Yet, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese are less linear <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e compact models<br />

usually found in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature. It is <strong>on</strong>ly in some particular instances <str<strong>on</strong>g>th</str<strong>on</strong>g>at we find<br />

back <str<strong>on</strong>g>th</str<strong>on</strong>g>e latter models. In particular, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at density dependence in primary<br />

infecti<strong>on</strong> dynamics has a pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ound influence <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e compact form. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

models seems to produce fairly similar dynamics, we highlight <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a structural<br />

difference between <str<strong>on</strong>g>th</str<strong>on</strong>g>e two wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>e co-existence, or competitive<br />

exclusi<strong>on</strong>, <str<strong>on</strong>g>of</str<strong>on</strong>g> different parasite strains.<br />

References.<br />

[1] Truscott JE, Webb CR, Gilligan CA (1997) Asymptotic analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic model wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

primary and sec<strong>on</strong>dary infecti<strong>on</strong>. Bulletin <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology 59(6):1101–1123.<br />

[2] Madden LV, van den Bosch F (2002) A populati<strong>on</strong>-dynamics approach to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reat <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

plant pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens as biological weap<strong>on</strong>s against annual crops. BioScience 52(1):65–74.<br />

[3] Madden LV, van den Bosch F (2007) The study <str<strong>on</strong>g>of</str<strong>on</strong>g> plant diseases epidemics. A.P.S. Press,<br />

Saint Paul.<br />

[4] van den Berg F, Bacaer N, Metz JAJ, Lannou C, van den Bosch F (2011) Periodic host<br />

absence can select for bo<str<strong>on</strong>g>th</str<strong>on</strong>g> higher or lower parasite transmissi<strong>on</strong> rates. Evoluti<strong>on</strong>ary Ecology.<br />

25(1):121-137.<br />

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective phenomena in biological systems; Saturday, July 2,<br />

08:30<br />

Danuta Makowiec<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Physics and Astrophysics<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Gdańsk, Gdańsk, Poland<br />

e-mail: fizdm@univ.gda.pl<br />

Discrete modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sinoatrial node automaticity<br />

Each heart cell — myocyte, communicates wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e outside world by rapid changes<br />

displayed by i<strong>on</strong> channels. The membrane activity is tranduced directly to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

neighboring cells establishing cell-to-cell communicati<strong>on</strong>. Because <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cell-tocell<br />

c<strong>on</strong>necti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart tissue is perfectly suited for modeling as a network <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

interacting units. Differences in intercellular c<strong>on</strong>necti<strong>on</strong>s are known to be crucial<br />

in forming physiologically different parts <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart tissue.<br />

The rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>mic c<strong>on</strong>tracti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart begin in <str<strong>on</strong>g>th</str<strong>on</strong>g>e area <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiac tissue<br />

located <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e right atrium called <str<strong>on</strong>g>th</str<strong>on</strong>g>e sinoatrial node (SAN), see [1] for descripti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> SAN physiology. Understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e SAN means to known how pacemaker<br />

cells maintain <str<strong>on</strong>g>th</str<strong>on</strong>g>e final functi<strong>on</strong>, namely, successful pacemaking <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole heart.<br />

Much difficulty in understanding is related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e arrangement <str<strong>on</strong>g>of</str<strong>on</strong>g> cells — how<br />

ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er poorly c<strong>on</strong>nected cells can produce a signal self-c<strong>on</strong>sistent enough to drive<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e heart c<strong>on</strong>tracti<strong>on</strong>. There are two basic approaches to <str<strong>on</strong>g>th</str<strong>on</strong>g>e organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

SAN cells: <str<strong>on</strong>g>th</str<strong>on</strong>g>e mosaic and gradient models. The first <strong>on</strong>e c<strong>on</strong>siders coexistence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> two types <str<strong>on</strong>g>of</str<strong>on</strong>g> cells: nodal and atrial. The sec<strong>on</strong>d approach assumes <str<strong>on</strong>g>th</str<strong>on</strong>g>e gradual<br />

change <str<strong>on</strong>g>of</str<strong>on</strong>g> properties <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals cells when moving from <str<strong>on</strong>g>th</str<strong>on</strong>g>e central part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

SAN to its border. The main objective <str<strong>on</strong>g>of</str<strong>on</strong>g> our presentati<strong>on</strong> is to find whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

SAN automaticity can result from heterogeneity <str<strong>on</strong>g>of</str<strong>on</strong>g> intercellular links.<br />

The complex cellular processes involved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e SAN functi<strong>on</strong>ing are modeled<br />

by modified Greenberg-Hastings cellular automat<strong>on</strong> [2]. Since, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a c<strong>on</strong>sensus<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at SAN cells are remains <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart tissue from its very early stage <str<strong>on</strong>g>of</str<strong>on</strong>g> development,<br />

namely from <str<strong>on</strong>g>th</str<strong>on</strong>g>e embryo, <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> intercellular c<strong>on</strong>necti<strong>on</strong>s<br />

rooted <strong>on</strong> stochastical square lattice is physiologically justified. Synchr<strong>on</strong>ic activati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e large parts <str<strong>on</strong>g>of</str<strong>on</strong>g> such network denotes adjusting <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular excitati<strong>on</strong>s into<br />

a robust spiral wave [3].<br />

Effects <str<strong>on</strong>g>of</str<strong>on</strong>g> perturbati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e topology <str<strong>on</strong>g>of</str<strong>on</strong>g> intercellular c<strong>on</strong>necti<strong>on</strong>s <strong>on</strong> periodicity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system are c<strong>on</strong>sidered. The focus is how <str<strong>on</strong>g>th</str<strong>on</strong>g>orough wrinkling <str<strong>on</strong>g>of</str<strong>on</strong>g> initially flat<br />

structure influences <str<strong>on</strong>g>th</str<strong>on</strong>g>e regular beating. Since automaticity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sinoatrial node<br />

relies <strong>on</strong> a single cell activity, cyclical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> individual cells are studied. It<br />

appears <str<strong>on</strong>g>th</str<strong>on</strong>g>at robust diversity <str<strong>on</strong>g>of</str<strong>on</strong>g> oscillati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> a cell depends <strong>on</strong> bo<str<strong>on</strong>g>th</str<strong>on</strong>g>: properties <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

intrinsic cellular dynamics and <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying topology <str<strong>on</strong>g>of</str<strong>on</strong>g> intercellular c<strong>on</strong>necti<strong>on</strong>s.<br />

Moderate n<strong>on</strong>uniformity <str<strong>on</strong>g>of</str<strong>on</strong>g> intercellular c<strong>on</strong>necti<strong>on</strong>s are found vital for <str<strong>on</strong>g>th</str<strong>on</strong>g>e proper<br />

functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sinoatrial node, namely, to resp<strong>on</strong>d effectively to <str<strong>on</strong>g>th</str<strong>on</strong>g>e aut<strong>on</strong>omic<br />

system c<strong>on</strong>trol [4].<br />

References.<br />

[1] M. E. Mang<strong>on</strong>i, and J. Nargeot, Genesis and Regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Herat Automaticity Physiol.<br />

Rev. 89 919-982.<br />

[2] J. M. Greenberg, and S. P. Hastings, Spatial patterns for discrete models <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong> in<br />

excitable media SIAM J. Appl. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. 34 515–523.<br />

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[3] G. Bub, A. Shrier, and L. Glass, Global Organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Dynamics in Oscillatory Heterogeneous<br />

Excitable Media. Phys. Rev. Lett. 94 028105-1 – 028105-4.<br />

[4] D. Makowiec, Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> intercellular c<strong>on</strong>necti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e sinoatrial node Acta Physica Pol<strong>on</strong>ica<br />

B Proceedings Supplement 3 377–390.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Heart rate dynamics: models and measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity (part I);<br />

Wednesday, June 29, 14:30<br />

Danuta Makowiec<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Physics and Astrophysics<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Gdańsk, Gdańsk, Poland<br />

e-mail: fizdm@univ.gda.pl<br />

A. Rynkiewicz<br />

J. Wdowczyk-Szulc<br />

M. Żarczyńska-Buchowiecka<br />

First Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Cardiology, Medical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Gdańsk<br />

Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y aging by multifractal analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> heart interbeat<br />

intervals<br />

Heart rate resp<strong>on</strong>ds dynamically to various intrinsic and envir<strong>on</strong>mental stimuli. The<br />

resp<strong>on</strong>se is supposed to be mediated by aut<strong>on</strong>omic nervous system. Multifractal<br />

analysis <str<strong>on</strong>g>of</str<strong>on</strong>g>fers a novel me<str<strong>on</strong>g>th</str<strong>on</strong>g>od to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>is resp<strong>on</strong>se. Fractal properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

power spectra in VLF (and ultra-low-frequency (ULF: ≤ 0.0033Hz)) have being<br />

analyzed for more <str<strong>on</strong>g>th</str<strong>on</strong>g>an 20 years and <str<strong>on</strong>g>th</str<strong>on</strong>g>ey were found to have prognostic significance<br />

in cardiac patients [1] <str<strong>on</strong>g>th</str<strong>on</strong>g>ough also <str<strong>on</strong>g>th</str<strong>on</strong>g>ey were questi<strong>on</strong>ed when <str<strong>on</strong>g>th</str<strong>on</strong>g>ey were used for an<br />

individual [2]. Therefore <str<strong>on</strong>g>th</str<strong>on</strong>g>e reliability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e approach has to be carefully validated.<br />

The me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g> effective reading <str<strong>on</strong>g>of</str<strong>on</strong>g> multifractal properties will be described.<br />

The me<str<strong>on</strong>g>th</str<strong>on</strong>g>od c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> two way analysis pertaining each signal. In parallel, a<br />

given signal analysis and integrated signal analysis are performed. Differences between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e multifractal spectra received from <str<strong>on</strong>g>th</str<strong>on</strong>g>e same signal are found important<br />

in discriminating m<strong>on</strong><str<strong>on</strong>g>of</str<strong>on</strong>g>ractality from multifractality.<br />

The me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is used in study 24-hour ECG recordings <str<strong>on</strong>g>of</str<strong>on</strong>g> RR interbeat intervals<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> 48 elderly volunteers, 40 middle-aged pers<strong>on</strong>s and 36 young adults in order to<br />

assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> aging <strong>on</strong> aut<strong>on</strong>omic regulati<strong>on</strong> during normal activity in heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y<br />

adults. The variability <str<strong>on</strong>g>of</str<strong>on</strong>g> heart interbeat intervals was evaluated in <str<strong>on</strong>g>th</str<strong>on</strong>g>e VLF band<br />

(32-420 RR intervals) to preserve links to standard measures <str<strong>on</strong>g>of</str<strong>on</strong>g> heart rate variability<br />

[1]. The nocturnal and diurnal multifractality was c<strong>on</strong>sidered separately.<br />

The switch from multi- to m<strong>on</strong><str<strong>on</strong>g>of</str<strong>on</strong>g>ractality is observed between diurnal and nocturnal<br />

series in <str<strong>on</strong>g>th</str<strong>on</strong>g>e group <str<strong>on</strong>g>of</str<strong>on</strong>g> young adults. That change can be directly related<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e circadian alternati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e central mechanisms c<strong>on</strong>trolling <str<strong>on</strong>g>th</str<strong>on</strong>g>e temporal<br />

organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cardiovascular system — nocturnal dominance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vagal t<strong>on</strong>e<br />

versus sympa<str<strong>on</strong>g>th</str<strong>on</strong>g>etic main drive during daily activities. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> aging <str<strong>on</strong>g>th</str<strong>on</strong>g>e multifractal<br />

structure <str<strong>on</strong>g>of</str<strong>on</strong>g> nocturnal signals declines. Our observati<strong>on</strong>s are c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> [3]<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at imbalance in <str<strong>on</strong>g>th</str<strong>on</strong>g>e aut<strong>on</strong>omic c<strong>on</strong>trol due to heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y aging should be related<br />

to changes <str<strong>on</strong>g>th</str<strong>on</strong>g>at are emerging from <str<strong>on</strong>g>th</str<strong>on</strong>g>e vagal t<strong>on</strong>e, what in c<strong>on</strong>sequence results in<br />

increasing activity <str<strong>on</strong>g>of</str<strong>on</strong>g> sympa<str<strong>on</strong>g>th</str<strong>on</strong>g>etic modulati<strong>on</strong>.<br />

References.<br />

[1] Tan C O, Cohen M A, Eckberg D L and Taylor J A, Fractal properties <str<strong>on</strong>g>of</str<strong>on</strong>g> human heart period<br />

variability: physiological and me<str<strong>on</strong>g>th</str<strong>on</strong>g>odological implicati<strong>on</strong>s J. Physiol. 587 3929<br />

[2] Task Force <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>European</str<strong>on</strong>g> Society <str<strong>on</strong>g>of</str<strong>on</strong>g> Cardiology <str<strong>on</strong>g>th</str<strong>on</strong>g>e Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> American Society <str<strong>on</strong>g>of</str<strong>on</strong>g> Pacing<br />

and Electrophysiology 1996 Heart rate variability. Standards <str<strong>on</strong>g>of</str<strong>on</strong>g> measurement, physiological<br />

interpretati<strong>on</strong>, and clinical use Eur. Heart J. 17 354–81<br />

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[3] Struzik Z R, Hayano J, Soma R, Kwak S and Yamamoto Y Aging <str<strong>on</strong>g>of</str<strong>on</strong>g> complex heart rate<br />

dynamics IEEE Transacti<strong>on</strong>s <strong>on</strong> Biomededical Engineering 53 89<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Adam Makuchowski<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: adam.makuchowski@polsl.pl<br />

mgr Adam Makuchowski<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

dr inż. Pokrzywa Rafał<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. dr hab. inż. Polaski Andrzej<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Cellular Systems Biology; Tuesday, June 28, 17:00<br />

Discovering motifs in DNA sequences<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e important aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular biology is to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex<br />

mechanisms regulating a gene expressi<strong>on</strong>. One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e steps in <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> exploring<br />

regulatory mechanisms is discovering regulatory motifs <str<strong>on</strong>g>th</str<strong>on</strong>g>at influence gene<br />

expressi<strong>on</strong>. Gene expressi<strong>on</strong> is transformed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong> factors<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir corresp<strong>on</strong>ding binding sites. The purpose <str<strong>on</strong>g>of</str<strong>on</strong>g> presented algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m is<br />

to detect <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>servative motifs in DNA sequences, in order to identify regulatory<br />

sites.<br />

New algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m is presented in <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows discovery <str<strong>on</strong>g>of</str<strong>on</strong>g> new motifs<br />

in a set <str<strong>on</strong>g>of</str<strong>on</strong>g> related regulatory DNA sequences and also in genome-wide search. This<br />

algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m uses a heuristic approach based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure <str<strong>on</strong>g>of</str<strong>on</strong>g> suffix trie. For representati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> motif sequences, we used a positi<strong>on</strong> specific scoring matrices (PSSMs),<br />

which are widely used for <str<strong>on</strong>g>th</str<strong>on</strong>g>is purpose. In additi<strong>on</strong>, two approaches have been<br />

examined: c<strong>on</strong>sidering prior residue probability <str<strong>on</strong>g>of</str<strong>on</strong>g> background, and omitting real<br />

value probability. Taking into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e actual likelihood <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e background during<br />

discovering <str<strong>on</strong>g>of</str<strong>on</strong>g> motifs, improves <str<strong>on</strong>g>th</str<strong>on</strong>g>e quality <str<strong>on</strong>g>of</str<strong>on</strong>g> found motifs. Proposed algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m<br />

was tested <strong>on</strong> reference genomes <str<strong>on</strong>g>of</str<strong>on</strong>g> human and mouse. The results obtained from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m were compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er known algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms. The comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms are performed based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e following comparis<strong>on</strong> measurements:<br />

nucleotide Performance Coefficien, Site Sensitivit, Site Positive Predicti<strong>on</strong>, and Site<br />

Average Performance. From experiments <strong>on</strong> real biological data sets, we observed<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e applicati<strong>on</strong>s such as genome-wide search can be identified, in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m behaves better <str<strong>on</strong>g>th</str<strong>on</strong>g>an o<str<strong>on</strong>g>th</str<strong>on</strong>g>er existing tools to search for motifs. But in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

case <str<strong>on</strong>g>of</str<strong>on</strong>g> smaller data sets, average values <str<strong>on</strong>g>of</str<strong>on</strong>g> measurements were comparable to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

existing motif finding tools.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models in Eco-epidemiology II; Wednesday, June 29, 11:00<br />

Horst Malchow<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Envir<strong>on</strong>mental Systems Research<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Osnabrück, 49069 Osnabrück, Germany<br />

e-mail: malchow@uos.de<br />

Infecti<strong>on</strong> and bioc<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> an invading competitor<br />

Biological invasi<strong>on</strong>s including <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases have str<strong>on</strong>g ecological<br />

and ec<strong>on</strong>omical impacts. The percepti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir <str<strong>on</strong>g>of</str<strong>on</strong>g>ten harmful effects has<br />

been c<strong>on</strong>tinuously growing bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in sciences and in <str<strong>on</strong>g>th</str<strong>on</strong>g>e public. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling<br />

is a suitable me<str<strong>on</strong>g>th</str<strong>on</strong>g>od to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> invasi<strong>on</strong>s, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> supplementary<br />

to and initiating field studies as well as c<strong>on</strong>trol measures.<br />

Holling-type II and III predati<strong>on</strong> as well as Lotka-Volterra competiti<strong>on</strong> models wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

possible infecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e prey or <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e competitors are introduced. The interplay<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> local predati<strong>on</strong>, intra- and interspecific competiti<strong>on</strong> as well as infecti<strong>on</strong> and<br />

diffusive spread <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong>s can cause spatial and spatiotemporal pattern<br />

formati<strong>on</strong>. The envir<strong>on</strong>mental noise may have c<strong>on</strong>structive as well as destructive<br />

effects.<br />

A plant competiti<strong>on</strong>-flow model is c<strong>on</strong>sidered for c<strong>on</strong>diti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> invasibility <str<strong>on</strong>g>of</str<strong>on</strong>g> a certain<br />

model area occupied by a native species. Short-distance invasi<strong>on</strong> is assumed as<br />

diffusi<strong>on</strong> whereas l<strong>on</strong>g-distance seed dispersal can be stratified diffusive or advective.<br />

The variability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment due to c<strong>on</strong>tingent landslides and artificial<br />

causes such as deforestati<strong>on</strong> or weed c<strong>on</strong>trol leads to <str<strong>on</strong>g>th</str<strong>on</strong>g>e temporary extincti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<strong>on</strong>e or bo<str<strong>on</strong>g>th</str<strong>on</strong>g> species at a randomly chosen time and spatial range. The spatiotemporal<br />

dimensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese extreme fragmentati<strong>on</strong> events as well as a possible selected<br />

harvesting or infecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e invading weed turn out to be <str<strong>on</strong>g>th</str<strong>on</strong>g>e crucial driving forces<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system dynamics.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biomechanical regulati<strong>on</strong> in b<strong>on</strong>e tissue (Sessi<strong>on</strong><br />

II); Wednesday, June 29, 11:00<br />

Solvey Mald<strong>on</strong>ado<br />

Chair for Systems Theory and Automatic C<strong>on</strong>trol<br />

Institute for Automati<strong>on</strong> Engineering<br />

Otto-V<strong>on</strong>-Guericke-Universität Magdeburg, Magdeburg, Germany<br />

e-mail: solvey.mald<strong>on</strong>ado@ovgu.de<br />

Rolf Findeisen<br />

Chair for Systems Theory and Automatic C<strong>on</strong>trol<br />

Institute for Automati<strong>on</strong> Engineering<br />

Otto-V<strong>on</strong>-Guericke-Universität Magdeburg, Magdeburg, Germany<br />

e-mail: rolf.findeisen@ovgu.de<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling and Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Force-induced B<strong>on</strong>e<br />

Adaptati<strong>on</strong><br />

In biological systems, all living organisms are able to react to <str<strong>on</strong>g>th</str<strong>on</strong>g>e biophysical signals<br />

arising in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir envir<strong>on</strong>ment. To do <str<strong>on</strong>g>th</str<strong>on</strong>g>at, <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>stituent cells are provided<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mechanisms <str<strong>on</strong>g>th</str<strong>on</strong>g>at allow <str<strong>on</strong>g>th</str<strong>on</strong>g>em to perceive biophysical signals and to react accordingly<br />

to accommodate to <str<strong>on</strong>g>th</str<strong>on</strong>g>e demanding envir<strong>on</strong>ment. B<strong>on</strong>e as a biological<br />

system is not exempted from <str<strong>on</strong>g>th</str<strong>on</strong>g>is mechanoresp<strong>on</strong>sive capacity. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e last decades<br />

significant progress has been made from <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental site as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e medical<br />

insights [1], to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects produced by applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanical loading<br />

<strong>on</strong> b<strong>on</strong>e tissue and <strong>on</strong> b<strong>on</strong>e cells. Experimental studies have shown <str<strong>on</strong>g>th</str<strong>on</strong>g>e key role<br />

played by mechanical usage <strong>on</strong> b<strong>on</strong>e tissue adaptati<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e promoti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular<br />

behaviors, like proliferati<strong>on</strong>, differentiati<strong>on</strong>, or apoptosis. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e precise<br />

biological mechanisms behind <str<strong>on</strong>g>th</str<strong>on</strong>g>e organizati<strong>on</strong> and regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e site-specific<br />

b<strong>on</strong>e adaptati<strong>on</strong> process remain poorly understood.<br />

The functi<strong>on</strong>al adaptati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e is <str<strong>on</strong>g>th</str<strong>on</strong>g>e process whereby b<strong>on</strong>e adapts its mass<br />

and structure to wi<str<strong>on</strong>g>th</str<strong>on</strong>g>stand changes in biophysical demands. The process <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e<br />

remodeling is <str<strong>on</strong>g>th</str<strong>on</strong>g>e suitable mechanism used by b<strong>on</strong>e to renew, repair and maintain<br />

b<strong>on</strong>e surfaces al<strong>on</strong>g life. In b<strong>on</strong>e remodeling, two cellular activities are highly<br />

coordinated to achieve <str<strong>on</strong>g>th</str<strong>on</strong>g>e renewal process at a particular site, mainly resorpti<strong>on</strong><br />

and formati<strong>on</strong>. Resorpti<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>e process by which highly specialized cells, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

osteoclasts, destroy b<strong>on</strong>e tissue by creating resorpti<strong>on</strong> pits, and afterwards release<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e matrix c<strong>on</strong>stituents to <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood. C<strong>on</strong>versely, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> process<br />

osteoblast cells syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esize and secrete <str<strong>on</strong>g>th</str<strong>on</strong>g>e osteoid, new unmineralized matrix, and<br />

afterwards organize as well <str<strong>on</strong>g>th</str<strong>on</strong>g>e osteoid mineralizati<strong>on</strong>.<br />

Following <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanostat hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis [2], b<strong>on</strong>e can adapt its shape and structure<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue level mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> modeling and/or remodeling. In b<strong>on</strong>e modeling,<br />

resorpti<strong>on</strong> and formati<strong>on</strong> happen <strong>on</strong> different b<strong>on</strong>e sites, a process <str<strong>on</strong>g>th</str<strong>on</strong>g>at arises<br />

during grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and development. C<strong>on</strong>versely, in b<strong>on</strong>e remodeling, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> cellular activities<br />

occur sequentially at <str<strong>on</strong>g>th</str<strong>on</strong>g>e same b<strong>on</strong>e site, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> resorpti<strong>on</strong> being followed by<br />

formati<strong>on</strong>. In adult skelet<strong>on</strong>, b<strong>on</strong>e remodeling runs in general as a self-maintenance<br />

mechanism used to repair microdamage or fractures, or to streng<str<strong>on</strong>g>th</str<strong>on</strong>g>en a b<strong>on</strong>e surface<br />

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supporting increasing mechanical stress. To organize and regulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e sequencing<br />

events in remodeling, <str<strong>on</strong>g>th</str<strong>on</strong>g>e involved cells act as a multicellular team which evolves<br />

accordingly and is known as <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic multicellular unit or BMU.<br />

To start b<strong>on</strong>e remodeling a b<strong>on</strong>e surface target is activated, maybe due to microdamage<br />

reparati<strong>on</strong> or osteocytes apoptosis. Then, <str<strong>on</strong>g>th</str<strong>on</strong>g>e BMU operati<strong>on</strong> starts by<br />

recruiting osteoclast and osteoblast progenitors to <str<strong>on</strong>g>th</str<strong>on</strong>g>e site to be resorbed. Osteoclast<br />

progenitors differentiate and get fused into multinucleated osteoclasts who are<br />

attracted to <str<strong>on</strong>g>th</str<strong>on</strong>g>e site and start resorpti<strong>on</strong>. In oste<strong>on</strong>al remodeling [3], a fully developed<br />

BMU c<strong>on</strong>tains teams <str<strong>on</strong>g>of</str<strong>on</strong>g> osteoclasts actively resorbing at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cutting c<strong>on</strong>e,<br />

followed by teams <str<strong>on</strong>g>of</str<strong>on</strong>g> osteoblasts producing and depositing layers <str<strong>on</strong>g>of</str<strong>on</strong>g> osteoid at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

closing c<strong>on</strong>e. The coupling am<strong>on</strong>g resorpti<strong>on</strong> and formati<strong>on</strong> may happen during<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e reversal stage coming after resorpti<strong>on</strong>, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e site may be prepared for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

coming formati<strong>on</strong> phase. During b<strong>on</strong>e remodeling tight organizati<strong>on</strong> and regulati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular interacti<strong>on</strong>s are required because sustained imbalances in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

quantity or quality <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e renewed b<strong>on</strong>e can derive in b<strong>on</strong>e disorders compromising<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e biomechanical integrity and performance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e skelet<strong>on</strong>.<br />

The b<strong>on</strong>e cells involved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e remodeling process are osteoclasts, osteoblasts,<br />

lining cells, and osteocytes. Osteoclasts are cells <str<strong>on</strong>g>of</str<strong>on</strong>g> hematopoietic origin resp<strong>on</strong>sible<br />

for b<strong>on</strong>e resorpti<strong>on</strong>, whereas osteoblasts are cells <str<strong>on</strong>g>of</str<strong>on</strong>g> mesenchymal origin <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

produce and deposit <str<strong>on</strong>g>th</str<strong>on</strong>g>e new matrix. Osteoclasts and osteoblasts are cells found,<br />

however, <strong>on</strong>ly temporary <strong>on</strong> b<strong>on</strong>e surfaces. Osteoclasts are found actively resorbing<br />

a surface, while osteoblasts are found actively producing new matrix. Instead,<br />

osteocytes and lining cells are <str<strong>on</strong>g>th</str<strong>on</strong>g>e osteoblastic lineage cells residing in <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e<br />

matrix. Lining cells derive from osteoblasts who have stopped syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esizing osteoid<br />

during b<strong>on</strong>e formati<strong>on</strong> and differentiate to a very flat cell covering <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e surfaces.<br />

Osteocytes are terminally differentiated osteoblasts, which are embedded<br />

into <str<strong>on</strong>g>th</str<strong>on</strong>g>e matrix during <str<strong>on</strong>g>th</str<strong>on</strong>g>e mineralizati<strong>on</strong> process. They live in lacunae <str<strong>on</strong>g>th</str<strong>on</strong>g>at are<br />

small cavities inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e matrix, and extend <str<strong>on</strong>g>th</str<strong>on</strong>g>eir cytoplasmic extensi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>rough<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e canaliculi. Due to <str<strong>on</strong>g>th</str<strong>on</strong>g>ese fingerlike extensi<strong>on</strong>s osteocytes keep in c<strong>on</strong>tact wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>er osteocytes wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e matrix and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er cells <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e surface, <str<strong>on</strong>g>th</str<strong>on</strong>g>us forming<br />

a highly interc<strong>on</strong>nected network <str<strong>on</strong>g>th</str<strong>on</strong>g>at makes <str<strong>on</strong>g>th</str<strong>on</strong>g>em <str<strong>on</strong>g>th</str<strong>on</strong>g>e suitable cells for sensing and<br />

transducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanochemical signals [4].<br />

The understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e remodeling dynamics and <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

b<strong>on</strong>e to mechanical loading is <str<strong>on</strong>g>of</str<strong>on</strong>g> relevant scientific interest due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential<br />

use <str<strong>on</strong>g>of</str<strong>on</strong>g> physical exercise to counteract aging-induced b<strong>on</strong>e loss and to avoid <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

decline <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e mass and streng<str<strong>on</strong>g>th</str<strong>on</strong>g> in c<strong>on</strong>diti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e loss, such as osteoporosis<br />

or immobilizati<strong>on</strong>. Osteoporosis is a worldwide spread b<strong>on</strong>e disorder where b<strong>on</strong>e<br />

streng<str<strong>on</strong>g>th</str<strong>on</strong>g> and mass are highly compromise <str<strong>on</strong>g>th</str<strong>on</strong>g>us increasing <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk <str<strong>on</strong>g>of</str<strong>on</strong>g> fractures.<br />

For instance, postmenopausal osteoporosis has been associated to a failure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

capacity <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e to maintain b<strong>on</strong>e streng<str<strong>on</strong>g>th</str<strong>on</strong>g> when estrogen levels are diminished [5].<br />

In additi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at astr<strong>on</strong>auts lose b<strong>on</strong>e mass during prol<strong>on</strong>ged spaceflights,<br />

or patients in bed rest c<strong>on</strong>diti<strong>on</strong> present osteopenia, show <str<strong>on</strong>g>th</str<strong>on</strong>g>e key role play by ear<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

gravity, locomoti<strong>on</strong> and physical activity <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e body, specially <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e skelet<strong>on</strong><br />

maintenance [1].<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, we employ a systems biology approach to get a better understanding<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> force induced b<strong>on</strong>e adaptati<strong>on</strong>. To achieve <str<strong>on</strong>g>th</str<strong>on</strong>g>is, firstly a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e adapti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e due to mechanical and chemical<br />

stimuli was developed [6,7], and sec<strong>on</strong>dly, system <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are applied<br />

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for <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex interacti<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>e design <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies<br />

for b<strong>on</strong>e disorders [8,9].<br />

The ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical descripti<strong>on</strong> focuses <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e remodeling process as an essential<br />

tissue level mechanism used by adult skelet<strong>on</strong> to maintaining b<strong>on</strong>e streng<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>roughout life. The main operati<strong>on</strong>al stages <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e multicellular unit during<br />

b<strong>on</strong>e remodeling covered are activati<strong>on</strong>, resorpti<strong>on</strong>, and formati<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e model,<br />

osteocytes are introduced as <str<strong>on</strong>g>th</str<strong>on</strong>g>e main mechanotransducers, sensing <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical<br />

loading changes and releasing local factors, e.g. nitric oxide and prostaglandins,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at influence <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s am<strong>on</strong>g osteoclast and osteoblast cell populati<strong>on</strong>s,<br />

mainly regulated <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e RANKL/RANK/OPG signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way.<br />

For a better understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e adaptati<strong>on</strong> process, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e identificati<strong>on</strong>/discriminati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> possible <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic targets for remodeling-related b<strong>on</strong>e<br />

disorders, a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for global sensitivity analysis is applied to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model to explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters/inputs variati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

stati<strong>on</strong>ary behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e cells and tissue adaptati<strong>on</strong>. In additi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods allows to explore for beneficial effects <str<strong>on</strong>g>of</str<strong>on</strong>g> combining mechanical<br />

and n<strong>on</strong>-mechanical agents in <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> particular b<strong>on</strong>e disorders, such as<br />

postmenopausal osteoporosis, or bed rest/immobilizati<strong>on</strong>.<br />

References.<br />

[1] H.M. Frost, The Utah Paradigm <str<strong>on</strong>g>of</str<strong>on</strong>g> Skeletal Physiology, W.S.S. Jee Ed., Greece: Internati<strong>on</strong>al<br />

Society <str<strong>on</strong>g>of</str<strong>on</strong>g> Musculoskeletal and Neur<strong>on</strong>al Interacti<strong>on</strong>s, 2004. Vol. I B<strong>on</strong>e and B<strong>on</strong>es and<br />

Associated Problems.<br />

[2] H. Frost, A 2003 Updated <str<strong>on</strong>g>of</str<strong>on</strong>g> B<strong>on</strong>e Physiology and Wolff’s Law for Clinicians, Angle Or<str<strong>on</strong>g>th</str<strong>on</strong>g>od,<br />

74, 3–15, 2004.<br />

[3] A. Parfitt, Oste<strong>on</strong>al and Hemi-Oste<strong>on</strong>al Remodeling: The Spatial and Temporal Framework<br />

for Signal Traffic in Adult Human B<strong>on</strong>e, Cell Biochem, 55, 273–286, 1994.<br />

[4] E Burger and J Klein-Nulend, Mechanotransducti<strong>on</strong> in b<strong>on</strong>e-role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lacunocanalicular<br />

network, FASEB Journal, 13, 101–112, 1999.<br />

[5] L Lany<strong>on</strong> and T Skerry, Postmenopausal Osteoporosis as a Failure <str<strong>on</strong>g>of</str<strong>on</strong>g> B<strong>on</strong>e’s Adaptati<strong>on</strong> to<br />

Functi<strong>on</strong>al Loading: A Hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis, J B<strong>on</strong>e Miner Res, 16, 1937–1947, 2001.<br />

[6] S. Mald<strong>on</strong>ado, R. Findeisen, and F Allgöwer, Describing Force-induced B<strong>on</strong>e Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and<br />

Adaptati<strong>on</strong> by a Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Model, J Musculoskeletal Neur<strong>on</strong>al Interacti<strong>on</strong>s, 8, 15–17, 2008.<br />

[7] S. Mald<strong>on</strong>ado, R. Findeisen, and F Allgöwer, Phenomenological Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling and<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Force-induced B<strong>on</strong>e Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and Adaptati<strong>on</strong>, In: Proc. 2nd. FOSBE, 147–152,<br />

2007.<br />

[8] S. Mald<strong>on</strong>ado, R. Findeisen, and F Allgöwer, Global Sensitivity Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Force-induced<br />

B<strong>on</strong>e Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and Adaptati<strong>on</strong> using Semidefinite Programming, In: Proc. 3nd. FOSBE, 141–<br />

144, 2009.<br />

[9] S. Mald<strong>on</strong>ado, and R. Findeisen, Force-induced B<strong>on</strong>e Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and Adaptati<strong>on</strong>: A System<br />

Theoretical Approach to Understanding B<strong>on</strong>e Mechanotransducti<strong>on</strong>, IOP C<strong>on</strong>f. Ser.: Mater.<br />

Sci. Eng. 10 012127 2010. doi: 10.1088/1757-899X/10/1/012127.<br />

625

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The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting cell systems: from intercellular interacti<strong>on</strong><br />

to tissue-level traits II; Wednesday, June 29, 17:00<br />

Jens Malmros<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical statistics, Stockholm University<br />

e-mail: jensm@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.su.se<br />

Ola Hössjer<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical statistics, Stockholm University<br />

e-mail: ola@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.su.se<br />

John Lock<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosciences and Nutriti<strong>on</strong>, Karolinska Institutet<br />

e-mail: john.lock@ki.se<br />

Joanna Tyrcha<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical statistics, Stockholm University<br />

e-mail: joanna@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.su.se<br />

Olivia Erikss<strong>on</strong><br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical statistics, Stockholm University<br />

e-mail: olivia@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.su.se<br />

Stochastic modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> cell migrati<strong>on</strong><br />

Cell migrati<strong>on</strong> is a central process in normal human tissue development as well<br />

as in numerous disease states. Metastatic spread <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer tumours occurs as a<br />

direct result <str<strong>on</strong>g>of</str<strong>on</strong>g> changes in cell migrati<strong>on</strong>, and fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms<br />

behind cell migrati<strong>on</strong> is <str<strong>on</strong>g>of</str<strong>on</strong>g> great importance in cancer research. CMACs (cellmatrix<br />

adhesi<strong>on</strong> complexes) are at <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e migratory system <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell;<br />

elucidati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> CMAC behaviour is essential in understanding cell migrati<strong>on</strong> [1] [2].<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, quantitative time-series live cell microscopy data are used toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> existing knowledge to develop a stochastic model describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e CMAC populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e wild-type cell wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to CMAC areas and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> CMACs. New CMACs are born according to a Poiss<strong>on</strong> process and <str<strong>on</strong>g>th</str<strong>on</strong>g>en<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e subsequent multiplicative grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and decline <str<strong>on</strong>g>of</str<strong>on</strong>g> CMAC area and final dea<str<strong>on</strong>g>th</str<strong>on</strong>g> is<br />

described by means <str<strong>on</strong>g>of</str<strong>on</strong>g> a random walk wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a Markov process regime. Analytical<br />

results are derived and simulati<strong>on</strong>s are performed to validate model performance.<br />

It is shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is able to mimic CMAC behaviour wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to most<br />

aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e properties described above, and also is able to predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> new perturbed experimental c<strong>on</strong>diti<strong>on</strong>s.<br />

References.<br />

[1] John G. Lock, Bernhard Wehrle-Haller and Staffan Strömblad, Cell–matrix adhesi<strong>on</strong> complexes:<br />

Master c<strong>on</strong>trol machinery <str<strong>on</strong>g>of</str<strong>on</strong>g> cell migrati<strong>on</strong> Seminars in Cancer Biology, Volume 18,<br />

Issue 1, February 2008, Pages 65-76.<br />

[2] John G. Lock and Staffan Strömblad, Systems microscopy: An emerging strategy for <str<strong>on</strong>g>th</str<strong>on</strong>g>e life<br />

sciences Experimental Cell Research, Volume 316, Issue 8, 1 May 2010, Pages 1438-1444.<br />

626

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Marcin Małogrosz<br />

Uniwersytet Warszawski<br />

e-mail: malogrosz@mimuw.edu.pl<br />

Models <str<strong>on</strong>g>of</str<strong>on</strong>g> morphogen transport<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Transport <str<strong>on</strong>g>of</str<strong>on</strong>g> morphogens is a process occurring in <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue, affecting cell differentiati<strong>on</strong>.<br />

In [?] au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors proposed several ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models (systems <str<strong>on</strong>g>of</str<strong>on</strong>g> PDEs<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong>-diffusi<strong>on</strong> type) <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is process. In [?] a detailed analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> two <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ose<br />

models was made in 1D setting. I will present my recent results c<strong>on</strong>cerning global<br />

in time existence and asymptotic behavior for <str<strong>on</strong>g>th</str<strong>on</strong>g>e 3D setting.<br />

References.<br />

[1] Lander, A. D., Nie, Q., Wan, Y. M. Do Morphogen Gradients Arise by Diffusi<strong>on</strong>? Dev. Cell,<br />

Vol. 2, pp. 785-796.<br />

[2] Krzyżanowski, P., Laurençot, P., Wrzosek, D. Well-posedness and c<strong>on</strong>vergence to <str<strong>on</strong>g>th</str<strong>on</strong>g>e steady<br />

state for a model <str<strong>on</strong>g>of</str<strong>on</strong>g> morphogen transport, SIAM J.MATH. ANAL. Vol. 40, No. 5, pp. 1725-<br />

1749.<br />

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Informati<strong>on</strong>, human behaviour and infecti<strong>on</strong> c<strong>on</strong>trol; Saturday, July 2, 08:30<br />

Piero Manfredi<br />

Dipartimento di Statistica e Matematica Applicata all’Ec<strong>on</strong>omia, Università<br />

di Pisa, Via Ridolfi 10, Pisa, 56124, Italy<br />

e-mail: manfredi@ec.unipi.it<br />

The impact <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccinating behaviour <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e natural history<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> immunizati<strong>on</strong> programmes.<br />

Recent <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical studies have provided increasing evidence <str<strong>on</strong>g>th</str<strong>on</strong>g>at human behaviour<br />

can play a critical role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e achievement <str<strong>on</strong>g>of</str<strong>on</strong>g> public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> targets, such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e mitigati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a pandemic influenza outbreak or <str<strong>on</strong>g>th</str<strong>on</strong>g>e success <str<strong>on</strong>g>of</str<strong>on</strong>g> a vaccinati<strong>on</strong> programme<br />

for a childhood infecti<strong>on</strong>. As for <str<strong>on</strong>g>th</str<strong>on</strong>g>e area <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccine preventable infecti<strong>on</strong>s, much <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e recent research has focused <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> immunizati<strong>on</strong> choices - modelled as<br />

an evoluti<strong>on</strong>ary game wi<str<strong>on</strong>g>th</str<strong>on</strong>g> imitati<strong>on</strong> dynamics - <strong>on</strong> voluntary vaccinati<strong>on</strong> regimes,<br />

particularly <str<strong>on</strong>g>th</str<strong>on</strong>g>e issue <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccinati<strong>on</strong> free-riding. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper we first use a simple<br />

transmissi<strong>on</strong> model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> vaccinati<strong>on</strong> pay<str<strong>on</strong>g>of</str<strong>on</strong>g>f modelled as an increasing functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e incidence <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccine side effects, to interpret historical trends in serious morbidity<br />

and mortality from various childhood infecti<strong>on</strong>s. This allows us to clearly show<br />

which are <str<strong>on</strong>g>th</str<strong>on</strong>g>e major killers <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccinati<strong>on</strong> programmes in industrialised countries.<br />

These seem mainly to be <str<strong>on</strong>g>th</str<strong>on</strong>g>e technological progress and <str<strong>on</strong>g>th</str<strong>on</strong>g>e ensuing epidemiological<br />

transiti<strong>on</strong>, which during <str<strong>on</strong>g>th</str<strong>on</strong>g>e last century have brought down to negligible levels<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e perceived risks <str<strong>on</strong>g>of</str<strong>on</strong>g> serious disease given infecti<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e sustained vaccinati<strong>on</strong><br />

programmes c<strong>on</strong>ducted in <str<strong>on</strong>g>th</str<strong>on</strong>g>e past, which have brought down to negligible levels<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e perceived risks <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong>. This yields ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er pessimistic predicti<strong>on</strong>s about <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

future lifetime <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccinati<strong>on</strong> programmes. Subsequently, motivated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact no<br />

current vaccinati<strong>on</strong> regimes are fully voluntary, we propose a new framework aimed<br />

to predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamic effects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay between inter-human and public<br />

informati<strong>on</strong> <strong>on</strong> vaccine uptake, based <strong>on</strong> a modified evoluti<strong>on</strong>ary game equati<strong>on</strong><br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e vaccinated proporti<strong>on</strong>, including <str<strong>on</strong>g>th</str<strong>on</strong>g>e effort <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> system as<br />

well. The underlying idea is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e hazard <str<strong>on</strong>g>of</str<strong>on</strong>g> becoming a vaccinator is <str<strong>on</strong>g>th</str<strong>on</strong>g>e sum <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

two comp<strong>on</strong>ents, <strong>on</strong>e due to informati<strong>on</strong> spread <str<strong>on</strong>g>th</str<strong>on</strong>g>rough inter-human c<strong>on</strong>tacts (e.g.<br />

imitati<strong>on</strong>), and <strong>on</strong>e due to informati<strong>on</strong> spread by <str<strong>on</strong>g>th</str<strong>on</strong>g>e public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> system. Unlike<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e former, <str<strong>on</strong>g>th</str<strong>on</strong>g>e latter aims to suggest a very small, possibly zero, perceived risk <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

vaccine side effects, and a larger, possibly prevalence independent, risk <str<strong>on</strong>g>of</str<strong>on</strong>g> disease.<br />

Our main results show <str<strong>on</strong>g>th</str<strong>on</strong>g>at public interventi<strong>on</strong> can play a stabilising role capable<br />

to reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e violence <str<strong>on</strong>g>of</str<strong>on</strong>g> ’imitati<strong>on</strong>’ induced oscillati<strong>on</strong>s, to allow for disease eliminati<strong>on</strong>,<br />

and to even make <str<strong>on</strong>g>th</str<strong>on</strong>g>e so called Disease Free Pure Vaccinators Equilibrium<br />

Globally attractive. This suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at keeping a degree <str<strong>on</strong>g>of</str<strong>on</strong>g> public interventi<strong>on</strong> in<br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>erwise voluntary vaccinati<strong>on</strong> regimes might be <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>ly way to mitigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

pessimistic c<strong>on</strong>clusi<strong>on</strong>s reported above.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Mosquito-Borne Diseases; Tuesday, June 28, 11:00<br />

Carrie Manore<br />

Oreg<strong>on</strong> State University<br />

e-mail: manorec@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.oreg<strong>on</strong>state.edu<br />

Nakul Chitnis<br />

Swiss Tropical and Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Institute<br />

Mac Hyman<br />

Tulane University<br />

A Model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Spread <str<strong>on</strong>g>of</str<strong>on</strong>g> Rift Valley Fever in Livestock<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Vertical Transmissi<strong>on</strong><br />

Rift Valley Fever (RVF) is a zo<strong>on</strong>otic infectious disease spread by mosquitoes and<br />

transmitted between several animals species and occasi<strong>on</strong>ally humans. We present<br />

and analyze a new model for mosquito-transmitted disease <str<strong>on</strong>g>th</str<strong>on</strong>g>at includes vertical<br />

transmissi<strong>on</strong> mechanisms from an infected mosquito mo<str<strong>on</strong>g>th</str<strong>on</strong>g>er to infected <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring.<br />

In particular, we model <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> RVF in cattle and mosquito populati<strong>on</strong>s,<br />

extending existing models for vector-borne diseases to include vertical transmissi<strong>on</strong><br />

and an egg/larvae stage. We analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> vertical transmissi<strong>on</strong> in<br />

predicting <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> RVF and discuss how modeling can reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e uncertainty<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e estimates <str<strong>on</strong>g>of</str<strong>on</strong>g> disease prevalence. We also make <str<strong>on</strong>g>th</str<strong>on</strong>g>is extended model reactive<br />

to envir<strong>on</strong>mental changes and dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at even if <str<strong>on</strong>g>th</str<strong>on</strong>g>e endemic equilibrium<br />

has a low ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious vectors and animals, a large pulse <str<strong>on</strong>g>of</str<strong>on</strong>g> vectors resulting<br />

from increased hatch and survival rates due to high rainfall events can result in a<br />

large epidemic.<br />

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Semigroups <str<strong>on</strong>g>of</str<strong>on</strong>g> Operators in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology I; Wednesday, June 29, 08:30<br />

Anna Marciniak-Czochra<br />

Interdisciplinary Center for Scientific Computing,<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and BIOQUANT,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Heidelberg<br />

e-mail: anna.marciniak@iwr.uni-heidelberg.de<br />

Structured populati<strong>on</strong> models in metric spaces<br />

Time evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a heterogeneous populati<strong>on</strong> parametrised by <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamically<br />

regulated properties <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals can be described by so called structured<br />

populati<strong>on</strong> models, which are first order hyperbolic equati<strong>on</strong>s defined <strong>on</strong> R + .<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk a new framework for <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> measure-valued soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

n<strong>on</strong>linear structured populati<strong>on</strong> model is presented. Existence and Lipschitz dependence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model parameters and initial data are shown using<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e properties <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear semigroups in suitably chosen metric spaces. The estimates<br />

for a corresp<strong>on</strong>ding linear model are obtained based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e duality formula<br />

for transport equati<strong>on</strong>s. The results are discussed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> applicati<strong>on</strong>s to<br />

biological data. In particularly, <str<strong>on</strong>g>th</str<strong>on</strong>g>e new framework is applied to describe a process<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cell differentiati<strong>on</strong>, which involves discrete and c<strong>on</strong>tinuous transiti<strong>on</strong>s.<br />

The presentati<strong>on</strong> is based <strong>on</strong> joint works wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Piotr Gwiazda (University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Warsaw) and Grzegorz Jamroz (University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw/University <str<strong>on</strong>g>of</str<strong>on</strong>g> Heidelberg).<br />

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Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part I;<br />

Tuesday, June 28, 11:00<br />

Anna Marciniak-Czochra<br />

Interdisciplinary Center for Scientific Computing,<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and BIOQUANT,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Heidelberg<br />

e-mail: anna.marciniak@iwr.uni-heidelberg.de<br />

Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> pattern formati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e models <str<strong>on</strong>g>of</str<strong>on</strong>g> early<br />

cancerogenesis<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we will explore a mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> pattern formati<strong>on</strong> arising in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

processes described by a system <str<strong>on</strong>g>of</str<strong>on</strong>g> a single reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong> couples wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

ordinary differential equati<strong>on</strong>s. Such models are very different from classical Turingtype<br />

models and <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pattern emerging from <str<strong>on</strong>g>th</str<strong>on</strong>g>e destabilisati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatially homogeneous steady state cannot be c<strong>on</strong>cluded based <strong>on</strong> linear<br />

stability analysis. The models exhibit qualitatively new patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s,<br />

including a str<strong>on</strong>g dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e emerging pattern <strong>on</strong> initial c<strong>on</strong>diti<strong>on</strong>s<br />

and quasi-stability followed by rapid grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s. In numerical simulati<strong>on</strong>s,<br />

soluti<strong>on</strong>s having <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> periodic or irregular spikes are observed. Recently we<br />

have proposed models <str<strong>on</strong>g>of</str<strong>on</strong>g> spatially-distributed grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> cl<strong>on</strong>al populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> precancerous<br />

cells, which remained under c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> endogenous or exogenous grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

factors diffusing in <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular medium and binding to <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell surface. We<br />

found c<strong>on</strong>diti<strong>on</strong>s for emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> patterns, which took <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> spiketype<br />

spatially inhomogeneous steady states. This multifocality is as expected from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e field <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> carcinogenesis.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we approach <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> stability <str<strong>on</strong>g>of</str<strong>on</strong>g> spike soluti<strong>on</strong>s, which is<br />

essential for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir observability in experiments. We study existence and stability <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

regular spatially inhomogeneous stati<strong>on</strong>ary soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> periodic type and <str<strong>on</strong>g>of</str<strong>on</strong>g> disc<strong>on</strong>tinuous<br />

patterns.<br />

The talk is a based <strong>on</strong> a series <str<strong>on</strong>g>of</str<strong>on</strong>g> joint works wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Marek Kimmel (Rice University),<br />

Kanako Suzuki (Tohoku University), Grzegorz Karch (University <str<strong>on</strong>g>of</str<strong>on</strong>g> Wroclaw)<br />

and Steffen Härting (University <str<strong>on</strong>g>of</str<strong>on</strong>g> Heidelberg)<br />

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Bioinformatics and System Biology; Wednesday, June 29, 14:30<br />

Michał Marczyk<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Automatic C<strong>on</strong>trol, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: Michal.Marczyk@polsl.pl<br />

Roman Jaksik<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Automatic C<strong>on</strong>trol, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Joanna Polańska<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Automatic C<strong>on</strong>trol, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Andrzej Polański<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Informatics, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Discriminative gene selecti<strong>on</strong> in low dose radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

microarray data for radiosensitivity pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile search<br />

In radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy total dose delivered to targeted tumor tissue is limited to minimize<br />

late side effects in normal tissue, which also limits its healing effect. Ability to adjust<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dose to <str<strong>on</strong>g>th</str<strong>on</strong>g>e individual patient radiosensitivity wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> given<br />

after low dose radiati<strong>on</strong> will help in reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e negative effects <str<strong>on</strong>g>of</str<strong>on</strong>g> radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

while increasing <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer treatment. In most gene expressi<strong>on</strong> studies<br />

selecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> significant features for sample classificati<strong>on</strong> is a comm<strong>on</strong> task. The<br />

main goal <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is step is to discover <str<strong>on</strong>g>th</str<strong>on</strong>g>e smallest possible set <str<strong>on</strong>g>of</str<strong>on</strong>g> genes <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows<br />

to achieve good predictive performance. However, in analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer patients<br />

radiosensitivity, differences between analyzed groups are hardly noticed. Also clinical<br />

observati<strong>on</strong>s indicate large variati<strong>on</strong>s between individuals wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in group, which<br />

provides a need to explore different me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> feature selecti<strong>on</strong>.<br />

Examined data c<strong>on</strong>tain two groups <str<strong>on</strong>g>of</str<strong>on</strong>g> breast cancer patients showing clinical<br />

differences in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir normal tissue late resp<strong>on</strong>se to radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy. Data pre-processing<br />

includes probe sets re-annotati<strong>on</strong> using PLANdbAffy database, tRMA background<br />

correcti<strong>on</strong>, normalizati<strong>on</strong> and summarizati<strong>on</strong>. Preliminary data analysis and quality<br />

c<strong>on</strong>trol pointed out str<strong>on</strong>g batch effect, which was corrected using ComBat<br />

s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware.<br />

To select significant genes, which can predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e status <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sample <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

basis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e expressi<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile, we use statistical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods (t-test, modified Welch<br />

test, F-test) and recurrent feature replacement me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods (Recursive Feature Eliminati<strong>on</strong>,<br />

fuzzy C-Means RFE). In statistical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods correcti<strong>on</strong> due to correlati<strong>on</strong><br />

between genes was applied. We perform comprehensive experiments to compare<br />

feature selecti<strong>on</strong> algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms using two classifiers as SVM, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> linear and n<strong>on</strong>linear<br />

kernel, and Naive Bayes. The validati<strong>on</strong> step was divided into 2 stages. Training<br />

pilot study patient set, which in opini<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> clinicians was more informative, and<br />

testing set, which c<strong>on</strong>tained <str<strong>on</strong>g>th</str<strong>on</strong>g>e rest <str<strong>on</strong>g>of</str<strong>on</strong>g> samples, were used to see if <str<strong>on</strong>g>th</str<strong>on</strong>g>ere exist gene<br />

signature related to radiosensitivity. Multiple random validati<strong>on</strong> procedure using<br />

all data was later performed to prove generalizability <str<strong>on</strong>g>of</str<strong>on</strong>g> selected features.<br />

As a result <str<strong>on</strong>g>of</str<strong>on</strong>g> applying <str<strong>on</strong>g>th</str<strong>on</strong>g>e above described algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms, it was possible to c<strong>on</strong>struct<br />

a classifier <str<strong>on</strong>g>th</str<strong>on</strong>g>at could discriminate patients based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir late resp<strong>on</strong>se to<br />

radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy treatment wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 25% error rate using SVM and n<strong>on</strong>linear kernel. This<br />

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result was proven <str<strong>on</strong>g>th</str<strong>on</strong>g>rough multiple random validati<strong>on</strong>. When comparing me<str<strong>on</strong>g>th</str<strong>on</strong>g>odologies<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> feature selecti<strong>on</strong> recruitment modified Welch test which deals wi<str<strong>on</strong>g>th</str<strong>on</strong>g> unequal<br />

variability <str<strong>on</strong>g>of</str<strong>on</strong>g> genes between groups performed best, however <strong>on</strong>ly wi<str<strong>on</strong>g>th</str<strong>on</strong>g> correcti<strong>on</strong><br />

due to correlati<strong>on</strong>.<br />

This work was supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>European</str<strong>on</strong>g> Program FP6 - 036452, GENEPIlowRT<br />

and Ministry <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Higher Educati<strong>on</strong> grant no N N519 647840.<br />

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Populati<strong>on</strong> Dynamics; Wednesday, June 29, 08:30<br />

Glenn Mari<strong>on</strong><br />

Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics & Statistics Scotland<br />

e-mail: glenn@bioss.ac.uk<br />

Stephen Catterall<br />

Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics & Statistics Scotland<br />

Alex R. Cook<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Statistics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Science, Nati<strong>on</strong>al University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Singapore<br />

Philip E. Hulme<br />

The Bio-Protecti<strong>on</strong> Research Centre, Lincoln University, New Zealand<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial spread <str<strong>on</strong>g>of</str<strong>on</strong>g> invasive aliens:<br />

process-based models and Bayesian inference<br />

Discrete state-space Markov processes provide a remarkably flexible framework bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

to describe and infer <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> a broad range <str<strong>on</strong>g>of</str<strong>on</strong>g> systems in epidemiology and<br />

bey<strong>on</strong>d. For many models <str<strong>on</strong>g>of</str<strong>on</strong>g> interest reversible jump Markov chain M<strong>on</strong>te Carlo<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are a practical approach to implementing statistically sound parameter estimati<strong>on</strong><br />

for such models when, as is typically <str<strong>on</strong>g>th</str<strong>on</strong>g>e case, <strong>on</strong>ly partial observati<strong>on</strong>s are<br />

available. We c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> such inference approaches, applied wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

spatial epidemic models, to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> invasive species at large spatial<br />

scales. In such applicati<strong>on</strong>s local envir<strong>on</strong>mental characteristics determine susceptibility<br />

(suitability for <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasive species) which emphasises <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> landscape<br />

heterogeneity.<br />

In particular we present a generic Bayesian approach to parameter inference<br />

in a grid-based stochastic, spatio-temporal model <str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal and establishment<br />

describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a regi<strong>on</strong> by an alien plant species. The me<str<strong>on</strong>g>th</str<strong>on</strong>g>od requires<br />

species distributi<strong>on</strong> data from multiple time points, and accounts for temporal uncertainty<br />

in col<strong>on</strong>isati<strong>on</strong> times inherent in such data. The impact <strong>on</strong> col<strong>on</strong>isati<strong>on</strong><br />

suitability <str<strong>on</strong>g>of</str<strong>on</strong>g> covariates, which capture landscape heterogeneities, is also inferred.<br />

The model and inference algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m are applied to British floristic atlas data for Heracleum<br />

mantegazzianum (giant hogweed), an invasive alien plant <str<strong>on</strong>g>th</str<strong>on</strong>g>at has rapidly<br />

increased its range since 1970. Using systematic surveys <str<strong>on</strong>g>of</str<strong>on</strong>g> species distributi<strong>on</strong><br />

across a 10km grid covering <str<strong>on</strong>g>th</str<strong>on</strong>g>e British Isles, we infer key characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

species, predict its future spread, and use <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting fitted model to inform a<br />

simulati<strong>on</strong>-based assessment <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology.<br />

634

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Cancer; Tuesday, June 28, 17:00<br />

A. Martínez-G<strong>on</strong>zález<br />

Departamento de Matemáticas, E.T.S. de Ingenieros Industriales &<br />

IMACI-Instituto de Matemática Aplicada a la Ciencia y la Ingeniería,<br />

Universidad de Castilla-La Mancha, 13071, Ciudad Real, Spain<br />

e-mail: alicia.martinez@uclm.es<br />

G. F. Calvo<br />

Departamento de Matemáticas, E.T.S. de Ingenieros de Caminos, Canales<br />

y Puertos & IMACI-Instituto de Matemática Aplicada a la Ciencia y<br />

la Ingeniería, Universidad de Castilla-La Mancha, 13071, Ciudad Real,<br />

Spain<br />

e-mail: gabriel.fernandez@uclm.es<br />

V. M. Pérez-García<br />

Departamento de Matemáticas, E.T.S. de Ingenieros Industriales &<br />

IMACI-Instituto de Matemática Aplicada a la Ciencia y la Ingeniería,<br />

Universidad de Castilla-La Mancha, 13071, Ciudad Real, Spain<br />

e-mail: victor.perezgarcia@uclm.es<br />

Hypoxic Migratory Cell Waves around Necrotic Cores in<br />

Glioblastomas: A Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Model<br />

Malignant gliomas are <str<strong>on</strong>g>th</str<strong>on</strong>g>e most comm<strong>on</strong> and deadly brain tumors. Survival<br />

for patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> glioblastoma (GBM), <str<strong>on</strong>g>th</str<strong>on</strong>g>e most aggressive glioma, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough individually<br />

variable, is in <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> 10 m<strong>on</strong><str<strong>on</strong>g>th</str<strong>on</strong>g>s to 14 m<strong>on</strong><str<strong>on</strong>g>th</str<strong>on</strong>g>s after diagnosis, using<br />

standard treatments which include surgery, radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy (temozolamide<br />

and antiangiogenic drugs such as bevacizumab) [1]. GBM is a rapidly evolving<br />

astrocytoma <str<strong>on</strong>g>th</str<strong>on</strong>g>at is distinguished pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologically from lower grade gliomas by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> necrosis and microvascular hyperplasia. Interestingly, necrotic foci<br />

are tipically surrounded by a populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> rapidly moving tumor cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at superimpose<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>emselves <strong>on</strong> a more stati<strong>on</strong>ary populati<strong>on</strong>, causing increased cell density,<br />

known as "pseudopalisades" [2, 3]. Evidence suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is tumor cell migrati<strong>on</strong><br />

is caused by a vaso-occlusive event where <str<strong>on</strong>g>th</str<strong>on</strong>g>e local tumor blood vessels no l<strong>on</strong>ger<br />

provide <str<strong>on</strong>g>th</str<strong>on</strong>g>e necessary oxygen supply. This leads to <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a wave <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor<br />

cells actively migrating away from central hypoxia (oxygen deprivati<strong>on</strong>) <str<strong>on</strong>g>th</str<strong>on</strong>g>at arises<br />

after a vascular insult. Indeed, pseudopalisading cells show nuclear expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

hypoxia-inducible factor 1α, c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir hypoxic nature [2, 3].<br />

We have developed a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>th</str<strong>on</strong>g>at incorporates <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal<br />

interplay am<strong>on</strong>g two tumor cell phenotypes, a necrotric core and <str<strong>on</strong>g>th</str<strong>on</strong>g>e oxygen distributi<strong>on</strong>.<br />

Our scenario c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor cells embedded wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in two blood<br />

vessels. We will assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypoxic phenotype is <str<strong>on</strong>g>th</str<strong>on</strong>g>e migratory <strong>on</strong>e but n<strong>on</strong>proliferative,<br />

whereas <str<strong>on</strong>g>th</str<strong>on</strong>g>e normoxic is less migratory but proliferative [4, 5]. In<br />

additi<strong>on</strong>, our model takes into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e switching mechanisms between bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

phenotypes when <str<strong>on</strong>g>th</str<strong>on</strong>g>e local oxygen levels cross a <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold value characteristic <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

hypoxia. Our numerical simulati<strong>on</strong>s reveal <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a superimposed travelling<br />

wave <str<strong>on</strong>g>of</str<strong>on</strong>g> hypoxic cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at qualitatively reproduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimentally observed<br />

patterns. This suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at our model could be fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er extended to include <str<strong>on</strong>g>th</str<strong>on</strong>g>e selective<br />

acti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor cells depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir oxic state.<br />

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References.<br />

[1] E. G. Van Meir, C. G. Hadjipanayis, A. D. Norden, H.-K. Shu, P. Y. Wen, and J. J. Ols<strong>on</strong>,<br />

Exciting New Advances in Neuro-Oncology: The Avenue to a Cure for Malignant Glioma,<br />

CA Cancer J. Clin. 60 166-193 (2010).<br />

[2] D. J. Brat, A. A. Castellano-Sanchez, S. B. Hunter, M. Pecot, C. Cohen, E. H. Hamm<strong>on</strong>d, S.<br />

N. Devi, B. Kaur, and E. G. Van Meir, Pseudopalisades in Glioblastoma Are Hypoxic, Express<br />

Extracellular Matrix Proteases, and Are Formed by an Actively Migrating Cell Populati<strong>on</strong>,<br />

Cancer Res. 64 920-927 (2004).<br />

[3] Y. R<strong>on</strong>g, D. L. Durden, E. G. Van Meir, and D. J. Brat, ’Pseudopalisading’ Necrosis in<br />

Glioblastoma: A Familiar Morphologic Feature That Links Vascular Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, Hypoxia, and<br />

Angiogenesis, J Neuropa<str<strong>on</strong>g>th</str<strong>on</strong>g>ol Exp Neurol 65 529-539 (2006).<br />

[4] A. Giese, R. Bjerkvig, M. E. Berens and M. Westphal, Cost <str<strong>on</strong>g>of</str<strong>on</strong>g> Migrati<strong>on</strong>: Invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Malignant<br />

Gliomas and Implicati<strong>on</strong>s for Treatment, J Clin Oncology 21 1624-1636 (2003).<br />

[5] R. G. Bristow and R. P. Hill, Hypoxia, DNA repair and genetic instability, Nature Rev Cancer<br />

8 180-192 (2008).<br />

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Modelling dengue fever epidemiology; Saturday, July 2, 08:30<br />

Marcos Amaku<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Veterinary Medicine, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> São Paulo, Brazil.<br />

Francisco Ant<strong>on</strong>io Bezerra Coutinho<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> São Paulo, and LIM 01 HCF-<br />

MUSP, Brazil.<br />

Eduardo Massad<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> São Paulo, and LIM 01 HCF-<br />

MUSP, Brazil.<br />

L<strong>on</strong>d<strong>on</strong> School <str<strong>on</strong>g>of</str<strong>on</strong>g> Hygiene and Tropical Medicine, UK.<br />

e-mail: edmassad@usp.br<br />

Why dengue and yellow fever coexist in some areas <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

world and not in o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers?<br />

Urban yellow fever and dengue coexist in Africa but not in Asia and Sou<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

America. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper we examine four hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses (and combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em)<br />

advanced to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e absence <str<strong>on</strong>g>of</str<strong>on</strong>g> yellow fever in urban areas <str<strong>on</strong>g>of</str<strong>on</strong>g> Asia and Sou<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

America. In additi<strong>on</strong>, we examine <strong>on</strong>e fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at would explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong>s in Africa and at <str<strong>on</strong>g>th</str<strong>on</strong>g>e same time explaining why <str<strong>on</strong>g>th</str<strong>on</strong>g>ey do<br />

not coexist in Asia and Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> America. The hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses advanced to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

n<strong>on</strong>existence <str<strong>on</strong>g>of</str<strong>on</strong>g> yellow fever in Asia and Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> America are: <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk <str<strong>on</strong>g>of</str<strong>on</strong>g> importati<strong>on</strong><br />

to Asia <str<strong>on</strong>g>of</str<strong>on</strong>g> a yellow fever viraemic pers<strong>on</strong> is very low; <str<strong>on</strong>g>th</str<strong>on</strong>g>e Asian Aedes aegypti is<br />

relatively incompetent to transmit yellow fever; <str<strong>on</strong>g>th</str<strong>on</strong>g>ere would exists a competiti<strong>on</strong><br />

between dengue and yellow fever viruses wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mosquitoes, as suggested by<br />

some in vitru studies, in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e dengue virus always wins; <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is an important<br />

cross-immunity between yellow fever and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er flaviviroses, dengue in particular,<br />

such <str<strong>on</strong>g>th</str<strong>on</strong>g>at a pers<strong>on</strong> recovered from a bout <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue would have his/her susceptibility<br />

to yellow fever diminished. This latter hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis is called hereafter <str<strong>on</strong>g>th</str<strong>on</strong>g>e “Asian<br />

hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis”. Finally, we hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esize <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong>s in Africa<br />

is due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e virtual absence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mosquito Aedes albopicuts, which competes wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Aedes aegypti, in Africa. We call <str<strong>on</strong>g>th</str<strong>on</strong>g>is latter hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>e “African hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis”. We<br />

c<strong>on</strong>struct a model <str<strong>on</strong>g>of</str<strong>on</strong>g> transmissi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows all <str<strong>on</strong>g>th</str<strong>on</strong>g>e above hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses to be tested.<br />

We c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e Asian and <str<strong>on</strong>g>th</str<strong>on</strong>g>e African hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses can explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed<br />

phenomena. The o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses do not explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed phenomena.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis I; Wednesday, June 29,<br />

08:30<br />

Susan Christine Massey<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Washingt<strong>on</strong> (UW)<br />

e-mail: suzyn03@u.washingt<strong>on</strong>.edu<br />

Russell Rockne<br />

Departments <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology and Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, UW<br />

e-mail: rockne@u.washingt<strong>on</strong>.edu<br />

Alexander R. Anders<strong>on</strong><br />

Integrated Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Oncology Center, H. Lee M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer<br />

Center & Research Institute<br />

e-mail: alexander.anders<strong>on</strong>@m<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt.org<br />

Kristin R. Swans<strong>on</strong><br />

Departments <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology and Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, UW<br />

e-mail: krae@u.washingt<strong>on</strong>.edu<br />

Parameter sensitivity investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> glioma angiogenesis via Latin hypercube sampling.<br />

Malignant glioblastoma multiforme (GBM) is a relatively rare cancer wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a very<br />

poor prognosis. It is unique am<strong>on</strong>g cancers in <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumors are quite diffuse<br />

and infiltrative, but do not metastasize out <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e CNS. This diffuse nature, as well<br />

as its locati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e brain, presents many challenges for treatment and disease<br />

m<strong>on</strong>itoring. Following <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> anti-angiogenic agents in <str<strong>on</strong>g>th</str<strong>on</strong>g>e past few<br />

years, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere has been much hope <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is form <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment might make great<br />

strides in <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment and management <str<strong>on</strong>g>of</str<strong>on</strong>g> malignant glioma, but clinical resp<strong>on</strong>se<br />

to date has been disappointing. Patients <str<strong>on</strong>g>of</str<strong>on</strong>g>ten show a str<strong>on</strong>g initial resp<strong>on</strong>se <strong>on</strong><br />

MRI, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> imageable tumor receding relatively so<strong>on</strong> following treatment initiati<strong>on</strong>.<br />

However, after some time <str<strong>on</strong>g>th</str<strong>on</strong>g>ey all progress, <str<strong>on</strong>g>of</str<strong>on</strong>g>ten wi<str<strong>on</strong>g>th</str<strong>on</strong>g> more diffuse, wide-spread<br />

disease <str<strong>on</strong>g>th</str<strong>on</strong>g>an prior to anti-angiogenic treatment. To better understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e role<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis and anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy in GBM patients, we have created a<br />

proliferati<strong>on</strong>-invasi<strong>on</strong>-hypoxia-necrosis-angiogenesis (PIHNA) ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> glioma grow<str<strong>on</strong>g>th</str<strong>on</strong>g> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> angiogenesis and have adapted it to simulate anti-angiogenic<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy. Based <strong>on</strong> our clinically validated, extensive work wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proliferati<strong>on</strong>invasi<strong>on</strong><br />

(PI) model <str<strong>on</strong>g>of</str<strong>on</strong>g> glioma grow<str<strong>on</strong>g>th</str<strong>on</strong>g> (1, 2, 3) <str<strong>on</strong>g>th</str<strong>on</strong>g>is model was developed to simulate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> hypoxia <strong>on</strong> vascular recruitment in glioma. It has been correlated<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> FMISO PET imaging data (4), and provides a basis from which we can better<br />

understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> anti-angiogenic treatment <strong>on</strong> vascular recruitment, as<br />

well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor envir<strong>on</strong>ment. Here we present our use <str<strong>on</strong>g>of</str<strong>on</strong>g> a sensitivity analysis<br />

technique incorporating latin hypercube sampling (LHS) to vary parameters against<br />

each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er and determine which parameters in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model have <str<strong>on</strong>g>th</str<strong>on</strong>g>e most significant<br />

influence <strong>on</strong> hypoxic burden and how treatment parameters fit in. This knowledge<br />

allows us to better assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e significance <str<strong>on</strong>g>of</str<strong>on</strong>g> anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies <strong>on</strong> tumor<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> patterns and give insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ships between <str<strong>on</strong>g>th</str<strong>on</strong>g>ese factors and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor microenvir<strong>on</strong>ment to enhance combat and c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease.<br />

638<br />

References.

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[1] H. L. P. Harpold, E. C. Alvord, Jr., K. R. Swans<strong>on</strong>, 2007. The evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> glioma grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and invasi<strong>on</strong>. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Neuropa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology and Experimental Neurology<br />

66(1) 1–9.<br />

[2] K. R. Swans<strong>on</strong>, R. Rostomily, E. C. Alvord, Jr., 2008. Predicting Survival <str<strong>on</strong>g>of</str<strong>on</strong>g> Patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Glioblastoma by Combining a Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Model and Pre-operative MR imaging Characteristics:<br />

A Pro<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Principle. British Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Cancer. 98 113–9.<br />

[3] C. Wang, J. K. Rockhill, M. Mrugala, D.L. Peacock, A. Lai, K. Jusenius, J. M. Wardlaw,<br />

T. Cloughesy, A. M. Spence, R. Rockne, E. C. Alvord Jr., K. R. Swans<strong>on</strong>, 2009. Prognostic<br />

significance <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> kinetics in newly diagnosed glioblastomas revealed by combining serial<br />

imaging wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a novel bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model. Cancer Research 69(23) 9133–40.<br />

[4] S. Gu, G. Chakraborty, K. Champley, A. Alessio, J. Claridge, R. Rockne, M. Muzi, K. A.<br />

Krohn, A. M. Spence, E. C. Alvord, Jr., A. R. A. Anders<strong>on</strong>, P. Kinahan, K. R. Swans<strong>on</strong>, 2010.<br />

Applying a Patient –Specific Bio-Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Model <str<strong>on</strong>g>of</str<strong>on</strong>g> Glioma Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> to Develop Virtual<br />

[18F]-FMISO-PET Images. Under review.<br />

639

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Moving Organisms: From Individuals to Populati<strong>on</strong>s; Wednesday, June 29, 17:00<br />

Franziska Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>äus 1<br />

Mario S. Mommer 2<br />

Marko Jagodič 3<br />

Tine Curk 4,6<br />

Jure Dobnikar 5,6<br />

1 BIOMS, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Heidelberg<br />

2 IWR, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Heidelberg<br />

3 Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Physics and Mechanics, Ljubljana, Slove-<br />

nia<br />

4 Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Natural Sciences and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Mari-<br />

bor, Slovenia<br />

5 Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Physics, Jožef Stefan Institute, Ljubl-<br />

jana, Slovenia<br />

6 Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Chemistry, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cambridge, UK<br />

Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>its from noise: <str<strong>on</strong>g>th</str<strong>on</strong>g>e example <str<strong>on</strong>g>of</str<strong>on</strong>g> E. coli moti<strong>on</strong> and<br />

chemotaxis<br />

E. coli bacteria propel <str<strong>on</strong>g>th</str<strong>on</strong>g>emselves <str<strong>on</strong>g>th</str<strong>on</strong>g>rough flagellar rotati<strong>on</strong>. The c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

flagella is given <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er simple signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way, involving <strong>on</strong>ly a very<br />

small number <str<strong>on</strong>g>of</str<strong>on</strong>g> enzymes. Despite its simplicity <str<strong>on</strong>g>th</str<strong>on</strong>g>is signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way regulates<br />

a number <str<strong>on</strong>g>of</str<strong>on</strong>g> complex behaviors like chemotaxis, adaptati<strong>on</strong>, and even Lévy walks.<br />

A Lévy walk is a special type <str<strong>on</strong>g>of</str<strong>on</strong>g> a random walk, characterized by a power-law run<br />

leng<str<strong>on</strong>g>th</str<strong>on</strong>g> distributi<strong>on</strong>. It has been proven to represent <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal search strategy to<br />

find randomly located and sparse targets. Interestingly, in E. coli bacteria <str<strong>on</strong>g>th</str<strong>on</strong>g>e Lévy<br />

walk is a result <str<strong>on</strong>g>of</str<strong>on</strong>g> noisy fluctuati<strong>on</strong>s affecting <str<strong>on</strong>g>th</str<strong>on</strong>g>e signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way. We use a model<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way given in <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> differential and algebraic equati<strong>on</strong>s,<br />

augmented by a stochastic term, to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> noise <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong><br />

dynamics and <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> single cells and populati<strong>on</strong>s. Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model we<br />

derive <str<strong>on</strong>g>th</str<strong>on</strong>g>e power-law run leng<str<strong>on</strong>g>th</str<strong>on</strong>g> distributi<strong>on</strong> analytically in dependence <strong>on</strong> and<br />

statistical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e noise and properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way. Our<br />

expressi<strong>on</strong> yields a power-law exp<strong>on</strong>ent <str<strong>on</strong>g>of</str<strong>on</strong>g> -2.2 which coincides wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental<br />

data. We also use <str<strong>on</strong>g>th</str<strong>on</strong>g>e model to simulate chemotactic behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> large populati<strong>on</strong>s<br />

in different chemical landscapes. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at also chemotactic behavior pr<str<strong>on</strong>g>of</str<strong>on</strong>g>its<br />

from noise, as it increases bacterial motility and behavioral variability.<br />

640

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Crowd Dynamics: Modeling, Analysis and Simulati<strong>on</strong> (Part 1); Wednesday,<br />

June 29, 11:00<br />

Maury Bertrand<br />

Laboratoire de Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ématiques d’Orsay, Université Paris-Sud 11, 91405<br />

Orsay cedex, France<br />

e-mail: Bertrand.Maury@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.u-psud.fr<br />

Handling <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>gesti<strong>on</strong> in crowd moti<strong>on</strong> modeling<br />

We propose a general framework to incorporate c<strong>on</strong>gesti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> crowd moti<strong>on</strong> in evacuati<strong>on</strong> situati<strong>on</strong>s. This approach can be seen as a first<br />

order (in time) counterpart <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> problem associated to <str<strong>on</strong>g>th</str<strong>on</strong>g>e collective<br />

moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> rigid spheres (or discs) wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a n<strong>on</strong> elastic collisi<strong>on</strong> law. In its simpler,<br />

microscopic, form (see [4]), <str<strong>on</strong>g>th</str<strong>on</strong>g>e approach we propose is based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e definiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a desired velocity (corresp<strong>on</strong>ding to <str<strong>on</strong>g>th</str<strong>on</strong>g>e velocity <strong>on</strong>e would have in <str<strong>on</strong>g>th</str<strong>on</strong>g>e absence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers); <str<strong>on</strong>g>th</str<strong>on</strong>g>e actual velocity is <str<strong>on</strong>g>th</str<strong>on</strong>g>en defined as <str<strong>on</strong>g>th</str<strong>on</strong>g>e projecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is desired velocity<br />

<strong>on</strong>to <str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> feasible velocities (velocity which do not violate <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>-overlapping<br />

c<strong>on</strong>straints between individuals). This model fits into <str<strong>on</strong>g>th</str<strong>on</strong>g>e general framework <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

sweeping processes by c<strong>on</strong>vex sets [5], and its generalizati<strong>on</strong> to n<strong>on</strong>-c<strong>on</strong>vex sets [1].<br />

Well-posedness results rely <strong>on</strong> a so called catching up algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m, which follows a<br />

predicti<strong>on</strong>-correcti<strong>on</strong> strategy, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e correcti<strong>on</strong> c<strong>on</strong>sists in projecting a c<strong>on</strong>figurati<strong>on</strong><br />

which violates <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>straints <strong>on</strong>to <str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> feasible c<strong>on</strong>figurati<strong>on</strong>s.<br />

We proposed recently a macroscopic versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach ([2]): <str<strong>on</strong>g>th</str<strong>on</strong>g>e crowd<br />

is described by a density which is subject to remain below a maximal value (c<strong>on</strong>gesti<strong>on</strong>).<br />

We shall present how <str<strong>on</strong>g>th</str<strong>on</strong>g>e general framework <str<strong>on</strong>g>of</str<strong>on</strong>g> optimal transportati<strong>on</strong><br />

endows <str<strong>on</strong>g>th</str<strong>on</strong>g>e space <str<strong>on</strong>g>of</str<strong>on</strong>g> densities wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a natural distance (Wasserstein distance) which<br />

makes it possible to generalize <str<strong>on</strong>g>th</str<strong>on</strong>g>e catching up approach to <str<strong>on</strong>g>th</str<strong>on</strong>g>is n<strong>on</strong>-Hilbertian<br />

setting [3].<br />

We shall address <str<strong>on</strong>g>th</str<strong>on</strong>g>e links and deep differences between micro and macro approaches,<br />

from bo<str<strong>on</strong>g>th</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and modeling standpoints.<br />

References.<br />

[1] J.F. Edm<strong>on</strong>d, L. Thibault, BV soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>c<strong>on</strong>vex sweeping process differential inclusi<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> perturbati<strong>on</strong>, J. Differential Equati<strong>on</strong>s 226(1) (2006) 135–179.<br />

[2] B. Maury, A. Roudneff-Chupin, F. Santambrogio, A macroscopic Crowd Moti<strong>on</strong> Model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

gradient-flow type, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models and Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in Applied Sciences Vol. 20, No. 10<br />

(2010) 1787-1821.<br />

[3] B. Maury, A. Roudneff-Chupin, F. Santambrogio, J. Venel, Handling C<strong>on</strong>gesti<strong>on</strong> in Crowd<br />

Moti<strong>on</strong> Modeling, submitted (arXiv:1101.4102v1).<br />

[4] B. Maury, J. Venel, A discrete C<strong>on</strong>tact Model for crowd Moti<strong>on</strong>, accepted in M2AN, 2010<br />

(hal-00350815).<br />

[5] J.J. Moreau, Evoluti<strong>on</strong> problem associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a moving c<strong>on</strong>vex set in a Hilbert space,<br />

J.Differential Equati<strong>on</strong>s 26(3) (1977) 346?374.<br />

641

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Jessica B. McGillen 1 , Eam<strong>on</strong>n A. Gaffney 1 , Natasha K. Martin 2,3 , Robert<br />

A. Gatenby 4 , Philip K. Maini 1<br />

1 Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, Oxford University<br />

2 Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Social Medicine, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bristol<br />

3 Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Global Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> and Development, L<strong>on</strong>d<strong>on</strong> School <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Hygiene and Tropical Medicine<br />

4 M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Research Centre<br />

e-mail: jessica.mcgillen@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> Cancer Ecology<br />

We model <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolism and behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> a developing tumour in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> its microenvir<strong>on</strong>ment, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e aim <str<strong>on</strong>g>of</str<strong>on</strong>g> elucidating what drives <str<strong>on</strong>g>th</str<strong>on</strong>g>e hallmarks<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> malignancy [1]. The multiscale, multistage, highly n<strong>on</strong>linear nature <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer<br />

progressi<strong>on</strong> [2] calls for a dual modelling approach <str<strong>on</strong>g>th</str<strong>on</strong>g>at can link c<strong>on</strong>tinuous tissuelevel<br />

spatiotemporal patterns wi<str<strong>on</strong>g>th</str<strong>on</strong>g> discrete cell-level adaptati<strong>on</strong>s at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumourhost<br />

interface. Of particular interest is <str<strong>on</strong>g>th</str<strong>on</strong>g>e acid-mediated invasi<strong>on</strong> hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis [3],<br />

which suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at tissue hypoxia, adopti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e glycolytic phenotype [4], and<br />

acquisiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance to acidic byproducts <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e glycolytic phenotype comprise<br />

a critical stage in tumour progressi<strong>on</strong>. Many open questi<strong>on</strong>s remain c<strong>on</strong>cerning<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e details <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis and how it fits into <str<strong>on</strong>g>th</str<strong>on</strong>g>e somatic evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer,<br />

illustrating just <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> many research avenues for modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e somatic evoluti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cancer in general. We have generalised an existing c<strong>on</strong>tinuum model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e acidmediated<br />

invasi<strong>on</strong> hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis [5] by c<strong>on</strong>sidering additi<strong>on</strong>al, potentially important,<br />

biological features <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer invasi<strong>on</strong>, such as realistic acid-induced cellular dea<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

terms and cellular competiti<strong>on</strong>. Using bo<str<strong>on</strong>g>th</str<strong>on</strong>g> analytical and numerical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods, we<br />

firstly explore how a wave <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour cell invasi<strong>on</strong> is influenced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e acquisiti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> acid resistance, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er studies investigating parameter sensitivity and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

impact <str<strong>on</strong>g>of</str<strong>on</strong>g> modelling invasi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> more <str<strong>on</strong>g>th</str<strong>on</strong>g>an <strong>on</strong>e spatial dimensi<strong>on</strong>.<br />

References.<br />

[1] D. Hanahan, RA. Weinberg, The hallmarks <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer Cell 100(1) 57-70.<br />

[2] RA. Gatenby, PK. Maini, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical <strong>on</strong>cology: cancer summed up Nature 421(6921) 321.<br />

[3] RJ. Gillies, RA. Gatenby, Hypoxia and adaptive landscapes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> carcinogenesis<br />

Cancer and Metastasis Reviews 26(2) 311-317.<br />

[4] O. Warburg, The Metabolism <str<strong>on</strong>g>of</str<strong>on</strong>g> Tumors, Arnold C<strong>on</strong>stable, L<strong>on</strong>d<strong>on</strong>.<br />

[5] RA. Gatenby, ET. Gawlinski, A reacti<strong>on</strong>-diffusi<strong>on</strong> model <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer invasi<strong>on</strong> Cancer Research<br />

56(24) 5745-5753.<br />

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Epidemic models: Networks and stochasticity II; Thursday, June 30, 11:30<br />

Alan McKane<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Manchester<br />

e-mail: alan.mckane@manchester.ac.uk<br />

Stochastic amplificati<strong>on</strong> in an epidemic model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> seas<strong>on</strong>al<br />

forcing<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I will discuss, using <str<strong>on</strong>g>th</str<strong>on</strong>g>e formalism <str<strong>on</strong>g>of</str<strong>on</strong>g> master equati<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e nature <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic dynamics which appears in models <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> biology, and in<br />

particular childhood epidemics. When <str<strong>on</strong>g>th</str<strong>on</strong>g>ey c<strong>on</strong>tain a large number <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>stituents,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models may be analysed using an expansi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e system<br />

size. To leading order <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic analogues <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e models can be compared to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong>s which are normally written down <strong>on</strong> phenomenological grounds, for<br />

example <str<strong>on</strong>g>th</str<strong>on</strong>g>e SIR (Susceptible-Infected-Recovered) differential equati<strong>on</strong>s. At nextto-leading<br />

order a simplified stochastic descripti<strong>on</strong> is obtained. Attenti<strong>on</strong> will focus<br />

<strong>on</strong> systems for which <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic descripti<strong>on</strong> fails to predict cycles, but where<br />

large cycles are found at next-to-leading order. These cycles have <str<strong>on</strong>g>th</str<strong>on</strong>g>eir origin in<br />

fluctuati<strong>on</strong>s due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e discrete nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system comp<strong>on</strong>ents, and are much<br />

larger <str<strong>on</strong>g>th</str<strong>on</strong>g>an would naively be expected because <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are amplified by a res<strong>on</strong>ance<br />

phenomen<strong>on</strong>. The applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese ideas to <str<strong>on</strong>g>th</str<strong>on</strong>g>e SIR model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> term-time<br />

forcing will be described.<br />

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Populati<strong>on</strong> Dynamics; Tuesday, June 28, 11:00<br />

Nicola McPhers<strong>on</strong><br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computing Science & Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling,<br />

Stirling FK9 4LA, UK<br />

e-mail: njm@cs.stir.ac.uk<br />

Dr. Rachel Norman<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computing Science & Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling,<br />

Stirling FK9 4LA, UK<br />

e-mail: ran@cs.stir.ac.uk<br />

Macroparasites in Managed Systems: Using ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

models to help reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e Impact <str<strong>on</strong>g>of</str<strong>on</strong>g> Argulus foliaceus in UK<br />

Fisheries<br />

Argulus foliaceus is a macroparasite which reduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e aes<str<strong>on</strong>g>th</str<strong>on</strong>g>etic appeal and catchability<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> rainbow (Oncorhynchus mykiss) and brown (Salmo trutta) trout in stillwater<br />

fisheries across <str<strong>on</strong>g>th</str<strong>on</strong>g>e UK; infecti<strong>on</strong> is detrimental to fish welfare, can lead to<br />

loss <str<strong>on</strong>g>of</str<strong>on</strong>g> revenue, and impacts negatively <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reputati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e affected fisheries.<br />

Current me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trol can be bo<str<strong>on</strong>g>th</str<strong>on</strong>g> extreme and ineffective, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parasite<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g>ten surviving in surprising circumstances, despite c<strong>on</strong>stant, expensive treatment.<br />

The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk is to present ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled<br />

n<strong>on</strong>-linear ODEs, which describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship between argulids and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir hosts,<br />

incorporating reduced catch rates and several different stocking me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods. Fishery<br />

managers can stock fish into <str<strong>on</strong>g>th</str<strong>on</strong>g>eir lakes in a number <str<strong>on</strong>g>of</str<strong>on</strong>g> different ways in order to<br />

make sure <str<strong>on</strong>g>th</str<strong>on</strong>g>at anglers catch enough fish and want to return to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir fishery. This<br />

talk will investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship between <str<strong>on</strong>g>th</str<strong>on</strong>g>ose stocking me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods, <str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>se<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fish to parasitism and <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> parasites in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lake. These combine to<br />

have a - sometimes counterintuitive - knock-<strong>on</strong> effect <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> fish caught<br />

and hence <str<strong>on</strong>g>th</str<strong>on</strong>g>e ec<strong>on</strong>omic viability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fishery.<br />

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Epidemics; Tuesday, June 28, 17:00<br />

O.A. Melnichenko<br />

moscow state university, faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> computati<strong>on</strong>al ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and<br />

cybernetics<br />

e-mail: olesya.melnichenko@gmail.com<br />

Tuberculosis in Russia: comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> TB c<strong>on</strong>trol<br />

programmes<br />

Tuberculosis is recognized as a major global public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> problem, so development<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> TB c<strong>on</strong>trol strategies and estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir efficiency are important tasks.<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling can be a tool for solving <str<strong>on</strong>g>th</str<strong>on</strong>g>ese problems.<br />

We compared c<strong>on</strong>trol programmes for 14 regi<strong>on</strong>s related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e Central Federal<br />

District <str<strong>on</strong>g>of</str<strong>on</strong>g> Russia. The initial values <str<strong>on</strong>g>of</str<strong>on</strong>g> indicators for m<strong>on</strong>itoring TB c<strong>on</strong>trol<br />

programmes were obtained from data analysis [1]. Average smear-positive case<br />

detecti<strong>on</strong> rate equals 74%, average treatment success rate equals 78%, average<br />

smear-negative case detecti<strong>on</strong> rate equals 34%.<br />

We c<strong>on</strong>sidered two TB c<strong>on</strong>trol programmes. The programme 1 is recommended<br />

by WHO, <str<strong>on</strong>g>th</str<strong>on</strong>g>e targets <str<strong>on</strong>g>of</str<strong>on</strong>g> programme are detecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> 80% <str<strong>on</strong>g>of</str<strong>on</strong>g> new smear-positive cases<br />

and cure <str<strong>on</strong>g>of</str<strong>on</strong>g> 85% <str<strong>on</strong>g>of</str<strong>on</strong>g> such cases. Russian heal<str<strong>on</strong>g>th</str<strong>on</strong>g> system c<strong>on</strong>siders two c<strong>on</strong>secutive<br />

stages <str<strong>on</strong>g>of</str<strong>on</strong>g> tuberculosis: smear-negative and smear-positive. Detecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> smearnegative<br />

cases is an important part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Russian TB c<strong>on</strong>trol programme and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erefore we c<strong>on</strong>sidered programme 2 focused <strong>on</strong> improvement <str<strong>on</strong>g>of</str<strong>on</strong>g> smear-negative<br />

case detecti<strong>on</strong>. The target <str<strong>on</strong>g>of</str<strong>on</strong>g> programme 2 is detecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> 40% <str<strong>on</strong>g>of</str<strong>on</strong>g> new smearnegative<br />

cases.<br />

To compare c<strong>on</strong>trol programmes we used a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>th</str<strong>on</strong>g>at describes<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> TB in populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Russia, <str<strong>on</strong>g>th</str<strong>on</strong>g>e values <str<strong>on</strong>g>of</str<strong>on</strong>g> model parameters were<br />

obtained from model fitting [1]. To analyze sensitivity <str<strong>on</strong>g>of</str<strong>on</strong>g> model soluti<strong>on</strong> to changes<br />

in model parameters we used a me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g> adjoint equati<strong>on</strong>s, also we obtained<br />

formulas for calculati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> changes in basic epidemiological indicators [2].<br />

The changes in TB mortality rate, TB incidence and number <str<strong>on</strong>g>of</str<strong>on</strong>g> people who<br />

infected by mycobacteria per year were calculated for each programme. Programme<br />

1 is more effective <str<strong>on</strong>g>th</str<strong>on</strong>g>an programme 2 in 9 regi<strong>on</strong>s and less effective in 3 regi<strong>on</strong>s.<br />

They are approximately equal in 2 regi<strong>on</strong>s. The results obtained show <str<strong>on</strong>g>th</str<strong>on</strong>g>at type<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trol programme should be chosen separately for each regi<strong>on</strong> after analysis <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

epidemic situati<strong>on</strong>.<br />

The technique developed can be used to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er TB<br />

c<strong>on</strong>trol programmes <str<strong>on</strong>g>th</str<strong>on</strong>g>at were not c<strong>on</strong>sidered in <str<strong>on</strong>g>th</str<strong>on</strong>g>is study. It can be a usefull tool<br />

to choose <str<strong>on</strong>g>th</str<strong>on</strong>g>e most effective programme.<br />

References.<br />

[1] O.A. Melnichenko, A.A. Romanyukha A model <str<strong>on</strong>g>of</str<strong>on</strong>g> tuberculosis epidemiology: estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

parameters and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> factors influencing <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic process Russ. J.<br />

Numer. Anal. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Modelling, 2008, vol. 23, No. 1, pp. 63-75.<br />

[2] O.A. Melnichenko Model <str<strong>on</strong>g>of</str<strong>on</strong>g> tuberculosis epidemiology: sensitivity analysis Proc. <str<strong>on</strong>g>of</str<strong>on</strong>g> 4<str<strong>on</strong>g>th</str<strong>on</strong>g> Internati<strong>on</strong>al<br />

<str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> C<strong>on</strong>trol Problems, Moscow, 2009, pp. 857–863. (in Russian)<br />

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Models in Spatial Ecology; Tuesday, June 28, 17:00<br />

, R.M.<br />

M.Z. Cardoso<br />

Departamento de Botânica, Ecologia e Zoologia, Universidade Federal<br />

do Rio Grande do Norte, Brazil<br />

e-mail: mzc@cb.ufrn.br<br />

G. Corso<br />

Departamento de Bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ísica e Farmacologia, Universidade Federal do<br />

Rio Grande do Norte, Brazil<br />

e-mail: corso@cb.ufrn.br<br />

R.M. Coutinho<br />

Instituto de Física Teórica Universidade Estadual Paulista - UNESP,<br />

São Paulo, Brazil<br />

e-mail: renatomc@ift.unesp<br />

R.A. Kraenkel<br />

Instituto de Física Teórica Universidade Estadual Paulista - UNESP,<br />

São Paulo, Brazil<br />

e-mail: kraenkel@ift.unesp.br<br />

C<strong>on</strong>nectivity and diffusi<strong>on</strong> for Helic<strong>on</strong>ius species in a<br />

seas<strong>on</strong>ally dry fragmented habitat<br />

In a fragmented landscape, <str<strong>on</strong>g>th</str<strong>on</strong>g>e capability <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong>s to move between habitat<br />

patches, called functi<strong>on</strong>al c<strong>on</strong>nectivity, is influenced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intervening<br />

matrix and how organisms resp<strong>on</strong>d to it. Models usually treat <str<strong>on</strong>g>th</str<strong>on</strong>g>e matrix as<br />

a fixed category and fail to appreciate <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamic matrix types. We<br />

studied <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> seas<strong>on</strong>al changes in matrix quality, given <str<strong>on</strong>g>th</str<strong>on</strong>g>at it differs between<br />

dry and wet seas<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e seas<strong>on</strong>al tropics. The durati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e favorable period<br />

for dispersal, <str<strong>on</strong>g>th</str<strong>on</strong>g>e species’ ability to disperse and <str<strong>on</strong>g>th</str<strong>on</strong>g>e distance between patches could<br />

be important factors determining patch c<strong>on</strong>nectivity. We explored <str<strong>on</strong>g>th</str<strong>on</strong>g>ese c<strong>on</strong>necti<strong>on</strong>s<br />

by employing a diffusi<strong>on</strong> model to a <strong>on</strong>e-dimensi<strong>on</strong>al landscape subjected to<br />

periodical fluctuati<strong>on</strong>s in matrix quality; diffusi<strong>on</strong> was curtailed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e dry seas<strong>on</strong><br />

and permitted in <str<strong>on</strong>g>th</str<strong>on</strong>g>e wet seas<strong>on</strong>. Our model predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>at, given a particular organism’s<br />

lifetime and diffusi<strong>on</strong> c<strong>on</strong>stant, c<strong>on</strong>nectivity will depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong><br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e durati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dispersal seas<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e time for <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> to<br />

fully extend into <str<strong>on</strong>g>th</str<strong>on</strong>g>e matrix. We parameterize our model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> demographic data<br />

from Helic<strong>on</strong>ius butterflies, finding <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e model successfully describes c<strong>on</strong>nectivity<br />

between habitat patches and so it could be used to model dispersal <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

organisms in seas<strong>on</strong>al envir<strong>on</strong>ments and to help guide restorati<strong>on</strong> efforts and design<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> protected areas in <str<strong>on</strong>g>th</str<strong>on</strong>g>e tropics.<br />

646

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Cancer; Wednesday, June 29, 11:00<br />

B. Mendoza-Juez<br />

Departamento de Matemáticas, E.T.S. de Ingenieros industriales &<br />

IMACI - Instituto de Matemática Aplicada a la Ciencia y la Ingeniería,<br />

Universidad de Castilla - La Mancha, 13071, Ciudad Real, Spain<br />

e-mail: berta.mendoza@uclm.es<br />

A. Martínez-G<strong>on</strong>zález, D. Diego, G. F. Calvo, V. M. Pérez-García<br />

Departamento de Matemáticas & IMACI - Instituto de Matemática<br />

Aplicada a la Ciencia y la Ingeniería, Universidad de Castilla - La<br />

Mancha, 13071, Ciudad Real, Spain<br />

e-mail: alicia.martinez@uclm.es, david.diego@uclm.es,<br />

gabriel.fernandez@uclm.es,victor.perezgarcia@uclm.es<br />

P. Melgar, P. Sanchez-Prieto<br />

Laboratorio de Oncología Molecular, CRIB, Facultad de Medicina,<br />

Universidad de Castilla - La Mancha, Avda. Almansa s/n, 02071 Albacete,<br />

Spain<br />

e-mail: pedro.melgar@uclm.es, ricardo.sanchez@uclm.es<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic symbiosis in tumors<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e 1920s <str<strong>on</strong>g>th</str<strong>on</strong>g>e findings by Otto Warburg’s highlighted <str<strong>on</strong>g>th</str<strong>on</strong>g>e fundamental differences<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolism <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cells. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>cogene revoluti<strong>on</strong> somehow<br />

pushed tumor metabolism to an ancillary level in cancer research. It is currently<br />

becoming clear <str<strong>on</strong>g>th</str<strong>on</strong>g>at many key <strong>on</strong>cogenic signalling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways c<strong>on</strong>verge to adapt tumor<br />

cell metabolism to support grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and survival, and some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese alterati<strong>on</strong>s<br />

seem to be required for malignant transformati<strong>on</strong> [1, 2, 3].<br />

The abnormal tumor microenvir<strong>on</strong>ment has a major role in determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

metabolic phenotype <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cells. Tumor vasculature is irregular and malfuncti<strong>on</strong>ing,<br />

creating spatial and temporal heterogeneity in oxygenati<strong>on</strong>, pH, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

c<strong>on</strong>centrati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose, lactate and many o<str<strong>on</strong>g>th</str<strong>on</strong>g>er metabolites. Under such varying<br />

and extreme c<strong>on</strong>diti<strong>on</strong>s, adaptive resp<strong>on</strong>ses are induced <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>tribute to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

switching metabolic phenotype <str<strong>on</strong>g>of</str<strong>on</strong>g> malignant cells greatly influencing tumor progressi<strong>on</strong>.<br />

Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough aerobic glycolysis (<str<strong>on</strong>g>th</str<strong>on</strong>g>e Warburg effect) is <str<strong>on</strong>g>th</str<strong>on</strong>g>e best documented<br />

metabolic phenotype <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cells, it is not a universal feature <str<strong>on</strong>g>of</str<strong>on</strong>g> all human cancers.<br />

Moreover, even in glycolytic tumors, oxidative phosphorylati<strong>on</strong> is not completely<br />

shut down.<br />

Hypoxic cells use glucose for glycolysis, producing large amounts <str<strong>on</strong>g>of</str<strong>on</strong>g> lactate<br />

and exporting it via m<strong>on</strong>ocarboxylate transporters (mainly <str<strong>on</strong>g>th</str<strong>on</strong>g>e is<str<strong>on</strong>g>of</str<strong>on</strong>g>orm MCT4), a<br />

family <str<strong>on</strong>g>of</str<strong>on</strong>g> proteins <str<strong>on</strong>g>th</str<strong>on</strong>g>at when expressed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e plasma membrane are resp<strong>on</strong>sible<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e transport <str<strong>on</strong>g>of</str<strong>on</strong>g> different types <str<strong>on</strong>g>of</str<strong>on</strong>g> molecules [4,5]. Because <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e accelerated<br />

metabolism <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cells, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese transporters are up-regulated in many different<br />

types <str<strong>on</strong>g>of</str<strong>on</strong>g> cancers [2,4,6]<br />

This fact has been recognized in <str<strong>on</strong>g>th</str<strong>on</strong>g>e last few years as opening a potential target<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies since blocking <str<strong>on</strong>g>th</str<strong>on</strong>g>e activity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese transporters might lead to different<br />

scenarios leading to <str<strong>on</strong>g>th</str<strong>on</strong>g>e dea<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor cell [2,7-10]<br />

647

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

It has been recently dem<strong>on</strong>strated [10] <str<strong>on</strong>g>th</str<strong>on</strong>g>at oxygenated cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor<br />

can import extracellular lactate using ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er transporter (MCT1) to fuel respirati<strong>on</strong>,<br />

preserving glucose for use by <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypoxic cells and regulating <str<strong>on</strong>g>th</str<strong>on</strong>g>e medium pH.<br />

This metabolic symbiosis between oxidative and glycolytic tumor cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at mutually<br />

regulate <str<strong>on</strong>g>th</str<strong>on</strong>g>eir access to energy metabolites and pH makes <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor progressi<strong>on</strong><br />

very robust. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, it has been shown in [10] <str<strong>on</strong>g>th</str<strong>on</strong>g>at inhibiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> MCT1 induces<br />

a switch <strong>on</strong> oxidative cells from lactate-fueled respirati<strong>on</strong> to glycolysis. As<br />

a c<strong>on</strong>sequence, hypoxic cells die from glucose starvati<strong>on</strong> rendering <str<strong>on</strong>g>th</str<strong>on</strong>g>e remaining<br />

better-oxygenated cells sensitive to irradiati<strong>on</strong> and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies.<br />

Similar symbiotic phenomena between <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor and its altered microenvir<strong>on</strong>ment<br />

have been reported in o<str<strong>on</strong>g>th</str<strong>on</strong>g>er tumor models [11,12].<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is communicati<strong>on</strong> we will present a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cells<br />

behavior in vitro able to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e glucose and lactate uptake in different scenarios.<br />

The model fits <str<strong>on</strong>g>th</str<strong>on</strong>g>e in-vitro experiments <str<strong>on</strong>g>of</str<strong>on</strong>g> Ref. [10], toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

measurements reported in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature [13], as well as our own experiments wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

glioma cell lines.<br />

We will discuss how to extend <str<strong>on</strong>g>th</str<strong>on</strong>g>e in-vitro model to incorporate o<str<strong>on</strong>g>th</str<strong>on</strong>g>er phenomena<br />

present in cancers such as hypoxia and reoxygenati<strong>on</strong>. Finally, it will be<br />

examined how <str<strong>on</strong>g>th</str<strong>on</strong>g>ese ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models can assist in <str<strong>on</strong>g>th</str<strong>on</strong>g>e design <str<strong>on</strong>g>of</str<strong>on</strong>g> optimized combinati<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapies wi<str<strong>on</strong>g>th</str<strong>on</strong>g> radiati<strong>on</strong> and inhibitors <str<strong>on</strong>g>of</str<strong>on</strong>g> m<strong>on</strong>ocarboxylate transporters.<br />

References.<br />

[1] M.G. Vander Heiden, L.C. Cantley and C.B. Thomps<strong>on</strong>, Understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e Warburg Effect:<br />

The Metabolic Requirements <str<strong>on</strong>g>of</str<strong>on</strong>g> Cell Proliferati<strong>on</strong>, Science 324 1029 (2009).<br />

[2] D.A. Tennant, R.V. Durán and E. Gottlieb, Targeting metabolic transformati<strong>on</strong> for cancer<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, Nature Reviews Cancer 10 267 (2010).<br />

[3] R. A. Cairns, I. S. Harris, T. W. Mak, Regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cell metabolism, Nature Reviews<br />

Cancer 11 85–95 (2011).<br />

[4] C. Pinheiro, R. M. Reis, S. Ricardo, A. L<strong>on</strong>gatto-Filho, F. Schmitt, and F. Baltazar, Expressi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> M<strong>on</strong>ocarboxylate Transporters 1, 2, and 4 in Human Tumours and Their Associati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

CD147 and CD44, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Biomedicine and Biotechnology 2010, 427694 (2010).<br />

[5] A. P. Halestrap, N. T. Price, The prot<strong>on</strong>-linked m<strong>on</strong>ocarboxylate transporter (MCT) family :<br />

structure, functi<strong>on</strong> and regulati<strong>on</strong>, Biochem. J. 343 (1999) 281-299.<br />

[6] C. Pinheiro et al., M<strong>on</strong>ocarboxylate transporter 1 is up-regulated in basal-like breast carcinoma,<br />

Histopa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology 56 (2010) 860-867.<br />

[7] K. M. Kennedy, M. W. Dewhrist, Tumor metabolism <str<strong>on</strong>g>of</str<strong>on</strong>g> lactate: <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence and <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic<br />

potential for MCT and CD147 regulati<strong>on</strong>, Future Oncology 6 (2010) 127.<br />

[8] S. P. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>upala, P. Parajuli, A. E. Sloan, Silencing <str<strong>on</strong>g>of</str<strong>on</strong>g> m<strong>on</strong>ocarboxylate transportes via siRNA<br />

inhibits glycolisis and induces cell dea<str<strong>on</strong>g>th</str<strong>on</strong>g> in malignant glioma: An in vitro study, Neurosurgery<br />

55 (2004) 1410<br />

[9] J. Fang, Q. J. Quin<strong>on</strong>es, T. L. Holman, M. J. Morowitz, Q. Wang, H. Zhao, F. Sivo, J. M.<br />

Maris, and M. L. Wahl, The H+-Linked M<strong>on</strong>ocarboxylate Transporter (MCT1/SLC16A1):<br />

A Potential Therapeutic Target for High-Risk Neuroblastoma, Molecular Pharmacology 70<br />

(2006) 2108.<br />

[10] P. S<strong>on</strong>veaux et al., Targeting lactate-fueled respirati<strong>on</strong> selectively kills hypoxic tumor cells in<br />

mice The Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Clinical Investigati<strong>on</strong> 118 3930 (2008).<br />

[11] S. Pavlides et al., The reverse Warburg effect: Aerobic glycolysis in cancer associated fibroblasts<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor stroma, Cell Cycle 8 (2009) 3984-4001.<br />

[12] G. Migneco et al., Glycolytic cancer associated fibroblasts promote breast cancer tumor<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out a measurable increase in angiogenesis: Evidence for stromal-epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial metabolic<br />

coupling, Cell Cycle 9 (2010) 2412-2422.<br />

[13] R. L. Elstrom, D. E. Bauer, M. Buzzai, R. Karnauskas, M. H. Harris,1 D. R. Plas, H. Zhuang,<br />

R. M. Cinalli, A. Alavi, C. M. Rudin, and C. B. Thomps<strong>on</strong>, Akt stimulates aerobic glycolisys<br />

in cancer cells, Cancer Research 64 (2004) 3892-3899.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Computati<strong>on</strong>al toxicology and pharmacology - in silico drug activity and<br />

safety assessment; Saturday, July 2, 11:00<br />

Aleksander Mendyk<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Pharmaceutical Technology and Biopharmaceutics Faculty<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Pharmacy Jagiell<strong>on</strong>ian University Medical College, Medyczna<br />

9 Street, Kraków 30-688, Poland<br />

e-mail: mfmendyk@cyf-kr.edu.pl<br />

Barbara Wiśniowska<br />

Unit <str<strong>on</strong>g>of</str<strong>on</strong>g> Pharmacoepidemiology and Pharmacoec<strong>on</strong>omics Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Pharmacy Jagiell<strong>on</strong>ian University Medical College, Medyczna 9 Street,<br />

Kraków 30-688, Poland<br />

Miłosz Polak<br />

Unit <str<strong>on</strong>g>of</str<strong>on</strong>g> Pharmacoepidemiology and Pharmacoec<strong>on</strong>omics Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Pharmacy Jagiell<strong>on</strong>ian University Medical College, Medyczna 9 Street,<br />

Kraków 30-688, Poland<br />

Jakub Szlęk<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Pharmaceutical Technology and Biopharmaceutics Faculty<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Pharmacy Jagiell<strong>on</strong>ian University Medical College, Medyczna<br />

9 Street, Kraków 30-688, Poland<br />

Anna Glinka<br />

Unit <str<strong>on</strong>g>of</str<strong>on</strong>g> Pharmacoepidemiology and Pharmacoec<strong>on</strong>omics Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Pharmacy Jagiell<strong>on</strong>ian University Medical College, Medyczna 9 Street,<br />

Kraków 30-688, Poland<br />

Sebastian Polak<br />

Unit <str<strong>on</strong>g>of</str<strong>on</strong>g> Pharmacoepidemiology and Pharmacoec<strong>on</strong>omics Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Pharmacy Jagiell<strong>on</strong>ian University Medical College, Medyczna 9 Street,<br />

Kraków 30-688, Poland<br />

Artificial neural networks for carditoxicity predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

drugs - practical c<strong>on</strong>siderati<strong>on</strong>s<br />

Introducti<strong>on</strong> Early toxicity predicti<strong>on</strong> for potential drugs is c<strong>on</strong>sidered as a necessary<br />

safety measure regarding recent wi<str<strong>on</strong>g>th</str<strong>on</strong>g>drawals <str<strong>on</strong>g>of</str<strong>on</strong>g> many substances from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

pharmaceutical market. The latter was substantially based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e identified cardiotoxicity<br />

related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e inhibiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e potassium channels encoded by hERG<br />

(<str<strong>on</strong>g>th</str<strong>on</strong>g>e human e<str<strong>on</strong>g>th</str<strong>on</strong>g>er-a-go-go related gene). Thus, <str<strong>on</strong>g>th</str<strong>on</strong>g>e drugs affinity to hERG channels<br />

is c<strong>on</strong>sidered now as <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e major screening factors for potentially dangerous<br />

substances. There are <str<strong>on</strong>g>th</str<strong>on</strong>g>eories describing relati<strong>on</strong>ships between hERG channels<br />

blocking activity and chemical structure but <str<strong>on</strong>g>th</str<strong>on</strong>g>ey <str<strong>on</strong>g>of</str<strong>on</strong>g>ten lack <str<strong>on</strong>g>of</str<strong>on</strong>g> physiological/pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ological<br />

factors and drug c<strong>on</strong>centrati<strong>on</strong> influence. Thus, it is feasible to<br />

use empirical modeling to fill <str<strong>on</strong>g>th</str<strong>on</strong>g>is gap. The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work was to create predictive<br />

model for chemical substances affinity to hERG channels by means <str<strong>on</strong>g>of</str<strong>on</strong>g> artificial<br />

neural networks (ANNs).<br />

Materials and me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods Database used for <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling purposes was recently<br />

published and is freely available from <str<strong>on</strong>g>th</str<strong>on</strong>g>e CompTox project website (www.toxportal.net).<br />

Input data were derived from <str<strong>on</strong>g>th</str<strong>on</strong>g>e published in vitro experiments. Inputs<br />

represented in vitro experiment settings, chemical descriptors <str<strong>on</strong>g>of</str<strong>on</strong>g> drugs and<br />

drug c<strong>on</strong>centrati<strong>on</strong>. Output was simply percent <str<strong>on</strong>g>of</str<strong>on</strong>g> hERG channel inhibiti<strong>on</strong> (range<br />

649

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

0 to 1). Final set c<strong>on</strong>tained 1969 records describing 200 drugs. Initial number <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

inputs was 109. Enhanced 10-fold cross validati<strong>on</strong> (10-cv) was applied, where whole<br />

drugs informati<strong>on</strong> was excluded from test sets. For external validati<strong>on</strong> a test set<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> 193 records (25 substances) for drugs bo<str<strong>on</strong>g>th</str<strong>on</strong>g> previously present (different in vitro<br />

settings) and absent in <str<strong>on</strong>g>th</str<strong>on</strong>g>e native dataset was used. Drugs chemical structures<br />

were drawn in MarvinSketch or downloaded from PubChem Compound database.<br />

The molecules were structurally optimized wi<str<strong>on</strong>g>th</str<strong>on</strong>g> use <str<strong>on</strong>g>of</str<strong>on</strong>g> molc<strong>on</strong>vert command-line<br />

program included in Marvin Beans package. Resulting *.sdf files were <str<strong>on</strong>g>th</str<strong>on</strong>g>e subject<br />

to descriptor calculati<strong>on</strong>s by cxcalc program wi<str<strong>on</strong>g>th</str<strong>on</strong>g> selected 41 plugins. The default<br />

parameters were used in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> cxcalc and molc<strong>on</strong>vert programs. Multi-layer<br />

perceptr<strong>on</strong>s (MLPs) and neuro-fuzzy ANNs (NFs) were trained wi<str<strong>on</strong>g>th</str<strong>on</strong>g> use <str<strong>on</strong>g>of</str<strong>on</strong>g> backpropagati<strong>on</strong><br />

(BP) algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m wi<str<strong>on</strong>g>th</str<strong>on</strong>g> momentum, delta-bar-delta and jog-<str<strong>on</strong>g>of</str<strong>on</strong>g>-weights<br />

modificati<strong>on</strong>s. Various activati<strong>on</strong> functi<strong>on</strong>s were tested: hyperbolic tangent, logari<str<strong>on</strong>g>th</str<strong>on</strong>g>mic,<br />

logistic and linear. MLPs architectures were varied from 1 to 6 hidden<br />

layers and up to 200 nodes in each layer. For NFs <str<strong>on</strong>g>of</str<strong>on</strong>g> Mamdani (multiple input<br />

single output) MISO type <strong>on</strong>ly <strong>on</strong>e layer was applied. Adjacent layers were fully interc<strong>on</strong>nected.<br />

Sensitivity analysis was performed in order to reduce initial number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> inputs to <str<strong>on</strong>g>th</str<strong>on</strong>g>e crucial variables set by means <str<strong>on</strong>g>of</str<strong>on</strong>g> iterative algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m wi<str<strong>on</strong>g>th</str<strong>on</strong>g> gradual<br />

inputs reducti<strong>on</strong> and models predictive performance assessment. The latter was<br />

generalizati<strong>on</strong> error estimated by means <str<strong>on</strong>g>of</str<strong>on</strong>g> 10-cv wi<str<strong>on</strong>g>th</str<strong>on</strong>g> root mean squared error<br />

(RMSE) measure. Ensemble ANNs systems were applied and combined by simple<br />

average <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir outputs in order to improve predictability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model.<br />

Results The input reducti<strong>on</strong> procedure resulted in 39 parameters describing<br />

in vitro setting (8), drug physico-chemical properties (30), and c<strong>on</strong>centrati<strong>on</strong> (1).<br />

The best ANNs architectures found were as follows: (1) ANN wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 3 hidden layers<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 15, 7 and 5 nodes in each <strong>on</strong>e respectively and logistic activati<strong>on</strong> functi<strong>on</strong>; 2)<br />

ANN wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 2 hidden layers wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 20 and 10 nodes. The resulting 10-cv RMSE was<br />

0.22 wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>e validati<strong>on</strong> data set RMSE = 0.2. This result, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough<br />

not satisfactory seems to be final wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e available data representati<strong>on</strong>. Future<br />

research will be devoted to <str<strong>on</strong>g>th</str<strong>on</strong>g>e improvement <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model by enhancing input data<br />

by new factors/variables, if available.<br />

650

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Friday, July 1, 14:30<br />

Carsten Mente<br />

Technische Universität Dresden, Center for Informati<strong>on</strong> Services and<br />

High Performance Computing, 01062 Dresden Germany<br />

e-mail: carsten.mente@tu-dresden.de<br />

Andreas Deutsch<br />

Technische Universität Dresden, Center for Informati<strong>on</strong> Services and<br />

High Performance Computing, 01062 Dresden Germany<br />

e-mail: andreas.deutsch@tu-dresden.de<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Tumor Cell Dynamics wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Individual-based<br />

Lattice-gas Cellular Automata<br />

Malignant tumors can be c<strong>on</strong>sidered as populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

a high amount <str<strong>on</strong>g>of</str<strong>on</strong>g> phenotypic heterogeneity. To model cooperative phenomena<br />

(e.g. cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g>) in interacting cell populati<strong>on</strong>s, lattice-gas cellular automat<strong>on</strong><br />

(LGCA) models are increasingly used. Major advantages <str<strong>on</strong>g>of</str<strong>on</strong>g> LGCA models are<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey admit computati<strong>on</strong>ally efficient simulati<strong>on</strong>s and <str<strong>on</strong>g>of</str<strong>on</strong>g>ten analytical treatment<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeled problem. However, it has not been possible so far to distinguish<br />

individual biological cells in LGCA models making <str<strong>on</strong>g>th</str<strong>on</strong>g>em unsuitable to model<br />

phenomena where <str<strong>on</strong>g>th</str<strong>on</strong>g>e explicit descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individual cells is required. However,<br />

lattice-gas cellular automata have been successfully applied to model specific tumors<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out specifically c<strong>on</strong>sidering individual cells, e.g. grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> glioblastoma<br />

tumors. N<strong>on</strong>e<str<strong>on</strong>g>th</str<strong>on</strong>g>eless, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are processes during tumor formati<strong>on</strong> for which a "classical<br />

lattice-gas model" is unsuitable. One such process is <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> surrounding<br />

tissue by single tumor cells, a prerequisite for <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> metastasis.<br />

We propose an extensi<strong>on</strong> to (classical) lattice-gas cellular automata which allows<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e identificati<strong>on</strong> and tracking <str<strong>on</strong>g>of</str<strong>on</strong>g> individual cells. In particular, we derive stochastic<br />

differential equati<strong>on</strong>s (Langevin equati<strong>on</strong>s) corresp<strong>on</strong>ding to specific LGCA<br />

models. The LGCA model toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding<br />

Langevin equati<strong>on</strong> allows computati<strong>on</strong>ally efficient simulati<strong>on</strong>s and feasible analytical<br />

treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> individual cells in populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting cells.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, our proposed approach facilitates <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individual-based<br />

LGCA models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> cell-dependent dynamics. This also supports <str<strong>on</strong>g>th</str<strong>on</strong>g>e incorporati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> LGCA models into multi-scale models which c<strong>on</strong>sider processes at sub-cellular<br />

and cellular scales.<br />

We present applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> our individual-based LGCA appoach to <str<strong>on</strong>g>th</str<strong>on</strong>g>e following<br />

examples: random walk, adhesi<strong>on</strong>, and collective moti<strong>on</strong>. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we use<br />

an individual-based LGCA model to investigate c<strong>on</strong>diti<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>set <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue<br />

invasi<strong>on</strong> by single tumor cells.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Saturday, July 2, 14:30<br />

Gülnihal Meral<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Arts and Sciences<br />

Z<strong>on</strong>guldak Karaelmas University<br />

67100 Z<strong>on</strong>guldak<br />

Turkey<br />

e-mail: gulnihal@karaelmas.edu.tr<br />

Christina Surulescu<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Numerical and Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Einsteinstr. 62<br />

48149 Münster<br />

Germany<br />

e-mail: christina.surulescu@uni-muenster.de<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling and Numerical Simulati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Influence <str<strong>on</strong>g>of</str<strong>on</strong>g> Heat Shock Proteins <strong>on</strong> Tumour Invasi<strong>on</strong><br />

Invasi<strong>on</strong> is a key property <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cells; <str<strong>on</strong>g>th</str<strong>on</strong>g>ereby, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey encounter a large variety<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> soluble and substratum-bound factors which can influence <str<strong>on</strong>g>th</str<strong>on</strong>g>e different stages<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir migrati<strong>on</strong>. There are at least two mechanisms promoted by such factors:<br />

chemotaxis and haptotaxis. These in turn are influenced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular dynamics.<br />

In our talk we focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> heat shock proteins (HSP), a class <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

functi<strong>on</strong>ally related proteins whose expressi<strong>on</strong> is enhanced when cells are exposed<br />

to elevated temperature or o<str<strong>on</strong>g>th</str<strong>on</strong>g>er stresses and which have been recently proposed to<br />

influence cancer cell migrati<strong>on</strong>. Our ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model has a multiscale character,<br />

accounting bo<str<strong>on</strong>g>th</str<strong>on</strong>g> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic, intracellular level <strong>on</strong> which <str<strong>on</strong>g>th</str<strong>on</strong>g>ese proteins<br />

are acting and for <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic level <str<strong>on</strong>g>of</str<strong>on</strong>g> cell populati<strong>on</strong>. It c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> a system<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e density <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells, <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular<br />

matrix and <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> matrix degrading enzymes, which is <str<strong>on</strong>g>th</str<strong>on</strong>g>en coupled<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a delay differential equati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e HSP dynamics. We propose several different<br />

ways for modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e time lag and perform numerical simulati<strong>on</strong>s in order<br />

to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> our choices <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Tuesday, June 28, 17:00<br />

Ge<str<strong>on</strong>g>of</str<strong>on</strong>g>fry N. Mercer<br />

Nati<strong>on</strong>al Centre for Epidemiology and PPopulati<strong>on</strong> Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, Australian<br />

Nati<strong>on</strong>al University, Canberra, ACT, AUSTRALIA<br />

e-mail: Ge<str<strong>on</strong>g>of</str<strong>on</strong>g>f.Mercer@anu.edu.au<br />

Hea<str<strong>on</strong>g>th</str<strong>on</strong>g> Kelly<br />

Victorian Infectious Disease Reference Laboratory, Melbourne, Victoria,<br />

AUSTRALIA<br />

e-mail: Hea<str<strong>on</strong>g>th</str<strong>on</strong>g>.Kelly@mh.org.au<br />

Did seas<strong>on</strong>al influenza vaccinati<strong>on</strong> increase <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

pandemic influenza infecti<strong>on</strong>?<br />

Recent studies have suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>at vaccinati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> seas<strong>on</strong>al influenza vaccine<br />

resulted in an apparent higher risk <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> pandemic influenza H1N1 2009.<br />

A simple ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model incorporating strain competiti<strong>on</strong> and a hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esised<br />

temporary strain-transcending immunity is c<strong>on</strong>structed to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>is observati<strong>on</strong>.<br />

Results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model over a range <str<strong>on</strong>g>of</str<strong>on</strong>g> reproducti<strong>on</strong> numbers and effective vaccinati<strong>on</strong><br />

coverage c<strong>on</strong>firm <str<strong>on</strong>g>th</str<strong>on</strong>g>is apparent increased risk in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Nor<str<strong>on</strong>g>th</str<strong>on</strong>g>ern, but not <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Sou<str<strong>on</strong>g>th</str<strong>on</strong>g>ern, hemisphere. This is due to unvaccinated individuals being more likely to<br />

be infected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> seas<strong>on</strong>al influenza (if it is circulating) and developing hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esised<br />

temporary immunity to <str<strong>on</strong>g>th</str<strong>on</strong>g>e pandemic strain. Because vaccinated individuals are<br />

less likely to have been infected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> seas<strong>on</strong>al influenza, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are less likely to have<br />

developed <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esised temporary immunity and are <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore more likely to<br />

be infected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> pandemic influenza. If <str<strong>on</strong>g>th</str<strong>on</strong>g>e reproducti<strong>on</strong> number for pandemic influenza<br />

is increased, as it is for children, an increase in <str<strong>on</strong>g>th</str<strong>on</strong>g>e apparent risk <str<strong>on</strong>g>of</str<strong>on</strong>g> seas<strong>on</strong>al<br />

vaccinati<strong>on</strong> is observed. The maximum apparent risk effect is found when seas<strong>on</strong>al<br />

vaccinati<strong>on</strong> coverage is in <str<strong>on</strong>g>th</str<strong>on</strong>g>e range 20-40%<br />

Only when pandemic influenza is recently preceded by seas<strong>on</strong>al influenza circulati<strong>on</strong><br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>ere a modelled increased risk <str<strong>on</strong>g>of</str<strong>on</strong>g> pandemic influenza infecti<strong>on</strong> associated<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> prior receipt <str<strong>on</strong>g>of</str<strong>on</strong>g> seas<strong>on</strong>al vaccine.<br />

653

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

From <strong>on</strong>e to many: Cell-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective, emergent behaviors<br />

in biology -I; Tuesday, June 28, 11:00<br />

Roeland M. H. Merks<br />

Centrum Wiskunde & Informatica (Amsterdam, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands)<br />

Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands C<strong>on</strong>sortium for Systems Biology (Amsterdam, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands)<br />

e-mail: roeland.merks@cwi.nl<br />

Cell-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> plant tissues using VirtualLeaf<br />

Plant organs, including leaves and roots, develop by means <str<strong>on</strong>g>of</str<strong>on</strong>g> a complicated,<br />

multi-level cross-talk between gene regulati<strong>on</strong>, patterned cell divisi<strong>on</strong> and cell expansi<strong>on</strong>,<br />

and tissue mechanics. In c<strong>on</strong>trast to <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells in many animal tissues, plant<br />

cells cannot migrate and, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> very few excepti<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey cannot slide past each<br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>er. C<strong>on</strong>sequently, plant morphogenesis depends entirely <strong>on</strong> patterned cell divisi<strong>on</strong>,<br />

cell expansi<strong>on</strong>, and cell differentiati<strong>on</strong>. Thus plant development requires different<br />

cell-centered models <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>ose developed for animal development, in which<br />

cell migrati<strong>on</strong> and tissue folding play a primary role. We will present a cell-centered<br />

computer-modeling framework for plant tissue morphogenesis <str<strong>on</strong>g>th</str<strong>on</strong>g>at we named VirtualLeaf<br />

[1]. We will illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e current use <str<strong>on</strong>g>of</str<strong>on</strong>g> VirtualLeaf wi<str<strong>on</strong>g>th</str<strong>on</strong>g> examples <str<strong>on</strong>g>of</str<strong>on</strong>g> auxindriven<br />

vasculature development, determinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> leaf shape, and meristem grow<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

VirtualLeaf defines a set <str<strong>on</strong>g>of</str<strong>on</strong>g> biologically intuitive C++ objects, including cells, cell<br />

walls, and diffusing and reacting chemicals, <str<strong>on</strong>g>th</str<strong>on</strong>g>at provide useful abstracti<strong>on</strong>s for<br />

building biological simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> developmental processes. VirtualLeaf-based models<br />

provide a means for plant researchers to analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> developmental<br />

genes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e biophysics <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and patterning. VirtualLeaf is an<br />

<strong>on</strong>going open-source s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware project (http://virtualleaf.googlecode.com) <str<strong>on</strong>g>th</str<strong>on</strong>g>at runs<br />

<strong>on</strong> Windows, Mac, and Linux.<br />

References.<br />

[1] R. M. H. Merks, M. Guravage, D. Inzé, G.T.S. Beemster. VirtualLeaf: an Open Source framework<br />

for cell-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> plant tissue grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and development Plant Physiology 155<br />

656–666, 2011.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis II; Wednesday, June<br />

29, 11:00<br />

Roeland M. H. Merks<br />

Centrum Wiskunde & Informatica (Amsterdam, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands)<br />

Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands C<strong>on</strong>sortium for Systems Biology (Amsterdam, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands)<br />

e-mail: roeland.merks@cwi.nl<br />

Cell-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenic blood vessel sprouting:<br />

cell-ECM interacti<strong>on</strong> and tip-cell selecti<strong>on</strong><br />

Angiogenesis is a topic <str<strong>on</strong>g>of</str<strong>on</strong>g> intensive experimental investigati<strong>on</strong> so its phenomenology<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular signals c<strong>on</strong>tributing to it have been well characterized. Yet<br />

it is poorly understood how <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological comp<strong>on</strong>ents fit toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er dynamically to<br />

drive <str<strong>on</strong>g>th</str<strong>on</strong>g>e outgrow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> blood vessels. Cell-based simulati<strong>on</strong> models <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis<br />

describe endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cell behaviour in detail, help analyze how cells assemble into<br />

blood vessels, and reveal how cell behaviour depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microenvir<strong>on</strong>ment <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cells <str<strong>on</strong>g>th</str<strong>on</strong>g>emselves produce. Our previous simulati<strong>on</strong> models, based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Cellular<br />

Potts model, have shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e el<strong>on</strong>gated shape <str<strong>on</strong>g>of</str<strong>on</strong>g> endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells is key to<br />

correct spatiotemporal in silico replicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular network grow<str<strong>on</strong>g>th</str<strong>on</strong>g> [1]. We also<br />

identified a new stochastic mechanism for angiogenic sprouting [2]. Here I will<br />

briefly discuss new insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> cell shape and stochastic motility during<br />

vascular branching. Then I will present recent results <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> tip cells,<br />

suggesting <str<strong>on</strong>g>th</str<strong>on</strong>g>at tip cell-stalk cell interacti<strong>on</strong>s accelerate angiogenic sprouting. I<br />

will also discuss our recent cell-based modeling studies <str<strong>on</strong>g>of</str<strong>on</strong>g> cell-extracellular matrix<br />

interacti<strong>on</strong>s during angiogenesis.<br />

References.<br />

[1] Merks, R.M.H., Brodsky, S.V., Goligorsky, M.S., Glazier J.A. Cell el<strong>on</strong>gati<strong>on</strong> is key to in silico<br />

replicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> in vitro vasculogenesis and subsequent remodeling. Developmental Biology 289<br />

44–54, 2006.<br />

[2] Merks, R.M.H., E.D. Perryn, A. Shirinifard, Glazier J.A. C<strong>on</strong>tact-inhibited chemotaxis in de<br />

novo and sprouting blood-vessel grow<str<strong>on</strong>g>th</str<strong>on</strong>g> PLoS Computati<strong>on</strong>al Biology 4 e1000163, 2008.<br />

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Speciati<strong>on</strong>; Wednesday, June 29, 08:30<br />

Géza Meszéna<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Physics, Eötvös University, Budapest<br />

e-mail: geza.meszena@elte.hu<br />

András Szilágyi<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Plant tax<strong>on</strong>omy and Ecology, Eötvös University, Budapest<br />

Liz Pásztor<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Genatics, Eötvös University, Budapest<br />

Darwinian speciati<strong>on</strong> <strong>on</strong> a regulated landscape<br />

Darwin envisi<strong>on</strong>ed speciati<strong>on</strong> as a gradual transformati<strong>on</strong> from wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-species diversity<br />

to between species <strong>on</strong>e, driven by <str<strong>on</strong>g>th</str<strong>on</strong>g>e fitness-advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> reduced competiti<strong>on</strong><br />

via niche-segregati<strong>on</strong>. We identify <str<strong>on</strong>g>th</str<strong>on</strong>g>ree issues why Darwins suggesti<strong>on</strong> has been<br />

c<strong>on</strong>sidered problematic since <str<strong>on</strong>g>th</str<strong>on</strong>g>e New Syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis: I: The noti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> niche and reduced<br />

competiti<strong>on</strong> have no meaning in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> a rigid adaptive landscape.<br />

Instead, <strong>on</strong>e has to c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e landscape (i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e fitness functi<strong>on</strong>) as a functi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e phenotype-distributi<strong>on</strong> in a functi<strong>on</strong>al analytic c<strong>on</strong>text. The functi<strong>on</strong>al<br />

derivative <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is map is <str<strong>on</strong>g>th</str<strong>on</strong>g>e competiti<strong>on</strong> functi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e correct biological meaning.<br />

The adaptive dynamics phenomenology, including evoluti<strong>on</strong>ary branching, can<br />

be derived from <str<strong>on</strong>g>th</str<strong>on</strong>g>is setup. II: The observed <str<strong>on</strong>g>of</str<strong>on</strong>g>ten-allopatric nature <str<strong>on</strong>g>of</str<strong>on</strong>g> speciati<strong>on</strong><br />

seems to exclude a role for competiti<strong>on</strong>. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> structured populati<strong>on</strong>s<br />

allows c<strong>on</strong>sidering spatially distributed populati<strong>on</strong>s as a single populati<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an over-all fitness value. Therefore, we can define <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptive landscape <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e large spatial scale and apply <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>siderati<strong>on</strong>s above for allopatric and parapatric<br />

speciati<strong>on</strong> modes analogously to <str<strong>on</strong>g>th</str<strong>on</strong>g>e sympatric case. III: Biological species<br />

c<strong>on</strong>cept declared reproductive isolati<strong>on</strong> as <str<strong>on</strong>g>th</str<strong>on</strong>g>e defining issue <str<strong>on</strong>g>of</str<strong>on</strong>g> speciati<strong>on</strong>. In our<br />

picture emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> isolati<strong>on</strong> is sec<strong>on</strong>dary to ecological segregati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulated/changing<br />

landscape. As selecti<strong>on</strong> for ecological divergence is caused by a<br />

fitness minimum, it is always accompanied by a selecti<strong>on</strong> pressure for isolati<strong>on</strong>.<br />

Whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>is pressure results in an evoluti<strong>on</strong>ary buildup <str<strong>on</strong>g>of</str<strong>on</strong>g> reproductive isolati<strong>on</strong><br />

depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e availability and genetic organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e possible isolating mechanisms.<br />

C<strong>on</strong>sidering <str<strong>on</strong>g>th</str<strong>on</strong>g>ese <str<strong>on</strong>g>th</str<strong>on</strong>g>ree issues toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er leads us to c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at Darwins<br />

original idea is still <str<strong>on</strong>g>th</str<strong>on</strong>g>e most parsim<strong>on</strong>ious <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> speciati<strong>on</strong>. Species diversity is<br />

necessarily based <strong>on</strong> competiti<strong>on</strong>-reducing niche segregati<strong>on</strong>, i.e. segregati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>e way <str<strong>on</strong>g>of</str<strong>on</strong>g> being regulated. This structure translates to <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

regulated adaptive landscape, providing selecti<strong>on</strong> pressure for competiti<strong>on</strong>-reducing<br />

branching evoluti<strong>on</strong>, which may, or may not be related to spatial segregati<strong>on</strong>.<br />

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Fractals and Complexity I; Wednesday, June 29, 14:30<br />

K<strong>on</strong>radin Metze<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Sciences , University <str<strong>on</strong>g>of</str<strong>on</strong>g> Campinas, Campinas, Brazil<br />

e-mail: kmetze@fmc.unicamp.br<br />

Fractality <str<strong>on</strong>g>of</str<strong>on</strong>g> chromatin<br />

The extensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fractal c<strong>on</strong>cept towards biology and medicine has improved<br />

our understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong>al properties and <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> physiological phenomena<br />

in living organisms Fractals are very useful to characterize properly <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> tissues by describing relevant underlying design principles [1]. Fractality<br />

has evoluti<strong>on</strong>ary advantages. Structures wi<str<strong>on</strong>g>th</str<strong>on</strong>g> fractal features can be built<br />

by simple, iterative programs. Fractal banching is a simple and efficient way for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> complex c<strong>on</strong>necti<strong>on</strong>s resulting in short distances for transport.<br />

Fractal foldings <str<strong>on</strong>g>of</str<strong>on</strong>g> membranes permit to create a large surface area wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a very<br />

small volume. Power law organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> physiological systems increase <str<strong>on</strong>g>th</str<strong>on</strong>g>e capacity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> adaptati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment [1]. Therefore we<br />

can expect <str<strong>on</strong>g>th</str<strong>on</strong>g>at fractality can also be found in <str<strong>on</strong>g>th</str<strong>on</strong>g>e organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e genome and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e epigenome. Several investigators showed <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> self-similarity in DNA<br />

sequences. Experimental data support <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> a fractal organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chromatin.<br />

In intact interphase chicken ery<str<strong>on</strong>g>th</str<strong>on</strong>g>rocytes, spectra obtained by small angle<br />

neutr<strong>on</strong> scattering. revealed a c<strong>on</strong>stant fractal dimensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein comp<strong>on</strong>ent,<br />

and a biphasic DNA organizati<strong>on</strong>, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a fractal dimensi<strong>on</strong> <strong>on</strong> lower scales and a<br />

different <strong>on</strong>e <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e larger scales [2]. Fractal structures can be created in polymers<br />

by iterative processes for instance by repeated folding during c<strong>on</strong>densati<strong>on</strong>. Thus a<br />

polymer can be packed in a small volume wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out entanglements, facilitating rapid<br />

unravelling when necessary. Recent experiments suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is process applies<br />

also to chromatin leading to a genome organizati<strong>on</strong> in form <str<strong>on</strong>g>of</str<strong>on</strong>g> a spatial segregati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> open and closed chromatin wi<str<strong>on</strong>g>th</str<strong>on</strong>g> knot-free fractal globule formati<strong>on</strong>s[3]. All <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

studies support <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> a fractal nature <str<strong>on</strong>g>of</str<strong>on</strong>g> DNA, nuclear chromatin and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

surrounding nucleoplasmic space, i.e. a fractal organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nucleus. Morphologists,<br />

using light and electr<strong>on</strong> microscopy, are dem<strong>on</strong>strating indirect evidence<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e fractal organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chromatin for nearly two decades . They differentiate<br />

basically two distinct chromatin c<strong>on</strong>formati<strong>on</strong>s: <str<strong>on</strong>g>th</str<strong>on</strong>g>e unc<strong>on</strong>densed euchromatin and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e much denser and darker heterochromatin, which is usually c<strong>on</strong>sidered to be transcripti<strong>on</strong>ally<br />

less active. Alterati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nuclear architecture reflect genomic and<br />

n<strong>on</strong>-genomic changes, which are very comm<strong>on</strong> in tumor cells. Genomic changes may<br />

be point mutati<strong>on</strong>s translocati<strong>on</strong>s, or amplificati<strong>on</strong>s or alterati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e chromosomal<br />

positi<strong>on</strong>. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore malignant tumors show widespread epigenetic changes<br />

including global hypome<str<strong>on</strong>g>th</str<strong>on</strong>g>ylati<strong>on</strong>, as well as focal hyperme<str<strong>on</strong>g>th</str<strong>on</strong>g>ylati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple<br />

CpG island gene regulatory regi<strong>on</strong>s. Hypome<str<strong>on</strong>g>th</str<strong>on</strong>g>ylati<strong>on</strong> is associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> dec<strong>on</strong>densing<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e chromatin structure and induces chromosomal instability. A more<br />

aggressive behaviour is usually observed in genetically unstable neoplasias wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an<br />

increasing number <str<strong>on</strong>g>of</str<strong>on</strong>g> genetic or epigenetic changes. Therefore unstable tumors are<br />

expected to show a more complex chromatin rearrangement, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a mixture <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

many chromatin areas wi<str<strong>on</strong>g>th</str<strong>on</strong>g> varying density (lighter and darker), equivalent to a<br />

higher fractal dimensi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e computerized image analysis[1]. Clinico-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologic<br />

studies dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at an increased fractal dimensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chromatin at diagnosis<br />

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was an independent adverse prognostic factor for survival <str<strong>on</strong>g>of</str<strong>on</strong>g> patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different<br />

malignant neoplasias, such as multiple myeloma , squamous cell carcinoma <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

oral cavity squamous cell carcinoma <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e larynx , and malignant melanoma <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e skin [4-7]. Therefore we may c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e chromatin<br />

architecture in neoplastic cells may reveal important prognostic informati<strong>on</strong>. In<br />

summary, fractal characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nucleus are essential for its functi<strong>on</strong> and are<br />

reflected in its chromatin structure, which may accompany pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologic processes ,<br />

such as carcinogenesis and tumor progressi<strong>on</strong>.<br />

References.<br />

[1] Metze K. Fractal dimensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chromatin and cancer prognosis. Epigenomics,2: 601-604 (2010)<br />

[2] Lebedev DV, Filatov MV, Kuklin AI, Islamov AKh, Kentzinger E, Pantina R, Toperverg BP,<br />

Isaev-Ivanov VV: Fractal nature <str<strong>on</strong>g>of</str<strong>on</strong>g> chromatin organizati<strong>on</strong> in interphase chicken ery<str<strong>on</strong>g>th</str<strong>on</strong>g>rocyte<br />

nuclei: DNA structure exhibits biphasic fractal properties. FEBS Lett 579:1465-1468(2005).<br />

[3] Lieberman-Aiden E, Van Berkum NL, Williams L, Imakaev M, Ragoczy T, Telling A, Amit<br />

I, Lajoie BR, Sabo PJ, Dorschner MO, Sandstrom R, Bernstein B, Bender MA, Groudine M,<br />

Gnirke A, Stamatoyannopoulos J, Mirny LA, Lander ES, Dekker J: Comprehensive mapping<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g-range interacti<strong>on</strong>s reveals folding principles <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e human genome. Science 326: 289-<br />

293(2009).<br />

[4] Delides A, Panayiotides I, Alegakis A, Kyroudi A, Banis C, Pavlaki A, Helid<strong>on</strong>is E, Kittas C:<br />

Fractal dimensi<strong>on</strong> as a prognostic factor for laryngeal carcinoma. Anticancer Res (2005) 25,<br />

2141-2144 (2005).<br />

[5] Goutzanis L, Papadogeorgakis N, Pavlopoulos PM, Katti K, Petsinis V, Plochoras I, Pantelidaki<br />

C, Kavantzas N, Patsouris E, Alexandridis C: Nuclear fractal dimensi<strong>on</strong> as a prognostic<br />

factor in oral squamous cell carcinoma. Oral Oncol 44, 345-353(2008).<br />

[6] Metze K, Ferro DP, Falc<strong>on</strong>i MA, Adam RL, Ortega M, Lima CP, De Souza AC, Lorand-Metze<br />

I: Fractal characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> nuclear chromatin in routinely stained cytology are independent<br />

prognostic factors in patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multiple myeloma. Virchows Archiv 2009<br />

[7] Bedin V, Adam RL, de Sá BC, Landman G, Metze K : Fractal dimensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chromatin is an<br />

independent prognostic factor for survival in melanoma. BMC Cancer 10, 260 (2010) .<br />

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Bridging <str<strong>on</strong>g>th</str<strong>on</strong>g>e Divide: Cancer Models in Clinical Practice; Thursday, June 30,<br />

11:30<br />

Michael Meyer-Hermann<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Systems Immunology, Helmholtz Centre for Infecti<strong>on</strong><br />

Research<br />

e-mail: michael.meyer-hermann@helmholtz-hzi.de<br />

Harald Kempf<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Systems Immunology, Helmholtz Centre for Infecti<strong>on</strong><br />

Research<br />

Optimised cancer treatment using cell cycle synchr<strong>on</strong>isati<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> heavy i<strong>on</strong> irradiati<strong>on</strong><br />

Cancer is a leading cause <str<strong>on</strong>g>of</str<strong>on</strong>g> dea<str<strong>on</strong>g>th</str<strong>on</strong>g> worldwide. As a c<strong>on</strong>sequence a multitude <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

experimental and ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical studies <strong>on</strong> cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and a diversity <str<strong>on</strong>g>of</str<strong>on</strong>g> treatments<br />

are being developed. Am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>ese is tumour irradiati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> heavy i<strong>on</strong>s.<br />

While <str<strong>on</strong>g>th</str<strong>on</strong>g>is novel me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology was restricted to research institutes for a l<strong>on</strong>g time,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is treatment became a full part <str<strong>on</strong>g>of</str<strong>on</strong>g> clinical reality now.<br />

We present an agent-based approach to <str<strong>on</strong>g>th</str<strong>on</strong>g>e modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular dynamics<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in tumour spheroids <str<strong>on</strong>g>th</str<strong>on</strong>g>at is based <strong>on</strong> experimentally accessible parameters and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>us is able to take advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> experimental data from irradiati<strong>on</strong> experiments.<br />

As <str<strong>on</strong>g>th</str<strong>on</strong>g>e model architecture is lattice-free and average-free, it can be c<strong>on</strong>sidered to<br />

be a realistic representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tumours. The model grows a tumour from a single<br />

malignant cell and <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in resp<strong>on</strong>se to irradiati<strong>on</strong> protocols<br />

can be tracked. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is single cell based we are able to provide an<br />

in dep<str<strong>on</strong>g>th</str<strong>on</strong>g> analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> all possible observables ranging from <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell cycle phase, pressure<br />

inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e spheroid, nutrient supply and limitati<strong>on</strong>s, up to genetic expressi<strong>on</strong><br />

pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles for <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular network. Target <str<strong>on</strong>g>of</str<strong>on</strong>g> our study is a detailed examinati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical reacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tumours to heavy-i<strong>on</strong> irradiati<strong>on</strong> treatment.<br />

It is found <str<strong>on</strong>g>th</str<strong>on</strong>g>at irradiati<strong>on</strong> treatment induces a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamical reacti<strong>on</strong>s<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a tumour. Reoxygenati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour volume and a decrease in pressure<br />

due to cell dea<str<strong>on</strong>g>th</str<strong>on</strong>g> lead to excessive regrow<str<strong>on</strong>g>th</str<strong>on</strong>g> after irradiati<strong>on</strong>. As expected fracti<strong>on</strong>ati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e radiati<strong>on</strong> dose changes <str<strong>on</strong>g>th</str<strong>on</strong>g>e degree <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour c<strong>on</strong>trol c<strong>on</strong>siderably<br />

depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e applied fracti<strong>on</strong>ati<strong>on</strong> scheme. A pr<strong>on</strong>ounced resynchr<strong>on</strong>isati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell cycle wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour after irradiati<strong>on</strong> is found which could be exploited<br />

in order to administer follow-up treatments in accordance to <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell’s most<br />

radiosensitive phases. This result has direct implicati<strong>on</strong>s for experimental studies<br />

and eventually for clinical trials.<br />

659

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

C<strong>on</strong>necting microscale and macroscale models <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular migrati<strong>on</strong>;<br />

Tuesday, June 28, 17:00<br />

Alistair Middlet<strong>on</strong><br />

Center for Biological Systems Analysis, Albert-Ludwigs-Universität<br />

Freiburg i.Br., Habsburgerstraße 49 79104 Freiburg i.Br.<br />

e-mail: alistair.middlet<strong>on</strong>@zbsa.de<br />

Christian Fleck<br />

Center for Biological Systems Analysis, Albert-Ludwigs-Universität<br />

Freiburg i.Br., Habsburgerstraße 49 79104 Freiburg i.Br.<br />

e-mail: Christian.Fleck@fdm.uni-freiburg.de<br />

Ram<strong>on</strong> Grima<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Edinburgh, School <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Sciences, C.H.<br />

Waddingt<strong>on</strong> Building, Room 3.03, King’s Buildings Campus, Mayfield<br />

Road, Edinburgh, Scotland<br />

e-mail: Ram<strong>on</strong>.Grima@ed.ac.uk<br />

From particles to PDEs: c<strong>on</strong>tinuum approximati<strong>on</strong>s to<br />

models <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular migrati<strong>on</strong><br />

Cell migrati<strong>on</strong> is a fundamental process in biology. Examples range from <str<strong>on</strong>g>th</str<strong>on</strong>g>e development<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> multi-cellular organisms, <str<strong>on</strong>g>th</str<strong>on</strong>g>rough to <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> complex spatial<br />

patterns in bacterial populati<strong>on</strong>s. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> cell migrati<strong>on</strong> can help<br />

increase our understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying biology. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e models <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

capture <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular scale interacti<strong>on</strong>s are typically ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er complex and can be<br />

difficult to analyze. Here, we explore <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem by developing a model based <strong>on</strong><br />

Langevin dynamics, whereby short-range intercellular interacti<strong>on</strong>s are represented<br />

using an appropriate potential functi<strong>on</strong>. Following Newman and Grima (2004),<br />

we obtain a mean field approximati<strong>on</strong> to our model, <str<strong>on</strong>g>th</str<strong>on</strong>g>is being an integro-partial<br />

differential equati<strong>on</strong>. By exploiting <str<strong>on</strong>g>th</str<strong>on</strong>g>e biologically plausible limit <str<strong>on</strong>g>of</str<strong>on</strong>g> intercellular<br />

interacti<strong>on</strong>s occurring <strong>on</strong> infinitesimally small leng<str<strong>on</strong>g>th</str<strong>on</strong>g> scales, we derive a system<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> partial differential equati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at can approximate <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean-field behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e original Langevin model and and is amenable to analysis. We will show how<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular scale details (represented by our choice <str<strong>on</strong>g>of</str<strong>on</strong>g> interacti<strong>on</strong> potential) are<br />

reflected in <str<strong>on</strong>g>th</str<strong>on</strong>g>e PDE approximati<strong>on</strong>. An analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting patterns will<br />

be given. Relevant applicati<strong>on</strong>s, such as cell-sorting and chemotaxis, will also be<br />

discussed.<br />

660

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Delay Differential Equati<strong>on</strong>s and Applicati<strong>on</strong>s I; Friday, July 1, 14:30<br />

Jacek Miekisz<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw<br />

e-mail: miekisz@mimuw.edu.pl<br />

Delayed protein degradati<strong>on</strong> does not cause oscillati<strong>on</strong>s<br />

It is well known <str<strong>on</strong>g>th</str<strong>on</strong>g>at time delays may cause oscillati<strong>on</strong>s in soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary<br />

differential equati<strong>on</strong>s. We would like to point out <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> oscillati<strong>on</strong>s<br />

depends <strong>on</strong> particular causes <str<strong>on</strong>g>of</str<strong>on</strong>g> a time delay.<br />

Models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> time delays may be divided into two families [1,2]. In socialtype<br />

models, where individuals react to <str<strong>on</strong>g>th</str<strong>on</strong>g>e informati<strong>on</strong> c<strong>on</strong>cerning <str<strong>on</strong>g>th</str<strong>on</strong>g>e state <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

populati<strong>on</strong> at some earlier time, we should expect oscillati<strong>on</strong>s. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand,<br />

in biological-type models, where some changes already take place in <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong><br />

at an earlier time, oscillati<strong>on</strong>s might not be present for any time delay. We will<br />

briefly review two specific examples <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary games - replicator dynamics<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> time delay [1].<br />

Our main goal is to show <str<strong>on</strong>g>th</str<strong>on</strong>g>at delayed degradati<strong>on</strong> does not cause oscillati<strong>on</strong>s<br />

as it was recently argued [3]. To do so we propose a new me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology to deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

time delays in biological systems and apply it to simple models <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> delayed degradati<strong>on</strong> [4].<br />

We develop a systematic analytical treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic models <str<strong>on</strong>g>of</str<strong>on</strong>g> time delays.<br />

Specifically, we take into account <str<strong>on</strong>g>th</str<strong>on</strong>g>at some reacti<strong>on</strong>s, for example degradati<strong>on</strong>,<br />

are c<strong>on</strong>suming, <str<strong>on</strong>g>th</str<strong>on</strong>g>at is <strong>on</strong>ce molecules start to degrade <str<strong>on</strong>g>th</str<strong>on</strong>g>ey cannot be part in<br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>er degradati<strong>on</strong> processes. It follows from our rigorous analysis <str<strong>on</strong>g>th</str<strong>on</strong>g>at <strong>on</strong>e should<br />

look for different mechanisms <str<strong>on</strong>g>th</str<strong>on</strong>g>an just delayed protein degradati<strong>on</strong> to explain<br />

causes <str<strong>on</strong>g>of</str<strong>on</strong>g> oscillati<strong>on</strong>s observed in certain biological experiments.<br />

References.<br />

[1] J. Alboszta and J. Miekisz, Stability <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>arily stable strategies in discrete replicator<br />

dynamics wi<str<strong>on</strong>g>th</str<strong>on</strong>g> time delay, J. Theor. Biol. 231: 175-179 (2004).<br />

[2] J. Miekisz, Evoluti<strong>on</strong>ary game <str<strong>on</strong>g>th</str<strong>on</strong>g>eory and populati<strong>on</strong> dynamics, Lecture Notes in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

1940: 269-316 (2008).<br />

[3] D. Bratsun, D. Volfs<strong>on</strong>, L. S. Tsimring, and J. Hasty, Delay-induced stochastic oscillati<strong>on</strong>s in<br />

gene regulati<strong>on</strong>, Proc. Natl. Acad. Sci. USA 102: 14593-14598 (2005).<br />

[4] J. Miekisz, J. Poleszczuk, M. Bodnar, and U. Forys, Stochastic models <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

delayed degradati<strong>on</strong>, Bull. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. DOI 10.1007/s11538-010-9622-4 (2011).<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling IV; Saturday, July 2, 08:30<br />

Jacek Miekisz<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw<br />

e-mail: miekisz@mimuw.edu.pl<br />

Simple stochastic models <str<strong>on</strong>g>of</str<strong>on</strong>g> gene regulati<strong>on</strong><br />

We will discuss simple models <str<strong>on</strong>g>of</str<strong>on</strong>g> gene regulati<strong>on</strong>. We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> mRNA and protein molecules is small and <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore to describe biochemical<br />

processes <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong>, translati<strong>on</strong>, and degradati<strong>on</strong>, we use bir<str<strong>on</strong>g>th</str<strong>on</strong>g> and dea<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

processes. We linearize Hill functi<strong>on</strong>s which describe regulati<strong>on</strong>, use <str<strong>on</strong>g>th</str<strong>on</strong>g>e generating<br />

functi<strong>on</strong> approach to <str<strong>on</strong>g>th</str<strong>on</strong>g>e Masters equati<strong>on</strong>s, and show <str<strong>on</strong>g>th</str<strong>on</strong>g>at translati<strong>on</strong>al repressi<strong>on</strong><br />

c<strong>on</strong>tributes greater noise to gene expressi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>an transcripti<strong>on</strong>al repressi<strong>on</strong> [1].<br />

Our main goal now is to derive analytical expressi<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e variance (noise)<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> protein molecules in models where changes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e DNA state<br />

between an active and inactive <strong>on</strong>e are governed by bir<str<strong>on</strong>g>th</str<strong>on</strong>g> and dea<str<strong>on</strong>g>th</str<strong>on</strong>g> processes<br />

whose intensities depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> protein molecules [2]. We will discuss<br />

different approaches to <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> closure <str<strong>on</strong>g>of</str<strong>on</strong>g> an infinite chain <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s for<br />

moments <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein probability distributi<strong>on</strong> and apply it to systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two<br />

gene copies [3].<br />

References.<br />

[1] M. Komorowski, J. Miekisz, and A. M. Kierzek, Translati<strong>on</strong>al repressi<strong>on</strong> c<strong>on</strong>tributes greater<br />

noise to gene expressi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>an transcripti<strong>on</strong>al repressi<strong>on</strong>, Biophysical Journal 96: 372384 (2009).<br />

[2] J. E. M. Hornos, D. Schultz, G. C. P. Innocentini, J. Wang, A. M. Walczak, J. N. Onuchic,<br />

and P. G. Wolynes, Self-regulating gene: an exact soluti<strong>on</strong>. Phys. Rev. E 72: 51907 (2005).<br />

[3] J. Miekisz and P. Szymanska, work in progress.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Recent developments in <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> Lotka-Volterra and Kolmogorov<br />

systems; Saturday, July 2, 14:30<br />

Janusz Mierczyński<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science, Wrocław University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: mierczyn@pwr.wroc.pl<br />

Permanence for Kolmogorov competitive systems <str<strong>on</strong>g>of</str<strong>on</strong>g> PDEs<br />

This talk is about recent results <strong>on</strong> permanence for Kolmogorov reacti<strong>on</strong>–diffusi<strong>on</strong><br />

systems <str<strong>on</strong>g>of</str<strong>on</strong>g> partial differential equati<strong>on</strong>s (PDE)<br />

∂ui<br />

∂t = ∆ui + fi(t, x, u1, . . . , uN)ui, 1 ≤ i ≤ N, t ∈ [0, ∞), x ∈ Ω.<br />

Here ui(t, x) measures <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> density <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e i-<str<strong>on</strong>g>th</str<strong>on</strong>g> species at time t and spatial<br />

locati<strong>on</strong> x, and Ω is a bounded habitat. The system is endowed wi<str<strong>on</strong>g>th</str<strong>on</strong>g> appropriate<br />

boundary c<strong>on</strong>diti<strong>on</strong>s.<br />

Systems are assumed to be competitive, which means <str<strong>on</strong>g>th</str<strong>on</strong>g>at ∂fi/∂uj ≤ 0 for<br />

1 ≤ i, j ≤ N, i = j (usually much more will be assumed).<br />

Permanence (sometimes called uniform persistence) means <str<strong>on</strong>g>th</str<strong>on</strong>g>at any positive<br />

soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system becomes bounded away from zero, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e ultimate bound<br />

is independent <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong>.<br />

We will give a survey <str<strong>on</strong>g>of</str<strong>on</strong>g> results <strong>on</strong> permanence for Kolmogorov competitive<br />

systems <str<strong>on</strong>g>of</str<strong>on</strong>g> PDEs, in particular wi<str<strong>on</strong>g>th</str<strong>on</strong>g> general dependence <strong>on</strong> time. Especially, c<strong>on</strong>necti<strong>on</strong>s<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> invasibility will be addressed.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis I; Wednesday, June 29,<br />

08:30<br />

Florian Milde<br />

Chair <str<strong>on</strong>g>of</str<strong>on</strong>g> Computati<strong>on</strong>al Science, ETH Zurich<br />

e-mail: mildef@e<str<strong>on</strong>g>th</str<strong>on</strong>g>z.ch<br />

Petros Koumoutsakos<br />

Chair <str<strong>on</strong>g>of</str<strong>on</strong>g> Computati<strong>on</strong>al Science, ETH Zurich<br />

e-mail: petros@e<str<strong>on</strong>g>th</str<strong>on</strong>g>z.ch<br />

Image Driven Computati<strong>on</strong>al models <str<strong>on</strong>g>of</str<strong>on</strong>g> Cell migrati<strong>on</strong><br />

Cell migrati<strong>on</strong> has been identified as <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fundamental mechanisms driving<br />

embryogenesis, organ development, angiogenesis and tumor invasi<strong>on</strong>. We develop<br />

computati<strong>on</strong>al models <str<strong>on</strong>g>of</str<strong>on</strong>g> cell migrati<strong>on</strong> and tissue infiltrati<strong>on</strong> to assist related experimental<br />

studies. C<strong>on</strong>tinuum models are developed to capture migrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell<br />

agglomerates at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue level resoluti<strong>on</strong> and a discrete particle model enables for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e explorati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell migrati<strong>on</strong> <strong>on</strong> a cellular scale.<br />

The models are validated against a set <str<strong>on</strong>g>of</str<strong>on</strong>g> in-vitro and in-vivo model systems.<br />

In order to facilitate <str<strong>on</strong>g>th</str<strong>on</strong>g>e validati<strong>on</strong> process, we develop a set <str<strong>on</strong>g>of</str<strong>on</strong>g> computati<strong>on</strong>al tools<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at allow for <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> relevant statistical metrics <strong>on</strong> biological experiments.<br />

Curvelet based image rec<strong>on</strong>structi<strong>on</strong> is used for vessel network and cell membrane<br />

segmentati<strong>on</strong> and Particle Image Velocimetry (PIV) <strong>on</strong> in-vitro experiments to<br />

register mass transport in migrating cell layers. We combine <str<strong>on</strong>g>th</str<strong>on</strong>g>ese me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods and<br />

present a robust algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m for in-vitro cell shape tracking <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple cells.<br />

References.<br />

[1] F. Milde, M. Bergdorf, and P. Koumoutsakos, Particle simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g>: Applicati<strong>on</strong> to<br />

angiogenesis Modeling Tumor Vasculature: Molecular, Cellular, and Tissue Level Aspects and<br />

Implicati<strong>on</strong>s. in press.<br />

[2] P. Koumoutsakos, B. Bayati, F. Milde, G. Tauriello, Particle Simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Morphogenesis<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Model Me<str<strong>on</strong>g>th</str<strong>on</strong>g> Appl Sci. accepted.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Judi<str<strong>on</strong>g>th</str<strong>on</strong>g> Miller<br />

Georgetown University<br />

e-mail: jrm32@georgetown.edu<br />

Evoluti<strong>on</strong>ary Ecology; Friday, July 1, 14:30<br />

Bey<strong>on</strong>d mutati<strong>on</strong> surfing: adaptati<strong>on</strong> during invasi<strong>on</strong>s<br />

We use stochastic simulati<strong>on</strong>s to model invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> new territory by a populati<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at evolves by natural selecti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e novel envir<strong>on</strong>ment, as well as by drift.<br />

Previous studies have resulted in competing claims to <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e process<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> invasi<strong>on</strong> may ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er promote or inhibit adaptati<strong>on</strong>. By comparing adaptati<strong>on</strong> in<br />

invading and established populati<strong>on</strong>s, we identify c<strong>on</strong>diti<strong>on</strong>s under which invasi<strong>on</strong><br />

facilitates adaptati<strong>on</strong> (when compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g> evoluti<strong>on</strong> in an established populati<strong>on</strong>),<br />

as well as regimes in which invasi<strong>on</strong> impedes adaptati<strong>on</strong>. We also discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e extent<br />

to which analytical models can provide insight <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Harriet Mills<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bristol<br />

e-mail: harriet.mills@bris.ac.uk<br />

Caroline Colijn<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bristol<br />

Ayalvadi Ganesh<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Bristol<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen spread <strong>on</strong> coupled networks: effect <str<strong>on</strong>g>of</str<strong>on</strong>g> host and<br />

network properties <strong>on</strong> transmissi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>resholds<br />

In recent years network models have been extensively used to study how spreading<br />

dynamics in human populati<strong>on</strong>s, such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> an infectious disease, a rumour<br />

or even a behaviour, depend <strong>on</strong> how individuals are c<strong>on</strong>nected to each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er.<br />

Real populati<strong>on</strong>s are c<strong>on</strong>nected via a large variety <str<strong>on</strong>g>of</str<strong>on</strong>g> networks; respiratory, sexual<br />

or <strong>on</strong>line social networks to name just a few. These networks, <str<strong>on</strong>g>th</str<strong>on</strong>g>ough generally<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> very difference structure, are not always independent and interacti<strong>on</strong>s <strong>on</strong> <strong>on</strong>e<br />

may influence interacti<strong>on</strong>s <strong>on</strong> ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er. For example, HIV is spread over a sexual<br />

network and TB over a respiratory network, infecti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> HIV raises <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

progressing from latent to active TB, potentially increasing transmissi<strong>on</strong> rates <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

TB across <str<strong>on</strong>g>th</str<strong>on</strong>g>e respiratory network. Here we develop <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory behind network<br />

models. First we c<strong>on</strong>sider two processes spreading <strong>on</strong> two distinct networks. Process<br />

B spreads <strong>on</strong>ly over network b, but process A spreads over bo<str<strong>on</strong>g>th</str<strong>on</strong>g> networks,<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a reduced transmissi<strong>on</strong> rate over network b. We examine how <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

transmissi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> process A over network b affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic, and find <str<strong>on</strong>g>th</str<strong>on</strong>g>at even a<br />

small amount <str<strong>on</strong>g>of</str<strong>on</strong>g> transmissi<strong>on</strong> across ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er network can greatly influence <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic<br />

size. Sec<strong>on</strong>dly, we c<strong>on</strong>sider how different host types in <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> affect<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold <str<strong>on</strong>g>of</str<strong>on</strong>g> a disease over <strong>on</strong>e network. We apply <str<strong>on</strong>g>th</str<strong>on</strong>g>ese frameworks<br />

to our motivating example <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV and TB.<br />

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Fractals and Complexity II; Wednesday, June 29, 17:00<br />

Nebojsa Milosevic<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biophysics, Medical faculty, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Belgrade,<br />

Serbia<br />

e-mail: mtn@med.bg.ac.rs<br />

Dusan Ristanovic<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biophysics, Medical faculty, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Belgrade<br />

Katarina Rajkovic<br />

Laboratory for Medical Imaging, Medical faculty, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Belgrade<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> box-counting analysis in <str<strong>on</strong>g>th</str<strong>on</strong>g>e human<br />

dentate nucleus during development<br />

Many disorders <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cerebellum may be developmental in origin. In order to<br />

recognize impaired development and better to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e etiology <str<strong>on</strong>g>of</str<strong>on</strong>g> various<br />

neurological disturbances <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cerebellum, a precise timetable <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular events<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at take place during normal development is needed. Therefore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e binary and<br />

skelet<strong>on</strong>ized two dimensi<strong>on</strong>al neur<strong>on</strong>al images <str<strong>on</strong>g>of</str<strong>on</strong>g> Golgi impregnated secti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

human dentate nucleus at various gestati<strong>on</strong>al periods were subjected to fractal<br />

analysis in order to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e morphology <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cells during development.<br />

Since <str<strong>on</strong>g>th</str<strong>on</strong>g>e results showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at bo<str<strong>on</strong>g>th</str<strong>on</strong>g> parameters increased during gestati<strong>on</strong>, a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model which quantitatively describes changes in morphology <str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>s<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e human dentate nucleus during development is proposed. While <str<strong>on</strong>g>th</str<strong>on</strong>g>e binary<br />

fractal dimensi<strong>on</strong> linearly increased wi<str<strong>on</strong>g>th</str<strong>on</strong>g> gestati<strong>on</strong>al time, <str<strong>on</strong>g>th</str<strong>on</strong>g>e skelet<strong>on</strong>ized fractal<br />

dimensi<strong>on</strong> increased wi<str<strong>on</strong>g>th</str<strong>on</strong>g> time exp<strong>on</strong>entially. The findings <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e present study are<br />

generally in accordance wi<str<strong>on</strong>g>th</str<strong>on</strong>g> previous qualitative data and provide better understanding<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e neur<strong>on</strong>al circuitry <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e human dentate nucleus.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Structure and Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemical Reacti<strong>on</strong> Networks II; Tuesday, June<br />

28, 17:00<br />

Maya Mincheva<br />

Nor<str<strong>on</strong>g>th</str<strong>on</strong>g>ern Illinois University<br />

e-mail: mincheva@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.niu..edu<br />

Oscillati<strong>on</strong>s in Biochemical Reacti<strong>on</strong> Networks<br />

Understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> interacti<strong>on</strong>s in complex biochemical networks is an<br />

important problem in modern biology. Biochemical reacti<strong>on</strong> networks are modeled<br />

by large n<strong>on</strong>linear dynamical systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> many unknown kinetic parameters,<br />

which complicates <str<strong>on</strong>g>th</str<strong>on</strong>g>eir numerical analysis. Important properties, such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a biochemical reacti<strong>on</strong> network to oscillate can be determined by <str<strong>on</strong>g>th</str<strong>on</strong>g>e network’s<br />

structure. We will discuss a new graph-<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretic c<strong>on</strong>diti<strong>on</strong> which includes<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e negative cycle c<strong>on</strong>diti<strong>on</strong> for oscillati<strong>on</strong>s as a special case.<br />

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Recent advances in infectious disease modelling I; Saturday, July 2, 11:00<br />

Rachelle Mir<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Ottawa<br />

e-mail: rachelle_mir<strong>on</strong>@hotmail.com<br />

Impulsive differential equati<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir applicati<strong>on</strong> to<br />

disease modelling<br />

Many evoluti<strong>on</strong>ary processes are characterized by <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at at certain moments<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> time <str<strong>on</strong>g>th</str<strong>on</strong>g>ey experience a change <str<strong>on</strong>g>of</str<strong>on</strong>g> state abruptly. These processes are subject<br />

to short-term perturbati<strong>on</strong>s which act instantaneously; <str<strong>on</strong>g>th</str<strong>on</strong>g>at is, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> impulses.<br />

Thus, impulsive differential equati<strong>on</strong>s - differential equati<strong>on</strong>s involving impulse<br />

effects - appear as a natural descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> observed evoluti<strong>on</strong> phenomena <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

several real-world problems. We will discuss how to solve linear homogeneous and<br />

n<strong>on</strong>-homogeneous impulsive differential equati<strong>on</strong>s as well as n<strong>on</strong>-linear aut<strong>on</strong>omous<br />

impulsive differential equati<strong>on</strong>s. We will also give an overview <str<strong>on</strong>g>of</str<strong>on</strong>g> existence and<br />

uniqueness <str<strong>on</strong>g>of</str<strong>on</strong>g> impulsive systems as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e issues <str<strong>on</strong>g>th</str<strong>on</strong>g>at arise wi<str<strong>on</strong>g>th</str<strong>on</strong>g> stability. We<br />

illustrate using a model for HIV drug <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy.<br />

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Developmental Biology; Thursday, June 30, 11:30<br />

Victoria Mir<strong>on</strong>ova<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> cytology and genetics, Novosibirsk, Russia<br />

e-mail: kviki@bi<strong>on</strong>et.nsc.ru<br />

Ekaterina Novoselova<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> cytology and genetics, Novosibirsk, Russia<br />

Nadya Omelyanchuk<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> cytology and genetics, Novosibirsk, Russia<br />

Vitaly Likhoshvai<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> cytology and genetics, Novosibirsk, Russia<br />

The combined mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reverse fountain and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

reflected flow provide for self-organizati<strong>on</strong> and maintenance<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e root apical meristem<br />

The phytohorm<strong>on</strong>e auxin is critical for patterning and morphogenesis in plants.<br />

In plant roots, auxin maxima coincide wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sites <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e root apical meristem<br />

(RAM) initiati<strong>on</strong> and functi<strong>on</strong>ing. By today, <str<strong>on</strong>g>th</str<strong>on</strong>g>e two main mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

auxin distributi<strong>on</strong> formati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e root tip were proposed. The reverse fountain<br />

mechanism is based <strong>on</strong> a specific RAM structure in which each cell has a specified<br />

set <str<strong>on</strong>g>of</str<strong>on</strong>g> directi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin efflux. A stable locati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e auxin maximum in silico<br />

is provided for by a reflux <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin from <str<strong>on</strong>g>th</str<strong>on</strong>g>e basipetal flow back to <str<strong>on</strong>g>th</str<strong>on</strong>g>e acropetal<br />

flow all al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e meristem, which transports auxin in a loop. The reflected flow<br />

mechanism is based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e auxin-dependent regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin acropetal flow: low<br />

auxin c<strong>on</strong>centrati<strong>on</strong>s activate <str<strong>on</strong>g>th</str<strong>on</strong>g>e transcripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> PIN1 genes, whereas <str<strong>on</strong>g>th</str<strong>on</strong>g>e high<br />

c<strong>on</strong>centrati<strong>on</strong>s induce degradati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> PIN1 proteins [2]. The mechanism explains<br />

self-organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e auxin distributi<strong>on</strong> pattern in an array <str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong>ally identical<br />

cells acquiring cell type specializati<strong>on</strong> due to auxin regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e level<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> PIN1 proteins in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cells. We suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e reverse fountain and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

reflected flow mechanisms are complementary in root development. In particular,<br />

<strong>on</strong>ly <str<strong>on</strong>g>th</str<strong>on</strong>g>e reflected flow mechanism operates at <str<strong>on</strong>g>th</str<strong>on</strong>g>e very early stages <str<strong>on</strong>g>of</str<strong>on</strong>g> root<br />

development. At later developmental stages, an anatomical structure forms and<br />

provides for <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong>ing <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reverse fountain mechanism <str<strong>on</strong>g>th</str<strong>on</strong>g>at serve for more<br />

robust maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e auxin maximum in <str<strong>on</strong>g>th</str<strong>on</strong>g>e RAM. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e reflected<br />

flow mechanism does not disappear, revealing itself if RAM structure is disrupted<br />

or <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment changes. To test <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis we combined bo<str<strong>on</strong>g>th</str<strong>on</strong>g> mechanisms<br />

in 2D ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model. This model describes (1) auxin flow from <str<strong>on</strong>g>th</str<strong>on</strong>g>e shoot; (2)<br />

auxin syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at is positively regulated by auxin itself; (3) irreversible loss <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

auxin (degradati<strong>on</strong>); (4) auxin diffusi<strong>on</strong>, providing for an isotropic distributi<strong>on</strong> in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e root; syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis and degradati<strong>on</strong> depending <strong>on</strong> auxin c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> (5) PIN1,<br />

(6) PIN2, (7) PIN3; (8) active auxin transport mediating by PINs proteins; (9)<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> root cells. Two cell types are c<strong>on</strong>sidered in <str<strong>on</strong>g>th</str<strong>on</strong>g>e 2D model:<br />

central cylinder and epidermis. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e central cylinder cells <str<strong>on</strong>g>th</str<strong>on</strong>g>e processes (1-5,7-9)<br />

are c<strong>on</strong>sidered and described as in [2]. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidermal cells <str<strong>on</strong>g>th</str<strong>on</strong>g>e processes (2-<br />

4,6-9) are c<strong>on</strong>sidered. As auxin transporters carry out different, <str<strong>on</strong>g>of</str<strong>on</strong>g>ten redundant,<br />

functi<strong>on</strong>s in specialized tissues, we introduced to <str<strong>on</strong>g>th</str<strong>on</strong>g>e model some simplificati<strong>on</strong>s.<br />

Only <str<strong>on</strong>g>th</str<strong>on</strong>g>ree auxin carriers are c<strong>on</strong>sidered: PIN1 transports auxin acropetally, PIN2<br />

mediates basipetal auxin flow as well as lateral transport from basipetal back to<br />

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acropetal flow, PIN3 regulates auxin redistributi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e root cap. Thus, PIN proteins<br />

have <str<strong>on</strong>g>th</str<strong>on</strong>g>e following locati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells: PIN1 is localized at <str<strong>on</strong>g>th</str<strong>on</strong>g>e basal side <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e central cylinder cells, PIN2 at <str<strong>on</strong>g>th</str<strong>on</strong>g>e lateral internal and apical sides <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidermal<br />

cells and PIN3 at all sides <str<strong>on</strong>g>of</str<strong>on</strong>g> potentially all cells. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e processes (1,3-5,8-9)<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter values were taken from [2]. O<str<strong>on</strong>g>th</str<strong>on</strong>g>er parameters were estimated so<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at: (1) PIN2 is expressed predominantly in epidermal cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> low auxin level;<br />

(2) PIN3 expressi<strong>on</strong> domain is localized in <str<strong>on</strong>g>th</str<strong>on</strong>g>e z<strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> high auxin level; (3) auxin<br />

syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis rates are high in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high auxin level. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is set <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters<br />

and initial uniform auxin distributi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model provides steady-state auxin<br />

distributi<strong>on</strong> pattern <str<strong>on</strong>g>th</str<strong>on</strong>g>at agree well wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental data. The mechanism<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> auxin distributi<strong>on</strong> self-organizati<strong>on</strong> found in <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting stati<strong>on</strong>ary soluti<strong>on</strong>s is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e following. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e first step, auxin maximum is generated in <str<strong>on</strong>g>th</str<strong>on</strong>g>e central cylinder<br />

cell array at <str<strong>on</strong>g>th</str<strong>on</strong>g>e distance from <str<strong>on</strong>g>th</str<strong>on</strong>g>e root end under <str<strong>on</strong>g>th</str<strong>on</strong>g>e reflected flow mechanism. As<br />

a result, <str<strong>on</strong>g>th</str<strong>on</strong>g>e z<strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> high auxin level in <str<strong>on</strong>g>th</str<strong>on</strong>g>e root tip is organized where PIN3 and<br />

auxin syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis rate are high. Sec<strong>on</strong>d, <str<strong>on</strong>g>th</str<strong>on</strong>g>e PIN3-mediated auxin redistributi<strong>on</strong> is<br />

switched <strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e root tip, and auxin moves to PIN2-mediated basipetal flow in<br />

epidermis. Third, As PIN2 is localized <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lateral internal cell sides in epidermis,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e reflux <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin from <str<strong>on</strong>g>th</str<strong>on</strong>g>e basipetal flow back to <str<strong>on</strong>g>th</str<strong>on</strong>g>e acropetal flow starts to<br />

work. Finally, <str<strong>on</strong>g>th</str<strong>on</strong>g>e auxin gradient associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximum is formed under <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

reverse fountain mechanism which finishes formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin distributi<strong>on</strong> pattern.<br />

In numerical experiments we showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e 2D model reveals bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e robustness<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e developmental processes from <str<strong>on</strong>g>th</str<strong>on</strong>g>e reverse fountain mechanism [1] and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e plasticity to <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment changes from <str<strong>on</strong>g>th</str<strong>on</strong>g>e reflected flow mechanism [2].<br />

Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese advantages <str<strong>on</strong>g>th</str<strong>on</strong>g>e 2D model gave new predicti<strong>on</strong>s about <str<strong>on</strong>g>th</str<strong>on</strong>g>e positi<strong>on</strong>al<br />

informati<strong>on</strong> in root patterning <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be checked in <str<strong>on</strong>g>th</str<strong>on</strong>g>e experiments. The 2D<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin distributi<strong>on</strong> in root can be a powerful tool for investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> root<br />

development in silico.<br />

The work was partially supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e RAS programs A.II.5.26, A.II.6.8,<br />

B.27.29, SB RAS 107, 119, and RFBR 10-01-00717-,11-04-01254-.<br />

1. Grieneisen VA, Xu J, Marée AF, Hogeweg P, Scheres B: Auxin transport<br />

is sufficient to generate a maximum and gradient guiding root grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. Nature<br />

2007, 449(7165):1008-1013. 2. VV Mir<strong>on</strong>ova, NA Omelyanchuk, G Yosiph<strong>on</strong>, SI<br />

Fadeev, NA Kolchanov, E Mjolsness, VA Likhoshvai A plausible mechanism for<br />

auxin patterning al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e developing root. BMC Systems Biology 2010, 4:98<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Statistical Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Signals II; Saturday, July 2, 11:00<br />

Mariola Molenda<br />

The Warsaw University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology,<br />

The Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Informati<strong>on</strong> Science<br />

e-mail: molenda.mariola@gmail.com<br />

Level crossings in biological time series<br />

Kedem in his research [1] made use <str<strong>on</strong>g>of</str<strong>on</strong>g> zero crossings <str<strong>on</strong>g>th</str<strong>on</strong>g>eory in time series analysis.<br />

Zero crossings are remarkably simple and effective tool to examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e autocorrelati<strong>on</strong><br />

structure <str<strong>on</strong>g>of</str<strong>on</strong>g> time series. The applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear binary transformati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> time series allows to retain informati<strong>on</strong> c<strong>on</strong>tained in <str<strong>on</strong>g>th</str<strong>on</strong>g>e autocorrelati<strong>on</strong> functi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e original data. Kedem (1989) found relati<strong>on</strong> between first order autocorrelati<strong>on</strong><br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e expected zero crossings rate. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> zero mean stati<strong>on</strong>ary<br />

Gaussian time series <str<strong>on</strong>g>th</str<strong>on</strong>g>ere exist explicit formula (cosine formula), c<strong>on</strong>necting <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

first order autocorrelati<strong>on</strong> ρ1 and <str<strong>on</strong>g>th</str<strong>on</strong>g>e expected number <str<strong>on</strong>g>of</str<strong>on</strong>g> zero crossings E[D]. The<br />

relati<strong>on</strong>ship looks as follows<br />

ρ1 = cos( πE[D]<br />

n − 1 ).<br />

Cosine formula is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore very useful for <str<strong>on</strong>g>th</str<strong>on</strong>g>e estimati<strong>on</strong> purposes. Having given<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> zero crossings, we can estimate first order autocorrelati<strong>on</strong> in a very<br />

simple and fast way. Using Electroencephalogram (EEG) signal we ilustrate how<br />

accurate <str<strong>on</strong>g>th</str<strong>on</strong>g>e cosine formula is. We also answer <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong> how far precisely we<br />

can compute <str<strong>on</strong>g>th</str<strong>on</strong>g>e first order autocorrelati<strong>on</strong> using zero crossings.<br />

References.<br />

[1] B.Kedem, Time Series Analysis by Higher Order Crossings IEEE Press New York 1993.<br />

[2] S.Y.Tseng, R.C.Chen, F.C.Ch<strong>on</strong>g, T.S.Kuo, Evaluati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> parametric me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in EEG signal<br />

analysis Medical Enginiering and Physics 17 71–78.<br />

[3] Z.Mu, J.Hu, Research <str<strong>on</strong>g>of</str<strong>on</strong>g> EEG identificati<strong>on</strong> computing based <strong>on</strong> AR model BioMedical Informati<strong>on</strong><br />

Engineering FBIE 2009 366–368.<br />

672

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> Macromolecules and Molecular Aggregates;<br />

Saturday, July 2, 14:30<br />

Rubem P. M<strong>on</strong>daini<br />

Federal University <str<strong>on</strong>g>of</str<strong>on</strong>g> Rio de Janeiro -ufrj- Centre <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology,<br />

Coppe, Biomat C<strong>on</strong>sortium<br />

21941-972, P. O. Box 68511, Rio de Janeiro, RJ, Brazil<br />

e-mail: rpm<strong>on</strong>daini@gmail.com<br />

Global optimizati<strong>on</strong> analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> viral capsids and amide<br />

planes<br />

A scheme <str<strong>on</strong>g>of</str<strong>on</strong>g> Combinatorial Optimizati<strong>on</strong> (CO) is introduced in order to describe<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e geometrical pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e macromolecular structures like A-DNA and<br />

molecular aggregates like Tobacco Mosaic Virus (TMV). Backb<strong>on</strong>e sequences <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

internal atom sites are seen to be associated to sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> Steiner points <str<strong>on</strong>g>of</str<strong>on</strong>g> an<br />

Euclidean Steiner Tree Problem. The agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental data is 94.6%<br />

and 98.2% for A-DNA and TMV, respectively.<br />

Ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er CO scheme in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e Steiner points have a fundamental role, is <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

introducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an objective functi<strong>on</strong> which minimum will lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>firmati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> Amide planes in protein structure. This is a Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Programming<br />

approach such <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e variables are small perturbati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>d and<br />

dihedral angles. Objective functi<strong>on</strong> and c<strong>on</strong>straints are derived <strong>on</strong>ly from knowledge<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e 3-dimensi<strong>on</strong>al molecular structure.<br />

These results provide excellent examples <str<strong>on</strong>g>of</str<strong>on</strong>g> robust me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> optimizati<strong>on</strong> as applied<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> geometrical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biopolymers and molecular aggregates.<br />

References.<br />

[1] R. P. M<strong>on</strong>daini, Steiner Ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> Biomolecular Structures - in Encyclopedia <str<strong>on</strong>g>of</str<strong>on</strong>g> Optimizati<strong>on</strong>,<br />

2nd ed., Springer Verlag, 2007, 6 3718–3723.<br />

[2] R. P. M<strong>on</strong>daini, The Steiner Tree problem and its applicati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> Biomolecular<br />

Structures - in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosystems, Applied Optimizati<strong>on</strong> Series, Springer<br />

Verlag, 2008, 102 199–220.<br />

[3] R. P. M<strong>on</strong>daini, An Analytical Me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for derivati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Steiner Ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> 3D Euclidean<br />

Steiner Trees - J. Global Optimizati<strong>on</strong>, 2009, 43 459–470.<br />

[4] R. P. M<strong>on</strong>daini, A Correlati<strong>on</strong> between Atom Sites and Amide Planes in Protein Structures<br />

- in BIOMAT 2009 Internati<strong>on</strong>al Symposium <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Computati<strong>on</strong>al Biology,<br />

BIOMAT Series, World Scientific, 2010, 136–151.<br />

[5] R. P. M<strong>on</strong>daini, S. P. Vilela, A Proposal for modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e Structure <str<strong>on</strong>g>of</str<strong>on</strong>g> Biomacromolecules<br />

- in BIOMAT 2010 Internati<strong>on</strong>al Symposium <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Computati<strong>on</strong>al Biology,<br />

BIOMAT Series, World Scientific, 2011, 61–72.<br />

673

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Wednesday, June 29, 11:00<br />

Shabnam Moobedmehdiabadi<br />

Deaprtment <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> California, Irvine, CA<br />

e-mail: smoobedm@uci.edu<br />

John Lowengrub<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> California, Irvine, CA<br />

e-mail: lowengrb@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.uci.edu<br />

Haralampos Hatzikirou<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> New<br />

Mexico, Albuquerque, NM<br />

e-mail: hhatzikirou@salud.unm.edu<br />

Lattice Gas Cellular Automata modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> lineage dynamics<br />

and feedback c<strong>on</strong>trol<br />

This study is important in understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanism and dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> some<br />

biological problems such as tumor invasi<strong>on</strong> and wound healing. Firstly, we describe<br />

microscopically <str<strong>on</strong>g>th</str<strong>on</strong>g>e model and we derive <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding mesoscopic approximati<strong>on</strong>,<br />

via <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean field assumpti<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e following, we upscale our model<br />

providing a PDE which serves as a macroscopic manifestati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying<br />

cellular interacti<strong>on</strong>s. We focus <strong>on</strong> investigating <str<strong>on</strong>g>th</str<strong>on</strong>g>e speed and <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong> fr<strong>on</strong>t, using <str<strong>on</strong>g>th</str<strong>on</strong>g>e above menti<strong>on</strong>ed approximati<strong>on</strong>s, as functi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

underling cell phenotypes and microenvir<strong>on</strong>mental factors (i.e. nutrients).<br />

References.<br />

[1] A. D. Lander, K. K. Gok<str<strong>on</strong>g>of</str<strong>on</strong>g>fski, F. Y. M. Wan, Q. Nie, A. L. Cal<str<strong>on</strong>g>of</str<strong>on</strong>g>, Cell lineages and <str<strong>on</strong>g>th</str<strong>on</strong>g>e logic<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> proliferative c<strong>on</strong>trol PLOSBiology, Vol 7,Issue 9, January 2009.<br />

[2] H. Hatzikirou, L.Brusch, A. Deutsch, From Cellular Automata rules to a macroscopic meanfield<br />

descripti<strong>on</strong> Acta Physica Pol<strong>on</strong>ica B Proceedings Supplement, Vol 3, 2010.<br />

674

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Developmental Biology; Saturday, July 2, 11:00<br />

Yoshihiro Morishita<br />

Kyushu University<br />

e-mail: ymorishi@bio-ma<str<strong>on</strong>g>th</str<strong>on</strong>g>10.biology.kyushu-u.ac.jp<br />

Coding design <str<strong>on</strong>g>of</str<strong>on</strong>g> positi<strong>on</strong>al informati<strong>on</strong> for robust<br />

morphogenesis<br />

Robust positi<strong>on</strong>ing <str<strong>on</strong>g>of</str<strong>on</strong>g> cells in a tissue against unavoidable noises is important for<br />

achieving normal and reproducible morphogenesis. The positi<strong>on</strong> in a tissue is represented<br />

by morphogen c<strong>on</strong>centrati<strong>on</strong>s, and cells read out <str<strong>on</strong>g>th</str<strong>on</strong>g>em to recognize <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

spatial coordinates. From <str<strong>on</strong>g>th</str<strong>on</strong>g>e engineering viewpoint, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese positi<strong>on</strong>ing processes<br />

can be regarded as an informati<strong>on</strong> coding. Organisms are c<strong>on</strong>jectured to adopt<br />

good coding designs wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high reliability for a given number <str<strong>on</strong>g>of</str<strong>on</strong>g> available morphogen<br />

species and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir chemical properties. To answer quantitatively <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong>s, how<br />

good coding is adopted? and when, where, and to what extent does each morphogen<br />

c<strong>on</strong>tribute to positi<strong>on</strong>ing?, we need a way to evaluate <str<strong>on</strong>g>th</str<strong>on</strong>g>e goodness <str<strong>on</strong>g>of</str<strong>on</strong>g> coding. In<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is paper, by introducing basic c<strong>on</strong>cepts <str<strong>on</strong>g>of</str<strong>on</strong>g> computer science, we ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically<br />

formulate coding processes in morphogen-dependent positi<strong>on</strong>ing, and define some<br />

key c<strong>on</strong>cepts such as encoding, decoding, and positi<strong>on</strong>al informati<strong>on</strong> and its precisi<strong>on</strong>.<br />

We dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>e best designs for pairs <str<strong>on</strong>g>of</str<strong>on</strong>g> encoding and decoding rules.<br />

We also discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e applicability <str<strong>on</strong>g>of</str<strong>on</strong>g> our <str<strong>on</strong>g>th</str<strong>on</strong>g>eory to biological data.<br />

675

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biomechanical regulati<strong>on</strong> in b<strong>on</strong>e tissue (Sessi<strong>on</strong><br />

I); Wednesday, June 29, 08:30<br />

Adam Moroz<br />

De M<strong>on</strong>tfort University,<br />

e-mail: amoroz@dmu.ac.uk<br />

Mikhail Goman<br />

De M<strong>on</strong>tfort University<br />

David I. Wimpenny<br />

De M<strong>on</strong>tfort University<br />

BMU remodelling simulati<strong>on</strong> using reducer order me<str<strong>on</strong>g>th</str<strong>on</strong>g>od<br />

Adam Moroz, Mikhail Goman, David I. Wimpenny BMU remodelling simulati<strong>on</strong><br />

using reducer order me<str<strong>on</strong>g>th</str<strong>on</strong>g>od The b<strong>on</strong>e remodelling process, performed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e B<strong>on</strong>e<br />

Multicellular Unit (BMU) is a key multi-hierarchically regulated process, which<br />

provides and supports various functi<strong>on</strong>ality <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e tissue. It is also plays a critical<br />

role in b<strong>on</strong>e disorders, as well as b<strong>on</strong>e tissue healing following damage. Modelling<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e turnover processes could play a significant role in helping to understand<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying cause <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e disorders and <str<strong>on</strong>g>th</str<strong>on</strong>g>us develop more effective treatment<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods. The reducer order approach to modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e turnover, based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

osteocyte loop <str<strong>on</strong>g>of</str<strong>on</strong>g> regulati<strong>on</strong>, have been employed, <str<strong>on</strong>g>th</str<strong>on</strong>g>in wide range <str<strong>on</strong>g>of</str<strong>on</strong>g> rate parameters<br />

using <str<strong>on</strong>g>th</str<strong>on</strong>g>e M<strong>on</strong>te Carlo me<str<strong>on</strong>g>th</str<strong>on</strong>g>od. The optimal c<strong>on</strong>trol framework for regulati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> remodelling has been discussed. The study illustrates <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> formalisati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolic processes and <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>s between hierarchical subsystems<br />

in hard tissue where a relatively small number <str<strong>on</strong>g>of</str<strong>on</strong>g> cells are active.<br />

676

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Stem cells and cancer; Wednesday, June 29, 14:30<br />

Charles Mort<strong>on</strong><br />

Center <str<strong>on</strong>g>of</str<strong>on</strong>g> Cancer Systems Biology - Tufts University School <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine<br />

e-mail: charles.mort<strong>on</strong>@tufts.edu<br />

Tumor Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> Kinetics Modulated by Generati<strong>on</strong>al<br />

Lifespan <str<strong>on</strong>g>of</str<strong>on</strong>g> N<strong>on</strong>-Stem Cancer Cells<br />

Numerous solid tumors are heterogeneous in compositi<strong>on</strong>. While grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is driven<br />

by cancer stem cells (CSCs), <str<strong>on</strong>g>th</str<strong>on</strong>g>e reported relative frequencies <str<strong>on</strong>g>of</str<strong>on</strong>g> CSC versus n<strong>on</strong>stem<br />

cancer cells span wide ranges wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in tumors arising from a given tissue type.<br />

We have previously shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> kinetics and compositi<strong>on</strong> can be<br />

studied <str<strong>on</strong>g>th</str<strong>on</strong>g>rough an agent-based cellular automat<strong>on</strong> model using minimal sets <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

biological assumpti<strong>on</strong>s and parameters. Herein we describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e pivotal role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

generati<strong>on</strong>al lifespan <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-stem cancer cells in modulating solid tumor progressi<strong>on</strong>.<br />

Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough CSCs are necessary for expansi<strong>on</strong>, tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> kinetics are surprisingly<br />

modulated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>-stem cancer cells. Our findings suggest<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at variance in tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> curves and CSC c<strong>on</strong>tent <str<strong>on</strong>g>of</str<strong>on</strong>g> solid tumors may be<br />

attributable to <str<strong>on</strong>g>th</str<strong>on</strong>g>e proliferative capacity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>-stem cancer cell populati<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at arises during asymmetric divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> CSCs. Remarkably, slight variati<strong>on</strong>s in<br />

proliferative capacity result in tumors wi<str<strong>on</strong>g>th</str<strong>on</strong>g> CSC fracti<strong>on</strong>s differing by multiple orders<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> magnitude. Larger proliferative capacities yield migrati<strong>on</strong>-limited tumors,<br />

as <str<strong>on</strong>g>th</str<strong>on</strong>g>e emerging populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-stem cancer cells spatially impedes expansi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e CSC compartment. C<strong>on</strong>versely, lower proliferative capacities yield persistencelimited<br />

tumors, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> symmetric divisi<strong>on</strong> frequency <str<strong>on</strong>g>of</str<strong>on</strong>g> CSCs determining tumor<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate. Intermediate proliferative capacities give rise to fastest-growing tumors,<br />

indicating a between self-metastatic grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough symmetric CSC divisi<strong>on</strong><br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e availability <str<strong>on</strong>g>of</str<strong>on</strong>g> space facilitated by removal <str<strong>on</strong>g>of</str<strong>on</strong>g> senescent n<strong>on</strong>-stem cancer<br />

cells. Our results <str<strong>on</strong>g>of</str<strong>on</strong>g>fer novel explanati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e large variati<strong>on</strong>s in CSC ratio<br />

reported in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature, and highlight <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-stem cancer cell<br />

dynamics in <str<strong>on</strong>g>th</str<strong>on</strong>g>e CSC hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis.<br />

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Patricia Mostardinha<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Aveiro<br />

e-mail: pmostardinha@ua.pt<br />

Fernão Vistulo de Abreu<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Aveiro<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Modelling Homeostatic Resp<strong>on</strong>ses<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is poster I will derive a set <str<strong>on</strong>g>of</str<strong>on</strong>g> differential equati<strong>on</strong>s describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a cellular frustrated system. I will c<strong>on</strong>centrate <strong>on</strong> how <str<strong>on</strong>g>th</str<strong>on</strong>g>e system is capable <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

performing immune resp<strong>on</strong>ses <str<strong>on</strong>g>th</str<strong>on</strong>g>at drive <str<strong>on</strong>g>th</str<strong>on</strong>g>e system back to homeostatic c<strong>on</strong>trol.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is way we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at cellular frustrated systems can resp<strong>on</strong>d to endogeneous<br />

or exogenous perturbati<strong>on</strong>s. The immunological significance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese results will be<br />

discussed, in particular in c<strong>on</strong>necti<strong>on</strong> to autoimunity or tumour eliminati<strong>on</strong>.<br />

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Populati<strong>on</strong> Genetics; Wednesday, June 29, 14:30<br />

M. G<strong>on</strong>zález<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics. University <str<strong>on</strong>g>of</str<strong>on</strong>g> Extremadura<br />

e-mail: mvelasco@unex.es<br />

C. Gutiérrez<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics. University <str<strong>on</strong>g>of</str<strong>on</strong>g> Extremadura<br />

e-mail: cgutierrez@unex.es<br />

R. Martínez<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics. University <str<strong>on</strong>g>of</str<strong>on</strong>g> Extremadura<br />

e-mail: rmartinez@unex.es<br />

M. Mota<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics. University <str<strong>on</strong>g>of</str<strong>on</strong>g> Extremadura<br />

e-mail: mota@unex.es<br />

C<strong>on</strong>diti<strong>on</strong>s for extincti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> some le<str<strong>on</strong>g>th</str<strong>on</strong>g>al alleles <str<strong>on</strong>g>of</str<strong>on</strong>g> X-linked<br />

genes<br />

Some le<str<strong>on</strong>g>th</str<strong>on</strong>g>al alleles <str<strong>on</strong>g>of</str<strong>on</strong>g> certain genes can cause <str<strong>on</strong>g>th</str<strong>on</strong>g>e dea<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e organisms <str<strong>on</strong>g>th</str<strong>on</strong>g>at carry<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>em. Some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese alleles, as could be <str<strong>on</strong>g>th</str<strong>on</strong>g>at resp<strong>on</strong>sible <str<strong>on</strong>g>of</str<strong>on</strong>g> hemophilia, corresp<strong>on</strong>d<br />

to genes linked to sex chromosomes, especially to X chromosome. If <str<strong>on</strong>g>th</str<strong>on</strong>g>ese alleles<br />

are dominant, all <str<strong>on</strong>g>th</str<strong>on</strong>g>e carriers die so <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are rarely detected due to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir rapid<br />

eliminati<strong>on</strong> from populati<strong>on</strong>s. However, recessive le<str<strong>on</strong>g>th</str<strong>on</strong>g>al alleles <strong>on</strong>ly cause dea<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> carrier males and homozygous carrier females, <str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e last <strong>on</strong>es must be<br />

daughters <str<strong>on</strong>g>of</str<strong>on</strong>g> a carrier male, so <str<strong>on</strong>g>th</str<strong>on</strong>g>ey rarely exist. Heterozygous carrier females<br />

are able to live and reproduce. They do not phenotypically express <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic<br />

c<strong>on</strong>diti<strong>on</strong> but can pass <str<strong>on</strong>g>th</str<strong>on</strong>g>e le<str<strong>on</strong>g>th</str<strong>on</strong>g>al allele <strong>on</strong>to <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, we introduce a multitype bisexual branching process for describing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals carrying <str<strong>on</strong>g>th</str<strong>on</strong>g>e alleles, R and r, <str<strong>on</strong>g>of</str<strong>on</strong>g> a gene<br />

linked to X chromosome. The R allele is c<strong>on</strong>sidered dominant and <str<strong>on</strong>g>th</str<strong>on</strong>g>e r allele is<br />

assumed to be recessive and le<str<strong>on</strong>g>th</str<strong>on</strong>g>al. Females can have two genotypes: homozygous,<br />

RR, and heterozygous, Rr, whereas <strong>on</strong>ly R males are able to live. Homozygous and<br />

heterozygous females have identical phenotypes so males do not know <str<strong>on</strong>g>th</str<strong>on</strong>g>e genotype<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir mates, it can be said <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey made a “blind” choice am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e two<br />

genotypes.<br />

In such a model, we take into account <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring <str<strong>on</strong>g>of</str<strong>on</strong>g> a couple wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a<br />

homozygous female do not carry <str<strong>on</strong>g>th</str<strong>on</strong>g>e le<str<strong>on</strong>g>th</str<strong>on</strong>g>al allele. However, couples wi<str<strong>on</strong>g>th</str<strong>on</strong>g> heterozygous<br />

females can give bir<str<strong>on</strong>g>th</str<strong>on</strong>g> to RR and Rr females and R and r males. Since r males<br />

die, Mendelian inheritance ratios <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese couples are altered. The total <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

each couple is modeled <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a random variable whose probability distributi<strong>on</strong><br />

is supposed to be different for homozygous and heterozygous females.<br />

We use <str<strong>on</strong>g>th</str<strong>on</strong>g>is model to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e extincti<strong>on</strong> probability <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese le<str<strong>on</strong>g>th</str<strong>on</strong>g>al alleles,<br />

i.e. under which c<strong>on</strong>diti<strong>on</strong>s it will eventually disappear and when it will survive<br />

al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e generati<strong>on</strong>s. Such c<strong>on</strong>diti<strong>on</strong>s are expressed in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e model. In case <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong> extincti<strong>on</strong>, we investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

carriers <str<strong>on</strong>g>of</str<strong>on</strong>g> such alleles.<br />

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Acknowledgements: Research supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ministerio de Ciencia e Innovación,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Junta de Extremadura and <str<strong>on</strong>g>th</str<strong>on</strong>g>e FEDER, grants MTM2009-13248 and<br />

GR10118.<br />

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Populati<strong>on</strong> Dynamics; Tuesday, June 28, 17:00<br />

Iw<strong>on</strong>a Mroz<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Experimental Physics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Wroclaw, Plac Maxa<br />

Borna 9, 50-204 Wroclaw, Poland<br />

e-mail: imroz@ifd.uni.wroc.pl<br />

Adaptati<strong>on</strong> to a given habitat as a factor influencing<br />

dynamics and evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> model populati<strong>on</strong>s.<br />

We investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s under which a model populati<strong>on</strong> can survive in a<br />

given habitat, col<strong>on</strong>ize a new (spatially separated) habitat and is able to co-exist<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a populati<strong>on</strong> living in a neighbouring habitat.<br />

Each habitat is represented by a square lattice and a model phenotype, describing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e phenotype <str<strong>on</strong>g>of</str<strong>on</strong>g> an individual <str<strong>on</strong>g>th</str<strong>on</strong>g>at is fully adapted to <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sidered habitat.<br />

The populati<strong>on</strong>s are composed <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals <str<strong>on</strong>g>th</str<strong>on</strong>g>at move over <str<strong>on</strong>g>th</str<strong>on</strong>g>e lattice, mate,<br />

produce <str<strong>on</strong>g>of</str<strong>on</strong>g>fsprings and die. The individuals are characterized by <str<strong>on</strong>g>th</str<strong>on</strong>g>eir genotypes,<br />

phenotypes and ages. The individuals adaptati<strong>on</strong> to a given habitat depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> its phenotypic features <str<strong>on</strong>g>th</str<strong>on</strong>g>at are <str<strong>on</strong>g>th</str<strong>on</strong>g>e same as <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding features<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> ’<str<strong>on</strong>g>th</str<strong>on</strong>g>e model phenotype’ according to a power functi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some exp<strong>on</strong>ent n. The<br />

value <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptati<strong>on</strong> is related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e individuals probability <str<strong>on</strong>g>of</str<strong>on</strong>g> survival.<br />

We discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e value <str<strong>on</strong>g>of</str<strong>on</strong>g> n <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> dynamics and<br />

its genetic and phenotypic variability. In particular, we compare <str<strong>on</strong>g>th</str<strong>on</strong>g>e situati<strong>on</strong>s<br />

when: n>1 (briefly, in <str<strong>on</strong>g>th</str<strong>on</strong>g>is case <strong>on</strong>ly <str<strong>on</strong>g>th</str<strong>on</strong>g>e individuals <str<strong>on</strong>g>th</str<strong>on</strong>g>at are quite similar to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

model phenotype can survive easily) and 0>n>1 (here, even small similarities between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e phenotype <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sidered individual and <str<strong>on</strong>g>th</str<strong>on</strong>g>e model phenotype may be<br />

significantly advantageous for survival). For co-existing populati<strong>on</strong>s, possibilities<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> hybrid z<strong>on</strong>es <str<strong>on</strong>g>of</str<strong>on</strong>g> different shapes are also investigated. Computer<br />

simulati<strong>on</strong>s based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard M<strong>on</strong>te Carlo technique are performed.<br />

References.<br />

[1] Mroz I, Pekalski A, Sznajd-Wer<strong>on</strong> K: C<strong>on</strong>diti<strong>on</strong>s for adaptati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an evolving populati<strong>on</strong>.<br />

Phys Rev Lett 76,(1996),3025-3028.<br />

[2] Mroz I, Pekalski A: Model <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong>s col<strong>on</strong>izing a new habitat. Eur Phys J B 10,(1999),181-<br />

186.<br />

[3] Mroz I: A model <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> dynamics - fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er investigati<strong>on</strong>s. Physica A 323,(2003),569-577.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Kalina Mrozek<br />

Proteome and Metabolome Research, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology, Bielefeld<br />

University, Germany<br />

e-mail: kalina.mrozek@uni-bielefeld.de<br />

Petra Lutter<br />

Proteome and Metabolome Research, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology, Bielefeld<br />

University, Germany<br />

Karsten Niehaus<br />

Proteome and Metabolome Research, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology, Bielefeld<br />

University, Germany<br />

Modelling calcium transients in plant pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen defence<br />

reacti<strong>on</strong>s<br />

Recogniti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> so-called pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen-associated molecular patterns (PAMPs) triggers<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e plant immunity. As a first line <str<strong>on</strong>g>of</str<strong>on</strong>g> defence <str<strong>on</strong>g>th</str<strong>on</strong>g>e producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> reactive oxygen<br />

species (ROS) is started. ROS are able to kill <str<strong>on</strong>g>th</str<strong>on</strong>g>e invading pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen and to crosslink<br />

cell wall comp<strong>on</strong>ents forming a barrier to block <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong>. The plant receptors<br />

perceive <str<strong>on</strong>g>th</str<strong>on</strong>g>e PAMPs <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell surface and transfer a signal into <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. As a<br />

c<strong>on</strong>sequence, <str<strong>on</strong>g>th</str<strong>on</strong>g>e release <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium from internal stores is mediated, generating a<br />

spike <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytosolic calcium c<strong>on</strong>centrati<strong>on</strong>. This increase depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e type<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> elicitor and can differ in lag time, magnitude, peak time, intensity and durati<strong>on</strong>.<br />

The project focuses <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e establishment <str<strong>on</strong>g>of</str<strong>on</strong>g> a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytosolic calcium signals up<strong>on</strong> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen c<strong>on</strong>tact and also should<br />

be expandable for integrating o<str<strong>on</strong>g>th</str<strong>on</strong>g>er comp<strong>on</strong>ents <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is signal transducti<strong>on</strong> chain.<br />

Initially, <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytosolic calcium levels are measured in aequorin-transformed tobacco<br />

cell cultures. Simultaneously, <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytosolic calcium c<strong>on</strong>centrati<strong>on</strong> is ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically<br />

described, based <strong>on</strong> a system <str<strong>on</strong>g>of</str<strong>on</strong>g> differential equati<strong>on</strong>s. The MatLab s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware<br />

is used for running simulati<strong>on</strong>s. The simulati<strong>on</strong>s imply <str<strong>on</strong>g>th</str<strong>on</strong>g>e variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> different<br />

sets <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e different kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium transients, doseresp<strong>on</strong>se-relati<strong>on</strong>ship<br />

curves and additi<strong>on</strong>ally reproducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e refractory behavior<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytosolic calcium increase for comparis<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e measured datasets.<br />

682

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Saturday, July 2, 14:30<br />

Maciej Mrugala<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Washingt<strong>on</strong> Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Neurology<br />

e-mail: mmrugala@u.washingt<strong>on</strong>.edu<br />

Kristin Swans<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Washingt<strong>on</strong> Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, Department <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

e-mail: krae@u.washingt<strong>on</strong>.edu<br />

Addie Bo<strong>on</strong>e<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Washingt<strong>on</strong> Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology<br />

Russell Rockne<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Washingt<strong>on</strong> Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, Department <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

Predicting pseudoprogressi<strong>on</strong> in glioblastoma patients: A<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and clinical perspective<br />

Background: Glioblastoma multiforme (GBM) is a highly invasive primary brain<br />

tumor <str<strong>on</strong>g>th</str<strong>on</strong>g>at diffusely invades <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding normal appearing tissue and yields<br />

short life expectancies despite aggressive treatment. A combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chemo and<br />

radiati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies is <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard <str<strong>on</strong>g>of</str<strong>on</strong>g> care for newly diagnosed GBM. However,<br />

published data estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>at 20%-50% <str<strong>on</strong>g>of</str<strong>on</strong>g> progressive enhancement <strong>on</strong> MRI occurring<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in 12 weeks post chemoradio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy is <str<strong>on</strong>g>th</str<strong>on</strong>g>e result <str<strong>on</strong>g>of</str<strong>on</strong>g> pseudoprogressi<strong>on</strong><br />

(Psp) and does not indicate true progressi<strong>on</strong> (TP) <str<strong>on</strong>g>of</str<strong>on</strong>g> disease. Though many novel<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods and modalities are currently being evaluated to distinguish Psp from TP,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ere is no widely accepted n<strong>on</strong>invasive mechanism to predict Psp in individual<br />

patients.<br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: A reacti<strong>on</strong>-diffusi<strong>on</strong> model has effectively quantified <str<strong>on</strong>g>th</str<strong>on</strong>g>e net proliferati<strong>on</strong><br />

() and invasti<strong>on</strong> rate (D) (P-I) <str<strong>on</strong>g>of</str<strong>on</strong>g> untreated glioma grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and invasi<strong>on</strong>.<br />

We investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e P-I model as a mechanism to predict which<br />

patents will be more likely to experience pseudoprogressi<strong>on</strong> and true progressive<br />

disease. The pre- and post-chemoradio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy MRI scans <str<strong>on</strong>g>of</str<strong>on</strong>g> 57 patients were reviewed<br />

retrospectively.<br />

Results: Eleven <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e 57 patients were clinically c<strong>on</strong>firmed to exhibit pseudoprogressi<strong>on</strong><br />

and 46 patients were c<strong>on</strong>firmed to exhibit true progressi<strong>on</strong>. These<br />

patients were <str<strong>on</strong>g>th</str<strong>on</strong>g>en evaluated based <strong>on</strong> model-generated parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e net migrati<strong>on</strong><br />

(D) and proliferati<strong>on</strong> rates () <str<strong>on</strong>g>of</str<strong>on</strong>g> each patients glioma tumor. Of <str<strong>on</strong>g>th</str<strong>on</strong>g>e 11<br />

Psp patients, 9 (82%) had pretreatment D/1 mm2.<br />

C<strong>on</strong>clusi<strong>on</strong>: A pre-treatment D/rho

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ecosystems Dynamics; Tuesday, June 28, 11:00<br />

Johannes Müller<br />

Technische Universität München„ Zentrum Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematik, Boltzmannstr. 3,<br />

85758 Garching / Munich, Germany<br />

e-mail: johannes.mueller@mytum.de<br />

Annett Henkel<br />

Technische Universität München, Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologie der Waldbäume, Hans-<br />

Carl-v<strong>on</strong>-Carlowitz-Platz 2, 85354 Freising<br />

e-mail: annett_henkel@email.de<br />

Christian Pötzsche<br />

Technische Universität München„ Zentrum Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematik, Boltzmannstr. 3,<br />

85758 Garching / Munich, Germany<br />

e-mail: poetzsch@ma.tum.de<br />

Modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e Spread <str<strong>on</strong>g>of</str<strong>on</strong>g> Phytoph<str<strong>on</strong>g>th</str<strong>on</strong>g>ora<br />

The genus Phytoph<str<strong>on</strong>g>th</str<strong>on</strong>g>ora de Bary is a well-known group <str<strong>on</strong>g>of</str<strong>on</strong>g> fungus-like pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> algal relatives which are <str<strong>on</strong>g>th</str<strong>on</strong>g>e causal agent <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most devastating plant diseases.<br />

Herbaceous crops like potatoes as well as woody crops like citrus or even<br />

trees in natural forests fall prey to <str<strong>on</strong>g>th</str<strong>on</strong>g>em and cause tremendous pecuniary and ecological<br />

losses each year which attract a lot <str<strong>on</strong>g>of</str<strong>on</strong>g> interest in <str<strong>on</strong>g>th</str<strong>on</strong>g>e investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

behaviour and <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> Phytoph<str<strong>on</strong>g>th</str<strong>on</strong>g>ora.<br />

We c<strong>on</strong>sider a model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e morphology and grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Phytoph<str<strong>on</strong>g>th</str<strong>on</strong>g>ora using <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

example <str<strong>on</strong>g>of</str<strong>on</strong>g> Phytoph<str<strong>on</strong>g>th</str<strong>on</strong>g>ora plurivora utilizing a correlated random walk describing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e density <str<strong>on</strong>g>of</str<strong>on</strong>g> tips. This correlated random walk incorporates some n<strong>on</strong>-standard<br />

aspects, as grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and change <str<strong>on</strong>g>of</str<strong>on</strong>g> directi<strong>on</strong> are intertwined, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> newly<br />

split tips is delayed (apical dominance).<br />

First we investigate running fr<strong>on</strong>ts, especially questi<strong>on</strong>ing <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is delay,<br />

for uniform- as well as n<strong>on</strong>-uniform turning kernels. We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is delay<br />

primarily influences <str<strong>on</strong>g>th</str<strong>on</strong>g>e slope <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fr<strong>on</strong>t and <str<strong>on</strong>g>th</str<strong>on</strong>g>erewi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e way <str<strong>on</strong>g>of</str<strong>on</strong>g> spatial appropriati<strong>on</strong>,<br />

and not its velocity. This <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical predicti<strong>on</strong> is c<strong>on</strong>firmed by experimental<br />

data <str<strong>on</strong>g>of</str<strong>on</strong>g> Phytoph<str<strong>on</strong>g>th</str<strong>on</strong>g>ora growing in Petri dishes.<br />

The sec<strong>on</strong>d questi<strong>on</strong> we are dealing wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk is c<strong>on</strong>cerning <str<strong>on</strong>g>th</str<strong>on</strong>g>e manner<br />

tips are interacting, especially <str<strong>on</strong>g>th</str<strong>on</strong>g>e point why tips stop to grow “behind” <str<strong>on</strong>g>th</str<strong>on</strong>g>e interface<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fr<strong>on</strong>t, respectively in c<strong>on</strong>fr<strong>on</strong>tati<strong>on</strong> experiments at <str<strong>on</strong>g>th</str<strong>on</strong>g>e interface between<br />

two col<strong>on</strong>ies. The combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> experimental data about <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial structured<br />

time course <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e glucose c<strong>on</strong>centrati<strong>on</strong> and simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> a model taking into<br />

account bo<str<strong>on</strong>g>th</str<strong>on</strong>g>, tips and glucose, reveals <str<strong>on</strong>g>th</str<strong>on</strong>g>at nutrient depleti<strong>on</strong> is most likely <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

central mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> tip interacti<strong>on</strong> and hyphal grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. We presume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e growing mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is Phytoph<str<strong>on</strong>g>th</str<strong>on</strong>g>ora in infected plant tissue and <str<strong>on</strong>g>th</str<strong>on</strong>g>is <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen will sap its hosts via energy depleti<strong>on</strong> and tissue destructi<strong>on</strong> in infected<br />

areas.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Sreeharish Muppirisetty<br />

The Micros<str<strong>on</strong>g>of</str<strong>on</strong>g>t Research - University <str<strong>on</strong>g>of</str<strong>on</strong>g> Trento COSBI<br />

e-mail: sreeharishm@cosbi.eu<br />

Federico Vaggi<br />

The Micros<str<strong>on</strong>g>of</str<strong>on</strong>g>t Research - University <str<strong>on</strong>g>of</str<strong>on</strong>g> Trento COSBI<br />

Yari Ciribilli<br />

Centre for Integrative Biology (CIBIO), University <str<strong>on</strong>g>of</str<strong>on</strong>g> Trento<br />

Alberto Inga<br />

Centre for Integrative Biology (CIBIO), University <str<strong>on</strong>g>of</str<strong>on</strong>g> Trento<br />

Attila Csikasz-Nagy<br />

The Micros<str<strong>on</strong>g>of</str<strong>on</strong>g>t Research - University <str<strong>on</strong>g>of</str<strong>on</strong>g> Trento COSBI<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> p53 transactivati<strong>on</strong> <strong>on</strong> different Resp<strong>on</strong>se<br />

Elements<br />

p53 is <str<strong>on</strong>g>th</str<strong>on</strong>g>e guardian <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e genome, it acts as a transcripti<strong>on</strong> factor regulating<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> several proteins up<strong>on</strong> DNA damage. Maybe <str<strong>on</strong>g>th</str<strong>on</strong>g>is is <str<strong>on</strong>g>th</str<strong>on</strong>g>e most<br />

investigated protein in human cells, still <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact mechanism how p53 binds to<br />

resp<strong>on</strong>se elements (REs) in <str<strong>on</strong>g>th</str<strong>on</strong>g>e DNA is still unclear. A yeast-based essay enables us<br />

to investigate its binding dynamics to REs <str<strong>on</strong>g>of</str<strong>on</strong>g> highly important targets. We collected<br />

time courses <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong>al activity at various REs by measuring luminescence<br />

induced by p53 regulated promoters at various p53 inducti<strong>on</strong> levels. We created a<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> p53 dimers and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir binding<br />

to REs. Alternative versi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model c<strong>on</strong>tain possible proposed binding orders<br />

and interacti<strong>on</strong>s. We perform large scale parameter estimati<strong>on</strong> to identify which<br />

model can give such parameter sets <str<strong>on</strong>g>th</str<strong>on</strong>g>at fits <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental measurements. Initial<br />

results revealed <str<strong>on</strong>g>th</str<strong>on</strong>g>at earlier time points need to be measured to allow proper fitting.<br />

We observed <str<strong>on</strong>g>th</str<strong>on</strong>g>at, some parameters show low sensitivity at all p53 inducti<strong>on</strong> levels.<br />

Thus we narrowed down <strong>on</strong> a subset <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters from <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial set and run <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

estimati<strong>on</strong> by fitting all <str<strong>on</strong>g>th</str<strong>on</strong>g>e measured REs toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er and observed <str<strong>on</strong>g>th</str<strong>on</strong>g>e intra RE and<br />

inter RE variati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter estimati<strong>on</strong> we plan to<br />

identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e details <str<strong>on</strong>g>of</str<strong>on</strong>g> p53 RE binding events. The emerging modeling results will<br />

be fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er validated experimentally.<br />

685

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Regulatory Networks; Friday, July 1, 14:30<br />

Daniele Muraro 1<br />

e-mail: daniele.muraro@nottingham.ac.uk<br />

Leah Band 1<br />

e-mail: leah.band@nottingham.ac.uk<br />

Helen Byrne 1,2<br />

e-mail: helen.byrne@nottingham.ac.uk<br />

John King 1,2<br />

e-mail: john.king@nottingham.ac.uk<br />

Ute Voß 1<br />

e-mail: ute.voss@nottingham.ac.uk<br />

Susana Ubeda Tomas 1<br />

e-mail: susana.ubeda-tomas@nottingham.ac.uk<br />

Joseph Kieber 3<br />

e-mail: jkieber@ad.unc.edu<br />

Malcolm Bennett 1<br />

e-mail: malcolm.bennett@nottingham.ac.uk<br />

[1]: Centre for Plant Integrative Biology, School <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosciences,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, Sutt<strong>on</strong> B<strong>on</strong>ingt<strong>on</strong> Campus, Loughborough<br />

LE12 5RD, UK<br />

[2]: School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, University<br />

Park, Nottingham NG7 2RD, UK<br />

[3]: Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina at<br />

Chapel Hill, Chapel Hill, Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina 27599-3280<br />

A multi-scale analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> horm<strong>on</strong>al<br />

cross-talk: cell-fate determinati<strong>on</strong> in Arabidopsis <str<strong>on</strong>g>th</str<strong>on</strong>g>aliana<br />

root development<br />

Root grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and development in Arabidopsis <str<strong>on</strong>g>th</str<strong>on</strong>g>aliana are sustained by a specialised<br />

z<strong>on</strong>e termed <str<strong>on</strong>g>th</str<strong>on</strong>g>e meristem, which c<strong>on</strong>tains a populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dividing and<br />

differentiating cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at is functi<strong>on</strong>ally analogous to a stem cell niche in animals.<br />

The size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e meristem is regulated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e balance between cell divisi<strong>on</strong> and<br />

cell differentiati<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>is balance is c<strong>on</strong>trolled antag<strong>on</strong>istically by <str<strong>on</strong>g>th</str<strong>on</strong>g>e horm<strong>on</strong>es<br />

auxin and cytokinin. Local accumulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin promotes cell divisi<strong>on</strong>, whereas<br />

high cytokinin c<strong>on</strong>centrati<strong>on</strong>s promote differentiati<strong>on</strong>. The cross-talk between <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

two horm<strong>on</strong>es is c<strong>on</strong>trolled by a genetic regulatory network.<br />

As a first step <str<strong>on</strong>g>of</str<strong>on</strong>g> our analysis, we propose and compare wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental observati<strong>on</strong>s<br />

a single-cell, deterministic ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is regulatory mechanism.<br />

We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough genetic mutati<strong>on</strong>s can reproduce qualitatively <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

effects <str<strong>on</strong>g>of</str<strong>on</strong>g> varying auxin and cytokinin supply <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir resp<strong>on</strong>se genes, <str<strong>on</strong>g>th</str<strong>on</strong>g>e general<br />

resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network is different and an analysis based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ratio between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese two horm<strong>on</strong>es may be misleading.<br />

Recently, gibberellin has been shown to be relevant in determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e adult<br />

size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e meristem by interacting wi<str<strong>on</strong>g>th</str<strong>on</strong>g> auxin and cytokinin. We propose a multiscale<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is interacti<strong>on</strong> and we validate <str<strong>on</strong>g>th</str<strong>on</strong>g>e results <str<strong>on</strong>g>of</str<strong>on</strong>g> our simulati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

experimental data. We c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at a multi-scale investigati<strong>on</strong> can provide insight<br />

into <str<strong>on</strong>g>th</str<strong>on</strong>g>e signalling network c<strong>on</strong>trolling meristematic activity, by enabling <str<strong>on</strong>g>th</str<strong>on</strong>g>e study<br />

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<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network in different tissues and <str<strong>on</strong>g>th</str<strong>on</strong>g>e identificati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> potential missing comp<strong>on</strong>ents.<br />

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Multiscale modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chaste framework;<br />

Tuesday, June 28, 11:00<br />

Philip J. Murray, Philip K. Maini, Ru<str<strong>on</strong>g>th</str<strong>on</strong>g> E. Baker<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, The Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Institute, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford.<br />

e-mail: murrayp@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

Using Chaste to simulate a multiscale problem in<br />

developmental biology<br />

During somitogenesis <str<strong>on</strong>g>th</str<strong>on</strong>g>e posterior PSM segments at regular time time intervals<br />

into blocks <str<strong>on</strong>g>of</str<strong>on</strong>g> epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells called somites. A clock and wavefr<strong>on</strong>t mechanism is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e widely accepted model for <str<strong>on</strong>g>th</str<strong>on</strong>g>is process, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> cellular clocks and a travelling<br />

molecular wavefr<strong>on</strong>t determining when and where <str<strong>on</strong>g>th</str<strong>on</strong>g>e somites form, respectively.<br />

Recent experimental findings in zebrafish have highlighted <str<strong>on</strong>g>th</str<strong>on</strong>g>e fundamental role <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Notch-Delta signalling in <str<strong>on</strong>g>th</str<strong>on</strong>g>e coupling <str<strong>on</strong>g>of</str<strong>on</strong>g> neighbouring cellular oscillators. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

framework <str<strong>on</strong>g>of</str<strong>on</strong>g> phase coupled oscillators to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e Notch-Delta coupled molecular<br />

oscillators, we dem<strong>on</strong>strate how oscillator coupling al<strong>on</strong>e is sufficient to yield a range<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> experimentally observed results. A notable feature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sidered phasecoupled<br />

framework is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e clock and wavefr<strong>on</strong>t are not separate entities, ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e wavefr<strong>on</strong>t <str<strong>on</strong>g>th</str<strong>on</strong>g>at slows clock oscillati<strong>on</strong>s is a gradient in clock phase.<br />

Cell movements in <str<strong>on</strong>g>th</str<strong>on</strong>g>e chick PSM have recently been quantified: cells are most<br />

motile in <str<strong>on</strong>g>th</str<strong>on</strong>g>e posterior PSM while cell densities are largest anteriorly. Using a<br />

cell-based model implemented in Chaste, we investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ree tightly-coupled processes: embryo el<strong>on</strong>gati<strong>on</strong>, embryo c<strong>on</strong>vergence and cell<br />

proliferati<strong>on</strong>. Results from <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical simulati<strong>on</strong>s are compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g> available<br />

experimental data and <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is used to suggest fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er experimental studies.<br />

688

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Modeling viral hepatitis dynamics in-vivo and in-vitro in <str<strong>on</strong>g>th</str<strong>on</strong>g>e era <str<strong>on</strong>g>of</str<strong>on</strong>g> direct<br />

anti-viral agents I; Tuesday, June 28, 17:00<br />

Robert B. Nachbar<br />

Merck Research Laboratories<br />

e-mail: nachbar@merck.com<br />

Matt S. Anders<strong>on</strong><br />

Merck Research Laboratories<br />

Diana M. Brainard<br />

Merck Research Laboratories (present address Gilead Sciences)<br />

Paul Panorchan<br />

Merck Research Laboratories (present address Vertex Pharmaceuticals)<br />

Jeffrey S. Saltzman<br />

Merck Research Laboratories<br />

Jack L. Valentine<br />

Merck Research Laboratories (present address Bristol-Myers Squibb)<br />

The use <str<strong>on</strong>g>of</str<strong>on</strong>g> viral dynamics modeling to optimize <str<strong>on</strong>g>th</str<strong>on</strong>g>e design <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a Phase Ib trial, facilitate its analysis, and inform <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

decisi<strong>on</strong> making for <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> directly acting HCV<br />

compounds<br />

Hepatitis C virus (HCV) causes a chr<strong>on</strong>ic infecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver, and leads to fibrosis,<br />

cirrhosis, and in some patients to hepatocellular carcinoma. Current standard <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

care (pegylated interfer<strong>on</strong> plus ribavirin for 48 weeks) is an arduous regimen for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

patient and has a cure rate <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>ly 50 % in genotype 1 (GT 1) patients. Therefore,<br />

in recent years <str<strong>on</strong>g>th</str<strong>on</strong>g>ere has been significant effort to develop directly acting antivirals<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at will have a substantially higher rate <str<strong>on</strong>g>of</str<strong>on</strong>g> cure and require a shorter period <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

treatment. This presentati<strong>on</strong> will describe how we used pharmacokinetic and viral<br />

dynamics modeling to design <str<strong>on</strong>g>th</str<strong>on</strong>g>e durati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment in a Phase Ib clinical trial <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

an HCV NS5B polymerase inhibitor in GT 1a, 1b, and 3 patients, and to determine<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal sampling times bo<str<strong>on</strong>g>th</str<strong>on</strong>g> during and after treatment. Quantitative analysis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting viral load data led to a much clearer understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>se<br />

across genotypes and supported <str<strong>on</strong>g>th</str<strong>on</strong>g>e decisi<strong>on</strong> making process in clinical development.<br />

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Bioinformatics and System Biology; Wednesday, June 29, 17:00<br />

J.C. Nacher 1<br />

e-mail: nacher@fun.ac.jp<br />

M. Hayashida 2<br />

e-mail: morihiro@kuicr.kyoto-u.ac.jp<br />

T. Akutsu 2<br />

e-mail: takutsu@kuicr.kyoto-u.ac.jp<br />

1 Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex and Intelligent Systems, Future University<br />

Hakodate, Japan<br />

2 Bioinformatics Center, Institute for Chemical Research, Kyoto Uni-<br />

versity, Uji, Japan<br />

Data analysis and ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> internal<br />

duplicati<strong>on</strong> process in multi-domain proteins<br />

Multi-domain proteins have likely been shaped by selective genome grow<str<strong>on</strong>g>th</str<strong>on</strong>g> dynamics<br />

during evoluti<strong>on</strong>. Emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> new protein domains allows to perform<br />

new functi<strong>on</strong>s as well as to create polypeptide structures <str<strong>on</strong>g>th</str<strong>on</strong>g>at fold <strong>on</strong> a biologically<br />

feasible time scale. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> genome grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough shuffling <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

protein domains have been studied extensively over decades, recent experimental<br />

observati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> a significantly large number <str<strong>on</strong>g>of</str<strong>on</strong>g> domain repeats <str<strong>on</strong>g>of</str<strong>on</strong>g> several domains<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e same family suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at <strong>on</strong>e more process involving domain recombinati<strong>on</strong><br />

may still remain hidden [1, 2]. Here we examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein domain statistics<br />

retrieved from Pfam, SMART, Gene3D, ProDom and TIGRFAMs databases and<br />

c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> 68 eukaryotic, 56 archaeal, and 929 bacterial organisms. We show<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is analysis c<strong>on</strong>firms earlier observati<strong>on</strong>s [3] and extends <str<strong>on</strong>g>th</str<strong>on</strong>g>em to numerous<br />

organisms in <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ree kingdoms <str<strong>on</strong>g>of</str<strong>on</strong>g> life. The results show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> total<br />

protein domains and <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> domain families in a protein are governed by<br />

different statistical laws. While <str<strong>on</strong>g>th</str<strong>on</strong>g>e former follows a power-law distributi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

latter exhibits an exp<strong>on</strong>ential statistics. We develop a me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology and propose<br />

an evoluti<strong>on</strong>ary dynamics model, based <strong>on</strong> a rate equati<strong>on</strong> formalism, and c<strong>on</strong>sisting<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> domain fusi<strong>on</strong>, mutati<strong>on</strong>, protein duplicati<strong>on</strong> and internal duplicati<strong>on</strong><br />

processes. We <str<strong>on</strong>g>th</str<strong>on</strong>g>en dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese distinct distributi<strong>on</strong>s are in fact rooted<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e internal domain duplicati<strong>on</strong> mechanism. The analytical results derived from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary dynamics model as well as computer simulati<strong>on</strong> show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

domain-repeats event generates a wide number <str<strong>on</strong>g>of</str<strong>on</strong>g> domains in a protein while at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

same time preserving a <str<strong>on</strong>g>th</str<strong>on</strong>g>in number <str<strong>on</strong>g>of</str<strong>on</strong>g> domain families across proteome species.<br />

To our knowledge, <str<strong>on</strong>g>th</str<strong>on</strong>g>is is <str<strong>on</strong>g>th</str<strong>on</strong>g>e first ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> protein domain evoluti<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at explicitly takes into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> internal duplicati<strong>on</strong> mechanism and<br />

provides analytical soluti<strong>on</strong>. These findings bring in our view new insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

fundamental mechanisms governing genome expansi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> potential implicati<strong>on</strong>s<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> protein interacti<strong>on</strong> network models and related evoluti<strong>on</strong>ary<br />

studies.<br />

References.<br />

[1] A.D. Moore, Arrangements in <str<strong>on</strong>g>th</str<strong>on</strong>g>e modular evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> proteins Trends in Biochemical Sciences<br />

33 444-451.<br />

[2] A.K. Björklund, D. Ekman and A. El<str<strong>on</strong>g>of</str<strong>on</strong>g>ss<strong>on</strong>, Expansi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> protein domain repeats PLoS Computati<strong>on</strong>al<br />

Biology 2, e114.<br />

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[3] E.V. Ko<strong>on</strong>in, Y.I. Wolf and G. P. Karev, The structure <str<strong>on</strong>g>of</str<strong>on</strong>g> protein universe and genome<br />

evoluti<strong>on</strong> Nature 420, 218-223.<br />

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Reports from US - African BioMa<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Initiative: C<strong>on</strong>servati<strong>on</strong><br />

Biology; Saturday, July 2, 14:30<br />

Robyn Nadolny<br />

Old Domini<strong>on</strong> University Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Sciences<br />

e-mail: rnado002@odu.edu<br />

Emna Harigua<br />

Institut Pasteur de Tunis<br />

Karen Wylie<br />

Rutgers University Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Ecology, Evoluti<strong>on</strong> & Natural Resources<br />

Oussama Souai<br />

Institut Pasteur de Tunis<br />

Canine Distemper Virus (CDV): Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for modeling<br />

spillover infecti<strong>on</strong>s for African Wild Dogs (Lyca<strong>on</strong> pictus) in<br />

a multi-host community<br />

Canine Distemper Virus (CDV) is a potentially le<str<strong>on</strong>g>th</str<strong>on</strong>g>al morbillivirus spread via<br />

aerosol. It is comm<strong>on</strong> in domestic dogs and also affects many wild carnivores,<br />

including li<strong>on</strong>s, hyenas, jackals and African wild dogs (AWDs). The AWD is a critically<br />

endangered canid <str<strong>on</strong>g>th</str<strong>on</strong>g>at is known to experience high mortality from epizootics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> CDV. AWDs are <strong>on</strong>ly known to survive in protected areas in Africa, which <str<strong>on</strong>g>th</str<strong>on</strong>g>ey<br />

share wi<str<strong>on</strong>g>th</str<strong>on</strong>g> li<strong>on</strong>s, hyenas and jackals. Inter-species interacti<strong>on</strong>s at shared kill sites<br />

provide an opportunity for CDV to spill over from <strong>on</strong>e infected species to ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

susceptible species. We aim to examine how CDV is transmitted between four<br />

different host species (li<strong>on</strong>s, jackals, hyenas and AWDs) wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a reserve.<br />

We c<strong>on</strong>structed a heterogeneous deterministic SEIR model to establish a diseasefree<br />

equilibrium for each species. We <str<strong>on</strong>g>th</str<strong>on</strong>g>en introduced stochasticity to our model to<br />

understand how CDV spreads <str<strong>on</strong>g>th</str<strong>on</strong>g>rough multispecies metapopulati<strong>on</strong>s. Stochasticity<br />

was introduced in <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong> process and in <str<strong>on</strong>g>th</str<strong>on</strong>g>e inter-species c<strong>on</strong>tact process.<br />

Due to variati<strong>on</strong> in collecti<strong>on</strong> techniques for demographic data in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature, our<br />

model was compromised since data for some species may already reflect <str<strong>on</strong>g>th</str<strong>on</strong>g>e endemic<br />

state <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease while o<str<strong>on</strong>g>th</str<strong>on</strong>g>er species are potentially disease-free. Never<str<strong>on</strong>g>th</str<strong>on</strong>g>eless,<br />

our model dem<strong>on</strong>strates a valid me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e sources and sinks <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

disease in a multi-host metapopulati<strong>on</strong>. We also plan to build a c<strong>on</strong>tact network<br />

model to avoid <str<strong>on</strong>g>th</str<strong>on</strong>g>e issue <str<strong>on</strong>g>of</str<strong>on</strong>g> mixing endemic host populati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> disease-free host<br />

populati<strong>on</strong>s. These models could be applied to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er metapopulati<strong>on</strong> systems to<br />

study or prevent disease spillovers between neighboring populati<strong>on</strong>s.<br />

692

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> gene regulati<strong>on</strong>; Tuesday, June 28, 11:00<br />

Felix Naef<br />

Ecole Polytechnique Federale de Lausanne (EPFL)<br />

e-mail: felix.naef@epfl.ch<br />

Calibrating stochastic models <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong>al bursting in<br />

single mammalian cells<br />

In bo<str<strong>on</strong>g>th</str<strong>on</strong>g> prokaryotes and eukaryotes, stochasticity in <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> mRNA and<br />

protein expressi<strong>on</strong> has important c<strong>on</strong>sequences <strong>on</strong> gene regulati<strong>on</strong> and <strong>on</strong> n<strong>on</strong>genetic<br />

cell-to-cell variability. Here, we show how disc<strong>on</strong>tinuous transcripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

mammalian genes leads to broad spectra <str<strong>on</strong>g>of</str<strong>on</strong>g> temporal bursting in mRNA syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis.<br />

To m<strong>on</strong>itor transcripti<strong>on</strong> at high temporal resoluti<strong>on</strong>, we designed chromosomallyintegrated<br />

vectors encoding a very short-lived luciferase in combinati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> ultrasensitive<br />

bioluminescence microscopy. These data enabled us to develop and calibrate<br />

a probabilistic model <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong> to estimate gene-specific transcripti<strong>on</strong><br />

burst sizes and switching rates. The model was fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er used to dec<strong>on</strong>volve <str<strong>on</strong>g>th</str<strong>on</strong>g>e time<br />

traces, which showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at rapid bursting at timescales <str<strong>on</strong>g>of</str<strong>on</strong>g> tens <str<strong>on</strong>g>of</str<strong>on</strong>g> minutes may be an<br />

intrinsic property <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong> in mammalian cells, and lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e characterizati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> refractory periods <str<strong>on</strong>g>of</str<strong>on</strong>g> variable durati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e inactive state. Experiments<br />

in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulatory elements were modified showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e bursting kinetics<br />

was markedly altered by sequence modificati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cis-regulatory sequences. This<br />

high temporal resoluti<strong>on</strong> m<strong>on</strong>itoring <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong> is readily applicable to many<br />

systems; including <str<strong>on</strong>g>th</str<strong>on</strong>g>e circadian oscillator in which we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at increased bursting<br />

frequency precede maximal burst sizes by few hours.<br />

693

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Mechanics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> and cortical actin at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular level;<br />

Saturday, July 2, 08:30<br />

Sundar Nagana<str<strong>on</strong>g>th</str<strong>on</strong>g>an, Justin Bois, Guillaume Salbreux, Stephan W. Grill<br />

MPI CBG<br />

e-mail: nagana<str<strong>on</strong>g>th</str<strong>on</strong>g>@mpi-cbg.de<br />

Actin binding proteins govern <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> polarizing<br />

cortical flows in C. elegans zygotes<br />

Establishment <str<strong>on</strong>g>of</str<strong>on</strong>g> polarity is essential for c<strong>on</strong>ferring different developmental fates to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dividing cells <str<strong>on</strong>g>of</str<strong>on</strong>g> an embryo. In Caenorhabditis elegans <strong>on</strong>e cell embryos, anteroposterior<br />

polarizati<strong>on</strong> is facilitated by l<strong>on</strong>g-ranged flow <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e actomyosin cortex.<br />

Even <str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e flowing cortex c<strong>on</strong>tains many actin binding proteins (ABPs) <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

c<strong>on</strong>tribute to its structure and dynamics, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are <strong>on</strong>ly a limited number <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanical<br />

properties <str<strong>on</strong>g>th</str<strong>on</strong>g>at are important at large leng<str<strong>on</strong>g>th</str<strong>on</strong>g> and time scales relevant for<br />

polarizati<strong>on</strong>, for example c<strong>on</strong>tractility and cortical viscosity (Mayer, Bois, Depken,<br />

Jülicher, Grill, 2010). Importantly, <str<strong>on</strong>g>th</str<strong>on</strong>g>is suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is <strong>on</strong>ly a reduced spectrum<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cortical flow phenotypes <str<strong>on</strong>g>th</str<strong>on</strong>g>at <strong>on</strong>e might expect to obtain by modulating<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese few mechanical properties <str<strong>on</strong>g>th</str<strong>on</strong>g>rough different molecular mechanisms. To bridge<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e gap between molecular and cellular scales, we here sought to investigate which<br />

cell-scale mechanical properties are c<strong>on</strong>trolled by which ABPs. We devised a candidate<br />

RNAi screen <str<strong>on</strong>g>of</str<strong>on</strong>g> ABPs and found <str<strong>on</strong>g>th</str<strong>on</strong>g>at several ABPs affect cortical flow. This<br />

was achieved by analyzing myosin foci size and density and several flow characteristics,<br />

such as peak velocities and spatio-temporal velocity-velocity correlati<strong>on</strong>s,<br />

for each ABP knockdown. The velocity-velocity correlati<strong>on</strong>s provided us wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an<br />

estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristic hydrodynamic leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> cortical flow, which describes<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e extent to which flows are l<strong>on</strong>g-ranged. Interestingly, all <str<strong>on</strong>g>th</str<strong>on</strong>g>ose ABPs<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at displayed a detectable cortical flow phenotype did so <str<strong>on</strong>g>th</str<strong>on</strong>g>rough affecting <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

hydrodynamic leng<str<strong>on</strong>g>th</str<strong>on</strong>g>. RNAi ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er resulted in short-ranged flows, indicative <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

less viscous cortex, or it resulted in flows <str<strong>on</strong>g>th</str<strong>on</strong>g>at were l<strong>on</strong>ger-ranged <str<strong>on</strong>g>th</str<strong>on</strong>g>an wild type,<br />

indicative <str<strong>on</strong>g>of</str<strong>on</strong>g> a cortex <str<strong>on</strong>g>th</str<strong>on</strong>g>at is more viscous <str<strong>on</strong>g>th</str<strong>on</strong>g>at under wild-type c<strong>on</strong>diti<strong>on</strong>s. Our<br />

results suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristic hydrodynamic leng<str<strong>on</strong>g>th</str<strong>on</strong>g> is a central physical<br />

property subject to precise regulati<strong>on</strong>. They also point towards a type <str<strong>on</strong>g>of</str<strong>on</strong>g> “mechanical<br />

redundancy” in animal development, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> many molecular mechanisms affecting<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e same cell-scale physical property.<br />

694

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling viral hepatitis dynamics in-vivo and in-vitro in <str<strong>on</strong>g>th</str<strong>on</strong>g>e era <str<strong>on</strong>g>of</str<strong>on</strong>g> direct<br />

anti-viral agents II; Wednesday, June 29, 08:30<br />

Jun Nakabayashi<br />

Graduate University for Advanced Studies (SOKENDAI)<br />

e-mail: nakabayashi_jun@soken.ac.jp<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular replicati<strong>on</strong> and<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in host evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> HBV and HCV<br />

Hepatitis virus type B (HBV) is a major causative agent <str<strong>on</strong>g>of</str<strong>on</strong>g> acute and chr<strong>on</strong>ic<br />

hepatitis. Especially, chr<strong>on</strong>ic hepatitis is a major risk factor <str<strong>on</strong>g>of</str<strong>on</strong>g> liver cirrhosis and<br />

hepatocellular carcinoma. During <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g time course <str<strong>on</strong>g>of</str<strong>on</strong>g> chr<strong>on</strong>ic hepatitis, severity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> hepatitis varies depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral load. It is important to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

viral kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> HBV for <str<strong>on</strong>g>th</str<strong>on</strong>g>e predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e outcome <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatitis. Though <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

detailed mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> HBV replicati<strong>on</strong> is revealed according to <str<strong>on</strong>g>th</str<strong>on</strong>g>e development<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> molecular biological technique, how reproducti<strong>on</strong> rate <str<strong>on</strong>g>of</str<strong>on</strong>g> HBV is determined in<br />

single cell level had not been clear yet. To investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular replicati<strong>on</strong><br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> HBV, a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> HBV replicati<strong>on</strong> process is c<strong>on</strong>structed.<br />

And how <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g time course <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatitis is affected by wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in host evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

HBV was investigated by using an evoluti<strong>on</strong>ary simulati<strong>on</strong> [1]. From <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> our model, <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e exacerbati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatitis during <str<strong>on</strong>g>th</str<strong>on</strong>g>e chr<strong>on</strong>ic<br />

hepatitis is obtained. It is shown by our model <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e waiting time for release<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> newly produced viri<strong>on</strong> from infected cell plays critical roles for determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

clinical course <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatitis. Now, a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> HCV is additi<strong>on</strong>ally<br />

c<strong>on</strong>structed to compare wi<str<strong>on</strong>g>th</str<strong>on</strong>g> HBV.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular replicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> virus, <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral genome should play several<br />

distinguished roles, as a template <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e genome replicati<strong>on</strong>, as a comp<strong>on</strong>ent <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

viral particle and as a template for <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral gene expressi<strong>on</strong>. Because it is impossible<br />

to simultaneously play many roles, it is necessary to optimally distribute <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

viral genome to <str<strong>on</strong>g>th</str<strong>on</strong>g>ese roles for <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficient replicati<strong>on</strong>. The optimum distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> genome is comm<strong>on</strong> problem for many viruses. HBV is DNA virus, <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

hand, HCV is <str<strong>on</strong>g>th</str<strong>on</strong>g>e positive strand RNA virus, and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir replicati<strong>on</strong> patterns are<br />

quite different. HBV and HCV respectively achieve <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimum distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

genome by different regulatory mechanism. The intracellular replicati<strong>on</strong> dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> HBV and HCV are drastically changed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genome. I would<br />

like to show how <str<strong>on</strong>g>th</str<strong>on</strong>g>e replicati<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> HBV and HCV is affected by <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir genome. And I would like to discuss how <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g time course <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

chr<strong>on</strong>ic hepatitis is affected by <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular dynamics and wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in host evoluti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> HBV and HCV in <str<strong>on</strong>g>th</str<strong>on</strong>g>is mini-symposium.<br />

References.<br />

[1] Nakabayashi J. and Sasaki A, A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular replicati<strong>on</strong> and wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in<br />

host evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatitis type B virus: Understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g time course <str<strong>on</strong>g>of</str<strong>on</strong>g> chr<strong>on</strong>ic hepatitis.<br />

J Theor Biol. 2011 269 318-329.<br />

695

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Turing !! Turing?? <strong>on</strong> morphogenesis via experimental and <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical<br />

approaches; Wednesday, June 29, 17:00<br />

Tetsuya Nakamura<br />

Developmental Genetics group<br />

Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Fr<strong>on</strong>tier Biosciences<br />

Osaka university, Japan<br />

e-mail: t-nakamura@fbs.osaka-u.ac.jp<br />

The Mechanism To Establish Robust Left-Right Asymmetry<br />

A development <str<strong>on</strong>g>of</str<strong>on</strong>g> animal body proceeds under <str<strong>on</strong>g>th</str<strong>on</strong>g>e intrinsic noise (gene expressi<strong>on</strong>,<br />

protein interacti<strong>on</strong>, cell migrati<strong>on</strong> etc.) and <str<strong>on</strong>g>th</str<strong>on</strong>g>e extrinsic noise (envir<strong>on</strong>ment).<br />

In spite <str<strong>on</strong>g>of</str<strong>on</strong>g> existence <str<strong>on</strong>g>of</str<strong>on</strong>g> so much noise, an animal development proceeds robustly<br />

and C.H.Waddingt<strong>on</strong> called a stability <str<strong>on</strong>g>of</str<strong>on</strong>g> a development, “Canalizati<strong>on</strong>”. Of course,<br />

left and right determinati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mouse is not excepti<strong>on</strong> and canalizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> L-R<br />

development attains 99.99 %.<br />

Our body has many internal organs <str<strong>on</strong>g>th</str<strong>on</strong>g>at show asymmetric morphologies about<br />

left-right axis and <str<strong>on</strong>g>th</str<strong>on</strong>g>ese morphologies play important roles in its functi<strong>on</strong>, such<br />

as <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart, liver, stomach and intestine. Recently, mechanisms to establish L-<br />

R asymmetry in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mouse embryo have been elucidated by using genetics and<br />

molecular approaches. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e mouse embryo, <str<strong>on</strong>g>th</str<strong>on</strong>g>e small leftward fluid flow in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

node produces first asymmetric informati<strong>on</strong> al<strong>on</strong>g L-R axis and <str<strong>on</strong>g>th</str<strong>on</strong>g>e left-side specific<br />

genes are expressed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e left lateral plate mesoderm subsequently.<br />

Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough some cascades <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong>s were studied, it is unknown how robust<br />

expressi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> left side specific genes are established from <str<strong>on</strong>g>th</str<strong>on</strong>g>e small asymmetric<br />

water flow in <str<strong>on</strong>g>th</str<strong>on</strong>g>e node. Nodal and Lefty, two members <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transforming grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

factor-β super family <str<strong>on</strong>g>of</str<strong>on</strong>g> proteins and are expressed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lateral plate mesoderm,<br />

have been implicated in Turing system. Turing system is a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> two diffusible molecules and may underlie pattern formati<strong>on</strong> during<br />

development. We have now examined <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential role <str<strong>on</strong>g>of</str<strong>on</strong>g> Turing system in<br />

left-right patterning bo<str<strong>on</strong>g>th</str<strong>on</strong>g> by experimentally manipulating Nodal and Lefty gene<br />

expressi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mouse embryos and by c<strong>on</strong>structing a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model.<br />

Our results suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at an initial small difference in <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> an activating<br />

signal between <str<strong>on</strong>g>th</str<strong>on</strong>g>e left and right sides <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e embryo is amplified and c<strong>on</strong>verted into<br />

robust asymmetry by Turing system involving Nodal and Lefty.<br />

References.<br />

[1] T. Nakamura, Generati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> robust left-right asymmetry in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mouse embryo requires a selfenhancement<br />

and lateral-inhibiti<strong>on</strong> system. Developmental Cell, 2006, Oct ; 11 (4) 495–504.<br />

[2] H. Hamada, Establishment <str<strong>on</strong>g>of</str<strong>on</strong>g> vertebrate left-right asymmetry. Nature Review Genetics, 2002,<br />

Feb ; 3 (2) 103–13.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Delay Differential Equati<strong>on</strong>s and Applicati<strong>on</strong>s I; Friday, July 1, 14:30<br />

Yukihiko Nakata<br />

BCAM-Basque Center for Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

e-mail: nakata@bcama<str<strong>on</strong>g>th</str<strong>on</strong>g>.org<br />

Philipp Getto<br />

BCAM-Basque Center for Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

e-mail: getto@bcama<str<strong>on</strong>g>th</str<strong>on</strong>g>.org<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> a characteristic equati<strong>on</strong> for a Delay Equati<strong>on</strong><br />

from cell populati<strong>on</strong> dynamics<br />

We present Delay Equati<strong>on</strong>s describing age-structured cell populati<strong>on</strong> dynamics<br />

where <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell populati<strong>on</strong> is divided into proliferative and quiescent cells. We derived<br />

a characteristic equati<strong>on</strong> for an interior equilibrium and analyzed <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e framework <str<strong>on</strong>g>of</str<strong>on</strong>g> [1, 2]. We will show how to use <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristic equati<strong>on</strong> to<br />

determine stability boundaries for <str<strong>on</strong>g>th</str<strong>on</strong>g>e interior equilibrium in two-parameter space.<br />

References.<br />

[1] O. Diekmann, S.A. van Gils, S.M.V. Lunel, H.O. Wal<str<strong>on</strong>g>th</str<strong>on</strong>g>er (1995) Delay equati<strong>on</strong>s: functi<strong>on</strong>al,<br />

complex,and n<strong>on</strong>linear analysis, vol 110 <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences. Springer-Verlag<br />

[2] O. Diekmann, Ph. Getto, M. Gyllenberg (2007) Stability and bifurcati<strong>on</strong> analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Volterra<br />

functi<strong>on</strong>al equati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e light <str<strong>on</strong>g>of</str<strong>on</strong>g> suns and stars. SIAM J Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Anal 39:1023-1069<br />

697

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ecosystems Dynamics; Tuesday, June 28, 14:30<br />

Toshiyuki Namba<br />

Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Science, Osaka Prefecture University<br />

e-mail: tnamba@b.s.osakafu-u.ac.jp<br />

Intraguild Predati<strong>on</strong> in a Source–Sink Metacommunity<br />

Dispersal <str<strong>on</strong>g>of</str<strong>on</strong>g> organisms in a heterogeneous landscape str<strong>on</strong>gly influences <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

persistence <str<strong>on</strong>g>of</str<strong>on</strong>g> indirectly interacting populati<strong>on</strong>s. The source–sink habitat structure<br />

is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e major mechanisms to promote coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> locally exclusive competitors.<br />

It is known <str<strong>on</strong>g>th</str<strong>on</strong>g>at two populati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at interfere wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er (Takeuchi<br />

1989) or compete exploitatively (Namba and Hashimoto, 2004; Abrams and Wils<strong>on</strong>,<br />

2004) or apparently (Namba, 2007) in spatially heterogeneous metacommunities can<br />

coexist regi<strong>on</strong>ally even if <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em is locally inferior in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> patches.<br />

Here, I c<strong>on</strong>sider a Lotka-Volterra model <str<strong>on</strong>g>of</str<strong>on</strong>g> intraguild predati<strong>on</strong> in two patches<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at have different envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s and are c<strong>on</strong>nected by dispersal:<br />

dR i<br />

dt = r i − aRRR i − aRCC i − aRP P i R i ,<br />

dC i<br />

dt = (−mC + eRCaRCR i − aCP P i )C i − dC(C i − C j ),<br />

dP i<br />

dt = (−mP + eRP aRP R i + eCP aCP C i )P i − dP (P i − P j ),<br />

(i, j) = (1.2) or (2, 1). r’s are intrinsic grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rates, m’s are mortalities, a’s are<br />

interacti<strong>on</strong> coefficients, e’s are c<strong>on</strong>versi<strong>on</strong> efficiencies, and m’s are diffusi<strong>on</strong> rates.<br />

The subscripts express species identity and <str<strong>on</strong>g>th</str<strong>on</strong>g>e superscripts denote patch number.<br />

I study c<strong>on</strong>diti<strong>on</strong>s for coexistence and competitive exclusi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e following<br />

four cases; (1) when <str<strong>on</strong>g>th</str<strong>on</strong>g>e intraguild prey is inferior in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> patches, (2) when <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

intraguild predator is inferior in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> patches, and (3) when <str<strong>on</strong>g>th</str<strong>on</strong>g>e local interacti<strong>on</strong>s<br />

are bistable and ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intraguild prey and predator can dominate each patch<br />

if it is initially abundant, (4) when <str<strong>on</strong>g>th</str<strong>on</strong>g>e intraguild prey is inferior in <strong>on</strong>e patch (a<br />

sink) and superior in ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er patch (a source). I will show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e intraguild prey<br />

and predator can coexist regi<strong>on</strong>ally in a habitat wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a source–sink structure even<br />

if <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em becomes competitively excluded in isolated patches in <str<strong>on</strong>g>th</str<strong>on</strong>g>e absence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal. When <str<strong>on</strong>g>th</str<strong>on</strong>g>e habitat is in a true source–sink structure and each species<br />

dominates <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two patches, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> patches may become sinks for <str<strong>on</strong>g>th</str<strong>on</strong>g>e intratuild<br />

prey when <str<strong>on</strong>g>th</str<strong>on</strong>g>e dispersal rate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intraguild predator is intermediate. I will<br />

also show <str<strong>on</strong>g>th</str<strong>on</strong>g>e stabilizing role <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong> when <str<strong>on</strong>g>th</str<strong>on</strong>g>e local dynamics are oscillatory.<br />

In summary, dispersal between patches in different envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s may<br />

ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er promote or demote coexistence depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e precise habitat c<strong>on</strong>diti<strong>on</strong>s<br />

and interacti<strong>on</strong> streng<str<strong>on</strong>g>th</str<strong>on</strong>g>s.<br />

References.<br />

[1] Abrams, P., and Wils<strong>on</strong>, W. G., 2004. Coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> competitors in metacommunities due<br />

to spatial variati<strong>on</strong> in resource grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rates; does R ∗ predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e outcome <str<strong>on</strong>g>of</str<strong>on</strong>g> competiti<strong>on</strong>?<br />

Ecology Letters 7 929–940.<br />

[2] Namba, T., 2007. Dispersal-mediated coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> indirect competitors in source–sink metacommunities.<br />

Japan Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Industrial and Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics 24 39–55.<br />

[3] Namba, T., and Hashimoto, C., 2004. Dispersal-mediated coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> competing predators.<br />

Theoretical Populati<strong>on</strong> Biology 66 53–70.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[4] Takeuchi, Y., 1989. Diffusi<strong>on</strong>–mediated persistence in two-species competiti<strong>on</strong> Lotka-Volterra<br />

model. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences 95 65–83.<br />

699

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Statistical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in computati<strong>on</strong>al neuroscience II; Wednesday, June 29,<br />

17:00<br />

Martin Paul Nawrot<br />

Neuroinformatics and Theoretical Neuroscience, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Biology, Freie Universität Berlin<br />

e-mail: martin.nawrot@fu-berlin.de<br />

Exploring <str<strong>on</strong>g>th</str<strong>on</strong>g>e Relati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Interval and Count Variability in<br />

Neural Spike Trains<br />

Understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e nature and origin <str<strong>on</strong>g>of</str<strong>on</strong>g> neural variability at <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> single<br />

neur<strong>on</strong>s and neural networks is fundamental to our understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> how neural<br />

systems can reliably process informati<strong>on</strong>. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> single neur<strong>on</strong> spike trains<br />

we discern two aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> variability. The variance <str<strong>on</strong>g>of</str<strong>on</strong>g> inter-spike intervals (ISIs)<br />

reflects intra-trial variability <strong>on</strong> a relatively fast time scale <str<strong>on</strong>g>of</str<strong>on</strong>g> tens to hundreds <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

millisec<strong>on</strong>ds. In c<strong>on</strong>trast, <str<strong>on</strong>g>th</str<strong>on</strong>g>e variance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> acti<strong>on</strong> potentials counted<br />

during repeated experimental observati<strong>on</strong>s reflects a variability <strong>on</strong> a comparably<br />

slow time scale <str<strong>on</strong>g>of</str<strong>on</strong>g> sec<strong>on</strong>ds or even minutes. On <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical grounds, interval and<br />

count statistics <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic point processes are fundamentally related. Analyzing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir empirical relati<strong>on</strong> in neural spike trains <str<strong>on</strong>g>th</str<strong>on</strong>g>us allows to better characterize <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

observed neural spiking processes [1].<br />

To estimate inter-spike interval variability I employ <str<strong>on</strong>g>th</str<strong>on</strong>g>e empirical coefficient <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

variati<strong>on</strong> (CV) defined as <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard deviati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ISIs normalized by <str<strong>on</strong>g>th</str<strong>on</strong>g>e average<br />

ISI. The empirical count variability is measured by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fano factor (FF) defined by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> count variance and mean count as estimated during repeated observati<strong>on</strong>s.<br />

For general stati<strong>on</strong>ary n<strong>on</strong>-renewal processes we obtain <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong><br />

<br />

∞<br />

(1) lim FF = CV21<br />

+ 2 ξ wi<str<strong>on</strong>g>th</str<strong>on</strong>g> ξ = ξi ,<br />

T →∞<br />

where ξi denotes <str<strong>on</strong>g>th</str<strong>on</strong>g>e i<str<strong>on</strong>g>th</str<strong>on</strong>g>-order serial interval correlati<strong>on</strong> coefficient. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e case<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a renewal process Eq.(1) simplifies to FF = CV 2 . I will discuss how deviati<strong>on</strong>s<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>is equality can be interpreted wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to n<strong>on</strong>-renewal properties and<br />

n<strong>on</strong>-stati<strong>on</strong>arity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed spiking processes [1].<br />

The relati<strong>on</strong> Eq.(1) transfers to <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> activity <str<strong>on</strong>g>of</str<strong>on</strong>g> superimposed point<br />

processes, which allows to deduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e average CV 2 and serial correlati<strong>on</strong> ξ <str<strong>on</strong>g>of</str<strong>on</strong>g> single<br />

neur<strong>on</strong> spike trains from <str<strong>on</strong>g>th</str<strong>on</strong>g>e so-called multi unit activity obtained in extracellular<br />

recordings [2].<br />

References.<br />

[1] M.P. Nawrot (2010) Analysis and Interpretati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Interval and Count Variability in Neural<br />

Spike Trains. In: S. Grün, S. Rotter (eds.), Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Parallel Spike Trains, Springer Series<br />

in Computati<strong>on</strong>al Neuroscience 7 37–58.<br />

[2] F. Farkhooi, E. Muller, M.P. Nawrot (2010) Adaptati<strong>on</strong> Reduces Variability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Neur<strong>on</strong>al<br />

Populati<strong>on</strong> Code. arXiv: 1007.3490<br />

700<br />

i=1

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Bakhyt Nedorezova<br />

The Research Center for Interdisciplinary Envir<strong>on</strong>mental Cooperati<strong>on</strong><br />

(INENCO) <str<strong>on</strong>g>of</str<strong>on</strong>g> Russian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Saint-Petersburg,<br />

Russian Federati<strong>on</strong><br />

e-mail: b.n.nedorezova@gmail.com<br />

L.V. Nedorezov<br />

The Research Center for Interdisciplinary Envir<strong>on</strong>mental Cooperati<strong>on</strong><br />

(INENCO) <str<strong>on</strong>g>of</str<strong>on</strong>g> Russian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Saint-Petersburg,<br />

Russian Federati<strong>on</strong><br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> pine lopper populati<strong>on</strong> dynamics wi<str<strong>on</strong>g>th</str<strong>on</strong>g> discrete<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models<br />

The well-known discrete time ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models (Moran Ricker model, modified<br />

discrete logistic model, Kostitzin model, Skellam model, and Varley Gradwell Morris<br />

model) were used for analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> pine lopper (Bupalus piniarius L.) populati<strong>on</strong><br />

dynamics in nati<strong>on</strong>al park De Hoge Veluwe (Klomp, 1966 The Global Populati<strong>on</strong><br />

Dynamics Database, N 2727, N 2728 and N 2729). Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree correlated<br />

time series (for larva, pupae, and eggs) showed, <str<strong>on</strong>g>th</str<strong>on</strong>g>at good approximati<strong>on</strong> (global<br />

fitting) can be obtained wi<str<strong>on</strong>g>th</str<strong>on</strong>g> discrete logistic model trajectories. It means <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

in c<strong>on</strong>sidering locati<strong>on</strong> populati<strong>on</strong> cannot realize its eruptive properties (Isaev et<br />

al., 1984, 2001), populati<strong>on</strong> dynamics can be explained as a result <str<strong>on</strong>g>of</str<strong>on</strong>g> influence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

intra-populati<strong>on</strong> self-regulative mechanisms, and its dynamics can be characterized<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e narrow phase portrait wi<str<strong>on</strong>g>th</str<strong>on</strong>g> unique stati<strong>on</strong>ary state.<br />

701

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Jost Neigenfind<br />

Max-Planck Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular plant physiology, potsdam, germany<br />

e-mail: Neigenfind@mpimp-golm.mpg.de<br />

Zoran Nikoloski<br />

Max-Planck Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular plant physiology and institute <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

biochemistry and biology, university <str<strong>on</strong>g>of</str<strong>on</strong>g> potsdam, potsdam, germany<br />

e-mail: Nikoloski@mpimp-golm.mpg.de<br />

Structural Sources <str<strong>on</strong>g>of</str<strong>on</strong>g> Robustness in Biochemical Reacti<strong>on</strong><br />

Networks Using a Simplified Analytical Me<str<strong>on</strong>g>th</str<strong>on</strong>g>od<br />

Robustness is a property <str<strong>on</strong>g>of</str<strong>on</strong>g> a biological system which enables maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

systemic functi<strong>on</strong>ality in presence <str<strong>on</strong>g>of</str<strong>on</strong>g> external and internal perturbati<strong>on</strong>s. Here, we<br />

investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> robustness for <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolite c<strong>on</strong>centrati<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles and<br />

its effects <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e robustness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system as a whole: Given a metabolic network<br />

operating in steady state, we are interested in characterizing and identifying <str<strong>on</strong>g>th</str<strong>on</strong>g>ose<br />

metabolites whose c<strong>on</strong>centrati<strong>on</strong> assumes <strong>on</strong>ly <strong>on</strong>e value under <str<strong>on</strong>g>th</str<strong>on</strong>g>e given internal<br />

c<strong>on</strong>diti<strong>on</strong>s (specified by <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong> rates). This c<strong>on</strong>cept has recently been termed<br />

absolute c<strong>on</strong>centrati<strong>on</strong> robustness (ACR) [1], since <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolite wi<str<strong>on</strong>g>th</str<strong>on</strong>g> such property<br />

has <str<strong>on</strong>g>th</str<strong>on</strong>g>e same c<strong>on</strong>centrati<strong>on</strong> in every positive steady state <str<strong>on</strong>g>th</str<strong>on</strong>g>e system might<br />

admit. Note <str<strong>on</strong>g>th</str<strong>on</strong>g>at a metabolic network in which some metabolites have <str<strong>on</strong>g>th</str<strong>on</strong>g>e ACR<br />

property requires smaller extent <str<strong>on</strong>g>of</str<strong>on</strong>g> regulati<strong>on</strong> to maintain a given steady state,<br />

rendering <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire system more robust. Moreover, Shinar and Feinberg have<br />

shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at metabolites endowed wi<str<strong>on</strong>g>th</str<strong>on</strong>g> ACR can be elegantly determined wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

apparatus <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chemical Reacti<strong>on</strong> Network Theory (CRNT) [1].<br />

Metabolic networks <str<strong>on</strong>g>of</str<strong>on</strong>g>ten show switching behavior related to multistati<strong>on</strong>arity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> metabolite c<strong>on</strong>centrati<strong>on</strong>s [2]. Moreover, metabolic network states, characterized<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> fluxes and metabolite c<strong>on</strong>centrati<strong>on</strong>s, may exhibit intrinsic<br />

flux and c<strong>on</strong>centrati<strong>on</strong> couplings. Therefore, for metabolic networks, <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

robustness should encompass <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay between reacti<strong>on</strong> fluxes and <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting<br />

metabolite c<strong>on</strong>centrati<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles. To capture <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay between multistati<strong>on</strong>arity<br />

and couplings in <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolic state, we generalize <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> ACR to a<br />

family <str<strong>on</strong>g>of</str<strong>on</strong>g> robustness types for <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolites. Unlike <str<strong>on</strong>g>th</str<strong>on</strong>g>e CRNTbased<br />

approach, we present an analysis based <strong>on</strong> commutative algebra and algebraic<br />

geometry <str<strong>on</strong>g>th</str<strong>on</strong>g>at helps to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e qualitative properties <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic networks<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at included elements endowed wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed robustness types. The c<strong>on</strong>cepts<br />

are illustrated <strong>on</strong> paradigmatic network models as well as existing metabolic<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways.<br />

References.<br />

[1] G. Shinar, M. Feinberg, Structual sources <str<strong>on</strong>g>of</str<strong>on</strong>g> robustness in biochemical reacti<strong>on</strong> networks Science<br />

327 1389–1391.<br />

[2] S. Grimbs, A. Arnold, A. Koseska, J. Kur<str<strong>on</strong>g>th</str<strong>on</strong>g>s, J. Selbig, Z. Nikoloski, Spatiotemporal dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Calvin cycle: Multistati<strong>on</strong>arity and symmetry breaking instabilities Biosystems 103<br />

212–223.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Zoltan Neufeld<br />

UCD Dublin<br />

e-mail: zoltan.neufeld@ucd.ie<br />

Luca Cer<strong>on</strong>e<br />

UCD Dublin<br />

Javier Munoz-Garcia<br />

UCD Dublin<br />

Cellular Systems Biology; Tuesday, June 28, 17:00<br />

Integrating multiple signals into cell decisi<strong>on</strong>s by a network<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> protein modificati<strong>on</strong> cycles<br />

Cell resp<strong>on</strong>ses to internal and external stimuli are governed by protein interacti<strong>on</strong>s.<br />

The enzymatic activity and biological functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> proteins is modulated<br />

by reversible post-translati<strong>on</strong>al modificati<strong>on</strong>s such as phosphorylati<strong>on</strong>, acetylati<strong>on</strong>,<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ylati<strong>on</strong>, ubiquitinati<strong>on</strong>, sumoylati<strong>on</strong>, etc. Here we present a general model <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

reversible protein modificati<strong>on</strong>s and show <str<strong>on</strong>g>th</str<strong>on</strong>g>at such system can integrate multiple<br />

input signals into digital-like resp<strong>on</strong>ses, representing robust cellular decisi<strong>on</strong>s. C<strong>on</strong>sequently,<br />

proteins modified by multiple enzymes can functi<strong>on</strong> as complex switches,<br />

playing a similar role in cellular informati<strong>on</strong> processing as neur<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e brain. We<br />

develop an analytical approach for c<strong>on</strong>structing <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase diagram <str<strong>on</strong>g>of</str<strong>on</strong>g> such systems<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein modificati<strong>on</strong> network, determining how switching<br />

between distinct resp<strong>on</strong>ses take place. This me<str<strong>on</strong>g>th</str<strong>on</strong>g>od can be applied to a broad class<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> protein modificati<strong>on</strong> systems and provides an alternative to numerical approaches<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at give limited insight when <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> unknown parameters is large.<br />

703

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Undergraduate Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Educati<strong>on</strong> Bey<strong>on</strong>d BIO 2010 (Part I);<br />

Wednesday, June 29, 14:30<br />

Claudia Neuhauser<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Minnesota Rochester<br />

e-mail: neuha001@umn.edu<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Statistics, and Biology: An Integrative<br />

Approach<br />

Over <str<strong>on</strong>g>th</str<strong>on</strong>g>e past five years, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> funding from <str<strong>on</strong>g>th</str<strong>on</strong>g>e Howard Hughes Medical Institute,<br />

we have developed courses and shorter teaching units to enhance <str<strong>on</strong>g>th</str<strong>on</strong>g>e quantitative<br />

educati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> life science majors. We will present examples <str<strong>on</strong>g>th</str<strong>on</strong>g>at illustrate how<br />

biological applicati<strong>on</strong>s can enhance ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and statistics courses at <str<strong>on</strong>g>th</str<strong>on</strong>g>e lower<br />

divisi<strong>on</strong> and how ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and statistics can be integrated into biology courses,<br />

in particular into labs. We will report <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e implementati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e curricula at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e University <str<strong>on</strong>g>of</str<strong>on</strong>g> Minnesota Rochester and <str<strong>on</strong>g>th</str<strong>on</strong>g>e disseminati<strong>on</strong> strategy <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Numbers Count website and workshops held in collaborati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> BioQUEST.<br />

704

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling viral hepatitis dynamics in-vivo and in-vitro in <str<strong>on</strong>g>th</str<strong>on</strong>g>e era <str<strong>on</strong>g>of</str<strong>on</strong>g> direct<br />

anti-viral agents I; Tuesday, June 28, 17:00<br />

Avidan U. Neumann<br />

Bar-Ilan University, Ramat-Gan, Israel<br />

e-mail: auneumann@gmail.com<br />

Tal Olshak<br />

ITB, Humboldt University, Berlin, Germany<br />

Deterministic and Stochastic Multi-level Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Hepatitis C Viral Kinetics and Resistance Evoluti<strong>on</strong><br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> viral dynamics and resistance evoluti<strong>on</strong> have brought important<br />

insights for understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV, HBV and HCV viral<br />

infecti<strong>on</strong>s. However, current models <str<strong>on</strong>g>of</str<strong>on</strong>g> in vivo anti-viral <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy (CI models) c<strong>on</strong>sider<br />

<strong>on</strong>ly cell to cell infecti<strong>on</strong> dynamics, disregarding <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> intra-cellular<br />

replicati<strong>on</strong> dynamics. This class <str<strong>on</strong>g>of</str<strong>on</strong>g> models shows ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er viral decline wi<str<strong>on</strong>g>th</str<strong>on</strong>g> n<strong>on</strong>resistant<br />

viral strains or a permanent viral rebound <strong>on</strong>ce a phenotypically resistant<br />

strain evolves. Indeed, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese are <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterns observed for HIV, where intra-cellular<br />

replicati<strong>on</strong> has less <str<strong>on</strong>g>of</str<strong>on</strong>g> an impact because integrated viral DNA is a static replicati<strong>on</strong><br />

unit and <str<strong>on</strong>g>th</str<strong>on</strong>g>e various resistance events occur at <str<strong>on</strong>g>th</str<strong>on</strong>g>e time scale <str<strong>on</strong>g>of</str<strong>on</strong>g> cell infecti<strong>on</strong>.<br />

However, o<str<strong>on</strong>g>th</str<strong>on</strong>g>er patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> viral evoluti<strong>on</strong> kinetics, which are c<strong>on</strong>tradictory to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

current models, were observed during direct anti-viral <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy against HCV, where<br />

intra-cellular dynamics play an important role.<br />

We have <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore developed a novel model (Guedj and Neumann, 2010) for<br />

resistance evoluti<strong>on</strong>, which includes viral dynamics and evoluti<strong>on</strong> in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular<br />

replicati<strong>on</strong> level and <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell-infecti<strong>on</strong> level (ICCI model). As a c<strong>on</strong>sequence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex interacti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e two levels <str<strong>on</strong>g>of</str<strong>on</strong>g> viral dynamics, <str<strong>on</strong>g>th</str<strong>on</strong>g>e ICCI model<br />

predicts a rich repertoire <str<strong>on</strong>g>of</str<strong>on</strong>g> viral kinetics and resistance evoluti<strong>on</strong> patterns. In particular,<br />

we predict <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>tinuous viral decline is possible even if a phenotypically<br />

resistant strain has emerged. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at a resistance related viral<br />

break<str<strong>on</strong>g>th</str<strong>on</strong>g>rough could be merely transient and never<str<strong>on</strong>g>th</str<strong>on</strong>g>eless resolved. In bo<str<strong>on</strong>g>th</str<strong>on</strong>g> cases,<br />

counter-intuitively to our experience wi<str<strong>on</strong>g>th</str<strong>on</strong>g> HIV, viral eradicati<strong>on</strong> may be achieved<br />

even wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a phenotypically resistant virus.<br />

In additi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e ICCI model allows for rapid emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance evoluti<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out <str<strong>on</strong>g>th</str<strong>on</strong>g>e need for rapid turnover <str<strong>on</strong>g>of</str<strong>on</strong>g> infected cells, i.e. new cells are not needed to<br />

be available for infecti<strong>on</strong> by resistance virus. This is due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular<br />

replicati<strong>on</strong> space can be freed for evoluti<strong>on</strong> to resistant virus wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at are already infected. This <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical possibility was verified also by stochastic<br />

modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intra-cellular resistance evoluti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a fixed populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> infected<br />

cells. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, stochastic simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ICCI model shows how different<br />

patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance evoluti<strong>on</strong> occur as functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intra-cellular parameters.<br />

These results elucidate what <str<strong>on</strong>g>th</str<strong>on</strong>g>e important parameters to measure empirically in<br />

order to understand what kind <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance patterns will occur during treatment.<br />

705

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Developmental Biology; Friday, July 1, 14:30<br />

Sergey Nikolaev<br />

The Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Cytology and Genetics The Siberian Branch <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Russian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

e-mail: nikolaev@bi<strong>on</strong>et.nsc.ru<br />

Spatial Distributed Genetic Mechanism for Stem Cell Niche<br />

Structure C<strong>on</strong>trol in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Shoot Apical Meristem<br />

There is a qualitative hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>of</str<strong>on</strong>g> interplay between CLV and WUS genes as a<br />

mechanism for <str<strong>on</strong>g>th</str<strong>on</strong>g>e SAM compartmentalizati<strong>on</strong> into central z<strong>on</strong>e (CZ stem cells),<br />

organizing center (OC), and peripheral z<strong>on</strong>e (PZ). The following is an important<br />

moment <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis: CLV3 expressi<strong>on</strong> occurs in <str<strong>on</strong>g>th</str<strong>on</strong>g>e central cells <str<strong>on</strong>g>of</str<strong>on</strong>g> 3 upper<br />

layers (CZ), while WUS expressi<strong>on</strong> occurs in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells <str<strong>on</strong>g>of</str<strong>on</strong>g> OC, just below CZ; and<br />

CLV3 by means <str<strong>on</strong>g>of</str<strong>on</strong>g> binding wi<str<strong>on</strong>g>th</str<strong>on</strong>g> putative receptor CLV1/CLV2 inhibits WUS expressi<strong>on</strong>,<br />

while WUS activates CLV3 expressi<strong>on</strong>. This interplay is believed to be<br />

able to regulate stem cell niche structure in <str<strong>on</strong>g>th</str<strong>on</strong>g>e SAM.<br />

We developed a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> spatial distributed molecular-genetic<br />

mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> such a compartmentalizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e SAM to test <str<strong>on</strong>g>th</str<strong>on</strong>g>e above hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis.<br />

We added a hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>etical gene expressing in <str<strong>on</strong>g>th</str<strong>on</strong>g>e uppermost cells. And we supposed<br />

regulatory molecules propagate across <str<strong>on</strong>g>th</str<strong>on</strong>g>e SAM by diffusi<strong>on</strong>. A resulting system<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> differential equati<strong>on</strong>s was numerically solved to obtain a stati<strong>on</strong>ary soluti<strong>on</strong> <strong>on</strong><br />

a 2D domain representing vertical cut <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e SAM.<br />

Obtained model parameters supply a stati<strong>on</strong>ary soluti<strong>on</strong> for spatial distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeled genes expressi<strong>on</strong> in qualitative accordance wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimentally<br />

observed data <strong>on</strong> vertical cuts <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e SAM.<br />

The hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esized mechanism for stem cell niche structure c<strong>on</strong>trol in <str<strong>on</strong>g>th</str<strong>on</strong>g>e SAM<br />

grasps main features <str<strong>on</strong>g>of</str<strong>on</strong>g> interacti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e compartments experimentally observed.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Thursday, June 30, 11:30<br />

Ryosuke Nishi<br />

Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Aer<strong>on</strong>autics and Astr<strong>on</strong>autics, The Univ. <str<strong>on</strong>g>of</str<strong>on</strong>g> Tokyo<br />

Japan Society for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Promoti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Science<br />

e-mail: tt097086@mail.ecc.u-tokyo.ac.jp<br />

Atsushi Kamimura<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Industrial Science, The Univ. <str<strong>on</strong>g>of</str<strong>on</strong>g> Tokyo<br />

Katsuhiro Nishinari<br />

Research Center for Advanced Science and Technology, The Univ. <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Tokyo<br />

PRESTO, Japan Science and Technology Agency<br />

Toru Ohira<br />

S<strong>on</strong>y Computer Science Laboratories, Inc.<br />

e-mail: ohira@csl.s<strong>on</strong>y.co.jp<br />

Chase and Escape in Groups: Vampire Problem<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most important issues in our society is how to understand and<br />

deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases. This is important not <strong>on</strong>ly in physical<br />

space but in cyberspace as well. There have been numerical and <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical<br />

models used to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e phenomena <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious spreads. SIR models such<br />

as <str<strong>on</strong>g>th</str<strong>on</strong>g>e Kermack-McKendrick model are based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> “susceptible,”<br />

“infected,” and “recovered” populati<strong>on</strong>s. The c<strong>on</strong>tact process is ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

representative <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical model.<br />

The main purpose <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper is to introduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e element <str<strong>on</strong>g>of</str<strong>on</strong>g> “chase and escape”<br />

into <str<strong>on</strong>g>th</str<strong>on</strong>g>e above phenomena <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious spreads. The problems <str<strong>on</strong>g>of</str<strong>on</strong>g> “chase and<br />

escape,” also referred to as “pursuit and evasi<strong>on</strong>,” have a l<strong>on</strong>g history in ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

literature [1]. They produce ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er complex and elegant trajectories out<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> simple problem settings. Traditi<strong>on</strong>ally, <str<strong>on</strong>g>th</str<strong>on</strong>g>e main interest has been <str<strong>on</strong>g>th</str<strong>on</strong>g>e problems<br />

in which a single chaser try to catch a single evader. Recently, we introduced <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

paradigm “group chase and escape,” in which <strong>on</strong>e group chases ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er group [2]. It<br />

was motivated by recent research interests in <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> groups, or swarms, such<br />

as <str<strong>on</strong>g>th</str<strong>on</strong>g>ose <str<strong>on</strong>g>of</str<strong>on</strong>g> humans, animals, insects, and cars [3]. We have found <str<strong>on</strong>g>th</str<strong>on</strong>g>at a ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

complex behavior arises from <str<strong>on</strong>g>th</str<strong>on</strong>g>e models for “group chase and escape.”<br />

Here, we will modify our original models for “group chase and escape” to better<br />

fit <str<strong>on</strong>g>th</str<strong>on</strong>g>e models for infectious spread. Previously, when a chaser caught an evader, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

evader perished. Therefore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> evaders decreased m<strong>on</strong>ot<strong>on</strong>ically as <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

process c<strong>on</strong>tinued. We will modify <str<strong>on</strong>g>th</str<strong>on</strong>g>e process so <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e evaders do not become<br />

extinct as <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are caught but are instead c<strong>on</strong>verted or infected to become chasers.<br />

Heuristically, <str<strong>on</strong>g>th</str<strong>on</strong>g>is is like vampires trying to increase <str<strong>on</strong>g>th</str<strong>on</strong>g>eir numbers by attacking<br />

people. In reality, a similar situati<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> rabies, in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong><br />

is transmitted <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e bites <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e infected.There are studies <str<strong>on</strong>g>of</str<strong>on</strong>g> models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

spatial spread <str<strong>on</strong>g>of</str<strong>on</strong>g> rabies. We will show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e element <str<strong>on</strong>g>of</str<strong>on</strong>g> “chase and escape” will<br />

bring in a new phase to <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviors <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e models.<br />

References.<br />

[1] P. J. Nahin, Chase and Escape: The ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics <str<strong>on</strong>g>of</str<strong>on</strong>g> pursuit and evasi<strong>on</strong> (Princet<strong>on</strong> Univ.<br />

Press, 2007).<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[2] A. Kamimura and T. Ohira, Group Chase and Escape New Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics 12 053013<br />

(2010).<br />

[3] T. Vicsek and A. Zafiris, Collective Moti<strong>on</strong> arXiv:c<strong>on</strong>d-mat:1010.5017 (2010).<br />

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Epidemics; Tuesday, June 28, 17:00<br />

Hiroshi Nishiura<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> H<strong>on</strong>g K<strong>on</strong>g and Japan Science and Technology Agency<br />

e-mail: nishiura@hku.hk<br />

Gerardo Chowell<br />

Ariz<strong>on</strong>a State University<br />

e-mail: gchowell@asu.edu<br />

Carlos Castillo-Chavez<br />

Ariz<strong>on</strong>a State University<br />

e-mail: ccchavez@asu.edu<br />

Validating early estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> potential <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

pandemic influenza (H1N1-2009): Sample size estimati<strong>on</strong> for<br />

post-epidemic seroepidemiological studies<br />

Seroepidemiological studies before and after <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic wave <str<strong>on</strong>g>of</str<strong>on</strong>g> influenza (H1N1-<br />

2009) are useful for estimating final size wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a potential to validate early estimates<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reproducti<strong>on</strong> number, R, in modeling studies. Never<str<strong>on</strong>g>th</str<strong>on</strong>g>eless, a glance at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e literature shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at various seroepidemiological studies published so far have<br />

adopted a binomial sampling process to quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e uncertainty <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proporti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> infected individuals. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e present study, <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> an asymptotic distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e final epidemic size <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows for <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> approximate 95% c<strong>on</strong>fidence<br />

intervals <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proporti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals in a populati<strong>on</strong> infected during<br />

an epidemic, is proposed since infecti<strong>on</strong> events are not independent. Let ˆρ be an<br />

observed final size, v be <str<strong>on</strong>g>th</str<strong>on</strong>g>e coefficient <str<strong>on</strong>g>of</str<strong>on</strong>g> variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e generati<strong>on</strong> time distributi<strong>on</strong>,<br />

and q be <str<strong>on</strong>g>th</str<strong>on</strong>g>e proporti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> initially immune individuals. Assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>at v<br />

and q are known, we propose <str<strong>on</strong>g>th</str<strong>on</strong>g>e Wald approximati<strong>on</strong> by which <str<strong>on</strong>g>th</str<strong>on</strong>g>e 100(1 − 2α)%<br />

c<strong>on</strong>fidence interval for ρ is calculated as<br />

(1) ˆρ ± zα<br />

<br />

ˆρ 3 (1 − ˆρ) + v 2 ˆρ(1 − ˆρ) 2 ln 2 (1 − ˆρ/(1 − q))<br />

n [ˆρ + (1 − ˆρ) ln(1 − ˆρ/(1 − q))]<br />

where n is <str<strong>on</strong>g>th</str<strong>on</strong>g>e sample size and zα denotes 1 − α quantile <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard normal<br />

distributi<strong>on</strong>. This approach allows <str<strong>on</strong>g>th</str<strong>on</strong>g>e comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> observed final sizes against<br />

model studies based predicti<strong>on</strong>s (R = 1.15, 1.40 and 1.90) while yielding simple formulae<br />

for determining acceptable sample sizes for future seroepidemiological studies.<br />

Eleven published seroepidemiological studies <str<strong>on</strong>g>of</str<strong>on</strong>g> H1N1-2009, which took place<br />

after observing <str<strong>on</strong>g>th</str<strong>on</strong>g>e peak incidence in a number <str<strong>on</strong>g>of</str<strong>on</strong>g> countries, are used in <str<strong>on</strong>g>th</str<strong>on</strong>g>e testing<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology. Observed seropositive proporti<strong>on</strong>s in six studies appear to be<br />

significantly smaller <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>ose predicted from R = 1.40; four <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e six studies<br />

sampled serum less <str<strong>on</strong>g>th</str<strong>on</strong>g>an <strong>on</strong>e m<strong>on</strong><str<strong>on</strong>g>th</str<strong>on</strong>g> after <str<strong>on</strong>g>th</str<strong>on</strong>g>e reported peak incidence. Comparis<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> observed final sizes against R = 1.15 provide evidence <str<strong>on</strong>g>th</str<strong>on</strong>g>at all eleven studies<br />

do not significantly deviate from <str<strong>on</strong>g>th</str<strong>on</strong>g>e predicti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> R = 1.15 while comparis<strong>on</strong>s<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> R = 1.90 suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e final sizes in nine studies would be overestimated.<br />

Sample sizes <str<strong>on</strong>g>of</str<strong>on</strong>g> published seroepidemiological studies were too small to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

validity <str<strong>on</strong>g>of</str<strong>on</strong>g> model predicti<strong>on</strong>s except when R = 1.90 was used. We recommend<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed approach in determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e sample size <str<strong>on</strong>g>of</str<strong>on</strong>g> post-epidemic<br />

709

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

seroepidemiological studies, calculating <str<strong>on</strong>g>th</str<strong>on</strong>g>e 95% c<strong>on</strong>fidence interval <str<strong>on</strong>g>of</str<strong>on</strong>g> observed final<br />

size, and c<strong>on</strong>ducting relevant hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis testing instead <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at rely <strong>on</strong> a binomial proporti<strong>on</strong>,<br />

710

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Robert Noble<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Zoology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: robert.noble@linacre.ox.ac.uk<br />

Zoe Christodoulou<br />

Wear<str<strong>on</strong>g>th</str<strong>on</strong>g>erall Institute for Molecular Medicine<br />

Robert Pinches<br />

Wear<str<strong>on</strong>g>th</str<strong>on</strong>g>erall Institute for Molecular Medicine<br />

Sue A. Kyes<br />

Wear<str<strong>on</strong>g>th</str<strong>on</strong>g>erall Institute for Molecular Medicine<br />

Chris I. Newbold<br />

Wear<str<strong>on</strong>g>th</str<strong>on</strong>g>erall Institute for Molecular Medicine<br />

Mario Recker<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Zoology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

Regulatory Networks; Tuesday, June 28, 17:00<br />

Using iterative me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to determine an antigenic switching<br />

network in Plasmodium falciparum<br />

Background: The malaria parasite Plasmodium falciparum evades host protective<br />

antibody resp<strong>on</strong>ses by transcripti<strong>on</strong>al switching between members <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e var gene<br />

family, which encode <str<strong>on</strong>g>th</str<strong>on</strong>g>e immunodominant surface proteins and virulence factors<br />

PfEMP1. This process <str<strong>on</strong>g>of</str<strong>on</strong>g> antigenic variati<strong>on</strong> must be coordinated across a whole<br />

populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> parasites during infecti<strong>on</strong> to minimise exposure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parasites limited<br />

antigenic repertoire. Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> in vitro transcripti<strong>on</strong> data has previously suggested<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is process underlies a n<strong>on</strong>-random pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong>al change<br />

in which activati<strong>on</strong> and silencing not <strong>on</strong>ly differs significantly between individual<br />

var genes but may also be biased [1,2].<br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: To elucidate whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er switching between var genes is predominantly<br />

governed by local switch hierarchies, whereby activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> var genes is dominated<br />

by switch biases between different genes, or by a more global hierarchy in which<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> activati<strong>on</strong> is independent <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e previously active gene, we analysed in<br />

vitro expressi<strong>on</strong> data from eleven cl<strong>on</strong>es <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e HB3 isolate toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parent<br />

culture. We used simulated annealing and a Markov Chain M<strong>on</strong>te Carlo me<str<strong>on</strong>g>th</str<strong>on</strong>g>od to<br />

determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>of</str<strong>on</strong>g>f-rates and switch biases <str<strong>on</strong>g>th</str<strong>on</strong>g>at best fitted <str<strong>on</strong>g>th</str<strong>on</strong>g>e data, enabling us to<br />

c<strong>on</strong>struct a global gene switching network <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e var gene repertoire <str<strong>on</strong>g>of</str<strong>on</strong>g> HB3. Tests<br />

using artificial data c<strong>on</strong>firmed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms can recover reliable estimates<br />

despite <str<strong>on</strong>g>th</str<strong>on</strong>g>e large parameter space.<br />

Principle findings: Our results suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e course <str<strong>on</strong>g>of</str<strong>on</strong>g> antigenic variati<strong>on</strong> in<br />

P. falciparum can be described by a fixed network <str<strong>on</strong>g>of</str<strong>on</strong>g> transiti<strong>on</strong> rates. C<strong>on</strong>sistent<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> previous studies we found <str<strong>on</strong>g>th</str<strong>on</strong>g>at activated var genes switch <str<strong>on</strong>g>of</str<strong>on</strong>g>f at fixed rates<br />

which range between 0.3% and 5.2% per generati<strong>on</strong>. Our results fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er show <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e likelihood <str<strong>on</strong>g>of</str<strong>on</strong>g> a particular var being activated depends <strong>on</strong> which var is switching<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g>f, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> biases towards <strong>on</strong>e dominant gene found to vary from less <str<strong>on</strong>g>th</str<strong>on</strong>g>an 25% to more<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>an 75%. This indicates <str<strong>on</strong>g>th</str<strong>on</strong>g>at var gene switching in P. falciparum is a combinati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> local switch biases and global activati<strong>on</strong> hierarchies.<br />

References.<br />

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[1] Horrocks, P., Pinches, R., Christodoulou, Z., Kyes, S.A., Newbold, C.I (2004) Variable var<br />

transiti<strong>on</strong> rates underlie antigenic variati<strong>on</strong> in malaria. Proc.Natl.Acad.Sci.U.S.A. 101(30):<br />

11129-11134<br />

[2] Recker, M., Buckee, C.O., Serazin, A., Kyes, S., Pinches, R., Christodoulou, Z., Springer, A.L.,<br />

Gupta, S., Newbold, C.I (in press) Antigenic variati<strong>on</strong> in Plasmodium falciparum malaria<br />

involves a highly structured switching pattern. PLoS Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

L. Noiret<br />

CoMPLEX, University College L<strong>on</strong>d<strong>on</strong> (UCL), UK<br />

e-mail: l.noiret@ucl.ac.uk<br />

S. Baigent<br />

Dept Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, UCL, UK<br />

e-mail: s.baigent@ucl.ac.uk<br />

R. Jalan<br />

Royal Free Hospital - UCL Medical School, UK<br />

e-mail: r.jalan@ucl.ac.uk<br />

S. R. Thomas<br />

IR4M UMR8081 CNRS, Universite Paris-Sud 11, Orsay, France<br />

e-mail: sr<str<strong>on</strong>g>th</str<strong>on</strong>g>omas@ibisc.univ-evry.fr<br />

Renal amm<strong>on</strong>ia handling in cirrhosis<br />

Background The kidney plays a dual role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e amm<strong>on</strong>ia metabolism by producing<br />

amm<strong>on</strong>ia and c<strong>on</strong>trolling <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount <str<strong>on</strong>g>of</str<strong>on</strong>g> amm<strong>on</strong>ia reabsorbed into <str<strong>on</strong>g>th</str<strong>on</strong>g>e renal vein<br />

or excreted into <str<strong>on</strong>g>th</str<strong>on</strong>g>e urine. In advanced stages <str<strong>on</strong>g>of</str<strong>on</strong>g> liver cirrhosis, renal reabsorpti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> amm<strong>on</strong>ia seems to diminish in favour <str<strong>on</strong>g>of</str<strong>on</strong>g> urinary excreti<strong>on</strong> ([1]). The underlying<br />

mechanisms are not fully understood, but it is likely <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e decrease is triggered<br />

by an elevated arterial c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> amm<strong>on</strong>ia and by functi<strong>on</strong>al alterati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e amm<strong>on</strong>ia transporter system al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e renal tubule. We developed a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> renal amm<strong>on</strong>ia handling to explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters associated<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an increased urinary excreti<strong>on</strong>.<br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods The model is an adaptati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a model by Hervy and Thomas ([2])<br />

and was initially designed to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e osmotic gradient in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

medullary interstitium. It simulates <str<strong>on</strong>g>th</str<strong>on</strong>g>e reabsorpti<strong>on</strong> and secreti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> solutes (NaCl,<br />

KCl, urea, amm<strong>on</strong>ia) and water al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e renal tubules. Each idealized tubule is<br />

composed <str<strong>on</strong>g>of</str<strong>on</strong>g> a loop <str<strong>on</strong>g>of</str<strong>on</strong>g> Henle and a collecting duct, and is supplied by a vasa recta.<br />

The tubes are ba<str<strong>on</strong>g>th</str<strong>on</strong>g>ed and exchange solutes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> in an interstitium, which is lumped<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ascending porti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vasa recta. The equati<strong>on</strong>s describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmural<br />

fluxes between <str<strong>on</strong>g>th</str<strong>on</strong>g>e tubes and interstitium due to osmosis, c<strong>on</strong>vecti<strong>on</strong>, diffusi<strong>on</strong> and<br />

active transport. Baseline parameters values were taken from <str<strong>on</strong>g>th</str<strong>on</strong>g>e rat literature.<br />

Results We compare <str<strong>on</strong>g>th</str<strong>on</strong>g>e outputs <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model obtained wi<str<strong>on</strong>g>th</str<strong>on</strong>g> parameters mimicking<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y and diseased states.<br />

References.<br />

[1] SWM Olde Damink, R Jalan, NEP Deutz, DN Redhead, CHC Dej<strong>on</strong>g,P Hynd, RA Jalan,PC<br />

Hayes, PB Soeters. The kidney plays a major role in amm<strong>on</strong>ia homeostasis after portasystemic<br />

shunting in patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> cirrhosis. Hepatology 37(6):1277–1285, 2006.<br />

[2] S Hervy, SR Thomas. Inner medullary lactate producti<strong>on</strong> and urine-c<strong>on</strong>centrating mechanism:<br />

a flat medullary model. Am J Physiol Renal Physiol 284(1): F65–81, 2003.<br />

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Plants, grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and transport processes II; Tuesday, June 28, 14:30<br />

Robert Nolet<br />

VU University Amsterdam<br />

e-mail: r.w.nolet@vu.nl<br />

J. Hulsh<str<strong>on</strong>g>of</str<strong>on</strong>g><br />

VU University Amsterdam<br />

G. Prokert<br />

Eindhoven University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Existence <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusive VSC model.<br />

The c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> a vesicle supply center (VSC), first proposed by Bartnicki-Garcia<br />

et al lies at <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis for a whole hierarchy <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models which attempt<br />

to explain tip grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in fungal hyphae. It assumes <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a point source in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e tip which distributes cell wall material for <str<strong>on</strong>g>th</str<strong>on</strong>g>e tip. Vesicles diffuse out from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e VSC to <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell wall, producing grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell wall or<str<strong>on</strong>g>th</str<strong>on</strong>g>og<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e wall<br />

surface. This yields a geometric evoluti<strong>on</strong> equati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e surface <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypha, in<br />

which <str<strong>on</strong>g>th</str<strong>on</strong>g>e normal velocity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e surface is proporti<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e flux <str<strong>on</strong>g>of</str<strong>on</strong>g> new material<br />

arriving at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell wall and <str<strong>on</strong>g>th</str<strong>on</strong>g>e inverse <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean curvature. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, we<br />

shall assume <str<strong>on</strong>g>th</str<strong>on</strong>g>e VSC is given a fixed velocity, we will <str<strong>on</strong>g>th</str<strong>on</strong>g>en show how to prove <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

existence <str<strong>on</strong>g>of</str<strong>on</strong>g> surfaces which stay stati<strong>on</strong>ary in a coordinate frame moving al<strong>on</strong>g wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e supply center.<br />

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Populati<strong>on</strong> Dynamics; Wednesday, June 29, 11:00<br />

Etsuko N<strong>on</strong>aka<br />

IceLab & Dept <str<strong>on</strong>g>of</str<strong>on</strong>g> Ecology and Envir<strong>on</strong>mental Science, Umeå University,<br />

Sweden<br />

e-mail: etsuko.n<strong>on</strong>aka@gmail.com<br />

David J. T. Sumpter<br />

Dept <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Uppsala University, Sweden<br />

Kalle Parvinen<br />

Dept <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Turku, Finland<br />

Åke Brännström<br />

IceLab & Dept <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Statistics, Umeå University,<br />

Sweden<br />

Adaptive advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> aggregati<strong>on</strong> in a populati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Allee effects<br />

Aggregati<strong>on</strong> is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten believed to be advantageous in populati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> positive density<br />

dependence at small populati<strong>on</strong> size (i.e., Allee effects). Many species <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>social<br />

animals aggregate to acquire resources for survival and reproducti<strong>on</strong>. By aggregating,<br />

organisms may create a more favorable envir<strong>on</strong>ment, reduce per capita<br />

predati<strong>on</strong> risk, or procure resources, n<strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> which is likely attainable for individuals<br />

acting al<strong>on</strong>e. However, when resources are scarce or populati<strong>on</strong> density is high,<br />

aggregati<strong>on</strong> likely results in overcrowding and severe competiti<strong>on</strong>. Moreover, aggregati<strong>on</strong><br />

behavior can affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e collective reproductive success <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>us can alter populati<strong>on</strong> dynamics and populati<strong>on</strong> density. Because benefits to aggregati<strong>on</strong><br />

behavior may be density dependent, its adaptive advantage can be more<br />

properly examined by explicitly accounting for <str<strong>on</strong>g>th</str<strong>on</strong>g>e feedback loop between behavior<br />

and populati<strong>on</strong> dynamics. The objective <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is project is to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s<br />

under which aggregati<strong>on</strong> is advantageous. We c<strong>on</strong>structed a minimal model<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at incorporates aggregati<strong>on</strong>, Allee effects, and scramble competiti<strong>on</strong>. The part <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e model describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> group formati<strong>on</strong> by preferential attachment is<br />

based <strong>on</strong> analytical soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic bir<str<strong>on</strong>g>th</str<strong>on</strong>g> and dea<str<strong>on</strong>g>th</str<strong>on</strong>g> processes <str<strong>on</strong>g>of</str<strong>on</strong>g> groups <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

different sizes. We <str<strong>on</strong>g>th</str<strong>on</strong>g>en used <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods from adaptive dynamics and performed<br />

invasi<strong>on</strong> analysis to examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong> fitness <str<strong>on</strong>g>of</str<strong>on</strong>g> various aggregati<strong>on</strong> tendencies.<br />

We found <str<strong>on</strong>g>th</str<strong>on</strong>g>at, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough a str<strong>on</strong>g tendency to join larger groups is advantageous for<br />

establishing a populati<strong>on</strong> from a small size, it is generally not advantageous. This<br />

is due to high populati<strong>on</strong> density produced by effective aggregati<strong>on</strong>. A strategy<br />

where individuals pick a group randomly is overall more advantageous and able<br />

to invade populati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a str<strong>on</strong>ger aggregati<strong>on</strong> tendency. In some regi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

parameter space, we observe evoluti<strong>on</strong>ary suicide where invaders go extinct after<br />

successfully invading <str<strong>on</strong>g>th</str<strong>on</strong>g>e resident populati<strong>on</strong>. Str<strong>on</strong>g tendencies for aggregati<strong>on</strong><br />

become advantageous enough to persist when some mechanisms regulating group<br />

size are included or when <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> frequently experiences a low density (e.g,<br />

dispersal, stochastic high mortality events). We c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at aggregati<strong>on</strong> al<strong>on</strong>e is<br />

mostly not advantageous and needs some additi<strong>on</strong>al mechanisms to ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er regulate<br />

group size or suppress populati<strong>on</strong> density.<br />

715

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Wednesday, June 29, 08:30<br />

Ekaterina A. Nosova<br />

Russian Federal Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

e-mail: cnosova@gmail.com<br />

Alexei A. Romanyukha<br />

Russian Academy od Sciences Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Numerical Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

Equilibrium in model <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV dynamics wi<str<strong>on</strong>g>th</str<strong>on</strong>g> transiti<strong>on</strong>s<br />

between risk group<br />

It is well known <str<strong>on</strong>g>th</str<strong>on</strong>g>at features <str<strong>on</strong>g>of</str<strong>on</strong>g> transmissi<strong>on</strong> for human immunodeficiency virus<br />

allow c<strong>on</strong>trol <str<strong>on</strong>g>th</str<strong>on</strong>g>e infecti<strong>on</strong> process by behavior change. Populati<strong>on</strong> heterogeneity in<br />

propensity to risky behavior leads to <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility <str<strong>on</strong>g>of</str<strong>on</strong>g> separating <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase transiti<strong>on</strong>s<br />

in epidemic dynamics. These phase transiti<strong>on</strong>s distinguish between low-level,<br />

c<strong>on</strong>centrated and generalized epidemics. Data analysis[1] shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at an important<br />

role in spreading HIV <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e territory <str<strong>on</strong>g>of</str<strong>on</strong>g> Russia is played by processes <str<strong>on</strong>g>of</str<strong>on</strong>g> social<br />

maladjustment: drug abuse, alcoholism and <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an increased risk <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

substance abuse pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e models have been applied before to explain<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e situati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e territory <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e former Soviet Uni<strong>on</strong>, including Russia,<br />

show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese risk-groups and its influence <strong>on</strong> HIV<br />

epidemics is more complicated <str<strong>on</strong>g>th</str<strong>on</strong>g>an it was represented[2,3]. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper we formulated<br />

a deterministic model <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV spread in a heterogeneous populati<strong>on</strong>, where<br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> risk groups is presented as a c<strong>on</strong>sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> social maladjustment. In<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is model an individual from general populati<strong>on</strong> can increase or decrease <str<strong>on</strong>g>th</str<strong>on</strong>g>e level<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> his/her social maladjustment being susceptible to <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus. In each <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

states, <strong>on</strong>e has a certain risk <str<strong>on</strong>g>of</str<strong>on</strong>g> being infected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> HIV. The proposed model in<br />

part is similar to <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> STIs in heterogeneous populati<strong>on</strong>,<br />

as proposed by Cooke and Yorke[4]. Unlike <str<strong>on</strong>g>th</str<strong>on</strong>g>e traditi<strong>on</strong>al approach <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

possibility <str<strong>on</strong>g>of</str<strong>on</strong>g> transfer individuals between risk groups was taken to account. Thus<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e formulated model bel<strong>on</strong>gs to a broader class <str<strong>on</strong>g>of</str<strong>on</strong>g> deterministic SI models. This<br />

generalizati<strong>on</strong> allows obtain new results about <str<strong>on</strong>g>th</str<strong>on</strong>g>e properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e equilibrium <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

system and c<strong>on</strong>diti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> existence and transiti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>em. Some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model we investigate in <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper.<br />

This work is supported by Russian Foundati<strong>on</strong> for Basic Research: RFBR 09-<br />

01-00098a. Data analysis was provided via financial support <str<strong>on</strong>g>of</str<strong>on</strong>g> UNDP: UNDP/212/2007.<br />

References.<br />

[1] E. A. Nosova, A. A. Romanyukha Regi<strong>on</strong>al index <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV infecti<strong>on</strong> risk based <strong>on</strong> factors <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

social disadaptati<strong>on</strong>. RJNAMM Vol 24 No 4 pp 325-340, 2009<br />

[2] Alistar S., Owens D., Brandeau M. Effectiveness and cost effectivenes <str<strong>on</strong>g>of</str<strong>on</strong>g> expanding drug<br />

treatment programs and HIV antiretroviral <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy in a mixed HIV epidemic: an Analysis for<br />

Ukraine. Russian Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> AIDS, Cancer and Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Vol. 14 No 1(29) p.44, 2010<br />

[3] Kupryashkina-McGill S. V. Influence <str<strong>on</strong>g>of</str<strong>on</strong>g> Global Fund grants <strong>on</strong> HIV/AIDS policy in Ukraine.<br />

Russian Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> AIDS, Cancer and Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Vol. 14 No 1(29) p.27, 2010<br />

[4] Cooke K. L., Yorke J. A. Some equati<strong>on</strong>s modelling grow<str<strong>on</strong>g>th</str<strong>on</strong>g> processes and g<strong>on</strong>orrhea epidemics.<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci., 16, pp. 75-101, 1973<br />

716

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ka<str<strong>on</strong>g>th</str<strong>on</strong>g>erine Novoselova<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> cytology and genetics SB RAS, Russia<br />

e-mail: esn@bi<strong>on</strong>et.nsc.ru<br />

Victoria Mir<strong>on</strong>ova<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> cytology and genetics SB RAS, Russia<br />

Nadezda Omelyanchuk<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> cytology and genetics SB RAS, Russia<br />

Vitaly Likhoshvai<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> cytology and genetics SB RAS, Russia<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Modelling auxin transport in root provascular tissues<br />

All vascular plants are called so because <str<strong>on</strong>g>th</str<strong>on</strong>g>ey have special vascular or c<strong>on</strong>ductive<br />

tissues providing effective transport <str<strong>on</strong>g>of</str<strong>on</strong>g> water, dissolved minerals and organic substances,<br />

including phytohorm<strong>on</strong>es. Root apical meristem (RAM) c<strong>on</strong>tains vascular<br />

initials from which protoxylem and protophloem differentiate fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er producing<br />

xylem and phloem, respectively. Acropetal flow <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin al<strong>on</strong>g root provascular<br />

tissues is required for normal functi<strong>on</strong>ing <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e RAM. Auxin distributes in plant<br />

tissue by means <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong> and active transport <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> membrane<br />

transporters (PINs, AUX/LAX etc). In protoxylem, auxin active transport is mediated<br />

by PIN efflux transporters <str<strong>on</strong>g>th</str<strong>on</strong>g>at are polarly localized at <str<strong>on</strong>g>th</str<strong>on</strong>g>e basal side <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cell membranes. In protophloem, additi<strong>on</strong>ally to PINs efflux transporters, AUX1<br />

influx carriers are localized at <str<strong>on</strong>g>th</str<strong>on</strong>g>e apical side <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e membranes provide for auxin<br />

transport. Thus, protoxylem and protophloem differ in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin<br />

active transport. To study how <str<strong>on</strong>g>th</str<strong>on</strong>g>ese differences in transporters affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e auxin<br />

distributi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese tissues we have created ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin transport<br />

in root protophloem and protoxylem. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> models use as a prototype <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

published model <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin transport al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e central axis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e root [Mir<strong>on</strong>ova<br />

et al., 2010]. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e protoxylem model, <str<strong>on</strong>g>th</str<strong>on</strong>g>e active auxin efflux is determined by<br />

PIN transporters, where auxin influx from <str<strong>on</strong>g>th</str<strong>on</strong>g>e intercellular space is provided <strong>on</strong>ly<br />

by diffusi<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e protophloem model, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> PIN and AUX1 transport systems<br />

are active. Initially, in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> protoxylem and protophloem simulati<strong>on</strong>s we used <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

same set <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters. Parameter values were (1) taken from <str<strong>on</strong>g>th</str<strong>on</strong>g>e prototype model<br />

[Mir<strong>on</strong>ova et al., 2010], (2) adjusted using <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental data <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e comparative<br />

efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin active transport and diffusi<strong>on</strong> [Yang and Murphy, 2009] and<br />

(3) estimated using <str<strong>on</strong>g>th</str<strong>on</strong>g>e microarray data [Pap<strong>on</strong>ov et al., 2008]. The protoxylem<br />

model soluti<strong>on</strong>s represented <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimentally observed auxin distributi<strong>on</strong> al<strong>on</strong>g<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e central axis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e root tip. The protophloem model provided <str<strong>on</strong>g>th</str<strong>on</strong>g>ese soluti<strong>on</strong>s<br />

<strong>on</strong>ly if <str<strong>on</strong>g>th</str<strong>on</strong>g>e values <str<strong>on</strong>g>of</str<strong>on</strong>g> some parameters were significantly changed. Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is, we<br />

proposed <str<strong>on</strong>g>th</str<strong>on</strong>g>e following hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses about <str<strong>on</strong>g>th</str<strong>on</strong>g>e differences in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin<br />

transport in protophloem and protoxylem: 1. Auxin-depended PINs degradati<strong>on</strong><br />

in protophloem occurs at higher levels <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin c<strong>on</strong>centrati<strong>on</strong>s; 2. Auxin-dependent<br />

activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> PINs syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis in protophloem occurs at lower auxin c<strong>on</strong>centrati<strong>on</strong>s;<br />

3. Auxin transport via PINs in protophloem is more efficient <str<strong>on</strong>g>th</str<strong>on</strong>g>an in protoxylem.<br />

The latter hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis was indirectly c<strong>on</strong>firmed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e recently published experimental<br />

data [Scacchi et al., 2010], where expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> protophloem marker gene<br />

BRX was shown to be activated by ARF5, <str<strong>on</strong>g>th</str<strong>on</strong>g>e transcripti<strong>on</strong> factor <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

auxin resp<strong>on</strong>se. In its turn, BRX activates <str<strong>on</strong>g>th</str<strong>on</strong>g>e PIN3 expressi<strong>on</strong>. One may assume<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at BRX-mediated PIN3 expressi<strong>on</strong> provides <str<strong>on</strong>g>th</str<strong>on</strong>g>e additi<strong>on</strong>al facility <str<strong>on</strong>g>th</str<strong>on</strong>g>at makes<br />

protophloem auxin transport more effective. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical simulati<strong>on</strong>s<br />

we c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e same pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin distributi<strong>on</strong> in provascular tissues<br />

provides for by <str<strong>on</strong>g>th</str<strong>on</strong>g>e quite different mechanisms.<br />

The work is partially supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e RAS programs A.II.5.26, A.II.6.8,<br />

B.27.29, SB RAS 107, 119, and RFBR 10-01-00717-,11-04-01254-.<br />

References.<br />

[1] Mir<strong>on</strong>ova VV, Omelyanchuk NA, Yosiph<strong>on</strong> G, Fadeev SI, Kolchanov NA, Mjolsness E, Likhoshvai<br />

VA: A plausible mechanism for auxin patterning al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e developing root. BMC Systems<br />

Biology 2010, 4:98.<br />

[2] Yang H and Murphy AS: Functi<strong>on</strong>al expressi<strong>on</strong> and characterizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Arabidopsis ABCB,<br />

AUX 1 and PIN auxin transporters in Schizosaccharomyces pombe. Plant J. 2009, 59(1):179-<br />

91.<br />

[3] Pap<strong>on</strong>ov IA, Pap<strong>on</strong>ova M, Tealea W, Mengesb M, Chakraborteeb S, Murray JAH and Palmea<br />

K: Comprehensive transcriptome analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin resp<strong>on</strong>ses in Arabidopsis. Mol Plant. 2008,<br />

1(2):321-37.<br />

[4] Scacchi E, Salinas P, Gujas B, Santuari L, Krogan N, Ragni L, Berle<str<strong>on</strong>g>th</str<strong>on</strong>g> T and Hardtke CS:<br />

Spatio-temporal sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> cross-regulatory events in root meristem grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. Proc Natl Acad<br />

Sci U S A. 2010, 107(52):22734-9.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Wednesday, June 29, 11:00<br />

Artem S. Novozhilov<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics–1, Moscow State University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Railway Engineering, Obraztsova 9, Moscow 127994, Russia<br />

e-mail: anovozhilov@gmail.com<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics in a closed heterogeneous<br />

populati<strong>on</strong>: Stochastic aspects<br />

In [1,2] we presented an attempt to formulate a general deterministic <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

spread <str<strong>on</strong>g>of</str<strong>on</strong>g> an infectious disease in a closed heterogeneous populati<strong>on</strong>. Specifically,<br />

we looked into heterogeneity in disease parameters (such as susceptibility to a disease);<br />

disease parameters were c<strong>on</strong>sidered as an inherent and invariant property <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

individuals, whereas <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter values could vary between individuals. The two<br />

major findings for a heterogeneous SIR model were: 1) we derived <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong> for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e final size <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic for an arbitrary initial distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> susceptibility,<br />

which shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial susceptibility distributi<strong>on</strong> is crucial in determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at escapes infecti<strong>on</strong>; 2) <str<strong>on</strong>g>th</str<strong>on</strong>g>e widely used power transmissi<strong>on</strong><br />

functi<strong>on</strong> was deduced from <str<strong>on</strong>g>th</str<strong>on</strong>g>e model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> distributed susceptibility and infectivity<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial gamma-distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease parameters, <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore, a mechanistic<br />

derivati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e phenomenological model, which is believed to mimic reality<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high accuracy, was provided.<br />

Here we additi<strong>on</strong>ally discuss stochastic aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, which are impossible<br />

to study wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e framework <str<strong>on</strong>g>of</str<strong>on</strong>g> deterministic models, namely:<br />

• In which way <str<strong>on</strong>g>th</str<strong>on</strong>g>e parametric heterogeneity changes <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

major outbreak;<br />

• What are <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parametric heterogeneity <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean<br />

durati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic;<br />

• What are <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean and variance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e final epidemic<br />

size for different initial susceptibility distributi<strong>on</strong>s.<br />

References.<br />

[1] A. S. Novozhilov. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics in a closed heterogeneous populati<strong>on</strong>. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

Biosciences, 215(2):177–185, 2008.<br />

[2] A. S. Novozhilov. Heterogeneous susceptibles–infectives model: Mechanistic derivati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

power law transmissi<strong>on</strong> functi<strong>on</strong>. Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> C<strong>on</strong>tinuous, Discrete and Impulsive Systems<br />

(Series A, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Analysis), 16(S1):136–140, 2009.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

V; Wednesday, June 29, 11:00<br />

A. Nowakowski, A. Popa<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Lodz, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> & Computer Sciences<br />

Hamilt<strong>on</strong>-Jacobi analysis for cancer treatment<br />

Tumor anti-angiogenesis is a cancer <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy approach <str<strong>on</strong>g>th</str<strong>on</strong>g>at targets <str<strong>on</strong>g>th</str<strong>on</strong>g>e vasculature<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a growing tumor. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e last fifteen years tumor anti-angiogenesis became<br />

an active area <str<strong>on</strong>g>of</str<strong>on</strong>g> research not <strong>on</strong>ly in medicine (see e.g. [2], [3]) but also in ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

biology (see e.g. [1], [6], [7]) and several models <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis<br />

have been described e.g. by Hahnfeldt et all [1], d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio [6], [7]. In a sequence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> papers [4], [5] Ledzewicz and Schaettler completely decribed and solved from<br />

optimal c<strong>on</strong>trol <str<strong>on</strong>g>th</str<strong>on</strong>g>eory point <str<strong>on</strong>g>of</str<strong>on</strong>g> view <str<strong>on</strong>g>th</str<strong>on</strong>g>e following or similar free terminal time T<br />

problem (P): minimize<br />

(1) J(p, q, u) = p(T ) + κ<br />

T<br />

0<br />

u(t)dt<br />

over all Lebesgue measurable functi<strong>on</strong>s u : [0, T ] → [0, a] = U subject to<br />

(2)<br />

<br />

p<br />

˙p = −ξp ln ,<br />

q<br />

p(0) = p0,<br />

<br />

(3) ˙q = bp −<br />

µ + dp 2<br />

3<br />

<br />

q − Guq, q(0) = q0.<br />

The term T<br />

u(t)dt is viewed as a measure for <str<strong>on</strong>g>th</str<strong>on</strong>g>e cost <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment or related<br />

0<br />

to side effects. The upper limit a in <str<strong>on</strong>g>th</str<strong>on</strong>g>e definiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol set U = [0, a] is a<br />

maximum dose at which inhibitors can be given. The time T is <str<strong>on</strong>g>th</str<strong>on</strong>g>e time when <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

maximum tumor reducti<strong>on</strong> achievable wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e given overall amount A <str<strong>on</strong>g>of</str<strong>on</strong>g> inhibitors<br />

is being realized. The state variables p and q are, respectively, <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary tumor<br />

volume and <str<strong>on</strong>g>th</str<strong>on</strong>g>e carrying capacity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vasculature. Tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is modelled by<br />

a Gompertzian grow<str<strong>on</strong>g>th</str<strong>on</strong>g> functi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> carrying capacity q, by equati<strong>on</strong> (2), where ξ<br />

denotes a tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> parameter. The dynamics for <str<strong>on</strong>g>th</str<strong>on</strong>g>e endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial support is<br />

described by (3), where bp models <str<strong>on</strong>g>th</str<strong>on</strong>g>e stimulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells by <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e term dp 2<br />

3 q models endogenous inhibiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor. The coefficients b<br />

and d are grow<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>stants. The terms µq and Guq describe, respectively, loss to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

carrying capacity <str<strong>on</strong>g>th</str<strong>on</strong>g>rough natural causes (dea<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells etc.), and loss<br />

due to extra outside inhibiti<strong>on</strong>. The variable u represents <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol in <str<strong>on</strong>g>th</str<strong>on</strong>g>e system<br />

and corresp<strong>on</strong>ds to <str<strong>on</strong>g>th</str<strong>on</strong>g>e angiogenic dose rate while G is a c<strong>on</strong>stant <str<strong>on</strong>g>th</str<strong>on</strong>g>at represents<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e anti-angiogenic killing parameter. Ledzewicz and Schaettler analysed <str<strong>on</strong>g>th</str<strong>on</strong>g>e above<br />

problem using first-order necessary c<strong>on</strong>diti<strong>on</strong>s for optimality <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>trol u given by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e P<strong>on</strong>tryagin Maximum Principle, <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d order: <str<strong>on</strong>g>th</str<strong>on</strong>g>e so-called streng<str<strong>on</strong>g>th</str<strong>on</strong>g>ened<br />

Legendre-Clebsch c<strong>on</strong>diti<strong>on</strong> and geometric me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> optimal c<strong>on</strong>trol <str<strong>on</strong>g>th</str<strong>on</strong>g>eory.<br />

In most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e menti<strong>on</strong>ed papers <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical calculati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> approximated<br />

soluti<strong>on</strong>s are presented. However in any <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are not proved asserti<strong>on</strong>s<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at calculated numerically soluti<strong>on</strong>s are really near <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal <strong>on</strong>e.<br />

The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper is an analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e porblem (1)-(3) from Hamilt<strong>on</strong>-<br />

Jacobi-Bellman point <str<strong>on</strong>g>of</str<strong>on</strong>g> view i.e. using dynamic programming approach and to<br />

720

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

prove <str<strong>on</strong>g>th</str<strong>on</strong>g>at for calculated numerically soluti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>e fucti<strong>on</strong>al (1) takes an approximate<br />

value wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a given accuracy ε > 0.<br />

References.<br />

[1] P. Hahnfeldt, D. Panigrahy, J. Folkman and L. Hlatky, Tumor development under angiogenic<br />

signaling: a dynamical <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, treatment resp<strong>on</strong>se, and postvascular<br />

dormancy, Cancer Research, 59, (1999), pp. 4770-4775.<br />

[2] R.S. Kerbel, Tumor angiogenesis: past, present and near future, Carcinogensis, 21, (2000),<br />

pp. 505-515<br />

[3] M. Klagsburn and S. Soker, VEGF/VPF: <str<strong>on</strong>g>th</str<strong>on</strong>g>e angiogenesis factor found?, Curr. Biol., 3, (1993),<br />

pp. 699-702<br />

[4] U. Ledzewicz and H. Schaettler, Optimal bang-bang c<strong>on</strong>trols for a 2-compartment model in<br />

cancer chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Optimizati<strong>on</strong> Theory and Applicati<strong>on</strong>s - JOTA, 114, (2002),<br />

pp. 609-637.<br />

[5] U. Ledzewicz and H. Schaettler, Anti-Angiogenic Therapy in Cancer treatment as an Optimal<br />

C<strong>on</strong>trol Problem, SIAM J. <strong>on</strong> C<strong>on</strong>trol and Optimizati<strong>on</strong>, 46 (3), (2007), pp. 1052-1079<br />

[6] A. d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio, Rapidly acting antitumoral anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies, Physical Review E, 76 (3),<br />

Art. No. 031920, 2007.<br />

[7] A. d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio and A. Gandolfi, Tumour eradicati<strong>on</strong> by antiangiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy: analysis and<br />

extensi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model by Hahnfeldt et al. (1999), Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci., 191, (2004), pp. 159-184.<br />

721

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Tuomas Nurmi<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Turku, Finland<br />

e-mail: tuomas.nurmi@utu.fi<br />

Evoluti<strong>on</strong>ary Ecology; Thursday, June 30, 11:30<br />

Joint evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> specializati<strong>on</strong> and dispersal in structured<br />

metapopulati<strong>on</strong>s<br />

I propose a metapopulati<strong>on</strong> model [1] <str<strong>on</strong>g>th</str<strong>on</strong>g>at is mechanistically based <strong>on</strong> individual<br />

level processes and <str<strong>on</strong>g>th</str<strong>on</strong>g>us suitable for evoluti<strong>on</strong>ary analysis. I use adaptive dynamics<br />

[2] to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal and specializati<strong>on</strong> in resource utilizati<strong>on</strong><br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case wi<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>sumers facing a trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f between abilities to c<strong>on</strong>sume two<br />

different but nutriti<strong>on</strong>ally equivalent resources. I illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary scenarios<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at are possible in <str<strong>on</strong>g>th</str<strong>on</strong>g>is model. Moreover, I illustrate how different ecological<br />

parameters affect evoluti<strong>on</strong>ary dynamics. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e main result [3], I show <str<strong>on</strong>g>th</str<strong>on</strong>g>at joint<br />

evoluti<strong>on</strong> may result in evoluti<strong>on</strong>arily stable coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree phenotypes, two<br />

specialists and a generalist, in a metapopulati<strong>on</strong> comprising several patch types.<br />

References.<br />

[1] Nurmi and Parvinen, 2008, On <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> specializati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a mechanistic underpinning<br />

in metapopulati<strong>on</strong>s Theor. Pop. Biol. 73 222–243.<br />

[2] Geritz et al, 1998, Evoluti<strong>on</strong>ary Singular Strategies and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Adaptive Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and Branching<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Evoluti<strong>on</strong>ary Tree Evol. Ecol. 12 35–57.<br />

[3] Nurmi and Parvinen. Joint evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> specializati<strong>on</strong> and dispersal in structured metapopulati<strong>on</strong>s.<br />

J. Theor. Biol. In press.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Statistical Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Signals I; Saturday, July 2, 08:30<br />

Boguslaw Obara<br />

Oxford e-Research Centre and Oxford Centre for Integrative Systems<br />

Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford, UK<br />

e-mail: boguslaw.obara@oerc.ox.ac.uk<br />

Mark Fricker<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Plant Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford, UK<br />

e-mail: mark.fricker@plants.ox.ac.uk<br />

Alexander Lichius<br />

Fungal Cell Biology Group, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Cell Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Edinburgh, UK<br />

e-mail: a.lichius@ed.ac.uk<br />

Nick Read<br />

Fungal Cell Biology Group, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Cell Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Edinburgh, UK<br />

e-mail: nick.read@ed.ac.uk<br />

David Gavaghan<br />

Computing Laboratory, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford, UK<br />

e-mail: david.gavaghan@comlab.ox.ac.uk<br />

Vicente Grau<br />

Oxford e-Research Centre and Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biomedical Engineering,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford, UK<br />

e-mail: vicente.grau@oerc.ox.ac.uk<br />

Analysis and Understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> Fungal Tip Grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Fungi cause devastating plant and human diseases. There is c<strong>on</strong>siderable evidence<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at much <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular machinery driving grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> invasive fungal hyphae is<br />

comm<strong>on</strong> across all fungi, including plant and mammalian pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens, and involves<br />

localized tip grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, successful fungal infecti<strong>on</strong> is critically dependent<br />

<strong>on</strong> accurate percepti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e host surface at <str<strong>on</strong>g>th</str<strong>on</strong>g>e tip to c<strong>on</strong>trol morphogenesis<br />

and trigger host invasi<strong>on</strong>. This suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at detailed investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese early<br />

morphogenetic and signalling events is crucial to a <str<strong>on</strong>g>th</str<strong>on</strong>g>orough understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> virulence.<br />

We are <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore developing high-<str<strong>on</strong>g>th</str<strong>on</strong>g>roughput automated microscope-based multidimensi<strong>on</strong>al<br />

image analysis systems to segment and characterize fungal grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, and<br />

characterize <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> protein localizati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e tip <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trol development.<br />

We propose a curvature-based approach to identify fungal cell tip and<br />

determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> directi<strong>on</strong>, based <strong>on</strong> segmentati<strong>on</strong> using local <str<strong>on</strong>g>th</str<strong>on</strong>g>resholding<br />

and ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical morphology me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods. The curvature <str<strong>on</strong>g>of</str<strong>on</strong>g> cell boundary is calculated<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e boundary point wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e highest curvature value defines <str<strong>on</strong>g>th</str<strong>on</strong>g>e tip cell<br />

positi<strong>on</strong>. For cell expressing key GFP-tagged regulatory proteins, <str<strong>on</strong>g>th</str<strong>on</strong>g>e image intensity<br />

pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e left and right side <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tip positi<strong>on</strong> are recorded to provide a<br />

map <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e plasmamembrane protein distributi<strong>on</strong>, and to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship<br />

between grow<str<strong>on</strong>g>th</str<strong>on</strong>g> vector and asymmetric localizati<strong>on</strong>. This procedure is repeated for<br />

all images in <str<strong>on</strong>g>th</str<strong>on</strong>g>e time-lapse.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

We tested <str<strong>on</strong>g>th</str<strong>on</strong>g>e performance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed c<strong>on</strong>cept <strong>on</strong> fluorescence images <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Neurospora crassa germlings expressing GFP-CRIB and GFP-tagged MAK2 kinase<br />

during hyphal avoidance resp<strong>on</strong>ses and c<strong>on</strong>idial anastomosis tube fusi<strong>on</strong>, respectively.<br />

References.<br />

[1] K. Kvilekval, D.Fedorov, B. Obara, A.K. Singh, B.S. Manjuna<str<strong>on</strong>g>th</str<strong>on</strong>g>, Bisque: a platform for<br />

bioimage analysis and management, Bioinformatics, 26, 544–552, 2010<br />

[2] J. Serra, Image Analysis And Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Morphology, Academic Press, New York, 1982<br />

724

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Regulatory Networks; Saturday, July 2, 11:00<br />

Anna Ochab-Marcinek<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physical Chemistry, Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warsaw,<br />

Poland<br />

e-mail: ochab@ichf.edu.pl<br />

Marcin Tabaka<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physical Chemistry, Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warsaw,<br />

Poland<br />

How stochasticity in gene expressi<strong>on</strong> differentiates<br />

phenotypes wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out changing genotypes<br />

Bimodal gene expressi<strong>on</strong> (<str<strong>on</strong>g>th</str<strong>on</strong>g>e statistical distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> gene products <str<strong>on</strong>g>th</str<strong>on</strong>g>at has two<br />

maxima), as an effect c<strong>on</strong>tributing to phenotypic diversity in genetically identical<br />

cell populati<strong>on</strong>s, enhances <str<strong>on</strong>g>th</str<strong>on</strong>g>e survival <str<strong>on</strong>g>of</str<strong>on</strong>g> cells in a fluctuating envir<strong>on</strong>ment. We<br />

study a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical model <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong> in a minimal gene cascade, in which<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e regulatory gene produces transcripti<strong>on</strong> factors <str<strong>on</strong>g>th</str<strong>on</strong>g>at have a n<strong>on</strong>linear effect <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e activity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e target gene. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at a unimodal distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong><br />

factors over <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell populati<strong>on</strong> can generate a bimodal steady-state output<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out cooperative transcripti<strong>on</strong> factor binding and wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out feedback loops. We<br />

introduce a simple me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g> geometric c<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows <strong>on</strong>e to predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

<strong>on</strong>set <str<strong>on</strong>g>of</str<strong>on</strong>g> bimodality. A. Ochab-Marcinek, M. Tabaka, Bimodal gene expressi<strong>on</strong> in<br />

n<strong>on</strong>cooperative regulatory systems , PNAS 107(51) (2010) 22096-22101<br />

725

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Fractals and Complexity II; Wednesday, June 29, 17:00<br />

Edward Oczeretko<br />

Bialystok University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: e.oczeretko@pb.edu.pl<br />

Marta Borowska<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Białystok<br />

Agnieszka Kitlas<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Białystok<br />

Fractal analysis in irregular regi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> interest<br />

Fractals have been successfully applied in many areas <str<strong>on</strong>g>of</str<strong>on</strong>g> science and technology.<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most prominent applicati<strong>on</strong>s is fractal analysis in medicine, especially in<br />

analyses <str<strong>on</strong>g>of</str<strong>on</strong>g> different kinds <str<strong>on</strong>g>of</str<strong>on</strong>g> images. For medical images diagnostically important<br />

informati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g>ten lies in <str<strong>on</strong>g>th</str<strong>on</strong>g>e texture. Fractal dimensi<strong>on</strong> may be used as an index<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> irregularity. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper we describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intensity difference<br />

scaling me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for assessment <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fractal dimensi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e irregular regi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

interest (irregular ROI-s). Near boundary between different tissues or structures <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

values <str<strong>on</strong>g>of</str<strong>on</strong>g> fractal dimensi<strong>on</strong>s changed significantly. The values <str<strong>on</strong>g>of</str<strong>on</strong>g> fractal dimensi<strong>on</strong>s<br />

were calculated <strong>on</strong> syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic fractal textures which ranged in fractal dimensi<strong>on</strong><br />

from 2.05 to 2.95 (2.05, 2.10, 2.20, 2.30, 2.40, 2.50, 2.60, 2.70, 2.80, 2.90, 2.95).<br />

For each value <str<strong>on</strong>g>of</str<strong>on</strong>g> fractal dimensi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>irty 64-by-64 images were obtained. The<br />

mean squared error (MSE) for <str<strong>on</strong>g>th</str<strong>on</strong>g>e 330 samples for each algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m was assessed.<br />

We tested 7 me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> computing <str<strong>on</strong>g>of</str<strong>on</strong>g> fractal dimensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> surfaces: rectangular<br />

prism surface area me<str<strong>on</strong>g>th</str<strong>on</strong>g>od (MSE = 0.0054), triangular prism surface area me<str<strong>on</strong>g>th</str<strong>on</strong>g>od<br />

(MSE = 0.0098), power spectral density me<str<strong>on</strong>g>th</str<strong>on</strong>g>od (MSE = 0.0241), me<str<strong>on</strong>g>th</str<strong>on</strong>g>od based <strong>on</strong><br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical morphology (MSE = 0.0093), variogram analysis (MSE = 0.0054),<br />

intensity difference scaling me<str<strong>on</strong>g>th</str<strong>on</strong>g>od (MSE = 0.0020), and our adaptati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> intensity<br />

difference scaling me<str<strong>on</strong>g>th</str<strong>on</strong>g>od in irregular ROI-s (MSE = 0,0017). Our experiments for<br />

dental radiovisiographic images, pantomograms and nuclear medicine scans showed<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at it is difficult to fit <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire regular regi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> interest wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e examined<br />

organ wi<str<strong>on</strong>g>th</str<strong>on</strong>g> simultaneous inclusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relevant fragment avoiding <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> boundaries and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er kinds <str<strong>on</strong>g>of</str<strong>on</strong>g> unnecessary structures at <str<strong>on</strong>g>th</str<strong>on</strong>g>e same time. Our<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g> assessment <str<strong>on</strong>g>of</str<strong>on</strong>g> fractal dimensi<strong>on</strong> in irregular regi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> interest solves<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese difficulties.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting cell systems: from intercellular interacti<strong>on</strong><br />

to tissue-level traits I; Wednesday, June 29, 14:30<br />

Reuben O’Dea<br />

Nottingham Trent University<br />

e-mail: reuben.odea@ntu.ac.uk<br />

Multiscale analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> pattern formati<strong>on</strong> and wave<br />

propagati<strong>on</strong> in a discrete cell signalling model<br />

It is well known <str<strong>on</strong>g>th</str<strong>on</strong>g>at cell-scale interacti<strong>on</strong>s can have pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ound effects <strong>on</strong> macroscale<br />

tissue grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. I will discuss two approaches to analysing such phenomena wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a<br />

c<strong>on</strong>tinuum framework, allowing <str<strong>on</strong>g>th</str<strong>on</strong>g>eir inclusi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in macroscale models <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

Firstly, a multiscale asymptotic me<str<strong>on</strong>g>th</str<strong>on</strong>g>od wi<str<strong>on</strong>g>th</str<strong>on</strong>g> which to analyse fine-grained<br />

patterning patterning in cellular differentiati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a c<strong>on</strong>tinuum framework is<br />

introduced, based <strong>on</strong> a generic discrete signalling model. Most applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> such<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are to c<strong>on</strong>tinuous systems, while here discreteness <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e short leng<str<strong>on</strong>g>th</str<strong>on</strong>g>scale<br />

must be taken into account.<br />

An important feature <str<strong>on</strong>g>of</str<strong>on</strong>g> such systems is <str<strong>on</strong>g>th</str<strong>on</strong>g>e progressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> pattern-forming<br />

modulated travelling waves across <str<strong>on</strong>g>th</str<strong>on</strong>g>e discrete lattice. Such phenomena have been<br />

widely studied wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in discrete diffusi<strong>on</strong> equati<strong>on</strong>s for m<strong>on</strong>ot<strong>on</strong>e waves; employing<br />

a WKBJ technique in place <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e standard travelling wave ansatz, I show how<br />

analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> such waves is greatly simplified and highlight <str<strong>on</strong>g>th</str<strong>on</strong>g>e crucial dependence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

wave propagati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying lattice geometry. In additi<strong>on</strong>, I extend <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

analysis to <str<strong>on</strong>g>th</str<strong>on</strong>g>e modulated travelling waves exhibited in cell signalling models.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Eryll Ogg<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling, UK and Cefas, UK<br />

e-mail: gill.ogg@cefas.co.uk<br />

Rachel Norman<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling, UK<br />

e-mail: ran@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.stir.ac.uk<br />

Nick Taylor<br />

Cefas, UK<br />

e-mail: nick.taylor@cefas.co.uk<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Modelling Aquatic Viral Dynamics<br />

Viral haemorrhagic septicaemia (VHS) and infectious haematopoietic necrosis (IHN)<br />

are two important viruses <str<strong>on</strong>g>of</str<strong>on</strong>g> rainbow trout (Oncorhynchus mykiss). Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> viruses<br />

have a significant impact <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e trout industry worldwide, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> VHS costing an<br />

estimated £10.3-31 milli<strong>on</strong> per year in Europe [1] and IHN costing <str<strong>on</strong>g>th</str<strong>on</strong>g>e US ec<strong>on</strong>omy<br />

£22.2 milli<strong>on</strong> per year (data up to 2005) [2]. Currently <str<strong>on</strong>g>th</str<strong>on</strong>g>e UK is free <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

viruses, but should <strong>on</strong>e or <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er enter <str<strong>on</strong>g>th</str<strong>on</strong>g>e UK, knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> how <str<strong>on</strong>g>th</str<strong>on</strong>g>ey may<br />

spread is vital to reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall impact. Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> introducti<strong>on</strong> are limited<br />

to ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er importati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> infected livestock or wild fish movements. Using deterministic<br />

models, we can investigate how <str<strong>on</strong>g>th</str<strong>on</strong>g>e viruses would spread geographically over<br />

time and predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> different c<strong>on</strong>trol measures to aid in minimising <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

overall impact an outbreak <str<strong>on</strong>g>of</str<strong>on</strong>g> ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er virus would cause.<br />

This poster will present some initial findings regarding stocking density and<br />

an outline <str<strong>on</strong>g>of</str<strong>on</strong>g> a preliminary first model, looking at viral movements wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a single<br />

tank <str<strong>on</strong>g>of</str<strong>on</strong>g> fish.<br />

References.<br />

[1] Gregory, A., Murray, A.G., Raynard, R.S. and Snow, M., A Risk Analysis Approach to Aquatic<br />

Disease Management [Poster] (2010)<br />

[2] Lorenzen, N. and LaPatra, S.E., DNA vaccines for aquacultured fish Characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

DNA vaccines against fish Revue Scientifique et Technique (Internati<strong>on</strong>al Office <str<strong>on</strong>g>of</str<strong>on</strong>g> Epizootics)<br />

24 201–213<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Genetics and Genomics; Wednesday, June 29, 08:30<br />

Łukasz Olczak<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Informatics, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: Lukasz.Olczak@polsl.pl<br />

Rafał Pokrzywa<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Informatics, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Andrzej Polaski<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Informatics, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> tandem repeat evoluti<strong>on</strong> based <strong>on</strong><br />

comparis<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Homo sapiens and Homo neander<str<strong>on</strong>g>th</str<strong>on</strong>g>alensis<br />

genomes<br />

Tandem repeats are genomic markers well suited for studying evoluti<strong>on</strong>ary scenarios<br />

for closely related species, due to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir high mutati<strong>on</strong> rates. There are many studies<br />

c<strong>on</strong>cerned wi<str<strong>on</strong>g>th</str<strong>on</strong>g> fitting evoluti<strong>on</strong>ary models to data <strong>on</strong> short tandem repeats wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

c<strong>on</strong>clusi<strong>on</strong>s leading to estimates <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> tandem repeats mutati<strong>on</strong> process,<br />

evoluti<strong>on</strong>ary and demographic scenarios <str<strong>on</strong>g>of</str<strong>on</strong>g> different species and populati<strong>on</strong>s etc.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we present coalescence based ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

tandem repeats based <strong>on</strong> comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genomes <str<strong>on</strong>g>of</str<strong>on</strong>g> homo sapiens and Homo neander<str<strong>on</strong>g>th</str<strong>on</strong>g>alensis.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e coalescence model we assume <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic moment <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

speciati<strong>on</strong> event leading to Homo sapiens and Homo neander<str<strong>on</strong>g>th</str<strong>on</strong>g>alensis species. The<br />

results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e coalescence model <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong> are probability distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> differences<br />

between numbers <str<strong>on</strong>g>of</str<strong>on</strong>g> repeats in two species. These probability distributi<strong>on</strong>s<br />

depend <strong>on</strong> parameters, mutati<strong>on</strong> intensities, different for models for evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

loci wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different motif leng<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

The obtained models are <str<strong>on</strong>g>th</str<strong>on</strong>g>en fitted to data <strong>on</strong> locati<strong>on</strong>s and structures <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

tandem repeat loci <str<strong>on</strong>g>of</str<strong>on</strong>g> homo sapiens and Homo neander<str<strong>on</strong>g>th</str<strong>on</strong>g>alensis genomes obtained<br />

by using <str<strong>on</strong>g>th</str<strong>on</strong>g>e recently developed genome browsing tool BWtrs and <str<strong>on</strong>g>th</str<strong>on</strong>g>e appropriately<br />

designed alignment algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m. Due to imperfecti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e assembly process for<br />

Homo neader<str<strong>on</strong>g>th</str<strong>on</strong>g>alensis genome <str<strong>on</strong>g>th</str<strong>on</strong>g>e model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> censored observati<strong>on</strong>s is applied and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e appropriate EM procedure is designed.<br />

Estimates <str<strong>on</strong>g>of</str<strong>on</strong>g> mutati<strong>on</strong>s rates for different sizes <str<strong>on</strong>g>of</str<strong>on</strong>g> repeat motifs are compared<br />

to results <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er populati<strong>on</strong> dynamics studies. Possible sources <str<strong>on</strong>g>of</str<strong>on</strong>g> biases in different<br />

approaches are highlighted and possible future improvements <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e developed<br />

model are presented.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Katarzyna Oleś<br />

Jagiell<strong>on</strong>ian University, M. Smoluchowski Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics,<br />

30-059 Krakow, ul. Reym<strong>on</strong>ta 4.<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling, Computing Science and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics,<br />

FK9 4LA Stirling, UK<br />

e-mail: kas@cs.stir.ac.uk<br />

Adam Kleczkowski<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling, Computing Science and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics,<br />

FK9 4LA Stirling, UK<br />

e-mail: ak@cs.stir.ac.uk<br />

Ewa Gudowska - Nowak<br />

Jagiell<strong>on</strong>ian University, M. Smoluchowski Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics,<br />

30-059 Krakow, ul. Reym<strong>on</strong>ta 4.<br />

e-mail: gudowska@<str<strong>on</strong>g>th</str<strong>on</strong>g>.if.uj.edu.pl<br />

Understanding disease c<strong>on</strong>trol: influence <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemiological<br />

and ec<strong>on</strong>omic factors<br />

The goal <str<strong>on</strong>g>of</str<strong>on</strong>g> our work is to find optimal c<strong>on</strong>trol strategy <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics. We have<br />

c<strong>on</strong>sidered extended SIR model including pre- and symptomatic cases for a disease<br />

spreading <strong>on</strong> regular network.<br />

The effective treatment strategies for a disease c<strong>on</strong>trol are expected to minimize<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e total cost <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic. In designing c<strong>on</strong>trol strategies, however, we<br />

have to c<strong>on</strong>sider bo<str<strong>on</strong>g>th</str<strong>on</strong>g> epidemiology and ec<strong>on</strong>omics. The most optimal c<strong>on</strong>trol is<br />

determined by <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative costs <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment and infecti<strong>on</strong>, as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial<br />

distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious cases and kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> its spread and transformati<strong>on</strong>. It has<br />

been shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen may be unknown and we are able to<br />

make predicti<strong>on</strong> based <strong>on</strong> ec<strong>on</strong>omics analysis <strong>on</strong>ly. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough ec<strong>on</strong>omics determines<br />

c<strong>on</strong>trol strategies, <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> applicability <str<strong>on</strong>g>of</str<strong>on</strong>g> scenarios depends <strong>on</strong> epidemiological<br />

factors such as infectiousness, detectability, recovery, removal and map <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tacts<br />

in populati<strong>on</strong>. Some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>at factors such as c<strong>on</strong>tagi<strong>on</strong> or mortality are str<strong>on</strong>gly c<strong>on</strong>nected<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> particular disease and we can hardly change <str<strong>on</strong>g>th</str<strong>on</strong>g>eir properties. However<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e rest <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters we have an influence. So <str<strong>on</strong>g>th</str<strong>on</strong>g>e quicker <str<strong>on</strong>g>th</str<strong>on</strong>g>e symptoms occur<br />

or <str<strong>on</strong>g>th</str<strong>on</strong>g>e higher recovery level, <str<strong>on</strong>g>th</str<strong>on</strong>g>e smaller c<strong>on</strong>trol radius. Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship<br />

between c<strong>on</strong>trol and infected neighbourhood size has been studied and an influence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> epidemiological parameters <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at relati<strong>on</strong> has been discussed.<br />

References.<br />

[1] Kleczkowski, A and Oleś, K and Gudowska - Nowak, E and Gilligan, CA Searching for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

most cost-effective strategy for c<strong>on</strong>trolling epidemics in prep.<br />

[2] Dybiec, B and Kleczkowski, A and Gilligan, CA C<strong>on</strong>trolling disease spread <strong>on</strong> networks wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

incomplete knowledge Physical Review E 70 066145.<br />

[3] Gersovitz, M and Hammer, JS, Infectious diseases, public policy, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e marriage <str<strong>on</strong>g>of</str<strong>on</strong>g> ec<strong>on</strong>omics<br />

and epidemiology WORLD BANK RESEARCH OBSERVER 18 129–157.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Fluid-structure interacti<strong>on</strong> problems in biomechanics; Saturday, July 2, 08:30<br />

Sarah Ols<strong>on</strong><br />

Tulane University<br />

e-mail: sols<strong>on</strong>2@tulane.edu<br />

Susan Suarez<br />

Cornell University<br />

Lisa Fauci<br />

Tulane University<br />

Coupling biochemistry, mechanics, and hydrodynamics to<br />

model sperm motility<br />

Calcium (Ca2+) dynamics in mammalian sperm are directly linked to motility.<br />

These dynamics depend <strong>on</strong> diffusi<strong>on</strong>, n<strong>on</strong>linear fluxes, Ca2+ channels specific to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e sperm flagellum, and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er signaling molecules. The goal <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is to<br />

couple Ca2+ dynamics to a mechanical model <str<strong>on</strong>g>of</str<strong>on</strong>g> a motile sperm wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a viscous,<br />

incompressible fluid. We will first discuss a model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e CatSper mediated<br />

Ca2+ dynamics relevant to hyperactivated motility. The me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g> regularized<br />

Stokeslets is used to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e hydrodynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> swimming sperm. Results<br />

showing emergent waveforms, swimming speeds, and trajectories will be compared<br />

to experimental data.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling physiological systems: model validati<strong>on</strong> and experimental design<br />

issues; Wednesday, June 29, 11:00<br />

Mette Olufsen<br />

Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina State University, Raleigh NC<br />

e-mail: msolufse@ncsu.edu<br />

Modeling and parameter estimati<strong>on</strong> in cardiovascular<br />

dynamics<br />

The main role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiovascular system is to maintain adequate oxygenati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> all tissues. This is accomplished by maintaining blood flow and pressure at a<br />

fairly c<strong>on</strong>stant level and transporting blood from <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart to <str<strong>on</strong>g>th</str<strong>on</strong>g>e periphery wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

a minimal loss <str<strong>on</strong>g>of</str<strong>on</strong>g> energy. In additi<strong>on</strong>, a number <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trol mechanisms are imposed<br />

regulating vascular resistance, compliance, pumping efficiency and frequency.<br />

In cardiovascular diseases, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transport system and its regulati<strong>on</strong> may be<br />

compromised, and for a number <str<strong>on</strong>g>of</str<strong>on</strong>g> diseases it is ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er not known or difficult to<br />

study what mechanism <str<strong>on</strong>g>th</str<strong>on</strong>g>at lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e breakdown <str<strong>on</strong>g>of</str<strong>on</strong>g> homeostasis. Typically, some<br />

general observati<strong>on</strong>s can be made, but <str<strong>on</strong>g>th</str<strong>on</strong>g>ese vary significant between individuals.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, for most patients <strong>on</strong>ly a few quantities can be measured, making it<br />

difficult to assess essential quantities such as cerebral vascular resistance, cardiac<br />

c<strong>on</strong>tractility, or <str<strong>on</strong>g>th</str<strong>on</strong>g>e gain and time c<strong>on</strong>stants associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong>. This<br />

presentati<strong>on</strong> will discuss development <str<strong>on</strong>g>of</str<strong>on</strong>g> patient specific models obtained by combining<br />

models predicting c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> blood flow and pressure wi<str<strong>on</strong>g>th</str<strong>on</strong>g> parameter estimati<strong>on</strong><br />

techniques. Models analyzed are composed <str<strong>on</strong>g>of</str<strong>on</strong>g> systems <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear equati<strong>on</strong>s each<br />

specified via a set <str<strong>on</strong>g>of</str<strong>on</strong>g> model parameters. Nominal parameter values are obtained<br />

from analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong>s and data available. Subsequently, sensitivity analysis,<br />

correlati<strong>on</strong> analysis, and subset selecti<strong>on</strong>, are combined wi<str<strong>on</strong>g>th</str<strong>on</strong>g> parameter estimati<strong>on</strong><br />

techniques to obtain a subset <str<strong>on</strong>g>of</str<strong>on</strong>g> patient specific parameters.<br />

732

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Mechanical Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Movement and Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cells and Tissues II;<br />

Wednesday, June 29, 17:00<br />

A model linking <str<strong>on</strong>g>th</str<strong>on</strong>g>e lamellipodial actin cytoskelet<strong>on</strong> to cell<br />

shape and movement.<br />

Dietmar Oelz<br />

RICAM (Rad<strong>on</strong> Institute for Compuati<strong>on</strong>al and Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics),<br />

Vienna/Linz, Austria<br />

e-mail: dietmar.oelz@univie.ac.at<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I will give an overview <strong>on</strong> a recent modelling effort c<strong>on</strong>cerning <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

lamellipodial Actin-cytoskelet<strong>on</strong>. In more detail I will outline <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical descripti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> protein linkages and compare two different scaling aproaches <str<strong>on</strong>g>th</str<strong>on</strong>g>at apply<br />

to ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er cross-linking proteins or adhesi<strong>on</strong> complexes. The results are macroscopic,<br />

possibly n<strong>on</strong>linear, fricti<strong>on</strong> coefficients. I wil also shortly menti<strong>on</strong> analytic results<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>cern <str<strong>on</strong>g>th</str<strong>on</strong>g>e interpretati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ryosuke Omori<br />

Kyushu University<br />

e-mail: omori@bio-ma<str<strong>on</strong>g>th</str<strong>on</strong>g>10.biology.kyushu-u.ac.jp<br />

Ben Adams<br />

Ba<str<strong>on</strong>g>th</str<strong>on</strong>g> University<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

The effect <str<strong>on</strong>g>of</str<strong>on</strong>g> disrupting seas<strong>on</strong>ality to dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

epidemics: <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> KHV<br />

Koi herpesvirus (KHV), a highly virulent disease affecting carp (fish in freshwater)<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at emerged in <str<strong>on</strong>g>th</str<strong>on</strong>g>e late 1990s, is a serious <str<strong>on</strong>g>th</str<strong>on</strong>g>reat to aquaculture industry. After a<br />

fish is infected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> KHV, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a temperature dependent delay before it becomes<br />

infectious, and a fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er delay before mortality. C<strong>on</strong>sequently KHV epidemiology<br />

is driven by seas<strong>on</strong>al changes in water temperature. It has also been proposed <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

outbreaks could be c<strong>on</strong>trolled by resp<strong>on</strong>sive management <str<strong>on</strong>g>of</str<strong>on</strong>g> water temperature in<br />

aquaculture setups. We use a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model to analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> seas<strong>on</strong>al<br />

temperature cycles <strong>on</strong> KHV epidemiology, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> attempting to c<strong>on</strong>trol<br />

outbreaks by disrupting <str<strong>on</strong>g>th</str<strong>on</strong>g>is cycle. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough disease progressi<strong>on</strong> is<br />

fast in summer and slow in winter, total mortality over a two year period is similar<br />

for outbreaks <str<strong>on</strong>g>th</str<strong>on</strong>g>at start in ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er seas<strong>on</strong>. However, for outbreaks <str<strong>on</strong>g>th</str<strong>on</strong>g>at start in late<br />

autumn, mortality may be low and immunity high. A single bout <str<strong>on</strong>g>of</str<strong>on</strong>g> water temperature<br />

management can be an effective outbreak c<strong>on</strong>trol strategy if it is started<br />

as so<strong>on</strong> as dead fish are detected and maintained for a l<strong>on</strong>g time. It can also be<br />

effective if <str<strong>on</strong>g>th</str<strong>on</strong>g>e frequency <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious fish is used as an indicator for <str<strong>on</strong>g>th</str<strong>on</strong>g>e beginning<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> treatment. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is case, however, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a risk <str<strong>on</strong>g>th</str<strong>on</strong>g>at starting <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment too<br />

so<strong>on</strong> will increase mortality relative to <str<strong>on</strong>g>th</str<strong>on</strong>g>e case when no treatment is used. This<br />

counterproductive effect can be avoided if multiple bouts <str<strong>on</strong>g>of</str<strong>on</strong>g> temperature management<br />

are used. We c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at disrupting normal seas<strong>on</strong>al patterns in water<br />

temperature can be an effective strategy for c<strong>on</strong>trolling koi herpesvirus. Exploiting<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e seas<strong>on</strong>al patterns, possibly in combinati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> temperature management, can<br />

also induce widespread immunity to KHV in a cohort <str<strong>on</strong>g>of</str<strong>on</strong>g> fish. However, employing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods successfully requires careful assessment to ensure <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment<br />

is started, and finished, at <str<strong>on</strong>g>th</str<strong>on</strong>g>e correct time.<br />

734

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Nooshin Omranian 1,2<br />

Bernd Mueller–Roeber 1,2<br />

Zoran Nikoloski 2<br />

1-University <str<strong>on</strong>g>of</str<strong>on</strong>g> Potsdam, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemistry and Biology, Karl-<br />

Liebknecht-Str. 24-25, 14476 Potsdam,Germany<br />

2-Systems Biology and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling, Max-Planck-Institute<br />

for Molecular Plant Physiology, Am Mühlenberg 1, 14476 Potsdam,<br />

Germany<br />

e-mail: omranian@mpimp-golm.mpg.de<br />

PageRank-based identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> signaling crosstalk from<br />

transcriptomics data in Arabidopsis <str<strong>on</strong>g>th</str<strong>on</strong>g>aliana<br />

The levels <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular organizati<strong>on</strong>, from gene transcripti<strong>on</strong> to translati<strong>on</strong> to proteinprotein<br />

interacti<strong>on</strong> and metabolism, operate via tightly regulated mutual interacti<strong>on</strong>s<br />

facilitating organismal adaptability and various stress resp<strong>on</strong>ses. Characterizing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e mutual interacti<strong>on</strong>s between genes, transcripti<strong>on</strong> factors, and proteins<br />

involved in signalling, termed crosstalk, is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore crucial for understanding<br />

and c<strong>on</strong>trolling cell’s functi<strong>on</strong>ality. Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e type <str<strong>on</strong>g>of</str<strong>on</strong>g> data used in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

analysis, <str<strong>on</strong>g>th</str<strong>on</strong>g>e existing me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for identifying crosstalk can be divided into two<br />

groups: (1) proteomics-based, relying <strong>on</strong> integrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> protein-protein interacti<strong>on</strong><br />

data wi<str<strong>on</strong>g>th</str<strong>on</strong>g> existing pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way informati<strong>on</strong> and (2) transcriptomics-based, employing<br />

high-<str<strong>on</strong>g>th</str<strong>on</strong>g>roughput transcriptomics data sets from different c<strong>on</strong>diti<strong>on</strong>s.<br />

Here we propose and analyze a novel me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for crosstalk identificati<strong>on</strong> which<br />

relies <strong>on</strong> transcriptomics data and overcomes <str<strong>on</strong>g>th</str<strong>on</strong>g>e lack <str<strong>on</strong>g>of</str<strong>on</strong>g> available informati<strong>on</strong> for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e signalling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways in Arabidopsis <str<strong>on</strong>g>th</str<strong>on</strong>g>aliana. Our me<str<strong>on</strong>g>th</str<strong>on</strong>g>od employs a networkbased<br />

transformati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e results from <str<strong>on</strong>g>th</str<strong>on</strong>g>e statistical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> differential gene<br />

expressi<strong>on</strong> in carefully c<strong>on</strong>structed groups <str<strong>on</strong>g>of</str<strong>on</strong>g> experiments (c<strong>on</strong>diti<strong>on</strong>s). Modificati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e PageRank algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m is <str<strong>on</strong>g>th</str<strong>on</strong>g>en used <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network c<strong>on</strong>structed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

previous step to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e putative transcripts interrelating different signalling<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e help <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed me<str<strong>on</strong>g>th</str<strong>on</strong>g>od, we analyze a transcriptomics<br />

data set incorporating experiments <strong>on</strong> four different stresses/signals: nitrate, sulfur,<br />

ir<strong>on</strong>, and horm<strong>on</strong>e and identified a promising gene candidates involved in crosstalk.<br />

In additi<strong>on</strong>, we c<strong>on</strong>duct a comparative analysis wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e state-<str<strong>on</strong>g>of</str<strong>on</strong>g>-<str<strong>on</strong>g>th</str<strong>on</strong>g>e art me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>is field which used a biclustering-based approach [1]. Unlike approaches<br />

based biclustering, our approach does not rely <strong>on</strong> any hidden parameters. To<br />

compare <str<strong>on</strong>g>th</str<strong>on</strong>g>e two approaches, we use transcriptomics data sets from Arabidopsis<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>aliana under 31 different experimental c<strong>on</strong>diti<strong>on</strong>s: 5 nitrate, 4 sulfur, 2 ir<strong>on</strong> and<br />

20 horm<strong>on</strong>e experiments. Surprisingly, <str<strong>on</strong>g>th</str<strong>on</strong>g>e biclustering-based approach fails to<br />

identify any candidate genes involved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e crosstalk <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e analyzed signals. On<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed me<str<strong>on</strong>g>th</str<strong>on</strong>g>od, we find a small set <str<strong>on</strong>g>of</str<strong>on</strong>g> interesting genes<br />

putatively involved in crosstalk (verified by literature search). The small number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> genes involved in crosstalk <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese signals could be attributed to: (1) <str<strong>on</strong>g>th</str<strong>on</strong>g>e heterogeneity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e analyzed data and (2) <str<strong>on</strong>g>th</str<strong>on</strong>g>e lack <str<strong>on</strong>g>of</str<strong>on</strong>g> raw data for all experiments,<br />

resulting in a n<strong>on</strong>-uniform normalizati<strong>on</strong>. C<strong>on</strong>sequently, we dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at our<br />

proposed me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is more efficient for species for which large transcriptomics data<br />

sets, normalized wi<str<strong>on</strong>g>th</str<strong>on</strong>g> same techniques, are available.<br />

735

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

References.<br />

[1] D. Nero, G. Krouk, D. Tranchina, GM. Coruzzi: A system biology approach highlights a<br />

horm<strong>on</strong>al enhancer effect <strong>on</strong> regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genes in a nitrate resp<strong>on</strong>sive "biomodule" BMC<br />

Syst Biol 3 59.<br />

736

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Natsuki Orita<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Informati<strong>on</strong> and Computer Sciences , Nara Women’s<br />

University<br />

e-mail: kol<strong>on</strong>x3@ics.nara-wu.ac.jp<br />

Fugo Takasu<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Informati<strong>on</strong> and Computer Sciences , Nara Women’s<br />

University<br />

e-mail: takasu@ics.nara-wu.ac.jp<br />

Individual-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> spatial populati<strong>on</strong> dynamics<br />

In last decades, a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical approaches have been explored and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ey have c<strong>on</strong>tributed much to better understand populati<strong>on</strong> dynamics in general.<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models have been accumulating. Many <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em, however , remain<br />

qualitative descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> dynamics focused at "populati<strong>on</strong> level" where<br />

analytical tractability is prioritized and mechanistic process <str<strong>on</strong>g>of</str<strong>on</strong>g> individual bir<str<strong>on</strong>g>th</str<strong>on</strong>g> and<br />

dea<str<strong>on</strong>g>th</str<strong>on</strong>g> are ignored.<br />

(1) Nt+1 = exp<br />

<br />

r 1 − Nt<br />

<br />

Nt<br />

K<br />

For example, <str<strong>on</strong>g>th</str<strong>on</strong>g>e assumpti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at per capita grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate linearly or exp<strong>on</strong>entially<br />

decreases wi<str<strong>on</strong>g>th</str<strong>on</strong>g> populati<strong>on</strong> size as assumed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ricker logistic model (1) is completely<br />

descriptive <strong>on</strong>e wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out any mechanistic process explicitly c<strong>on</strong>sidered at<br />

individual level; we just assume it and start from such a descriptive model.<br />

In order to understand populati<strong>on</strong> dynamics in general, we <str<strong>on</strong>g>th</str<strong>on</strong>g>ink it is necessary<br />

to link populati<strong>on</strong> dynamics, a phenomen<strong>on</strong> at populati<strong>on</strong> level, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mechanistic<br />

processes <str<strong>on</strong>g>of</str<strong>on</strong>g> bir<str<strong>on</strong>g>th</str<strong>on</strong>g> and dea<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>at occur at individual level. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper, we aim to<br />

rec<strong>on</strong>struct a populati<strong>on</strong> dynamics in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> individual bir<str<strong>on</strong>g>th</str<strong>on</strong>g> and dea<str<strong>on</strong>g>th</str<strong>on</strong>g> and try to<br />

derive a dynamical system based <strong>on</strong> mechanistic interacti<strong>on</strong>s between individuals.<br />

We first c<strong>on</strong>struct a spatial populati<strong>on</strong> dynamics where an individual is a point<br />

located in a c<strong>on</strong>tinuous two dimensi<strong>on</strong>al space and a populati<strong>on</strong> is represented as a<br />

point pattern. Each individual has a territory wi<str<strong>on</strong>g>th</str<strong>on</strong>g> radius σc and c<strong>on</strong>sumes renewable<br />

resource to reproduce. Interacti<strong>on</strong> between individuals occurs when territories<br />

overlap and overlapped area is handled according to a certain rule each individual<br />

adopts. These algori<str<strong>on</strong>g>th</str<strong>on</strong>g>mic rule c<strong>on</strong>stitutes a point process and we have built a flexible<br />

framework to implement <str<strong>on</strong>g>th</str<strong>on</strong>g>ese rules as individual-based simulati<strong>on</strong> model. We<br />

analyze how <str<strong>on</strong>g>th</str<strong>on</strong>g>e point pattern changes temporarily in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> size and<br />

pair correlati<strong>on</strong> functi<strong>on</strong>. And we derive a dynamical system to explain behaviors<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e individual-based simulati<strong>on</strong>.<br />

(2) Nt+1 =<br />

∞<br />

Nt−1Ck(4πσ<br />

k=0<br />

2 c ) k (1 − 4πσ 2 c ) Nt−1−k e r ×Max<br />

<br />

1 − αk<br />

, 0<br />

2<br />

where α is <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> coefficient.<br />

Our final goal is to understand phenomena at populati<strong>on</strong> level based <strong>on</strong> mechanistic<br />

interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> individual level and how such interacti<strong>on</strong>s can be described<br />

as a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical form. Our individual-based framework also allows to explore<br />

evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters such as territory size and dispersal range. We discuss an<br />

<br />

Nt<br />

737

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

individual-based approach to better understand populati<strong>on</strong> dynamics as well as<br />

evoluti<strong>on</strong>ary dynamics.<br />

738

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chaste framework;<br />

Tuesday, June 28, 11:00<br />

Dr James Osborne<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: james.osborne@comlab.ox.ac.uk<br />

A multiscale computati<strong>on</strong>al framework for modelling<br />

biological systems: Chaste<br />

The Chaste framework (http://web.comlab.ox.ac.uk/chaste) in an Open Source numerical<br />

library which enables multicellular and multiscale simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> biological<br />

processes. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is, <str<strong>on</strong>g>th</str<strong>on</strong>g>e first talk <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mini-symposium, we introduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e multiscale<br />

framework <strong>on</strong> which Chaste is based <strong>on</strong>, discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e framework,<br />

and provide a dem<strong>on</strong>strati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> how to set up a simulati<strong>on</strong>.<br />

The ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical framework is based up<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e natural<br />

structural unit <str<strong>on</strong>g>of</str<strong>on</strong>g> biology is <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell, and it c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree main scales: <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue<br />

level (macro-scale); <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell level (meso-scale); and <str<strong>on</strong>g>th</str<strong>on</strong>g>e sub-cellular level (microscale),<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> interacti<strong>on</strong>s occurring between all scales. The cell level is central to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e framework and cells are modelled as discrete interacting entities using <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a number <str<strong>on</strong>g>of</str<strong>on</strong>g> possible modelling paradigms, including lattice based models (cellular<br />

automata and cellular Potts) and <str<strong>on</strong>g>of</str<strong>on</strong>g>f-lattice models (cell centre and vertex based<br />

representati<strong>on</strong>s). The sub-cellular level c<strong>on</strong>cerns numerous metabolic and biochemical<br />

processes represented by interacti<strong>on</strong> networks rendered stochastically or into<br />

ODEs. The outputs from such systems influence <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell level affecting<br />

properties such as adhesi<strong>on</strong> and also influencing cell mitosis and apoptosis.<br />

Tissue level behaviour is represented by field equati<strong>on</strong>s for nutrient or messenger<br />

c<strong>on</strong>centrati<strong>on</strong>, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> cells functi<strong>on</strong>ing as sinks and sources. This modular approach<br />

enables multiple models to be simulated and is easily extensible allowing more<br />

realistic behaviour to be c<strong>on</strong>sidered at each scale.<br />

Chaste is comprised <str<strong>on</strong>g>of</str<strong>on</strong>g> libraries <str<strong>on</strong>g>of</str<strong>on</strong>g> object orientated C++, developed using an<br />

agile development approach. All s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware is tested, robust, reliable and extensible.<br />

The library enables general simulati<strong>on</strong>s to be undertaken and includes tools to automatically<br />

curate and store simulati<strong>on</strong> results expediting model development. One<br />

key aspect <str<strong>on</strong>g>of</str<strong>on</strong>g> such a framework is <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability to model specific biological systems using<br />

multiple modelling paradigms, as a case study we present a simple model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

colorectal crypt using four different cell level models and illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e similarities<br />

and differences.<br />

739

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Yo-Hey Otake<br />

NISTEP, MEXT, Government <str<strong>on</strong>g>of</str<strong>on</strong>g> Japan<br />

e-mail: otake@nistep.go.jp<br />

Populati<strong>on</strong> Dynamics; Saturday, July 2, 14:30<br />

C<strong>on</strong>vergence properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e law <str<strong>on</strong>g>of</str<strong>on</strong>g> reproducti<strong>on</strong> by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

first principle derivati<strong>on</strong> in populati<strong>on</strong> dynamics<br />

We want to relate <str<strong>on</strong>g>th</str<strong>on</strong>g>e law <str<strong>on</strong>g>of</str<strong>on</strong>g> reproducti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> interacti<strong>on</strong> between individuals. For<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is purpose, we use <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> infinite series, which is called “first principle derivati<strong>on</strong>”<br />

[5, chapter 4]. By <str<strong>on</strong>g>th</str<strong>on</strong>g>is me<str<strong>on</strong>g>th</str<strong>on</strong>g>od, we can derive <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> reproducti<strong>on</strong><br />

functi<strong>on</strong> from <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ships <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals (<str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> functi<strong>on</strong> between individuals). Previous research[1, 5] has<br />

derived a few c<strong>on</strong>cave functi<strong>on</strong>s, which are Ricker model and Skellam model. We<br />

extended previous research in ec<strong>on</strong>omical viewpoint. As a result, we could derive<br />

new types <str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong> like Holling’s type III functi<strong>on</strong>al resp<strong>on</strong>se [2], so we could represent<br />

bistability in populati<strong>on</strong> dynamics[3]. The reas<strong>on</strong> comes from <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e derived functi<strong>on</strong> has c<strong>on</strong>vexity in case <str<strong>on</strong>g>th</str<strong>on</strong>g>at populati<strong>on</strong> is small. Previous research<br />

did not have <str<strong>on</strong>g>th</str<strong>on</strong>g>is property. Our model, in o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, c<strong>on</strong>tains bo<str<strong>on</strong>g>th</str<strong>on</strong>g> density<br />

dependent effect and Allee effect. In order to clarify <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical properties <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e law <str<strong>on</strong>g>of</str<strong>on</strong>g> reproducti<strong>on</strong> from “first principle derivati<strong>on</strong>”, we analysed <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability<br />

and bifurcati<strong>on</strong> structure <str<strong>on</strong>g>of</str<strong>on</strong>g> fixed points <str<strong>on</strong>g>of</str<strong>on</strong>g> our infinite series functi<strong>on</strong>[4, chapter 2].<br />

References.<br />

[1] Å. Brännström and D. J. T. Sumpter, The role <str<strong>on</strong>g>of</str<strong>on</strong>g> competiti<strong>on</strong> and clustering in populati<strong>on</strong><br />

dynamics Proc. R. Soc. B 272(1576) : 2065–2072, oct 2005.<br />

[2] C. S. Holling, The comp<strong>on</strong>ents <str<strong>on</strong>g>of</str<strong>on</strong>g> predati<strong>on</strong> as revealed by a study <str<strong>on</strong>g>of</str<strong>on</strong>g> small-mammal predati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e european pine sawfly Canad. Entomol. 91(5) : 293–320, may 1959.<br />

[3] Yo-Hey Otake et al., Clustering and relati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> neighbors in populati<strong>on</strong> dynamics: Expansi<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> individual-based first principle derivati<strong>on</strong> RIMS Kokyuroku, Kyoto-U 1556 : 59–102,<br />

mar 2007. (in Japanese)<br />

[4] Yo-Hey Otake, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Study <strong>on</strong> Decisi<strong>on</strong> Making and Collective Behavior in Social<br />

Relati<strong>on</strong>ship PhD <str<strong>on</strong>g>th</str<strong>on</strong>g>esis, U-Tokyo , mar 2008. (in Japanese)<br />

[5] T. Royama, Populati<strong>on</strong> process models , Chapman & Hall, L<strong>on</strong>d<strong>on</strong>, 1992.<br />

740

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Mechanical Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Movement and Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cells and Tissues I;<br />

Wednesday, June 29, 14:30<br />

Hans G. O<str<strong>on</strong>g>th</str<strong>on</strong>g>mer<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics & Digital Technology Center, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Minnesota<br />

e-mail: o<str<strong>on</strong>g>th</str<strong>on</strong>g>mer@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.umn.edu<br />

From Crawlers to Swimmers — Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and<br />

Computati<strong>on</strong>al Problems in Cell Motility<br />

Cell locomoti<strong>on</strong> is essential for early development, angiogenesis, tissue regenerati<strong>on</strong>,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e immune resp<strong>on</strong>se, and wound healing in multicellular organisms, and plays a<br />

very deleterious role in cancer metastasis in humans. Locomoti<strong>on</strong> involves <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

detecti<strong>on</strong> and transducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> extracellular chemical and mechanical signals, integrati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e signals into an intracellular signal, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal c<strong>on</strong>trol<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular biochemical and mechanical resp<strong>on</strong>ses <str<strong>on</strong>g>th</str<strong>on</strong>g>at lead to force generati<strong>on</strong>,<br />

morphological changes and directed movement. While many single-celled<br />

organisms use flagella or cilia to swim, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are two basic modes <str<strong>on</strong>g>of</str<strong>on</strong>g> movement<br />

used by eukaryotic cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at lack such structures – mesenchymal and amoeboid.<br />

The former, which can be characterized as ‘crawling’ in fibroblasts or ‘gliding’ in<br />

keratocytes, involves <str<strong>on</strong>g>th</str<strong>on</strong>g>e extensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> finger-like filopodia or pseudopodia and/or<br />

broad flat lamellipodia, whose protrusi<strong>on</strong> is driven by actin polymerizati<strong>on</strong> at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

leading edge. This mode dominates in cells such as fibroblasts when moving <strong>on</strong> a 2D<br />

substrate. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e amoeboid mode, which does not rely <strong>on</strong> str<strong>on</strong>g adhesi<strong>on</strong>, cells are<br />

more rounded and employ shape changes to move – in effect ’jostling <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

crowd’ or ‘swimming’. Here force generati<strong>on</strong> relies more heavily <strong>on</strong> actin bundles<br />

and <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> myosin c<strong>on</strong>tractility. Leukocytes use <str<strong>on</strong>g>th</str<strong>on</strong>g>is mode for movement<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular matrix in <str<strong>on</strong>g>th</str<strong>on</strong>g>e absence <str<strong>on</strong>g>of</str<strong>on</strong>g> adhesi<strong>on</strong> sites, as does<br />

Dictyostelium discoideum when cells sort in <str<strong>on</strong>g>th</str<strong>on</strong>g>e slug. However, recent experiments<br />

have shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at numerous cell types display enormous plasticity in locomoti<strong>on</strong> in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey sense <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir envir<strong>on</strong>ment and adjust <str<strong>on</strong>g>th</str<strong>on</strong>g>e balance<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e modes accordingly by altering <str<strong>on</strong>g>th</str<strong>on</strong>g>e balance between parallel signal<br />

transducti<strong>on</strong> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways. Thus pure crawling and pure swimming are <str<strong>on</strong>g>th</str<strong>on</strong>g>e extremes<br />

<strong>on</strong> a c<strong>on</strong>tinuum <str<strong>on</strong>g>of</str<strong>on</strong>g> locomoti<strong>on</strong> strategies, but many cells can sense <str<strong>on</strong>g>th</str<strong>on</strong>g>eir envir<strong>on</strong>ment<br />

and use <str<strong>on</strong>g>th</str<strong>on</strong>g>e most efficient strategy in a given c<strong>on</strong>text. We will discuss some<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and computati<strong>on</strong>al challenges <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is diversity poses.<br />

741

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

From <strong>on</strong>e to many: Cell-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective, emergent behaviors<br />

in biology -II; Tuesday, June 28, 14:30<br />

Hans G O<str<strong>on</strong>g>th</str<strong>on</strong>g>mer<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics & Digital Technology Center, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Minnesota<br />

e-mail: o<str<strong>on</strong>g>th</str<strong>on</strong>g>mer@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.umn.edu<br />

Multiscale Modeling in Biology — The Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and<br />

Computati<strong>on</strong>al Challenges<br />

New techniques in cell and molecular biology have produced a better understanding<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cell-level processes <str<strong>on</strong>g>th</str<strong>on</strong>g>at has in turn led to better cell-level models for problems<br />

ranging from bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm formati<strong>on</strong> to embry<strong>on</strong>ic development and cancer. However <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

raises <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> how to incorporate detailed descripti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> individual-level<br />

behavior, be it at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell, tissue or organ level, into populati<strong>on</strong> level descripti<strong>on</strong>s.<br />

We will illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and computati<strong>on</strong>al challenges involved wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an<br />

f example from pattern formati<strong>on</strong> in bacteria, and will discuss some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e open<br />

problems in <str<strong>on</strong>g>th</str<strong>on</strong>g>is area.<br />

742

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling physiological systems: model validati<strong>on</strong> and experimental design<br />

issues; Wednesday, June 29, 11:00<br />

Johnny Ottesen<br />

Roskilde University<br />

e-mail: Johnny@ruc.dk<br />

Patient specific modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart as a tool for early<br />

diagnoses and treatment planning.<br />

The perspective for Patient Specific Modeling (PSM) is to create and develop medical<br />

decisi<strong>on</strong> system based ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying mechanisms<br />

and statistics. We will give an example <str<strong>on</strong>g>of</str<strong>on</strong>g> PSM <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart including<br />

a discussi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> patient specific parameter estimati<strong>on</strong> based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model in<br />

combinati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> new individual patient data obtained from MR measurements <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

various relevant blood volumes (and flows). Such parameters will characterize <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

state <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e patients in far more details <str<strong>on</strong>g>th</str<strong>on</strong>g>an clinical investigati<strong>on</strong>s unveil today.<br />

Thus <str<strong>on</strong>g>th</str<strong>on</strong>g>ese parameters will define diagnosed heart illnesses in a refined manner<br />

and pinpoint exactly where in <str<strong>on</strong>g>th</str<strong>on</strong>g>e physiological system malfuncti<strong>on</strong>ing appears.<br />

This opens up for early diagnoses and individual treatments targeting <str<strong>on</strong>g>th</str<strong>on</strong>g>e actual<br />

malfuncti<strong>on</strong>ing part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e physiological system.<br />

Recently precise and detailed volume data have become assessable by help<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> MR scanning and imaging technologies. The associated finding c<strong>on</strong>firm earlier<br />

results except <str<strong>on</strong>g>th</str<strong>on</strong>g>at atria volumes may show <strong>on</strong>e hump or two hump and all intermediate<br />

c<strong>on</strong>figurati<strong>on</strong>s in between during <strong>on</strong>e heart cycle. These findings are reflected<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding ventricle volume curves but are not so pr<strong>on</strong>ounced. In additi<strong>on</strong>,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese curves vary very much wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tractile streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e atria and ventricles and <str<strong>on</strong>g>th</str<strong>on</strong>g>us it become reduced in cicatrical myocardial tissue<br />

(after an infarcti<strong>on</strong>) and wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart valves.<br />

Data from 40 subjects encompass left atria volume, left ventricle volume, right<br />

atria volume, right ventricle volume, flow from left ventricle into aorta, and flow<br />

from right ventricle into pulm<strong>on</strong>ary aorta versus time during <strong>on</strong>e heart cycle. Data<br />

was recorded for objects at rest and for objects given dobutrex and robinul as well.<br />

Our model describe preload to atria, atria itself, ventricle, and afterload for<br />

left heart using ordinary differential equati<strong>on</strong>s. Based <strong>on</strong> data, sensitivities <strong>on</strong><br />

and correlati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e model parameters will be investigated and parameter<br />

estimati<strong>on</strong> <strong>on</strong> a meaningful subset will be performed. Thus various pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologies,<br />

including decreased c<strong>on</strong>tractile capacities and stenosis, will be categorizes in terms<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model parameters.<br />

743

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Saturday, July 2, 08:30<br />

Aziz Ouhinou<br />

African Institute for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, 6 Melrose Road, Muizenberg,<br />

7945, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Africa<br />

e-mail: aziz@aims.ac.za<br />

Semu Mitiku Kassa<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Addis Ababa University,<br />

P.O.Box 1176 Addis Ababa, E<str<strong>on</strong>g>th</str<strong>on</strong>g>iopia<br />

e-mail: smtk@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.aau.edu.et<br />

Epidemiological Models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Prevalence Dependent<br />

Endogenous Self-Protecti<strong>on</strong> Measure<br />

A simple ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for human disease epidemics <str<strong>on</strong>g>th</str<strong>on</strong>g>at takes <str<strong>on</strong>g>th</str<strong>on</strong>g>e human<br />

learning behaviour and self-protective measures into account is proposed. We<br />

analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> endogenous self-protective measures wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>e prevalence<br />

level <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease and c<strong>on</strong>versely. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e model it is assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at people<br />

start reacting against c<strong>on</strong>tracting a disease wi<str<strong>on</strong>g>th</str<strong>on</strong>g> self protective measures whenever<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ey are informed about <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease and when <str<strong>on</strong>g>th</str<strong>on</strong>g>e burden <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease is in a<br />

recognizable stage. We show how suppressing <str<strong>on</strong>g>th</str<strong>on</strong>g>e prevalence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease is more<br />

sensitive to <str<strong>on</strong>g>th</str<strong>on</strong>g>e average effectiveness <str<strong>on</strong>g>of</str<strong>on</strong>g> self-protective measures <str<strong>on</strong>g>th</str<strong>on</strong>g>an increasing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

proporti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals in a populati<strong>on</strong> into which awareness is created.<br />

References.<br />

[1] Z. Mukandavire, W. Garira, Effects <str<strong>on</strong>g>of</str<strong>on</strong>g> public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> educati<strong>on</strong>al campaigns and <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> sex<br />

workers <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV/AIDS am<strong>on</strong>g heterosexuals, Theoretical Populati<strong>on</strong> Biology, 72<br />

(2007) 346-365.<br />

[2] Z. Mukandavire, W. Garira, J.M. Tchuenche, Modelling effects <str<strong>on</strong>g>of</str<strong>on</strong>g> public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> educati<strong>on</strong>al<br />

campaigns <strong>on</strong> HIV/AIDS transmissi<strong>on</strong> dynamics, Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling, 33 (2009)<br />

2084–2095.<br />

[3] H. Ying-Hen, K. Cooke, Behaviour change and treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> core groups: its effect <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

spread <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV/AIDS, IMA Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Applied in Medicine and Biology, 17<br />

(2000) 213-241.<br />

[4] F. Baryarama, J. Y. T. Mugisha, L. S. Luboobi, A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> HIV/AIDS wi<str<strong>on</strong>g>th</str<strong>on</strong>g> gradual behaviour change, Computati<strong>on</strong>al and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in<br />

Medicine, 7 (2006) 15-26.<br />

[5] A. Galata, N. Johns<strong>on</strong>, D. Hogg, Learning behaviour models <str<strong>on</strong>g>of</str<strong>on</strong>g> human activities, In Proc.<br />

British Machine Visi<strong>on</strong> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g>, BMVC’99, Sept. 1999.<br />

744

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modelling bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms: from gene regulati<strong>on</strong> to large-scale structure and<br />

functi<strong>on</strong>; Wednesday, June 29, 17:00<br />

Niels Chr Overgaard<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Lund University, Sweden<br />

e-mail: nco@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.l<str<strong>on</strong>g>th</str<strong>on</strong>g>.se<br />

A new necessary c<strong>on</strong>diti<strong>on</strong> for coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> species in<br />

equilibrium states <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Wanner-Gujer-Kissel bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm model<br />

We c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical Wanner-Gujer-Kissel 1D-model [1,2] in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> two<br />

bacterial species competing for space and a single limiting substrate in a bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

given fixed <str<strong>on</strong>g>th</str<strong>on</strong>g>ickness. We focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model’s ability to describe equilibrium states<br />

in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e two species coexist. If we let f(z, t) = (f1(z, t), f2(z, t)), 0 ≤ z ≤ L,<br />

t ≥ 0, denote <str<strong>on</strong>g>th</str<strong>on</strong>g>e volume fracti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two species and S(z, t) <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e limiting substrate, <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>e model c<strong>on</strong>sistes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e following system <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear<br />

PDEs:<br />

(1) ft + (vf)z = A(S)f, f1(z, t) + f2(z, t) = 1, v(0, t) = 0,<br />

and<br />

(2) St − DSzz + λ T A(S)f = 0, Sz(0) = 0, S(L) = S 0 ,<br />

al<strong>on</strong>g wi<str<strong>on</strong>g>th</str<strong>on</strong>g> appropriate initial data. Here v = v(z, t) is a (scalar) velocity field,<br />

A(S) = diag(a1(S), a2(S)) <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> matrix, and S 0 <str<strong>on</strong>g>th</str<strong>on</strong>g>e bulk c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e substrate at <str<strong>on</strong>g>th</str<strong>on</strong>g>e bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm-water interface z = L. Moreover, D denotes diffusivity<br />

and λ is a vector c<strong>on</strong>taining reciprocal yield coefficients. More about ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm modelling can be found in a recent overview by Klapper and Dockery [3]<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we derive a new necessary c<strong>on</strong>diti<strong>on</strong>, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> an inequality,<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> coexistence equilibrium states to <str<strong>on</strong>g>th</str<strong>on</strong>g>e model (1) and (2). This<br />

c<strong>on</strong>diti<strong>on</strong> is used in numerical experiments to locate model parameters which exibit<br />

coexistence states, some<str<strong>on</strong>g>th</str<strong>on</strong>g>ing which would be difficult o<str<strong>on</strong>g>th</str<strong>on</strong>g>erwise. The equilibrium is<br />

computed using a robust numerical me<str<strong>on</strong>g>th</str<strong>on</strong>g>od developed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e au<str<strong>on</strong>g>th</str<strong>on</strong>g>or and presented<br />

at <str<strong>on</strong>g>th</str<strong>on</strong>g>e ECMTB 2008 in Edinburgh. It is hoped <str<strong>on</strong>g>th</str<strong>on</strong>g>at our necessary c<strong>on</strong>diti<strong>on</strong> could<br />

be a stepping st<strong>on</strong>e in <str<strong>on</strong>g>th</str<strong>on</strong>g>e search for a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically rigorous pro<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> coexcistence equilibrium states for bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is class.<br />

A motivati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is a recent article by Klapper and Szomolay [4],<br />

where an exclusi<strong>on</strong> principle for ruling out occurence <str<strong>on</strong>g>of</str<strong>on</strong>g> certain coexistence equilibrium<br />

states is presented. While <str<strong>on</strong>g>th</str<strong>on</strong>g>is principle is correct, it is exemplified wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

a bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm system, <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e kind studied here, for which <str<strong>on</strong>g>th</str<strong>on</strong>g>e au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors seem to imply<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at a coexistence equilibrium may occur <strong>on</strong>ly for <strong>on</strong>e special value <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e applied<br />

substrate bulk c<strong>on</strong>centrati<strong>on</strong> S 0 . Our investigati<strong>on</strong>s indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e situati<strong>on</strong> is<br />

far more favorable, and <str<strong>on</strong>g>th</str<strong>on</strong>g>at coexistence equilibria actually exists for a whole range<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> values <str<strong>on</strong>g>of</str<strong>on</strong>g> S 0 , and <str<strong>on</strong>g>th</str<strong>on</strong>g>at for each such value, <str<strong>on</strong>g>th</str<strong>on</strong>g>e system is actually attracted to a<br />

coexistence equilibrium state.<br />

References.<br />

[1] Wanner, O. and W. Gujer, A multispecies bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm model. Biotechnol. Bioengn. 28, 314–328,<br />

1986.<br />

[2] Kissel, J.C., P.L. McCarty and R.L. Street, Numerical simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> mixed-culture bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm. J.<br />

Envir<strong>on</strong>. Eng. 110, 391–411, 1984.<br />

745

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[3] Klapper, I. and J. Dockery, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> microbial bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms, SIAM Rev. 52,<br />

221–265, 2010.<br />

[4] Klapper, I. and B. Szomolay, An Exclusi<strong>on</strong> Principle and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Importance <str<strong>on</strong>g>of</str<strong>on</strong>g> Motility for<br />

a Class <str<strong>on</strong>g>of</str<strong>on</strong>g> Bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm Models. Bull. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. Published <strong>on</strong>line: 15 January 2011, DOI:<br />

10.1007/s11538-010-9621-5.<br />

746

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Marcin Pacholczyk<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Automatic C<strong>on</strong>trol, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology,<br />

Poland<br />

e-mail: marcin.pacholczyk@polsl.pl<br />

Marek Kimmel<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Statistics, Rice University, TX USA<br />

e-mail: kimmel@rice.edu<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> protein - small molecule interacti<strong>on</strong>s using<br />

probilistic approach<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> protein - small molecule interacti<strong>on</strong>s is crucial in <str<strong>on</strong>g>th</str<strong>on</strong>g>e discovery <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

new drug candidates and lead structure optimizati<strong>on</strong>. Small biomolecules (ligands)<br />

are highly flexible and may adopt numerous c<strong>on</strong>formati<strong>on</strong>s up<strong>on</strong> binding to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

protein. Using computer simulati<strong>on</strong>s instead <str<strong>on</strong>g>of</str<strong>on</strong>g> sophisticated laboratory procedures<br />

may significantly reduce cost <str<strong>on</strong>g>of</str<strong>on</strong>g> some stages <str<strong>on</strong>g>of</str<strong>on</strong>g> drug development. Inspired<br />

by probabilistic pa<str<strong>on</strong>g>th</str<strong>on</strong>g> planning in robotics, stochastic roadmap me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology can be<br />

regarded as a very interesting approach to effective sampling <str<strong>on</strong>g>of</str<strong>on</strong>g> ligand c<strong>on</strong>formati<strong>on</strong>al<br />

space around a protein molecule. Protein - ligand interacti<strong>on</strong>s are divided<br />

into two parts electrostatics, modeled by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Poiss<strong>on</strong>-Boltzmann equati<strong>on</strong>, and van<br />

der Waals interacti<strong>on</strong>s represented by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Lennard-J<strong>on</strong>es potential. The results are<br />

promising since it can be shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at locati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> binding sites predicted by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

simulati<strong>on</strong> are in agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ose revealed by experimental x-ray crystallography<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> protein-ligand complexes. We would like to extend our knowledge bey<strong>on</strong>d<br />

scope available to most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e current molecular modeling tools toward better understanding<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ligand binding process. We try to accomplish <str<strong>on</strong>g>th</str<strong>on</strong>g>is goal using<br />

two-level model <str<strong>on</strong>g>of</str<strong>on</strong>g> protein-ligand interacti<strong>on</strong> and sampling <str<strong>on</strong>g>of</str<strong>on</strong>g> ligand c<strong>on</strong>formati<strong>on</strong>al<br />

space covering <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire surface <str<strong>on</strong>g>of</str<strong>on</strong>g> protein target.<br />

References.<br />

[1] Apaydin MS, Guestrin CE, Varma C, Brutlag DL, Latombe JC. 2002. Stochastic roadmap<br />

simulati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> ligand-protein interacti<strong>on</strong>s. Bioinformatics 18,S18–S26.<br />

[2] Apaydin MS, Brutlag DL, Guestrin C, Hsu D, Latombe JC, Varma C. 2003. Stochastic roadmap<br />

simulati<strong>on</strong>: An efficient representati<strong>on</strong> and algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m for analyzing molecular moti<strong>on</strong>. Journal<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Computati<strong>on</strong>al Biology 10,257–281.<br />

[3] Taylor HM, Karlin S. 1998. Markov Chains: Introducti<strong>on</strong>. In An Introducti<strong>on</strong> to Stochastic<br />

Modelling, Academic Press, San Diego. 95–198.<br />

[4] B-Rao C, Subramanian J, Sharma SD. 2009. Managing protein flexibility in docking and its<br />

applicati<strong>on</strong>s. Drug Discovery Today 14,394–400.<br />

[5] Laurie ATR, Jacks<strong>on</strong> RM. 2006. Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for <str<strong>on</strong>g>th</str<strong>on</strong>g>e predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> protein-ligand binding sites<br />

for Structure-Based Drug Design and virtual ligand screening. Current Protein and Peptide<br />

Science 7,395-406.<br />

747

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cell migrati<strong>on</strong> during development: modelling and experiment; Saturday,<br />

July 2, 08:30<br />

Kevin Painter<br />

Heriot-Watt University<br />

e-mail: painter@ma.hw.ac.uk<br />

Richard L. Mort<br />

MRC Human Genetics Unit, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Genetics and Molecular Medicine,<br />

Edinburgh<br />

Ian J. Jacks<strong>on</strong><br />

MRC Human Genetics Unit, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Genetics and Molecular Medicine,<br />

Edinburgh<br />

An integrated experimental/<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical approach to explore<br />

cell migrati<strong>on</strong> during embry<strong>on</strong>ic development<br />

Cell migrati<strong>on</strong> is critical to multiple developmental processes, from early embry<strong>on</strong>ic<br />

reorganisati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e intricate wiring <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nervous system. Neural crest<br />

cells (NCCs) form a highly motile populati<strong>on</strong> characterised by an epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial to<br />

mesenchymal transformati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows <str<strong>on</strong>g>th</str<strong>on</strong>g>eir migrati<strong>on</strong> to various remote target<br />

tissues, where <str<strong>on</strong>g>th</str<strong>on</strong>g>ey differentiate into multiple cell types. Failure to migrate, proliferate<br />

or differentiate leads to a ple<str<strong>on</strong>g>th</str<strong>on</strong>g>ora <str<strong>on</strong>g>of</str<strong>on</strong>g> bir<str<strong>on</strong>g>th</str<strong>on</strong>g> defects. Melanoblasts, a subtype<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> NCC and <str<strong>on</strong>g>th</str<strong>on</strong>g>e embry<strong>on</strong>ic precursors <str<strong>on</strong>g>of</str<strong>on</strong>g> melanocytes, serve as a model system for<br />

cell migrati<strong>on</strong> during development and in pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologies such as cancer cell metastasis.<br />

Melanoblasts migrate out <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e neural crest into <str<strong>on</strong>g>th</str<strong>on</strong>g>e developing skin before localising<br />

into <str<strong>on</strong>g>th</str<strong>on</strong>g>e developing embry<strong>on</strong>ic hair follicles. A variety <str<strong>on</strong>g>of</str<strong>on</strong>g> factors may c<strong>on</strong>tribute<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir col<strong>on</strong>isati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e embry<strong>on</strong>ic skin, including tissue grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, melanoblast<br />

motility, melanoblast proliferati<strong>on</strong> and extracellular signaling factors. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk<br />

I will discuss our integrated experimental/<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical approach to understanding<br />

melanoblast invasi<strong>on</strong>, in which data obtained in an ex vivo system for live imaging<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> melanoblast migrati<strong>on</strong> in embry<strong>on</strong>ic skin is incorporated into ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

models which, in turn, are used to test distinct hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses for col<strong>on</strong>isati<strong>on</strong> and<br />

formulate experimentally testable predicti<strong>on</strong>s.<br />

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Modeling and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor invasi<strong>on</strong> II; Tuesday, June 28, 14:30<br />

Kevin Painter<br />

Heriot-Watt University<br />

e-mail: painter@ma.hw.ac.uk<br />

The impact <str<strong>on</strong>g>of</str<strong>on</strong>g> a heterogeneous envir<strong>on</strong>ment <strong>on</strong> invasive<br />

processes<br />

The invasi<strong>on</strong> or migrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells in tissues, ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er during embry<strong>on</strong>ic development,<br />

normal physiological processes such as tissue repair or as a result <str<strong>on</strong>g>of</str<strong>on</strong>g> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologies<br />

such as cancer, can be highly variable according to cellular and tissue type. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

talk I will present a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> results, based <strong>on</strong> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> indivudual and c<strong>on</strong>tinuous<br />

level models, <str<strong>on</strong>g>th</str<strong>on</strong>g>at examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular matrix envir<strong>on</strong>ment <strong>on</strong><br />

invasi<strong>on</strong>. Specifically, I will examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> a heterogeneous adhesive<br />

envir<strong>on</strong>ment surrounding cells and varying degrees <str<strong>on</strong>g>of</str<strong>on</strong>g> anisotropy resulting from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

oriented structure <str<strong>on</strong>g>of</str<strong>on</strong>g> matrix fibres.<br />

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Laurence Palk<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Auckland<br />

e-mail: l.palk@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.auckland.ac.nz<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> fluid secreti<strong>on</strong> and calcium<br />

dynamics in <str<strong>on</strong>g>th</str<strong>on</strong>g>e salivary gland.<br />

It is estimated <str<strong>on</strong>g>th</str<strong>on</strong>g>at 20% <str<strong>on</strong>g>of</str<strong>on</strong>g> adults in <str<strong>on</strong>g>th</str<strong>on</strong>g>e US will suffer xerostomia, a c<strong>on</strong>diti<strong>on</strong><br />

whereby a lack <str<strong>on</strong>g>of</str<strong>on</strong>g> saliva producti<strong>on</strong> causes issues wi<str<strong>on</strong>g>th</str<strong>on</strong>g> dental cavities, oral pain and<br />

infecti<strong>on</strong>. We c<strong>on</strong>struct a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parotid acinar cell wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

aim <str<strong>on</strong>g>of</str<strong>on</strong>g> investigating how <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> K+ channels and Ca2+ wave speed<br />

affects saliva producti<strong>on</strong>. Secreti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> fluid is initiated by Ca2+ signals acting <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Ca2+ dependent K+ and Cl- channels. The opening <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese channels facilitates <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

movement <str<strong>on</strong>g>of</str<strong>on</strong>g> Cl- i<strong>on</strong>s into <str<strong>on</strong>g>th</str<strong>on</strong>g>e lumen which water follows by osmosis. We use recent<br />

results into bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e release <str<strong>on</strong>g>of</str<strong>on</strong>g> Ca2+ from internal stores via <str<strong>on</strong>g>th</str<strong>on</strong>g>e inositol (1,4,5)trisphosphate<br />

receptor (IP3R) and IP3 dynamics to create a physiologically realistic<br />

Ca2+ model which is able to recreate important experimentally observed behaviours<br />

seen in parotid acinar cells. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at maximum saliva producti<strong>on</strong> occurs when<br />

a small amount <str<strong>on</strong>g>of</str<strong>on</strong>g> K+ c<strong>on</strong>ductance is located at <str<strong>on</strong>g>th</str<strong>on</strong>g>e apical membrane, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

majority in <str<strong>on</strong>g>th</str<strong>on</strong>g>e basal membrane. We simulate Ca2+ waves as periodic functi<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> time at bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e apical and basal membranes. This enables us in investigate<br />

how <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase difference <str<strong>on</strong>g>of</str<strong>on</strong>g> apical and basal Ca2+ signals affects fluid flow. We<br />

find maximum fluid flow when Ca2+ signals are in-sync, predicting increased cell<br />

efficiency wi<str<strong>on</strong>g>th</str<strong>on</strong>g> faster Ca2+ waves.<br />

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Systems Biology <str<strong>on</strong>g>of</str<strong>on</strong>g> Development; Saturday, July 2, 14:30<br />

Margriet M. Palm<br />

Centrum Wiskunde & Informatica (Amsterdam, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands)<br />

and Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands C<strong>on</strong>sortium for Systems Biology (Amsterdam, The<br />

Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands), Science Park 123, 1098 XG The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

e-mail: m.m.palm@cwi.nl<br />

Roeland M.H. Merks<br />

Centrum Wiskunde & Informatica (Amsterdam, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands)<br />

and Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands C<strong>on</strong>sortium for Systems Biology (Amsterdam, The<br />

Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands), Science Park 123, 1098 XG The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

e-mail: roeland.merks@cwi.nl<br />

Cell el<strong>on</strong>gati<strong>on</strong> and cell adhesi<strong>on</strong> suffice for vascular network<br />

formati<strong>on</strong><br />

The formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> blood vessels is crucial in many biological processes including<br />

embry<strong>on</strong>ic development, wound healing and cancer. Vascular networks form by<br />

migrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir interacti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ECM. A multitude <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

computati<strong>on</strong>al models explain vascular network formati<strong>on</strong> by means <str<strong>on</strong>g>of</str<strong>on</strong>g> chemotaxis<br />

driven aggregati<strong>on</strong>. However, experiments suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at vascular networks may form<br />

also wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out secreted chemoattractants [1].<br />

Previously, we have highlighted cell leng<str<strong>on</strong>g>th</str<strong>on</strong>g> as a key property for vascular-like<br />

network formati<strong>on</strong> [2]: a cell-based, Cellular Potts model indicated <str<strong>on</strong>g>th</str<strong>on</strong>g>at chemotaxis<br />

and cell el<strong>on</strong>gati<strong>on</strong>, toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er, suffice for forming stable, regular networks. We have<br />

now analyzed <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model in absence <str<strong>on</strong>g>of</str<strong>on</strong>g> chemotaxis, and find <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

cell el<strong>on</strong>gati<strong>on</strong> and cell adhesi<strong>on</strong> al<strong>on</strong>e suffice for forming network-like structures.<br />

The deformability <str<strong>on</strong>g>of</str<strong>on</strong>g> cells and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir adhesi<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e ECM turn out to be key to<br />

network formati<strong>on</strong>. Flexible, adherent cells form blobs wi<str<strong>on</strong>g>th</str<strong>on</strong>g> individual cells packed<br />

closely toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er. More rigid, el<strong>on</strong>gated cells cannot assume <str<strong>on</strong>g>th</str<strong>on</strong>g>eir ideal shape inside<br />

a blob, making network-like structures <str<strong>on</strong>g>th</str<strong>on</strong>g>e preferred c<strong>on</strong>figurati<strong>on</strong>. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out chemotaxis,<br />

network-like patterns form in a narrow regi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> parameter space; chemotaxis<br />

dramatically widens <str<strong>on</strong>g>th</str<strong>on</strong>g>is regi<strong>on</strong> and sharpens <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase transiti<strong>on</strong>s between blobs<br />

and networks. C<strong>on</strong>cluding, vascular network formati<strong>on</strong> does not necessarily require<br />

chemotaxis or similar, midrange attractive forces between cells, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough such forces<br />

make network-like patterning more robust.<br />

References.<br />

[1] Andras Szabó, Network Formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Tissue Cells via Preferential Attracti<strong>on</strong> to El<strong>on</strong>gated<br />

Structures Phys Rev Lett 2007<br />

[2] Roeland M.H. Merks et al, Cell el<strong>on</strong>gati<strong>on</strong> is key to in silico replicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> in vitro vasculogenesis<br />

and subsequent remodeling Dev Biol 2006<br />

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Populati<strong>on</strong> Dynamics; Thursday, June 30, 11:30<br />

Peter Pang<br />

Nati<strong>on</strong>al University <str<strong>on</strong>g>of</str<strong>on</strong>g> Singapore (Dept <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>)<br />

e-mail: matpyh@nus.edu.sg<br />

H. L. Li<br />

Sou<str<strong>on</strong>g>th</str<strong>on</strong>g>east University, China<br />

M. X. Wang<br />

Harbin Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, China<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> an ecosystem wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-level<br />

trophic interacti<strong>on</strong>s<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, <str<strong>on</strong>g>th</str<strong>on</strong>g>e speaker will discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatiotemporal<br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> an ecosystem wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-level trophic interacti<strong>on</strong>s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

model, a general trophic functi<strong>on</strong> based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ratio between <str<strong>on</strong>g>th</str<strong>on</strong>g>e prey and a linear<br />

functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e predator is used at each level. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e two limits <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is trophic<br />

functi<strong>on</strong>, <strong>on</strong>e recovers <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical prey-dependent (Lotka-Volterra type) predati<strong>on</strong><br />

model and <str<strong>on</strong>g>th</str<strong>on</strong>g>e ratio-dependent predati<strong>on</strong> model, respectively.<br />

The model results in a str<strong>on</strong>gly-coupled system <str<strong>on</strong>g>of</str<strong>on</strong>g> parabolic partial differential<br />

equati<strong>on</strong>s. The speaker will analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence, uniqueness, stability and bifurcati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> equilibrium (steady state) soluti<strong>on</strong>s using <str<strong>on</strong>g>th</str<strong>on</strong>g>e upper-lower soluti<strong>on</strong>s me<str<strong>on</strong>g>th</str<strong>on</strong>g>od<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e topological degree me<str<strong>on</strong>g>th</str<strong>on</strong>g>od. He will also interpret some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese results in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> different predati<strong>on</strong> behaviors (prey-dependent vs ratio-dependent).<br />

The speaker also points out <str<strong>on</strong>g>th</str<strong>on</strong>g>at he and his co-au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors have used similar me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

to study ecosystems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different predati<strong>on</strong> behaviors and strategies, different<br />

spatial features, as well as different species grow<str<strong>on</strong>g>th</str<strong>on</strong>g> patterns. This talk will include<br />

a brief survey <str<strong>on</strong>g>of</str<strong>on</strong>g> some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese results (which have been published in a series <str<strong>on</strong>g>of</str<strong>on</strong>g> papers<br />

in Proc Roy Soc Edinburgh, Proc L<strong>on</strong>d<strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Soc, J Differential Equati<strong>on</strong>s,<br />

IMA J Appl Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>, SIAM J Appl Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> etc).<br />

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Statistical Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Signals II; Saturday, July 2, 11:00<br />

A. Panorska<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nevada, Reno<br />

e-mail: ania@unr.edu<br />

The joint distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sum and maximum <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

exp<strong>on</strong>ential random variables wi<str<strong>on</strong>g>th</str<strong>on</strong>g> applicati<strong>on</strong>s to biology<br />

We c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximum Y and sum X <str<strong>on</strong>g>of</str<strong>on</strong>g> n iid exp<strong>on</strong>ential<br />

random variables. We present <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact joint distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vector (X, Y)<br />

toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> its marginals and c<strong>on</strong>diti<strong>on</strong>als. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er, we extend our result to<br />

stochastic number <str<strong>on</strong>g>of</str<strong>on</strong>g> terms, and present <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact joint distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e random<br />

vector (N, X, Y), when N has a geometric distributi<strong>on</strong>. Then, X is <str<strong>on</strong>g>th</str<strong>on</strong>g>e random sum<br />

and Y is <str<strong>on</strong>g>th</str<strong>on</strong>g>e random maximum <str<strong>on</strong>g>of</str<strong>on</strong>g> N iid exp<strong>on</strong>ential random variables. We illustrate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling potential <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese distributi<strong>on</strong>s using applicati<strong>on</strong>s in biology.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Structure and Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemical Reacti<strong>on</strong> Networks I; Tuesday, June<br />

28, 14:30<br />

Casian Pantea<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Wisc<strong>on</strong>sin-Madis<strong>on</strong><br />

e-mail: pantea@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.wisc.edu<br />

Persistence and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Global Attractor C<strong>on</strong>jecture: Recent<br />

Approaches<br />

We describe recent approaches to proving <str<strong>on</strong>g>th</str<strong>on</strong>g>e Persistence C<strong>on</strong>jecture (which describes<br />

a class <str<strong>on</strong>g>of</str<strong>on</strong>g> mass-acti<strong>on</strong> systems for which variables do not approach zero) and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Global Attractor C<strong>on</strong>jecture (which describes a class <str<strong>on</strong>g>of</str<strong>on</strong>g> mass-acti<strong>on</strong> systems for<br />

which trajectories c<strong>on</strong>verge to a single positive equilibrium). We introduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e class<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> "endotactic" networks (which c<strong>on</strong>tains <str<strong>on</strong>g>th</str<strong>on</strong>g>e class <str<strong>on</strong>g>of</str<strong>on</strong>g> weakly reversible networks),<br />

and formulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e Extended Persistence C<strong>on</strong>jecture, which says <str<strong>on</strong>g>th</str<strong>on</strong>g>at endotactic<br />

mass-acti<strong>on</strong> systems are persistent, even if <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong> rate parameters are allowed<br />

to vary in time (to incorporate <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> external signals). We describe a pro<str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Extended Persistence C<strong>on</strong>jecture for systems <str<strong>on</strong>g>th</str<strong>on</strong>g>at have two-dimensi<strong>on</strong>al stoichiometric<br />

subspace. In particular, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at in weakly reversible mass-acti<strong>on</strong><br />

systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two-dimensi<strong>on</strong>al stoichiometric subspace all bounded trajectories are<br />

persistent. These ideas also apply to power-law systems and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er n<strong>on</strong>linear dynamical<br />

systems. Moreover, we use <str<strong>on</strong>g>th</str<strong>on</strong>g>ese results to prove <str<strong>on</strong>g>th</str<strong>on</strong>g>e Global Attractor<br />

C<strong>on</strong>jecture for systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-dimensi<strong>on</strong>al stoichiometric subspace. This is<br />

joint work wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Gheorghe Craciun and Fedor Nazarov.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Je<strong>on</strong>g-Man Park<br />

The Ca<str<strong>on</strong>g>th</str<strong>on</strong>g>olic University <str<strong>on</strong>g>of</str<strong>on</strong>g> Korea<br />

e-mail: jmanpark@ca<str<strong>on</strong>g>th</str<strong>on</strong>g>olic.ac.kr<br />

Mark Ancliff<br />

The Ca<str<strong>on</strong>g>th</str<strong>on</strong>g>olic University <str<strong>on</strong>g>of</str<strong>on</strong>g> Korea<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Spin coherent state representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Crow-Kimura and<br />

Eigen models <str<strong>on</strong>g>of</str<strong>on</strong>g> quasispecies <str<strong>on</strong>g>th</str<strong>on</strong>g>eory<br />

We present a spin coherent state representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Crow-Kimura and Eigen<br />

models <str<strong>on</strong>g>of</str<strong>on</strong>g> biological evoluti<strong>on</strong>. We deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> quasispecies models where <str<strong>on</strong>g>th</str<strong>on</strong>g>e fitness<br />

is a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Hamming distances from <strong>on</strong>e or more reference sequences. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

limit <str<strong>on</strong>g>of</str<strong>on</strong>g> large sequence leng<str<strong>on</strong>g>th</str<strong>on</strong>g> N, we find exact expressi<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean fitness and<br />

magnetizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymptotic quasispecies distributi<strong>on</strong> in symmetric fitness landscapes.<br />

The results are obtained by c<strong>on</strong>structing a pa<str<strong>on</strong>g>th</str<strong>on</strong>g> integral for <str<strong>on</strong>g>th</str<strong>on</strong>g>e propagator<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e coset SU(2)/U(1) and taking <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical limit. The classical limit gives a<br />

Hamilt<strong>on</strong>ian functi<strong>on</strong> <strong>on</strong> a circle for <strong>on</strong>e reference sequence, and <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e product <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

2m − 1 circles for m reference sequences. We apply our representati<strong>on</strong> to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Schuster-Swetina phenomena, where a wide lower peak is selected over a narrow<br />

higher peak. The quadratic landscape wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two reference sequences is also analyzed<br />

specifically and we present <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase diagram <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutati<strong>on</strong>-fitness parameter<br />

phase space. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we use our me<str<strong>on</strong>g>th</str<strong>on</strong>g>od to investigate more biologically relevant<br />

system, a model <str<strong>on</strong>g>of</str<strong>on</strong>g> escape from adaptive c<strong>on</strong>flict <str<strong>on</strong>g>th</str<strong>on</strong>g>rough gene duplicati<strong>on</strong>,<br />

and find <str<strong>on</strong>g>th</str<strong>on</strong>g>ree different phases for <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymptotic populati<strong>on</strong> distributi<strong>on</strong>.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Genetics; Wednesday, June 29, 17:00<br />

Su-Chan Park<br />

The Ca<str<strong>on</strong>g>th</str<strong>on</strong>g>olic University <str<strong>on</strong>g>of</str<strong>on</strong>g> Korea, Republic <str<strong>on</strong>g>of</str<strong>on</strong>g> Korea<br />

e-mail: spark0@ca<str<strong>on</strong>g>th</str<strong>on</strong>g>olic.ac.kr<br />

Kavita Jain<br />

Jawaharlal Nehru Centre for Advanced Scientific Research, India<br />

Joachim Krug<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cologne, Germany<br />

Evoluti<strong>on</strong>ary advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> small populati<strong>on</strong>s <strong>on</strong> complex<br />

fitness landscapes<br />

Recent experimental (Rozen et al. 2008) and <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical (Handel and Rozen, 2009)<br />

studies have shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at small asexual populati<strong>on</strong>s evolving <strong>on</strong> complex fitness landscapes<br />

may achieve a higher fitness <str<strong>on</strong>g>th</str<strong>on</strong>g>an large <strong>on</strong>es due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e increased heterogeneity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> adaptive trajectories. Here we introduce a class <str<strong>on</strong>g>of</str<strong>on</strong>g> haploid <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-locus fitness<br />

landscapes <str<strong>on</strong>g>th</str<strong>on</strong>g>at allow <str<strong>on</strong>g>th</str<strong>on</strong>g>e investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is scenario in a precise and quantitative<br />

way. Our main result derived analytically shows how <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>of</str<strong>on</strong>g> choosing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e largest initial fitness increase grows wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> size. This<br />

makes large populati<strong>on</strong>s more likely to get trapped at local fitness peaks and implies<br />

an advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> small populati<strong>on</strong>s at intermediate time scales. The range <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

populati<strong>on</strong> sizes where <str<strong>on</strong>g>th</str<strong>on</strong>g>is effect is operative coincides wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>set <str<strong>on</strong>g>of</str<strong>on</strong>g> cl<strong>on</strong>al<br />

interference. Additi<strong>on</strong>al studies using ensembles <str<strong>on</strong>g>of</str<strong>on</strong>g> random fitness landscapes show<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e results achieved for a particular choice <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-locus landscape parameters<br />

are robust and also persist as <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> loci increases. Our study indicates<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at an advantage for small populati<strong>on</strong>s is likely whenever <str<strong>on</strong>g>th</str<strong>on</strong>g>e fitness landscape<br />

c<strong>on</strong>tains local maxima. The advantage appears at intermediate time scales, which<br />

are l<strong>on</strong>g enough for trapping at local fitness maxima to have occurred but too short<br />

for peak escape by <str<strong>on</strong>g>th</str<strong>on</strong>g>e creati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple mutants. This presentati<strong>on</strong> is based <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e paper (Jain et al. 2011).<br />

References.<br />

[1] Rozen, D. E., M. G. J. L. Habets, A. Handel, and J. A. G. M. de Visser. 2008. Heterogeneous<br />

adaptive trajectories <str<strong>on</strong>g>of</str<strong>on</strong>g> small populati<strong>on</strong>s <strong>on</strong> complex fitness landscapes. PLoS ONE 3:e1715.<br />

[2] Handel, A., and D. E. Rozen. 2009. The impact <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> size <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> asexual<br />

microbes <strong>on</strong> smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> versus rugged fitness landscapes. BMC Evoluti<strong>on</strong>ary Biology 9:236.<br />

[3] Jain, K., J. Krug, and S.-C. Park. 2011. Evoluti<strong>on</strong>ary advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> small populati<strong>on</strong>s <strong>on</strong><br />

complex fitness landscapes, to appear in Evoluti<strong>on</strong>.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Evoluti<strong>on</strong>ary Ecology; Thursday, June 30, 11:30<br />

Kalle Parvinen<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Turku, Finland<br />

e-mail: kalle.parvinen@utu.fi<br />

Joint evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal and cooperati<strong>on</strong> in a locally<br />

stochastic metapopulati<strong>on</strong> model<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I will investigate a structured metapopulati<strong>on</strong> model [2], c<strong>on</strong>sisting<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> small local populati<strong>on</strong>s. Local populati<strong>on</strong> dynamics (bir<str<strong>on</strong>g>th</str<strong>on</strong>g>, dea<str<strong>on</strong>g>th</str<strong>on</strong>g>, emigrati<strong>on</strong><br />

and immigrati<strong>on</strong>) is <str<strong>on</strong>g>th</str<strong>on</strong>g>us stochastic. The evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal in <str<strong>on</strong>g>th</str<strong>on</strong>g>is model has<br />

been earlier studied [3]: <str<strong>on</strong>g>th</str<strong>on</strong>g>e dispersal rate evolves, because catastrophes and demographic<br />

stochasticity result in sparsely populated patches, into which immigrati<strong>on</strong><br />

is beneficial. In additi<strong>on</strong>, dispersal reduces kin competiti<strong>on</strong>.<br />

Recently, <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> public goods cooperati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>is model has also been<br />

studied [4]. In each habitat patch, individuals can c<strong>on</strong>tribute to a comm<strong>on</strong> resource,<br />

which benefits <str<strong>on</strong>g>th</str<strong>on</strong>g>e reproducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> all individuals <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e patch. C<strong>on</strong>tributi<strong>on</strong> is<br />

costly, and increases <str<strong>on</strong>g>th</str<strong>on</strong>g>e dea<str<strong>on</strong>g>th</str<strong>on</strong>g> rate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tributor. I assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at cooperati<strong>on</strong><br />

is altruistic, <str<strong>on</strong>g>th</str<strong>on</strong>g>us <str<strong>on</strong>g>th</str<strong>on</strong>g>e direct benefits from <str<strong>on</strong>g>th</str<strong>on</strong>g>e own acti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a focal individual will<br />

never exceed <str<strong>on</strong>g>th</str<strong>on</strong>g>eir direct costs. Never<str<strong>on</strong>g>th</str<strong>on</strong>g>eless cooperati<strong>on</strong> can evolve, because <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

benefits to own kin.<br />

It is obvious <str<strong>on</strong>g>th</str<strong>on</strong>g>at dispersal affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cooperati<strong>on</strong>: for low dispersal<br />

rates relatedness is high, and cooperati<strong>on</strong> can evolve. Increasing <str<strong>on</strong>g>th</str<strong>on</strong>g>e dispersal rate<br />

is expected to decrease relatedness, and <str<strong>on</strong>g>th</str<strong>on</strong>g>us make cooperati<strong>on</strong> less favorable. This<br />

is, however, not always <str<strong>on</strong>g>th</str<strong>on</strong>g>e case, and even evoluti<strong>on</strong>ary suicide can be observed<br />

[4]. Cooperati<strong>on</strong> will also affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal: a highly cooperating<br />

individual is expected to disperse less <str<strong>on</strong>g>th</str<strong>on</strong>g>an an individual, which cooperates <strong>on</strong>ly<br />

little or not at all. These effects give motivati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint evoluti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal and cooperati<strong>on</strong> using <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> adaptive dynamics [1]. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

talk I will present various evoluti<strong>on</strong>ary outcomes possible in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, including<br />

evoluti<strong>on</strong>ary branching and evoluti<strong>on</strong>ary suicide. I will also discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

essential parameters.<br />

References.<br />

[1] Geritz, S. A. H., É. Kisdi, G. Meszéna, and J. A. J. Metz. Evoluti<strong>on</strong>arily singular strategies<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptive grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and branching <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary tree. Evol. Ecol. 12, 35–57, 1998.<br />

[2] J. A. J. Metz and M. Gyllenberg. How should we define fitness in structured metapopulati<strong>on</strong><br />

models? Including an applicati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e calculati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ES dispersal strategies. Proc. Royal<br />

Soc. L<strong>on</strong>d<strong>on</strong> B, 268:499–508, 2001.<br />

[3] K. Parvinen, U. Dieckmann, M. Gyllenberg, and J. A. J. Metz. Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal in<br />

metapopulati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> local density dependence and demographic stochasticity. J. Evol. Biol,<br />

16:143–153, 2003.<br />

[4] K. Parvinen. Adaptive dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> altruistic cooperati<strong>on</strong> in a metapopulati<strong>on</strong>: Evoluti<strong>on</strong>ary<br />

emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> cooperators and defectors or evoluti<strong>on</strong>ary suicide? Bull. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol., in press<br />

DOI: 10.1007/s11538-011-9638-4<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Virginia Pasour<br />

US Army Research Office<br />

e-mail: virginia.pasour@us.army.mil<br />

Laura Miller<br />

UNC - Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

Steve Ellner<br />

Cornell - EEB<br />

Ecosystems Dynamics; Tuesday, June 28, 14:30<br />

Influence <str<strong>on</strong>g>of</str<strong>on</strong>g> Macrophytes <strong>on</strong> Biological Residence Time in a<br />

Flow-Through System<br />

While plankt<strong>on</strong> have <str<strong>on</strong>g>of</str<strong>on</strong>g>ten been <str<strong>on</strong>g>th</str<strong>on</strong>g>ought to behave as passive tracers, completely at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e mercy <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hydrodynamic flow, <str<strong>on</strong>g>th</str<strong>on</strong>g>e comm<strong>on</strong>ness <str<strong>on</strong>g>of</str<strong>on</strong>g> plankt<strong>on</strong> patches, as well<br />

as field studies showing evidence <str<strong>on</strong>g>of</str<strong>on</strong>g> microorganism movement against <str<strong>on</strong>g>th</str<strong>on</strong>g>e bulk (or<br />

mean) flow, suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at individual plankt<strong>on</strong> behavior such as vertical/horiz<strong>on</strong>tal<br />

migrati<strong>on</strong> may dominate at smaller scales. In natural water bodies such as embayments<br />

and estuaries, macrophytes can have a significant and complex effect <strong>on</strong><br />

water flow and can greatly complicate physical/biological interacti<strong>on</strong>s. Using a<br />

two-dimensi<strong>on</strong>al hydrodynamic model to create flows in an idealized channel wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

macrophytes modeled as a porous layer, we first model <str<strong>on</strong>g>th</str<strong>on</strong>g>e channel under a number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> different macrophyte regimes, varying <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> patches and height and<br />

density <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e macrophytes. We next model plankt<strong>on</strong> behavior under <str<strong>on</strong>g>th</str<strong>on</strong>g>ese different<br />

flow regimes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an individual-based model and explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e extent to which<br />

vertical migrati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> macrophytes affects plankt<strong>on</strong> trajectories. In<br />

particular, we are interested in studying how <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> plankt<strong>on</strong> migrati<strong>on</strong><br />

behaviors and macrophyte structures affect biological retenti<strong>on</strong> and whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er a set<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> migrati<strong>on</strong> regimes exists for a given hydrodynamic forcing <str<strong>on</strong>g>th</str<strong>on</strong>g>at will allow <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

plankt<strong>on</strong> to stay wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e study system (avoid washout) ’forever.’<br />

758

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling I; Tuesday, June 28, 17:00<br />

Pawel Paszek<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Liverpool<br />

e-mail: paszek@liv.ac.uk<br />

Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. Michael White<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Manchester<br />

Oscillati<strong>on</strong>s and feedback regulati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e NF-B signalling<br />

Time-lapse cell imaging showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at in resp<strong>on</strong>se to Tumour Necrosis Factor alpha<br />

(TNF) Nuclear Factor kappa B (NF-B) transcripti<strong>on</strong> factor oscillates between <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cytoplasm and nucleus (Nels<strong>on</strong> et al., (2004) Science 306: 704). Treatment wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

repeat pulses <str<strong>on</strong>g>of</str<strong>on</strong>g> TNF at different intervals enabled frequency-dependent encoding<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> target gene expressi<strong>on</strong> (Ashall et al., (2009) Science 324: 242). Development <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a highly c<strong>on</strong>strained ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>at cellular variati<strong>on</strong> in NF-B<br />

dynamics arises from a dual-delayed negative feedback motif (involving stochastic<br />

transcripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> IB and IB). We suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is feedback motif enables NF-B<br />

signalling to generate robust single cell oscillati<strong>on</strong>s by reducing sensitivity to key<br />

parameter perturbati<strong>on</strong>s. Enhanced cell heterogeneity may represent a mechanism<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trols <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall coordinati<strong>on</strong> and stability <str<strong>on</strong>g>of</str<strong>on</strong>g> cell populati<strong>on</strong> resp<strong>on</strong>ses by<br />

decreasing temporal fluctuati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> paracrine signalling (Paszek et al., (2010) PNAS<br />

107: 11644). We have also shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell to cell heterogeneity is pr<str<strong>on</strong>g>of</str<strong>on</strong>g>oundly<br />

increased following low-dose stimulati<strong>on</strong>. Low doses <str<strong>on</strong>g>of</str<strong>on</strong>g> TNF resulted in stochastic<br />

delays in single cells, but <strong>on</strong>ce <str<strong>on</strong>g>th</str<strong>on</strong>g>e first translocati<strong>on</strong> occurs <str<strong>on</strong>g>th</str<strong>on</strong>g>e typical 100 min<br />

period was maintained (Turner, et al., (2010) J. Cell Sci. 15: 2834). Our analyses<br />

dem<strong>on</strong>strate a fundamental role <str<strong>on</strong>g>of</str<strong>on</strong>g> oscillatory dynamics in c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> inflammatory<br />

signalling at different levels <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular organisati<strong>on</strong>.<br />

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Recent advances in infectious disease modelling I; Saturday, July 2, 11:00<br />

Kasia Pawelek<br />

Oakland University<br />

e-mail: kmarzec@oakland.edu<br />

Modeling wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-host dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> influenza virus infecti<strong>on</strong><br />

including kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> innate and adaptive immune resp<strong>on</strong>ses<br />

Despite vaccines and antiviral agents, influenza infecti<strong>on</strong> remains a major public<br />

heal<str<strong>on</strong>g>th</str<strong>on</strong>g> problem worldwide. It is <str<strong>on</strong>g>of</str<strong>on</strong>g> great importance to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological events<br />

underlying virus replicati<strong>on</strong> and host immune resp<strong>on</strong>se in order to develop more<br />

effective vaccines, treatments, and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er preventi<strong>on</strong> strategies. Here, we develop a<br />

new ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-host dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> influenza infecti<strong>on</strong>.<br />

By comparing modeling predicti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> interfer<strong>on</strong> and virus kinetic data, we<br />

examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative roles <str<strong>on</strong>g>of</str<strong>on</strong>g> target cell availability, innate and adaptive immune<br />

resp<strong>on</strong>se in c<strong>on</strong>trolling <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus. This work provides a detailed and quantitative<br />

understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological factors <str<strong>on</strong>g>th</str<strong>on</strong>g>at can explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e virus kinetics during a<br />

typical influenza infecti<strong>on</strong>.<br />

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling IV; Saturday, July 2, 08:30<br />

Jakub Pekalski 1 , Paweł Żuk 1 , Savas Tay 2 and Tomasz Lipniacki 3<br />

e-mail: jpek@ippt.gov.pl<br />

e-mail: pzuk@ippt.gov.pl<br />

e-mail: savas.tay@gmail.com<br />

e-mail: tlipnia@ippt.gov.pl<br />

1 University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, Poland<br />

2 ETH Zurich Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosystems Science and Engineering, Basel,<br />

Switzerland.<br />

3 Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research - Polish Academy<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warsaw, Poland<br />

Positive feedback in NF-κB signaling<br />

NF-κB is a key transcripti<strong>on</strong> factor c<strong>on</strong>trolling immune resp<strong>on</strong>ses, such as inflammati<strong>on</strong>,<br />

proliferati<strong>on</strong> and apoptosis. Its regulatory system is tightly c<strong>on</strong>trolled<br />

by several feedback loops. The two negative loops mediated by NF-κB inducible<br />

inhibitors, IκBα and A20, provide <str<strong>on</strong>g>th</str<strong>on</strong>g>e oscillatory resp<strong>on</strong>ses to <str<strong>on</strong>g>th</str<strong>on</strong>g>e t<strong>on</strong>ic TNFα<br />

stimulati<strong>on</strong>, in which NF-κB translocates in and out <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nucleus wi<str<strong>on</strong>g>th</str<strong>on</strong>g> period <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

about 100 min. These oscillati<strong>on</strong>s maintain NF-κB phosphorylati<strong>on</strong>, and are indispensable<br />

for NF-κB dependent signalling. Here, we explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e feedback<br />

loop mediated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e NF-κB inducible cytokine TNFα, which is secreted by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

activated cells and can bind TNFα membrane receptors <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e neighboring cells,<br />

or <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same cell <str<strong>on</strong>g>th</str<strong>on</strong>g>at give rise to <str<strong>on</strong>g>th</str<strong>on</strong>g>e positive feedback regulati<strong>on</strong>. This positive<br />

feedback is negligible in most <str<strong>on</strong>g>of</str<strong>on</strong>g> cell lines, but may become, as suggested by our<br />

study, dominant in immune cells like m<strong>on</strong>ocytes or macrophages <str<strong>on</strong>g>th</str<strong>on</strong>g>at have a high<br />

level <str<strong>on</strong>g>of</str<strong>on</strong>g> TNFα expressi<strong>on</strong>.<br />

The proposed stochastic model pursues our earlier studies [1-2], by including<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e positive feedback loop regulati<strong>on</strong>. The bifurcati<strong>on</strong> analysis performed for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

deterministic approximati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic model, revealed <str<strong>on</strong>g>th</str<strong>on</strong>g>at for a broad range<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bifurcati<strong>on</strong> parameter (rate <str<strong>on</strong>g>of</str<strong>on</strong>g> TNFα syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis) <str<strong>on</strong>g>th</str<strong>on</strong>g>e limit cycle and stable<br />

steady state coexist. As a result single cells stochastic trajectories may jump between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese two attractors. Such jumps corresp<strong>on</strong>d to <str<strong>on</strong>g>th</str<strong>on</strong>g>e sp<strong>on</strong>taneous activatory –<br />

inactivatory transiti<strong>on</strong>s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic model <str<strong>on</strong>g>th</str<strong>on</strong>g>e bifurcati<strong>on</strong> parameter c<strong>on</strong>trols<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong> and <str<strong>on</strong>g>of</str<strong>on</strong>g>f rates and <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>th</str<strong>on</strong>g>at cell is in <str<strong>on</strong>g>th</str<strong>on</strong>g>e oscillatory state. Interestingly,<br />

even in <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter range in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e limit cycle oscillati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

deterministic approximati<strong>on</strong> are not present, <str<strong>on</strong>g>th</str<strong>on</strong>g>e sp<strong>on</strong>taneous activati<strong>on</strong> probability<br />

is not zero. The model satisfactorily reproduces single cell kinetic <str<strong>on</strong>g>of</str<strong>on</strong>g> SK-N-AS<br />

cell [3], which exhibit sp<strong>on</strong>taneous activati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e absence <str<strong>on</strong>g>of</str<strong>on</strong>g> TNF stimulati<strong>on</strong>.<br />

This study was supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Polish Ministry <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Higher Educati<strong>on</strong><br />

grant N N501 132936 and Foundati<strong>on</strong> for Polish Science grant TEAM/2009-<br />

3/6.<br />

References.<br />

[1] Lipniacki, T., Puszynski, K., Paszek, P., Brasier, A.R., Kimmel, M., 2007. Single TNFα trimers<br />

mediating NF-κB activati<strong>on</strong>: Stochastic robustness <str<strong>on</strong>g>of</str<strong>on</strong>g> NF-κB signaling. BMC Bioinformatics<br />

8, 376.<br />

761

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[2] S. Tay, J. Hughey, T. Lee, T. Lipniacki, M. Covert, S. Quake., Single-cell NF-κB dynamics<br />

reveal digital activati<strong>on</strong> and analogue informati<strong>on</strong> processing Nature. 466 267-271.<br />

[3] Turner DA, Paszek P, Woodcock DJ, Nels<strong>on</strong> DE, Hort<strong>on</strong> CA, Wang Y, Spiller DG, Rand DA,<br />

White MR, Harper CV., Physiological levels <str<strong>on</strong>g>of</str<strong>on</strong>g> TNFα stimulati<strong>on</strong> induce stochastic dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> NF-κB resp<strong>on</strong>ses in single living cells J Cell Sci. 123 2834-43.<br />

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling V; Saturday, July 2, 11:00<br />

Zbigniew Peradzynski<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics<br />

and Mechanics, Banacha 2, 00-097 Warsaw, Poland<br />

and<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research, 02-106 Warsaw<br />

e-mail: zperadz@mimuw.edu.pl<br />

On mechanical effects accompanying and influencing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium.<br />

We discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e coupling between chemical and mechanical processes which are<br />

accompanying and influencing <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium in biological tissues. The<br />

tissue as a whole, similarly as a single cell, is treated as a visco-elastic medium.<br />

The diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium is enhanced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e autocatalytic release <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium, and<br />

modified by reacti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> diffusing buffers. In additi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical strain<br />

can also influence <str<strong>on</strong>g>th</str<strong>on</strong>g>e release <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytosolic calcium. As a result, <str<strong>on</strong>g>th</str<strong>on</strong>g>e waves <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

calcium c<strong>on</strong>centrati<strong>on</strong> can be excited by <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical as well as by <str<strong>on</strong>g>th</str<strong>on</strong>g>e chemical<br />

means. Developing certain asymptotic procedures wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>e viscosity <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e medium as well as wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to its size (a <str<strong>on</strong>g>th</str<strong>on</strong>g>in cylinder as a model <str<strong>on</strong>g>of</str<strong>on</strong>g> a cell and<br />

a <str<strong>on</strong>g>th</str<strong>on</strong>g>in layer <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue), and finally assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>e fast reacti<strong>on</strong> terms in equati<strong>on</strong>s for<br />

buffers, we reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e full system <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s to a single n<strong>on</strong>linear reacti<strong>on</strong> diffusi<strong>on</strong><br />

equati<strong>on</strong>. The dimensi<strong>on</strong>ality <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is equati<strong>on</strong> corresp<strong>on</strong>ds to <str<strong>on</strong>g>th</str<strong>on</strong>g>e dimensi<strong>on</strong>ality <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e problem (a single space variable for <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell, two space variables for a <str<strong>on</strong>g>th</str<strong>on</strong>g>in layer<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tissue, and <str<strong>on</strong>g>th</str<strong>on</strong>g>ree space variables in case <str<strong>on</strong>g>of</str<strong>on</strong>g> a bulk medium).<br />

This study was supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Polish Ministry <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Higher Educati<strong>on</strong><br />

grant N N501 132936.<br />

References.<br />

[1] B. Kazmierczak. Z. Peradzynski, Calcium waves wi<str<strong>on</strong>g>th</str<strong>on</strong>g> fast buffers and mechanical effects, J.<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. 62 (2011), 1-38.<br />

[2] Z. Peradzynski, Diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium in biological tissues and accompanying mechano-chemical<br />

effects, Arch. Mech., 62 (2010), Issue 6, 423-440.<br />

763

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Tuesday, June 28, 11:00<br />

Víctor M. Pérez-García<br />

Departamento de Matemáticas, E.T.S. de Ingenieros Industriales &<br />

IMACI-Instituto de Matemática Aplicada a la Ciencia y la Ingeniería,<br />

Universidad de Castilla-La Mancha, 13071, Ciudad Real, Spain<br />

e-mail: victor.perezgarcia@uclm.es<br />

J. Belm<strong>on</strong>te-Beitia, G. F. Calvo, D. Diego<br />

Departamento de Matemáticas, IMACI-Instituto de Matemática Aplicada<br />

a la Ciencia y la Ingeniería, Universidad de Castilla-La Mancha,<br />

13071, Ciudad Real, Spain<br />

Bright solit<strong>on</strong>s in malignant gliomas<br />

Malignant gliomas are <str<strong>on</strong>g>th</str<strong>on</strong>g>e most comm<strong>on</strong> and deadly brain tumors. Survival<br />

for patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> glioblastoma multiforme (GBM), <str<strong>on</strong>g>th</str<strong>on</strong>g>e most aggressive glioma, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough<br />

individually variable, is in <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> 10 m<strong>on</strong><str<strong>on</strong>g>th</str<strong>on</strong>g>s to 14 m<strong>on</strong><str<strong>on</strong>g>th</str<strong>on</strong>g>s after diagnosis,<br />

using standard treatments which include surgery, radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy, chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

(temozolamide and antiangiogenic drugs such as bevacizumab) [1]. GBM is a<br />

rapidly evolving astrocytoma <str<strong>on</strong>g>th</str<strong>on</strong>g>at is distinguished pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologically from lower grade<br />

gliomas by <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> necrosis and microvascular hyperplasia.<br />

Many ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models have been proposed to describe specific aspects <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

GBM cell lines in vitro [2,3] and <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in vivo even under <str<strong>on</strong>g>th</str<strong>on</strong>g>e acti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy [4-6]. Recently some applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models have been used<br />

to predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e survival <str<strong>on</strong>g>of</str<strong>on</strong>g> patients after surgical resecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> GBMs [7].<br />

Most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models in use for GBM are based <strong>on</strong> a simple<br />

reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong>: <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fischer equati<strong>on</strong> [8]. This equati<strong>on</strong> in <strong>on</strong>e spatial<br />

dimensi<strong>on</strong>s has travelling wave soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> kink type but has no travelling<br />

wave soluti<strong>on</strong>s in higher dimensi<strong>on</strong>s [9].<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is communicati<strong>on</strong> we will first describe two extensi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fischer equati<strong>on</strong>,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e first <strong>on</strong>e accounting for <str<strong>on</strong>g>th</str<strong>on</strong>g>e necrotic core and <str<strong>on</strong>g>th</str<strong>on</strong>g>e normal tissue and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

sec<strong>on</strong>d <strong>on</strong>e incorporating <str<strong>on</strong>g>th</str<strong>on</strong>g>e vasculature. We will <str<strong>on</strong>g>th</str<strong>on</strong>g>en show how bright tumor<br />

solit<strong>on</strong>s arise sp<strong>on</strong>taneously separating a kink <str<strong>on</strong>g>of</str<strong>on</strong>g> normal tissue from a kink <str<strong>on</strong>g>of</str<strong>on</strong>g> growing<br />

necrotic tissue. We will relate <str<strong>on</strong>g>th</str<strong>on</strong>g>e solit<strong>on</strong> parameters (corresp<strong>on</strong>ding to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

active tumor area) to <str<strong>on</strong>g>th</str<strong>on</strong>g>e clinically relevant parameters. The effect <str<strong>on</strong>g>of</str<strong>on</strong>g> surgical resecti<strong>on</strong><br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>linear dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system will be discussed. In our analysis<br />

we will resort to different tools <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear waves: time-dependent<br />

variati<strong>on</strong>al me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods [10], moment me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods [11], Lie group <str<strong>on</strong>g>th</str<strong>on</strong>g>eory me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods [12],<br />

similarity transformati<strong>on</strong>s [13], and numerical simulati<strong>on</strong>s. We will also discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

existence <str<strong>on</strong>g>of</str<strong>on</strong>g> multidimensi<strong>on</strong>al travelling waves employing analytical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods and<br />

advanced numerical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods incorporating <str<strong>on</strong>g>th</str<strong>on</strong>g>e system’s geometry [14].<br />

References.<br />

[1] E. G. Van Meir, C. G. Hadjipanayis, A. D. Norden, H.-K. Shu, P. Y. Wen, and J. J. Ols<strong>on</strong>,<br />

Exciting New Advances in Neuro-Oncology: The Avenue to a Cure for Malignant Glioma,<br />

CA Cancer J. Clin. 60 166-193 (2010).<br />

[2] E. Khain and L. M. Sander, Dynamics and Pattern Formati<strong>on</strong>s in Invasive Tumor Grow<str<strong>on</strong>g>th</str<strong>on</strong>g>,<br />

Physical Review Letters, 96, 188103 (2006).<br />

[3] K. Swans<strong>on</strong>, Quantifying glioma cell grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and invasi<strong>on</strong> in vitro, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Computer<br />

Modelling 47 638-648 (2008).<br />

764

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[4] P.-Y. B<strong>on</strong>diau, O. Clatz, M. Sermensant, P.-Y. Marcy, H. Delingette, M. Frenay, N. Ayache,<br />

Biocomputing: numerical simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> glioblastoma grow<str<strong>on</strong>g>th</str<strong>on</strong>g> using diffusi<strong>on</strong> tensor imaging,<br />

Physics in Medicine and Biology 53 879-893 (2008).<br />

[5] E. K<strong>on</strong>ukoglu, O. Clatz, P.-Y. B<strong>on</strong>diau, H. Delingette, N. Ayache, Medical Image Analysis 14<br />

111-125 (2010).<br />

[6] R. Rockne, J. Rockhill, M. Mrugala, A. M. Spence, I. Kalet, K. Hendricks<strong>on</strong>, A. Lai, T.<br />

Cloughesy, E. C. Alvord, K. R. Swans<strong>on</strong>, Predicting <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficacy <str<strong>on</strong>g>of</str<strong>on</strong>g> radio<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy in individual<br />

glioblastoma patients in vivo: a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling approach, Physics in Medicine and<br />

Biology 55 3271-3285 (2010).<br />

[7] K.R. Swans<strong>on</strong>, R.C. Rostomily and E.C. Alvord Jr, A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling tool for predicting<br />

survival <str<strong>on</strong>g>of</str<strong>on</strong>g> individual patients following resecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> glioblastoma: a pro<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> principle,<br />

British Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Cancer 98 113-119 (2008).<br />

[8] J. D . Murray, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical biology, Springer, Third Editi<strong>on</strong> (2007).<br />

[9] P. V. Brazhnik, J. J. Tys<strong>on</strong>, On travelling wave soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Fischers equati<strong>on</strong> in two spatial<br />

dimensi<strong>on</strong>s, SIAM J. <strong>on</strong> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics 60 371 (2000).<br />

[10] B. A. Malomed, Variati<strong>on</strong>al me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in n<strong>on</strong>linear fiber optics and related fields, Progress in<br />

Optics 43 71-193 (2002).<br />

[11] Víctor M. Pérez-García, P. J. Torres, G. D. M<strong>on</strong>tesinos, The me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g> moments for n<strong>on</strong>linear<br />

Schrödinger equati<strong>on</strong>s: Theory and Applicati<strong>on</strong>s, SIAM J. Appl. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. 67 990-1015 (2007).<br />

[12] J. Belm<strong>on</strong>te-Beitia, Víctor M. Pérez-García, V. Vekslerchik, P. Torres, Lie symmetries and<br />

solit<strong>on</strong>s in n<strong>on</strong>linear systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> spatially inhomogeneous n<strong>on</strong>linearities, Physical Review<br />

Letters 98 064102 (2007).<br />

[13] J. Belm<strong>on</strong>te-Beitia, Víctor M. Pérez-García, V. Vekslerchik, V. V. K<strong>on</strong>otop, Localized n<strong>on</strong>linear<br />

waves in systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> time- and space-modulated n<strong>on</strong>linearities, Physical Review Letters<br />

100 164102 (2008).<br />

[14] A. Bueno-Orovio, Víctor M. Pérez-García, F. H. Fent<strong>on</strong>, Spectral Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for Partial Differential<br />

Equati<strong>on</strong>s in Irregular Domains: The Spectral Smoo<str<strong>on</strong>g>th</str<strong>on</strong>g>ed Boundary Me<str<strong>on</strong>g>th</str<strong>on</strong>g>od, SIAM<br />

Journal <strong>on</strong> Scientific Computing 28 886 (2006).<br />

765

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modelling bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms: from gene regulati<strong>on</strong> to large-scale structure and<br />

functi<strong>on</strong>; Wednesday, June 29, 17:00<br />

J. Pérez-Velázquez<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Biometry, Helmholtz Zentrum München<br />

e-mail: perez-velazquez@helmholtz-muenchen.de<br />

B. A. Hense<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Biometry, Helmholtz Zentrum München<br />

e-mail: burkhard.hense@helmholtz-muenchen.de<br />

C. Kuttler<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Science, Technical University Munich<br />

e-mail: kuttler@ma.tum.de<br />

J. Müller<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Science, Technical University Munich<br />

e-mail: johannes.mueller@mytum.de<br />

R. Schlicht<br />

Universität Greifswald, Institut für Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematik und Informatik<br />

e-mail: schlichtr@uni-greifswald.de<br />

G. Dulla<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Washingt<strong>on</strong>, Dept. Civil and Envir<strong>on</strong>mental Engineering<br />

e-mail: gfjdulla@uw.edu<br />

Early stages <str<strong>on</strong>g>of</str<strong>on</strong>g> bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Pseudom<strong>on</strong>a syringae <strong>on</strong><br />

leaves surfaces<br />

Bacterial aggregates observed <strong>on</strong> leaf surfaces can be compared to bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilms in<br />

aquatic and medical envir<strong>on</strong>ments due to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir nutrient heterogeneity, and c<strong>on</strong>stantly<br />

changing water c<strong>on</strong>diti<strong>on</strong>s. Bacteria <strong>on</strong> leaves surface are found forming<br />

aggregates <str<strong>on</strong>g>of</str<strong>on</strong>g> a wide range <str<strong>on</strong>g>of</str<strong>on</strong>g> sizes. A localized high level <str<strong>on</strong>g>of</str<strong>on</strong>g> density <str<strong>on</strong>g>of</str<strong>on</strong>g> cells may<br />

foster genetic and metabolic exchange; fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore epiphytic survival <str<strong>on</strong>g>of</str<strong>on</strong>g> bacteria<br />

during desiccati<strong>on</strong> is likely enhanced when <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are aggregated. Aggregates may<br />

also locally facilitate coordinated bacterial populati<strong>on</strong> resp<strong>on</strong>ses for traits expressed<br />

in a density-dependent manner <str<strong>on</strong>g>th</str<strong>on</strong>g>rough quorum sensing. We developed a stochastic<br />

model to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e frequency, size, and spatial distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e gram-negative<br />

bacterium Pseudom<strong>on</strong>as syringae aggregates <strong>on</strong> bean leaf surfaces. Our model, a<br />

logistic bir<str<strong>on</strong>g>th</str<strong>on</strong>g>-dea<str<strong>on</strong>g>th</str<strong>on</strong>g> model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> migrati<strong>on</strong> (time-homogeneous Markov process), is<br />

able to elucidate two factors fostering aggregate formati<strong>on</strong>: migrati<strong>on</strong> and variability<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e leaf surface envir<strong>on</strong>ment. Our results successfully explain quantitative<br />

experimental data available. We discuss how to analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

numbers <str<strong>on</strong>g>of</str<strong>on</strong>g> aggregates <str<strong>on</strong>g>of</str<strong>on</strong>g> different sizes at a given time and explore how to account<br />

for new aggregates being created, <str<strong>on</strong>g>th</str<strong>on</strong>g>at is, <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e family size<br />

statistics c<strong>on</strong>diti<strong>on</strong>al <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e total number <str<strong>on</strong>g>of</str<strong>on</strong>g> aggregates. Through simulati<strong>on</strong>s we<br />

examine several migrati<strong>on</strong> regimes in order to find out how <str<strong>on</strong>g>th</str<strong>on</strong>g>is affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e aggregates<br />

size distributi<strong>on</strong>. We discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e ecological significance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e large aggregates<br />

formed <strong>on</strong> leaves as early stages <str<strong>on</strong>g>of</str<strong>on</strong>g> bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ilm formati<strong>on</strong>. Aggregati<strong>on</strong> formati<strong>on</strong> is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ought to be <str<strong>on</strong>g>th</str<strong>on</strong>g>e first step towards pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenic behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is bacterium; understanding<br />

aggregate size distributi<strong>on</strong> would prove useful to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e switch<br />

from epiphytic to pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenic behaviour.<br />

766

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

References.<br />

[1] Dulla, G., Lindow, S. E. Quorum size <str<strong>on</strong>g>of</str<strong>on</strong>g> Pseudom<strong>on</strong>as syringae is small and dictated by<br />

water availability <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e leaf surface. Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Nati<strong>on</strong>al Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences 105<br />

(8), 3082-3087, , 2008.<br />

[2] Dulla, G., Marco, M., Quin<strong>on</strong>es, B., Lindow, S. A Closer Look at Pseudom<strong>on</strong>as syringae as<br />

a Leaf Col<strong>on</strong>ist - The pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen P-syringae <str<strong>on</strong>g>th</str<strong>on</strong>g>rives <strong>on</strong> heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y plants by employing quorum<br />

sensing, virulence factors, and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er traits. ASM NEWS 71 (10), 469+, 2005<br />

767

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

From <strong>on</strong>e to many: Cell-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective, emergent behaviors<br />

in biology -II; Tuesday, June 28, 14:30<br />

Holger Perfahl<br />

Center Systems Biology, University Stuttgart, Germany<br />

e-mail: holger.perfahl@ibvt.uni-stuttgart.de<br />

Helen M. Byrne<br />

Centre <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Medicine and Biology, School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, Nottingham, UK<br />

e-mail: helen.byrne@nottingham.ac.uk<br />

Tomás Alarcón<br />

Centre de Recerca Matemàtica, Campus de Bellaterra.Barcel<strong>on</strong>a,<br />

Spain<br />

e-mail: talarc<strong>on</strong>@crm.cat<br />

Alexei Lapin<br />

Center Systems Biology, University Stuttgart, Germany<br />

e-mail: lapin@ibvt.uni-stuttgart.de<br />

Philip K. Maini<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Institute, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford, Oxford, UK<br />

Oxford Centre for Integrative Systems Biology, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemistry,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford, Oxford, UK<br />

e-mail: maini@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ias Reuss<br />

Center Systems Biology, University Stuttgart, Germany<br />

e-mail: reuss@ibvt.uni-stuttgart.de<br />

Markus R. Owen<br />

Centre <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Medicine and Biology, School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, Nottingham, UK<br />

e-mail: markus.owen@nottingham.ac.uk<br />

Multiscale modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and<br />

angiogenesis<br />

A <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-dimensi<strong>on</strong>al multiscale model <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is presented. In<br />

our model, cells are modelled as individual entities (agent-based approach) each<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir own cell cycle and subcellular-signalling machinery. Nutrients are supplied<br />

by a dynamic vascular network, which is subject to remodelling and angiogenesis.<br />

The model is formulated <strong>on</strong> a regular grid <str<strong>on</strong>g>th</str<strong>on</strong>g>at subdivides <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> domain<br />

into lattice sites. Each lattice site can be occupied by several biological cells<br />

whose movement <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lattice is governed by reinforced random walks, and whose<br />

proliferati<strong>on</strong> is c<strong>on</strong>trolled by a subcellular cell cycle model. The vascular network<br />

c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> vessel segments c<strong>on</strong>necting adjacent nodes <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lattice, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> defined<br />

inflow and outflow nodes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> prescribed pressures. We also specify <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> haematocrit entering <str<strong>on</strong>g>th</str<strong>on</strong>g>e system <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e inlets. The vessel network evolves<br />

via sprouting <str<strong>on</strong>g>of</str<strong>on</strong>g> tip cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a probability <str<strong>on</strong>g>th</str<strong>on</strong>g>at increases wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e local VEGF<br />

c<strong>on</strong>centrati<strong>on</strong>, tip cell movement is described by a reinforced random walk, and<br />

new c<strong>on</strong>necti<strong>on</strong>s forming via anastomosis. In additi<strong>on</strong>, vessel segments wi<str<strong>on</strong>g>th</str<strong>on</strong>g> low<br />

768

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

wall shear stress may be pruned away. Elliptic reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen and VEGF are implemented <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same spatial lattice<br />

using finite difference approximati<strong>on</strong>s, and include source and sink terms based <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e locati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> vessels (which act as sources <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen and sinks <str<strong>on</strong>g>of</str<strong>on</strong>g> VEGF) and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

different cell types (e.g. cells act as sinks for oxygen and hypoxic cells as sources <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

VEGF).<br />

In our simulati<strong>on</strong>s we dem<strong>on</strong>strate how our model may be combined wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental<br />

data, to predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a vascular tumour<br />

toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> angiogenesis.<br />

769

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bridging <str<strong>on</strong>g>th</str<strong>on</strong>g>e Divide: Cancer Models in Clinical Practice; Thursday, June 30,<br />

11:30<br />

Holger Perfahl<br />

Center Systems Biology, University Stuttgart, Germany<br />

e-mail: holger.perfahl@ibvt.uni-stuttgart.de<br />

Helen M. Byrne<br />

Centre <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Medicine and Biology, School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, Nottingham, UK<br />

e-mail: helen.byrne@nottingham.ac.uk<br />

Tomás Alarcón<br />

Centre de Recerca Matemàtica, Campus de Bellaterra.Barcel<strong>on</strong>a,<br />

Spain<br />

e-mail: talarc<strong>on</strong>@crm.cat<br />

Philip K. Maini<br />

Centre for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Institute, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford, Oxford, UK<br />

Oxford Centre for Integrative Systems Biology, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemistry,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford, Oxford, UK<br />

e-mail: maini@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ias Reuss<br />

Center Systems Biology, University Stuttgart, Germany<br />

e-mail: reuss@ibvt.uni-stuttgart.de<br />

Markus R. Owen<br />

Centre <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Medicine and Biology, School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham, Nottingham, UK<br />

e-mail: markus.owen@nottingham.ac.uk<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e Spatio-Temporal Distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Drugs in<br />

Tumours<br />

The distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> drugs in tumours is studied in a multiscale modelling framework.<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular scale we analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>e random walk <str<strong>on</strong>g>of</str<strong>on</strong>g> drug molecules <str<strong>on</strong>g>th</str<strong>on</strong>g>rough<br />

subsystems <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vascular network, from which molecules extravasate into <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

tissue, diffuse in <str<strong>on</strong>g>th</str<strong>on</strong>g>e interstitial space, bind to receptors <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e surfaces <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour<br />

cells and finally induce apoptosis. Knowledge gained <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular scale, like<br />

diffusi<strong>on</strong> coefficients and reacti<strong>on</strong> rates, is <str<strong>on</strong>g>th</str<strong>on</strong>g>en incorporated in a multiscale model<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> vascular tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and angiogenesis. The model combines blood flow,<br />

angiogenesis, vascular remodelling, interacti<strong>on</strong>s between normal and tumour cells<br />

and diffusive nutrient / VEGF transport as well as cell-cycle dynamics wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in each<br />

cell. To study <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model enables us to include a drug specific<br />

intracellular resp<strong>on</strong>se (modelled by ordinary differential equati<strong>on</strong>s) and link it to an<br />

extracellular drug c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at is described by reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong>s.<br />

Drugs are supplied by <str<strong>on</strong>g>th</str<strong>on</strong>g>e vascular system and adsorbed by normal and cancer cells,<br />

as well as decomposed by natural decay.<br />

The numerical simulati<strong>on</strong>s let us analyse how <str<strong>on</strong>g>th</str<strong>on</strong>g>e heterogeneity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour<br />

structure influences <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug distributi<strong>on</strong> and lead to predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic<br />

efficacy.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Valeriy Perminov<br />

"BioTeckFarm, Ltd"<br />

e-mail: vdperm@yandex.ru<br />

Epidemics; Thursday, June 30, 11:30<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>e reproducti<strong>on</strong> number in different infectious diseases<br />

models<br />

The classical Kermack-McKendrick homogeneous SIR (susceptible, infected and<br />

removed) model is well known. Its general soluti<strong>on</strong> is a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e unique<br />

parameter (<str<strong>on</strong>g>th</str<strong>on</strong>g>e reproducti<strong>on</strong> number) <str<strong>on</strong>g>th</str<strong>on</strong>g>at is equal to a mean number <str<strong>on</strong>g>of</str<strong>on</strong>g> sec<strong>on</strong>dary<br />

cases produced by a typical infected individual in a completely susceptible populati<strong>on</strong>.<br />

If <str<strong>on</strong>g>th</str<strong>on</strong>g>e reproducti<strong>on</strong> number is more <str<strong>on</strong>g>th</str<strong>on</strong>g>an <strong>on</strong>e (<str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold value) its value<br />

describes an epidemic level larger values corresp<strong>on</strong>d to str<strong>on</strong>ger epidemics. This<br />

model bases <strong>on</strong> two assumpti<strong>on</strong>s 1) all members <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> have <str<strong>on</strong>g>th</str<strong>on</strong>g>e equal<br />

probability to get infected and 2) mixing in <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> is uniform. It is clear<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese assumpti<strong>on</strong>s are n<strong>on</strong>realistic for any large human populati<strong>on</strong>. In<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e more complex compartment SIR models <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> is divided into several<br />

n<strong>on</strong>-overlapping groups. It allows us to partly remove assumpti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical<br />

model. Twenty years ago Diekmann et al 1 showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at for <str<strong>on</strong>g>th</str<strong>on</strong>g>is kind <str<strong>on</strong>g>of</str<strong>on</strong>g> models, just<br />

as for <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical model <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold parameter R0. Usually it is called<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e same name <str<strong>on</strong>g>th</str<strong>on</strong>g>e reproducti<strong>on</strong> number <str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e physical meaning <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

parameter has changed. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>is new parameter is a not unique measure <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

an epidemic severity (it will be proven during my talk). In particular it means <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

for such models comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e severity <str<strong>on</strong>g>of</str<strong>on</strong>g> two epidemics by simple comparing<br />

values <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir reproducti<strong>on</strong> numbers is incorrect. Since <str<strong>on</strong>g>th</str<strong>on</strong>g>e more realistic model<br />

has to c<strong>on</strong>tain much more parameters for more detailed descripti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong><br />

and epidemic itself, we can be sure <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e last c<strong>on</strong>clusi<strong>on</strong> is valid for <str<strong>on</strong>g>th</str<strong>on</strong>g>e real<br />

epidemics too. Individual-based models (IBMs) are more complex in comparis<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e compartment <strong>on</strong>es since <str<strong>on</strong>g>th</str<strong>on</strong>g>ey use overlapping groups (school children are<br />

members <str<strong>on</strong>g>of</str<strong>on</strong>g> a family also, for example). This peculiarity <str<strong>on</strong>g>of</str<strong>on</strong>g> IBMs makes Diekmanns<br />

calculati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reproducti<strong>on</strong> number inapplicable. Moreover <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is no<br />

usual ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical formulati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e IBMs (by differential equati<strong>on</strong>s, for example).<br />

It means <str<strong>on</strong>g>th</str<strong>on</strong>g>at we may not use analytic me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> research and <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore,<br />

an existence <str<strong>on</strong>g>of</str<strong>on</strong>g> any similarity parameter in <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> (for example, a <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold<br />

c<strong>on</strong>diti<strong>on</strong> or some analog <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reproducti<strong>on</strong> number) has to be proved numerically.<br />

Unfortunately, papers wi<str<strong>on</strong>g>th</str<strong>on</strong>g> misunderstandings <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e IBMs peculiarities c<strong>on</strong>tinue<br />

to appear.<br />

References.<br />

[1] Diekmann, O., J. A. P. Heesterbeek, J. A. J. Metz, 1990. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e definiti<strong>on</strong> and computati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproducti<strong>on</strong> ratio R0 in models for infectious diseases in heterogeneous populati<strong>on</strong>s.<br />

J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol., 28, pp.365-382.<br />

771

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting cell systems: from intercellular interacti<strong>on</strong><br />

to tissue-level traits II; Wednesday, June 29, 17:00<br />

Fernando Peruani<br />

Max Planck Institute for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Physics <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Systems, Nö<str<strong>on</strong>g>th</str<strong>on</strong>g>nitzer<br />

Str. 38, 01187 Dresden, Germany<br />

e-mail: peruani@pks.mpg.de<br />

Understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> bacteria<br />

The spatial self-organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> bacteria can be understood by <str<strong>on</strong>g>th</str<strong>on</strong>g>inking <str<strong>on</strong>g>of</str<strong>on</strong>g> bacteria<br />

as self-propelled rods <str<strong>on</strong>g>th</str<strong>on</strong>g>at interact by pushing each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er. Despite <str<strong>on</strong>g>th</str<strong>on</strong>g>e simplicity <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e model, it is possible to show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two ingredients, selfpropulsi<strong>on</strong><br />

and volume exclusi<strong>on</strong>, is enough to reproduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e phenomena observed<br />

in experiments: collective moti<strong>on</strong>, clustering, and aggregati<strong>on</strong>. Interestingly, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> self-propulsi<strong>on</strong> and volume exclusi<strong>on</strong> can induced a surprisingly<br />

rich variety <str<strong>on</strong>g>of</str<strong>on</strong>g> self-organized patterns which is not limited to <str<strong>on</strong>g>th</str<strong>on</strong>g>e above menti<strong>on</strong>ed<br />

patterns. As a pro<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> principles, it will be shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at when volume exclusi<strong>on</strong><br />

induces stagnati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells, a new phenomenology driven by <str<strong>on</strong>g>th</str<strong>on</strong>g>e jamming <str<strong>on</strong>g>of</str<strong>on</strong>g> cells<br />

emerges.<br />

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Heart rate dynamics: models and measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity (part II);<br />

Wednesday, June 29, 17:00<br />

M<strong>on</strong>ika Petelczyc<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, Warsaw University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Warsaw, Poland<br />

e-mail: petelczyc_m@if.pw.edu.pl<br />

Jan Jacek Żebrowski<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, Warsaw University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Warsaw, Poland<br />

e-mail: zebra@if.pw.edu.pl<br />

Rafał Baranowski<br />

Nati<strong>on</strong>al Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Cardiology, Warsaw, Poland<br />

e-mail: rbaranowski@ikard.pl<br />

Correlati<strong>on</strong> in human heart rate variability from a stochastic<br />

model<br />

The extracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Kramers-Moyal coefficients [1] from measurement data was applied<br />

to human heart rate variability. The expansi<strong>on</strong> truncated at <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d element<br />

is known as <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fokker-Planck equati<strong>on</strong>. The Langevin equati<strong>on</strong> is equivalent<br />

to a model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system dynamics c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> two parts: a deterministic <strong>on</strong>e<br />

and a stochastic term. The necessary assumpti<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e noise term be due to<br />

δ-correlated noise [2,3]. For heart rate variability, we found <str<strong>on</strong>g>th</str<strong>on</strong>g>at such a descripti<strong>on</strong><br />

is valid <strong>on</strong>ly for daytime recordings <str<strong>on</strong>g>of</str<strong>on</strong>g> heart rate variability. Nighttime heart<br />

rate variability is characterised by n<strong>on</strong>-negligible higher order Kramers-Moyal coefficients<br />

[4]. This effect can be explained by <str<strong>on</strong>g>th</str<strong>on</strong>g>e correlati<strong>on</strong> properties <str<strong>on</strong>g>of</str<strong>on</strong>g> heart rate<br />

variability. Correlati<strong>on</strong>s may be related to bo<str<strong>on</strong>g>th</str<strong>on</strong>g> deterministic and stochastic comp<strong>on</strong>ents<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart rate. Using Kramers-Moyal expansi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e drift (deterministic)<br />

and diffusi<strong>on</strong> (stochastic) terms are calculated. Deterministic term coresp<strong>on</strong>ds to<br />

regulatory processes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiorespiratory coupling. The stochastic <strong>on</strong>e is a measure<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e noise amplitude.<br />

We will present <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> shortterm correlati<strong>on</strong>s. Especially a particular,<br />

asymmetric form <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> coefficient <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart rate<br />

will be discussed. This is a measure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system to leng<str<strong>on</strong>g>th</str<strong>on</strong>g>en and<br />

shorten <str<strong>on</strong>g>th</str<strong>on</strong>g>e RR intervals [5]. Moreover, for different recordings we obtained a different<br />

ranges and shapes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e slow-varing diffusi<strong>on</strong> term as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart<br />

rate close to its minimum. This property can be related to arrhytmic RR intervals.<br />

To ilustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>is, several recordings from patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> hypertrophic cardiomyopa<str<strong>on</strong>g>th</str<strong>on</strong>g>y<br />

will be compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g> time series from heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y men.<br />

We will also focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurence <str<strong>on</strong>g>of</str<strong>on</strong>g> higher order Kramers-Moyal coefficients and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir meaning in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> correlati<strong>on</strong>s [4]. We will discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e variability <str<strong>on</strong>g>of</str<strong>on</strong>g> heart<br />

rate (mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> increasing and <str<strong>on</strong>g>of</str<strong>on</strong>g> decreasing <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart rate ) including <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

effect <str<strong>on</strong>g>of</str<strong>on</strong>g> recorded pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e obtained Kramers-Moyal expansi<strong>on</strong>.<br />

References.<br />

[1] H. Risken The Fokker–Planck Equati<strong>on</strong> Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> Soluti<strong>on</strong>s and Applicati<strong>on</strong>s (Springer<br />

Series in Synergetics) (Berlin: Springer) (1989)<br />

[2] F. Ghasemi, M. Sahimi, J. Peinke and M. Reza Rahimi Tabar, J. <str<strong>on</strong>g>of</str<strong>on</strong>g> Biol. Phys. 32, 117 (2006)<br />

[3] T. Kuusela, Phys. Rev E 69, 031916 (2004)<br />

[4] M. Petelczyc, J. J. Żebrowski, R. Baranowski Phys. Rev. E 80, 031127 (2009)<br />

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[5] M. Petelczyc, J. J. Żebrowski, R. Baranowski and L. Chojnowska Physiol. Meas. 31, 1635<br />

(2010)<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Aleksandra Pfeifer<br />

Maria Sklodowska-Curie Memorial Cancer Center and Institute <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Oncology, Gliwice Branch; Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Poland<br />

e-mail: apfeifer@io.gliwice.pl<br />

Małgorzata Oczko-Wojciechowska<br />

Maria Sklodowska-Curie Memorial Cancer Center and Institute <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Oncology, Gliwice Branch, Poland<br />

Michał Świerniak<br />

Maria Sklodowska-Curie Memorial Cancer Center and Institute <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Oncology, Gliwice Branch; Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Poland<br />

Michał Jarząb<br />

Maria Sklodowska-Curie Memorial Cancer Center and Institute <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Oncology, Gliwice Branch, Poland<br />

Barbara Jarząb<br />

Maria Sklodowska-Curie Memorial Cancer Center and Institute <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Oncology, Gliwice Branch, Poland<br />

Sources <str<strong>on</strong>g>of</str<strong>on</strong>g> variability in <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene expressi<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

follicular <str<strong>on</strong>g>th</str<strong>on</strong>g>yroid tumours: SVD analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> microarray data<br />

Many attempts have been performed by microarray gene expressi<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iling <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>yroid follicular tumours in order to find genes <str<strong>on</strong>g>th</str<strong>on</strong>g>at distinguish adenomas and<br />

carcinomas. The two types <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>yroid follicular tumours: adenomas (benign) and<br />

carcinomas (malignant) are indistinguishable before surgical procedure by classical<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology. A hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at gene expressi<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iling by microarray test may aid<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e diagnosis has not been fully verified. The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> our study was to apply<br />

unsupervised me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong> analysis to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e main sources <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

variability in follicular tumors which may influence <str<strong>on</strong>g>th</str<strong>on</strong>g>e feasibility <str<strong>on</strong>g>of</str<strong>on</strong>g> genetic testing<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>is disease. We performed microarray gene expressi<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iling in 45 follicular<br />

tumours by Affymetrix hgu133plus2 microarray. We performed Singular Value Decompositi<strong>on</strong><br />

(SVD) analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole dataset to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e supergenes (modes)<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at characterise <str<strong>on</strong>g>th</str<strong>on</strong>g>e main sources <str<strong>on</strong>g>of</str<strong>on</strong>g> variati<strong>on</strong> and are more representative/stable<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>an single transcripts. Next we analysed <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological meaning <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e variability<br />

related to each supergene. We selected genes <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>tribute most to each <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e supergenes and analysed <str<strong>on</strong>g>th</str<strong>on</strong>g>em wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different biological mining me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: gene<br />

<strong>on</strong>tology analysis, gene groups analysis and hierarchical clustering <str<strong>on</strong>g>of</str<strong>on</strong>g> samples. We<br />

revealed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e main sources <str<strong>on</strong>g>of</str<strong>on</strong>g> variance in <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysed dataset are related to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e immune resp<strong>on</strong>se (1st, 3rd and 6<str<strong>on</strong>g>th</str<strong>on</strong>g> supergenes), cell proliferati<strong>on</strong> (2nd and<br />

5<str<strong>on</strong>g>th</str<strong>on</strong>g> supergenes) and differentiati<strong>on</strong> (2nd supergene). Am<strong>on</strong>g genes <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>tribute<br />

most to <str<strong>on</strong>g>th</str<strong>on</strong>g>e 1st, 3rd and 4<str<strong>on</strong>g>th</str<strong>on</strong>g> supergene, many are related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e difference between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>yroid carcinoma and normal <str<strong>on</strong>g>th</str<strong>on</strong>g>yroid tissue. As in <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis we noted certain<br />

arbitrary steps, we also performed SVD analysis <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e artificial microarray dataset<br />

to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese parameters <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e results. Comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> SVD to<br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>er unsupervised me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods will also be presented.<br />

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Plants, grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and transport processes I; Tuesday, June 28, 11:00<br />

Roland Pieruschka<br />

Forschungszentrum Jülch<br />

e-mail: r.pieruschka@fz-juelich.de<br />

The interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> leaves wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment<br />

Plant leaves are highly specialized organs to facilitate gas exchange, carb<strong>on</strong> uptake<br />

and water loss usually up<strong>on</strong> illuminati<strong>on</strong>. Leaf internal structures have an enormous<br />

influence <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese processes. For example, heterobaric leaves have bundle shea<str<strong>on</strong>g>th</str<strong>on</strong>g>s<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> extensi<strong>on</strong>s which reach from <str<strong>on</strong>g>th</str<strong>on</strong>g>e upper to <str<strong>on</strong>g>th</str<strong>on</strong>g>e lower epidermis and create<br />

closed compartments. Homobaric leaves, <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand lack <str<strong>on</strong>g>th</str<strong>on</strong>g>ese extensi<strong>on</strong>s<br />

and have large interc<strong>on</strong>nected intercellular spaces so <str<strong>on</strong>g>th</str<strong>on</strong>g>at lateral diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> CO2<br />

can substantially support photosyn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis in particular, when <strong>on</strong>e part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e leaf is<br />

shaded being a CO2 source while <str<strong>on</strong>g>th</str<strong>on</strong>g>e adjacent leaf area is illuminated and a CO2<br />

sink. Light envir<strong>on</strong>ment also plays a key role for a range <str<strong>on</strong>g>of</str<strong>on</strong>g> plant processes. A light<br />

beam interacting wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a leaf penetrates <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidermis wi<str<strong>on</strong>g>th</str<strong>on</strong>g> little interacti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

largest part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e energy is absorbed by<str<strong>on</strong>g>th</str<strong>on</strong>g>e pigments in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mesophyll cells driving<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g>f water vapor which in turn affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidermis wi<str<strong>on</strong>g>th</str<strong>on</strong>g> stomata. This interacti<strong>on</strong><br />

feeds back <strong>on</strong> stomata and provides a c<strong>on</strong>trol mechanism for <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

stomata wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment. These processes aim at a mechanistic descripti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> plants wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment. Comprehensive understanding<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> plant interacti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment for a predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> plant performance<br />

requires a measurement <str<strong>on</strong>g>of</str<strong>on</strong>g> phenotyping variati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a range <str<strong>on</strong>g>of</str<strong>on</strong>g> genotypes. This<br />

approach called plant phenotyping is a rapidly evolving c<strong>on</strong>cept <str<strong>on</strong>g>th</str<strong>on</strong>g>at links genomics<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> ecophysiology and agr<strong>on</strong>omy. The basis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>cept is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong>al<br />

plant body (phenotype) originates during plant grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and development from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

dynamic interacti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e plant genetic background and <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment in<br />

which <str<strong>on</strong>g>th</str<strong>on</strong>g>e plant develops.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Delay Differential Equati<strong>on</strong>s and Applicati<strong>on</strong>s II; Saturday, July 2, 08:30<br />

M<strong>on</strong>ika Piotrowska<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics and Mechanics<br />

e-mail: m<strong>on</strong>ika@mimuw.edu.pl<br />

Urszula Foryś<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics and Mechanics<br />

Gompertz model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> time delays<br />

We study <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> time delays <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical Gompertz<br />

model. First we c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <strong>on</strong>e discrete delay introduced in two<br />

different ways and next <str<strong>on</strong>g>th</str<strong>on</strong>g>e models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two delays. We present <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic properties<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> investigated models including <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymptotic behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

examinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Hopf bifurcati<strong>on</strong> occurrence and stability switches. We also show<br />

results for <str<strong>on</strong>g>th</str<strong>on</strong>g>e types <str<strong>on</strong>g>of</str<strong>on</strong>g> occurring bifurcati<strong>on</strong>s. The analytical results are illustrated<br />

and completed by numerical simulati<strong>on</strong>s.<br />

777

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Heart rate dynamics: models and measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity (part II);<br />

Wednesday, June 29, 17:00<br />

J. Piskorski<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Ziel<strong>on</strong>a Gora, Szafrana 4a, Ziel<strong>on</strong>a<br />

Gora, Poland<br />

e-mail: jaropis@zg.home.pl<br />

P. Guzik<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Cardiology - Intensive Therapy and Internal Diseases,<br />

Poznan University <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Sciences, Przybyszewskiego 49, Poznan,<br />

Poland<br />

e-mail: pguzik@ptkardio.pl<br />

Structure <str<strong>on</strong>g>of</str<strong>on</strong>g> heart rate asymmetry<br />

Heart rate asymmetry (HRA) is a physiological phenomen<strong>on</strong> reflecting <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

heart rate decelerati<strong>on</strong>s c<strong>on</strong>tribute more to short-term HRV <str<strong>on</strong>g>th</str<strong>on</strong>g>an accelerati<strong>on</strong>s, and<br />

accelerati<strong>on</strong>s c<strong>on</strong>tribute more to l<strong>on</strong>g-term and total HRV <str<strong>on</strong>g>th</str<strong>on</strong>g>an decelerati<strong>on</strong>s. These<br />

HRA me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are variance-based, and can be called macrostructural. Recently, a<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods based <strong>on</strong> a counting statistics which depends <strong>on</strong> fast- and slow- changing<br />

rate <str<strong>on</strong>g>of</str<strong>on</strong>g> microstructure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e RR intervals time series was defined. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is study we<br />

show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e related entropic parameters HAR (dependent <strong>on</strong> accelerati<strong>on</strong>s) and<br />

HDR (dependent <strong>on</strong> decelerati<strong>on</strong>s) are asymmetric. The nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is asymmetry<br />

is exactly <str<strong>on</strong>g>th</str<strong>on</strong>g>e same as wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e variance-based descriptors: it is unidirecti<strong>on</strong>al and<br />

c<strong>on</strong>sistent.<br />

Materials and me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: 24-hour Holter ECG recordings were obtained from<br />

50 heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y subjects, including 27 women. The microstructure related to decelerati<strong>on</strong>s<br />

and accelerati<strong>on</strong>s was calculated from <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting RR time series and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

HAR and HDR were computed. This was repeated for <str<strong>on</strong>g>th</str<strong>on</strong>g>e same recordings in<br />

shuffled order, for which <str<strong>on</strong>g>th</str<strong>on</strong>g>e shuffling distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> microstructure is known for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical c<strong>on</strong>siderati<strong>on</strong>s. The HAR and HDR were compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e t-test after<br />

establishing normal distributi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Shapiro-Wilk test. The presence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

asymmetry in <str<strong>on</strong>g>th</str<strong>on</strong>g>e studied group was established wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e binomial test.<br />

Results: The value <str<strong>on</strong>g>of</str<strong>on</strong>g> HAR was 1.08±0.021 and HDR 1.01±0.18. This difference<br />

is statistically significant wi<str<strong>on</strong>g>th</str<strong>on</strong>g> p<br />

HDR, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e binomial test for equality <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> proporti<strong>on</strong>s being equal gives<br />

a statistically significant result p

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biomechanical regulati<strong>on</strong> in b<strong>on</strong>e tissue (Sessi<strong>on</strong><br />

I); Wednesday, June 29, 08:30<br />

Peter Piv<strong>on</strong>ka, Stefan Scheiner, Pascal Buenzli, David W. Smi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Engineering, Computing, and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, The University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Western Australia, Australia<br />

e-mail: peter.piv<strong>on</strong>ka@uwa.edu.au<br />

Christian Hellmich<br />

Institute for Mechanics <str<strong>on</strong>g>of</str<strong>on</strong>g> Materials and Structures, Vienna University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Austria<br />

Lynda B<strong>on</strong>ewald<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Dentistry, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Missouri-Kansas City, USA<br />

A coupled systems biology-micromechanical model for<br />

mechanostat-type regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e remodeling<br />

The capacity <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e tissue to alter its mass and structure in resp<strong>on</strong>se to mechanical<br />

demands was recognized more <str<strong>on</strong>g>th</str<strong>on</strong>g>an a century ago and Frost formulated<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e so-called mechanostat <str<strong>on</strong>g>th</str<strong>on</strong>g>eory for capturing <str<strong>on</strong>g>th</str<strong>on</strong>g>is phenomen<strong>on</strong> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically.<br />

This <str<strong>on</strong>g>th</str<strong>on</strong>g>eory proposes <str<strong>on</strong>g>th</str<strong>on</strong>g>at b<strong>on</strong>e resp<strong>on</strong>ds to changes from a loading relating to an<br />

equilibrated b<strong>on</strong>e turnover by triggering ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er increased b<strong>on</strong>e resorpti<strong>on</strong> or formati<strong>on</strong><br />

as resp<strong>on</strong>se to decreased or increased loading. While <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>ceptual <str<strong>on</strong>g>th</str<strong>on</strong>g>eory<br />

is useful for a qualitative understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e tissue level resp<strong>on</strong>ses to mechanical<br />

loading no quantitative estimates <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e volume/mass changes can be made.<br />

Also incorporati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying cellular mechanisms is still outstanding. Over<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e last several years significant progress has been made to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells and<br />

signaling molecules involved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical adaptati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e. It is now well<br />

accepted <str<strong>on</strong>g>th</str<strong>on</strong>g>at osteocytes act as mechanosensory cells in b<strong>on</strong>e which express several<br />

signaling molecules able to trigger b<strong>on</strong>e adaptati<strong>on</strong> resp<strong>on</strong>ses. Here we present an<br />

extended b<strong>on</strong>e cell populati<strong>on</strong> model incorporating a simplified osteocyte-feedback<br />

to simulate b<strong>on</strong>e remodeling events corresp<strong>on</strong>ding to <str<strong>on</strong>g>th</str<strong>on</strong>g>e actual mechanical loading.<br />

The mechanical feedback to b<strong>on</strong>e biology is achieved by employing c<strong>on</strong>tinuum<br />

micromechanics-based homogenizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e stiffness, allowing for estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e deformati<strong>on</strong> osteocytes are subjected to. This me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology allows for m<strong>on</strong>itoring<br />

effects <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanical load changes <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e compositi<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>us <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

load-carrying capacity <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e. To <str<strong>on</strong>g>th</str<strong>on</strong>g>e au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors knowledge, <str<strong>on</strong>g>th</str<strong>on</strong>g>is is <str<strong>on</strong>g>th</str<strong>on</strong>g>e first model<br />

which incorporates <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanostat <str<strong>on</strong>g>th</str<strong>on</strong>g>eory based <strong>on</strong> cellular feedback mechanisms.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Tuesday, June 28, 11:00<br />

Mateusz M. Pluciński<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Envir<strong>on</strong>mental Science, Policy and Management, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> California, Berkeley. Berkeley, CA, 94720<br />

e-mail: mateusz@berkeley.edu<br />

Human social network structure is reflected in sequence data<br />

for commensal bacteria<br />

DNA sequence data has traditi<strong>on</strong>ally been used to infer transmissi<strong>on</strong> networks <strong>on</strong>ly<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics and outbreaks <str<strong>on</strong>g>of</str<strong>on</strong>g> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens, but it can analogously<br />

be applied to cases <str<strong>on</strong>g>of</str<strong>on</strong>g> ubiquitous commensal bacteria in order to infer informati<strong>on</strong><br />

about host c<strong>on</strong>tact networks. Here, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at multilocus DNA sequence data,<br />

based <strong>on</strong> multilocus sequence typing schemes (MLST), from isolates <str<strong>on</strong>g>of</str<strong>on</strong>g> commensal<br />

bacteria circulating in an endemic equilibrium can be used to infer bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

local and global properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tact networks <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong>s being sampled.<br />

Indeed, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at MLST data obtained from simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> spread <strong>on</strong> a<br />

small-world network can be used to robustly estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e small world parameter<br />

c<strong>on</strong>trolling <str<strong>on</strong>g>th</str<strong>on</strong>g>e degree <str<strong>on</strong>g>of</str<strong>on</strong>g> structure in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tact network. Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>e pairwise<br />

distances in <str<strong>on</strong>g>th</str<strong>on</strong>g>e network — degrees <str<strong>on</strong>g>of</str<strong>on</strong>g> separati<strong>on</strong> — correlate wi<str<strong>on</strong>g>th</str<strong>on</strong>g> genetic distances<br />

between isolates meaning <str<strong>on</strong>g>th</str<strong>on</strong>g>at how far apart two individuals in <str<strong>on</strong>g>th</str<strong>on</strong>g>e network are can<br />

be inferred from MLST analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir commensal bacteria. This result has important<br />

c<strong>on</strong>sequences, and we show an example from epidemiology — how <str<strong>on</strong>g>th</str<strong>on</strong>g>is result<br />

could be used to test for infectious origins <str<strong>on</strong>g>of</str<strong>on</strong>g> diseases <str<strong>on</strong>g>of</str<strong>on</strong>g> unknown etiology. We also<br />

extend our previous work to include <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> commensal bacteria<br />

<strong>on</strong> scale-free networks; in particular, we examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> highly c<strong>on</strong>nected<br />

individuals in determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> sequence types.<br />

780

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Heart rate dynamics: models and measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity (part II);<br />

Wednesday, June 29, 17:00<br />

Piotr Podziemski<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, Warsaw University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: podziemski@if.pw.edu.pl<br />

Jan J. Żebrowski<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, Warsaw University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: zebra@if.pw.edu.pl<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e human atrium using Liénard equati<strong>on</strong>s<br />

Liénard systems can be used for modeling oscillatory behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> many phenomena<br />

- starting from chemical reacti<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>rough neur<strong>on</strong> excitability [1], up to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

acti<strong>on</strong> potential in <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart muscle. The universality <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Liénard systems and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er well-established ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical knowledge about <str<strong>on</strong>g>th</str<strong>on</strong>g>em creates a flexible<br />

framework for designing simple models. Such models are very robust and computati<strong>on</strong>ally<br />

efficient. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trary, <str<strong>on</strong>g>th</str<strong>on</strong>g>e existing physiological i<strong>on</strong>ic channel models<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cardiac cells are too complex to allow an investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g time dynamical<br />

properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart. As a c<strong>on</strong>sequence, very rarely do <str<strong>on</strong>g>th</str<strong>on</strong>g>ey address <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> heart rate variability comparable wi<str<strong>on</strong>g>th</str<strong>on</strong>g> portable ECG recordings.<br />

We focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> human atria, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> acti<strong>on</strong> potential<br />

propagati<strong>on</strong> affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e sinus ry<str<strong>on</strong>g>th</str<strong>on</strong>g>m <str<strong>on</strong>g>th</str<strong>on</strong>g>e most. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e right<br />

atrium proposed here, we describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e various anatomical parts <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e atrium by<br />

means <str<strong>on</strong>g>of</str<strong>on</strong>g> different equati<strong>on</strong>s but all <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same class <str<strong>on</strong>g>of</str<strong>on</strong>g> Liénard equati<strong>on</strong>s. The<br />

two nodes - <str<strong>on</strong>g>th</str<strong>on</strong>g>e sinoatrial and <str<strong>on</strong>g>th</str<strong>on</strong>g>e atrioventricular node are modeled by diffusively<br />

coupled modified van der Pol-Duffing oscillators while <str<strong>on</strong>g>th</str<strong>on</strong>g>e atrial muscle tissue is<br />

currently represented by a diffusively coupled modified FitzHugh-Nagumo system.<br />

Models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sinoatrial and atrio-ventricular nodes were developed taking into<br />

account physiologically important properties such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase resp<strong>on</strong>se curve, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

refracti<strong>on</strong> period and <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold potential. Several modificati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e models presented<br />

in [2] allowed to achieve a more physiological behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model. The<br />

effect <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e aut<strong>on</strong>omous nervous system activity is incorporated into <str<strong>on</strong>g>th</str<strong>on</strong>g>e model in<br />

a simple way.<br />

We performed a series <str<strong>on</strong>g>of</str<strong>on</strong>g> simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e atrium, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> differing anatomical<br />

simplificati<strong>on</strong>s varying from a simple 1 dimensi<strong>on</strong>al chain <str<strong>on</strong>g>of</str<strong>on</strong>g> oscillators to a twodimensi<strong>on</strong>al<br />

mapping <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e atrium wi<str<strong>on</strong>g>th</str<strong>on</strong>g> chosen anatomical details included. The<br />

simulati<strong>on</strong>s allowed to rec<strong>on</strong>struct such effects as <str<strong>on</strong>g>th</str<strong>on</strong>g>e AV node reentry tachycardia<br />

- bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in an extended <strong>on</strong>e dimensi<strong>on</strong>al model and in <str<strong>on</strong>g>th</str<strong>on</strong>g>e 2D simulati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase<br />

relati<strong>on</strong>s between sinus rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>m and <str<strong>on</strong>g>th</str<strong>on</strong>g>e locati<strong>on</strong> and properties <str<strong>on</strong>g>of</str<strong>on</strong>g> an ectopic source<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir effects <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resultant rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>m.<br />

References.<br />

[1] D. Postnov, K. H. Seung, and K. Hyungtae, Synchr<strong>on</strong>izati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusively coupled oscillators<br />

near <str<strong>on</strong>g>th</str<strong>on</strong>g>e homoclinic bifurcati<strong>on</strong> Phys. Rev. E 60, 2799.2807 (1999).<br />

781

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[2] J.J. Żebrowski, P. Kuklik, T. Buchner. R. Baranowski, Assessment and clinical applicati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cardiovascular oscillati<strong>on</strong>s IEEE Eng. In Med. And Biol. Mag., Nov./Dec. 2009 .<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models in Eco-epidemiology I; Wednesday, June 29, 08:30<br />

J.-C. Poggiale<br />

Aix-Marseille University<br />

A spatially extended trophic chain model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> recycling :<br />

how spatial structure determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e matter cycle?<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, we study spatially extended trophic chain models. We focus <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> nutrient recycling <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e food chain dynamics. Top predators recycling<br />

is known to have some positive effects <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary producers and <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

importance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese effects can be compared to <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>th</str<strong>on</strong>g>at top predators have<br />

<strong>on</strong> primary producers by regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> herbivores. The role <str<strong>on</strong>g>of</str<strong>on</strong>g> recycling is here<br />

investigated by means <str<strong>on</strong>g>of</str<strong>on</strong>g> two models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different levels <str<strong>on</strong>g>of</str<strong>on</strong>g> details. Then <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

models are spatially extended to understand how <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial structure affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

trophic chain dynamics. The spatial scales are assumed to be small enough to<br />

allow individuals to move fast wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to local populati<strong>on</strong> dynamics. We aim<br />

to provide a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical formulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong>al resp<strong>on</strong>ses at <str<strong>on</strong>g>th</str<strong>on</strong>g>e global<br />

scale, which can be suggested as <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong>al resp<strong>on</strong>ses to use at larger scales.<br />

The global functi<strong>on</strong>al resp<strong>on</strong>ses integrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial effect and <str<strong>on</strong>g>th</str<strong>on</strong>g>e recycling effects.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Ondrej Pokora<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Science,<br />

Masaryk University, Kotlarska 2, 611 37 Brno, Czech Republic<br />

e-mail: pokora@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.muni.cz<br />

Petr Lansky<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physiology, Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Czech Republic,<br />

Videnska 1083, 142 20 Prague, Czech Republic<br />

e-mail: lansky@biomed.cas.cz<br />

Estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individual firing frequencies from superposed<br />

spike train<br />

When m<strong>on</strong>itoring neur<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> single extracellular electrode <str<strong>on</strong>g>th</str<strong>on</strong>g>e acti<strong>on</strong> potentials<br />

from different neur<strong>on</strong>s are comm<strong>on</strong>ly recorded. One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e problems is to<br />

identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e active neur<strong>on</strong>s. The analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pooled record <str<strong>on</strong>g>of</str<strong>on</strong>g> several independent<br />

spike trains wi<str<strong>on</strong>g>th</str<strong>on</strong>g> refractory period leads to identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> specific groups <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e spikes appearing in time intervals shorter <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e refractory period (<str<strong>on</strong>g>th</str<strong>on</strong>g>ese are<br />

usually called doublets, triplets, etc.). In (Meunier et al., 2003), <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem was<br />

solved for two independent spike trains and <str<strong>on</strong>g>th</str<strong>on</strong>g>e result is generalized for any number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> independent records here.<br />

How <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing frequencies <str<strong>on</strong>g>of</str<strong>on</strong>g> individual neur<strong>on</strong>s are related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative<br />

frequencies <str<strong>on</strong>g>of</str<strong>on</strong>g> occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> doublets, triplets, etc. in <str<strong>on</strong>g>th</str<strong>on</strong>g>e superposed spike train<br />

is shown. The closed form-relati<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>e respective firing frequencies and<br />

properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e superposed record are derived. A me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> respective<br />

firing frequencies <str<strong>on</strong>g>of</str<strong>on</strong>g> any number <str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>s, producing indistinguishable spikes,<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e superposed record, number <str<strong>on</strong>g>of</str<strong>on</strong>g> recorded neur<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

refractory period is presented. The task is similar to <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> coincidence<br />

detecti<strong>on</strong> (Grün et al., 1999; Krips & Furst, 2009).<br />

References.<br />

[1] Grün S., Diesmann. M., Gramm<strong>on</strong>t, F., Riehle, A., Aersten, A. (1999), Detecting unitary<br />

events wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out discretizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> time Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Neuroscience Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods 93 67–79.<br />

[2] Krips, R., Furst, M. (2009), Stochastic properties <str<strong>on</strong>g>of</str<strong>on</strong>g> coincidence-detector neural cells Neural<br />

Computati<strong>on</strong> 21 2524–2553.<br />

[3] Meunier, M., Mari<strong>on</strong>-Poll, F., Lansky, P., Rospars, J.-P. (2003), Estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e individual<br />

firing frequencies <str<strong>on</strong>g>of</str<strong>on</strong>g> two neur<strong>on</strong>s recorded wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a single electrode Chemical Senses 28 671–679.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Computati<strong>on</strong>al toxicology and pharmacology - in silico drug activity and<br />

safety assessment; Saturday, July 2, 11:00<br />

Sebastian Polak<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Pharmacy Jagiell<strong>on</strong>ian University Medical College<br />

e-mail: spolak@cm-uj.krakow.pl<br />

Barbara Wiśniowska<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Pharmacy Jagiell<strong>on</strong>ian University Medical College<br />

Systems Biology in drug development - cardiotoxicity<br />

predicti<strong>on</strong><br />

Cardiac liability testing <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e drugs candidates during development process has<br />

gained increased regulatory and public attenti<strong>on</strong> due to a growing awareness <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiac risks across a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> marketed products. Nowadays, cardiac safety<br />

assessment in pre-approval clinical trials is obligatory and possible failure at <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

late stage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e R&D pipeline has tremendous impact <strong>on</strong> pay-<str<strong>on</strong>g>of</str<strong>on</strong>g>f <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole process.<br />

Thus it is desirable to screen compounds as early as possible, before large<br />

amounts <str<strong>on</strong>g>of</str<strong>on</strong>g> time and m<strong>on</strong>ey have been spent. Traditi<strong>on</strong>al pre-clinical in vivo and<br />

ex vivo animal studies employed in risk assessment are criticised due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e e<str<strong>on</strong>g>th</str<strong>on</strong>g>ical<br />

and meritorious reas<strong>on</strong>s and in vitro cell lines based studies are currently effectively<br />

utilized. Results extrapolati<strong>on</strong> from <str<strong>on</strong>g>th</str<strong>on</strong>g>e in vitro tests to in vivo human risk<br />

became an issue and systems biology approach is proposed to derive appropriate<br />

c<strong>on</strong>clusi<strong>on</strong>s from in vitro lab observati<strong>on</strong>s. Developed system is hybrid in nature<br />

and combines ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e human left ventricle cardiomyocyte wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

in vitro assessed drug induced i<strong>on</strong>ic channels inhibiti<strong>on</strong>. The <str<strong>on</strong>g>th</str<strong>on</strong>g>ird main element is<br />

a virtual populati<strong>on</strong> generator. Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e data derived from available scientific<br />

literature dynamic database <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> was developed. Randomly chosen<br />

virtual individuals are described by physiological and genetic parameters, namely<br />

cardiomyocyte volume, sarcoplasmic reticulum volume, cell electric capacitance,<br />

potassium channels genetic polymorphism, which are used as simulati<strong>on</strong> parameters.<br />

Therefore <str<strong>on</strong>g>th</str<strong>on</strong>g>e system allows for <str<strong>on</strong>g>th</str<strong>on</strong>g>e inter-individual variability assessment<br />

which is a fundamental advantage comparing wi<str<strong>on</strong>g>th</str<strong>on</strong>g> animal in vivo and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er available<br />

muli-scale models. Combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> above-described approach wi<str<strong>on</strong>g>th</str<strong>on</strong>g> physiology<br />

based pharmacokinetic models (PBPK) used for plasma and tissues drug c<strong>on</strong>centrati<strong>on</strong><br />

changes predicti<strong>on</strong> can be used for c<strong>on</strong>centrati<strong>on</strong> dependent in vitro - in<br />

vivo extrapolati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiotoxic effect for new chemical entities.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

II; Tuesday, June 28, 14:30<br />

Jan Poleszczuk<br />

College <str<strong>on</strong>g>of</str<strong>on</strong>g> Inter-faculty Individual Studies in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Natural<br />

Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, Warsaw Poland<br />

e-mail: j.poleszczuk@mimuw.edu.pl<br />

Urszula Foryś<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics,<br />

Informatics and Mechanics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, Warsaw<br />

Poland<br />

e-mail: urszula@mimuw.edu.pl<br />

M<strong>on</strong>ika Joanna Piotrowska<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics,<br />

Informatics and Mechanics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, Warsaw<br />

Poland<br />

e-mail: m<strong>on</strong>ika@mimuw.edu.pl<br />

Optimal and suboptimal treatment protocols for<br />

anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

In 1971 Judah Folman discovered <str<strong>on</strong>g>th</str<strong>on</strong>g>at grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> any tumour is str<strong>on</strong>gly dependent<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount <str<strong>on</strong>g>of</str<strong>on</strong>g> blood vessels <str<strong>on</strong>g>th</str<strong>on</strong>g>at it induces to grow. He surmised <str<strong>on</strong>g>th</str<strong>on</strong>g>at, if a<br />

tumour could be stopped from growing its own blood supply, it would wi<str<strong>on</strong>g>th</str<strong>on</strong>g>er and<br />

die. Anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy is a novel treatment approach <str<strong>on</strong>g>th</str<strong>on</strong>g>at aims at preventing<br />

a tumour from developing its own blood supply system.<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e biologically validated model proposed by Hahnfeldt, Panigrahy,<br />

Folkman and Hlatky in 1999, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e usage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal c<strong>on</strong>trol <str<strong>on</strong>g>th</str<strong>on</strong>g>eory,<br />

some protocols <str<strong>on</strong>g>of</str<strong>on</strong>g> anti-angiogenic treatment were proposed. However, in our opini<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e formulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>at model is valid <strong>on</strong>ly for <str<strong>on</strong>g>th</str<strong>on</strong>g>e anti-vascular treatment, <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

is treatment <str<strong>on</strong>g>th</str<strong>on</strong>g>at is focused <strong>on</strong> destroying endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells. Therefore, we propose<br />

a modificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e original model which is valid in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment which<br />

is focused <strong>on</strong> blocking angiogenic signaling.<br />

We propose also a new ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e anti-angiogenic treatment<br />

goal. In current studies it is assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e main goal <str<strong>on</strong>g>of</str<strong>on</strong>g> anti-angiogenic<br />

treatment is to minimize <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor volume at <str<strong>on</strong>g>th</str<strong>on</strong>g>e end <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

hand, chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy is still <str<strong>on</strong>g>th</str<strong>on</strong>g>e main kind <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer treatment, while anti-angiogenic<br />

treatment is <strong>on</strong>ly a supplement. The efficient treatment wi<str<strong>on</strong>g>th</str<strong>on</strong>g> chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy is possible<br />

<strong>on</strong>ly when <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug can be distributed evenly, <str<strong>on</strong>g>th</str<strong>on</strong>g>at is when vessels penetrate<br />

most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour regi<strong>on</strong>s.<br />

Therefore, we assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e main goal <str<strong>on</strong>g>of</str<strong>on</strong>g> anti-angiogenic treatment, despite<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e minimizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour volume, is to maintain high ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> vessels volume<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at support <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour to <str<strong>on</strong>g>th</str<strong>on</strong>g>e actual tumour volume. We analyze it as an optimal<br />

c<strong>on</strong>trol problem and a soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem is given in some cases.<br />

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Developmental Biology; Friday, July 1, 14:30<br />

Andrey A. Polezhaev<br />

Maria Yu. Borina<br />

P. N. Lebedev Physical Institute, Moscow, Russia<br />

e-mail: apol@lpi.ru<br />

Mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> pattern formati<strong>on</strong> in biological systems<br />

caused by diffusi<strong>on</strong> instability<br />

Pattern formati<strong>on</strong> in living systems including morphogenesis is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most<br />

challenging problems <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical biology. Starting from early seventies a number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> models based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e idea <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e so-called Turing instability [1] were suggested (<strong>on</strong>e<br />

can find some examples in [2]). Turing instability is a type <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong> instability<br />

when <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e eigenvalues <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e linearized problem becomes positive in a certain<br />

n<strong>on</strong>-zero range <str<strong>on</strong>g>of</str<strong>on</strong>g> wave vectors. This instability may be resp<strong>on</strong>sible for stati<strong>on</strong>ary<br />

n<strong>on</strong>homogeneous pattern formati<strong>on</strong>.<br />

Ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er type <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong> instability is <str<strong>on</strong>g>th</str<strong>on</strong>g>e wave instability when a pair <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

complex c<strong>on</strong>jugate eigenvalues acquires a positive real part in a certain range <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

wave vectors. Wave instability may be resp<strong>on</strong>sible for a lot <str<strong>on</strong>g>of</str<strong>on</strong>g> spatial-temporal<br />

patterns observed bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in biological (for example, in bacterial col<strong>on</strong>ies) and in<br />

chemical systems (Belousov-Zhabotinsky reacti<strong>on</strong> in microemulsi<strong>on</strong> [3]). While<br />

Turing instability can arise in a two-variable reacti<strong>on</strong>-diffusi<strong>on</strong> model, not less <str<strong>on</strong>g>th</str<strong>on</strong>g>an<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ree equati<strong>on</strong>s are necessary for <str<strong>on</strong>g>th</str<strong>on</strong>g>e wave instability.<br />

We obtain <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s for bo<str<strong>on</strong>g>th</str<strong>on</strong>g> Turing and wave instabilities in a <str<strong>on</strong>g>th</str<strong>on</strong>g>reevariable<br />

reacti<strong>on</strong> diffusi<strong>on</strong> model which follow from linear analysis and formulate<br />

qualitative properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system for each <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e instabilities to occur. While for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Turing bifurcati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system should possess an autocatalytic variable which has<br />

a sufficiently small diffusi<strong>on</strong> coefficient compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers (it coincides<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>is bifurcati<strong>on</strong> in a two-variable model), <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e wave bifurcati<strong>on</strong> are somewhat different. Autocatalysis is necessary but not<br />

sufficient. Namely, <str<strong>on</strong>g>th</str<strong>on</strong>g>e sum <str<strong>on</strong>g>of</str<strong>on</strong>g> two terms <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e main diag<strong>on</strong>al <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e linearizati<strong>on</strong><br />

matrix should be positive and <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> coefficient <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ird variable should<br />

be sufficiently large. It is essential <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two bifurcati<strong>on</strong>s do<br />

not c<strong>on</strong>tradict and bo<str<strong>on</strong>g>th</str<strong>on</strong>g> instabilities can take place simultaneously.<br />

Numerical simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e modified Brusselator model support analytic results<br />

and dem<strong>on</strong>strate a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> spatial-temporal patterns for different regi<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parametric space. Finally we discuss biological systems in which pattern<br />

formati<strong>on</strong> may be caused by <str<strong>on</strong>g>th</str<strong>on</strong>g>e above mechanisms.<br />

This work was supported by grant No. 08-01-00131 from <str<strong>on</strong>g>th</str<strong>on</strong>g>e Russian Foundati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Basic Research.<br />

References.<br />

[1] A.M. Turing, The chemical basis <str<strong>on</strong>g>of</str<strong>on</strong>g> morphogenesis Philos. Trans. R. Soc. L<strong>on</strong>d<strong>on</strong> B 237 37–2,<br />

1952.<br />

[2] J.D. Murray, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology: II. Spatial Models and Biomedical Applicati<strong>on</strong>s Springer-<br />

Verlag, 3rd ed., 2003.<br />

[3] V.K. Vanag, Waves and patterns in reacti<strong>on</strong>-diffusi<strong>on</strong> systems. Belousov-Zhabotinsky reacti<strong>on</strong><br />

in water-in-oil microemulsi<strong>on</strong>s Phys. Usp. 47 923–941, 2004.<br />

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Rosalyn Porter<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling<br />

e-mail: rbp@cs.stir.ac.uk<br />

Epidemics; Tuesday, June 28, 14:30<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> acaricide in preventing tick borne<br />

disease in a wild game bird.<br />

The incidence <str<strong>on</strong>g>of</str<strong>on</strong>g> tick borne diseases is increasing which has <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential to impact<br />

<strong>on</strong> humans, live stock and wildlife. Ticks feed <strong>on</strong> a number <str<strong>on</strong>g>of</str<strong>on</strong>g> different host species<br />

which can play different roles in disease transmissi<strong>on</strong> acting i) as a disease host<br />

which cannot sustain <str<strong>on</strong>g>th</str<strong>on</strong>g>e ticks, ii)a tick and disease host, iii) a tick host which does<br />

not transmit <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease but does increase <str<strong>on</strong>g>th</str<strong>on</strong>g>e tick populati<strong>on</strong>. Here we will use<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models to c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>th</str<strong>on</strong>g>at acaricide can play in reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

tick populati<strong>on</strong>, preventing tick bites and reducing disease incidence.<br />

We c<strong>on</strong>sider in particular <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> louping ill virus (LIV) a potentially<br />

fatal tick borne disease affecting red grouse, an important ec<strong>on</strong>omic game bird<br />

in upland Britain. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is case sheep and red deer bo<str<strong>on</strong>g>th</str<strong>on</strong>g> play a crucial role in<br />

maintaining <str<strong>on</strong>g>th</str<strong>on</strong>g>e tick populati<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>eory any efforts made to reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e tick<br />

populati<strong>on</strong> should reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e opportunity for ticks to bite grouse and hence lower<br />

virus incidence. Here we discuss SIR type models c<strong>on</strong>sidering multiple hosts and<br />

including management strategies <str<strong>on</strong>g>th</str<strong>on</strong>g>at use acaricide to achieve <str<strong>on</strong>g>th</str<strong>on</strong>g>e reducti<strong>on</strong> in virus<br />

incidence. We also discuss whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> individual grouse broods can<br />

provide protecti<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e rest <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e grouse populati<strong>on</strong>.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Zdeněk Pospíšil<br />

Masaryk University, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Science, Brno, Czech Republic<br />

e-mail: pospisil@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.muni.cz<br />

Eva Janoušová<br />

Masaryk University, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biostatistics and Analyses, Brno,<br />

Czech Republic<br />

e-mail: janousova@iba.muni.cz<br />

Tomáš Pavlík<br />

Masaryk University, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biostatistics and Analyses, Brno,<br />

Czech Republic<br />

e-mail: pavlik@iba.muni.cz<br />

Jiří Mayer<br />

University Hospital, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Internal Medicine and Hemato<strong>on</strong>cology,<br />

Brno, Czech Republic<br />

e-mail: jmayer@fnbrno.cz<br />

Marek Trněný<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Hematology and Blood Transfusi<strong>on</strong>, Prague, Czech Republic<br />

e-mail: Marek.Trneny@uhkt.cz<br />

Disease-free survival – (n<strong>on</strong>-)parametric estimati<strong>on</strong><br />

Treatment efficacy in patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a disease is usually expressed using <str<strong>on</strong>g>th</str<strong>on</strong>g>e diseasefree<br />

survival, i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>of</str<strong>on</strong>g> staying in a remissi<strong>on</strong> after its achievement or<br />

after a <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic interventi<strong>on</strong>. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>cept does not allow to evaluate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e proporti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> disease-free patients in subsequent remissi<strong>on</strong> after fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er possible<br />

relapses. The me<str<strong>on</strong>g>th</str<strong>on</strong>g>od proposed by Klein et al. enables to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> being in first and sec<strong>on</strong>d remissi<strong>on</strong>s.<br />

The c<strong>on</strong>tributi<strong>on</strong> presents two new me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> estimati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

being in any <str<strong>on</strong>g>of</str<strong>on</strong>g> remissi<strong>on</strong>s. The first <strong>on</strong>e extends <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>-parametric estimati<strong>on</strong><br />

proposed by Klein et al. <str<strong>on</strong>g>th</str<strong>on</strong>g>at is based <strong>on</strong> Kaplan-Meier estimators <str<strong>on</strong>g>of</str<strong>on</strong>g> survival<br />

functi<strong>on</strong>s. The sec<strong>on</strong>d <strong>on</strong>e utilizes a multistate model and it adopts <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for<br />

matrix model parameters identificati<strong>on</strong> based <strong>on</strong> quadratic programming (<str<strong>on</strong>g>th</str<strong>on</strong>g>e idea<br />

originally elaborated by Wood) to estimate probabilities <str<strong>on</strong>g>of</str<strong>on</strong>g> remissi<strong>on</strong>s and relapses<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> any rank. The me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are illustrated <strong>on</strong> data <str<strong>on</strong>g>of</str<strong>on</strong>g> chr<strong>on</strong>ic myeloid leukaemia<br />

patients.<br />

References.<br />

[1] J. P. Klein, N. Keiding, Y. Shu, R. M. Szydlo, J. M. Goldman, Summary curves for patients<br />

transplanted for chr<strong>on</strong>ic myeloid leukaemia salvaged by a d<strong>on</strong>or lymphocyte infusi<strong>on</strong>: <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

current leukaemia-free survival curve. British J. <str<strong>on</strong>g>of</str<strong>on</strong>g> Haematology 109 148–152.<br />

[2] S. N. Wood, Inverse problems and structured-populati<strong>on</strong> dynamics. In S. Tuljapurkar,<br />

H. Caswell (eds.) Structured-populati<strong>on</strong> models in marine, terrestrial and freshwater systems.<br />

Chapman& Hall, N.Y. 1997, 555-586.<br />

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Cellular Systems Biology; Saturday, July 2, 11:00<br />

Ilya Potapov<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Signal Processing, Tampere University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology,<br />

Korkeakoulunkatu 10, Tampere, Finland and Biophysics Department,<br />

Lom<strong>on</strong>osov Moscow State University, GSP-1, Leninskie Gory, Moscow,<br />

Russia<br />

e-mail: ilya.potapov@tut.fi<br />

Evgenii Volkov<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Physics, Lebedev Physical Inst., Leninskii<br />

53, Moscow, Russia<br />

e-mail: volkov@td.lpi.ru<br />

Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic genetic repressilators wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

phase-repulsive coupling<br />

Oscillatory processes have been discovered in various biological c<strong>on</strong>texts. Circadian<br />

clock [1], biochemical oscillati<strong>on</strong>s [2] and cell cycle [3] are <str<strong>on</strong>g>th</str<strong>on</strong>g>e well-known<br />

examples.<br />

Recently, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere were c<strong>on</strong>structed genetic networks exhibiting a specific type<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> dynamical behavior [4, 5, 6]. A prominent example <str<strong>on</strong>g>of</str<strong>on</strong>g> syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic genetic circuit<br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>e repressilator c<strong>on</strong>structed <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree transcripti<strong>on</strong> factors inhibiting each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

in cyclic way. The obvious output <str<strong>on</strong>g>of</str<strong>on</strong>g> such interacti<strong>on</strong> is oscillati<strong>on</strong>s in protein<br />

c<strong>on</strong>centrati<strong>on</strong>s [4].<br />

Syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic genetic circuits are organized simpler <str<strong>on</strong>g>th</str<strong>on</strong>g>an natural <strong>on</strong>es and can<br />

evince important details <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e latter.<br />

Given <str<strong>on</strong>g>th</str<strong>on</strong>g>at cells interact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er it would be <str<strong>on</strong>g>of</str<strong>on</strong>g> particular interest to<br />

investigate dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> such integrated populati<strong>on</strong>. Quorum sensing is <str<strong>on</strong>g>th</str<strong>on</strong>g>e coupling<br />

mechanism found in many bacteria and utilizes a small molecule, autoinducer, which<br />

diffuses <str<strong>on</strong>g>th</str<strong>on</strong>g>rough cell membrane and activates some target gene [7].<br />

Two <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical schemes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e repressilator wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e quorum sensing coupling<br />

mechanism were proposed earlier: phase-attractive [8] and phase-repulsive [9]. The<br />

latter <strong>on</strong>e utilizes a negative feedback loop in <str<strong>on</strong>g>th</str<strong>on</strong>g>e autoinducer producti<strong>on</strong> module<br />

in additi<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e average negative feedback loop <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e repressilator core. The<br />

following system <str<strong>on</strong>g>of</str<strong>on</strong>g> dimensi<strong>on</strong>less equati<strong>on</strong>s describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled repressilators<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> phase-repulsive coupling [9]:<br />

dai<br />

dt = −ai + α<br />

1+Cn ;<br />

i<br />

dbi<br />

dt = −bi + α<br />

1+An ;<br />

i<br />

dci<br />

dt = −ci + α<br />

1+Bn i<br />

+ κ Si<br />

1+Si ;<br />

dAi<br />

dt = −β(Ai − ai)<br />

dBi<br />

dt = −β(Bi − bi)<br />

dCi<br />

dt = −β(Ci − ci)<br />

dSi<br />

dt = −ks0Si + ks1Bi − η(Si − Q ¯ S)<br />

The uppercase letters Ai, Bi and Ci denote protein c<strong>on</strong>centrati<strong>on</strong>s, while lower-<br />

case ai, bi and ci are proporti<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> mRNA corresp<strong>on</strong>ding to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ose proteins, Si denotes AI c<strong>on</strong>centrati<strong>on</strong>, where i is a cell index. ¯ S = 1 N<br />

Si,<br />

N<br />

790<br />

i=1

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

where N is <str<strong>on</strong>g>th</str<strong>on</strong>g>e total number <str<strong>on</strong>g>of</str<strong>on</strong>g> cells. α is a maximal transcripti<strong>on</strong> rate. n is Hill<br />

coefficient or cooperativity. Q is proporti<strong>on</strong>al to populati<strong>on</strong> density. β is <str<strong>on</strong>g>th</str<strong>on</strong>g>e ratio<br />

between mRNA and protein lifetimes.<br />

We have investigated dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic genetic oscillators — repressilators<br />

— coupled <str<strong>on</strong>g>th</str<strong>on</strong>g>rough autoinducer diffusi<strong>on</strong> in phase-repulsive manner. We have<br />

examined emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> periodic regimes, stable inhomogeneous steady states depending<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e main systems’ parameters: coupling streng<str<strong>on</strong>g>th</str<strong>on</strong>g> and maximal transcripti<strong>on</strong><br />

rate. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese regimes were shown to exist in [9].<br />

It has been found <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e autoinducer producti<strong>on</strong> module added to <str<strong>on</strong>g>th</str<strong>on</strong>g>e isolated<br />

repressilator causes <str<strong>on</strong>g>th</str<strong>on</strong>g>e limit cycle to disappear <str<strong>on</strong>g>th</str<strong>on</strong>g>rough infinite period bifurcati<strong>on</strong><br />

for sufficiently large transcripti<strong>on</strong> rate (α). We have found hysteresis <str<strong>on</strong>g>of</str<strong>on</strong>g> limit cycle<br />

and stable steady state, <str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> which is determined by ratio between mRNA<br />

and protein lifetimes.<br />

Two coupled oscillators system dem<strong>on</strong>strates stable anti-phase oscillati<strong>on</strong>s which<br />

can become a chaotic regime <str<strong>on</strong>g>th</str<strong>on</strong>g>rough invariant torus emergence, <str<strong>on</strong>g>th</str<strong>on</strong>g>at was investigated<br />

in [10], or via Feigenbaum period doubling bifurcati<strong>on</strong> cascade [11], which is<br />

alternative way to chaos found by us in <str<strong>on</strong>g>th</str<strong>on</strong>g>e system.<br />

References.<br />

[1] J. Dunlap, Molecular bases for circadian clocks Cell 96 271–290.<br />

[2] A.K. Ghosh and B. Chance,Oscillati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> glycolytic intermediates in yeast cells Biochem.<br />

Biophys. Res. Commun. 16 174–181.<br />

[3] P. Nurse, A l<strong>on</strong>g twentie<str<strong>on</strong>g>th</str<strong>on</strong>g> century <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell cycle and bey<strong>on</strong>d Cell 100 71–78.<br />

[4] M. Elowitz and S. Leibler, A syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic oscillatory network <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong>al regulators Nature<br />

403 335–338.<br />

[5] T.S. Gardner, C.R. Cantor and J.J. Collins, C<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a genetic toggle switch in Escherichia<br />

coli Nature 403 339–342.<br />

[6] M. Atkins<strong>on</strong>, M. Savageau, J. Myers and A. Ninfa, Development <str<strong>on</strong>g>of</str<strong>on</strong>g> genetic circuitry exhibiting<br />

toggle switch or oscillatory behavior in Escherichia coli Cell 113 597–607.<br />

[7] C.M. Waters and B.L. Bassler, Quorum sensing: cell-to-cell communicati<strong>on</strong> in bacteria Ann.<br />

Rev. Cell Dev. Biol. 21 319–346.<br />

[8] J. García-Ojalvo, M. Elowitz and S. Strogatz, Modeling a syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic multicellular clock: Repressilators<br />

coupled by quorum sensing Proc. Natl. Acad. Sci. U.S.A. 101 10955–10960.<br />

[9] E. Ullner, A. Zaikin, E. Volkov and J. García-Ojalvo, Multistability and clustering in a populati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic genetic oscillators via phase-repulsive cell-to-cell communicati<strong>on</strong> Phys.<br />

Rev. Lett. 99 148103.<br />

[10] E. Ullner, A. Koseska, J. Kur<str<strong>on</strong>g>th</str<strong>on</strong>g>s, E. Volkov, H. Kantz and J. García-Ojalvo, Multistability <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic genetic networks wi<str<strong>on</strong>g>th</str<strong>on</strong>g> repressive cell-to-cell communicati<strong>on</strong> Phys. Rev. E. 78 031904.<br />

[11] M. Feigenbaum, Quantitative universality for a class <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear transformati<strong>on</strong>s J. Stat.<br />

Phys. 19 25–52.<br />

791

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Tuesday, June 28, 14:30<br />

Gibin Powa<str<strong>on</strong>g>th</str<strong>on</strong>g>il<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee, Dundee, United Kingdom.<br />

e-mail: gibin@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.dundee.ac.uk<br />

Mark Chaplain<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee, Dundee, United Kingdom.<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> cell-cycle heterogeneity <strong>on</strong> tumour<br />

resp<strong>on</strong>se to chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy: Biological insights from a hybrid<br />

multi-scale cellular automat<strong>on</strong> model<br />

The <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> a solid tumour depends critically <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>ses <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

individual cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>stitute <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire tumour mass. A particular cells spatial<br />

locati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour and intracellular interacti<strong>on</strong>s, including <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell cycle wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in each cell, has an impact <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir decisi<strong>on</strong> to grow and<br />

divide. They are also influenced by external signals from o<str<strong>on</strong>g>th</str<strong>on</strong>g>er cells, and oxygen<br />

and nutrient c<strong>on</strong>centrati<strong>on</strong>s. Hence, it is important to take <str<strong>on</strong>g>th</str<strong>on</strong>g>ese into account when<br />

modelling tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>se to various cell-kill <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies, including<br />

chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy.<br />

In order to address <str<strong>on</strong>g>th</str<strong>on</strong>g>is multi-scale nature <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, we propose a<br />

hybrid, individual-based approach <str<strong>on</strong>g>th</str<strong>on</strong>g>at analyses spatio-temporal dynamics at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

level <str<strong>on</strong>g>of</str<strong>on</strong>g> cells, linking individual cell behaviour wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> cell<br />

organisati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e microenvir<strong>on</strong>ment. The individual tumour cells are modelled<br />

by using a cellular automat<strong>on</strong> (CA) approach, where each cell has its own internal<br />

cell cycle, modelled using a system <str<strong>on</strong>g>of</str<strong>on</strong>g> ODEs. The internal cell-cycle dynamics<br />

determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> strategy in <str<strong>on</strong>g>th</str<strong>on</strong>g>e CA model, making it more predictive and<br />

biologically relevant. It also helps to classify <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells according to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir cell-cycle<br />

states and to analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> various cell-cycle dependent cytotoxic drugs.<br />

Moreover, we have incorporated <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen dynamics wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>is hybrid<br />

model in order to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microenvir<strong>on</strong>ment in cell-cycle regulati<strong>on</strong><br />

and tumour treatments. An important factor from <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment point <str<strong>on</strong>g>of</str<strong>on</strong>g> view is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e low c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen can result in a hypoxia-induced quiescence<br />

(G0/G1 arrest) <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer cells, making <str<strong>on</strong>g>th</str<strong>on</strong>g>em resistant to key cytotoxic drugs.<br />

Using <str<strong>on</strong>g>th</str<strong>on</strong>g>is multi-scale model, we investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> oxygen heterogeneity <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal patterning <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell distributi<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir cell-cycle status.<br />

We dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at oxygen transport limitati<strong>on</strong>s result in significant heterogeneity<br />

in HIF-1 alpha signalling and cell-cycle status, and when <str<strong>on</strong>g>th</str<strong>on</strong>g>ese are combined wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

drug transport limitati<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficacy <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy is significantly impaired.<br />

792

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: from physical tools to<br />

applicati<strong>on</strong>s in cancer modeling II; Saturday, July 2, 11:00<br />

Applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> phase field models in biological systems<br />

Sim<strong>on</strong> Praetorius<br />

Institut für Wissenschaftliches Rechnen, Technische Universität Dresden,<br />

Zellescher Weg 12-14, 01062 Dresden, Germany<br />

e-mail: s.praetorius@googlemail.com<br />

Shapes <str<strong>on</strong>g>of</str<strong>on</strong>g> complex geometry are ubiquitous in our natural envir<strong>on</strong>ment. A few<br />

examples are snow flakes, crack patterns, microstructures in materials or <str<strong>on</strong>g>th</str<strong>on</strong>g> evein<br />

network in plant leaves. These shapes have in comm<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are created by<br />

out-<str<strong>on</strong>g>of</str<strong>on</strong>g>-equilibrium phenomena and <str<strong>on</strong>g>th</str<strong>on</strong>g>us evolve in time. The understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> a diverse<br />

array <str<strong>on</strong>g>of</str<strong>on</strong>g> phenomena involving complex time-dependent shapes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e physical<br />

and biological sciences has been greatly enhanced by a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical/computati<strong>on</strong>al<br />

framework rooted in statistical physics, <str<strong>on</strong>g>th</str<strong>on</strong>g>at is comm<strong>on</strong>ly refered to as phase-field<br />

modeling. The main challenge in <str<strong>on</strong>g>th</str<strong>on</strong>g>is field is to c<strong>on</strong>struct models which encompass<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> practically relevant materials or biological systems, are capable <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

making quantitatively accurate predicti<strong>on</strong>s and are ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically simple enough<br />

to be solved <strong>on</strong> physically realistic time and leng<str<strong>on</strong>g>th</str<strong>on</strong>g> scales.<br />

We present various applicati<strong>on</strong>s in biological systems, including cell dynamics,<br />

viral capsides and b<strong>on</strong>e remodeling.<br />

793

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Jamie Prentice<br />

SAC<br />

e-mail: jamie@bioss.ac.uk<br />

Epidemics; Tuesday, June 28, 14:30<br />

The Perturbati<strong>on</strong> Effect in wildlife diseases: An emergent<br />

behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> simple models<br />

Populati<strong>on</strong> reducti<strong>on</strong> is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten used as a disease c<strong>on</strong>trol strategy when dealing wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

wildlife hosts; however, in some systems it has been associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an increase<br />

in disease (including bovine tuberculosis in badgers and classical swine fever virus<br />

in wild boar). This increase in disease following populati<strong>on</strong> reducti<strong>on</strong> is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten<br />

referred to as <str<strong>on</strong>g>th</str<strong>on</strong>g>e perturbati<strong>on</strong> effect. Several possible reas<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e perturbati<strong>on</strong><br />

effect have been suggested, including increased movement and c<strong>on</strong>tact rates, and<br />

compensatory reproducti<strong>on</strong> following populati<strong>on</strong> reducti<strong>on</strong>.<br />

We use ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical epidemiological SI models c<strong>on</strong>taining key processes, to<br />

investigate properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e perturbati<strong>on</strong> effect and study how it arises as an emergent<br />

property <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying populati<strong>on</strong> and disease dynamic.<br />

In a n<strong>on</strong>-spatial c<strong>on</strong>text, we investigate how a change in host behaviour (as a<br />

c<strong>on</strong>sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> reducti<strong>on</strong>) leading to an increase in horiz<strong>on</strong>tal disease<br />

transmissi<strong>on</strong>, can give rise to <str<strong>on</strong>g>th</str<strong>on</strong>g>e perturbati<strong>on</strong> effect. We also investigate how<br />

characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> demography and disease affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e magnitude <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is increase.<br />

In a stochastic spatial c<strong>on</strong>text, we investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> density dependent<br />

movement between multiple sub populati<strong>on</strong>s, and how <str<strong>on</strong>g>th</str<strong>on</strong>g>e horiz<strong>on</strong>tal disease transmissi<strong>on</strong><br />

between groups can affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e increase. Finally we investigate how different<br />

populati<strong>on</strong> reducti<strong>on</strong> strategies can maximise <str<strong>on</strong>g>th</str<strong>on</strong>g>e perturbati<strong>on</strong> effect.<br />

We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e perturbati<strong>on</strong> effect is most likely to occur in disease systems<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> low disease prevalence, where populati<strong>on</strong>s are close to <str<strong>on</strong>g>th</str<strong>on</strong>g>e carrying capacity<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease is spatially heterogeneous in nature.<br />

794

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: from physical tools to<br />

applicati<strong>on</strong>s in cancer modeling I; Saturday, July 2, 08:30<br />

Luigi Preziosi<br />

Dip. Matematica, Politecnico di Torino<br />

e-mail: luigi.preziosi@polito.it<br />

Guido Vitale<br />

Dip. Matematica, Politecnico di Torino<br />

e-mail: guido.vitale@polito.it<br />

Cell Adhesi<strong>on</strong> and Re-organisati<strong>on</strong> in a Multiphase Model<br />

Describing Tumour and Tissue Grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

The main aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e talk is to describe how to embed <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental results<br />

recently obtained studying <str<strong>on</strong>g>th</str<strong>on</strong>g>e detachment force <str<strong>on</strong>g>of</str<strong>on</strong>g> single adhesi<strong>on</strong> b<strong>on</strong>ds in<br />

a multiphase model developed to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> tumours and tissues in<br />

general. In order to do <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic infomati<strong>on</strong> is upscaled to <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic<br />

level to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> some crucial terms appearing in <str<strong>on</strong>g>th</str<strong>on</strong>g>e PDE<br />

model <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sub-cellular dynamics involving, for instance, <str<strong>on</strong>g>th</str<strong>on</strong>g>e density <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>ds<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane, <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>d rupture and <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>d formati<strong>on</strong>.<br />

In fact, adhesi<strong>on</strong> phenomena influence bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> forces am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>stituents<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mixtures and <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>stitutive equati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e stress <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular<br />

comp<strong>on</strong>ents.<br />

Studying <str<strong>on</strong>g>th</str<strong>on</strong>g>e former terms a relati<strong>on</strong>ship between interacti<strong>on</strong> forces and relative<br />

velocity is found. The dynamics presents a behaviour resembling <str<strong>on</strong>g>th</str<strong>on</strong>g>e transiti<strong>on</strong> from<br />

epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial to mesenhymal cells or from mesenchymal to ameboid moti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

chemical cues triggering such transiti<strong>on</strong>s are not c<strong>on</strong>sidered here.<br />

The latter terms are dealt wi<str<strong>on</strong>g>th</str<strong>on</strong>g> using <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> evolving natural c<strong>on</strong>figurati<strong>on</strong>s<br />

c<strong>on</strong>sisting in decomposing in a multiplicative way <str<strong>on</strong>g>th</str<strong>on</strong>g>e deformati<strong>on</strong> gradient<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular c<strong>on</strong>stituent distinguishing <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tributi<strong>on</strong>s due to grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, to cell rearrangement<br />

and to elastic deformati<strong>on</strong>. This allows to describe situati<strong>on</strong>s in which<br />

if in some points <str<strong>on</strong>g>th</str<strong>on</strong>g>e ensemble <str<strong>on</strong>g>of</str<strong>on</strong>g> cells is subject to a stress above a <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold, <str<strong>on</strong>g>th</str<strong>on</strong>g>en<br />

locally some b<strong>on</strong>ds may break and some o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers may form, giving rise to an internal<br />

re-organisati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows to relax exceedingly high stresses.<br />

795

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Tadeáš Přiklopil<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Helsinki<br />

e-mail: tadeas.priklopil@helsinki.fi<br />

Speciati<strong>on</strong>; Wednesday, June 29, 08:30<br />

Magic traits, mate choice and speciati<strong>on</strong><br />

Many <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical models <strong>on</strong> sympatric speciati<strong>on</strong> rely <strong>on</strong> assortative mating functi<strong>on</strong>s,<br />

in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>th</str<strong>on</strong>g>at two individuals mate decreases wi<str<strong>on</strong>g>th</str<strong>on</strong>g> increasing<br />

phenotypic difference. We give results <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> assortative mating functi<strong>on</strong>s<br />

in models, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e trait <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trols mate choice also determines fitness<br />

in ecological selecti<strong>on</strong> (so called magic traits). In particular, we c<strong>on</strong>centrate <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e deficiencies <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese mating functi<strong>on</strong>s and c<strong>on</strong>trast <str<strong>on</strong>g>th</str<strong>on</strong>g>e results wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mate choice<br />

which is also based <strong>on</strong> indicators <str<strong>on</strong>g>of</str<strong>on</strong>g> adaptedness. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er, we introduce mate choice<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at is based <strong>on</strong> a strategy <str<strong>on</strong>g>of</str<strong>on</strong>g> sequential search, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e decisi<strong>on</strong> to mate depends<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e density distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e fitness returns to <str<strong>on</strong>g>th</str<strong>on</strong>g>e searcher.<br />

References.<br />

[1] E. Kisdi & T. Priklopil, Evoluti<strong>on</strong>ary branching <str<strong>on</strong>g>of</str<strong>on</strong>g> a magic trait J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. DOI<br />

10.1007/s00285-010-0377-1<br />

796

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Stephen Proulx<br />

UC Santa Barbara<br />

e-mail: stephen.proulx@gmail.com<br />

Alexey Yanchukov<br />

UC Santa Barbara<br />

Speciati<strong>on</strong>; Wednesday, June 29, 08:30<br />

Evoluti<strong>on</strong>ary resp<strong>on</strong>ses to migrati<strong>on</strong> load: A tall fence or a<br />

melting pot?<br />

Gene flow between populati<strong>on</strong>s in different ecological c<strong>on</strong>diti<strong>on</strong>s can reduce fitness in<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> populati<strong>on</strong>s. This can be due to immigrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> alleles <str<strong>on</strong>g>th</str<strong>on</strong>g>at are not adapted to<br />

local ecological c<strong>on</strong>diti<strong>on</strong> or because hybrids between populati<strong>on</strong>s have lower fitness.<br />

But <str<strong>on</strong>g>th</str<strong>on</strong>g>is reducti<strong>on</strong> in fitness, or genetic load, is also a potential engine to drive<br />

evoluti<strong>on</strong>: The magnitude <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic load sets an upper bound to <str<strong>on</strong>g>th</str<strong>on</strong>g>e streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

selecti<strong>on</strong> to compensate for <str<strong>on</strong>g>th</str<strong>on</strong>g>e cost <str<strong>on</strong>g>of</str<strong>on</strong>g> migrati<strong>on</strong>. This load can be reduced <str<strong>on</strong>g>th</str<strong>on</strong>g>rough<br />

mating preferences for high quality mates, mating preferences for local genotypes,<br />

or by changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic architecture. Preferences for local mates would lead<br />

to reinforcement <str<strong>on</strong>g>of</str<strong>on</strong>g> low hybrid fitness and potentially speciati<strong>on</strong>. Alternatively,<br />

preferences for high quality mates or changes to <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic architecture might allow<br />

incipient species to c<strong>on</strong>tinue to transfer genetic informati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out populati<strong>on</strong><br />

collapse. I will discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> each pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way and <str<strong>on</strong>g>th</str<strong>on</strong>g>e implicati<strong>on</strong>s<br />

for local adaptati<strong>on</strong> and speciati<strong>on</strong>.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Jens Przybilla<br />

Interdisciplinary Centre for Bioinformatics, Institute for Medical<br />

Informatics, Statistics and Epidemiology, Leipzig University, Germany<br />

e-mail: przybilla@izbi.uni-leipzig.de<br />

Markus Löffler<br />

Institute for Medical Informatics, Statistics and Epidemiology, Interdisciplinary<br />

Centre for Bioinformatics, Leipzig University, Germany<br />

e-mail: markus.loeffler@imise.uni-leipzig.de<br />

Jörg Galle<br />

Interdisciplinary Centre for Bioinformatics, Leipzig University, Germany<br />

e-mail: galle@izbi.uni-leipzig.de<br />

Towards a whole-tissue model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intestine.<br />

The intestinal epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elium is a paradigmatic system to study regenerative tissues.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is tissue <str<strong>on</strong>g>th</str<strong>on</strong>g>e stem cells are c<strong>on</strong>fined to a well-defined niche at <str<strong>on</strong>g>th</str<strong>on</strong>g>e bottom<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> invaginati<strong>on</strong>s called crypts. The progeny <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese stem cells specify into different<br />

functi<strong>on</strong>al lineages and regenerate <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire tissue wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a few days.<br />

A multitude <str<strong>on</strong>g>of</str<strong>on</strong>g> genetically altered mouse stems show not <strong>on</strong>ly changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

turnover but also clear morphological changes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire intestine. In order<br />

to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>ese phenotypes a whole-tissue approach is required.<br />

Recently, we introduced an <str<strong>on</strong>g>of</str<strong>on</strong>g>f-lattice model <str<strong>on</strong>g>of</str<strong>on</strong>g> single crypt dynamics [1]. This<br />

model explains crypt dynamics in steady state and after perturbati<strong>on</strong>s in agreement<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental data. We here present a modelling framework <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows<br />

extending <str<strong>on</strong>g>th</str<strong>on</strong>g>is model to multi-crypt systems representing a first step towards a<br />

whole-tissue model.<br />

We implemented a Cellular Potts Model <strong>on</strong> a curved surface representing multiple<br />

crypts and applied <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulatory mechanisms and organisati<strong>on</strong> c<strong>on</strong>cepts <str<strong>on</strong>g>of</str<strong>on</strong>g> our <str<strong>on</strong>g>of</str<strong>on</strong>g>flattice<br />

model. This enables us to cover <str<strong>on</strong>g>th</str<strong>on</strong>g>e self-organisati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell producti<strong>on</strong> and<br />

loss in <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue, which is assumed as fixed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e former model. We provide first<br />

simulati<strong>on</strong> results applying <str<strong>on</strong>g>th</str<strong>on</strong>g>is model to circadian rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms <str<strong>on</strong>g>of</str<strong>on</strong>g> intestinal turnover<br />

and compare <str<strong>on</strong>g>th</str<strong>on</strong>g>e results to experimental data [2].<br />

References.<br />

[1] P. Buske et.al., A comprehensive model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal stem cell and tissue organisati<strong>on</strong><br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e intestinal crypt. PLoS Comput Biol 2011 7 e1001045.<br />

[2] J.M. Qiu, et.al.,Cell migrati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e small and large bowel shows a str<strong>on</strong>g circadian rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>m.<br />

Epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial Cell Biol 1994 3(4) 137–148.<br />

798

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Piotr Przymus<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science, Nicolaus Copernicus<br />

University, Chopina 12/18, 87-100 Toruń, Poland<br />

e-mail: eror@mat.umk.pl,<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Rykaczewski<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science, Nicolaus Copernicus<br />

University, Chopina 12/18, 87-100 Toruń, Poland<br />

e-mail: mozgun@mat.umk.pl<br />

Recurrence plot analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> time series derived from<br />

observati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Dreissena polymorpha<br />

Biological Early Warning Systems provide a rapid warning <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

c<strong>on</strong>taminants in water at c<strong>on</strong>centrati<strong>on</strong>s which could be immediate <str<strong>on</strong>g>th</str<strong>on</strong>g>reat to living<br />

organisms. In our work we use l<strong>on</strong>g-term observati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> freshwater mussels for<br />

m<strong>on</strong>itoring water c<strong>on</strong>taminati<strong>on</strong>. This paper presents a recurrence plot (RP) based<br />

approach to analyse data derived from <str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Dreissena polymorpha.<br />

Studying <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>-linear characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> data sequences can assist in understanding<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ships between measured mussel activities and actual state in surrounding<br />

envir<strong>on</strong>ment. Data sequences are extended to m-dimensi<strong>on</strong>al phase space and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>en we use recurrence plots to visualize recurrences <str<strong>on</strong>g>of</str<strong>on</strong>g> trajectories <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamical<br />

systems. Finally, <str<strong>on</strong>g>th</str<strong>on</strong>g>e recurrence quantificati<strong>on</strong> analysis (RQA) is used to quantify<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e structures found in RPs and to classify <str<strong>on</strong>g>th</str<strong>on</strong>g>em. In order to check <str<strong>on</strong>g>th</str<strong>on</strong>g>e effectiveness<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach, we need to examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e adequacy <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods used at various<br />

stages <str<strong>on</strong>g>of</str<strong>on</strong>g> analysis. Therefore, we will discuss usage <str<strong>on</strong>g>of</str<strong>on</strong>g> various parameters for RP<br />

and RQA and classificati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods (SVM, KNN, FDA,SRDA, PDA, DLDA). Preliminary<br />

experiments and previous results <str<strong>on</strong>g>of</str<strong>on</strong>g> work show <str<strong>on</strong>g>th</str<strong>on</strong>g>at such formulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e problem allows to extract relevant informati<strong>on</strong> from signal and lead to effective<br />

soluti<strong>on</strong>s to c<strong>on</strong>sidered problem. It is found, for example, <str<strong>on</strong>g>th</str<strong>on</strong>g>at RQA may support<br />

identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> polluti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e water.<br />

References.<br />

[Bis06] Ch. M. Bishop. Pattern Recogniti<strong>on</strong> and Machine Learning. Springer, 2006.<br />

[Bor06] Jost Borcherding. Ten years <str<strong>on</strong>g>of</str<strong>on</strong>g> practical experience wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dreissena-m<strong>on</strong>itor, a biological<br />

early warning system for c<strong>on</strong>tinuous water quality m<strong>on</strong>itoring. Hydrobiologia,<br />

556:417–426, 2006.<br />

[EKR87] J.-P. Eckmann, S.O. Kamphorst, and D. Ruelle. Recurrence plots <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamical system.<br />

Europhys. Lett., 4:973–977, 1987.<br />

[Gud03] Alexander V. Gudimov. Elementary behavioral acts <str<strong>on</strong>g>of</str<strong>on</strong>g> valve movements in mussels<br />

(mytilus edulis l.). Doklady Biological Sciences, 391:346–348, 2003. Translated from<br />

Doklady Akademii Nauk, Vol. 391, No. 3, 2003, pp. 422-425.<br />

[KKCC06] Cheol-Ki Kim, Inn-Sil Kwak, Eui-Young Cha, and Tae-Soo Ch<strong>on</strong>. Implementati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

wavelets and artificial neural networks to detecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> toxic resp<strong>on</strong>se behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> chir<strong>on</strong>omids<br />

(chir<strong>on</strong>omidae: Diptera) for water quality m<strong>on</strong>itoring. Ecol. Model., 195:61–<br />

71, 2006.<br />

[LRM08] Petr<strong>on</strong>e L., Norman L. C Ragg, and A. James McQuillan. In situ infrared spectroscopic<br />

investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> perna canaliculus mussel larvae primary settlement. Bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ouling.,<br />

24(6):405–413, 2008.<br />

799

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[RSH + 06] David L. Rodland, Bernd R. Schöne, Samuli O. Helama, Jan Kresten Nielsen, and<br />

Sven M. Baier. A clockwork mollusc: Ultradian rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms in bivalve activity revealed<br />

by digital photography. J. Exp. Mar. Biol. Ecol., 334:316–323, 2006.<br />

[Wiś91] Ryszard Wiśniewski. New me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for recording activity pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> bivalves: A preliminary<br />

report <strong>on</strong> dreissena polymorpha pallas during ecological stress. In Ten<str<strong>on</strong>g>th</str<strong>on</strong>g> Intern.<br />

Malacol. C<strong>on</strong>gress, pages 363–365, 1991.<br />

[WZ94] C.L. Webber and J.P. Zbilut. Dynamical assessment <str<strong>on</strong>g>of</str<strong>on</strong>g> physiological systems and states<br />

using recurrence plot strategies. J. Appl. Physiology, 76(2):965–973, 1994.<br />

[ZW92] J. P. Zbilut and C. L. Webber. Embeddings and delays as derived from quantificati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> recurrence plots. Phys. Lett. A, 171(3-4):199–203, 1992.<br />

800

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Tuesday, June 28, 17:00<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Psiuk-Maksymowicz<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Automatic C<strong>on</strong>trol,<br />

Gliwice, Poland<br />

e-mail: Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g>.Psiuk-Maksymowicz@polsl.pl<br />

Computati<strong>on</strong>al study <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

in resp<strong>on</strong>se to combined <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies<br />

The microvascular network plays crucial role in development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e solid tumours.<br />

It c<strong>on</strong>stitutes a source <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nutrient for <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour and enables its c<strong>on</strong>tinuous<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. However, due to fast metabolism <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour cells hypoxic regi<strong>on</strong>s<br />

may occur. Such regi<strong>on</strong>s are <str<strong>on</strong>g>th</str<strong>on</strong>g>en cause <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e angiogenesis. This study is intended<br />

to analyse computati<strong>on</strong>ally interplay between <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour cells and vascular network,<br />

and additi<strong>on</strong>ally to find optimal scheduling for <str<strong>on</strong>g>th</str<strong>on</strong>g>e combined chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

and anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy [1].<br />

The deterministic model is represented by a system <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-linear partial differential<br />

equati<strong>on</strong>s and enables to simulate grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e solid tumour in its vascular<br />

phase as well as a process <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e angiogenesis. In c<strong>on</strong>trast to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er models (e.g. [2])<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e microvascular network is modelled explicite, not as a density <str<strong>on</strong>g>of</str<strong>on</strong>g> blood vessels.<br />

It enables to capture <str<strong>on</strong>g>th</str<strong>on</strong>g>e heterogeneity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour tissue, not <strong>on</strong>ly its averaged<br />

picture. In order to find optimal parameters for <str<strong>on</strong>g>th</str<strong>on</strong>g>e combined chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy and<br />

anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy a few heuristic algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms are employed, including simulated<br />

annealing [3] and evoluti<strong>on</strong>ary algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m.<br />

References.<br />

[1] A. Swierniak, M. Kimmel and J. Smieja, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling as a tool for planning anticancer<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy <str<strong>on</strong>g>European</str<strong>on</strong>g> Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Pharmacology 625 (2009) 108–121.<br />

[2] J. Panovska, H.M. Byrne and P.K. Maini Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

and implicati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Systems, Volume I: Modeling<br />

and Simulati<strong>on</strong> in Science, Engineering and Technology, 2007, Part IV, 205–216.<br />

[3] Z. Agur, R. Hassin and S. Levy, Optimizing chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy scheduling using local search heuristics<br />

Operati<strong>on</strong>s Research 54 (2006) 829–846.<br />

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Plants, grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and transport processes I; Tuesday, June 28, 11:00<br />

Mariya Ptashnyk<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics I, RWTH Aachen University, Wüllnerstr.<br />

5b, D-52056 Aachen<br />

e-mail: ptashnyk@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>1.rw<str<strong>on</strong>g>th</str<strong>on</strong>g>-aachen.de<br />

Andres Chavarría-Krauser<br />

BIOQUANT, Heidelberg University, Im Neuenheimer Feld 267, D-69120<br />

Heidelberg<br />

e-mail: andres.chavarria@bioquant.uni-heidelberg.de<br />

Transport <str<strong>on</strong>g>of</str<strong>on</strong>g> metal and water in plant roots: Modelling and<br />

Analysis<br />

We study <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> metal and water transport <str<strong>on</strong>g>th</str<strong>on</strong>g>rough plant roots. The<br />

model equati<strong>on</strong>s reflect <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex microscopic structure <str<strong>on</strong>g>of</str<strong>on</strong>g> a root tissue. We<br />

distinguish between apoplastic and symplastic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways for metal and water transport.<br />

The active water transport is modelled by Stokes equati<strong>on</strong>s and is defined<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e pressure difference between roots and atmosphere and by <str<strong>on</strong>g>th</str<strong>on</strong>g>e osmotic pressure<br />

in cells. The transport <str<strong>on</strong>g>of</str<strong>on</strong>g> metal molecules is specified by reacti<strong>on</strong>-diffusi<strong>on</strong>c<strong>on</strong>vecti<strong>on</strong><br />

equati<strong>on</strong>s. The ordinary differential equati<strong>on</strong>s describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamic <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

metal transporter c<strong>on</strong>centrati<strong>on</strong>s <strong>on</strong> cell membranes. Using multiscale analysis we<br />

derive a macroscopic model for transport processes defined <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e scale <str<strong>on</strong>g>of</str<strong>on</strong>g> a whole<br />

root branch. The c<strong>on</strong>vergence <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear terms is shown applying <str<strong>on</strong>g>th</str<strong>on</strong>g>e unfolding<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>od.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Genetics; Friday, July 1, 14:30<br />

Robert Puddicombe<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Computing, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Surrey, Guildford, Surrey,<br />

GU2 7XH, UK<br />

e-mail: R.Puddicombe@surrey.ac.uk<br />

Dr André Grüning<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Computing, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Surrey, Guildford, Surrey,<br />

GU2 7XH, UK<br />

Development <str<strong>on</strong>g>of</str<strong>on</strong>g> distinct col<strong>on</strong>ies <str<strong>on</strong>g>of</str<strong>on</strong>g> genotype in a sympatric<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> diploid entities<br />

As part <str<strong>on</strong>g>of</str<strong>on</strong>g> an investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> sympatric speciati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is study used a computer<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> a populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> diploid entities to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> stable<br />

col<strong>on</strong>ies <str<strong>on</strong>g>of</str<strong>on</strong>g> genotypes. The investigati<strong>on</strong> tested development in variously shaped<br />

spaces where, in order to maintain a sympatric envir<strong>on</strong>ment, uniform developmental<br />

characteristics were applied in all areas.<br />

The objective <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is to establish whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er species can separate in a<br />

uniform envir<strong>on</strong>ment simply by random genetic development. The study’s dem<strong>on</strong>strati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> stable ’col<strong>on</strong>ies’ wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a uniform space seems to imply <str<strong>on</strong>g>th</str<strong>on</strong>g>at sympatric<br />

speciati<strong>on</strong> is possible.<br />

The computer model represented chromosomes as binary numbers, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each<br />

digit equivalent to a gene: being ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er ’wild’ or mutated. Processes <str<strong>on</strong>g>of</str<strong>on</strong>g> inheritance<br />

were modelled using probabilistic rates <str<strong>on</strong>g>of</str<strong>on</strong>g> mutati<strong>on</strong> and cross-over. The populati<strong>on</strong><br />

was subject to a randomly-applied dea<str<strong>on</strong>g>th</str<strong>on</strong>g>-rate and <str<strong>on</strong>g>of</str<strong>on</strong>g>f-spring competed for <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting<br />

space. A key characteristic <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model was <str<strong>on</strong>g>th</str<strong>on</strong>g>e limited range for selecting<br />

a mate and placing <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring. This places <str<strong>on</strong>g>th</str<strong>on</strong>g>e model between models which allow<br />

panmictic mating and <str<strong>on</strong>g>th</str<strong>on</strong>g>ose which employ sexual selecti<strong>on</strong> mechanisms.<br />

In a ring-shaped corridor, starting wi<str<strong>on</strong>g>th</str<strong>on</strong>g> uniform or random populati<strong>on</strong>s, four<br />

or five distinct col<strong>on</strong>ies <str<strong>on</strong>g>of</str<strong>on</strong>g> genotypes developed and remained stable for several<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ousand generati<strong>on</strong>s. These col<strong>on</strong>ies were similar to biological ’ring-species’ but<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model all <str<strong>on</strong>g>th</str<strong>on</strong>g>e neighbouring col<strong>on</strong>ies become equally incompatible wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each<br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>er. The development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese col<strong>on</strong>ies was found to be related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e wid<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e corridor, as well as to <str<strong>on</strong>g>th</str<strong>on</strong>g>e rates <str<strong>on</strong>g>of</str<strong>on</strong>g> recombinati<strong>on</strong> and mutati<strong>on</strong> which were<br />

applied. In a narrow corridor several distinct col<strong>on</strong>ies persisted whereas in a wide<br />

corridor <strong>on</strong>e dominant type quickly developed.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er study is required to establish whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>ese col<strong>on</strong>ies can be c<strong>on</strong>sidered<br />

as proper examples <str<strong>on</strong>g>of</str<strong>on</strong>g> sympatric speciati<strong>on</strong>.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Tuesday, June 28, 11:00<br />

Andrea Pugliese<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Trento, Italy<br />

e-mail: pugliese@science.unitn.it<br />

Gianpaolo Scalia Tomba<br />

Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Roma Tor Vergata<br />

Ant<strong>on</strong>ella Lunelli<br />

Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Trento, Italy<br />

Approximati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong> spread in multigroup SIR models<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough homogeneous models<br />

In recent years <str<strong>on</strong>g>th</str<strong>on</strong>g>ere has been a tremendous increase in <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemic<br />

models developed for <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong> in humans; <str<strong>on</strong>g>of</str<strong>on</strong>g>ten models include<br />

households and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er types <str<strong>on</strong>g>of</str<strong>on</strong>g> mixing groups, as well as heterogeneities due to age,<br />

behaviour, etc. In ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er directi<strong>on</strong>, a great number <str<strong>on</strong>g>of</str<strong>on</strong>g> data <strong>on</strong> infecti<strong>on</strong> spread<br />

have been analysed wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models, which <str<strong>on</strong>g>of</str<strong>on</strong>g>ten are based<br />

<strong>on</strong> homogeneous mixing, or simple variants <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>at. Aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is starting<br />

to understand why, while definitely mixing patterns and individual behaviour are<br />

complicated, simple homogeneous models may still reproduce adequately <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall<br />

epidemic spread. Our prototype <str<strong>on</strong>g>of</str<strong>on</strong>g> complex models is relatively simple, namely<br />

a stochastic SIR model for a closed populati<strong>on</strong> divided in groups, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> uniform<br />

global transmissi<strong>on</strong> and heterogeneous local transmissi<strong>on</strong>; simulati<strong>on</strong>s show <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is type <str<strong>on</strong>g>of</str<strong>on</strong>g> models can be approximated adequately by a homogeneous model, as<br />

l<strong>on</strong>g as <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> groups is sufficiently large. Heuristic me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

relati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e homogeneous model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e original<br />

parameters. Extensi<strong>on</strong>s to models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> differential transmissi<strong>on</strong> routes are being<br />

examined.<br />

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Małgorzata Pułka<br />

Gdansk University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: mpulka@mif.pg.gda.pl<br />

Populati<strong>on</strong> Genetics; Wednesday, June 29, 14:30<br />

N<strong>on</strong>homogeneous Markov chains and quadratic stochastic<br />

processes in biology<br />

N<strong>on</strong>linear mappings appear in many branches <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and its applicati<strong>on</strong>s.<br />

In ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical biology, so-called quadratic stochastic processes (QSP) are used<br />

to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems. We examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e limit behavior<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> such processes as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship between <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymptotic properties <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

n<strong>on</strong>homogeneous Markov chain and asymptotic properties <str<strong>on</strong>g>of</str<strong>on</strong>g> QSP. Moreover, we<br />

study <str<strong>on</strong>g>th</str<strong>on</strong>g>e geometric structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> Markov chains wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a particular limit<br />

bahavior.<br />

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Neurosciences; Wednesday, June 29, 08:30<br />

Jan Pyrzowski<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Neurology, Medical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Gdansk<br />

e-mail: jan.pyrzowski@gmail.com<br />

A dynamical model <str<strong>on</strong>g>of</str<strong>on</strong>g> epilepsy in a plastic neur<strong>on</strong>al network<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> self-organizati<strong>on</strong> scenarios<br />

taking place in a neur<strong>on</strong>al network model equipped wi<str<strong>on</strong>g>th</str<strong>on</strong>g> activity-dependent synaptic<br />

plasticity [1]. We identify several distinct stati<strong>on</strong>ary states as well as parameter<br />

regi<strong>on</strong>s in which two or more states are unstable and <str<strong>on</strong>g>th</str<strong>on</strong>g>e system displays sp<strong>on</strong>taneous<br />

dynamic transiti<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>em. Such transiti<strong>on</strong>s take place recurrently,<br />

in various patterns, and involve abrupt reorganizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong>al c<strong>on</strong>nectivity<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> simultaneous appearance <str<strong>on</strong>g>of</str<strong>on</strong>g> new oscillatory behavior. For selected parameter<br />

regi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>e pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> transiti<strong>on</strong>s suggestively resembles stereotypical seizurelike<br />

events <str<strong>on</strong>g>th</str<strong>on</strong>g>at reproduce some important pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ophysiological features <str<strong>on</strong>g>of</str<strong>on</strong>g> epilepsy.<br />

These include: a pr<strong>on</strong>ounced peak in neur<strong>on</strong>al activity accompanied by hypersynchr<strong>on</strong>izati<strong>on</strong><br />

during <str<strong>on</strong>g>th</str<strong>on</strong>g>e events and l<strong>on</strong>g, irregular inter-event intervals. We also<br />

dem<strong>on</strong>strate transient "pre-seizure states", a feature which has been recently identified<br />

by n<strong>on</strong>linear EEG analysis in some forms <str<strong>on</strong>g>of</str<strong>on</strong>g> epilepsy [2]. Our model suggests<br />

a novel hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis for <str<strong>on</strong>g>th</str<strong>on</strong>g>e still poorly understood basic mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> epilepsy and<br />

seizure generati<strong>on</strong>. We discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological plausibility and bio-medical implicati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> our findings and outline some possible interpretati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

phase transiti<strong>on</strong>s and complex systems <str<strong>on</strong>g>th</str<strong>on</strong>g>eory.<br />

References.<br />

[1] Izhikevich EM, Polychr<strong>on</strong>izati<strong>on</strong>: Computati<strong>on</strong> Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Spikes, Neural Comput. (2006) 18:245-<br />

282.<br />

[2] Le van Quyen M et al., Characterizing Neurodynamic Changes Before Seizures, J Clin Neurophysiol.<br />

(2001) 18(3):191-208.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis I; Wednesday, June 29,<br />

08:30<br />

Amina Qutub<br />

Rice University<br />

e-mail: aminaq@rice.edu<br />

Characterizing Endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial Cell Behavior and Adaptati<strong>on</strong><br />

During Brain Capillary Regenerati<strong>on</strong> by Rule Oriented<br />

Modeling<br />

Cell-cell communicati<strong>on</strong> defines how blood vessels regenerate <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a process<br />

called angiogenesis. Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factors like vascular endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factor (VEGF)<br />

and brain-derived grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factor (BDNF) guide angiogenic sprouting in <str<strong>on</strong>g>th</str<strong>on</strong>g>e brain,<br />

in c<strong>on</strong>diti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> hypoxia, such as during a stroke or in brain cancer. Here, we<br />

present a computati<strong>on</strong>al strategy to characterize <str<strong>on</strong>g>th</str<strong>on</strong>g>e sequence and magnitude <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cell-cell interacti<strong>on</strong>s, allowing us to quantify how each endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cell behavior<br />

inhibits or augments each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er. We introduce a novel rule-oriented agent-based<br />

programming me<str<strong>on</strong>g>th</str<strong>on</strong>g>od to allow rapid testing and comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses<br />

in silico to in vitro angiogenic experiments. Results show <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tip<br />

and stalk endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells, and predict how migrati<strong>on</strong>, proliferati<strong>on</strong>, branching,<br />

el<strong>on</strong>gati<strong>on</strong> and quiescence states inhibit or enhance <strong>on</strong>e ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er to form capillary<br />

structures wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in an in vitro 3D matrix, leading to distinct capillary phenotypes<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> VEGF and BDNF. This quantitative understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> how cells<br />

move as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular stimuli, and form vessels, will be used to help<br />

guide small molecule drugs and tissue engineering <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies targeting <str<strong>on</strong>g>th</str<strong>on</strong>g>e brain<br />

microvasculature.<br />

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Multiscale modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong> kinetics in biology; Tuesday, June 28, 14:30<br />

Ovidiu Radulescu<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> M<strong>on</strong>tpellier 2<br />

e-mail: ovidiu.radulescu@univ-m<strong>on</strong>tp2.fr<br />

Guilherme Innocentini<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sao Paolo<br />

Timescales <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic gene expressi<strong>on</strong><br />

Gene expressi<strong>on</strong> exhibits a high degree <str<strong>on</strong>g>of</str<strong>on</strong>g> stochasticity when studied at <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

individual cells. Even in genetically identical cell populati<strong>on</strong>s exposed to a uniform<br />

envir<strong>on</strong>ment, gene activity levels and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir phenotypic c<strong>on</strong>sequences are subject to<br />

random fluctuati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at generate cell-to-cell variati<strong>on</strong>s and eventually lead to alternative<br />

cell fates. This stochastic noise in gene expressi<strong>on</strong> is a critical, biologically<br />

relevant property <str<strong>on</strong>g>of</str<strong>on</strong>g> genetic circuits in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> microbial and eukaryotic cells.<br />

Many studies underlined <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> network architecture and <str<strong>on</strong>g>of</str<strong>on</strong>g> feedback<br />

loops for shaping and c<strong>on</strong>trolling <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene expressi<strong>on</strong> noise. Here we defend<br />

a different point <str<strong>on</strong>g>of</str<strong>on</strong>g> view, according to which in many situati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>e order relati<strong>on</strong>s<br />

between different timescales <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e biochemical processes are determinant <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

expressi<strong>on</strong> fluctuati<strong>on</strong>s.<br />

In order to cope wi<str<strong>on</strong>g>th</str<strong>on</strong>g> network multi-scaleness we developed hybrid stochastic<br />

approaches (Crudu et al 2009). These me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods distinguish between molecular<br />

species according to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir abundances. Species in small amounts can be treated as<br />

discrete variables, whereas species in large amounts can be c<strong>on</strong>sidered c<strong>on</strong>tinuous.<br />

For computati<strong>on</strong>al ends, hybrid approaches can be used to simplify biochemical<br />

mechanisms, accelerate simulati<strong>on</strong> and facilitate model analysis.<br />

Hybrid stochastic approaches can also be used to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

multi-scaleness <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e expressi<strong>on</strong> noise in gene networks. We distinguish between<br />

two situati<strong>on</strong>s referred to as normal and inverted time hierarchies. The noise can<br />

be buffered by network feed-back in <str<strong>on</strong>g>th</str<strong>on</strong>g>e first situati<strong>on</strong>, whereas can have rich, <str<strong>on</strong>g>of</str<strong>on</strong>g>ten<br />

counterintuitive behaviour in <str<strong>on</strong>g>th</str<strong>on</strong>g>e latter.<br />

The <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical results are supported by recent experimental findings c<strong>on</strong>cerning<br />

stochastic noise in <str<strong>on</strong>g>th</str<strong>on</strong>g>e bacterium catabolite repressi<strong>on</strong> (Fergus<strong>on</strong> et al).<br />

References.<br />

[1] A.Crudu, A.Debussche, and O.Radulescu, BMC Systems Biology (2009) 3:89.<br />

[2] M.L. Fergus<strong>on</strong>, D. Le Coq, M. Jules, B. Chun, S. Aymerich, O. Radulescu, N. Declerck, C.A.<br />

Royer, submitted.<br />

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Populati<strong>on</strong> Genetics; Friday, July 1, 14:30<br />

Marina Rafajlovic<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg, SE-41296 Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg,<br />

Sweden<br />

e-mail: Marina.Rafajlovic@physics.gu.se<br />

Linkage disequilibrium in populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> variable size<br />

We c<strong>on</strong>sider neutral evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a large populati<strong>on</strong> subject to changes in its populati<strong>on</strong><br />

size to understand how <str<strong>on</strong>g>th</str<strong>on</strong>g>e covariance <str<strong>on</strong>g>of</str<strong>on</strong>g> gene-histories and linkage disequilibrium<br />

are influenced by such populati<strong>on</strong>-size fluctuati<strong>on</strong>s. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e coalescent<br />

approximati<strong>on</strong>, using <str<strong>on</strong>g>th</str<strong>on</strong>g>e approach employed by [2] and <str<strong>on</strong>g>th</str<strong>on</strong>g>e result <str<strong>on</strong>g>of</str<strong>on</strong>g> [3], we have<br />

obtained an exact expressi<strong>on</strong> (see [1]) for <str<strong>on</strong>g>th</str<strong>on</strong>g>e covariance <str<strong>on</strong>g>of</str<strong>on</strong>g> gene-histories in a populati<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a populati<strong>on</strong> size <str<strong>on</strong>g>th</str<strong>on</strong>g>at randomly jumps between two values. We show<br />

under which circumstances an effective-populati<strong>on</strong>-size approximati<strong>on</strong> is appropriate,<br />

and when it fails. In additi<strong>on</strong>, we identify a parameter regime where two-locus<br />

gene-history correlati<strong>on</strong>s are well described by a coalescent process wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multiple<br />

mergers.<br />

References.<br />

[1] Schaper, E., A. Erikss<strong>on</strong>, M. Rafajlovic, S. Sagitov and B. Mehlig. Linkage disequilibrium in<br />

populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> variable size. (unpublished).<br />

[2] Erikss<strong>on</strong>, A. and B. Mehlig, 2004. Gene-history correlati<strong>on</strong> and populati<strong>on</strong> structure. Phys.<br />

Biol. I: 220–228.<br />

[3] Erikss<strong>on</strong>, A., B. Mehlig, M. Rafajlovic and S. Sagitov, 2010. The total branch leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> sample<br />

genealogies in populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> variable size. Genetics 186: 601–611.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Nomenjanahary Alexia Raharinirina<br />

African Institute for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences(AIMS), 6 Melrose road<br />

Muizenberg, Cape Town<br />

e-mail: alexia@address<br />

Dr. Aziz Ouhinou<br />

AIMS, 6 Melrose road Muizenberg, Cape Town<br />

e-mail: aziz@aims.ac.za<br />

Dr. Lafras Uys<br />

AIMS, 6 Melrose road Muizenberg, Cape Town<br />

e-mail: lafras@aims.ac.za<br />

Flagellar dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e directi<strong>on</strong>al persistence for<br />

bacterial run and tumble chemotaxis<br />

Motivated by experimental data, we extend an existing individual based model for<br />

bacterial run and tumble chemotaxis to include <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e directi<strong>on</strong>al<br />

persistence <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> CW-rotating flagella. The model is built in two<br />

dimensi<strong>on</strong>al space for a fixed source <str<strong>on</strong>g>of</str<strong>on</strong>g> nutrient. We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e nutrient<br />

c<strong>on</strong>centrati<strong>on</strong> has a Gaussian distributi<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile. We measure <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> flagellar<br />

cooperativeness <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e chemotactic performance by <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bacterium to<br />

reach a favourable regi<strong>on</strong> and to stay in <str<strong>on</strong>g>th</str<strong>on</strong>g>at z<strong>on</strong>e. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore we analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

effect <str<strong>on</strong>g>of</str<strong>on</strong>g> varying <str<strong>on</strong>g>th</str<strong>on</strong>g>e directi<strong>on</strong>al persistence <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimality <str<strong>on</strong>g>of</str<strong>on</strong>g> run and tumble<br />

chemotaxis and compare <str<strong>on</strong>g>th</str<strong>on</strong>g>e obtained results wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ose found in o<str<strong>on</strong>g>th</str<strong>on</strong>g>er works.<br />

810

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ecosystems Dynamics; Tuesday, June 28, 17:00<br />

A. Ramanantoanina<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, Stellenbosch University, Private<br />

Bag XI, Matieland 7602, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Africa<br />

e-mail: ar@aims.ac.za<br />

A. Ouhinou<br />

African Institute for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, 6 Melrose Road, Muizenberg<br />

7945, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Africa<br />

e-mail: aziz@aims.ac.za<br />

C. Hui<br />

Center <str<strong>on</strong>g>of</str<strong>on</strong>g> Invasi<strong>on</strong> Biology, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Botany and Zoology, Private<br />

Bag XI, Matieland 7602, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Africa<br />

e-mail: chui@sun.ac.za<br />

A density-dependent diffusi<strong>on</strong> model for a two-phase<br />

invasi<strong>on</strong><br />

A break <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e slope between <str<strong>on</strong>g>th</str<strong>on</strong>g>e range expansi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial years <str<strong>on</strong>g>of</str<strong>on</strong>g> invasi<strong>on</strong><br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e later years has been observed for different species. We present an approach<br />

to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>is two-phase invasi<strong>on</strong> using a model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> n<strong>on</strong>-linear density-dependent<br />

diffusi<strong>on</strong>. We establish <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> a travelling wave soluti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model. We investigate also <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e density-dependent diffusi<strong>on</strong> <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e speed <str<strong>on</strong>g>of</str<strong>on</strong>g> species expansi<strong>on</strong> during <str<strong>on</strong>g>th</str<strong>on</strong>g>e two phases <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong>, and study <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

durati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> each phase.<br />

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Applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>negative Rad<strong>on</strong> measure spaces wi<str<strong>on</strong>g>th</str<strong>on</strong>g> metric structure<br />

to populati<strong>on</strong> dynamic models; Wednesday, June 29, 17:00<br />

Gael Raoul<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cambridge<br />

e-mail: g.raoul@damtp.cam.ac.uk<br />

Structured populati<strong>on</strong> models for evoluti<strong>on</strong><br />

We are interested in an integro-differential model <str<strong>on</strong>g>th</str<strong>on</strong>g>at describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

populati<strong>on</strong> structured wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to a c<strong>on</strong>tinuous trait. Those model are able<br />

to capture various biological phenomena, and in particular <str<strong>on</strong>g>th</str<strong>on</strong>g>e speciati<strong>on</strong> process,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at is <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> around a finite number <str<strong>on</strong>g>of</str<strong>on</strong>g> traits. We<br />

analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>is property, and relate it to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical tool used by <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical<br />

biologists. We are also able to analyse some cases pointed out by biologists, where<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong> phenomena does not occur.<br />

812

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Dynamics; Saturday, July 2, 11:00<br />

J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an Rault<br />

BIOCORE / INRIA sophia Antipolis FRANCE<br />

e-mail: j<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an.rault@inria.fr<br />

Eric Benoit<br />

Laboratoire de Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ématiques / Université de La Rochelle FRANCE<br />

e-mail: ebenoit@univ-lr.fr<br />

Equilibria and stability results for some zooplankt<strong>on</strong><br />

size-structured models<br />

Structured models are increasingly used in biological modelling, particularly to<br />

describe marine ecosystems, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals is str<strong>on</strong>gly dependant<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir size. To modelize zooplankt<strong>on</strong> community, we first have to describe<br />

how an individual <str<strong>on</strong>g>of</str<strong>on</strong>g> some size feeds, and <str<strong>on</strong>g>th</str<strong>on</strong>g>en how it uses <str<strong>on</strong>g>th</str<strong>on</strong>g>e acquired food to grow<br />

and reproduce (according to some dynamic energy budget in order to guarantee<br />

mass c<strong>on</strong>servati<strong>on</strong>). Since <str<strong>on</strong>g>th</str<strong>on</strong>g>e model includes cannibalism <str<strong>on</strong>g>th</str<strong>on</strong>g>roughout zooplankt<strong>on</strong><br />

populati<strong>on</strong>, we obtain a variant <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e well-known McKendrick-v<strong>on</strong> Foerster<br />

equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> integral terms which appear in grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, mortality and reproducti<strong>on</strong>.<br />

Such models are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten hard to analyse ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically. Never<str<strong>on</strong>g>th</str<strong>on</strong>g>eless, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some<br />

more hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cannibalism behavior, we can find equilibria <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

as fixed points <str<strong>on</strong>g>of</str<strong>on</strong>g> a functi<strong>on</strong> in a finite dimensi<strong>on</strong>al space. The linearized system<br />

around <str<strong>on</strong>g>th</str<strong>on</strong>g>e equilibrium provides us, <str<strong>on</strong>g>th</str<strong>on</strong>g>anks to <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> linear semigroup <str<strong>on</strong>g>th</str<strong>on</strong>g>eory,<br />

some local (un)stability results about <str<strong>on</strong>g>th</str<strong>on</strong>g>ese equilibria.<br />

Results obtained will be applied to a simple versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, which allows<br />

us to go fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er into <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis.<br />

Keywords : Size-structured models, Zooplankt<strong>on</strong> ecosystem, Cannibalism, Str<strong>on</strong>gly<br />

c<strong>on</strong>tinuous semigroups.<br />

References.<br />

[1] Maury O., Faugeras B., Shin Y.-J., et al, Modelling envir<strong>on</strong>mental effects <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e size-structured<br />

energy flow <str<strong>on</strong>g>th</str<strong>on</strong>g>rough marine ecosystems. Part 1: <str<strong>on</strong>g>th</str<strong>on</strong>g>e model. Progr. Oceanogr. 2007;74:479-499.<br />

[2] Farkas Jozsef Z. and Hagen Thomas, Stability and regularity results for a size-structured<br />

populati<strong>on</strong> model. J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Anal. Appl. 328 (2007) 119–136.<br />

[3] Benoît E. and Rochet M.J., A c<strong>on</strong>tinuous Model <str<strong>on</strong>g>of</str<strong>on</strong>g> Biomass Size Spectra Governed by Predati<strong>on</strong>,<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Effects <str<strong>on</strong>g>of</str<strong>on</strong>g> Fishing <strong>on</strong> Them. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology, Vol. 226(2004), pp<br />

9-21.<br />

[4] Vandromme P., Decadal evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ligurian sea zooplankt<strong>on</strong> linked to envir<strong>on</strong>mental fluctuati<strong>on</strong>s.<br />

From imaging systems to size-based models. PhD <str<strong>on</strong>g>th</str<strong>on</strong>g>esis (2010). http://www.obsvlfr.fr/LOV/ZooPart/ZooScan/<br />

813

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Mario Recker<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: mario.recker@zoo.ox.ac.uk<br />

Vector-borne diseases; Tuesday, June 28, 14:30<br />

Evoluti<strong>on</strong>ary determinants <str<strong>on</strong>g>of</str<strong>on</strong>g> antigenic variati<strong>on</strong> in malaria<br />

Many pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenic bacteria, fungi, and protozoa achieve chr<strong>on</strong>ic infecti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough an<br />

immune evasi<strong>on</strong> strategy known as antigenic variati<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e human malaria parasite<br />

Plasmodium falciparum, <str<strong>on</strong>g>th</str<strong>on</strong>g>is involves transcripti<strong>on</strong>al switching am<strong>on</strong>g members<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e var gene family, causing parasites wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different antigenic and phenotypic<br />

characteristics to appear at different times wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a populati<strong>on</strong>. Here we use a<br />

genome-wide approach to explore <str<strong>on</strong>g>th</str<strong>on</strong>g>is process in vitro wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a set <str<strong>on</strong>g>of</str<strong>on</strong>g> cl<strong>on</strong>ed parasite<br />

populati<strong>on</strong>s. Our analyses reveal a n<strong>on</strong>-random, highly structured switch pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way<br />

where an initially dominant transcript switches via a set <str<strong>on</strong>g>of</str<strong>on</strong>g> switch-intermediates<br />

ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er to a new dominant transcript, or back to <str<strong>on</strong>g>th</str<strong>on</strong>g>e original. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

specific pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way can arise <str<strong>on</strong>g>th</str<strong>on</strong>g>rough an evoluti<strong>on</strong>ary c<strong>on</strong>flict in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen<br />

has to optimise between safeguarding its limited antigenic repertoire and remaining<br />

capable <str<strong>on</strong>g>of</str<strong>on</strong>g> establishing infecti<strong>on</strong>s in n<strong>on</strong>-naïve individuals. Our results <str<strong>on</strong>g>th</str<strong>on</strong>g>us dem<strong>on</strong>strate<br />

a crucial role for structured switching during <str<strong>on</strong>g>th</str<strong>on</strong>g>e early phases <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong>s<br />

and provide a unifying <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> antigenic variati<strong>on</strong> in P. falciparum malaria as a<br />

balanced process <str<strong>on</strong>g>of</str<strong>on</strong>g> parasite-intrinsic switching and immune-mediated selecti<strong>on</strong>.<br />

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From <strong>on</strong>e to many: Cell-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective, emergent behaviors<br />

in biology -II; Tuesday, June 28, 14:30<br />

Charles Reichhardt<br />

Los Alamos Nati<strong>on</strong>al Laboratory<br />

e-mail: charlesr@cnls.lanl.gov<br />

Guided Moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Individual and Collective Swimmers in<br />

Funnel Arrays<br />

We generalize a model <str<strong>on</strong>g>of</str<strong>on</strong>g> swimming bacteria in asymmetric arrays <str<strong>on</strong>g>of</str<strong>on</strong>g> obstacles [1]<br />

to include different rules <str<strong>on</strong>g>of</str<strong>on</strong>g> moti<strong>on</strong>, including various rules for collective behvaiors.<br />

For individual n<strong>on</strong>interacting swimmers, we observe guided moti<strong>on</strong> and rectificati<strong>on</strong><br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e asymmetric barriers when <str<strong>on</strong>g>th</str<strong>on</strong>g>e particles align wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e walls <str<strong>on</strong>g>th</str<strong>on</strong>g>ey c<strong>on</strong>tact, but<br />

we find no rectificati<strong>on</strong> if <str<strong>on</strong>g>th</str<strong>on</strong>g>e particles are reflected by <str<strong>on</strong>g>th</str<strong>on</strong>g>e walls or bounce <str<strong>on</strong>g>of</str<strong>on</strong>g>f <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

walls. For collectively interacting swimmers, it is possible for <str<strong>on</strong>g>th</str<strong>on</strong>g>e particles to form<br />

large swimming clumps <str<strong>on</strong>g>th</str<strong>on</strong>g>at can move against <str<strong>on</strong>g>th</str<strong>on</strong>g>e normal rectificati<strong>on</strong> directi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e asymmetric barrier array. In general, <str<strong>on</strong>g>th</str<strong>on</strong>g>e rectificati<strong>on</strong> by <str<strong>on</strong>g>th</str<strong>on</strong>g>e barriers is lost<br />

when <str<strong>on</strong>g>th</str<strong>on</strong>g>e leng<str<strong>on</strong>g>th</str<strong>on</strong>g> scale <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e swarms <str<strong>on</strong>g>of</str<strong>on</strong>g> collectively moving particles is significantly<br />

larger <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e leng<str<strong>on</strong>g>th</str<strong>on</strong>g> scale <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e funnel shaped barriers. A particle swarm can<br />

become trapped inside a funnel; however, individual strings <str<strong>on</strong>g>of</str<strong>on</strong>g> particles <str<strong>on</strong>g>th</str<strong>on</strong>g>at follow<br />

each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er can escape from <str<strong>on</strong>g>th</str<strong>on</strong>g>e trap and move against <str<strong>on</strong>g>th</str<strong>on</strong>g>e funnel directi<strong>on</strong>. [1] M.B.<br />

Wan, C.J. Ols<strong>on</strong> Reichhardt, Z. Nussinov, and C. Reichhardt, Phys. Rev. Lett.<br />

101, 018102 (2008).<br />

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Mechanical Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Movement and Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cells and Tissues I;<br />

Wednesday, June 29, 14:30<br />

Katarzyna Rejniak<br />

M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Research Institute<br />

e-mail: Kasia.Rejniak@m<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt.org<br />

Forcing <str<strong>on</strong>g>th</str<strong>on</strong>g>e way to metastasis: mechanical interacti<strong>on</strong>s<br />

between endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial and circulating tumor cells<br />

Metastasis to distant organs is an ominous feature <str<strong>on</strong>g>of</str<strong>on</strong>g> most malignant tumors, and it<br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>e major cause <str<strong>on</strong>g>of</str<strong>on</strong>g> mortality. However, no more <str<strong>on</strong>g>th</str<strong>on</strong>g>an 0.01% <str<strong>on</strong>g>of</str<strong>on</strong>g> circulating tumor<br />

cells is able to wi<str<strong>on</strong>g>th</str<strong>on</strong>g>stand all steps <str<strong>on</strong>g>of</str<strong>on</strong>g> a metastatic cascade, such as an escape from<br />

primary tumor mass into <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood stream, circulati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood flow and<br />

extravasati<strong>on</strong> into <str<strong>on</strong>g>th</str<strong>on</strong>g>e new site <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be subsequently col<strong>on</strong>ized. The process <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

tumor cells extravasati<strong>on</strong>, i.e., <str<strong>on</strong>g>th</str<strong>on</strong>g>eir ability to leave <str<strong>on</strong>g>th</str<strong>on</strong>g>e circulati<strong>on</strong> system under <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

physiological blood flow is still poorly understood. I will present a biomechanical<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> circulating tumor cells and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells forming<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e vascular wall. This model will be subsequently used to analyze various modes<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cell translocati<strong>on</strong> under <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood flow: from circulati<strong>on</strong> to rolling, to<br />

crawling, to transmigrati<strong>on</strong>.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Fluid-structure interacti<strong>on</strong> problems in biomechanics; Saturday, July 2, 08:30<br />

Katarzyna A. Rejniak<br />

M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Research Institute<br />

e-mail: Kasia.Rejniak@m<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt.org<br />

Interacti<strong>on</strong>s between interstitial fluid and tumor<br />

microenvir<strong>on</strong>ment in chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

Interstitial fluid, a soluti<strong>on</strong> filling <str<strong>on</strong>g>th</str<strong>on</strong>g>e space between stromal cells, provides a means<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> delivering various molecules (such as nutrients, oxygen or drugs) to <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells, as<br />

well as removal <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic waste. In tumorous tissues, <str<strong>on</strong>g>th</str<strong>on</strong>g>e transport <str<strong>on</strong>g>of</str<strong>on</strong>g> anticancer<br />

drugs is moderated by differences in interstitial fluid pressure <str<strong>on</strong>g>th</str<strong>on</strong>g>at varies in<br />

different tumors and at different tumor sides, as well as by changes in stromal tissue<br />

structure. I will discuss computati<strong>on</strong>al simulati<strong>on</strong>s showing how tumor tissue<br />

metabolic state (its oxygenati<strong>on</strong> and acidity) become modified due to acti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic drugs leading to <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor z<strong>on</strong>es wi<str<strong>on</strong>g>th</str<strong>on</strong>g> potentially<br />

drug-resistant cells and/or to tumor areas <str<strong>on</strong>g>th</str<strong>on</strong>g>at are not exposed to drugs at all.<br />

Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese phenomena can c<strong>on</strong>tribute to <str<strong>on</strong>g>th</str<strong>on</strong>g>e moderate clinical success <str<strong>on</strong>g>of</str<strong>on</strong>g> many<br />

anticancer drugs.<br />

817

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

From <strong>on</strong>e to many: Cell-based modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective, emergent behaviors<br />

in biology -I; Tuesday, June 28, 11:00<br />

Katarzyna A. Rejniak<br />

M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Research Institute<br />

e-mail: Kasia.Rejniak@m<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt.org<br />

C<strong>on</strong>tributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Individual cells to homeostatic balance and<br />

imbalance in epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elia<br />

Epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial tissues (simple or stratified) form multicellular systems <str<strong>on</strong>g>of</str<strong>on</strong>g> well defined<br />

topology and functi<strong>on</strong>. In order to maintain such a fine tissue microarchitecture<br />

individual cells must act collectively and resp<strong>on</strong>d to signals from <str<strong>on</strong>g>th</str<strong>on</strong>g>eir neighbors<br />

and from <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment. I will present a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model and computati<strong>on</strong>al<br />

simulati<strong>on</strong>s addressing <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> individual c<strong>on</strong>tributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells<br />

to tissue homeostatic balance during its development and turnover. In c<strong>on</strong>trast, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

disrupti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue structure is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e initiati<strong>on</strong> and progressi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> abnormal tissue states, such as tumors. Specific local cell-cell interacti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

can lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> abnormalities <strong>on</strong> tissue scale will be also discussed.<br />

818

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Informati<strong>on</strong>, human behaviour and infecti<strong>on</strong> c<strong>on</strong>trol; Saturday, July 2, 08:30<br />

Timo<str<strong>on</strong>g>th</str<strong>on</strong>g>y Reluga<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Pennsylvania State University, USA<br />

e-mail: treluga@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.psu.edu, http://www.ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.psu.edu/treluga<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Epidemiology and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ec<strong>on</strong>omics <str<strong>on</strong>g>of</str<strong>on</strong>g> Social<br />

Planning<br />

Over <str<strong>on</strong>g>th</str<strong>on</strong>g>e last 50 years, ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical biologists have developed a deep <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

infectious disease dynamics. Today, management problems are as much ec<strong>on</strong>omic<br />

and social as biological. We face a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> social, behavioral, and political challenges<br />

today in <str<strong>on</strong>g>th</str<strong>on</strong>g>e public-heal<str<strong>on</strong>g>th</str<strong>on</strong>g> management <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e last few<br />

years, a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> new modelling approaches including social networks, game <str<strong>on</strong>g>th</str<strong>on</strong>g>eory,<br />

informati<strong>on</strong> propagati<strong>on</strong> and explicit-behavioral models have been proposed as<br />

descripti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> how <str<strong>on</strong>g>th</str<strong>on</strong>g>ese ec<strong>on</strong>omic influences interact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e biology <str<strong>on</strong>g>of</str<strong>on</strong>g> disease<br />

transmissi<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, I will review some <str<strong>on</strong>g>of</str<strong>on</strong>g> recent work I’ve been involved<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> in game-<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretic ec<strong>on</strong>omics models <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious disease management, and<br />

menti<strong>on</strong>ing some open problems in <str<strong>on</strong>g>th</str<strong>on</strong>g>e field.<br />

819

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Structure and Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemical Reacti<strong>on</strong> Networks II; Tuesday, June<br />

28, 17:00<br />

Grzegorz A. Rempala<br />

Georgia Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Sciences University<br />

e-mail: grempala@mcg.edu<br />

Jaejik Kim<br />

Georgia Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Sciences University<br />

Statistical inference for reacti<strong>on</strong> c<strong>on</strong>stants in stochastic<br />

biochemical networks<br />

The problem <str<strong>on</strong>g>of</str<strong>on</strong>g> estimating values <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong> c<strong>on</strong>stants in biochemical networks if<br />

fundamental for any network rec<strong>on</strong>structi<strong>on</strong> from <str<strong>on</strong>g>th</str<strong>on</strong>g>e trajectory data. The talk<br />

will outline some recent developments in statistical inferential procedures for reacti<strong>on</strong><br />

c<strong>on</strong>stants in stochastic biochemical network models. We will especially focus<br />

<strong>on</strong> some newly proposed dynamical programming me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods, which are similar to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Viterbi-type imputati<strong>on</strong> algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms for hidden Markov chain and are especially<br />

suitable when observed trajectories c<strong>on</strong>tain missing data for some species. It will be<br />

shown how <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> dynamic programming principles allows for efficient inference<br />

via ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e Gibbs sampler or <str<strong>on</strong>g>th</str<strong>on</strong>g>e EM algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m and g <str<strong>on</strong>g>th</str<strong>on</strong>g>e so-called uniformizati<strong>on</strong><br />

representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a Markov jump process. The applicability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e inferential<br />

procedures will be illustrated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> data from <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>gitudinal mamalian genetic<br />

studies as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e US CDC data from <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>set <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e 2009 H1N1 flu pandemic<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e US<br />

820

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Wednesday, June 29, 11:00<br />

Sarunas Repsys<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Informatics, 24 Naugarduko, LT-03225<br />

Vilnius<br />

e-mail: sarunas.repsys1@mif.vu.lt<br />

Vladas Skakauskas<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Informatics, 24 Naugarduko, LT-03225<br />

Vilnius<br />

e-mail: vladas.skakauskas@maf.vu.lt<br />

A brood-parasites dynamics model<br />

We c<strong>on</strong>sider a Comm<strong>on</strong> Cuckoo dynamics deterministic model. It is a broodparasite<br />

which lays its egg in <str<strong>on</strong>g>th</str<strong>on</strong>g>e nest <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er bird species and use host individuals<br />

to raise its young. We present a Comm<strong>on</strong> Cuckoo and a host species dynamics<br />

deterministic model taking into account a discrete set <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g>fsprings and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir care.<br />

All individuals have pre-reproductive, reproductive, and post-reproductive age intervals.<br />

Individuals <str<strong>on</strong>g>of</str<strong>on</strong>g> reproductive age are divided into single and <str<strong>on</strong>g>th</str<strong>on</strong>g>ose who care<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> young <str<strong>on</strong>g>of</str<strong>on</strong>g>fsprings. All individuals <str<strong>on</strong>g>of</str<strong>on</strong>g> pre-reproductive age are divided into young<br />

(under maternal care) and juvenile classes. Juveniles can live wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out maternal care<br />

but cannot produce <str<strong>on</strong>g>th</str<strong>on</strong>g>eir <str<strong>on</strong>g>of</str<strong>on</strong>g>fsprings. It is assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at after <str<strong>on</strong>g>th</str<strong>on</strong>g>e dea<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> mo<str<strong>on</strong>g>th</str<strong>on</strong>g>er all<br />

her young <str<strong>on</strong>g>of</str<strong>on</strong>g>fsprings die. The model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> integro-partial differential equati<strong>on</strong>s<br />

subject to <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e integral type. Number <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese equati<strong>on</strong>s depends<br />

<strong>on</strong> a biologically possible maximal number <str<strong>on</strong>g>of</str<strong>on</strong>g> eggs laid by a hen <str<strong>on</strong>g>of</str<strong>on</strong>g> host species in<br />

a nest. Separable soluti<strong>on</strong>s and numerical results will be discussed.<br />

References.<br />

[1] V. Skakauskas, A <strong>on</strong>e-sex populati<strong>on</strong> dynamics model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> discrete set <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g>fsprings band child<br />

care, N<strong>on</strong>linear analysis: modelling and c<strong>on</strong>trol, 13(4) 525–552, 2008.<br />

[2] S. Repsys and V. Skakauskas, Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> a <strong>on</strong>e-sex age-structured populati<strong>on</strong> dynamics wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

child care, N<strong>on</strong>linear analysis: modelling and c<strong>on</strong>trol, 12(1) 77–94, 2007.<br />

821

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Jennifer Reynolds<br />

Heriot-Watt University<br />

e-mail: jjr6@hw.ac.uk<br />

Populati<strong>on</strong> Dynamics; Friday, July 1, 14:30<br />

The role <str<strong>on</strong>g>of</str<strong>on</strong>g> silica defences in driving vole populati<strong>on</strong> cycles<br />

As wi<str<strong>on</strong>g>th</str<strong>on</strong>g> many small mammals, vole populati<strong>on</strong>s are comm<strong>on</strong>ly characterized by<br />

multi-year cycles <str<strong>on</strong>g>of</str<strong>on</strong>g> abundance. Uncertainty remains over <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms underpinning<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese populati<strong>on</strong> cycles. One possible factor is <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

voles and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir food.<br />

Some grass species mount a delayed defensive resp<strong>on</strong>se to grazing by increasing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir rate <str<strong>on</strong>g>of</str<strong>on</strong>g> uptake and depositi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> silica. This induced resp<strong>on</strong>se occurs when<br />

herbivore populati<strong>on</strong>s are high. Elevated silica levels make <str<strong>on</strong>g>th</str<strong>on</strong>g>e grass a lower quality<br />

food for herbivores, leading to a reducti<strong>on</strong> in herbivore performance. When grazing<br />

impact is lessened, silica defences relax and plant quality recovers. This inducible<br />

defence may have an important role in driving cycles in some populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> voles.<br />

We have developed a delay differential equati<strong>on</strong> model to represent <str<strong>on</strong>g>th</str<strong>on</strong>g>is herbivoreplant<br />

interacti<strong>on</strong>. This has been parameterized using empirical data from a particular<br />

system, namely field voles (Microtus agrestis) and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir principal food species,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e grass Deschampsia caespitosa, in Kielder Forest in Nor<str<strong>on</strong>g>th</str<strong>on</strong>g>ern England. I will<br />

discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model, and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir implicati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

silica defences shape <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> cyclic vole populati<strong>on</strong>s.<br />

822

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Tuesday, June 28, 17:00<br />

Benjamin Ribba<br />

INRIA, project-team NUMED, Ecole Normale Supérieure de Ly<strong>on</strong>, 46<br />

allée d’Italie, Ly<strong>on</strong> cedex 07, France<br />

François Ducray<br />

Hospices Civils de Ly<strong>on</strong>, Hôpital Neurologique, Neuro-<strong>on</strong>cologie,Ly<strong>on</strong>,<br />

69003 France<br />

Evaluati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e antitumor effect <str<strong>on</strong>g>of</str<strong>on</strong>g> PCV chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy <strong>on</strong><br />

diffuse low-grade gliomas wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a l<strong>on</strong>gitudinal tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

inhibiti<strong>on</strong> model<br />

Objective: To develop a tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> inhibiti<strong>on</strong> (TGI) model able to describe<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> diffuse low-grade gliomas (LGGs) grow<str<strong>on</strong>g>th</str<strong>on</strong>g> dynamics after first-line<br />

PCV chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy and to use <str<strong>on</strong>g>th</str<strong>on</strong>g>is model as a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical tool to suggest potential<br />

improvements <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e PCV chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy regimen.<br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: The model was formulated as systems <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary differential equati<strong>on</strong>s<br />

distinguishing between two cell populati<strong>on</strong>s: <strong>on</strong>e proliferative treatmentsensitive<br />

cell populati<strong>on</strong> and <strong>on</strong>e quiescent treatment-resistant cell populati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

sp<strong>on</strong>taneously undergoes apoptosis. Model evaluati<strong>on</strong> was performed in a series <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

21 patients treated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> first-line PCV chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

mean tumor diameter had been previously assessed.<br />

Results: C<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> LGGs biology, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model estimated <str<strong>on</strong>g>th</str<strong>on</strong>g>at LGGs c<strong>on</strong>sist<br />

mostly <str<strong>on</strong>g>of</str<strong>on</strong>g> quiescent cells. Despite large inter-individual variability <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

correctly predicted individual tumor resp<strong>on</strong>se pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles in <str<strong>on</strong>g>th</str<strong>on</strong>g>e 21 patients. Unexpectedly,<br />

model simulati<strong>on</strong>s suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e 6 weeks interval between PCV cycles<br />

might be suboptimal and <str<strong>on</strong>g>th</str<strong>on</strong>g>at leng<str<strong>on</strong>g>th</str<strong>on</strong>g>ening <str<strong>on</strong>g>th</str<strong>on</strong>g>e time interval between cycles might<br />

significantly improve treatment efficacy.<br />

Interpretati<strong>on</strong>: Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at LGGs c<strong>on</strong>sist <str<strong>on</strong>g>of</str<strong>on</strong>g> proliferative<br />

treatment-sensitive cells and quiescent treatment-resistant cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at sp<strong>on</strong>taneously<br />

undergo apoptosis we propose a mixed-effect model <str<strong>on</strong>g>th</str<strong>on</strong>g>at accurately describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese tumors during and after PCV chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy. Model simulati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> different PCV schedules illustrate how <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach could possibly help<br />

designing more effective chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy regimens for LGGs.<br />

823

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics <str<strong>on</strong>g>of</str<strong>on</strong>g> liver: bridging molecular systems biology to<br />

virtual physiological human scale; Wednesday, June 29, 11:00<br />

Tim Ricken<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Duisburg-Essen<br />

e-mail: tim.ricken@uni-due.de<br />

Uta Dahmen<br />

University Hospital <str<strong>on</strong>g>of</str<strong>on</strong>g> Essen<br />

Olaf Dirsch<br />

German Heart Institute Berlin<br />

A biphasic Finitee-Element-Model for Sinusoidal Liver<br />

Perfusi<strong>on</strong> Remodeling<br />

Liver resecti<strong>on</strong> can lead to focal outflow obstructi<strong>on</strong> due to transecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> hepatic<br />

veins. Outflow obstructi<strong>on</strong> may cause additi<strong>on</strong>al damage to <str<strong>on</strong>g>th</str<strong>on</strong>g>e small remnant liver.<br />

Drainage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e obstructed territories is reestablished via dilatati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> sinusoids.<br />

Subsequently sinusoidal canals are formed draining <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood from <str<strong>on</strong>g>th</str<strong>on</strong>g>e obstructed<br />

territory to <str<strong>on</strong>g>th</str<strong>on</strong>g>e neighboring unobstructed territories. We raised <str<strong>on</strong>g>th</str<strong>on</strong>g>e phenomenological<br />

hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood pressure gradient is <str<strong>on</strong>g>th</str<strong>on</strong>g>e main driving force for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> sinusoidal vascular canals. Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> porous media we<br />

generated a biphasic mechanical model to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>is vascular remodeling process<br />

in relati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e variable pressure gradient. Therefore, we introduced a transverse<br />

isotropic permeability relati<strong>on</strong> as well as an evoluti<strong>on</strong>al optimizati<strong>on</strong> rule to describe<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship between pressure gradient and <str<strong>on</strong>g>th</str<strong>on</strong>g>e directi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sinusoidal blood<br />

flow in <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluid phase. As a next step, we developed a framework for <str<strong>on</strong>g>th</str<strong>on</strong>g>e calculati<strong>on</strong><br />

c<strong>on</strong>cept including <str<strong>on</strong>g>th</str<strong>on</strong>g>e representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e governing weak formulati<strong>on</strong>s.<br />

The governing equati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model are developed <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>sistent<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ermo-mechanical approach including <str<strong>on</strong>g>th</str<strong>on</strong>g>e momentum and mass balances <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

solid and fluid phases. The ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical c<strong>on</strong>cept describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e solid<br />

phases coupled by <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluid transport due to pressure development. The <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical<br />

formulati<strong>on</strong>s are implemented into <str<strong>on</strong>g>th</str<strong>on</strong>g>e finite element code FEAP. Then, we examined<br />

a representative numerical example wi<str<strong>on</strong>g>th</str<strong>on</strong>g> simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood flow under<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>diti<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e physiological situati<strong>on</strong> as well as after outflow obstructi<strong>on</strong>.<br />

We based our simulati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanical-induced remodeling. We<br />

incorporated <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluid directly into <str<strong>on</strong>g>th</str<strong>on</strong>g>e model as a mixture toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e solid.<br />

We hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esized <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e reorientati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sinusoidal flow and <str<strong>on</strong>g>th</str<strong>on</strong>g>e remodeling<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sinusoidal structure depends mainly <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluid pressure and <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluid pressure<br />

gradient caused by <str<strong>on</strong>g>th</str<strong>on</strong>g>e outflow obstructi<strong>on</strong>. We tested <str<strong>on</strong>g>th</str<strong>on</strong>g>is hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a<br />

numerical simulati<strong>on</strong> and compared <str<strong>on</strong>g>th</str<strong>on</strong>g>e results to <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental findings. As we<br />

did not implement liver resecti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model presented here, but<br />

c<strong>on</strong>centrated <strong>on</strong> focal outflow obstructi<strong>on</strong> <strong>on</strong>ly, liver grow<str<strong>on</strong>g>th</str<strong>on</strong>g> (=regenerati<strong>on</strong>) was<br />

not addressed. Doing so, we were able to reproduce numerically <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimentally<br />

observed process <str<strong>on</strong>g>of</str<strong>on</strong>g> reestablishing hepatic venous drainage via redirecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> blood<br />

flow and formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> new vascular structures in respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluid flow. The calculated<br />

results support <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e reorientati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> blood flow mainly<br />

depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pressure gradient. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er investigati<strong>on</strong>s are needed to determine<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e micromechanical influences <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reorientati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sinusoids.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Rachel Rider<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling, UK<br />

e-mail: rar@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.stir.ac.uk<br />

Andy Hoyle<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling, UK<br />

e-mail: ash@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.stir.ac.uk<br />

Rachel Norman<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stirling, UK<br />

e-mail: ran@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.stir.ac.uk<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Optimal C<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> Disease in Multihost System<br />

The majority <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e world’s pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens are generalist wi<str<strong>on</strong>g>th</str<strong>on</strong>g> approximately 80% <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

livestock diseases able to transmit between different species [1]. It is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore essential<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at any c<strong>on</strong>trol strategy takes into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is interacti<strong>on</strong><br />

to c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e full impact <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease. The two species apparent competiti<strong>on</strong><br />

model has been widely studied and well understood. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods developed<br />

by Greenman and Hoyle [2] <str<strong>on</strong>g>th</str<strong>on</strong>g>is model has been extended to include <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> distinct spatial groups. This metapopulati<strong>on</strong>-type approach allows us to<br />

c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e impacts <str<strong>on</strong>g>of</str<strong>on</strong>g> disease spread over a much wider scale and to account for<br />

changes in spatial distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> infected individuals due to c<strong>on</strong>trol. An increase<br />

in ranging behaviour has been observed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>European</str<strong>on</strong>g> Badger (Meles meles) in<br />

resp<strong>on</strong>se to culling as a me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g> bovine TB (Mycobacterium bovis) c<strong>on</strong>trol in<br />

England [3]. This model may be employed to provide a l<strong>on</strong>g term predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

effect <str<strong>on</strong>g>of</str<strong>on</strong>g> badger culling <strong>on</strong> a large scale and to optimise c<strong>on</strong>trol strategies to reduce<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> bovine TB from England.<br />

References.<br />

[1] Woolhouse, M.E.J., Taylor, L.H., Hayd<strong>on</strong>, D.T. Populati<strong>on</strong> biology <str<strong>on</strong>g>of</str<strong>on</strong>g> multihost pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens<br />

Science (2001) 292 1109-1112.<br />

[2] Greenman, J.V. and Hoyle, A. Exclusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> generalist pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens in multi-host communities<br />

American Naturalist (2008) 172 576-584.<br />

[3] ] Bourne F.J. Bovine TB: The Scientific Evidence Final report <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Independent Scientific<br />

Group <strong>on</strong> Cattle TB (2007)<br />

825

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis I; Wednesday, June 29,<br />

08:30<br />

Heiko Rieger, Michael Welter<br />

Theoretical Physics, Saarland University, D-66041 Saarbücken<br />

e-mail: h.rieger@mx.uni-saarland,de<br />

Blood vessel network remodeling during tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e help <str<strong>on</strong>g>of</str<strong>on</strong>g> a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical model <str<strong>on</strong>g>th</str<strong>on</strong>g>e process in which a growing tumor<br />

transforms a hierarchically organized arterio-venous blood vessel network into a<br />

tumor specific vasculature is analyzed. The determinants <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is remodeling process<br />

involve <str<strong>on</strong>g>th</str<strong>on</strong>g>e morphological and hydrodynamic properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial network,<br />

generati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> new vessels (sprouting angiogenesis), vessel dilati<strong>on</strong> (circumferential<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g>), blood flow correlated vessel regressi<strong>on</strong>, tumor cell proliferati<strong>on</strong> and<br />

dea<str<strong>on</strong>g>th</str<strong>on</strong>g>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e interdependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese processes via spatio-temporal changes <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

blood flow parameters, oxygen / nutrient supply and grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factor c<strong>on</strong>centrati<strong>on</strong><br />

fields. The emerging tumor vasculature is n<strong>on</strong>-hierarchical and compartmentalized<br />

into different z<strong>on</strong>es. It displays a complex geometry wi<str<strong>on</strong>g>th</str<strong>on</strong>g> necrotic z<strong>on</strong>es and "hot<br />

spots" <str<strong>on</strong>g>of</str<strong>on</strong>g> increased vascular density and blood flow <str<strong>on</strong>g>of</str<strong>on</strong>g> varying size. The origin <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese hot spots is discussed. The blood vessel network transports drug injecti<strong>on</strong>s<br />

efficiently, but <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interstitial fluid flow shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

drug is quickly washed out from <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor after extravasati<strong>on</strong>.<br />

826

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemiology, Eco-Epidemiology and Evoluti<strong>on</strong>; Saturday, July 2, 11:00<br />

Jordi Ripoll<br />

Departament d’Informàtica i Matemàtica Aplicada, Universitat de Gir<strong>on</strong>a,<br />

17071 Gir<strong>on</strong>a, Spain<br />

e-mail: jripoll@ima.udg.edu<br />

Eusebi Calle<br />

Institut d’Informàtica i Aplicaci<strong>on</strong>s, Universitat de Gir<strong>on</strong>a, 17071 Gir<strong>on</strong>a,<br />

Spain<br />

e-mail: eusebi@eia.udg.edu<br />

Marc Manzano<br />

Institut d’Informàtica i Aplicaci<strong>on</strong>s, Universitat de Gir<strong>on</strong>a, 17071 Gir<strong>on</strong>a,<br />

Spain<br />

e-mail: mmanzano@eia.udg.edu<br />

An epidemic model <strong>on</strong> computer networks<br />

We study failure spread scenarios in computer/communicati<strong>on</strong> networks. A general<br />

epidemic model <str<strong>on</strong>g>of</str<strong>on</strong>g> type Susceptible-Infected-Disabled is analyzed and takes into<br />

account two levels <str<strong>on</strong>g>of</str<strong>on</strong>g> failure caused by <str<strong>on</strong>g>th</str<strong>on</strong>g>e attack <str<strong>on</strong>g>of</str<strong>on</strong>g> a virus or a worm for instance.<br />

The first level takes place when <str<strong>on</strong>g>th</str<strong>on</strong>g>e failure can be repaired wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out disc<strong>on</strong>necting<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e node, preserving <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>necti<strong>on</strong>s passing <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>is node. The sec<strong>on</strong>d failure<br />

level involves <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e node must be replaced and, c<strong>on</strong>sequently, <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>necti<strong>on</strong>s<br />

are dropped.<br />

The dynamic process is given by a Markov chain in c<strong>on</strong>tinuous time according<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> and recovery processes. Several results <strong>on</strong> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> types <str<strong>on</strong>g>of</str<strong>on</strong>g> steady<br />

states, disease-free and endemic, are given and an epidemic <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold is stated.<br />

Here <str<strong>on</strong>g>th</str<strong>on</strong>g>e network features are summarized by <str<strong>on</strong>g>th</str<strong>on</strong>g>e largest eigenvalue <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e weighted<br />

adjacency matrix <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network.<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, a sec<strong>on</strong>d model is presented according to <str<strong>on</strong>g>th</str<strong>on</strong>g>e heterogeneous<br />

mean-field approach. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is case, <str<strong>on</strong>g>th</str<strong>on</strong>g>e network features are given by bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e node<br />

degree distributi<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>al probabilities (i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>necti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

neighbours <str<strong>on</strong>g>of</str<strong>on</strong>g> each node).<br />

We have carried out several stochastic simulati<strong>on</strong>s using different network<br />

topologies (e.g. scale-free generated via Barabási-Albert, random generated via<br />

Erdős-Rényi, homogeneous, ...). Finally, a complete-parameter comparis<strong>on</strong> is performed<br />

in order to evaluate <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical approaches presented.<br />

References.<br />

[1] E. Calle, J. Ripoll, J. Segovia, P. Vilà and M. Manzano, A Multiple Failure Propagati<strong>on</strong> Model<br />

in GMPLS-based Networks, IEEE Network, 24(6):17–22, 2010.<br />

[2] D. Juher, J. Ripoll and J. Saldaña, Analysis and M<strong>on</strong>te Carlo simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> a model for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases in heterogeneous metapopulati<strong>on</strong>s, Phys. Rev. E 80, 041920<br />

(2009).<br />

[3] T. Kostova, Interplay <str<strong>on</strong>g>of</str<strong>on</strong>g> node c<strong>on</strong>nectivity and epidemic rates in <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemic<br />

networks, J. Difference Equ. Appl. 15, no. 4, 415–428 (2009).<br />

[4] O. Diekmann and J.A.P. Heesterbeek, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical epidemiology <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases. Model<br />

building, analysis and interpretati<strong>on</strong>. Wiley Series in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Computati<strong>on</strong>al Biology.<br />

John Wiley & S<strong>on</strong>s, Ltd., Chichester, 2000.<br />

[5] P. Van Mieghem, J. Omic and R. Kooij, Virus spread in networks, IEEE/ACM Trans. Netw.<br />

17, 1–14 (2009)<br />

827

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Regulatory Networks; Tuesday, June 28, 17:00<br />

E. S. Roberts<br />

Randall Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cell and Molecular Biophysics,<br />

King’s College L<strong>on</strong>d<strong>on</strong><br />

e-mail: ekaterina.roberts@kcl.ac.uk<br />

A. C. C. Coolen<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics,<br />

King’s College L<strong>on</strong>d<strong>on</strong><br />

e-mail: t<strong>on</strong>.coolen@kcl.ac.uk<br />

T. Schlitt<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical and Molecular Genetics,<br />

King’s College L<strong>on</strong>d<strong>on</strong><br />

e-mail: <str<strong>on</strong>g>th</str<strong>on</strong>g>omas.schlitt@kcl.ac.uk<br />

Tailored graph ensembles as proxies or null models for real<br />

networks<br />

There is a great demand, especially in cellular biology, for precise ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

approaches to studying <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed topology <str<strong>on</strong>g>of</str<strong>on</strong>g> networks. We generate new<br />

tools wi<str<strong>on</strong>g>th</str<strong>on</strong>g> which to quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic topological structure <str<strong>on</strong>g>of</str<strong>on</strong>g> large directed<br />

networks, via a statistical mechanical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>strained maximum entropy<br />

ensembles <str<strong>on</strong>g>of</str<strong>on</strong>g> directed random graphs. We look at prescribed joint distributi<strong>on</strong>s<br />

for in- and out-degrees and prescribed degree-degree correlati<strong>on</strong> functi<strong>on</strong>s. We follow<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e approach pi<strong>on</strong>eered in [1] for undirected networks. Applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

tools include: comparing networks; distinguishing between meaningful and random<br />

structural features; and, defining and generating tailored random graphs as null<br />

models. We calculate exact and explicit formulae for <str<strong>on</strong>g>th</str<strong>on</strong>g>e leading orders in <str<strong>on</strong>g>th</str<strong>on</strong>g>e system<br />

size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Shann<strong>on</strong> entropies and complexities <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese ensembles. The results<br />

are applied to data <strong>on</strong> gene regulati<strong>on</strong> networks.<br />

References.<br />

[1] Annibale A , Coolen A C C , Fernandes L P , Fraternali F and Kleinjung J, Tailored graph<br />

ensembles as proxies or null models for real networks I: tools for quantifying structure J. Phys.<br />

A, 42 (48):485001, (2009)<br />

[2] Roberts E S , Coolen A C C , and Schlitt T Tailored graph ensembles as proxies or null models<br />

for real networks II: results <strong>on</strong> directed graphs In preparati<strong>on</strong>.<br />

[3] Fernandes L P, Annibale A, Kleinjung J, Coolen A C C, and Fraternali F, Protein networks<br />

reveal detecti<strong>on</strong> bias and species c<strong>on</strong>sistency when analysed by informati<strong>on</strong>-<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretic me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

J. PLoS ONE, 5 :e12083, (2010).<br />

828

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Mick Roberts<br />

Massey University, Albany, New Zealand<br />

e-mail: m.g.roberts@massey.ac.nz<br />

Epidemic models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> uncertainty<br />

Epidemics; Tuesday, June 28, 14:30<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e first quantities to be estimated at <str<strong>on</strong>g>th</str<strong>on</strong>g>e start <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic is <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic<br />

reproducti<strong>on</strong> number, R0. The progress <str<strong>on</strong>g>of</str<strong>on</strong>g> an epidemic is sensitive to <str<strong>on</strong>g>th</str<strong>on</strong>g>e value <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

R0, hence we need me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for exploring <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> uncertainty in <str<strong>on</strong>g>th</str<strong>on</strong>g>e estimate.<br />

I will analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>e Kermack-McKendrick model, and its special case <str<strong>on</strong>g>th</str<strong>on</strong>g>e SIR<br />

model, by expanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e state variable in or<str<strong>on</strong>g>th</str<strong>on</strong>g>og<strong>on</strong>al polynomials in uncertainty<br />

space. The resulting dynamical systems need <strong>on</strong>ly be solved <strong>on</strong>ce to produce a deterministic<br />

stochastic soluti<strong>on</strong>. The me<str<strong>on</strong>g>th</str<strong>on</strong>g>od will be applied to data from <str<strong>on</strong>g>th</str<strong>on</strong>g>e New<br />

Zealand epidemic <str<strong>on</strong>g>of</str<strong>on</strong>g> H1N1 influenza in 2009, to dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> uncertainty<br />

when making projecti<strong>on</strong>s based <strong>on</strong> a limited amount <str<strong>on</strong>g>of</str<strong>on</strong>g> data.<br />

829

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Cancer; Wednesday, June 29, 08:30<br />

Mark Roberts<strong>on</strong>-Tessi<br />

Integrated Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Oncology, M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center, Tampa,<br />

FL<br />

e-mail: mark.roberts<strong>on</strong>tessi@m<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt.org<br />

R. J. Gillies<br />

M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center, Tampa, FL<br />

R. A. Gatenby<br />

M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center, Tampa, FL<br />

A. R. A. Anders<strong>on</strong><br />

M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center, Tampa, FL<br />

Metabolism: Integrating cellular and microenvir<strong>on</strong>mental<br />

heterogeneity to drive tumor progressi<strong>on</strong><br />

Clinical and experimental evidence increasingly suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at cellular and microenvir<strong>on</strong>mental<br />

heterogeneity plays a significant role in tumor progressi<strong>on</strong> and resp<strong>on</strong>se<br />

to treatment. Z<strong>on</strong>es <str<strong>on</strong>g>of</str<strong>on</strong>g> hypoxia, acidosis, and necrosis in <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor and surrounding<br />

tissue can exert selecti<strong>on</strong> pressure <strong>on</strong> a dynamic heterogeneous tumor populati<strong>on</strong>,<br />

driving <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> increasingly aggressive phenotypes. Critically, cellular<br />

metabolism acts as a key integrator between <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cellular and microenvir<strong>on</strong>mental<br />

comp<strong>on</strong>ents. In order to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex interplay between <str<strong>on</strong>g>th</str<strong>on</strong>g>ese elements,<br />

we have developed a hybrid multi-scale ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in a<br />

vascularized tissue. Cellular behavior, including proliferati<strong>on</strong>, migrati<strong>on</strong>, dea<str<strong>on</strong>g>th</str<strong>on</strong>g> and<br />

signaling, are driven by microenvir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s, mediated <str<strong>on</strong>g>th</str<strong>on</strong>g>rough cellular<br />

metabolism. A range <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor phenotypes emerges due to selecti<strong>on</strong> by <str<strong>on</strong>g>th</str<strong>on</strong>g>e heterogeneous<br />

microenvir<strong>on</strong>ment. The resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> a tumor to treatment depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

presence <str<strong>on</strong>g>of</str<strong>on</strong>g> different tumor phenotypes, as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e local c<strong>on</strong>diti<strong>on</strong>s. By tracking<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e multiple routes <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor progressi<strong>on</strong>, we use <str<strong>on</strong>g>th</str<strong>on</strong>g>e model to predict optimal<br />

treatment strategies <str<strong>on</strong>g>th</str<strong>on</strong>g>at can block <str<strong>on</strong>g>th</str<strong>on</strong>g>e most malignant routes.<br />

830

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Undergraduate Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Educati<strong>on</strong> Bey<strong>on</strong>d BIO 2010 (Part I);<br />

Wednesday, June 29, 14:30<br />

Raina Robeva<br />

Sweet Briar College<br />

e-mail: robeva@sbc.edu<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> Horm<strong>on</strong>e Network<br />

Horm<strong>on</strong>e secreti<strong>on</strong> patterns are determined by <str<strong>on</strong>g>th</str<strong>on</strong>g>e frequency <str<strong>on</strong>g>of</str<strong>on</strong>g> secreti<strong>on</strong> events,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e amount secreted, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> time <str<strong>on</strong>g>th</str<strong>on</strong>g>e secreti<strong>on</strong> event lasts. They encode<br />

messages for <str<strong>on</strong>g>th</str<strong>on</strong>g>e target cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trol vital physiological processes, and<br />

an alterati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a secreti<strong>on</strong> pattern may impede <strong>on</strong>e or more <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese processes.<br />

Understanding horm<strong>on</strong>e secreti<strong>on</strong> and developing <str<strong>on</strong>g>th</str<strong>on</strong>g>e capability to recognize bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

normal and pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ological patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> horm<strong>on</strong>e producti<strong>on</strong> is <str<strong>on</strong>g>of</str<strong>on</strong>g> utmost importance<br />

for establishing medical diagnoses, initiating treatment, and assessing <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> treatment. It is generally impossible to collect data directly from <str<strong>on</strong>g>th</str<strong>on</strong>g>e endocrine<br />

glands, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e horm<strong>on</strong>es are secreted. Secreti<strong>on</strong> patterns have to be inferred<br />

from horm<strong>on</strong>e c<strong>on</strong>centrati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood where distorti<strong>on</strong>s, due to binding, excreti<strong>on</strong><br />

and/or biotransformati<strong>on</strong>, begin immediately after <str<strong>on</strong>g>th</str<strong>on</strong>g>e horm<strong>on</strong>es enter <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

bloodstream. Thus, ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e horm<strong>on</strong>e network interacti<strong>on</strong>s and<br />

c<strong>on</strong>trol mechanisms play a critical role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> endocrine osciallati<strong>on</strong>s.<br />

The talk will outline a model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> horm<strong>on</strong>e network and a related<br />

undergraduate project appropriate for use in calculus-based courses.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bridging Time Scales in Biological Sciences; Saturday, July 2, 14:30<br />

Susanna Röblitz<br />

Zuse Institute Berlin (ZIB)<br />

e-mail: susanna.roeblitz@zib.de<br />

Rare events in chemical reacti<strong>on</strong> systems<br />

Chemical kinetics can usually be described by a deterministic system <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary<br />

differential equati<strong>on</strong>s. However, when <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> certain species become<br />

small, stochastic fluctuati<strong>on</strong>s play an important role, which can be modeled by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

chemical master equati<strong>on</strong> (CME). For some systems, <str<strong>on</strong>g>th</str<strong>on</strong>g>e steady state soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e CME is a multimodal distributi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> small transiti<strong>on</strong> rates (rare events), a<br />

situati<strong>on</strong> comparable to metastable molecular c<strong>on</strong>formati<strong>on</strong>s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we will<br />

present a mesh-free discrete Galerkin me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e CME, which<br />

allows for an efficient computati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> transiti<strong>on</strong> rates. In particular, we will discuss<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e future potential <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> endocrinological networks.<br />

832

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Tuesday, June 28, 14:30<br />

Russell Rockne<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Washingt<strong>on</strong> Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, Department <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

e-mail: rockne@uw.edu<br />

Susan Massey<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Washingt<strong>on</strong> Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

Maciej M. Mrugala<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Washingt<strong>on</strong> Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Neurology<br />

Alexandar R. A. Anders<strong>on</strong><br />

M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center Integrative Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Oncology<br />

Kristin R. Swans<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Washingt<strong>on</strong> Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ology, Department <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

Resp<strong>on</strong>se to anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy in human brain tumors:<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microenvir<strong>on</strong>ment and heterogeneity<br />

Background: Gliomas are diffuse and invasive primary brain tumors <str<strong>on</strong>g>th</str<strong>on</strong>g>at are notoriously<br />

difficult to treat and uniformly fatal. Angiogenesis is <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> neovascularizati<strong>on</strong><br />

and is a hall mark <str<strong>on</strong>g>of</str<strong>on</strong>g> glioblastoma, which are c<strong>on</strong>sidered am<strong>on</strong>gst <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

most angiogenic <str<strong>on</strong>g>of</str<strong>on</strong>g> tumors. This suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at interacti<strong>on</strong>s between glioma cells<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e cascade <str<strong>on</strong>g>of</str<strong>on</strong>g> biological events leading to tumor-induced neoangiogenesis play<br />

an important role in aggressive tumor formati<strong>on</strong> and progressi<strong>on</strong>.<br />

Anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies have been used in <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> gliomas wi<str<strong>on</strong>g>th</str<strong>on</strong>g> spurious<br />

results ranging from no apparent resp<strong>on</strong>se to significant imaging improvement<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> extremely diffuse patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor recurrence. The clinical task <str<strong>on</strong>g>of</str<strong>on</strong>g> assessing<br />

a patients resp<strong>on</strong>se to brain tumor <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy is difficult, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e topic <str<strong>on</strong>g>of</str<strong>on</strong>g> much current<br />

debate. Paradoxically, anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies likely increase <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficiency<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tumor vasculature <str<strong>on</strong>g>th</str<strong>on</strong>g>rough normalizati<strong>on</strong>, leading to a resoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> abnormality<br />

<strong>on</strong> imaging, while at <str<strong>on</strong>g>th</str<strong>on</strong>g>e same time increasing <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumors invasive phenotype and<br />

actually promote ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an hinder tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. As a result, resp<strong>on</strong>se to antiangiogenic<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapies is inadequately assessed by current imaging techniques but<br />

may be interpretable by multi-modality approaches combined wi<str<strong>on</strong>g>th</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

modeling.<br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: Much <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e difficulty in improving <str<strong>on</strong>g>th</str<strong>on</strong>g>e outcomes <str<strong>on</strong>g>of</str<strong>on</strong>g> patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

gliomas lies wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e extensive invasive potential and incredible phenotypic heterogeneity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese tumors. To quantitatively explore <str<strong>on</strong>g>th</str<strong>on</strong>g>ese tumor-microenvir<strong>on</strong>ment<br />

interacti<strong>on</strong>s, we extend our previous experience wi<str<strong>on</strong>g>th</str<strong>on</strong>g> biologically-based ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

models for glioma grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and invasi<strong>on</strong> to explicitly incorporate <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> normoxic glioma cells, hypoxic glioma cells, vascular endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells, diffusible<br />

angiogenic factors and <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> necrosis, hallmarks <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e histological diagnosis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> glioma and investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e role and effects <str<strong>on</strong>g>of</str<strong>on</strong>g> anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies in<br />

silico.<br />

Results: Using in silico experimentati<strong>on</strong>, we find <str<strong>on</strong>g>th</str<strong>on</strong>g>at anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies<br />

drastically decrease <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypoxic phenotype and promote <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasive phenotype.<br />

However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e degree and characterizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> resp<strong>on</strong>se to anti-angiogenic <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies<br />

depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative extent <str<strong>on</strong>g>of</str<strong>on</strong>g> invasi<strong>on</strong> and proliferati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor, and can<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

vary from <strong>on</strong>e patient to <str<strong>on</strong>g>th</str<strong>on</strong>g>e next. Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese effects vary across histologic<br />

grades and may promote malignant progressi<strong>on</strong> from low to higher grades. These<br />

results suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at a combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies must be used if anti-angiogenic<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapies are to be effective in human gliomas.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modelling dengue fever epidemiology; Saturday, July 2, 08:30<br />

Helena S<str<strong>on</strong>g>of</str<strong>on</strong>g>ia Rodrigues<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Business Studies - Viana do Castelo Polytechnic Institute<br />

e-mail: s<str<strong>on</strong>g>of</str<strong>on</strong>g>iarodrigues@esce.ipvc.pt<br />

M. Teresa T. M<strong>on</strong>teiro<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Producti<strong>on</strong> and Systems, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Minho<br />

e-mail: tm@dps.uminho.pt<br />

Delfim F. M. Torres<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Aveiro, Portugal<br />

e-mail: delfim@ua.pt<br />

Simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a dengue vaccine<br />

Dengue is a vector-borne disease. It is nowadays endemic in more <str<strong>on</strong>g>th</str<strong>on</strong>g>an <strong>on</strong>e<br />

hundred countries, predominantly in tropical and subtropical areas. Up to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

moment, <str<strong>on</strong>g>th</str<strong>on</strong>g>e effectiveness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e programs for vector c<strong>on</strong>trol is low and, unfortunately,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ere is no specific effective treatment for dengue. For recent ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

investigati<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e subject, we refer to [1, 2] and references <str<strong>on</strong>g>th</str<strong>on</strong>g>erein.<br />

There are no commercially available dengue clinical cures or vaccine, but efforts<br />

are underway to develop <strong>on</strong>e [3]. So far, <str<strong>on</strong>g>th</str<strong>on</strong>g>e difficulties in elaborating a vaccine<br />

stemmed from <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e vaccine must protect simultaneously against <str<strong>on</strong>g>th</str<strong>on</strong>g>e four<br />

serotypes <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue. This is a difficult but crucial c<strong>on</strong>straint, because protecti<strong>on</strong><br />

against <strong>on</strong>ly <strong>on</strong>e or two dengue viruses could actually increase <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk <str<strong>on</strong>g>of</str<strong>on</strong>g> Dengue<br />

Haemorrhagic Fever. The populati<strong>on</strong> effect <str<strong>on</strong>g>of</str<strong>on</strong>g> a vaccinati<strong>on</strong> programme may be<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ought <str<strong>on</strong>g>of</str<strong>on</strong>g> as <str<strong>on</strong>g>th</str<strong>on</strong>g>e collective impact <str<strong>on</strong>g>of</str<strong>on</strong>g> individual vaccinati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

infecti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>at populati<strong>on</strong>. While direct individual protecti<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>e major focus<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> mass vaccinati<strong>on</strong> programmes, populati<strong>on</strong> effects also c<strong>on</strong>tribute indirectly to<br />

individual protecti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough herd immunity, providing protecti<strong>on</strong> for unprotected<br />

individuals.<br />

We present a SVIR-ASI epidemiological model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e human and mosquito<br />

populati<strong>on</strong>s, respectively. It is c<strong>on</strong>sidered an imperfect vaccine, where a proporti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> is vaccinated. Some simulati<strong>on</strong>s, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different levels <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccine efficacy,<br />

are studied. It is shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficacy <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vaccine has a prep<strong>on</strong>derant<br />

role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e reducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease.<br />

References.<br />

[1] H. S. Rodrigues, M. T. T. M<strong>on</strong>teiro and D. F. M. Torres, Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue epidemics when<br />

using optimal c<strong>on</strong>trol, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Comput. Modelling 52 (2010), no. 9-10, 1667–1673.<br />

[2] H. S. Rodrigues, M. T. T. M<strong>on</strong>teiro, D. F. M. Torres and A. Zinober, Dengue disease, basic<br />

reproducti<strong>on</strong> number and c<strong>on</strong>trol, Int. J. Comput. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. (2011), in press.<br />

[3] WHO, Immuniological correlates <str<strong>on</strong>g>of</str<strong>on</strong>g> protecti<strong>on</strong> induced by dengue vaccines, Vaccine 25 (2007),<br />

4130–4139.<br />

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Cancer; Friday, July 1, 14:30<br />

Joanna M. Rodríguez Chrobak<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Castilla - La Mancha, Avda.<br />

Camilo José Cela No. 3, 13071 Ciudad Real, Spain<br />

e-mail: Joanna.Chrobak@uclm.es<br />

Henar Herrero<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Castilla - La Mancha, Avda.<br />

Camilo José Cela No. 3, 13071 Ciudad Real, Spain<br />

e-mail: Henar.Herrero@uclm.es<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> lymphoma as a failure in<br />

maintanance <str<strong>on</strong>g>of</str<strong>on</strong>g> naïve T cell repertoire<br />

We introduce a stochastic model <str<strong>on</strong>g>of</str<strong>on</strong>g> lymphoma based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e competitive<br />

exclusi<strong>on</strong> between different cl<strong>on</strong>otypes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e naïve T<br />

cell repertoire [1,2]. Two cl<strong>on</strong>otypes <str<strong>on</strong>g>of</str<strong>on</strong>g> T cells compete wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er and wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>er cl<strong>on</strong>otypes for survival stimuli provided by pr<str<strong>on</strong>g>of</str<strong>on</strong>g>essi<strong>on</strong>al cells (APCs) [3,4]. We<br />

assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cl<strong>on</strong>otypes is normal and <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er is tumorous. We model<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e competiti<strong>on</strong> as a c<strong>on</strong>tinuous-time bivariate Markov process [5]. To model <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumorous cl<strong>on</strong>otype we introduce an augmented rate <str<strong>on</strong>g>of</str<strong>on</strong>g> influx <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

new naïve T cells, descendants <str<strong>on</strong>g>of</str<strong>on</strong>g> mutated stem cells, from <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ymus. We obtain<br />

a deterministic approximati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic model using Van Kampen’s large<br />

N expansi<strong>on</strong> technique [6] and analyse four cases <str<strong>on</strong>g>of</str<strong>on</strong>g> competiti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e two<br />

cl<strong>on</strong>otypes <str<strong>on</strong>g>of</str<strong>on</strong>g> T cells, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> analitically and numerically.<br />

We obtain two possible scenarios, depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e values <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters: ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> cl<strong>on</strong>otypes survive in <str<strong>on</strong>g>th</str<strong>on</strong>g>e repertoire or <str<strong>on</strong>g>th</str<strong>on</strong>g>e cl<strong>on</strong>otype <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e normal T cells<br />

becomes extinct, meanwhile <str<strong>on</strong>g>th</str<strong>on</strong>g>e cl<strong>on</strong>otype <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumorous T cells is maintained,<br />

after achieving some maximum level <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at if <str<strong>on</strong>g>th</str<strong>on</strong>g>e income <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

new T cells from <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ymus is augmented, <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumorous cl<strong>on</strong>otype, which<br />

is very competitive, would never be removed from <str<strong>on</strong>g>th</str<strong>on</strong>g>e repertoire; meanwhile <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

normal cl<strong>on</strong>otype could become extinct if it was not specialized enough to compete<br />

effectively for survival stimuli. This result supports <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>of</str<strong>on</strong>g> mutated<br />

stem cells as <str<strong>on</strong>g>th</str<strong>on</strong>g>e origin <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer, in particular lymphoma. Any <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cells might<br />

initiate an outbreak <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e illness, so as l<strong>on</strong>g as we do not entirely get rid <str<strong>on</strong>g>of</str<strong>on</strong>g> all <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

mutated stem cells, we can not successfully defeat lymphoma.<br />

References.<br />

[1] E. R. Stirk, C. Molina-París and H. A. van den Berg, Stochastic niche structure and diversity<br />

maintenance in <str<strong>on</strong>g>th</str<strong>on</strong>g>e T cell repertoire Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology 255 (2008) 237–249.<br />

[2] E. R. Stirk, G. Ly<str<strong>on</strong>g>th</str<strong>on</strong>g>e, H. A. van den Berg and C. Molina-París, Stochastic competitive<br />

exclusi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e naïve T cell repertoire Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology<br />

265 (2010) 396–410.<br />

[3] R. J.De Boer and A. S. Perels<strong>on</strong>, T cell repertoires and competitive exclusi<strong>on</strong> Journal <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Theoretical Biology 169 (1994) 375–390.<br />

[4] A. W. Goldra<str<strong>on</strong>g>th</str<strong>on</strong>g> and M. J. Bevan, Selecting and maintining a diverse t-cell repertoire Nature<br />

402 (1999) 255–262.<br />

[5] L. J. S. Allen, An introducti<strong>on</strong> to stochastic processes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> applicati<strong>on</strong>s to biology Prentice<br />

Hall (2003).<br />

[6] N. G. Van Kampen, Stochastic processes in physics and chemistry Nor<str<strong>on</strong>g>th</str<strong>on</strong>g>-Holland Pers<strong>on</strong>al<br />

Library (2007).<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Dynamics; Thursday, June 30, 11:30<br />

Roberto Rosà<br />

F<strong>on</strong>dazi<strong>on</strong>e Edmund Mach, San Michele all’Adige (TN) - ITALY<br />

e-mail: rosa@cealp.it<br />

Luca Bolz<strong>on</strong>i<br />

F<strong>on</strong>dazi<strong>on</strong>e Edmund Mach, San Michele all’Adige (TN) - ITALY<br />

Andrea Pugliese<br />

Dipartimento di Matematica, Universita’ di Trento, Povo (TN) - ITALY<br />

Fausta Rosso<br />

F<strong>on</strong>dazi<strong>on</strong>e Edmund Mach, San Michele all’Adige (TN) - ITALY<br />

Annapaola Rizzoli<br />

F<strong>on</strong>dazi<strong>on</strong>e Edmund Mach, San Michele all’Adige (TN) - ITALY<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> helmin<str<strong>on</strong>g>th</str<strong>on</strong>g> parasite <strong>on</strong> rock partridge<br />

populati<strong>on</strong> dynamics<br />

The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work was to explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> helmin<str<strong>on</strong>g>th</str<strong>on</strong>g> parasites <strong>on</strong> rock partridge<br />

(Alectoris graeca saxatilis) populati<strong>on</strong> dynamics in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Dolomitic Alps (nor<str<strong>on</strong>g>th</str<strong>on</strong>g>ern<br />

Italy). Specifically, we investigated <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e nematode parasite Ascaridia<br />

compar can drive populati<strong>on</strong> cycles in rock partridge dynamics. In order<br />

to support <str<strong>on</strong>g>th</str<strong>on</strong>g>is hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis, we compared <str<strong>on</strong>g>th</str<strong>on</strong>g>e predicti<strong>on</strong>s obtained from a hostmacroparasite<br />

interacti<strong>on</strong> model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multi-annual empirical data <str<strong>on</strong>g>of</str<strong>on</strong>g> A. compar<br />

infecti<strong>on</strong> in natural host populati<strong>on</strong>s. We estimated host demographic parameters<br />

from rock partridge census data, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e parasitological parameters from a<br />

series <str<strong>on</strong>g>of</str<strong>on</strong>g> experimental infecti<strong>on</strong>s in a rock partridge captive populati<strong>on</strong>. Our model<br />

predicts higher levels <str<strong>on</strong>g>of</str<strong>on</strong>g> A. compar infestati<strong>on</strong> for rock partridge populati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

a cyclic dynamics respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>ose wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a n<strong>on</strong>-cyclic dynamics. In additi<strong>on</strong>, for<br />

populati<strong>on</strong>s exhibiting cyclic dynamics, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model predicts a positive correlati<strong>on</strong><br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean parasite burden and <str<strong>on</strong>g>th</str<strong>on</strong>g>e leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> cycle period. Model predicti<strong>on</strong>s<br />

are well-supported by field data; in fact, a significant differences in parasite<br />

infecti<strong>on</strong> between cyclic and n<strong>on</strong> cyclic populati<strong>on</strong>s and wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in cyclic populati<strong>on</strong>s<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different oscillati<strong>on</strong> periods were observed. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese results, we<br />

c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at helmin<str<strong>on</strong>g>th</str<strong>on</strong>g> parasites can be a possible driver for rock partridge populati<strong>on</strong><br />

dynamics and must be c<strong>on</strong>sidered when planning c<strong>on</strong>servati<strong>on</strong> strategies <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is <str<strong>on</strong>g>th</str<strong>on</strong>g>reatened species.<br />

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Plants, grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and transport processes I; Tuesday, June 28, 11:00<br />

Anita Ro<str<strong>on</strong>g>th</str<strong>on</strong>g>-Nebelsick<br />

State Museum <str<strong>on</strong>g>of</str<strong>on</strong>g> Natural History Stuttgart, Rosenstein 1, D-70191<br />

Stuttgart<br />

e-mail: anita.ro<str<strong>on</strong>g>th</str<strong>on</strong>g>nebelsick@smns-bw.de<br />

Wilfried K<strong>on</strong>rad<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Tübingen, Institute for Geosciences, Sigwartstrasse 10,<br />

D-72070 Tübingen<br />

e-mail: wilfried.k<strong>on</strong>rad@uni-tuebingen.de<br />

Plant gas exchange: Theoretical c<strong>on</strong>siderati<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e level<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> single stomata<br />

Plant gas exchange: Theoretical c<strong>on</strong>siderati<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> single stomata<br />

Land plants require gas exchange between leaf interior and atmosphere to obtain<br />

sufficient amounts <str<strong>on</strong>g>of</str<strong>on</strong>g> CO2 for photosyn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis. Stomata, micropores <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e leaf<br />

surface, are <str<strong>on</strong>g>th</str<strong>on</strong>g>e gateways for plant gas exchange. The stomatal pore is formed by<br />

two guard cells whose shape change (caused by changing turgor) c<strong>on</strong>trols <str<strong>on</strong>g>th</str<strong>on</strong>g>e aperture<br />

wid<str<strong>on</strong>g>th</str<strong>on</strong>g>. This in turn c<strong>on</strong>trols stomatal c<strong>on</strong>ductance. Tight c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> stomatal<br />

c<strong>on</strong>ductance is necessary since diffusi<strong>on</strong>al CO2 influx <str<strong>on</strong>g>th</str<strong>on</strong>g>rough open stomata is accompanied<br />

by water vapour loss (= transpirati<strong>on</strong>). Besides stomatal pore area <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

is c<strong>on</strong>trolled by <str<strong>on</strong>g>th</str<strong>on</strong>g>e guard cells, <str<strong>on</strong>g>th</str<strong>on</strong>g>e actual stomatal c<strong>on</strong>ductance is dependent <strong>on</strong><br />

various o<str<strong>on</strong>g>th</str<strong>on</strong>g>er anatomical traits, such as stomatal density and dep<str<strong>on</strong>g>th</str<strong>on</strong>g> and shape <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e stomatal pore [1, 2].<br />

The entire diffusi<strong>on</strong> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way is, however, more complex in reality. In most<br />

cases, it is still unclear where evaporati<strong>on</strong> inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e leaf occurs. If cutinizati<strong>on</strong><br />

does not reach bey<strong>on</strong>d <str<strong>on</strong>g>th</str<strong>on</strong>g>e stomatal channel, i.e. if internal cuticles are absent, <str<strong>on</strong>g>th</str<strong>on</strong>g>en<br />

evaporati<strong>on</strong> should occur close to <str<strong>on</strong>g>th</str<strong>on</strong>g>e stomata [3, 4]. If internal cuticles are present,<br />

evaporating sites are seated more deeply wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e leaves. Shifting evaporati<strong>on</strong><br />

deeper into <str<strong>on</strong>g>th</str<strong>on</strong>g>e mesophyll by cutinizati<strong>on</strong> bey<strong>on</strong>d <str<strong>on</strong>g>th</str<strong>on</strong>g>e stomatal channel can lead<br />

to a substantial decrease in stomatal c<strong>on</strong>ductance for water vapour (wi<str<strong>on</strong>g>th</str<strong>on</strong>g> all o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

parameters c<strong>on</strong>stant) [4].<br />

Details <str<strong>on</strong>g>of</str<strong>on</strong>g> leaf internal diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> water vapour and CO2 are <str<strong>on</strong>g>of</str<strong>on</strong>g> interest, due<br />

to different aspects. For example, measurement <str<strong>on</strong>g>of</str<strong>on</strong>g> stomatal c<strong>on</strong>ductance for water<br />

vapour is used also for analyses <str<strong>on</strong>g>of</str<strong>on</strong>g> photosyn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis, implicitly assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>at diffusi<strong>on</strong><br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways <str<strong>on</strong>g>of</str<strong>on</strong>g> CO2 and water vapour are mostly identical. In ecophysiology, various<br />

modificati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> stomata are ascribed to adaptati<strong>on</strong>s to envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s.<br />

For example, arrangement <str<strong>on</strong>g>of</str<strong>on</strong>g> stomata in stomatal crypts, <str<strong>on</strong>g>th</str<strong>on</strong>g>at are depressi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

leaf surface in which stomata are seated, should restrict water loss. It is, however,<br />

questi<strong>on</strong>able whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>is really happens, or if o<str<strong>on</strong>g>th</str<strong>on</strong>g>er functi<strong>on</strong>al benefits may linked<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>ese kind <str<strong>on</strong>g>of</str<strong>on</strong>g> structures. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, variati<strong>on</strong>s in stomatal structure and/or<br />

arrangement add more parameters to <str<strong>on</strong>g>th</str<strong>on</strong>g>e stomatal pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way, <str<strong>on</strong>g>th</str<strong>on</strong>g>ereby altering <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

c<strong>on</strong>tributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>trollable stomatal channel to overall c<strong>on</strong>ductance.<br />

As a whole, important details <str<strong>on</strong>g>of</str<strong>on</strong>g> stomatal diffusi<strong>on</strong> are still not well understood.<br />

Analyzing gas diffusi<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> single stomata, and wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mesophyll,<br />

can c<strong>on</strong>tribute substantial informati<strong>on</strong> to various topics in ecophysiology and plant<br />

physiology.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

References.<br />

[1] J.-Y. Parlange and P. E. Wagg<strong>on</strong>er, Plant Physiology, 1970, 46, 337-342.<br />

[2] H. Kaiser, Plant, Cell and Envir<strong>on</strong>ment, 2009, 32, 1091-1098.<br />

[3] M. T. Tyree and P. Yianoulis, Annals <str<strong>on</strong>g>of</str<strong>on</strong>g> Botany, 1980, 46, 175-193.<br />

[4] A. Ro<str<strong>on</strong>g>th</str<strong>on</strong>g>-Nebelsick, Annals <str<strong>on</strong>g>of</str<strong>on</strong>g> Botany, 2007, 100, 23-32.<br />

839

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Elina Roto<br />

graduate student<br />

e-mail: elina.roto@helsinki.fi<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Unravelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> streptococcus<br />

pneum<strong>on</strong>iae wi<str<strong>on</strong>g>th</str<strong>on</strong>g> approximate bayesian computati<strong>on</strong><br />

Approximate Bayesian computati<strong>on</strong> (ABC) provides an appealing me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for c<strong>on</strong>necting<br />

stochastic models to observed data. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e help <str<strong>on</strong>g>of</str<strong>on</strong>g> ABC, it is possible<br />

to distinguish probabilistically, given <str<strong>on</strong>g>th</str<strong>on</strong>g>e data, between different model candidates,<br />

and finally learn <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> model parameters. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, having posterior<br />

distributi<strong>on</strong>s for models and model parameters, <strong>on</strong>e can calculate posterior<br />

means, and perform predicti<strong>on</strong>.<br />

Streprococcus pneum<strong>on</strong>iae is a bacteria col<strong>on</strong>izing especially children. After<br />

introducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccine against <str<strong>on</strong>g>th</str<strong>on</strong>g>e most comm<strong>on</strong> strains, what has been observed<br />

is a fast serotype replacement, after which <str<strong>on</strong>g>th</str<strong>on</strong>g>e prevalence <str<strong>on</strong>g>of</str<strong>on</strong>g> streptococcus pneum<strong>on</strong>ia<br />

strains in general remains unchanged. Large carriage studies from children<br />

were c<strong>on</strong>ducted during <str<strong>on</strong>g>th</str<strong>on</strong>g>ese years. To understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

streprococcus pneum<strong>on</strong>ia, as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed diversity and fast serotype replacement,<br />

we aim to c<strong>on</strong>duct ABC model selecti<strong>on</strong> and parameter learning. This<br />

could help to say whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>ere exists fittness differences between different strains,<br />

and what <str<strong>on</strong>g>th</str<strong>on</strong>g>e ultimate effects <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccinati<strong>on</strong> will be.<br />

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The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting cell systems: from intercellular interacti<strong>on</strong><br />

to tissue-level traits I; Wednesday, June 29, 14:30<br />

Robert Rovetti<br />

Loyola Marymount University<br />

e-mail: rrovetti@lmu.edu<br />

Periodicity, spatial correlati<strong>on</strong>s, and waves in a probabilistic<br />

lattice model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiac cell.<br />

Cardiac cells have a surprisingly complex internal architecture, and dynamic instabilities<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e calcium signaling wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>em may lead to ventricular fibrillati<strong>on</strong>,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e leading cause <str<strong>on</strong>g>of</str<strong>on</strong>g> sudden cardiac dea<str<strong>on</strong>g>th</str<strong>on</strong>g>. We study a system <str<strong>on</strong>g>of</str<strong>on</strong>g> locally-coupled<br />

stochastically-excitable elements in a 2D automata lattice <str<strong>on</strong>g>th</str<strong>on</strong>g>at replicates physiological<br />

features <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiac cell, including <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold excitati<strong>on</strong>, refractory period,<br />

global periodic forcing signal, and spatial nearest-neighbor interacti<strong>on</strong>s. We first<br />

derive a simple mean-field difference equati<strong>on</strong> which models <str<strong>on</strong>g>th</str<strong>on</strong>g>e expected excitati<strong>on</strong><br />

rate at each beat, and find c<strong>on</strong>diti<strong>on</strong>s under which it can undergo a bifurcati<strong>on</strong><br />

to period-2 behavior (mimicking <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ological c<strong>on</strong>diti<strong>on</strong> known as "alternans").<br />

Using a local structure approximati<strong>on</strong> to account for pairwise (and higher-order)<br />

correlati<strong>on</strong>, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>ese c<strong>on</strong>diti<strong>on</strong>s are dependent <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e neighborto-neighbor<br />

coupling, as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e geometry <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell itself. We finally c<strong>on</strong>sider<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tinuous-time case, which allows for cascading spatial interacti<strong>on</strong>s, resulting<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> excitati<strong>on</strong> waves.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Peter Rowat<br />

Institute for Neural Computati<strong>on</strong>, University <str<strong>on</strong>g>of</str<strong>on</strong>g> California San Diego,<br />

USA<br />

e-mail: prowat@ucsd.edu<br />

Priscilla Greenwood<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> British Columbia, Vancouver,<br />

BC, Canada<br />

Identificati<strong>on</strong> and c<strong>on</strong>tinuity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

burst-leng<str<strong>on</strong>g>th</str<strong>on</strong>g> and inter-spike-intervals in <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic<br />

Morris-Lecar neur<strong>on</strong><br />

Using <str<strong>on</strong>g>th</str<strong>on</strong>g>e Morris-Lecar model neur<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a type II parameter set and K+ channel<br />

noise, we investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e inter-spike interval distributi<strong>on</strong> as increasing levels <str<strong>on</strong>g>of</str<strong>on</strong>g> applied<br />

current drive <str<strong>on</strong>g>th</str<strong>on</strong>g>e model <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a sub-critical Hopf bifurcati<strong>on</strong>. Our goal was<br />

to provide a quantitative descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong>s associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> spiking as<br />

a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> applied current. The model generates bursty spiking behavior wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> random numbers <str<strong>on</strong>g>of</str<strong>on</strong>g> spikes (bursts) separated by inter-burst intervals<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> random leng<str<strong>on</strong>g>th</str<strong>on</strong>g>. This kind <str<strong>on</strong>g>of</str<strong>on</strong>g> spiking behavior is found in many places in <str<strong>on</strong>g>th</str<strong>on</strong>g>e nervous<br />

system, most notably, perhaps, in stuttering inhibitory interneur<strong>on</strong>s in cortex.<br />

Here we show several practical and inviting aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model, combining analysis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> estimati<strong>on</strong> based <strong>on</strong> simulati<strong>on</strong>s.<br />

We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameter <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e exp<strong>on</strong>ential tail <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ISI distributi<strong>on</strong> is in<br />

fact c<strong>on</strong>tinuous over <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire range <str<strong>on</strong>g>of</str<strong>on</strong>g> plausible applied current, regardless <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

bifurcati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase-portrait <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e spike<br />

sequence leng<str<strong>on</strong>g>th</str<strong>on</strong>g>, apparently studied for <str<strong>on</strong>g>th</str<strong>on</strong>g>e first time here, has a geometric distributi<strong>on</strong><br />

whose associated parameter is c<strong>on</strong>tinuous as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> applied current<br />

over <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire input range. Hence <str<strong>on</strong>g>th</str<strong>on</strong>g>is model is applicable over a much wider range<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> applied current <str<strong>on</strong>g>th</str<strong>on</strong>g>an has been <str<strong>on</strong>g>th</str<strong>on</strong>g>ought.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Piotr Przymus<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science, Nicolaus Copernicus<br />

University, Chopina 12/18, 87-100 Toruń, Poland<br />

e-mail: eror@mat.umk.pl,<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Rykaczewski<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science, Nicolaus Copernicus<br />

University, Chopina 12/18, 87-100 Toruń, Poland<br />

e-mail: mozgun@mat.umk.pl<br />

Extracti<strong>on</strong> and detecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> freshwater mussels behaviours,<br />

using wavelets and kernel me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

Some species <str<strong>on</strong>g>of</str<strong>on</strong>g> mussels are well-known bioindicators and may be used to create<br />

a Biological Early Warning System. Such systems use l<strong>on</strong>g-term observati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

mussels activity for m<strong>on</strong>itoring purposes. Yet, many <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese systems are based<br />

<strong>on</strong> statistical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods and do not use all <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential <str<strong>on</strong>g>th</str<strong>on</strong>g>at stays behind <str<strong>on</strong>g>th</str<strong>on</strong>g>e data<br />

derived from <str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong>s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e paper we propose an algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m based <strong>on</strong><br />

wavelets and kernel me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to detect behaviour events in <str<strong>on</strong>g>th</str<strong>on</strong>g>e collected data. It<br />

c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> raw data obtaining, pre-processing and feature extracti<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e preprocessing<br />

step, a high-pass filters and white de-noising were used. During <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

recogniti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> events wavelet packet was applied and <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>e data was averaged by<br />

kernel me<str<strong>on</strong>g>th</str<strong>on</strong>g>od. Our motivati<strong>on</strong> was to highlight <str<strong>on</strong>g>th</str<strong>on</strong>g>e multiple time scale properties<br />

and to exam <str<strong>on</strong>g>th</str<strong>on</strong>g>e possible c<strong>on</strong>necti<strong>on</strong>s between behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> zebra mussel and water<br />

state. Results show <str<strong>on</strong>g>th</str<strong>on</strong>g>at polluti<strong>on</strong> could be characterized by <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological signal<br />

generated by Dreissena polymorpha. Our study also showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at wavelet transforms<br />

could be powerful me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for probing <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical relati<strong>on</strong>ship between <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

signal and envir<strong>on</strong>ment variability.<br />

References.<br />

[asi00] J. T. Białasiewicz. Wavelets and Approximati<strong>on</strong>s (in polish “Falki i aproksymacje”).<br />

Wydawnictwo Naukowo Techniczne, Warszawa, 2000.<br />

[Bis06] Ch. M. Bishop. Pattern Recogniti<strong>on</strong> and Machine Learning. Springer, 2006.<br />

[Bor06] Jost Borcherding. Ten years <str<strong>on</strong>g>of</str<strong>on</strong>g> practical experience wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dreissena-m<strong>on</strong>itor, a biological<br />

early warning system for c<strong>on</strong>tinuous water quality m<strong>on</strong>itoring. Hydrobiologia,<br />

556:417–426, 2006.<br />

[Gud03] Alexander V. Gudimov. Elementary behavioral acts <str<strong>on</strong>g>of</str<strong>on</strong>g> valve movements in mussels<br />

(mytilus edulis l.). Doklady Biological Sciences, 391:346–348, 2003. Translated from<br />

Doklady Akademii Nauk, Vol. 391, No. 3, 2003, pp. 422-425.<br />

[KKCC06] Cheol-Ki Kim, Inn-Sil Kwak, Eui-Young Cha, and Tae-Soo Ch<strong>on</strong>. Implementati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

wavelets and artificial neural networks to detecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> toxic resp<strong>on</strong>se behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> chir<strong>on</strong>omids<br />

(chir<strong>on</strong>omidae: Diptera) for water quality m<strong>on</strong>itoring. Ecol. Model., 195:61–<br />

71, 2006.<br />

[LRM08] Petr<strong>on</strong>e L., Norman L. C Ragg, and A. James McQuillan. In situ infrared spectroscopic<br />

investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> perna canaliculus mussel larvae primary settlement. Bi<str<strong>on</strong>g>of</str<strong>on</strong>g>ouling.,<br />

24(6):405–413, 2008.<br />

[RSH + 06] David L. Rodland, Bernd R. Schöne, Samuli O. Helama, Jan Kresten Nielsen, and<br />

Sven M. Baier. A clockwork mollusc: Ultradian rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms in bivalve activity revealed<br />

by digital photography. J. Exp. Mar. Biol. Ecol., 334:316–323, 2006.<br />

[Wiś91] Ryszard Wiśniewski. New me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for recording activity pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> bivalves: A preliminary<br />

report <strong>on</strong> dreissena polymorpha pallas during ecological stress. In Ten<str<strong>on</strong>g>th</str<strong>on</strong>g> Intern.<br />

Malacol. C<strong>on</strong>gress, pages 363–365, 1991.<br />

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Neurosciences; Thursday, June 30, 11:30<br />

Laura Sacerdote<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics “G. Peano”, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Torino, Via<br />

Carlo Alberto 10, Torino, Italy<br />

e-mail: laura.sacerdote@unito.it<br />

Massimiliano Tamborrino<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Copenhagen, Universitetsparken<br />

5, DK 2100, Copenhagen, Denmark.<br />

e-mail: mt@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ku.dk<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>e Interspike Times <str<strong>on</strong>g>of</str<strong>on</strong>g> two Coupled Neur<strong>on</strong>s<br />

Stochastic Leaky Integrate and Fire models describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane<br />

potential {Xt} t≥0 <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e Stein equati<strong>on</strong><br />

<br />

dXt = − Xt<br />

τ dt + adN + t + idN − t .<br />

X0 = x0<br />

Here, a > 0, i < 0 are c<strong>on</strong>stants representing excitatory and inhibitory inputs,<br />

τ is <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane time c<strong>on</strong>stant and x0 is <str<strong>on</strong>g>th</str<strong>on</strong>g>e resting potential. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore,<br />

+ −<br />

N t and Nt are two independent Poiss<strong>on</strong> processes <str<strong>on</strong>g>of</str<strong>on</strong>g> rates λ > 0 and β > 0,<br />

respectively. The release <str<strong>on</strong>g>of</str<strong>on</strong>g> a spike corresp<strong>on</strong>ds to <str<strong>on</strong>g>th</str<strong>on</strong>g>e first time when <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane<br />

potential attains a <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold value S > x0. After a spike, <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane<br />

potential is reset to its resting value and <str<strong>on</strong>g>th</str<strong>on</strong>g>e process restarts its evoluti<strong>on</strong> until a<br />

time tmax. The Interspike Intervals (ISI) are modeled <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e random variables<br />

T = inf {t : Xt > S}. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e seventies, <str<strong>on</strong>g>th</str<strong>on</strong>g>e difficulty <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e first passage time<br />

problem for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Stein process has motivated <str<strong>on</strong>g>th</str<strong>on</strong>g>e introducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong> limits for<br />

its equati<strong>on</strong>. As result, an Ornstein-Uhlenbeck process is obtained. It models <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

sub-<str<strong>on</strong>g>th</str<strong>on</strong>g>reshold membrane potential dynamics and it has developed <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

input-output relati<strong>on</strong>ships <str<strong>on</strong>g>of</str<strong>on</strong>g> a single neur<strong>on</strong>.<br />

However, <strong>on</strong>e should c<strong>on</strong>sider two or more dependent neur<strong>on</strong>s to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

transmissi<strong>on</strong> <strong>on</strong> informati<strong>on</strong> in a network. Here, we extend <str<strong>on</strong>g>th</str<strong>on</strong>g>e Stein process to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

case <str<strong>on</strong>g>of</str<strong>on</strong>g> k neur<strong>on</strong>s, modeling its spiking activity. For <str<strong>on</strong>g>th</str<strong>on</strong>g>is aim, we prove <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>vergence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a k-dimensi<strong>on</strong>al Stein process to a k-dimensi<strong>on</strong>al Ornstein-Uhlenbeck <strong>on</strong>e.<br />

We also prove <str<strong>on</strong>g>th</str<strong>on</strong>g>e weak c<strong>on</strong>vergence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir ISIs.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e two dimensi<strong>on</strong>al case, we numerically determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e ISIs <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two neur<strong>on</strong>s. Finally, we illustrate some results <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependencies<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese times.<br />

844

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Reports from US - African BioMa<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Initiative: C<strong>on</strong>servati<strong>on</strong><br />

Biology; Saturday, July 2, 14:30<br />

Holly Gaff, Sadie Ryan<br />

Old Domini<strong>on</strong> University, SUNY-ESF<br />

e-mail: HGaff@odu.edu<br />

Looking to <str<strong>on</strong>g>th</str<strong>on</strong>g>e future: how to progress to success from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

US-Africa Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Initiative<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is sessi<strong>on</strong>, we have heard reports from <str<strong>on</strong>g>th</str<strong>on</strong>g>e US-Africa Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Initiative’s<br />

two Advanced Studies Institutes (ASIs) for C<strong>on</strong>servati<strong>on</strong> Biology. The<br />

questi<strong>on</strong> remains, what happens next? The original goals <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e initiative were to<br />

bring toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er US and African students to examine questi<strong>on</strong>s in c<strong>on</strong>servati<strong>on</strong> biology<br />

in Africa, using a combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and biological approaches. This<br />

goal has been achieved and has produced results bey<strong>on</strong>d original expectati<strong>on</strong>s. In<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, we will address how to progress from here: <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> publicati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

potential for future work, communicating results back to c<strong>on</strong>servati<strong>on</strong> biologists.<br />

We will also discuss how participants will take <str<strong>on</strong>g>th</str<strong>on</strong>g>is experience back to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir home<br />

instituti<strong>on</strong>s, and avenues for sharing <str<strong>on</strong>g>th</str<strong>on</strong>g>e benefits <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e experience. We hope <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is will enable us all to distill important less<strong>on</strong>s in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> collaborati<strong>on</strong> and higher<br />

educati<strong>on</strong> pedagogical and communicati<strong>on</strong> abilities.<br />

845

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bioinformatics and System Biology; Wednesday, June 29, 11:00<br />

Eugene Bushmelev<br />

Siberian Federal university<br />

e-mail: hoochie_cool@list.ru<br />

Michael Sadovsky<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> computati<strong>on</strong>al modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> SB RAS<br />

e-mail: msad@icm.krasn.ru<br />

Close order in triplet compositi<strong>on</strong> in genomes<br />

We studied a two-particle distributi<strong>on</strong> functi<strong>on</strong> l (ω1, ω2) <str<strong>on</strong>g>of</str<strong>on</strong>g> a distance defined in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> nucleotides between two given triplets ω1 = ν1ν2ν3 and ω2 = µ1µ2µ3.<br />

For each entry <str<strong>on</strong>g>of</str<strong>on</strong>g> a given triplet ω1 <str<strong>on</strong>g>th</str<strong>on</strong>g>e distance to <str<strong>on</strong>g>th</str<strong>on</strong>g>e nearest given triplet ω2 has<br />

been determined, <str<strong>on</strong>g>th</str<strong>on</strong>g>us revealing <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> functi<strong>on</strong> l (ω1, ω2) <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e couples<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> triplets in a genetic entity. The functi<strong>on</strong> is defined in ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er multi-dimensi<strong>on</strong>al<br />

space (64 2 = 4096) <str<strong>on</strong>g>th</str<strong>on</strong>g>at makes <str<strong>on</strong>g>th</str<strong>on</strong>g>e problems <str<strong>on</strong>g>of</str<strong>on</strong>g> its analysis and visualizati<strong>on</strong> ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

acute.<br />

The distributi<strong>on</strong> functi<strong>on</strong> l (ω1, ω2) was found to be ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er complex; it has<br />

several maxima, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e number and locati<strong>on</strong> (relative distance) <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ose maxima<br />

are specific, for various couples <str<strong>on</strong>g>of</str<strong>on</strong>g> triplets. For yeast genome <str<strong>on</strong>g>of</str<strong>on</strong>g> Pichia stipitis CBS<br />

6054, typical number <str<strong>on</strong>g>of</str<strong>on</strong>g> maxima was equal to <str<strong>on</strong>g>th</str<strong>on</strong>g>ree, for any chromosome. Intragenomic<br />

variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e shape <str<strong>on</strong>g>of</str<strong>on</strong>g> l (ω1, ω2) is ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er significant; at least, different<br />

chromosomes have indistinctively discrete types <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong>.<br />

Special attenti<strong>on</strong> has been paid to <str<strong>on</strong>g>th</str<strong>on</strong>g>e couples <str<strong>on</strong>g>of</str<strong>on</strong>g> triplets <str<strong>on</strong>g>th</str<strong>on</strong>g>at make so called<br />

complementary palindrome. That latter is a couple <str<strong>on</strong>g>of</str<strong>on</strong>g> triplets read equally in opposite<br />

directi<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>e complimentary rule substituti<strong>on</strong>, say, ATG ↔ CAT<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> GCA ↔ TGC. Such triplets (and l<strong>on</strong>ger strings) are well known for a kind <str<strong>on</strong>g>of</str<strong>on</strong>g> symmetry<br />

in genomes: <str<strong>on</strong>g>th</str<strong>on</strong>g>e frequency <str<strong>on</strong>g>of</str<strong>on</strong>g> each string in a complementary palindrome is<br />

pretty close each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er. Informati<strong>on</strong> charge <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e triplets composing a complimentary<br />

palindrome is ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er important issue, for <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e close order in<br />

genomes. This former is a ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> real frequency fν1ν2ν3 to <str<strong>on</strong>g>th</str<strong>on</strong>g>e mostly expected<br />

<strong>on</strong>e fν1ν2ν3, which is defined as<br />

fν1ν2ν3<br />

= fν1ν2 × fν2ν3<br />

Informati<strong>on</strong> charge pν1ν2ν3 is more sensitive to <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological peculiarities <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

genetic entity under c<strong>on</strong>siderati<strong>on</strong>.<br />

We have examined more <str<strong>on</strong>g>th</str<strong>on</strong>g>an 20 genomes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> as many sequences, as <strong>on</strong>e<br />

hundred. All <str<strong>on</strong>g>th</str<strong>on</strong>g>e investigated genetic entities exhibit <str<strong>on</strong>g>th</str<strong>on</strong>g>e close order <str<strong>on</strong>g>of</str<strong>on</strong>g> triplet<br />

compositi<strong>on</strong>. The pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e order was different for <str<strong>on</strong>g>th</str<strong>on</strong>g>e different species (and<br />

higher taxa). Moreover, even an intra-genetic variability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterns was high<br />

enough to put <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e comprehensive analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pattern itself.<br />

To verify <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterns observed at <str<strong>on</strong>g>th</str<strong>on</strong>g>e real genetic entities, we have carried out<br />

several computati<strong>on</strong>al experiments. We have generated a surrogate random n<strong>on</strong>correlated<br />

sequence wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same frequencies <str<strong>on</strong>g>of</str<strong>on</strong>g> nucleotides and <str<strong>on</strong>g>th</str<strong>on</strong>g>e same leng<str<strong>on</strong>g>th</str<strong>on</strong>g>,<br />

and developed similar patterns to figure out <str<strong>on</strong>g>th</str<strong>on</strong>g>e deviati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e patterns observed<br />

over a real sequence from similar observed over a surrogate. Significant difference<br />

has been detected.<br />

846<br />

fν2<br />

.

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Some biological issues <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed order are discussed. The work is a part<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a greater project <str<strong>on</strong>g>of</str<strong>on</strong>g> a study <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>ger strings wi<str<strong>on</strong>g>th</str<strong>on</strong>g> increased<br />

informati<strong>on</strong> charge al<strong>on</strong>gside a genome.<br />

847

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Koichi Saeki<br />

Kyushu University<br />

e-mail: saekikou@bio-ma<str<strong>on</strong>g>th</str<strong>on</strong>g>10.biology.kyushu-u.ac.jp<br />

Yoh Iwasa<br />

Kyushu University<br />

Immunology; Wednesday, June 29, 17:00<br />

T cell anergy as a strategy to reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

autoimmunity<br />

Some self-reactive immature T cells escape negative selecti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ymus and<br />

may cause autoimmune diseases later. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e periphery, if T cells are stimulated<br />

insufficiently by peptide-major histocompatibility complex, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey become inactive<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cytokines changes, a phenomen<strong>on</strong> called "T cell anergy".<br />

We explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at T cell anergy may functi<strong>on</strong> to reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

autoimmunity. The underlying logic is as follows: Since <str<strong>on</strong>g>th</str<strong>on</strong>g>ose self-reactive T cells<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at receive str<strong>on</strong>g stimuli from self-antigens are eliminated in <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ymus, T cells<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at receive str<strong>on</strong>g stimuli in <str<strong>on</strong>g>th</str<strong>on</strong>g>e periphery are likely to be n<strong>on</strong>-self-reactive. As a<br />

c<strong>on</strong>sequence, when a T cell receives a weak stimulus, <str<strong>on</strong>g>th</str<strong>on</strong>g>e likelihood <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell is<br />

self-reactive is higher <str<strong>on</strong>g>th</str<strong>on</strong>g>an in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>th</str<strong>on</strong>g>at it receives a str<strong>on</strong>g stimulus. Therefore,<br />

inactivati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e T cell may reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e danger <str<strong>on</strong>g>of</str<strong>on</strong>g> autoimmunity. We c<strong>on</strong>sider<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e formalism in which each T cell chooses its resp<strong>on</strong>se depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e streng<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> stimuli in order to reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk <str<strong>on</strong>g>of</str<strong>on</strong>g> autoimmune diseases while maintaining its<br />

ability to attack n<strong>on</strong>-self-antigens effectively. The numerical calculati<strong>on</strong> reveals <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

T cell anergy is <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal resp<strong>on</strong>se when a T cell meets wi<str<strong>on</strong>g>th</str<strong>on</strong>g> antigen-presenting<br />

cells many times in its lifetime, and when <str<strong>on</strong>g>th</str<strong>on</strong>g>e product <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e autoimmunity risk<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> self-reactive T cells has an intermediate value.<br />

848

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Roberto Saenz<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cambridge<br />

e-mail: ras93@cam.ac.uk<br />

Steve C. Essen<br />

Veterinary Laboratories Agency<br />

Bryan T. Grenfell<br />

Princet<strong>on</strong> University<br />

John W. McCauley<br />

MRC Nati<strong>on</strong>al Institute for Medical Research<br />

Ian H. Brown<br />

Veterinary Laboratories Agency<br />

Julia R. Gog<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cambridge<br />

Epidemics; Wednesday, June 29, 08:30<br />

Quantifying transmissi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> high- and low-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenicity<br />

H7N1 avian influenza in turkeys<br />

Outbreaks <str<strong>on</strong>g>of</str<strong>on</strong>g> avian influenza in poultry can be devastating, and yet many <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

basic parameters have not been accurately characterised. In 1999-2000 in Nor<str<strong>on</strong>g>th</str<strong>on</strong>g>ern<br />

Italy, outbreaks <str<strong>on</strong>g>of</str<strong>on</strong>g> H7N1 low-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenicity avian influenza virus (LPAI) preceded<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> H7N1 high-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenicity avian influenza virus (HPAI). This study<br />

investigates <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> dynamics in turkeys <str<strong>on</strong>g>of</str<strong>on</strong>g> representative HPAI and LPAI<br />

H7N1 virus strains from <str<strong>on</strong>g>th</str<strong>on</strong>g>is outbreak in an experimental setting, allowing direct<br />

comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two strains. The fi<br />

tted transmissi<strong>on</strong> rates for <str<strong>on</strong>g>th</str<strong>on</strong>g>e two strains are similar: 2.04 (1.5-2.7) for HPAI,<br />

2.01 (1.6-2.5) for LPAI. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean infecti<strong>on</strong>s period is far shorter for HPAI,<br />

due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e rapid dea<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> infected turkeys: 1.48 (1.3-1.7) days for HPAI, 7.65 (7.0-<br />

8.4) days for LPAI. Hence <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproductive ratio, R0 is significantly lower for<br />

HPAI <str<strong>on</strong>g>th</str<strong>on</strong>g>an for LPAI: 3.01 (2.2-4.0) for HPAI, 15.37 (11.8-19.8) for LPAI. To be able<br />

to extrapolate experimental results from relatively small numbers <str<strong>on</strong>g>of</str<strong>on</strong>g> birds to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

commercial poultry flock size, two competing hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses for how transmissi<strong>on</strong> rates<br />

vary wi<str<strong>on</strong>g>th</str<strong>on</strong>g> populati<strong>on</strong> size were investigated. Frequency-dependent transmissi<strong>on</strong> was<br />

determined to give a better<br />

fit to data from experiments wi<str<strong>on</strong>g>th</str<strong>on</strong>g> varying number <str<strong>on</strong>g>of</str<strong>on</strong>g> birds.<br />

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Cellular Systems Biology; Tuesday, June 28, 14:30<br />

Max Sajitz-Hermstein and Zoran Nikoloski<br />

Systems Biology and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling Group<br />

Max-Planck Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular Plant Physiology, 14476 Potsdam,<br />

Germany<br />

e-mail: sajitz@mpimp-golm.mpg.de<br />

e-mail: nikoloski@mpimp-golm.mpg.de<br />

Biochemical reacti<strong>on</strong> networks meet Coaliti<strong>on</strong>al Game<br />

Theory: The importance <str<strong>on</strong>g>of</str<strong>on</strong>g> not being single<br />

A fundamental questi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> complex biological networks is how to<br />

determine which comp<strong>on</strong>ents (e.g. reacti<strong>on</strong>s) are most important regarding specific<br />

functi<strong>on</strong>. Virtually all existing approaches for establishing <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

reacti<strong>on</strong> in a biological network are based <strong>on</strong> vitality-like indices. The importance<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a reacti<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>en specified by <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> its removal, emulating single knockout<br />

experiments in biology. However, such technique neglects topological features, like<br />

bypassing pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways, which are crucial for network robustness. Coaliti<strong>on</strong>al game<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eory provides a framework for extending <str<strong>on</strong>g>th</str<strong>on</strong>g>e vitality-like indices by c<strong>on</strong>sidering<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> single network elements wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to all <str<strong>on</strong>g>of</str<strong>on</strong>g> its interacti<strong>on</strong>s<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e network, based purely <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network topology. Here we propose a me<str<strong>on</strong>g>th</str<strong>on</strong>g>od<br />

combining cooperative game <str<strong>on</strong>g>th</str<strong>on</strong>g>eory wi<str<strong>on</strong>g>th</str<strong>on</strong>g> flux balance analysis, a standard technique<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic networks. We employ <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>od to rank reacti<strong>on</strong>s<br />

in metabolic networks wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to a biologic functi<strong>on</strong>, in particular biomass<br />

producti<strong>on</strong>. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, our me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is used in <str<strong>on</strong>g>th</str<strong>on</strong>g>e design <str<strong>on</strong>g>of</str<strong>on</strong>g> a novel approach for<br />

determining network robustness to changes imposed by gene knock-outs.<br />

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Mechanics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> and cortical actin at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular level;<br />

Saturday, July 2, 08:30<br />

Guillaume Salbreux<br />

Max Planck Institute for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Physics <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Systems, Dresden<br />

e-mail: salbreux@pks.mpg.de<br />

Role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e polar actin cortex in cytokinesis<br />

During cytokinesis, <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> physical separati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell into two daughter<br />

cells, actin filaments accumulate at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cleavage furrow, producing <str<strong>on</strong>g>th</str<strong>on</strong>g>e force for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

equatorial c<strong>on</strong>stricti<strong>on</strong>. A cortical network is however also present at <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two cellular poles. The actin network is dynamically polymerized and<br />

depolymerized, and myosin molecular motors generate internal stresses in <str<strong>on</strong>g>th</str<strong>on</strong>g>e layer,<br />

putting <str<strong>on</strong>g>th</str<strong>on</strong>g>e cortex under tensi<strong>on</strong>. Here we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at for a sufficiently large value <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e polar cortical tensi<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e symmetric shape <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dividing cell is <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretically<br />

unstable, and oscillati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e volume <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular poles are expected to occur<br />

for a sufficiently slow actin turnover rate. Such oscillati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> dividing cells are<br />

experimentally observed and are well described by <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical framework we<br />

propose.<br />

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Statistical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in computati<strong>on</strong>al neuroscience II; Wednesday, June 29,<br />

17:00<br />

Susanne Ditlevsen<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Copenhagen<br />

e-mail: susanne@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ku.dk<br />

Adeline Sams<strong>on</strong><br />

Laboratoire MAP5 CNRS UMR 8145, University Paris Descartes<br />

e-mail: adeline.sams<strong>on</strong>@parisdescartes.fr<br />

Parameter estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic Morris-Lecar model<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> particle filter me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

Stochastic Morris Lecar model is a well-known two-dimensi<strong>on</strong>al stochastic differential<br />

equati<strong>on</strong> (SDE) describing neur<strong>on</strong>al activity by taking into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e random<br />

behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>s. Drift and volatility functi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is SDE are n<strong>on</strong>-linear functi<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e process and depend <strong>on</strong> unknown physiological parameters. Statistical<br />

estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese parameters from neur<strong>on</strong>al data is very difficult. Indeed, neur<strong>on</strong>al<br />

measurements corresp<strong>on</strong>d to discrete observati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>ly <str<strong>on</strong>g>th</str<strong>on</strong>g>e first coordinate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

system. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e SDE has no explicit soluti<strong>on</strong>. We propose an estimati<strong>on</strong><br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>od based <strong>on</strong> a stochastic versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e EM algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m, <str<strong>on</strong>g>th</str<strong>on</strong>g>e SAEM algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m,<br />

which requires <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hidden coordinate c<strong>on</strong>diti<strong>on</strong>ally to <str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong>s.<br />

We propose to perform <str<strong>on</strong>g>th</str<strong>on</strong>g>is simulati<strong>on</strong> step wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a Particle Markov Chain<br />

M<strong>on</strong>te Carlo algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m. We illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e performance <str<strong>on</strong>g>of</str<strong>on</strong>g> our estimati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od<br />

<strong>on</strong> simulated and real data.<br />

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Yara Elena Sanchez Corrales<br />

J<strong>on</strong>h Innes Centre<br />

e-mail: yara.sanchez-corrales@bbsrc.ac.uk<br />

Stan Maree<br />

John Innes Centre<br />

Ver<strong>on</strong>ica Grieneisen<br />

John Innes Centre<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

LC-Elliptical Fourier Analysis for quantitative Pavement<br />

Cell shape analysis<br />

Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough c<strong>on</strong>siderable progress has been made in identifying genes <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>trol cell<br />

polarity, it is still unclear how <str<strong>on</strong>g>th</str<strong>on</strong>g>ey work toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er to generate cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> particular<br />

shapes. Indeed, we have limited understanding <strong>on</strong> how multicellular dynamics and<br />

patterning is linked to cell shape and how cell shape in turn influences intracellular<br />

dynamics.<br />

The complex pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> lobes and indentati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Pavement Cells in <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidermis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e leaf <str<strong>on</strong>g>of</str<strong>on</strong>g> Arabidopsis <str<strong>on</strong>g>th</str<strong>on</strong>g>aliana <str<strong>on</strong>g>of</str<strong>on</strong>g>fers an ideal system to address <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

problem. To quantify cell shape changes in a growing leaf is extremely important<br />

to gain insight <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e time scale involved in cell morphogenesis and cell polarity<br />

coordinati<strong>on</strong>. Moreover, how <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> cell morphogenesis is regulated and<br />

influenced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e positi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e leaf and leaf developmental stage has remained<br />

elusive.<br />

Quantitative me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for shape analysis are essential to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cell shape <strong>on</strong> cell intracellular dynamics and to analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>e polarity effects <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a given mutati<strong>on</strong> or treatment. We propose a new me<str<strong>on</strong>g>th</str<strong>on</strong>g>od to quantify cell shape<br />

changes based <strong>on</strong> Elliptical Fourier Analysis(EFA). Our new me<str<strong>on</strong>g>th</str<strong>on</strong>g>od called Lobe-<br />

C<strong>on</strong>tributi<strong>on</strong> EFA provide a measurement <str<strong>on</strong>g>th</str<strong>on</strong>g>at directly relates to morphological<br />

periodicities and provide a good separati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells according wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir degree <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

lobbing in analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cell after a Principal Comp<strong>on</strong>ent Analysis.<br />

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Populati<strong>on</strong> Dynamics; Tuesday, June 28, 14:30<br />

Luis Sanz<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics. E.T.S.I.I, Universidad Politécnica de<br />

Madrid. Madrid, Spain<br />

e-mail: lsanz@etsii.upm.es<br />

Juan Ant<strong>on</strong>io Al<strong>on</strong>so<br />

e-mail: jal<strong>on</strong>so@etsii.upm.es<br />

Exp<strong>on</strong>ential grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and extincti<strong>on</strong> in age structured<br />

populati<strong>on</strong>s incorporating envir<strong>on</strong>mental stochasticity<br />

We study different strategies to ascertain grow<str<strong>on</strong>g>th</str<strong>on</strong>g> or extincti<strong>on</strong> in Leslie type<br />

matrix models for age structured populati<strong>on</strong>s subjected to envir<strong>on</strong>mental stochasticity<br />

[1]. We <str<strong>on</strong>g>th</str<strong>on</strong>g>ink <str<strong>on</strong>g>of</str<strong>on</strong>g> a populati<strong>on</strong> described at time n by vector Xn = (x 1 n, ..., x N n ) T<br />

and living in an ambient in which <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are s different envir<strong>on</strong>mental states. The<br />

vital rates corresp<strong>on</strong>ding to each <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese envir<strong>on</strong>ments are given by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Leslie<br />

matrices Lα ∈ R N×N , α = 1, ..., s in such a way <str<strong>on</strong>g>th</str<strong>on</strong>g>at, for each α, Lα c<strong>on</strong>tains <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

fertility and survival rates <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> in envir<strong>on</strong>ment α. The envir<strong>on</strong>mental<br />

variati<strong>on</strong> is characterized by a sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> random variables τn, <str<strong>on</strong>g>th</str<strong>on</strong>g>at we will c<strong>on</strong>sider<br />

to be an irreducible and aperiodic Markov chain, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> state space {1, ..., s}<br />

in such a way <str<strong>on</strong>g>th</str<strong>on</strong>g>at τn+1 describes for <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e system<br />

between times n and n + 1. Thus, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model reads<br />

(1) Xn+1 = Lτn+1 Xn<br />

where X0 ≥ 0 is a fixed (n<strong>on</strong> random) n<strong>on</strong>-zero vector. Moreover, we assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> matrices <str<strong>on</strong>g>of</str<strong>on</strong>g> vital rates meets a certain technical c<strong>on</strong>diti<strong>on</strong> (ergodic set).<br />

The most important parameter c<strong>on</strong>cerning <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> (1) is <str<strong>on</strong>g>th</str<strong>on</strong>g>e so called<br />

stochastic grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate (s.g.r.) defined as a := limn→∞ log Xn /n, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> probability<br />

<strong>on</strong>e [2]. Therefore, a > 0 implies <str<strong>on</strong>g>th</str<strong>on</strong>g>at every realizati<strong>on</strong> grows asymptotically<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> rate e a , and a < 0 implies <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> goes extinct wi<str<strong>on</strong>g>th</str<strong>on</strong>g> probability<br />

<strong>on</strong>e. However, even in very simple situati<strong>on</strong>s, it is not possible to calculate a analytically.<br />

In order to find a useful way to study <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models, <str<strong>on</strong>g>th</str<strong>on</strong>g>e so called “lognormal<br />

approximati<strong>on</strong>” has been proposed [2]. It c<strong>on</strong>sists in assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> size has a lognormal distributi<strong>on</strong>. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is way an approximate s.g.r. â<br />

can be defined. The validity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is approximati<strong>on</strong> has <strong>on</strong>ly been tested numerically<br />

and in very specific situati<strong>on</strong>s [3]. Moreover, in principle <str<strong>on</strong>g>th</str<strong>on</strong>g>e approximati<strong>on</strong> does<br />

not allow <strong>on</strong>e to calculate â analytically.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e first place, <str<strong>on</strong>g>th</str<strong>on</strong>g>is work examines bo<str<strong>on</strong>g>th</str<strong>on</strong>g> numerically and <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretically, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

validity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lognormal approximati<strong>on</strong>, finding <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> situati<strong>on</strong>s in which<br />

it can be c<strong>on</strong>sidered <str<strong>on</strong>g>th</str<strong>on</strong>g>at it works well. Moreover, we build different bounds for a<br />

and for â, and analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s under which each bound works best. This is<br />

used to give necessary-sufficient c<strong>on</strong>diti<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e explosi<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e extincti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong>. The results are applied to <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> a populati<strong>on</strong> structured in<br />

juveniles and adults living in an ambient wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a “good” and a “bad” envir<strong>on</strong>ment.<br />

References.<br />

[1] H. Caswell. Matrix Populati<strong>on</strong> Models (2 nd ed.) Sinauer Associates Inc., Sunderland (2001).<br />

[2] S. Tuljapurkar. Populati<strong>on</strong> Dynamics in Variable Envir<strong>on</strong>ments Springer-Verlag, (1990).<br />

854

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[3] S. Tuljapurkar, S. Orzack. Populati<strong>on</strong> dynamics in variable envir<strong>on</strong>ments. I. L<strong>on</strong>g-run grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

rates and extincti<strong>on</strong> Theor. Popul. Biol. 18 314–342 (1980).<br />

855

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ecology and evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases; Friday, July 1, 14:30<br />

Akira Sasaki<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Evoluti<strong>on</strong>ary Studies <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosystems, The Graduate<br />

University for Advanced Studies (Sokendai), Hayama, Kanagawa 240-<br />

0193, Japan<br />

e-mail: sasaki_akira@soken.ac.jp<br />

Sayaki U. Suzuki<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Science, Kyushu University, Fukuoka<br />

812-8581, Japan<br />

e-mail: suzuki_sayaki@soken.ac.jp<br />

Resistance <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold in spatially explicit epidemic model:<br />

Finite size scaling applied to dynamic percolati<strong>on</strong> in<br />

epidemic processes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mixed cultivar planting<br />

We examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e fracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> resistant cultivars necessary to prevent a global<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen outbreak (<str<strong>on</strong>g>th</str<strong>on</strong>g>e resistance <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold) using a spatially explicit epidemiological<br />

model (SIR model) in a finite, two-dimensi<strong>on</strong>al, lattice-structured host<br />

populati<strong>on</strong> [1] . Threshold behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is spatially explicit SIR model cannot be<br />

reduced to <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>d percolati<strong>on</strong>, as was previously noted in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature, unless<br />

extremely unrealistic assumpti<strong>on</strong>s are imposed <strong>on</strong> infecti<strong>on</strong> process. The resistance<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>reshold is significantly lower <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>venti<strong>on</strong>al mean-field epidemic<br />

models, and is even lower if <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial c<strong>on</strong>figurati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> resistant and susceptible<br />

crops are negatively correlated. Finite size scaling applied to <str<strong>on</strong>g>th</str<strong>on</strong>g>e resistance <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold<br />

reveals <str<strong>on</strong>g>th</str<strong>on</strong>g>at its difference from static percolati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold (0.41) is inversely<br />

proporti<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproductive ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen. Estimated value, 4.7,<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> critical basic reproductive ratio in a universally susceptible populati<strong>on</strong> is much<br />

larger <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding critical value (1) in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean-field model and nearly<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ree times larger <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>of</str<strong>on</strong>g> SIS model.<br />

References.<br />

[1] Suzuki, S.U. and Sasaki, A. How does <str<strong>on</strong>g>th</str<strong>on</strong>g>e resistance <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold in spatially explicit epidemic<br />

dynamics depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproductive ratio and spatial correlati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> crop genotypes?<br />

Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology 276 117–125 (2011).<br />

856

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Akiko Satake<br />

Hokkaido University, Japan<br />

e-mail: satake@ees.hokudai.ac.jp<br />

Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 08:30<br />

A computati<strong>on</strong>al model <str<strong>on</strong>g>of</str<strong>on</strong>g> plant life cycle: genetic<br />

mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> local adaptati<strong>on</strong> in flowering time<br />

The timing <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transiti<strong>on</strong> from vegetative to reproductive development is a critical<br />

adaptive trait as it is essential for plants to complete seed producti<strong>on</strong> in favorable<br />

c<strong>on</strong>diti<strong>on</strong>s. Proposed in A. <str<strong>on</strong>g>th</str<strong>on</strong>g>aliana, <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene regulatory model <str<strong>on</strong>g>of</str<strong>on</strong>g> floral transiti<strong>on</strong><br />

describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex interacti<strong>on</strong>s between envir<strong>on</strong>mental signals (e.g., photoperiod<br />

and temperature) and endogenous cues (e.g., size, leaf number, or age). I<br />

modeled <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> between photoperiod and vernalizati<strong>on</strong> (low-temperature)<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways, and combined <str<strong>on</strong>g>th</str<strong>on</strong>g>is gene regulati<strong>on</strong> dynamics and grow<str<strong>on</strong>g>th</str<strong>on</strong>g> dynamics in<br />

a genetic-physiological model to explore local adaptati<strong>on</strong> to two different envir<strong>on</strong>ments<br />

(Hyogo; <str<strong>on</strong>g>th</str<strong>on</strong>g>e western part <str<strong>on</strong>g>of</str<strong>on</strong>g> central H<strong>on</strong>shu, and Hakodate; <str<strong>on</strong>g>th</str<strong>on</strong>g>e sou<str<strong>on</strong>g>th</str<strong>on</strong>g>ern<br />

part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nor<str<strong>on</strong>g>th</str<strong>on</strong>g> island in Japan). Temperature is warmer and seas<strong>on</strong>al variati<strong>on</strong>s<br />

in dayleng<str<strong>on</strong>g>th</str<strong>on</strong>g> are smaller in Hyogo <str<strong>on</strong>g>th</str<strong>on</strong>g>an Hakodate. For simplicity, I assumed<br />

l<strong>on</strong>g-day plants <str<strong>on</strong>g>th</str<strong>on</strong>g>at are self-compatible and evergreen. The analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a clear difference in sensitivity to dayleng<str<strong>on</strong>g>th</str<strong>on</strong>g> between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e two plant populati<strong>on</strong>s. It was predicted <str<strong>on</strong>g>th</str<strong>on</strong>g>at a Hakodate populati<strong>on</strong> resp<strong>on</strong>ds<br />

to more extreme critical dayleng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>e in Hyogo, which enables <str<strong>on</strong>g>th</str<strong>on</strong>g>e plant<br />

flower in appropriate seas<strong>on</strong> in mid spring in Hakodate. I discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e validity <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical predicti<strong>on</strong> using <str<strong>on</strong>g>th</str<strong>on</strong>g>e data <str<strong>on</strong>g>of</str<strong>on</strong>g> Arabidopsis halleri.<br />

857

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Andrew Savory<br />

University Of Dundee<br />

e-mail: asavory@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.dundee.ac.uk<br />

Populati<strong>on</strong> Dynamics; Tuesday, June 28, 17:00<br />

Swimming Patterns Of Zoospores<br />

Oomycetes are a group <str<strong>on</strong>g>of</str<strong>on</strong>g> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens <str<strong>on</strong>g>th</str<strong>on</strong>g>at cause many destructive diseases in animals<br />

and plants. One species in particular, Phytoph<str<strong>on</strong>g>th</str<strong>on</strong>g>ora Infestans, is perhaps <str<strong>on</strong>g>th</str<strong>on</strong>g>e most<br />

well known and is resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>e potato blight disease. This causes severe<br />

ec<strong>on</strong>omic damage estimated at 3 billi<strong>on</strong> per annum. The epidemic spread <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

disease is primarily based <strong>on</strong> rapid dispersal from host to host by free-swimming<br />

zoospore cells. These are single-nucleated, wall-less cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at are released <strong>on</strong>ly<br />

into aqueous envir<strong>on</strong>ments. Zoospores exhibit a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> tactic resp<strong>on</strong>ses to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

envir<strong>on</strong>ment to locate suitable infecti<strong>on</strong> sites. We have begun to model <str<strong>on</strong>g>th</str<strong>on</strong>g>is process<br />

using a PDE chemotaxis model <str<strong>on</strong>g>of</str<strong>on</strong>g> Keller-Segel type and in <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is approach captures some general behaviour seen in experiments. We will also<br />

discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s to <str<strong>on</strong>g>th</str<strong>on</strong>g>ese equati<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>e metastability <str<strong>on</strong>g>of</str<strong>on</strong>g> such<br />

soluti<strong>on</strong>s.<br />

858

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

P. Colli Franz<strong>on</strong>e<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Pavia<br />

e-mail: colli@imati.cnr.it<br />

L. F. Pavarino<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Milan<br />

e-mail: luca.pavarino@unimi.it<br />

S. Scacchi<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Milan<br />

e-mail: sim<strong>on</strong>e.scacchi@unimi.it<br />

Bioengineering; Tuesday, June 28, 14:30<br />

The anisotropic Bidomain model <str<strong>on</strong>g>of</str<strong>on</strong>g> electrocardiology: a<br />

comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled and uncoupled parallel<br />

prec<strong>on</strong>diti<strong>on</strong>ers<br />

The anisotropic Bidomain model describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e bioelectric activity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiac<br />

tissue and c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> a system <str<strong>on</strong>g>of</str<strong>on</strong>g> a parabolic n<strong>on</strong>-linear partial differential equati<strong>on</strong><br />

(PDE) and an elliptic linear PDE. The PDEs are coupled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a system <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary<br />

differential equati<strong>on</strong>s (ODEs), modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular membrane i<strong>on</strong>ic currents.<br />

The discretizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Bidomain model in <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-dimensi<strong>on</strong>al (3D) ventricular geometries<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> realistic size yields <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> large scale and ill-c<strong>on</strong>diti<strong>on</strong>ed linear<br />

systems at each time step. The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is to c<strong>on</strong>struct and study parallel<br />

multilevel and block prec<strong>on</strong>diti<strong>on</strong>ers, in order to str<strong>on</strong>gly reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e high computati<strong>on</strong>al<br />

costs <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Bidomain model, allowing <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole heart<br />

beat in 3D realistic domains. We analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e scalability <str<strong>on</strong>g>of</str<strong>on</strong>g> multilevel Schwarz<br />

block-diag<strong>on</strong>al and block-factorized prec<strong>on</strong>diti<strong>on</strong>ers for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Bidomain model and<br />

compare <str<strong>on</strong>g>th</str<strong>on</strong>g>em wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multilevel Schwarz coupled prec<strong>on</strong>diti<strong>on</strong>ers. 3D parallel numerical<br />

tests show <str<strong>on</strong>g>th</str<strong>on</strong>g>at block prec<strong>on</strong>diti<strong>on</strong>ers are scalable, but less efficient <str<strong>on</strong>g>th</str<strong>on</strong>g>an<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e coupled prec<strong>on</strong>diti<strong>on</strong>ers. Finally, we present simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiac virtual<br />

electrode phenomen<strong>on</strong>, yielding anode make and break mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> excitati<strong>on</strong>,<br />

using <str<strong>on</strong>g>th</str<strong>on</strong>g>e developed parallel solver.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Crowd Dynamics: Modeling, Analysis and Simulati<strong>on</strong> (Part 2); Wednesday,<br />

June 29, 14:30<br />

Andreas Schadschneider<br />

Institute for Theoretical Physics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Cologne, Zülpicher<br />

Str. 77, 50937 Köln, Germany<br />

e-mail: as@<str<strong>on</strong>g>th</str<strong>on</strong>g>p.uni-koeln.de<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> pedestrian dynamics – Cellular automata<br />

models<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e talk we first give a classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e different modelling approaches<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at have been used to describe pedestrian flows and crowd dynamics. The merits<br />

and problems <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese approaches are discussed [1, 2].<br />

Then we focus <strong>on</strong> cellular automata models. This model class has successfully<br />

been applied to a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> complex systems [2]. One main advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

approach is its computi<strong>on</strong>al efficiency. Large crowds can be simulated faster <str<strong>on</strong>g>th</str<strong>on</strong>g>an<br />

real-time. The floor field model [3, 4, 5, 6] is introduced which allows to reproduce<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e empirically observed collective phenomena like lane formati<strong>on</strong>. The interacti<strong>on</strong>s<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e pedestrians are implemented in <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> virtual chemotaxis [6].<br />

Several extensi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model are discussed which improve its realism in certain<br />

situati<strong>on</strong>s. We also present a calibrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model using empirical data from<br />

laboratory experiments and an applicati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e evacuati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a football stadium.<br />

References.<br />

[1] A. Schadschneider, W. Klingsch, H. Klüpfel, T. Kretz, C. Rogsch, A. Seyfried, Evacuati<strong>on</strong><br />

Dynamics: Empirical Results, Modeling and Applicati<strong>on</strong>s, Encyclopedia <str<strong>on</strong>g>of</str<strong>on</strong>g> Complexity and<br />

System Science 3142 (2009).<br />

[2] A. Schadschneider, D. Chowdhury und K. Nishinari, Stochastic Transport in Complex Systems:<br />

From Molecules to Vehicles, Elsevier (2010).<br />

[3] C. Burstedde, K. Klauck, A. Schadschneider, J. Zittartz, Simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> pedestrian dynamics<br />

using a 2-dimensi<strong>on</strong>al cellular automat<strong>on</strong> Physica A 295 507 (2001).<br />

[4] A. Kirchner, A. Schadschneider, Simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> evacuati<strong>on</strong> processes using a bi<strong>on</strong>ics-inspired<br />

cellular automat<strong>on</strong> model for pedestrian dynamics, Physica A 312 260 (2002).<br />

[5] A. Kirchner, K. Nishinari, A. Schadschneider, Fricti<strong>on</strong> effects and clogging in a cellular automat<strong>on</strong><br />

model for pedestrian dynamics, Phys. Rev. E 67 056122 (2003).<br />

[6] A. Schadschneider, A. Kirchner, K. Nishinari, From ant trails to pedestrian dynamics, Applied<br />

Bi<strong>on</strong>ics and Biomechanics 1 11 (2003).<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models for cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and treatment, Part<br />

V; Wednesday, June 29, 11:00<br />

Heinz Schaettler<br />

Washingt<strong>on</strong> University, USA<br />

e-mail: hms@wustl.edu<br />

Urszula Ledzewicz<br />

Sou<str<strong>on</strong>g>th</str<strong>on</strong>g>ern Illinois University Edwardsville, USA<br />

Optimal protocols for chemo- and immuno<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy in a<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor-immune interacti<strong>on</strong>s<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, a classical model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s between tumor and <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune<br />

system under treatment is c<strong>on</strong>sidered as an optimal c<strong>on</strong>trol problem wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multiple<br />

c<strong>on</strong>trols representing acti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cytotoxic drugs as well as <str<strong>on</strong>g>of</str<strong>on</strong>g> agents <str<strong>on</strong>g>th</str<strong>on</strong>g>at give a boost<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune system. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e objective, a weighted average <str<strong>on</strong>g>of</str<strong>on</strong>g> several quantities<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e effectiveness <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment is minimized. These terms include (i)<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells at <str<strong>on</strong>g>th</str<strong>on</strong>g>e terminal time, (ii) a measure for <str<strong>on</strong>g>th</str<strong>on</strong>g>e immunocompetent<br />

cell densities at <str<strong>on</strong>g>th</str<strong>on</strong>g>e terminal point (included as a negative term), (iii) a<br />

measure for <str<strong>on</strong>g>th</str<strong>on</strong>g>e side effects and cost <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment in form <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall amount <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

agents given and (iv) a small penalty <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e terminal time <str<strong>on</strong>g>th</str<strong>on</strong>g>at limits <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapy horiz<strong>on</strong> which is assumed to be free. This last term is essential in obtaining<br />

a well-posed problem formulati<strong>on</strong>. The form <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e objective is motivated by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out treatment and models <str<strong>on</strong>g>th</str<strong>on</strong>g>e goal to move <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

state <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system from a regi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> malignant cancer grow<str<strong>on</strong>g>th</str<strong>on</strong>g> into a benign regi<strong>on</strong>.<br />

Employing a Gompertzian grow<str<strong>on</strong>g>th</str<strong>on</strong>g> model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer cells, for various scenarios<br />

optimal c<strong>on</strong>trols and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir corresp<strong>on</strong>ding system resp<strong>on</strong>ses are calculated. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cases <str<strong>on</strong>g>of</str<strong>on</strong>g> m<strong>on</strong>o- and combinati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies will be c<strong>on</strong>sidered.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Sascha Schäuble 1 , Ines Heiland 1 , S. Schuster 1<br />

1 Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioinformatics, Friedrich–Schiller–University Jena,<br />

Ernst-Abbe-Platz 2, 07743 Jena, Germany<br />

e-mail: {sascha.schaeuble, heiland.ines, stefan.schu}@uni-jena.de<br />

Olga Voytsekh 2 , Maria Mittag 2<br />

2 Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> General Botany, Friedrich–Schiller–University Jena,<br />

Am Planetarium 1,07743 Jena, Germany<br />

e-mail: {olga-olegovna.voytsekh, m.mittag}@uni-jena.de<br />

New developments in <str<strong>on</strong>g>th</str<strong>on</strong>g>e diurnal changes <str<strong>on</strong>g>of</str<strong>on</strong>g> nitrogen<br />

metabolism in Chlamydom<strong>on</strong>as reinhardtii<br />

The capability <str<strong>on</strong>g>of</str<strong>on</strong>g> plants to assimilate nitrogen plays a crucial role in optimising<br />

biomass producti<strong>on</strong>. This is <str<strong>on</strong>g>of</str<strong>on</strong>g> particular interest for maximising crop yields as<br />

well as for detoxifying stressed soils.<br />

The green algae Chlamydom<strong>on</strong>as reinhardtii renders a suitable model organism,<br />

as it is ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er easily accessible compared to higher plants and shows circadian<br />

oscillati<strong>on</strong>s, which are involved in many metabolic and physiological processes [1].<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, new findings reveal <str<strong>on</strong>g>th</str<strong>on</strong>g>at several RNAs are alternatively spliced in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

green algae [2]. We dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at stoichiometric data are sufficient to provide<br />

valuable insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nitrogen uptake system. This is achieved<br />

by c<strong>on</strong>sidering different carb<strong>on</strong> sources, envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e repressive<br />

behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e circadian regulated mRNA-binding protein CHLAMY1 [3] and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Elementary Flux Mode analysis [4]. We retrieved <str<strong>on</strong>g>th</str<strong>on</strong>g>e most efficient<br />

fluxes in regard to <str<strong>on</strong>g>th</str<strong>on</strong>g>e biosyn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>of</str<strong>on</strong>g> amino acids <str<strong>on</strong>g>th</str<strong>on</strong>g>at show a high nitrogen to<br />

carb<strong>on</strong> ratio. Moreover, we provide clues for <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> CHLAMY1 in <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> nitrogen uptake and show a reas<strong>on</strong>able time course <str<strong>on</strong>g>of</str<strong>on</strong>g> nitrogen incorporati<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>roughout <str<strong>on</strong>g>th</str<strong>on</strong>g>e day.<br />

An investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> amino acids in C. reinhardtii<br />

reveals a ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er high abundance <str<strong>on</strong>g>of</str<strong>on</strong>g> simple amino acids in <str<strong>on</strong>g>th</str<strong>on</strong>g>e green algae. Thus, we<br />

included <str<strong>on</strong>g>th</str<strong>on</strong>g>ese amino acids into our metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way analysis as <str<strong>on</strong>g>th</str<strong>on</strong>g>ey c<strong>on</strong>stitute<br />

a potential alternative nitrogen deposit.<br />

References.<br />

[1] Nakahata et al., Circadian c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e NAD+ salvage pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way by CLOCK-SIRT1. Science<br />

324 654–657, 2009.<br />

[2] Labadorf et al., Genome-wide analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> alternative splicing in Chlamydom<strong>on</strong>as reinhardtii.<br />

BMC Genomics 11 114, 2010.<br />

[3] Kiaulehn et al., The Presence <str<strong>on</strong>g>of</str<strong>on</strong>g> UG-repeat sequences in <str<strong>on</strong>g>th</str<strong>on</strong>g>e 3’-UTRs <str<strong>on</strong>g>of</str<strong>on</strong>g> reporter luciferase<br />

mRNAs mediates circadian expressi<strong>on</strong> and can determine acrophase in Chlamydom<strong>on</strong>as reinhardtii.<br />

J Biol Rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms 22 275–277, 2007.<br />

[4] Schuster, S. and Hilgetag, C., On Elementary Flux Modes in biochemical reacti<strong>on</strong> systems at<br />

steady state J Biol Syst 2 165–182, 1994.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Regulatory Networks; Friday, July 1, 14:30<br />

Daniella Schittler<br />

Institute for Systems Theory and Automatic C<strong>on</strong>trol, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Stuttgart<br />

e-mail: schittler@ist.uni-stuttgart.de<br />

Christian Breindl<br />

Institute for Systems Theory and Automatic C<strong>on</strong>trol, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Stuttgart<br />

Frank Allgower<br />

Institute for Systems Theory and Automatic C<strong>on</strong>trol, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Stuttgart<br />

Model selecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> networks <str<strong>on</strong>g>th</str<strong>on</strong>g>at are robust against kinetic<br />

uncertainties<br />

Gene regulatory networks are driving major biological processes, such as cell differentiati<strong>on</strong>.<br />

Dynamical models can <str<strong>on</strong>g>of</str<strong>on</strong>g>ten be built <strong>on</strong> a small number <str<strong>on</strong>g>of</str<strong>on</strong>g> key regulators,<br />

but are usually hampered by <str<strong>on</strong>g>th</str<strong>on</strong>g>e lack <str<strong>on</strong>g>of</str<strong>on</strong>g> quantitative knowledge about <str<strong>on</strong>g>th</str<strong>on</strong>g>e detailed<br />

interacti<strong>on</strong> kinetics. Thus, it is desirable to deduce certain system properties already<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e qualitative interacti<strong>on</strong> structure.<br />

This study aims at selecting prototypes <str<strong>on</strong>g>of</str<strong>on</strong>g> minimalistic <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-node network<br />

motifs, <str<strong>on</strong>g>th</str<strong>on</strong>g>at can serve as a genetic switch model driving cell differentiati<strong>on</strong>. As a<br />

selecti<strong>on</strong> criteri<strong>on</strong>, we demand <str<strong>on</strong>g>th</str<strong>on</strong>g>at a candidate model must be able to produce<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e biologically observed <str<strong>on</strong>g>th</str<strong>on</strong>g>ree cell states: a progenitor, and two differentiated<br />

cell types. The goal is to find necessary c<strong>on</strong>diti<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> structure<br />

such <str<strong>on</strong>g>th</str<strong>on</strong>g>at a network exhibits <str<strong>on</strong>g>th</str<strong>on</strong>g>e required stable steady states, and to classify <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

robustness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is capability. For <str<strong>on</strong>g>th</str<strong>on</strong>g>is model selecti<strong>on</strong>, we employ a qualitative<br />

modeling framework based <strong>on</strong> ordinary differential equati<strong>on</strong>s, but requiring <strong>on</strong>ly<br />

few qualitative assumpti<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic interacti<strong>on</strong>s. The robustness <str<strong>on</strong>g>of</str<strong>on</strong>g> a model<br />

is defined as <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximum perturbati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> functi<strong>on</strong>s under which<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e model criteria are still fulfilled, and <str<strong>on</strong>g>th</str<strong>on</strong>g>us measures <str<strong>on</strong>g>th</str<strong>on</strong>g>e validity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model if<br />

<strong>on</strong>ly qualitative knowledge is available.<br />

In particular, we focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e operator combining <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s<br />

acting <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same node: These can be c<strong>on</strong>nected in an OR-fashi<strong>on</strong> (i.e. ingoing<br />

activators and inhibitors act independently <str<strong>on</strong>g>of</str<strong>on</strong>g> each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er), or in an AND-fashi<strong>on</strong><br />

(resulting e.g. from complex formati<strong>on</strong>s at gene promoters). We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at nei<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e OR-networks selected as models for <str<strong>on</strong>g>th</str<strong>on</strong>g>e system are a subset <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ANDnetworks<br />

selected as models, nor vice versa; but am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>em are networks <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

meet <str<strong>on</strong>g>th</str<strong>on</strong>g>e selecti<strong>on</strong> criteria for OR- as well as for AND-kinetics. This n<strong>on</strong>empty<br />

set <str<strong>on</strong>g>of</str<strong>on</strong>g> models can be regarded as robust not <strong>on</strong>ly against quantitative uncertainties,<br />

but also against uncertain knowledge about <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact interacti<strong>on</strong> c<strong>on</strong>juncti<strong>on</strong>s.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e network c<strong>on</strong>nectivity is directly correlated to <str<strong>on</strong>g>th</str<strong>on</strong>g>e robustness <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e network capability to meet <str<strong>on</strong>g>th</str<strong>on</strong>g>e model selecti<strong>on</strong> criteria. In c<strong>on</strong>clusi<strong>on</strong>, for some<br />

specific interacti<strong>on</strong> networks it may be uncritical whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are modeled wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

OR- or AND-interacti<strong>on</strong> kinetics, but also in many cases <strong>on</strong>ly <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two opti<strong>on</strong>s<br />

can successfully result in a model <str<strong>on</strong>g>th</str<strong>on</strong>g>at reproduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e system properties.<br />

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Cancer; Wednesday, June 29, 08:30<br />

Daniela Schlüter<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee<br />

e-mail: dkschlueter@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.dundee.ac.uk<br />

Ignacio Ramis-C<strong>on</strong>de<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Educati<strong>on</strong> Cuenca, Universidad<br />

de Castilla la Mancha<br />

e-mail: ignacio@ramis-c<strong>on</strong>de.com<br />

Mark Chaplain<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee<br />

e-mail: chaplain@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.dundee.ac.uk<br />

The Role <str<strong>on</strong>g>of</str<strong>on</strong>g> Cell-Cell and Cell-Matrix Adhesi<strong>on</strong> in Cancer<br />

Cell Invasi<strong>on</strong>: A Multiscale Individual-Based Modelling<br />

Approach<br />

The malignancy <str<strong>on</strong>g>of</str<strong>on</strong>g> almost all types <str<strong>on</strong>g>of</str<strong>on</strong>g> solid tumours is determined by <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cancer cells to invade <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding tissues and <str<strong>on</strong>g>th</str<strong>on</strong>g>en to form sec<strong>on</strong>dary tumours<br />

(metastases) at distant sites in <str<strong>on</strong>g>th</str<strong>on</strong>g>e body. These metastases are resp<strong>on</strong>sible for 90%<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cancer dea<str<strong>on</strong>g>th</str<strong>on</strong>g>s. In order to advance and improve cancer treatment strategies, it<br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore <str<strong>on</strong>g>of</str<strong>on</strong>g> high importance to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e processes involved in cancer cell<br />

invasi<strong>on</strong>.We focus <strong>on</strong> modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e first steps driving localised cancer cell invasi<strong>on</strong><br />

and try to identify key processes <str<strong>on</strong>g>th</str<strong>on</strong>g>at lead to observed invasi<strong>on</strong> patterns and <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

allow collective cell migrati<strong>on</strong> and/or <str<strong>on</strong>g>th</str<strong>on</strong>g>e detachment <str<strong>on</strong>g>of</str<strong>on</strong>g> individual cells or small<br />

cell clusters from <str<strong>on</strong>g>th</str<strong>on</strong>g>e main tumour mass.<br />

In order to do <str<strong>on</strong>g>th</str<strong>on</strong>g>is, we use an individual-based, force-based multi-scale approach<br />

and model <str<strong>on</strong>g>th</str<strong>on</strong>g>e physical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells and intra- and inter-cellular protein<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways involved in tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, cell-cell and cell-matrix adhesi<strong>on</strong>. The key<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways include <str<strong>on</strong>g>th</str<strong>on</strong>g>ose <str<strong>on</strong>g>of</str<strong>on</strong>g> E-cadherin and beta-catenin. Our approach also allows<br />

us to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e comp<strong>on</strong>ents <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular matrix explicitly (e.g. fibr<strong>on</strong>ectin<br />

fibres).<br />

Using computati<strong>on</strong>al simulati<strong>on</strong>s, we c<strong>on</strong>sider a growing mass <str<strong>on</strong>g>of</str<strong>on</strong>g> cells and investigate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> E-cadherin and beta-catenin levels in<br />

individual cancer cells and predict what implicati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>is has for <str<strong>on</strong>g>th</str<strong>on</strong>g>e adhesi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer cells to each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er and to <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular matrix. By examining <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cell-matrix interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> our model we can fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore highlight <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microenvir<strong>on</strong>ment in tumour progressi<strong>on</strong> and how <str<strong>on</strong>g>th</str<strong>on</strong>g>e compositi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e matrix toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e E-cadherin/beta-catenin dynamics may lead to different<br />

invasi<strong>on</strong> patterns. We also show <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> matrix realignment caused by<br />

cell tracti<strong>on</strong> forces <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells’ invasive behaviour and <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatio-temporal patterns<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at emerge.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Christoph Schmal<br />

Theorie der K<strong>on</strong>densierten Materie, Fakultät für Physik, Universität<br />

Bielefeld<br />

e-mail: schmal@physik.uni-bielefeld.de<br />

Doro<str<strong>on</strong>g>th</str<strong>on</strong>g>ee Staiger<br />

Molekulare Zellphysiologie, Fakultät für Biologie, Universität Bielefeld<br />

Peter Reimann<br />

Theorie der K<strong>on</strong>densierten Materie, Fakultät für Physik, Universität<br />

Bielefeld<br />

The network <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e RNA-binding protein AtGRP7, a<br />

comp<strong>on</strong>ent <str<strong>on</strong>g>of</str<strong>on</strong>g> a molecular slave oscillator in Arabidopsis<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>aliana<br />

The AtGRP7 autoregulatory circuit is <str<strong>on</strong>g>th</str<strong>on</strong>g>e first identified molecular "slave" oscillator<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at is coupled to <str<strong>on</strong>g>th</str<strong>on</strong>g>e circadian ("master") oscillator <str<strong>on</strong>g>of</str<strong>on</strong>g> Arabidopsis <str<strong>on</strong>g>th</str<strong>on</strong>g>aliana.<br />

The AtGRP7 protein regulates <str<strong>on</strong>g>th</str<strong>on</strong>g>e accumulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> its own mRNA at <str<strong>on</strong>g>th</str<strong>on</strong>g>e posttranscripti<strong>on</strong>al<br />

level via alternative splicing. It was recently shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is also a<br />

cross regulati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e AtGRP8 autoregulatory circuit. We modeled <str<strong>on</strong>g>th</str<strong>on</strong>g>e system<br />

composed <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese autoregulatory circuits interc<strong>on</strong>nected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e "master" oscillator<br />

via an ordinary differential equati<strong>on</strong> approach. As for many biological systems<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese equati<strong>on</strong>s are barely known. We defined a cost functi<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at quantifies <str<strong>on</strong>g>th</str<strong>on</strong>g>e overlap between our model and key experimental features. A<br />

search in parameter space should evaluate if our proposed model fits wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e given<br />

experimental data.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Christine Schmeitz<br />

Systems Immunology, Helmholtz Centre for Infecti<strong>on</strong> Research<br />

e-mail: Christine.Schmeitz@helmholtz-hzi.de<br />

Michael Meyer-Hermann<br />

Systems Immunology, Helmholtz Centre for Infecti<strong>on</strong> Research<br />

e-mail: Michael.Meyer-Hermann@helmholtz-hzi.de<br />

Modeling approach to T cell electrophysiology<br />

An effective immune resp<strong>on</strong>se to invading pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenic microorganisms requires <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

regulated interplay <str<strong>on</strong>g>of</str<strong>on</strong>g> T-lymphocytes and antigen-presenting cells (APC) facilitated<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e support <str<strong>on</strong>g>of</str<strong>on</strong>g> various cytokines. The activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> T helper cells requires<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e recogniti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> antigen, which is bound to major histocompatibility complex<br />

molecules, type class II, <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e APC. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e purpose <str<strong>on</strong>g>of</str<strong>on</strong>g> activati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e T cell receptor<br />

(TCR), assisted by coreceptors including CD4, interacts wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bound<br />

antigen and builds up <str<strong>on</strong>g>th</str<strong>on</strong>g>e so called immunological synapse. These complex interacti<strong>on</strong>s<br />

imply sophisticated signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lymphocyte cells and implicates<br />

a network <str<strong>on</strong>g>of</str<strong>on</strong>g> i<strong>on</strong> channels in T cells for managing signals.<br />

Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> regard to <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways and corresp<strong>on</strong>ding<br />

i<strong>on</strong> fluxes <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e T cell membrane, a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling approach<br />

to T cell electrophysiology, based <strong>on</strong> experimental data <str<strong>on</strong>g>of</str<strong>on</strong>g> electrophysiological<br />

measurements, is needed for understanding and illustrating <str<strong>on</strong>g>th</str<strong>on</strong>g>is functi<strong>on</strong>al network.Technically,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e background <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e projected simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> T cell electrophysiology<br />

is based <strong>on</strong> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e electrophysiology <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pancreatic<br />

beta cell [1]. The T cell model is based <strong>on</strong> single protein c<strong>on</strong>ductance data and, in a<br />

first step, is focussed <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e electrophysiology <str<strong>on</strong>g>of</str<strong>on</strong>g> a resting T helper cell. In a sec<strong>on</strong>d<br />

step, <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resting T lymphocyte will be adapted to <str<strong>on</strong>g>th</str<strong>on</strong>g>e activated<br />

T cell state. Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is simulati<strong>on</strong> it is planned to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> inhibiting<br />

and exciting drugs <strong>on</strong>to T cell activati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium dynamics.<br />

References.<br />

[1] Meyer-Hermann, Michael E. The Electrophysiology <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ß-Cell Based <strong>on</strong> Single Transmembrane<br />

Protein Characteristics. Biophysical Journal 93, 2007: 2952-2968<br />

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Modeling Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Biological Systems; Tuesday, June 28, 17:00<br />

Deena Schmidt<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biosciences Institute, Ohio State University<br />

e-mail: dschmidt@mbi.osu.edu<br />

Janet Best<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Ohio State University<br />

e-mail: jbest@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ohio-state.edu<br />

Mark S. Blumberg<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Psychology, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Iowa<br />

e-mail: mark-blumberg@uiowa.edu<br />

Linking network structure and stochastic dynamics to neural<br />

activity patterns involved in sleep-wake regulati<strong>on</strong><br />

Sleep and wake states are each maintained by activity in a corresp<strong>on</strong>ding neur<strong>on</strong>al<br />

network, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mutually inhibitory c<strong>on</strong>necti<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>e networks. In infant<br />

mammals, <str<strong>on</strong>g>th</str<strong>on</strong>g>e durati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> states are exp<strong>on</strong>entially distributed, whereas in<br />

adults, <str<strong>on</strong>g>th</str<strong>on</strong>g>e wake states yield a heavy-tailed distributi<strong>on</strong>. What drives <str<strong>on</strong>g>th</str<strong>on</strong>g>is transformati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e wake distributi<strong>on</strong>? Is it <str<strong>on</strong>g>th</str<strong>on</strong>g>e altered network structure or a change in<br />

neur<strong>on</strong>al dynamics? What properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network are necessary for maintenance<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> neural activity <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network and what mechanisms are involved in transiti<strong>on</strong>ing<br />

between sleep and wake states? We explore <str<strong>on</strong>g>th</str<strong>on</strong>g>ese issues using random graph <str<strong>on</strong>g>th</str<strong>on</strong>g>eory,<br />

specifically looking at stochastic processes occurring <strong>on</strong> random graphs, and also<br />

by investigating <str<strong>on</strong>g>th</str<strong>on</strong>g>e accuracy <str<strong>on</strong>g>of</str<strong>on</strong>g> predicti<strong>on</strong>s made by deterministic approximati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic processes <strong>on</strong> networks.<br />

References.<br />

[1] D. Schmidt, J. Best, M.S. Blumberg, Random graph and stochastic process c<strong>on</strong>tributi<strong>on</strong>s to<br />

network dynamics (submitted).<br />

[2] M.S. Blumberg et al., Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> sleep-wake cyclicity in developing rats PNAS 102 14860–<br />

14864.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> physiological processes in patients <strong>on</strong> dialysis;<br />

Saturday, July 2, 11:00<br />

Daniel Schneditz<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physiology, Medical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Graz, Graz, Austria<br />

e-mail: daniel.schneditz@medunigraz.at<br />

Physiology-based approach to modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> dialysis<br />

Physiologically based pharmacokinetic models attempt to utilize basic physiological,<br />

biochemical, biophysical, and physicochemical informati<strong>on</strong> to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

distributi<strong>on</strong>, dispositi<strong>on</strong>, c<strong>on</strong>versi<strong>on</strong>, and eliminati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a given substance. More<br />

specifically, such models require informati<strong>on</strong> about organ volumes, physiological<br />

blood flow rates, solute generati<strong>on</strong> rates, enzymatic reacti<strong>on</strong>s, as well as informati<strong>on</strong><br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ermodynamic characteristics such as solubilities, dissociati<strong>on</strong> c<strong>on</strong>stants, partiti<strong>on</strong><br />

coefficients, diffusivities, and membrane permeabilities. Teorell was am<strong>on</strong>g<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e first to present a physiologically based pharmacokinetic model more <str<strong>on</strong>g>th</str<strong>on</strong>g>an 70<br />

years ago [1].<br />

The distributi<strong>on</strong> volume, <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> compartments, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e exchange <str<strong>on</strong>g>of</str<strong>on</strong>g> solute<br />

between compartments are important comp<strong>on</strong>ents <str<strong>on</strong>g>of</str<strong>on</strong>g> a kinetic model. Models<br />

for hemodialysis are characteristic for assuming a change in compartment volume<br />

because <str<strong>on</strong>g>of</str<strong>on</strong>g> ultrafiltrati<strong>on</strong>. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, rate c<strong>on</strong>stants describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e exchange<br />

between compartments, <str<strong>on</strong>g>th</str<strong>on</strong>g>e generati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e eliminati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> solute are<br />

generally assumed as c<strong>on</strong>stant.<br />

Parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> physiologically based models have an important meaning. For example,<br />

transport wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in and between compartments is described by c<strong>on</strong>vecti<strong>on</strong> and<br />

diffusi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiovascular system. Two limiting cases <str<strong>on</strong>g>of</str<strong>on</strong>g> transport may<br />

be distinguished: Flow-limited transport for solutes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high diffusivity and membrane<br />

permeability such as urea, and diffusi<strong>on</strong>-limited transport for solutes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> low<br />

membrane permeability such as creatinine. Notice <str<strong>on</strong>g>th</str<strong>on</strong>g>at transport <str<strong>on</strong>g>of</str<strong>on</strong>g> solutes between<br />

organs is determined by c<strong>on</strong>vecti<strong>on</strong> irrespective <str<strong>on</strong>g>of</str<strong>on</strong>g> solute diffusivity. The importance<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> organ perfusi<strong>on</strong> for solute kinetics in hemodialysis was first recognized by<br />

Dedrick [2]. Thus, even if diffusi<strong>on</strong> across cell membranes is almost instantaneous<br />

for substances such as urea, <str<strong>on</strong>g>th</str<strong>on</strong>g>e equilibrati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>roughout <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole body during<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e typical post-dialysis urea rebound takes about 30 min because <str<strong>on</strong>g>of</str<strong>on</strong>g> differences<br />

in regi<strong>on</strong>al perfusi<strong>on</strong> [3]. Surprisingly, a similar time course is observed for o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

solutes such as creatinine which, unlike urea, have much reduced membrane permeability.<br />

The kinetics for bo<str<strong>on</strong>g>th</str<strong>on</strong>g> urea and creatinine (and possibly o<str<strong>on</strong>g>th</str<strong>on</strong>g>er solutes)<br />

can be described by a unified model combining flow-limited transport between organs<br />

and diffusi<strong>on</strong>-limited transport wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in organs [4]. The assumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>stant<br />

exchange rates between compartments must be questi<strong>on</strong>ed when hemodialysis and<br />

ultrafiltrati<strong>on</strong>-induced changes in blood volume are known to affect cardiovascular<br />

c<strong>on</strong>trol and regi<strong>on</strong>al blood flow distributi<strong>on</strong> [5, 6].<br />

Indicator diluti<strong>on</strong> has a l<strong>on</strong>g traditi<strong>on</strong> in physiology to model characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

solute transport and to identify important model parameters inaccessible to direct<br />

measurement [7, 8]. In hemodialysis, <str<strong>on</strong>g>th</str<strong>on</strong>g>e focus <str<strong>on</strong>g>of</str<strong>on</strong>g> indicator diluti<strong>on</strong> is <strong>on</strong> measuring<br />

blood flows such as access blood flow and cardiac output, and distributi<strong>on</strong> volumes<br />

such as central blood volume and lung water [9, 10]. A variant <str<strong>on</strong>g>of</str<strong>on</strong>g> indicator diluti<strong>on</strong><br />

868

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> ultrafiltrati<strong>on</strong>-induced changes in blood volume and vascular refilling<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e microcirculati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e purpose <str<strong>on</strong>g>of</str<strong>on</strong>g> understanding fluid balance during<br />

hemodialysis [11, 12].<br />

Physiologic models are more complex and require more data <str<strong>on</strong>g>th</str<strong>on</strong>g>at usually cannot<br />

be obtained in <str<strong>on</strong>g>th</str<strong>on</strong>g>e single experiment. It is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten impossible to analyze various<br />

tissues relating to specific compartments, especially in man, and <strong>on</strong>e has to rely<br />

<strong>on</strong> in-vitro or animal data. In additi<strong>on</strong> to data acquisiti<strong>on</strong> problems, <str<strong>on</strong>g>th</str<strong>on</strong>g>e models<br />

are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten composed <str<strong>on</strong>g>of</str<strong>on</strong>g> complex sets <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear differential equati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at must<br />

be solved numerically. Also, <str<strong>on</strong>g>th</str<strong>on</strong>g>e expansi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> compartments has been criticized as<br />

an additi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> arbitrary parameters to artificially improve <str<strong>on</strong>g>th</str<strong>on</strong>g>e model fit whereas<br />

in reality each additi<strong>on</strong>al compartment represents a c<strong>on</strong>straint <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be checked<br />

against real data should <str<strong>on</strong>g>th</str<strong>on</strong>g>ey become available [13].<br />

Physiologically based kinetic models can be used to identify meaningful physiological<br />

parameters inaccessible to direct measurements such as volumes, flows,<br />

and permeabilities. Unlike statistical models extrapolati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanistic models<br />

outside <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> data is possible wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some c<strong>on</strong>fidence. In hemodialysis <str<strong>on</strong>g>th</str<strong>on</strong>g>is is<br />

important when scaling <str<strong>on</strong>g>th</str<strong>on</strong>g>e treatment wi<str<strong>on</strong>g>th</str<strong>on</strong>g> regard to treatment durati<strong>on</strong>, treatment<br />

frequency, and body size [14, 15].<br />

References.<br />

[1] Teorell T. Kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> substances administered to <str<strong>on</strong>g>th</str<strong>on</strong>g>e body. Arch Int Pharmacodyn<br />

Therap 1937; 57: 205-240<br />

[2] Dedrick RL, Gabelnick HL, Bisch<str<strong>on</strong>g>of</str<strong>on</strong>g>f KB. Kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> urea distributi<strong>on</strong>. Proc XXI EMBS 1968;<br />

10: 36.1<br />

[3] Schneditz D, Van St<strong>on</strong>e JC, Daugirdas JT. A regi<strong>on</strong>al blood circulati<strong>on</strong> alternative to in-series<br />

two compartment urea kinetic modeling. ASAIO J 1993; 39: M573-M577<br />

[4] Schneditz D, Platzer D, Daugirdas JT. A diffusi<strong>on</strong>-adjusted regi<strong>on</strong>al blood flow model to<br />

predict solute kinetics during haemodialysis. Nephrol Dial Transplant 2009; 24: 2218-2224<br />

[5] George TO, Priester-Coary A, Dunea G, et al. Cardiac output and urea kinetics in dialysis<br />

patients: Evidence supporting <str<strong>on</strong>g>th</str<strong>on</strong>g>e regi<strong>on</strong>al blood flow model. Kidney Int 1996; 50: 1273-1277<br />

[6] Kanagasundaram NS, Greene T, Larive AB, et al. Dosing intermittent haemodialysis in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

intensive care unit patient wi<str<strong>on</strong>g>th</str<strong>on</strong>g> acute renal failure–estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> urea removal and evidence<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e regi<strong>on</strong>al blood flow model. Nephrol Dial Transplant 2008; 23: 2286-2298<br />

[7] Bassing<str<strong>on</strong>g>th</str<strong>on</strong>g>waighte JB, Ackerman FH, Wood EH. Applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lagged normal density<br />

curve as a model for arterial diluti<strong>on</strong> curves. Circ Res 1966; 18: 398-415<br />

[8] Krejcie TC, Hen<str<strong>on</strong>g>th</str<strong>on</strong>g>orn TK, Niemann CU, et al. Recirculatory pharmacokinetic models <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

markers <str<strong>on</strong>g>of</str<strong>on</strong>g> blood, extracellular fluid and total body water administered c<strong>on</strong>comitantly. J<br />

Pharmacol Exp Ther 1996; 278: 1050-1057<br />

[9] Depner TA, Krivitski NM. Clinical measurement <str<strong>on</strong>g>of</str<strong>on</strong>g> blood flow in hemodialysis access fistulae<br />

and grafts by ultrasound diluti<strong>on</strong>. ASAIO J 1995; 41: M745-M749<br />

[10] Krivitski NM, Depner TA. Cardiac output and central blood volume during hemodialysis:<br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology. Adv Ren Replace Ther 1999; 6: 225-232<br />

[11] Schneditz D, Roob JM, Oswald M, et al. Nature and rate <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular refilling during hemodialysis<br />

and ultrafiltrati<strong>on</strong>. Kidney Int 1992; 42: 1425-1433<br />

[12] Chamney PW, Johner C, Aldridge C, et al. Fluid balance modelling in patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> kidney<br />

failure. J Med Eng Technol 1999; 23: 45-52<br />

[13] Alquist M, Thysell H, Ungerstedt U, Hegbrant J. Urea c<strong>on</strong>centrati<strong>on</strong> gradient between muscle<br />

interstitium and plasma develops during hemodialysis. In: J Am Soc Nephrol, 1996, p. 1505<br />

[14] Daugirdas JT, Tattersall J. Effect <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment spacing and frequency <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree measures <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

equivalent clearance, including standard Kt/V. Nephrol Dial Transplant 2010; 25: 558-561<br />

[15] Daugirdas JT, Levin NW, Kotanko P, et al. Comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> proposed alternative me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

for rescaling dialysis dose: resting energy expenditure, high metabolic rate organ mass, liver<br />

size, and body surface area. Semin Dialysis 2008; 21: 377-384<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Kristan Schneider<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

e-mail: kristan.schneider@univie.ac.at<br />

Speciati<strong>on</strong>; Wednesday, June 29, 08:30<br />

Can dominance prevent <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> assortative mating<br />

and sympatric speciati<strong>on</strong>?<br />

C<strong>on</strong>sider a quantitative trait <str<strong>on</strong>g>th</str<strong>on</strong>g>at is under a mixture <str<strong>on</strong>g>of</str<strong>on</strong>g> frequency-independent<br />

stabilizing selecti<strong>on</strong> and density- and frequency-dependent selecti<strong>on</strong> caused by intraspecific<br />

competiti<strong>on</strong> for a c<strong>on</strong>tinuum <str<strong>on</strong>g>of</str<strong>on</strong>g> resources. The trait is determined by a<br />

single (ecological) locus and expresses intermediate dominance, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong><br />

mates assortatively wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>is trait.<br />

We study wea<str<strong>on</strong>g>th</str<strong>on</strong>g>er mutati<strong>on</strong>s at modifier loci can invade, which ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er increase<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> dominance or <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> assortment. From a naïve point <str<strong>on</strong>g>of</str<strong>on</strong>g> view,<br />

complete dominance and complete assortative mating seem to be two alternative<br />

mechanisms to eliminate unfit <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring wi<str<strong>on</strong>g>th</str<strong>on</strong>g> intermediate traits. However, we will<br />

see <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> assortative mating and dominance is ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er complex. The<br />

two evoluti<strong>on</strong>ary resp<strong>on</strong>ses can promote each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er or hinder each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er. Overall,<br />

we find <str<strong>on</strong>g>th</str<strong>on</strong>g>at dominance might be <str<strong>on</strong>g>th</str<strong>on</strong>g>e more likely evoluti<strong>on</strong>ary outcome, and <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> assortative mating in small steps leading to sympatric speciati<strong>on</strong><br />

seems unlikely.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Structure and Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemical Reacti<strong>on</strong> Networks II; Tuesday, June<br />

28, 17:00<br />

Santiago Schnell<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Michigan Medical School<br />

e-mail: schnells@umich.edu<br />

A model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold behavior reveals rescue mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

bystander proteins in c<strong>on</strong>formati<strong>on</strong>al diseases<br />

C<strong>on</strong>formati<strong>on</strong>al diseases result from <str<strong>on</strong>g>th</str<strong>on</strong>g>e failure <str<strong>on</strong>g>of</str<strong>on</strong>g> a speci<br />

c protein to fold into its correct functi<strong>on</strong>al state. The misfolded proteins can<br />

lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e toxic aggregati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> proteins. Protein misfolding in c<strong>on</strong>formati<strong>on</strong>al diseases<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g>ten displays a <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold behavior characterized by a sudden shift between<br />

n<strong>on</strong>toxic to toxic levels <str<strong>on</strong>g>of</str<strong>on</strong>g> protein misfolds. In some c<strong>on</strong>formati<strong>on</strong>al diseases, evidence<br />

suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at misfolded proteins interact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> bystander proteins (unfolded<br />

and native folded proteins), eliciting a misfolded phenotype. These bystander isomers<br />

would follow <str<strong>on</strong>g>th</str<strong>on</strong>g>eir normal physiological pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways in absence <str<strong>on</strong>g>of</str<strong>on</strong>g> misfolded<br />

proteins. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper we present a general mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> bystander and misfolded<br />

protein interacti<strong>on</strong> which we have used to investigate how <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold behavior<br />

in protein misfolding is triggered in c<strong>on</strong>formati<strong>on</strong>al diseases. Using a c<strong>on</strong>tinuous<br />

flow reactor model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e endoplasmic reticulum, we found <str<strong>on</strong>g>th</str<strong>on</strong>g>at slight changes in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e bystander protein residence time in <str<strong>on</strong>g>th</str<strong>on</strong>g>e endoplasmic reticulum or <str<strong>on</strong>g>th</str<strong>on</strong>g>e ratio <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

basal misfolded to bystander protein in ow rates can trigger <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold behavior<br />

in protein misfolding. Our analysis reveals <str<strong>on</strong>g>th</str<strong>on</strong>g>ree mechanisms to rescue bystander<br />

proteins in c<strong>on</strong>formati<strong>on</strong>al diseases. The results <str<strong>on</strong>g>of</str<strong>on</strong>g> our model can now help direct<br />

experiments to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold behavior and develop <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic strategies<br />

targeting <str<strong>on</strong>g>th</str<strong>on</strong>g>e modulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>formati<strong>on</strong>al diseases.<br />

871

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis II; Wednesday, June<br />

29, 11:00<br />

Richard Schugart<br />

Western Kentucky University<br />

e-mail: richard.schugart@wku.edu<br />

Jennifer Flegg<br />

Queensland University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: j.flegg@qut.edu.au<br />

D.L.S. McElwain<br />

Queensland University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: s.mcelwain@qut.edu.au<br />

Using ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling to assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e efficacy <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

oxygen for problem wounds: use <str<strong>on</strong>g>of</str<strong>on</strong>g> hyperbaric or topical<br />

oxygen <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies<br />

We extend a previously developed ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model [1] for acute wound healing<br />

to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> hyperbaric and topical oxygen <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies to treat<br />

acute, delayed, and chr<strong>on</strong>ic wounds. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, I will present <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, a sensitivity<br />

analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, and simulati<strong>on</strong> results for treating <str<strong>on</strong>g>th</str<strong>on</strong>g>e wound wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

hyperbaric and topical oxygen <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies.<br />

References.<br />

[1] R.C. Schugart, A. Friedman, R. Zhao, C.K. Sen, Wound angiogenesis as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue<br />

oxygen tensi<strong>on</strong>: a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model PNAS USA 105 2628–33.<br />

872

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Anna Schulze<br />

German Cancer Research Center (DKFZ)<br />

e-mail: anna.schulze@dkfz.de<br />

Luca Sime<strong>on</strong>i<br />

Otto-v<strong>on</strong>-Guericke-University Magdeburg<br />

Thomas Hoefer<br />

German Cancer Research Center (DKFZ)<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> T-Cell Signaling: Anergy versus Proliferati<strong>on</strong><br />

T-cells are activated by interacti<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>e T-cell receptor (TCR) and peptides<br />

bound to <str<strong>on</strong>g>th</str<strong>on</strong>g>e major histocompatibility complex (MHC). The activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

TCRs initiates several signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways <str<strong>on</strong>g>th</str<strong>on</strong>g>at are necessary for <str<strong>on</strong>g>th</str<strong>on</strong>g>e proper cellular<br />

resp<strong>on</strong>se to <str<strong>on</strong>g>th</str<strong>on</strong>g>e presented peptides. We investigated <str<strong>on</strong>g>th</str<strong>on</strong>g>e activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Erk<br />

Protein by means <str<strong>on</strong>g>of</str<strong>on</strong>g> a data-based ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model, focusing <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e feedback<br />

mechanisms wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>is pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way <str<strong>on</strong>g>th</str<strong>on</strong>g>at could explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed kinetics. T-cells<br />

were stimulated by antibodies cross-linked in soluti<strong>on</strong> (sAbs) as well as by antibodies<br />

immobilized <strong>on</strong> microbeads (iAbs). The stimulati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> sAbs shows a str<strong>on</strong>g,<br />

but transient signal whereas <str<strong>on</strong>g>th</str<strong>on</strong>g>e iAbs stimulus leads to a sustained signal <str<strong>on</strong>g>th</str<strong>on</strong>g>at results<br />

in a str<strong>on</strong>g activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Erk. The str<strong>on</strong>ger stimulus (sAbs) results in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

weaker activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Erk, which indicates <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Erk is regulated by<br />

feedback. We developed a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model based <strong>on</strong> ordinary differential equati<strong>on</strong>s,<br />

which promotes LAT as an important element <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e feedback mechanisms.<br />

Depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e input signal LAT reaches different states <str<strong>on</strong>g>of</str<strong>on</strong>g> phosphorylati<strong>on</strong>. By<br />

splitting <str<strong>on</strong>g>th</str<strong>on</strong>g>e signal at LAT level feedback can be regulated by <str<strong>on</strong>g>th</str<strong>on</strong>g>ose different states<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> LAT. First simulati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental-observed<br />

dynamics can be explained much better <str<strong>on</strong>g>th</str<strong>on</strong>g>an wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a simpler model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at also includes feedback, but no signal splitting at LAT.<br />

873

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Noisy Cells; Saturday, July 2, 14:30<br />

Tilo Schwalger<br />

Max Planck Institute for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Physics <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Systems<br />

e-mail: tilo@pks.mpg.de<br />

How stochastic adaptati<strong>on</strong> currents shape interspike interval<br />

statistics <str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>s - <str<strong>on</strong>g>th</str<strong>on</strong>g>eory and experiment<br />

Trial-to-trial variability and irregular spiking is an ubiquitous phenomen<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>roughout<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e nervous system. In many cases, <str<strong>on</strong>g>th</str<strong>on</strong>g>e origin <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is neural noise is not known<br />

and difficult to access experimentally. Here, we explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility to distinguish<br />

between two kinds <str<strong>on</strong>g>of</str<strong>on</strong>g> intrinsic noise solely from <str<strong>on</strong>g>th</str<strong>on</strong>g>e interspike interval (ISI)<br />

statistics <str<strong>on</strong>g>of</str<strong>on</strong>g> a neur<strong>on</strong>. To <str<strong>on</strong>g>th</str<strong>on</strong>g>is end, we c<strong>on</strong>sider an integrate-and-fire model wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

spike-frequency adaptati<strong>on</strong> in which fluctuati<strong>on</strong>s (channel noise) are ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er associated<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> fast i<strong>on</strong>ic currents or wi<str<strong>on</strong>g>th</str<strong>on</strong>g> slow adaptati<strong>on</strong> currents. We show by means<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> analytical techniques <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e shape <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ISI histograms and <str<strong>on</strong>g>th</str<strong>on</strong>g>e ISI correlati<strong>on</strong>s<br />

are markedly different in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> cases: for a deterministic adaptati<strong>on</strong> current,<br />

ISIs are distributed according to an inverse Gaussian density and <str<strong>on</strong>g>th</str<strong>on</strong>g>e ISI correlati<strong>on</strong>s<br />

are negative. In c<strong>on</strong>trast, for stochastic adaptati<strong>on</strong> currents, <str<strong>on</strong>g>th</str<strong>on</strong>g>e ISI density<br />

is more peaked <str<strong>on</strong>g>th</str<strong>on</strong>g>an an inverse Gaussian density and <str<strong>on</strong>g>th</str<strong>on</strong>g>e serial correlati<strong>on</strong>s are<br />

positive. We applied <str<strong>on</strong>g>th</str<strong>on</strong>g>ese measures to intracellular recordings <str<strong>on</strong>g>of</str<strong>on</strong>g> locust auditory<br />

receptor cells in vivo. By varying <str<strong>on</strong>g>th</str<strong>on</strong>g>e stimulus intensity, we observed intriguingly<br />

similar statistics corresp<strong>on</strong>ding to bo<str<strong>on</strong>g>th</str<strong>on</strong>g> cases <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model. The results suggest<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at stochasticity <str<strong>on</strong>g>of</str<strong>on</strong>g> slow adaptati<strong>on</strong> currents may c<strong>on</strong>tribute to neural variability<br />

in sensory neur<strong>on</strong>s.<br />

References.<br />

[1] Schwalger T, Fisch K, Benda J, Lindner B: How noisy adaptati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>s shapes interspike<br />

interval histograms and correlati<strong>on</strong>s. PLoS Comput Biol 2010, 6(12): e1001026<br />

874

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Genetics and Genomics; Wednesday, June 29, 08:30<br />

Veit Schwämmle<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemistry and Molecular Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Sou<str<strong>on</strong>g>th</str<strong>on</strong>g>ern Denmark, Campusvej 55, DK-5230 Odense M, Denmark<br />

e-mail: veits@bmb.sdu.dk<br />

Kim Sneppen<br />

Center for Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Life, Niels Bohr Institute, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Copenhagen,<br />

Blegdamsvej 17, 2100 Copenhagen Ø, Denmark<br />

Ole Nørregaard Jensen<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemistry and Molecular Biology, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Sou<str<strong>on</strong>g>th</str<strong>on</strong>g>ern Denmark, Campusvej 55, DK-5230 Odense M, Denmark<br />

The formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> hist<strong>on</strong>e modificati<strong>on</strong> domains<br />

Hist<strong>on</strong>es proteins are key players in <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> eukaryotes. Many <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir wi<str<strong>on</strong>g>th</str<strong>on</strong>g> post-translati<strong>on</strong>al modificati<strong>on</strong>s decorated is<str<strong>on</strong>g>of</str<strong>on</strong>g>orms are organized in spatial<br />

domains al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e DNA string <str<strong>on</strong>g>of</str<strong>on</strong>g> a chromosome. For instance, a large part <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e transcripti<strong>on</strong>ally inactive genome is densely packed and forms large domains.<br />

This heterochromatin has its hist<strong>on</strong>es modified by me<str<strong>on</strong>g>th</str<strong>on</strong>g>ylati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nin<str<strong>on</strong>g>th</str<strong>on</strong>g> amino<br />

acid (a lysine) <str<strong>on</strong>g>of</str<strong>on</strong>g> hist<strong>on</strong>e type H3 (H3K9me). We propose a simple computer model<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at simulates <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> heterochromatin over <str<strong>on</strong>g>th</str<strong>on</strong>g>e human chromosomes<br />

by assuming a competiti<strong>on</strong> between H3K9 me<str<strong>on</strong>g>th</str<strong>on</strong>g>ylati<strong>on</strong> and H3K4 me<str<strong>on</strong>g>th</str<strong>on</strong>g>ylati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

latter being an abundant activating modificati<strong>on</strong>. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> marks are related to nucleati<strong>on</strong><br />

sites <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e genome and spread from <str<strong>on</strong>g>th</str<strong>on</strong>g>ese sites due to simple mechanisms.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> marks are mutually exclusive [2] and <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore compete against<br />

each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model, we are able to explain why heterochromatin does<br />

not occupy <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire chromosomes and could reproduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> measured<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e ChIP-seq experiments from [1]. The fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er extensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model to a<br />

large number <str<strong>on</strong>g>of</str<strong>on</strong>g> hist<strong>on</strong>e modificati<strong>on</strong>s allows <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> complex switch-like<br />

behavior.<br />

References.<br />

[1] A. Barski et al., High-resoluti<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iling <str<strong>on</strong>g>of</str<strong>on</strong>g> hist<strong>on</strong>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>ylati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e human genome. Cell,<br />

129 823–837 2007.<br />

[2] K. Nishioka et al., Set9, a novel hist<strong>on</strong>e H3 me<str<strong>on</strong>g>th</str<strong>on</strong>g>yltransferase <str<strong>on</strong>g>th</str<strong>on</strong>g>at facilitates transcripti<strong>on</strong> by<br />

precluding hist<strong>on</strong>e tail modificati<strong>on</strong>s required for heterochromatin formati<strong>on</strong>. Genes Dev. 16<br />

479–489 2002.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Recent advances in infectious disease modelling I; Saturday, July 2, 11:00<br />

Elissa Schwartz<br />

Washingt<strong>on</strong> State University<br />

e-mail: ejs@wsu.edu<br />

Immune Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Equine Infectious Anemia Virus<br />

Equine Infectious Anemia Virus (EIAV) is a retrovirus <str<strong>on</strong>g>th</str<strong>on</strong>g>at establishes a persistent<br />

infecti<strong>on</strong> in horses and p<strong>on</strong>ies. The virus is in <str<strong>on</strong>g>th</str<strong>on</strong>g>e same lentivirus subgroup <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

includes human immunodeficiency virus (HIV). The similarities between <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two<br />

viruses make <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune resp<strong>on</strong>se to EIAV relevant to research <strong>on</strong><br />

HIV. We developed a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> in-host EIAV infecti<strong>on</strong> dynamics <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

c<strong>on</strong>tains bo<str<strong>on</strong>g>th</str<strong>on</strong>g> humoral and cell-mediated immune resp<strong>on</strong>ses. The model is parameterized<br />

using clinical, virological, and immunological data from horses infected wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

EIAV. Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model yields results <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>resholds <str<strong>on</strong>g>th</str<strong>on</strong>g>at would be necessary<br />

for a combined immune resp<strong>on</strong>se to successfully c<strong>on</strong>trol infecti<strong>on</strong>. Numerical simulati<strong>on</strong>s<br />

are presented to illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e results. These findings have <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential to<br />

lead to immunological c<strong>on</strong>trol measures for retroviral infecti<strong>on</strong>.<br />

876

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multi-scale ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver: From intracellular signaling to<br />

intercellular interacti<strong>on</strong>; Wednesday, June 29, 08:30<br />

Lars Ole Schwen<br />

Fraunh<str<strong>on</strong>g>of</str<strong>on</strong>g>er MEVIS, Bremen, Germany<br />

e-mail: ole.schwen@mevis.fraunh<str<strong>on</strong>g>of</str<strong>on</strong>g>er.de<br />

Tobias Preusser<br />

Fraunh<str<strong>on</strong>g>of</str<strong>on</strong>g>er MEVIS, Bremen, Germany<br />

C<strong>on</strong>structive Algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms for Modeling Realistic Vascular<br />

Structures<br />

The liver is <str<strong>on</strong>g>th</str<strong>on</strong>g>e major metabolic organ in <str<strong>on</strong>g>th</str<strong>on</strong>g>e human body as it fulfills a huge variety<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> vital metabolic tasks. The most important link between <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver and <str<strong>on</strong>g>th</str<strong>on</strong>g>e rest <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e organism is <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood flow <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ree vascular systems (hepatic artery,<br />

portal vein, hepatic vein). In order to properly model <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver, it<br />

is crucial to have an appropriate model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood transportati<strong>on</strong> systems.<br />

In vivo 3D CT imaging and subsequent image processing provides <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> vascular systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> limited resoluti<strong>on</strong> far from <str<strong>on</strong>g>th</str<strong>on</strong>g>e scale <str<strong>on</strong>g>of</str<strong>on</strong>g> individual lobule,<br />

sinusoids and liver cells <strong>on</strong> which <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolic functi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e liver take place.<br />

To bridge <str<strong>on</strong>g>th</str<strong>on</strong>g>is gap in resoluti<strong>on</strong>, models for vascular structures can be used. In<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e talk, we present an extensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e C<strong>on</strong>strained C<strong>on</strong>structive Optimizati<strong>on</strong><br />

(Schreiner et al.) and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Global C<strong>on</strong>structive Optimizati<strong>on</strong> (Georg et al.) approach<br />

for hepatic blood vessels. Based <strong>on</strong> topological and geometrical analyses<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> many different human hepatic vascular structures, we evaluate <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms.<br />

We introduce parameters and adapt <str<strong>on</strong>g>th</str<strong>on</strong>g>em such <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e generated vascular<br />

systems geometrically closely resemble natural <strong>on</strong>es. This resemblance is quantified<br />

by a statistical comparis<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e geometric properties <str<strong>on</strong>g>of</str<strong>on</strong>g> real human hepatic<br />

vascular structures.<br />

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Mechanical Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Movement and Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cells and Tissues II;<br />

Wednesday, June 29, 17:00<br />

Marco Scianna<br />

Politecnico di Torino<br />

e-mail: marcosci1@alice.it<br />

Multiscale model <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor-derived capillary-like network<br />

formati<strong>on</strong><br />

Solid tumors must recruit and form new blood vessels for maintenance, grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

and detachments <str<strong>on</strong>g>of</str<strong>on</strong>g> metastases [1]. Vascularizati<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>us a pivotal switch in cancer<br />

malignancy and an accurate analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> its driving processes is a big issue for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> pharmacological treatments, giving rise to multiple experimental<br />

models. In particular, tubulogenic assays have dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at tumor-derived<br />

endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells (TECs), cultured in Matrigel (a commercial gelatinous protein mixture<br />

acting as basement membrane matrix), are able to aut<strong>on</strong>omously organize in a<br />

c<strong>on</strong>nected network, which mimics an in vivo capillary plexus [3]. Such a process is<br />

promoted by <str<strong>on</strong>g>th</str<strong>on</strong>g>e activity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluble peptide vascular endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factor<br />

(VEGF, [2]) as well as by <str<strong>on</strong>g>th</str<strong>on</strong>g>e induced intracellular calcium signals [5]. We here<br />

propose and discuss a multilevel hybrid model which reproduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e main features<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental system: it incorporates a c<strong>on</strong>tinuous model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic<br />

VEGF-induced calcium-dependent regulatory cascades, and a discrete mesoscopic<br />

Cellular Potts Model (CPM, [4]) describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e phenomenological evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

single cells. The two comp<strong>on</strong>ents are unified and interfaced, and produce a multiscale<br />

framework characterized by a c<strong>on</strong>stant flux <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> from finer to<br />

coarser levels: in particular, <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular sub-cellular events realistically regulate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e mesoscopic biophysical properties, behaviors and interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulated<br />

TECs. The model results are in good agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis performed in<br />

published experimental data, allowing to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e key mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> network<br />

formati<strong>on</strong> as well as to characterize its topological properties [7]. Moreover, by<br />

varying important model parameters, we are able to simulate some pharmacological<br />

interventi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at are currently in use, c<strong>on</strong>firming <str<strong>on</strong>g>th</str<strong>on</strong>g>eir efficiency, and, more<br />

interestingly, to propose some new <str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic approaches, <str<strong>on</strong>g>th</str<strong>on</strong>g>at are counter intuitive<br />

but potentially effective [6].<br />

References.<br />

[1] Carmeliet, P., Jain, R. K., 2000. Angiogenesis in cancer and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er diseases. Nature, 407,<br />

249–257.<br />

[2] Carmeliet, P., 2005. VEGF as a key mediator <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis in cancer. Oncology, 69, 4 –<br />

10.<br />

[3] Fiorio Pla, A., Grange, C., Ant<strong>on</strong>iotti, S., Tomatis, C., Merlino, A., Bussolati, B., Munar<strong>on</strong>,<br />

L., 2008. Arachid<strong>on</strong>ic acid-induced Ca2+ entry is involved in early steps <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor angiogenesis.<br />

Mol Cancer Res, 6 (4), 535–545.<br />

[4] Graner, F., Glazier, J. A., 1992. Simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biological cell sorting using a two dimensi<strong>on</strong>al<br />

extended Potts model. Phys Rev Lett, 69, 2013–2017.<br />

[5] Munar<strong>on</strong>, L., Tomatis, C., Fiorio Pla, A., 2008. The secret marriage between calcium and<br />

tumor angiogenesis. Technol Cancer Res Treat, 7 (4), 335–339.<br />

[6] Scianna, M., Munar<strong>on</strong>, L., Preziosi, L., 2010. A multiscale hybrid approach for<br />

vasculogenesis and related potential blocking <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies. Prog Biophys Mol Biol, doi:<br />

10.1016/j.pbiomolbio.2011.01.004, in press.<br />

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[7] Scianna, M., Munar<strong>on</strong>, L., 2010. Multiscale model <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor-derived capillary-like network<br />

formati<strong>on</strong>. Submitted for publicati<strong>on</strong>.<br />

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Evoluti<strong>on</strong>ary Ecology; Friday, July 1, 14:30<br />

Jacob Scott<br />

Integrative Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Oncology, H. Lee M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center<br />

e-mail: jacob.g.scott@gmail.com<br />

David Basanta<br />

Integrative Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Oncology, H. Lee M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center<br />

Alexander Anders<strong>on</strong><br />

Integrative Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Oncology, H. Lee M<str<strong>on</strong>g>of</str<strong>on</strong>g>fitt Cancer Center<br />

Choose your neighbourhood wisely: <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

neighbourhood geometry in spatial agent based models <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

biological systems<br />

Agent based spatial models are <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e best known ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical tools to model<br />

biological systems. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart <str<strong>on</strong>g>of</str<strong>on</strong>g> most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models is a lattice which <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

agents inhabit and where <str<strong>on</strong>g>th</str<strong>on</strong>g>ey behave depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

agents in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir neighbourhood. Despite its importance, <str<strong>on</strong>g>th</str<strong>on</strong>g>e choice <str<strong>on</strong>g>of</str<strong>on</strong>g> nearestneighbor<br />

geometry is usually arbitrarily made wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out regard to <str<strong>on</strong>g>th</str<strong>on</strong>g>e bias <str<strong>on</strong>g>th</str<strong>on</strong>g>at it<br />

might introduce into <str<strong>on</strong>g>th</str<strong>on</strong>g>e results from <str<strong>on</strong>g>th</str<strong>on</strong>g>e model.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is abstract we explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> nearest neighbor geometry <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

propagati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>ary strategies wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e help <str<strong>on</strong>g>of</str<strong>on</strong>g> a cellular automat<strong>on</strong> in<br />

which cells play <str<strong>on</strong>g>th</str<strong>on</strong>g>e pris<strong>on</strong>er’s dilemma game. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>is CA we compare several<br />

2-dimensi<strong>on</strong>al architectures (v<strong>on</strong> Neumann and Moore neighbourhoods as well as a<br />

regular hexag<strong>on</strong>al lattice). We also explore how <str<strong>on</strong>g>th</str<strong>on</strong>g>e outcomes change as we move<br />

from 2 to 3 dimensi<strong>on</strong>s.<br />

Our research highlights <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> neighbourhood architecture in agent<br />

based spatial ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models and suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at some models will have to<br />

c<strong>on</strong>sider different neighbourhood geometries as <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological system being modeled<br />

evolves. This work has implicati<strong>on</strong>s in many areas <str<strong>on</strong>g>of</str<strong>on</strong>g> biological modeling where<br />

tissue architecture changes <str<strong>on</strong>g>th</str<strong>on</strong>g>roughout development, but is most germane to cancer,<br />

microbiology and developmental biology.<br />

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Megan Selbach-Allen<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Liverpool<br />

e-mail: mesa@liv.ac.uk<br />

Dr. Kieran Sharkey<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Liverpool<br />

Epidemics; Wednesday, June 29, 11:00<br />

An investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold phenomen<strong>on</strong> in<br />

complex networks<br />

Classic mean-field models <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics are well known to exhibit <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold phenomena<br />

which are typically characterised by <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproductive ratio R0. A<br />

range <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical results can be obtained for <str<strong>on</strong>g>th</str<strong>on</strong>g>ese simple systems regarding<br />

aspects such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e final epidemic size and <str<strong>on</strong>g>th</str<strong>on</strong>g>e likelihood <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics occurring.<br />

Here we make an investigati<strong>on</strong> into <str<strong>on</strong>g>th</str<strong>on</strong>g>ese quantities for more complex epidemic<br />

systems. In particular, we c<strong>on</strong>sider epidemics propagated <strong>on</strong> c<strong>on</strong>tact networks. By<br />

using stochastic simulati<strong>on</strong>, we make an investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold phenomen<strong>on</strong><br />

and generate some novel insights wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some potential significance in real, heterogeneous<br />

systems. Additi<strong>on</strong>ally, by relating <str<strong>on</strong>g>th</str<strong>on</strong>g>ese quantities to steady state systems,<br />

we potentially gain a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical handle <strong>on</strong> analysing <str<strong>on</strong>g>th</str<strong>on</strong>g>ese systems.<br />

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Regulatory Networks; Tuesday, June 28, 17:00<br />

Lorenzo Sella † ‡ , Sander Hille † , Michael Emmerich ‡<br />

† Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Leiden University,<br />

‡ Leiden Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Advanced Computer Science<br />

e-mail: lsella@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.leidenuniv.nl, shille@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.leidenuniv.nl,<br />

emmerich@liacs.nl<br />

Simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> signaling and regulatory networks in B. subtilis<br />

B. subtilis is a Gram-positive bacterium comm<strong>on</strong>ly found in <str<strong>on</strong>g>th</str<strong>on</strong>g>e soil. This bacterium<br />

has been studied extensively especially for <str<strong>on</strong>g>th</str<strong>on</strong>g>e way it manages to induce<br />

itself to sporulate [1-4]. Sporulati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e creati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a spore is a last resort alternative<br />

a bacterium chooses to undertake when <str<strong>on</strong>g>th</str<strong>on</strong>g>e resources in <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment<br />

are not compatible wi<str<strong>on</strong>g>th</str<strong>on</strong>g> maintaining a normal metabolism, especially when <str<strong>on</strong>g>th</str<strong>on</strong>g>ere<br />

is shortage <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose, <str<strong>on</strong>g>th</str<strong>on</strong>g>e input <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular respirati<strong>on</strong>.<br />

In such c<strong>on</strong>diti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> an isogenic populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> B.subtilis is not<br />

uniform. Some bacteria sporulate, some faster <str<strong>on</strong>g>th</str<strong>on</strong>g>an o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers, some do not. This kind<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> behaviour is called bet hedging, and it is understood as a differentiati<strong>on</strong> strategy<br />

which maximize <str<strong>on</strong>g>th</str<strong>on</strong>g>e survival <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e col<strong>on</strong>y. In facts if <str<strong>on</strong>g>th</str<strong>on</strong>g>e shortage <str<strong>on</strong>g>of</str<strong>on</strong>g> resources is<br />

l<strong>on</strong>g lasting, sporulati<strong>on</strong> truly gives an advantage to individuals producing spores.<br />

Spores have very str<strong>on</strong>g endurance and almost a frozen metabolism. These spores<br />

can reactivate <str<strong>on</strong>g>th</str<strong>on</strong>g>eir metabolism when <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s turn to be more favourable.<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand if <str<strong>on</strong>g>th</str<strong>on</strong>g>e shortage <str<strong>on</strong>g>of</str<strong>on</strong>g> resource is <strong>on</strong>ly temporary <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

producing a spore is not advantageous because it is energetically expensive and<br />

it is not reversible; from an early stage <str<strong>on</strong>g>of</str<strong>on</strong>g> sporulati<strong>on</strong> any quick reappearance <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

resources would have not been exploited by <str<strong>on</strong>g>th</str<strong>on</strong>g>e new born spore.<br />

Sporulati<strong>on</strong> is a quite complex process which entails <str<strong>on</strong>g>th</str<strong>on</strong>g>e activity <str<strong>on</strong>g>of</str<strong>on</strong>g> more <str<strong>on</strong>g>th</str<strong>on</strong>g>an<br />

500 genes in a period <str<strong>on</strong>g>of</str<strong>on</strong>g> about 10 hours.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we want to c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e phase which trigger <str<strong>on</strong>g>th</str<strong>on</strong>g>e sporulati<strong>on</strong>, a<br />

phase where <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell produces <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein σ H , a sigma factor which plays a key role<br />

in triggering sporulati<strong>on</strong> in B. subtilis.<br />

Few parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is regulatory network are available in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

are mostly <str<strong>on</strong>g>th</str<strong>on</strong>g>e leng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> genes <str<strong>on</strong>g>of</str<strong>on</strong>g> proteins involved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e network. Statistical<br />

descripti<strong>on</strong> about chemical reacti<strong>on</strong>s rates, spatial dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> molecules and syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis<br />

producti<strong>on</strong> are almost totally unknown.<br />

Estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> order <str<strong>on</strong>g>of</str<strong>on</strong>g> magnitude <str<strong>on</strong>g>of</str<strong>on</strong>g> some parameters can be made by looking<br />

at <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>dent parameters in o<str<strong>on</strong>g>th</str<strong>on</strong>g>er species like E. choli.<br />

We combine <str<strong>on</strong>g>th</str<strong>on</strong>g>is comparis<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a rigorous approach. We have developed a<br />

s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware which perform a stochastic simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network which produces σ H .<br />

We <str<strong>on</strong>g>th</str<strong>on</strong>g>en identify unknown parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network by comparing <str<strong>on</strong>g>th</str<strong>on</strong>g>e output <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

our simulati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental data.<br />

The available experimental data is in <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> time series <str<strong>on</strong>g>of</str<strong>on</strong>g> proteins KinA,<br />

Spo0A, Spo0B, Spo0F and sigmaH in arbitrary unit. The measurement has been<br />

performed in bacterial col<strong>on</strong>ies by using green fluorescent protein (GFP). The measurement<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> each protein occurred in different experiments (<strong>on</strong>e for protein) where<br />

a gene <str<strong>on</strong>g>of</str<strong>on</strong>g> GFP was insert in a suitable locati<strong>on</strong> to keep track <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e producti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e protein. The amount <str<strong>on</strong>g>of</str<strong>on</strong>g> luminescence is proporti<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount <str<strong>on</strong>g>of</str<strong>on</strong>g> GFP<br />

882

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

present in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell which can be assumed proporti<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e protein.<br />

The simulati<strong>on</strong> produces as output time series for each protein in a form homogeneous<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental data. We compare <str<strong>on</strong>g>th</str<strong>on</strong>g>e two time series wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

root square mean error. We use evoluti<strong>on</strong>ary strategies [5] to perform a black box<br />

optimizati<strong>on</strong> in order to find <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters which minimize <str<strong>on</strong>g>th</str<strong>on</strong>g>is error.<br />

In our talk we are going to discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e results we obtained and we compare<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>em wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e present literature.<br />

References.<br />

[1] D. Schultz, P. Wolynes, E. Jacob, J. Onuchic Deciding fate in adverse times: sporulati<strong>on</strong> and<br />

competence in Bacillus subtilis PNAS Vol. 106 No. 50.<br />

[2] A. Chastanet, D. Vitkup, G. Yuan, T. Norman, J. Liu, R. Losick Broadly heterogeneous<br />

activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e master regulator for sporulati<strong>on</strong> in Bacillus subtilis PNAS 107:8486–8491.<br />

[3] Hoch, J.A. Regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e phosphorelay and <str<strong>on</strong>g>th</str<strong>on</strong>g>e initiati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> sporulati<strong>on</strong> in bacillus subtilis<br />

Annu Rev Microbiol 47 (1993) 441-65<br />

[4] I. G. de J<strong>on</strong>g, J. Veening, and O. P. Kuipers Heterochr<strong>on</strong>ic Phosphorelay Gene Expressi<strong>on</strong> as<br />

a Source <str<strong>on</strong>g>of</str<strong>on</strong>g>Heterogeneity in Bacillus subtilis Spore Formati<strong>on</strong> Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Bacterelology, Vol.<br />

192, No. 8<br />

[5] T. Bäck, Evoluti<strong>on</strong>ary algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms in <str<strong>on</strong>g>th</str<strong>on</strong>g>eory and practice: evoluti<strong>on</strong> strategies, evoluti<strong>on</strong>ary<br />

programming, genetic algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms. Oxford University Press, Oxford,UK (1996).<br />

883

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Dynamics; Wednesday, June 29, 08:30<br />

Hiromi Seno<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Life Sciences, Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Science, Hiroshima University, Higashi-hiroshima, 739-8526, Japan<br />

e-mail: seno@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.sci.hiroshima-u.ac.jp<br />

Ayaka Terada<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Science, Hiroshima University,<br />

Higashi-hiroshima, 739-8526, Japan<br />

A simple ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e annual variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

epidemic outbreak wi<str<strong>on</strong>g>th</str<strong>on</strong>g> preventi<strong>on</strong> level affected by<br />

incidence size in <str<strong>on</strong>g>th</str<strong>on</strong>g>e last seas<strong>on</strong><br />

Annual or seas<strong>on</strong>al fluctuati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e incidence size has been observed for a variety<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases, for example, influenza, measles, rubella, mumps, chickenpox<br />

etc. Here <str<strong>on</strong>g>th</str<strong>on</strong>g>e incidence size in <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic seas<strong>on</strong> means <str<strong>on</strong>g>th</str<strong>on</strong>g>e final size <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

epidemic at <str<strong>on</strong>g>th</str<strong>on</strong>g>e seas<strong>on</strong>, which gives <str<strong>on</strong>g>th</str<strong>on</strong>g>e fracti<strong>on</strong> or <str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> infected populati<strong>on</strong><br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic seas<strong>on</strong>. Such fluctuati<strong>on</strong>s have been attracting many researchers in<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical biology, and giving discussi<strong>on</strong>s about its driving factors. It would be<br />

taken natural <str<strong>on</strong>g>th</str<strong>on</strong>g>at <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e important factors is seas<strong>on</strong>ally varying envir<strong>on</strong>ment,<br />

caused by <str<strong>on</strong>g>th</str<strong>on</strong>g>e temporal variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tact rate, infecti<strong>on</strong> rate, or recruitment rate,<br />

for example due to social aggregati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> hosts or seas<strong>on</strong>ally restricted breeding seas<strong>on</strong>.<br />

In our work, in c<strong>on</strong>trast to <str<strong>on</strong>g>th</str<strong>on</strong>g>ese factors <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> dynamics, we c<strong>on</strong>sider<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> a change <str<strong>on</strong>g>of</str<strong>on</strong>g> social behavior which determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e preventi<strong>on</strong> level for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

c<strong>on</strong>sidered infectious disease. In case when <str<strong>on</strong>g>th</str<strong>on</strong>g>e incidence size in <str<strong>on</strong>g>th</str<strong>on</strong>g>e last epidemic<br />

seas<strong>on</strong> is large, <str<strong>on</strong>g>th</str<strong>on</strong>g>e people in <str<strong>on</strong>g>th</str<strong>on</strong>g>e community would tend to increase <str<strong>on</strong>g>th</str<strong>on</strong>g>e preventi<strong>on</strong><br />

level against <str<strong>on</strong>g>th</str<strong>on</strong>g>e infectious disease, for instance, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> promoting washing hands,<br />

gargling, wearing a mask, and available vaccinati<strong>on</strong>. Such increase <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e preventi<strong>on</strong><br />

level is reflected to <str<strong>on</strong>g>th</str<strong>on</strong>g>e reducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong> rate or recovery rate according to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

disease. Differently from <str<strong>on</strong>g>th</str<strong>on</strong>g>ose factors potentially causing <str<strong>on</strong>g>th</str<strong>on</strong>g>e annual or seas<strong>on</strong>al<br />

fluctuati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e incidence size, <str<strong>on</strong>g>th</str<strong>on</strong>g>is social factor is what is affected by <str<strong>on</strong>g>th</str<strong>on</strong>g>e incidence<br />

size in <str<strong>on</strong>g>th</str<strong>on</strong>g>e last seas<strong>on</strong> or <str<strong>on</strong>g>th</str<strong>on</strong>g>e past seas<strong>on</strong>s.<br />

To c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e essential effect <str<strong>on</strong>g>of</str<strong>on</strong>g> such social factor <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e potentiality <str<strong>on</strong>g>of</str<strong>on</strong>g> incidence<br />

size fluctuati<strong>on</strong>, we c<strong>on</strong>struct and analyze a simple ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> discrete<br />

dynamical system, which is derived from <str<strong>on</strong>g>th</str<strong>on</strong>g>e final-size equati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Kermack–<br />

McKendrick SIR model. We dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at such social factor could potentially<br />

or partially c<strong>on</strong>tribute to <str<strong>on</strong>g>th</str<strong>on</strong>g>e driving force causing <str<strong>on</strong>g>th</str<strong>on</strong>g>e annual or seas<strong>on</strong>al fluctuati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e incidence size for some infectious diseases.<br />

884

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 11:00<br />

Anne Seppänen<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, FI-20014 University <str<strong>on</strong>g>of</str<strong>on</strong>g> Turku, Finland<br />

e-mail: anne.seppanen@utu.fi<br />

Kalle Parvinen<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, FI-20014 University <str<strong>on</strong>g>of</str<strong>on</strong>g> Turku, Finland<br />

e-mail: kalparvi@utu.fi<br />

John Nagy<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Life Sciences, Scottsdale Community College, Scottsdale,<br />

AZ 85256-2626, USA<br />

e-mail: john.nagy@sccmail.maricopa.edu<br />

Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Dispersal and Global Climate Change<br />

Global climate change (GCC) can challenge species’ survival by shifting and<br />

(or) shrinking suitable habitats, leading to habitat fragmentati<strong>on</strong>. American pikas<br />

(Ochot<strong>on</strong>a princeps)—small, talus-dwelling, m<strong>on</strong>tane lagomorphs physiologically<br />

adapted to cold climates—are <str<strong>on</strong>g>th</str<strong>on</strong>g>ought to face precisely <str<strong>on</strong>g>th</str<strong>on</strong>g>is sort to <str<strong>on</strong>g>th</str<strong>on</strong>g>reat from<br />

GCC. Recent climate changes appear to have decreased suitability <str<strong>on</strong>g>of</str<strong>on</strong>g> pika habitat<br />

in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Great Basin and adjacent Sierra Nevada[1,2]. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand,<br />

pika populati<strong>on</strong>s in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese regi<strong>on</strong>s appear robust[3]. One hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis explaining<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese c<strong>on</strong>tradictory observati<strong>on</strong>s suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at pikas may adapt to climate change by<br />

evolving compensatory dispersal strategies <str<strong>on</strong>g>th</str<strong>on</strong>g>at blunt <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> fragmentati<strong>on</strong>.<br />

Here we address <str<strong>on</strong>g>th</str<strong>on</strong>g>is hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis using adaptive dynamics[4] to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal strategies in pikas. Inspired by <str<strong>on</strong>g>th</str<strong>on</strong>g>e models <str<strong>on</strong>g>of</str<strong>on</strong>g> Metz and Gyllenberg[5]<br />

and Parvinen[6], we c<strong>on</strong>struct a novel model <str<strong>on</strong>g>of</str<strong>on</strong>g> pika metapopulati<strong>on</strong><br />

dynamics and derive a fitness measure <str<strong>on</strong>g>of</str<strong>on</strong>g> a rare mutant in an envir<strong>on</strong>ment set by<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e resident. We use a semi-discrete time approach wi<str<strong>on</strong>g>th</str<strong>on</strong>g> discrete phases defined<br />

by sequential breeding seas<strong>on</strong>s and c<strong>on</strong>tinuous wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-phase processes (e.g. emigrati<strong>on</strong>,<br />

immigrati<strong>on</strong>). Local catastrophes occur wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a rate which can depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

patch populati<strong>on</strong> size. We c<strong>on</strong>sider climate change as shifts in model parameters,<br />

including fecundity, survival and catastrophe rates al<strong>on</strong>g wi<str<strong>on</strong>g>th</str<strong>on</strong>g> dispersal cost, and<br />

analyze how such changes affect evoluti<strong>on</strong>arily stable dispersal strategies.<br />

References.<br />

[1] D. K. Grays<strong>on</strong>, A brief history <str<strong>on</strong>g>of</str<strong>on</strong>g> Great Basin pikas, J. Biogeogr. 32 2103–2111, 2005<br />

[2] C. Moritz and J. L. Patt<strong>on</strong> and C. J. C<strong>on</strong>roy and J. L. Parra and G. C. White and S. R.<br />

Beissinger, Impact <str<strong>on</strong>g>of</str<strong>on</strong>g> a century <str<strong>on</strong>g>of</str<strong>on</strong>g> climate change <strong>on</strong> small-mammal communities in Yosemite<br />

Nati<strong>on</strong>al Park, USA, Science, 322 261–264, 2008<br />

[3] C. I. Millar and R. D. Westfall, Distributi<strong>on</strong> and climatic relati<strong>on</strong>ships <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e American pika<br />

(Ochot<strong>on</strong>a princeps) in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Sierra Nevada and western Great Basin, U.S.A.; periglacial landforms<br />

as refugia in warming climates, Arctic, Antarctic Alpine Res. 42 76–88, 2010<br />

[4] S. A. H. Geritz and É. Kisdi and G. Meszéna and J. A. J. Metz, Evoluti<strong>on</strong>arily singular<br />

strategies and <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptive grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and branching <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary tree, Evol. Ecol. 12<br />

35–57, 1998<br />

[5] J. A. J. Metz and M. Gyllenberg, How should we define fitness in structured metapopulati<strong>on</strong><br />

models? Including an applicati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e calculati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ES dispersal strategies, Proc. Royal<br />

Soc. L<strong>on</strong>d<strong>on</strong> B, 268 499–508, 2001<br />

[6] K. Parvinen, Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal in a structured metapopulati<strong>on</strong> model in discrete time,<br />

Bull. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. 68 655–678, 2006<br />

885

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Raffaello Seri<br />

Università degli Studi dell’Insubria<br />

e-mail: raffaello.seri@uninsubria.it<br />

Bioimaging; Tuesday, June 28, 11:00<br />

C<strong>on</strong>fidence sets for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Aumann mean <str<strong>on</strong>g>of</str<strong>on</strong>g> a random closed set<br />

The objective <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e talk is to develop a set <str<strong>on</strong>g>of</str<strong>on</strong>g> reliable me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to build c<strong>on</strong>fidence<br />

sets for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Aumann mean <str<strong>on</strong>g>of</str<strong>on</strong>g> a random closed set (RACS) as estimated<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e Minkowski empirical mean. In order to do so, we introduce a procedure<br />

to build a c<strong>on</strong>fidence set based <strong>on</strong> an asymptotic distributi<strong>on</strong>al result for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Hausdorff distance between <str<strong>on</strong>g>th</str<strong>on</strong>g>e Minkowski empirical and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Aumann means; <str<strong>on</strong>g>th</str<strong>on</strong>g>en,<br />

we introduce ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er procedure based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e support functi<strong>on</strong>.<br />

The me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods are based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e wid<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e RACS <strong>on</strong> a<br />

set <str<strong>on</strong>g>of</str<strong>on</strong>g> directi<strong>on</strong>s and are <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore suitable for computerized tomography, tactile<br />

sensing and laser-radar systems. Some M<strong>on</strong>te Carlo results show how <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods<br />

work in practice.<br />

This c<strong>on</strong>tributi<strong>on</strong> is joint work wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Christine Choirat (Universidad de Navarra,<br />

Spain).<br />

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Semigroups <str<strong>on</strong>g>of</str<strong>on</strong>g> Operators in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology I; Wednesday, June 29, 08:30<br />

Robert Service<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Helsinki, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics<br />

e-mail: robert.service@helsinki.fi<br />

Finite populati<strong>on</strong>s c<strong>on</strong>diti<strong>on</strong>ed <strong>on</strong> n<strong>on</strong>-extincti<strong>on</strong><br />

It is well known <str<strong>on</strong>g>th</str<strong>on</strong>g>at stochastic models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> finite populati<strong>on</strong>s tend to<br />

fall into two categories (when <str<strong>on</strong>g>th</str<strong>on</strong>g>e system is closed): <str<strong>on</strong>g>th</str<strong>on</strong>g>ose <str<strong>on</strong>g>th</str<strong>on</strong>g>at allow for unlimited<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> positive probability and <str<strong>on</strong>g>th</str<strong>on</strong>g>ose for which extincti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g run is certain.<br />

In practice <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g>ten expects extincti<strong>on</strong> times to be sufficiently l<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>at useful<br />

c<strong>on</strong>clusi<strong>on</strong>s such as stabilisati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> structure can be drawn from deterministic<br />

populati<strong>on</strong> models. The talk is about work, old and new, aiming to justify<br />

such c<strong>on</strong>clusi<strong>on</strong>s rigorously.<br />

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Crowd Dynamics: Modeling, Analysis and Simulati<strong>on</strong> (Part 2); Wednesday,<br />

June 29, 14:30<br />

Armin Seyfried<br />

Jülich Supercomputing Centre, Forschungszentrum Jülich<br />

e-mail: a.seyfried@fz-juelich.de<br />

Quantitative descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> pedestrian dynamics:<br />

Experiments and Modeling<br />

The first part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lecture gives an introducti<strong>on</strong> to empirical results in pedestrian<br />

dynamics. Basic quantities <str<strong>on</strong>g>of</str<strong>on</strong>g> pedestrian streams (density, flow and velocity) are<br />

introduced al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e measurement me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods. But density and flow are c<strong>on</strong>cepts<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> fluid mechanics where <str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e particles is much smaller <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e size<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e measurement area. Thus standard me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in pedestrian dynamics suffer<br />

from large scatter when local measurements are needed. A c<strong>on</strong>cept for measuring<br />

microscopic characteristics <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> trajectories is introduced. Assigning a<br />

pers<strong>on</strong>al space to every pedestrian via a Vor<strong>on</strong>oi diagram reduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e scatter and<br />

allows analyzing <str<strong>on</strong>g>th</str<strong>on</strong>g>e fine structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e data.<br />

The sec<strong>on</strong>d part focuses <strong>on</strong> a model c<strong>on</strong>tinuous in space. Basic ideas <str<strong>on</strong>g>of</str<strong>on</strong>g> a force<br />

model representing pedestrians as self driven particles interacting via a repulsive<br />

force are outlined. To get precise volume exclusi<strong>on</strong> in two dimensi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

represents <str<strong>on</strong>g>th</str<strong>on</strong>g>e velocity dependent shape <str<strong>on</strong>g>of</str<strong>on</strong>g> pedestrians by ellipses changing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir semiaxis wi<str<strong>on</strong>g>th</str<strong>on</strong>g> speed. In additi<strong>on</strong> routing strategies are modeled to<br />

incorporate certain intelligence to <str<strong>on</strong>g>th</str<strong>on</strong>g>e self driven particles. The particles perceive<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir envir<strong>on</strong>ment and take <str<strong>on</strong>g>th</str<strong>on</strong>g>eir decisi<strong>on</strong> based <strong>on</strong> an observati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e current<br />

situati<strong>on</strong>.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

A Finite Element simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lamellipodial actin<br />

cytoskelet<strong>on</strong><br />

Nikolaos Sfakianakis<br />

Johannes Gutenberg-University, Mainz, Germany<br />

Dietmar Oelz<br />

RICAM (Rad<strong>on</strong> Institute for Computati<strong>on</strong>al and Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics),<br />

Vienna/Linz, Austria<br />

Christian Schmeiser<br />

RICAM and Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Vienna, Vienna,<br />

Austria<br />

e-mail: sfakiana@uni-mainz.de<br />

This poster presents a Finite Element me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lamellipodial<br />

part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> living cells.<br />

The numerical me<str<strong>on</strong>g>th</str<strong>on</strong>g>od resolves a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>th</str<strong>on</strong>g>at has been developed<br />

by Ch.Schmeiser and his collaborators (V. Small, D. Oelz, N. Sfakianakis, A. Manhart,<br />

V. Milisic) in Vienna. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e model several properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> are<br />

included: polymerizati<strong>on</strong> and bending <str<strong>on</strong>g>of</str<strong>on</strong>g> actin filaments, stretching and twisting <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

crosslink proteins, adhesi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e substrate and myosin c<strong>on</strong>tractile forces.<br />

We present simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e previously mechanical characteristic<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong>. Special emphasis is given in <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulati<strong>on</strong> results propagating<br />

lamellipodia under <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> an external force and/or variable filament<br />

polymerizati<strong>on</strong> rate.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Nazgol Shahbandi<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Waterloo<br />

e-mail: nshahban@uwaterloo.ca<br />

Mohammad Kohandel<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Waterloo<br />

Interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Brain Cancer Stem Cells and Tumour<br />

Microenvir<strong>on</strong>ment: A Computati<strong>on</strong>al Study<br />

Glioblastoma Multiforme (GBM) is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most comm<strong>on</strong> and aggressive primary<br />

brain tumors, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a median patient survival time <str<strong>on</strong>g>of</str<strong>on</strong>g> 6-12 m<strong>on</strong><str<strong>on</strong>g>th</str<strong>on</strong>g>s in adults. It<br />

has been recently suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>at a typically small subpopulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> brain tumour<br />

cells, in possessi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> certain defining properties <str<strong>on</strong>g>of</str<strong>on</strong>g> stem cells, is resp<strong>on</strong>sible for<br />

initiating and maintaining <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour. More recent experiments have studied <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

interacti<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>is subpopulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> brain cancer cells and tumour microenvir<strong>on</strong>mental<br />

factors such as hypoxia, in additi<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir c<strong>on</strong>tributi<strong>on</strong> to angiogenesis<br />

and vasculogenesis. We propose a computati<strong>on</strong>al model <str<strong>on</strong>g>th</str<strong>on</strong>g>at includes a heterogeneous<br />

populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells and investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> tumour grow<str<strong>on</strong>g>th</str<strong>on</strong>g> as<br />

well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumour microenvir<strong>on</strong>ment. The model is compared wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

available experimental data.<br />

References.<br />

[1] PB. Dirks, Brain tumor stem cells: <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer stem cell hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis writ large. Mol Oncol. 2010<br />

420-30.<br />

[2] SK. Singh et al., Identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> human brain tumour initiating cells. Nature. 2004 432(7015)<br />

396-401.<br />

[3] RE McLend<strong>on</strong>, JN. Rich, Glioblastoma Stem Cells: A Neuropa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologist’s View. J Oncol. 2011<br />

397195.<br />

[4] AB Hjelmeland et al., Acidic stress promotes a glioma stem cell phenotype. Cell Dea<str<strong>on</strong>g>th</str<strong>on</strong>g> Differ.<br />

2010; doi: 10.1038/cdd.2010.150<br />

[5] L. Ricci-Vitiani et al., Tumour vascularizati<strong>on</strong> via endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial differentiati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> glioblastoma<br />

stem-like cells. Nature. 2010 468(7325) 824-8.<br />

[6] R. Wang et al., Glioblastoma stem-like cells give rise to tumour endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elium. Nature. 2010<br />

468(7325) 829-33.<br />

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Epidemic models: Networks and stochasticity I; Wednesday, June 29, 14:30<br />

Kieran Sharkey<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Liverpool<br />

e-mail: kjs@liv.ac.uk<br />

Towards understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e correlati<strong>on</strong>s in epidemic<br />

dynamics <strong>on</strong> c<strong>on</strong>tact networks via <str<strong>on</strong>g>th</str<strong>on</strong>g>e master equati<strong>on</strong><br />

It is well-known <str<strong>on</strong>g>th</str<strong>on</strong>g>at deterministic epidemic models such as mean-field or pairapproximati<strong>on</strong><br />

models can fail <strong>on</strong> c<strong>on</strong>tact networks because <str<strong>on</strong>g>th</str<strong>on</strong>g>ey ignore correlati<strong>on</strong>s<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at occur between populati<strong>on</strong>s. While <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a substantial amount <str<strong>on</strong>g>of</str<strong>on</strong>g> intuiti<strong>on</strong><br />

about <str<strong>on</strong>g>th</str<strong>on</strong>g>ese correlati<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature lacks a more analytic approach to <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

effects.<br />

Here, by directly relating <str<strong>on</strong>g>th</str<strong>on</strong>g>ese epidemic models to <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying master equati<strong>on</strong>s<br />

we can understand precisely where and why <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models fail. In particular,<br />

comm<strong>on</strong> models such as mean-field and pair-approximati<strong>on</strong> models are shown to<br />

c<strong>on</strong>tain implicit anomalous terms describing unbiological processes whereby individuals<br />

can be bo<str<strong>on</strong>g>th</str<strong>on</strong>g> susceptible and infectious at <str<strong>on</strong>g>th</str<strong>on</strong>g>e same time. This c<strong>on</strong>tradicts<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e assumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a compartmental model. It is <str<strong>on</strong>g>th</str<strong>on</strong>g>ese implicit terms which lead to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e observed inaccuracies in <str<strong>on</strong>g>th</str<strong>on</strong>g>e models.<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese terms enables us to gain a more analytic perspective <strong>on</strong> correlati<strong>on</strong>s<br />

in epidemic models and <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> network clustering <strong>on</strong> epidemic<br />

propagati<strong>on</strong>.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ryan Sharp<br />

Ro<str<strong>on</strong>g>th</str<strong>on</strong>g>amsted Research<br />

e-mail: rtsharp@live.co.uk<br />

Frank van den Bosch<br />

Ro<str<strong>on</strong>g>th</str<strong>on</strong>g>amsted Research<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen emergence under temporal heterogeneity<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e key factors driving <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> disease is changes to climate.<br />

Climate change is expected to not <strong>on</strong>ly alter <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean <str<strong>on</strong>g>of</str<strong>on</strong>g> various envir<strong>on</strong>mental<br />

variables but also <str<strong>on</strong>g>th</str<strong>on</strong>g>eir variability. The effect <str<strong>on</strong>g>of</str<strong>on</strong>g> changes to <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>mental<br />

mean <strong>on</strong> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen emergence has received c<strong>on</strong>siderable attenti<strong>on</strong>.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we propose a <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical approach to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

changes to envir<strong>on</strong>mental variability <strong>on</strong> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen emergence and develop a multitype<br />

branching process incorporating temporal heterogeneity and pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen adaptati<strong>on</strong>.<br />

Previous studies have found <str<strong>on</strong>g>th</str<strong>on</strong>g>at increases to envir<strong>on</strong>mental variability cause<br />

a decrease to pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen emergence in a n<strong>on</strong>-evoluti<strong>on</strong>ary system. Our results agree<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is finding and find <str<strong>on</strong>g>th</str<strong>on</strong>g>is is also true when pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens must adapt to survive<br />

and cause an epidemic. It has also been shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> incorporating<br />

evoluti<strong>on</strong> can <str<strong>on</strong>g>of</str<strong>on</strong>g>ten outweigh o<str<strong>on</strong>g>th</str<strong>on</strong>g>er effects, we find however even in an evoluti<strong>on</strong>ary<br />

system temporal heterogeneity can significantly affect pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen emergence. The<br />

greatest effect being <strong>on</strong> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens whose survival is not str<strong>on</strong>gly dependent <strong>on</strong> its<br />

need to adapt and pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens already adapted to its envir<strong>on</strong>ment but wi<str<strong>on</strong>g>th</str<strong>on</strong>g> low<br />

infectivity.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Eunha Shim<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Epidemiology, Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Pittsburgh<br />

e-mail: eshim@pitt.edu<br />

Steven M. Albert<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Behavioral & Community Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, Sciences Graduate<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Pittsburgh<br />

John Grefenstette<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biostatistics, Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Pittsburgh<br />

D<strong>on</strong>ald S. Burke<br />

Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Public Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Pittsburgh<br />

Impact <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccine refusal <strong>on</strong> vaccine-preventable disease<br />

outbreaks<br />

The MMR scare and resulting measles outbreak in <str<strong>on</strong>g>th</str<strong>on</strong>g>e UK and US in 2008 prove<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e effectiveness <str<strong>on</strong>g>of</str<strong>on</strong>g> mass vaccinati<strong>on</strong> program can be hampered by <str<strong>on</strong>g>th</str<strong>on</strong>g>e public<br />

percepti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccine risk. By coupling game models and epidemic models, we<br />

examined vaccinati<strong>on</strong> choice for populati<strong>on</strong> stratified into two behavioral groups,<br />

pro-vaccinators and vaccine hesitators. Two behavioral groups are assumed to be<br />

heterogeneous wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir percepti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccine and infecti<strong>on</strong> risks. We<br />

dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e pursuit <str<strong>on</strong>g>of</str<strong>on</strong>g> self-interest am<strong>on</strong>g vaccine-hesitators <str<strong>on</strong>g>of</str<strong>on</strong>g>ten leads to<br />

vaccinati<strong>on</strong> levels <str<strong>on</strong>g>th</str<strong>on</strong>g>at are suboptimal for a community, even if complete coverage is<br />

achieved am<strong>on</strong>g pro-vaccinators. The demand for MMR vaccine across populati<strong>on</strong><br />

driven by individual self-interest was found to be more sensitive to <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

vaccine hesitators <str<strong>on</strong>g>th</str<strong>on</strong>g>an to <str<strong>on</strong>g>th</str<strong>on</strong>g>e extent to which vaccine hesitators misperceive <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> vaccine. Our results show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e discrepancy between <str<strong>on</strong>g>th</str<strong>on</strong>g>e MMR coverages <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

are driven by self-interest and populati<strong>on</strong> interest becomes larger when <str<strong>on</strong>g>th</str<strong>on</strong>g>e cost <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

vaccinati<strong>on</strong> increases. This research illustrates <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> public educati<strong>on</strong><br />

<strong>on</strong> vaccine safety and infecti<strong>on</strong> risk in order to maintain vaccinati<strong>on</strong> levels <str<strong>on</strong>g>th</str<strong>on</strong>g>at are<br />

sufficient to derive herd immunity.<br />

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Stochastic models in computati<strong>on</strong>al neuroscience I; Wednesday, June 29, 14:30<br />

Shigeru Shinomoto<br />

Dept Physics, Kyoto University, Kyoto 606-8502, JAPAN<br />

e-mail: shinomoto@scphys.kyoto-u.ac.jp<br />

A state space me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for decoding neur<strong>on</strong>al spiking signals<br />

Cortical neur<strong>on</strong>s in vivo have <str<strong>on</strong>g>of</str<strong>on</strong>g>ten been approximated as Poiss<strong>on</strong> spike generators<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>vey no informati<strong>on</strong> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> random firing. Recently, it has<br />

been revealed by using a metric for analyzing local variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> interspike intervals<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at individual neur<strong>on</strong>s express specific patterns in generating spikes, which may<br />

symbolically be termed regular, random or bursty [1,2]. Two hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses have been<br />

proposed for potential advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> using n<strong>on</strong>-Poiss<strong>on</strong> spike trains in transmitting<br />

informati<strong>on</strong>; neur<strong>on</strong>s may signal <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing irregularity by changing it in additi<strong>on</strong><br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> firing [3], or alternatively, <str<strong>on</strong>g>th</str<strong>on</strong>g>e receiver may estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing rate<br />

accurately by making <str<strong>on</strong>g>th</str<strong>on</strong>g>e most <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-Poiss<strong>on</strong> inter-spike dependency in <str<strong>on</strong>g>th</str<strong>on</strong>g>e received<br />

signals [4-6]. In order to determine which hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis is more plausible for<br />

a given spike train, we have implemented a state space me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for simultaneously<br />

estimating firing irregularity and <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing rate moment by moment [7,8]. I review<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e recent development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e state space analysis and dem<strong>on</strong>strate new results<br />

obtained for a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> electrophysiological data.<br />

References.<br />

[1] S. Shinomoto, K. Shima, & J. Tanji (2003), Differences in spiking patterns am<strong>on</strong>g cortical<br />

neur<strong>on</strong>s. Neural Computati<strong>on</strong> 15 2823–2842.<br />

[2] S. Shinomoto et al. (2009), Relating neur<strong>on</strong>al firing patterns to functi<strong>on</strong>al differentiati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cerebral cortex. PLoS Computati<strong>on</strong>al Biology 5 e1000433.<br />

[3] R.M. Davies, G.L. Gerstein, & S.N. Baker (2006) Measurement <str<strong>on</strong>g>of</str<strong>on</strong>g> time-dependent changes in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e irregularity <str<strong>on</strong>g>of</str<strong>on</strong>g> neural spiking. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Neurophysiology 96 906–918.<br />

[4] R. Barbieri et al., C<strong>on</strong>structi<strong>on</strong> and analysis <strong>on</strong> n<strong>on</strong>-Poiss<strong>on</strong> stimulus-resp<strong>on</strong>se models <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

neural spiking activity. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Neuroscience Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods 105 25–37.<br />

[5] J.P. Cunningham et al. (2008), Inferring neural firing rates from spike trains using Gaussian<br />

processes. Advances in Neural Informati<strong>on</strong> Processing Systems 20.<br />

[6] S. Koyama, & S. Shinomoto (2005) Empirical Bayes interpretati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> random point events.<br />

Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics A - Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and General 38 L531–L537.<br />

[7] T. Shimokawa & S. Shinomoto (2009) Estimating instantaneous irregularity <str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>al firing.<br />

Neural Computati<strong>on</strong> 21 1931–1951.<br />

[8] T. Shimokawa, S. Koyama, & S. Shinomoto (2010) A characterizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e time-rescaled<br />

gamma process as a model for spike trains. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Computati<strong>on</strong>al Neuroscience 29 183–<br />

191.<br />

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B and T cell immune resp<strong>on</strong>ses; Wednesday, June 29, 11:00<br />

Andrey Shuvaev<br />

Inserm U897, University Bordeaux 2, France<br />

e-mail: andrey.n.shuvaev@gmail.com<br />

Thea Hogan<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Child Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, UCL, UK<br />

Daniel Commenges<br />

Inserm U897, University Bordeaux 2, France<br />

Bennedict Sedd<strong>on</strong><br />

Nati<strong>on</strong>al Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Research, MRC, UK<br />

Robin Callard<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Child Heal<str<strong>on</strong>g>th</str<strong>on</strong>g>, UCL, UK<br />

Rodolphe Thiébaut<br />

Inserm U897, University Bordeaux 2, France<br />

Modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e T-cells dynamics in lymphopenic c<strong>on</strong>diti<strong>on</strong>s<br />

We investigated divisi<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> two types <str<strong>on</strong>g>of</str<strong>on</strong>g> CD8 T-cells (OT1 and F5) in<br />

lymphopenic c<strong>on</strong>diti<strong>on</strong>s. We used two markers: 1) CFSE (Carboxyfluorescein succinimidyl<br />

ester) – to calculate <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> divisi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells have made at<br />

a given time, 2) 7AAD (7-Aminoactinomycin D) – to determine in what period <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cell cycle cells were at a given time.<br />

A modified Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>-Martin model was used [1, 2] for <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed data. This<br />

model assume a cell cycle c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> two parts: A-phase wi<str<strong>on</strong>g>th</str<strong>on</strong>g> stochastic durati<strong>on</strong><br />

and following after it B-phase wi<str<strong>on</strong>g>th</str<strong>on</strong>g> deterministic durati<strong>on</strong>. There were four main<br />

parameters: transfer rate from A to B-phase λ, durati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> B-phase ∆, time <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

triggering to divisi<strong>on</strong> T0 and dea<str<strong>on</strong>g>th</str<strong>on</strong>g> rate δ. To estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>em we used a minimizati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sum <str<strong>on</strong>g>of</str<strong>on</strong>g> weighted squared residuals wi<str<strong>on</strong>g>th</str<strong>on</strong>g> comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g>: 1) predicted and<br />

observed frequencies <str<strong>on</strong>g>of</str<strong>on</strong>g> cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> given number <str<strong>on</strong>g>of</str<strong>on</strong>g> divisi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at was made to a<br />

given time, 2) predicti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> fracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells in B-phase wi<str<strong>on</strong>g>th</str<strong>on</strong>g> observed fracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

7AAD+ cells. Comparis<strong>on</strong>s between models were performed using a cross-validati<strong>on</strong><br />

criteri<strong>on</strong>.<br />

It was found <str<strong>on</strong>g>th</str<strong>on</strong>g>at OT1 cells divides faster (higher transfer rate λ and earlier<br />

triggering to divisi<strong>on</strong>) <str<strong>on</strong>g>th</str<strong>on</strong>g>an F5 cells. Durati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> B-phase ∆ was slightly higher<br />

for OT1 cells. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>e informati<strong>on</strong> from 7AAD marker toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> CFSE data<br />

improved parameters identifiability.<br />

References.<br />

[1] J. Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>, and L. Martin, Do cells cycle?, PNAS, 70, 1263–1267, 1963.<br />

[2] A. Yates, and M. Saini, A. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>iot, B. Sedd<strong>on</strong>, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling Reveals <str<strong>on</strong>g>th</str<strong>on</strong>g>e Biological<br />

Program Regulating Lymphopenia-Induced Proliferati<strong>on</strong>, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Immunology, 1800, 1414–<br />

1422, 2008.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models in Eco-epidemiology I; Wednesday, June 29, 08:30<br />

Michael Sieber<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Envir<strong>on</strong>mental Systems Research, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

and Computer Science, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Osnabrück, 49069 Osnabrück,<br />

Germany<br />

e-mail: msieber@uni-osnabrueck.de<br />

Intraguild predati<strong>on</strong> or not? Taking a different perspective<br />

<strong>on</strong> some eco-epidemiological models<br />

The field <str<strong>on</strong>g>of</str<strong>on</strong>g> eco-epidemiology has integrated epidemiology wi<str<strong>on</strong>g>th</str<strong>on</strong>g> community ecology<br />

and similarities between host-parasitoid and host-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

classical intraguild predati<strong>on</strong> (IGP) have been noticed. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I want to show<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at certain eco-epidemiological scenarios not <strong>on</strong>ly fit into <str<strong>on</strong>g>th</str<strong>on</strong>g>e IGP framework, but<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey may suggest a different perspective <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying community structure.<br />

After an appropriate transformati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> variables particular cases <str<strong>on</strong>g>of</str<strong>on</strong>g> IGP are<br />

found to be structurally similar to “simpler” community modules and <str<strong>on</strong>g>th</str<strong>on</strong>g>is structural<br />

similarity also translates into remarkably similar community dynamics.<br />

References.<br />

[1] Sieber, M. and Hilker, F. M. (2011). Prey, predators, parasites: intraguild predati<strong>on</strong> or simpler<br />

community modules in disguise? Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Animal Ecology, 80:414-421.<br />

896

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Neurosciences; Wednesday, June 29, 08:30<br />

Justyna Signerska<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warszawa, Poland<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Technical Physics, Gdańsk University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Gdańsk, Poland<br />

e-mail: j.signerska@impan.pl<br />

Wacław Marzantowicz<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Sci., Adam Mickiewicz University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Poznań, Poznań, Poland<br />

e-mail: marzan@amu.edu.pl<br />

Firing map for integrate–and–fire models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> almost<br />

periodic stimulus<br />

In integrate–and–fire systems <str<strong>on</strong>g>th</str<strong>on</strong>g>e sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>secutive spikes can be recovered<br />

via iterati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e so–called firing map. Until now analytical approaches<br />

mainly c<strong>on</strong>centrated <strong>on</strong> models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e type ˙x = f(t, x) when <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong> f was<br />

c<strong>on</strong>tinuous and periodic in <str<strong>on</strong>g>th</str<strong>on</strong>g>e time variable ([1],[2],[3]). We analyze firing maps<br />

and firing sequences for <str<strong>on</strong>g>th</str<strong>on</strong>g>e class <str<strong>on</strong>g>of</str<strong>on</strong>g> integrate–and–fire models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stimulus<br />

functi<strong>on</strong> almost periodic in time (ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er uniformly almost periodic or in a Stepanov<br />

sense) and prove <str<strong>on</strong>g>th</str<strong>on</strong>g>at many required properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing map still hold for<br />

leaky integrate-and fire ˙x = −σx + f(t) or Perfect Integrator ˙x = f(t) models when<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong> f is <strong>on</strong>ly locally integrable. We prepare a formal framework for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

study <str<strong>on</strong>g>of</str<strong>on</strong>g> discrete dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing map arising from almost periodically driven<br />

integrate–and–fire systems. In particular, results c<strong>on</strong>cerning almost periodic displacement<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing map and regularity properties (semi–/almost periodicity) <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> interspike intervals will be shown.<br />

References.<br />

[1] R. Brette, Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>e–dimensi<strong>on</strong>al spiking neur<strong>on</strong> model, J.Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.Biol., 48 (2004), 38–<br />

56.<br />

[2] H. Carrillo, F. A. Ongay, On <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing maps <str<strong>on</strong>g>of</str<strong>on</strong>g> a general class <str<strong>on</strong>g>of</str<strong>on</strong>g> forced integrate and fire<br />

neur<strong>on</strong>s, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci., 172 (2001), 33–53.<br />

[3] S. Coombes, P. C. Bressl<str<strong>on</strong>g>of</str<strong>on</strong>g>f, Mode locking and Arnold t<strong>on</strong>gues in integrate–and–fire neural<br />

oscillators, Phys. Rev. E, 60 (1999), 2086–2096.<br />

[4] W. Marzantowicz, J.Signerska, Firing map <str<strong>on</strong>g>of</str<strong>on</strong>g> an almost periodic input functi<strong>on</strong>, AIMS Proceedings<br />

2011, in print.<br />

897

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Wer<strong>on</strong>ika Sikora-Wohlfeld<br />

Biotechnology Center, TU Dresden, Germany<br />

e-mail: wer<strong>on</strong>ika.sikora@biotec.tu-dresden.de<br />

Andreas Beyer<br />

Biotechnology Center, TU Dresden, Germany<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> protein complexes maintaining Oct4<br />

expressi<strong>on</strong> in mouse ES cells<br />

Octamer binding transcripti<strong>on</strong> factor-4 (Oct4) is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e key factors c<strong>on</strong>trolling<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e fate <str<strong>on</strong>g>of</str<strong>on</strong>g> embry<strong>on</strong>ic stem (ES) cells. Oct4 expressi<strong>on</strong> at a specific level is<br />

required to maintain <str<strong>on</strong>g>th</str<strong>on</strong>g>e ES cells’ capability for self-renewal, i.e. ability to replicate<br />

indefinitely wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out loss <str<strong>on</strong>g>of</str<strong>on</strong>g> pluripotency. Whereas numerous studies focused <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

target genes or direct protein interactors <str<strong>on</strong>g>of</str<strong>on</strong>g> Oct4, <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Oct4 expressi<strong>on</strong><br />

itself is less explored.<br />

Our work aims at finding <str<strong>on</strong>g>th</str<strong>on</strong>g>e genes and protein complexes involved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Oct4 expressi<strong>on</strong>. The study is based <strong>on</strong> two independent genomewide<br />

siRNA screens [1, 2] c<strong>on</strong>ducted in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mouse ES cell line, Oct4-GiP, which<br />

allows to measure <str<strong>on</strong>g>th</str<strong>on</strong>g>e change <str<strong>on</strong>g>of</str<strong>on</strong>g> Oct4 expressi<strong>on</strong> up<strong>on</strong> siRNA knock-down <str<strong>on</strong>g>of</str<strong>on</strong>g> query<br />

genes.<br />

Direct comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e results from bo<str<strong>on</strong>g>th</str<strong>on</strong>g> screens at <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene level did not<br />

show a statistically significant c<strong>on</strong>sistency between <str<strong>on</strong>g>th</str<strong>on</strong>g>e screens. Possible causes <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is disagreement include variati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental setup (different siRNA<br />

libraries), variability related to high-<str<strong>on</strong>g>th</str<strong>on</strong>g>roughput experiments and drawbacks <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

siRNA screening me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology (false discoveries resulting e.g. from <str<strong>on</strong>g>of</str<strong>on</strong>g>f-target effects).<br />

We reas<strong>on</strong>ed <str<strong>on</strong>g>th</str<strong>on</strong>g>at incorporati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> additi<strong>on</strong>al or<str<strong>on</strong>g>th</str<strong>on</strong>g>og<strong>on</strong>al informati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

analysis might remove noise and improve <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sistency between screens. We<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erefore mapped <str<strong>on</strong>g>th</str<strong>on</strong>g>e genes tested in siRNA screens to known protein complexes,<br />

assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>at genes participating in <str<strong>on</strong>g>th</str<strong>on</strong>g>e same complex should cause similar phenotypes.<br />

To identify complexes enriched wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high-scoring genes, we tested several set<br />

enrichment me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods (hypergeometric test, weighted Kolmogorov-Smirnov statistic,<br />

Bayesian network and regularized linear regressi<strong>on</strong>). The resulting scoring <str<strong>on</strong>g>of</str<strong>on</strong>g> protein<br />

complexes showed c<strong>on</strong>siderably greater c<strong>on</strong>sistency between screens <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

original gene scores. Subsequently we combined <str<strong>on</strong>g>th</str<strong>on</strong>g>e results from bo<str<strong>on</strong>g>th</str<strong>on</strong>g> screens in<br />

order to obtain a single set <str<strong>on</strong>g>of</str<strong>on</strong>g> high-c<strong>on</strong>fidence complexes enriched for genes causing<br />

Oct4-related phenotypes. Thereby we obtained several complexes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> known functi<strong>on</strong>s<br />

related to cell-cycle or stem cell maintenance. Importantly, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese complexes<br />

c<strong>on</strong>tain many genes <str<strong>on</strong>g>th</str<strong>on</strong>g>at were not identified as significant “hit genes” in <str<strong>on</strong>g>th</str<strong>on</strong>g>e original<br />

screens.<br />

The performed analysis reveals <str<strong>on</strong>g>th</str<strong>on</strong>g>at combining results <str<strong>on</strong>g>of</str<strong>on</strong>g> siRNA screens and<br />

adding external data helps to extract more comprehensive informati<strong>on</strong> from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

experiments. Our analysis identifies a catalogue <str<strong>on</strong>g>of</str<strong>on</strong>g> protein complexes critically<br />

involved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Oct4 expressi<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>us important for ES cells maintenance.<br />

898<br />

References.

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[1] L. Ding et al., A genome-scale RNAi screen for Oct4 modulators defines a role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Paf1<br />

complex for embry<strong>on</strong>ic stem cell identity Cell Stem Cell. 4(5) 403–415.<br />

[2] G. Hu et al., A genome-wide RNAi screen identifies a new transcripti<strong>on</strong>al module required for<br />

self-renewal Genes Dev. 23(7) 837–848.<br />

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Epidemic models: Networks and stochasticity I; Wednesday, June 29, 14:30<br />

Peter Sim<strong>on</strong><br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Eotvos Lorand University, Budapest<br />

e-mail: sim<strong>on</strong>p@cs.elte.hu<br />

Exact and approximate epidemic models <strong>on</strong> networks<br />

The rigorous linking <str<strong>on</strong>g>of</str<strong>on</strong>g> exact stochastic models to mean-field pair and triple approximati<strong>on</strong>s<br />

is studied. Using a c<strong>on</strong>tinuous time Markov Chain, we start from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

exact formulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a simple epidemic model <strong>on</strong> a completely c<strong>on</strong>nected network<br />

and rigorously derive <str<strong>on</strong>g>th</str<strong>on</strong>g>e well-known mean-field pair approximati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at is usually<br />

justified under <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at infected nodes are distributed randomly.<br />

In additi<strong>on</strong>, we propose a new approach <str<strong>on</strong>g>th</str<strong>on</strong>g>at is based <strong>on</strong> deriving a countable<br />

system <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary differential equati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e moments <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> infected nodes. We show how <str<strong>on</strong>g>th</str<strong>on</strong>g>e usual mean-field pair approximati<strong>on</strong><br />

can be derived from <str<strong>on</strong>g>th</str<strong>on</strong>g>is countable system, and prove <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>verges to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

exact soluti<strong>on</strong> given by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Kolmogorov equati<strong>on</strong>s as order 1/N. We discuss how<br />

our new approach relates to <str<strong>on</strong>g>th</str<strong>on</strong>g>e generally cited results by Kurtz.<br />

Finally, <str<strong>on</strong>g>th</str<strong>on</strong>g>e performance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e triple closure approximati<strong>on</strong> is investigated<br />

numerically. It will be shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e usual triple closure yields a soluti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

also c<strong>on</strong>verges as order 1/N to <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact soluti<strong>on</strong>, and we propose a novel triple<br />

closure where <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>vergence is <str<strong>on</strong>g>of</str<strong>on</strong>g> order 1/N2.<br />

900

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

C<strong>on</strong>necting microscale and macroscale models <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular migrati<strong>on</strong>;<br />

Tuesday, June 28, 17:00<br />

Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ew Simps<strong>on</strong><br />

Queensland University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ew.simps<strong>on</strong>@qut.edu.au<br />

Models <str<strong>on</strong>g>of</str<strong>on</strong>g> collective cell spreading wi<str<strong>on</strong>g>th</str<strong>on</strong>g> variable cell aspect<br />

ratio: A motivati<strong>on</strong> for degenerate diffusi<strong>on</strong> models<br />

C<strong>on</strong>tinuum diffusi<strong>on</strong> models are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten used to represent <str<strong>on</strong>g>th</str<strong>on</strong>g>e collective moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cell populati<strong>on</strong>s. Most previous studies have simply used linear diffusi<strong>on</strong> to represent<br />

collective cell spreading, while o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers found <str<strong>on</strong>g>th</str<strong>on</strong>g>at degenerate n<strong>on</strong>linear diffusi<strong>on</strong><br />

provides a better match to experimental cell density pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell modeling<br />

literature <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is no guidance available wi<str<strong>on</strong>g>th</str<strong>on</strong>g> regard to which approach is more appropriate<br />

for representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e spreading <str<strong>on</strong>g>of</str<strong>on</strong>g> cell populati<strong>on</strong>s. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is<br />

no knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> particular experimental measurements <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be made to distinguish<br />

between situati<strong>on</strong>s where <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two models are appropriate. Here we provide<br />

a link between individual-based and c<strong>on</strong>tinuum models using a multi-scale approach<br />

in which we analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e collective moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting agents in a<br />

generalized lattice-based exclusi<strong>on</strong> process. For round agents <str<strong>on</strong>g>th</str<strong>on</strong>g>at occupy a single<br />

lattice site, we find <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e relevant c<strong>on</strong>tinuum descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system is a linear<br />

diffusi<strong>on</strong> equati<strong>on</strong>, whereas for el<strong>on</strong>gated rod-shaped agents <str<strong>on</strong>g>th</str<strong>on</strong>g>at occupy L adjacent<br />

lattice sites we find <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e relevant c<strong>on</strong>tinuum descripti<strong>on</strong> is c<strong>on</strong>nected to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

porous media equati<strong>on</strong> (pme). The exp<strong>on</strong>ent in <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>linear diffusivity functi<strong>on</strong> is<br />

related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e aspect ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e agents. Our work provides a physical c<strong>on</strong>necti<strong>on</strong><br />

between modeling collective cell spreading and <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e linear diffusi<strong>on</strong><br />

equati<strong>on</strong> or <str<strong>on</strong>g>th</str<strong>on</strong>g>e pme to represent cell density pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles. Results suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at when<br />

using c<strong>on</strong>tinuum models to represent cell populati<strong>on</strong> spreading, we should take care<br />

to account for variati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell aspect ratio because different aspect ratios lead<br />

to different c<strong>on</strong>tinuum models.<br />

901

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cell migrati<strong>on</strong> during development: modelling and experiment; Saturday,<br />

July 2, 08:30<br />

Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ew Simps<strong>on</strong><br />

Queensland University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ew.simps<strong>on</strong>@qut.edu.au<br />

Modelling cell invasi<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> proliferati<strong>on</strong> mechanisms<br />

motivated by time-lapse data<br />

Cell invasi<strong>on</strong> involves a populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells which are motile and proliferative.<br />

Traditi<strong>on</strong>al lattice-based discrete models <str<strong>on</strong>g>of</str<strong>on</strong>g> cell proliferati<strong>on</strong> involve agents depositing<br />

daughter agents <strong>on</strong> nearest neighbour lattice sites. Our new work is motivated<br />

by time-lapse images <str<strong>on</strong>g>of</str<strong>on</strong>g> cell invasi<strong>on</strong> associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e enteric<br />

nervous system where a populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> precursor neural crest cells invades <str<strong>on</strong>g>th</str<strong>on</strong>g>e developing<br />

gut tissues. Using time-lapse data, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e traditi<strong>on</strong>al proliferati<strong>on</strong><br />

model is inappropriate and we propose a new proliferati<strong>on</strong> model c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

time-lapse observati<strong>on</strong>s. Using simulati<strong>on</strong> and analysis, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e discrete<br />

model is related to a family <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong>s and can be used to make<br />

predicti<strong>on</strong>s over a range <str<strong>on</strong>g>of</str<strong>on</strong>g> scales appropriate for interpreting experimental data<br />

902

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemic models: Networks and stochasticity I; Wednesday, June 29, 14:30<br />

David Sirl<br />

Loughborough University<br />

e-mail: d.sirl@lboro.ac.uk<br />

Household epidemic models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> variable infecti<strong>on</strong> severity<br />

We explore SIR (Susceptible → Infective → Removed) epidemic models wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

household structure and <str<strong>on</strong>g>th</str<strong>on</strong>g>e feature <str<strong>on</strong>g>th</str<strong>on</strong>g>at infectives can be ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er mildly or severely<br />

infective. We analyse two different models which describe such behaviour, <strong>on</strong>e where<br />

individual’s severities are pre-determined (perhaps due to prior partial immunity)<br />

and <strong>on</strong>e where <str<strong>on</strong>g>th</str<strong>on</strong>g>e an individual’s severity is influenced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e severity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

individual <str<strong>on</strong>g>th</str<strong>on</strong>g>at infects it and whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>is infecti<strong>on</strong> resulted from a wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in- or<br />

between-household c<strong>on</strong>tact. The aim is to determine whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er it is possible to find<br />

which <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two models best explains <str<strong>on</strong>g>th</str<strong>on</strong>g>e varying resp<strong>on</strong>se when given final size<br />

household outbreak data c<strong>on</strong>taining mild and severe cases. We c<strong>on</strong>duct numerical<br />

studies from which we c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is discriminati<strong>on</strong> usually is possible.<br />

This is joint work wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Frank Ball (University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham) and Tom Britt<strong>on</strong><br />

(Stockholm University).<br />

903

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Stochastic models in computati<strong>on</strong>al neuroscience I; Wednesday, June 29, 14:30<br />

Roberta Sirovich<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Torino<br />

e-mail: roberta.sirovich@unito.it<br />

About a modificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing time definiti<strong>on</strong> in<br />

stochastic leaky integrate–and–fire neur<strong>on</strong> models<br />

The integrate-and-fire neur<strong>on</strong> model is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most widely used models for<br />

studies <str<strong>on</strong>g>of</str<strong>on</strong>g> neural coding [1,2]. It describes <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane potential <str<strong>on</strong>g>of</str<strong>on</strong>g> a neur<strong>on</strong><br />

in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e synaptic inputs and <str<strong>on</strong>g>th</str<strong>on</strong>g>e injected current <str<strong>on</strong>g>th</str<strong>on</strong>g>at it receives. An acti<strong>on</strong><br />

potential (spike) is generated whenever <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane potential crosses some<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>reshold level from below. In integrate-and-fire models <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> an acti<strong>on</strong> potential<br />

is not described explicitly. Spikes are formal events fully characterized by<br />

a ‘firing time’ after which <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane potential is reset and <str<strong>on</strong>g>th</str<strong>on</strong>g>e process starts<br />

from scratch.<br />

The observati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> experimental intracellular recordings seems to suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane potential may cross <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold level several times before an acti<strong>on</strong><br />

potential is detected [3]. We study a modified versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e leaky integrate-and-fire<br />

neur<strong>on</strong> model where a spike is generated whenever <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane potential remains<br />

above <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold level for a ‘sufficiently’ l<strong>on</strong>g time. Hence <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing time is not<br />

defined by an instantaneous crossing <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e level, but depends <strong>on</strong> a l<strong>on</strong>ger history <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

fluctuati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane potential. Comparis<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics exhibited<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical models are presented.<br />

References.<br />

[1] A. N. Burkitt, A review <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e integrate–and–fire neur<strong>on</strong> model: I. Homogeneous synaptic<br />

input Biol Cybern (2006) 95 1–19.<br />

[2] A. N. Burkitt, A review <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e integrate–and–fire neur<strong>on</strong> model: II. Inhomogeneous synaptic<br />

input and network properties Biol Cybern (2006) 95 97–112.<br />

[3] P. Lansky, P. Sanda and J. He The parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic leaky integrate–and–fire<br />

neur<strong>on</strong>al model J Comput Neurosci 21 211.<br />

904

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Immunology; Wednesday, June 29, 17:00<br />

Vladas Skakauskas<br />

Naugarduko 24, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Informatics, Vilnius University,<br />

Vilnius, Li<str<strong>on</strong>g>th</str<strong>on</strong>g>uania<br />

e-mail: vladas.skakauskas@maf.vu.lt<br />

Pranas Katauskis<br />

Naugarduko 24, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Informatics, Vilnius University,<br />

Vilnius, Li<str<strong>on</strong>g>th</str<strong>on</strong>g>uania<br />

e-mail: pranas.katauskis@mif.vu.lt<br />

Alex Skvortsov<br />

DSTO, Fishermans Bend, Vic 3207, Australia<br />

e-mail: alex.skvortsov@dsto.defence.gov.au<br />

Numerical study <str<strong>on</strong>g>of</str<strong>on</strong>g> Receptor-Toxin-Antibody Interacti<strong>on</strong><br />

Problem<br />

The successful bio-medical applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> antibodies is well-documented and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ere is increasing interest in <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> antibodies for mitigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

toxins associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e various biological <str<strong>on</strong>g>th</str<strong>on</strong>g>reats. Such toxins are an important<br />

potential target for designing <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies against <str<strong>on</strong>g>th</str<strong>on</strong>g>ese <str<strong>on</strong>g>th</str<strong>on</strong>g>reats and a brood range <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

approaches has been taken to develop inhibitors <str<strong>on</strong>g>th</str<strong>on</strong>g>at may be <str<strong>on</strong>g>of</str<strong>on</strong>g> prophylactic or<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic use. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e progress in bio-engineering many antibodies have been<br />

generated for <str<strong>on</strong>g>th</str<strong>on</strong>g>is purpose wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different affinity parameters and, as a result, different<br />

properties. However affinity, by itself, is a poor predictor <str<strong>on</strong>g>of</str<strong>on</strong>g> protective or<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erapeutic potential which is determined by a new c<strong>on</strong>solidated kinetic parameter<br />

Receptor-Toxin-Antibody (RTA) kinetics and relative c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> species.<br />

Generati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> any new antibody necessitates development <str<strong>on</strong>g>of</str<strong>on</strong>g> a high fidelity model<br />

for RTA interacti<strong>on</strong>.<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e important step in improvement <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model is incorporati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong>-diffusi<strong>on</strong> fluxes <str<strong>on</strong>g>of</str<strong>on</strong>g> species. Incorporati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong> fluxes <str<strong>on</strong>g>of</str<strong>on</strong>g> toxin,<br />

antibody, and associated complex into <str<strong>on</strong>g>th</str<strong>on</strong>g>e RTA model leads to a PDEs model.<br />

Numerical study <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e protective efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> antibody against a given toxin<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model <str<strong>on</strong>g>of</str<strong>on</strong>g> cells placed into a toxin-antibody soluti<strong>on</strong> will be discussed.<br />

References.<br />

[1] A. Skvortsov, P. Gray, Modelling and simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> receptor-toxin-antibody interacti<strong>on</strong>, in:<br />

18<str<strong>on</strong>g>th</str<strong>on</strong>g> World IMACS/MODSIM C<strong>on</strong>gress, Australia, 2009, 185-191.<br />

[2] B. Goldstein, M. Dembo, Approximating <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong> <strong>on</strong> reversible reacti<strong>on</strong>s at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cell surface: Ligand-receptor kinetics, Biophys. J. 68 (1995) 1222-1230.<br />

[3] M. Coppey, A.M. Berezhkovskii, S.C. Sealf<strong>on</strong>, S.Y. Shvartsman, Time and lenght scales <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

autocrine signals in <str<strong>on</strong>g>th</str<strong>on</strong>g>ree dimensi<strong>on</strong>s, Biophys. J. 93 (2007) 1917-1922.<br />

905

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Noisy Cells; Saturday, July 2, 14:30<br />

Alexander Skupin<br />

Luxembourg Centre for Systems Biomedicine, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Luxembourg,<br />

Luxembourg<br />

e-mail: alexander.skupin@uni.lu<br />

Moritz Schütte<br />

MPI <str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular Plant Physiology, Potsdam-Golm, Germany<br />

e-mail: schuette@mpimp-golm.mpg.de<br />

Oliver Ebenhöh<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Systems and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Aberdeen, U.K.<br />

e-mail: ebenhoeh@abdn.ac.uk<br />

Modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> enzyme-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way coevoluti<strong>on</strong><br />

Metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways must have coevolved wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding enzyme gene<br />

sequences. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary dynamics ensuing from <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay between<br />

metabolic networks and genomes is still poorly understood. Here, we present<br />

a computati<strong>on</strong>al model <str<strong>on</strong>g>th</str<strong>on</strong>g>at generates putative evoluti<strong>on</strong>ary walks <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolic<br />

network using a parallel evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic reacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir catalyzing<br />

enzymes. Starting from an initial set <str<strong>on</strong>g>of</str<strong>on</strong>g> compounds and enzymes, we expand <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

metabolic network iteratively by adding new enzymes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a probability <str<strong>on</strong>g>th</str<strong>on</strong>g>at depends<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir sequence-based similarity to already present enzymes. Thus, we<br />

obtain simulated time courses <str<strong>on</strong>g>of</str<strong>on</strong>g> chemical evoluti<strong>on</strong> in which we can m<strong>on</strong>itor <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

appearance <str<strong>on</strong>g>of</str<strong>on</strong>g> new metabolites, enzyme sequences, or even entire organisms. We<br />

observe <str<strong>on</strong>g>th</str<strong>on</strong>g>at new enzymes do not appear gradually but ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er in clusters which corresp<strong>on</strong>d<br />

to enzyme classes. A comparis<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Brownian moti<strong>on</strong> dynamics indicates<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at our system displays biased random walks similar to diffusi<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolic<br />

network wi<str<strong>on</strong>g>th</str<strong>on</strong>g> l<strong>on</strong>g range correlati<strong>on</strong>s. This suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at a quantitative molecular<br />

principle may underlie <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> punctuated equilibrium as enzymes occur in<br />

bursts ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an by phyletic gradualism. Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>e simulated time courses<br />

lead to a putative time-order <str<strong>on</strong>g>of</str<strong>on</strong>g> enzyme and organism appearance. Am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

patterns we detect in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese evoluti<strong>on</strong>ary trends is a significant correlati<strong>on</strong> between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e time <str<strong>on</strong>g>of</str<strong>on</strong>g> appearance and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir enzyme repertoire size. Hence, our approach to<br />

metabolic evoluti<strong>on</strong> may help understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e rise in complexity at <str<strong>on</strong>g>th</str<strong>on</strong>g>e biochemical<br />

and genomic levels.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling III; Wednesday, June 29,<br />

17:00<br />

Alexander Skupin<br />

Luxembourg Centre for Systems Biomedicine, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Luxembourg,<br />

Luxembourg<br />

e-mail: alexander.skupin@uni.lu<br />

How spatial cell properties shape Ca 2+ signals<br />

Ca 2+ plays a major role in many physiological processes including muscle c<strong>on</strong>tracti<strong>on</strong><br />

and gene regulati<strong>on</strong>. The versatility is achieved by a wide spectrum <str<strong>on</strong>g>of</str<strong>on</strong>g> Ca 2+<br />

signals ranging from fast local events to cell wide repetitive spiking and plateau<br />

resp<strong>on</strong>ses. It is still a challenge to understand how cells generate reliable cellular<br />

signals wi<str<strong>on</strong>g>th</str<strong>on</strong>g> microscopic noisy Ca 2+ release channels like IP3Rs. We have recently<br />

shown in experiments <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic fluctuati<strong>on</strong>s are carried <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cell by <str<strong>on</strong>g>th</str<strong>on</strong>g>e hierarchical organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ca 2+ pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way. Here we use our<br />

detailed modelling approach to analyze how Ca 2+ signals depend <strong>on</strong> physiological<br />

parameters. The model describes individual release channels by Markov chains <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

states <str<strong>on</strong>g>of</str<strong>on</strong>g> which act as stochastic source terms in a reacti<strong>on</strong> diffusi<strong>on</strong> system representing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. This allows for following <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ca 2+ signal from its local triggering<br />

event to <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell wide resp<strong>on</strong>se. In extensive simulati<strong>on</strong>s we analyzed how <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

spatial properties shape Ca 2+ signals. The simulati<strong>on</strong>s can quantitatively describe<br />

experiments in which Ca 2+ diffusi<strong>on</strong> is reduced by additi<strong>on</strong>al buffer. In fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

simulati<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e temperature dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> Ca 2+ signals could be mapped to a<br />

change in <str<strong>on</strong>g>th</str<strong>on</strong>g>e SERCA pump streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>at determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial coupling between<br />

release sites. All <str<strong>on</strong>g>th</str<strong>on</strong>g>ese modelled and experimental data are in additi<strong>on</strong> analyzed<br />

and compared by a moment based approach <str<strong>on</strong>g>th</str<strong>on</strong>g>at points to a functi<strong>on</strong>al robustness<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ca 2+ pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Urszula Skwara<br />

Maria Curie Skłodowska University<br />

e-mail: uskwara@o2.pl<br />

Populati<strong>on</strong> Dynamics; Wednesday, June 29, 11:00<br />

Asymptotic properties <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic symbiosis model<br />

We discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> various stochastic perturbati<strong>on</strong>s <strong>on</strong> symbiosis system.<br />

We c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e following system <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic equati<strong>on</strong>s<br />

<br />

dX(t) = ((a1 + b1Y (t) − c1X(t)) dt + ρ11 dW1(t) + ρ12 dW2(t)) X(t)<br />

(1)<br />

dY (t) = ((a2 + b2X(t) − c2Y (t)) dt + ρ21 dW1(t) + ρ22 dW2(t)) Y (t),<br />

which describes relati<strong>on</strong>s between two populati<strong>on</strong>s living in symbiosis. We assume<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at ai, bi, ci > 0 (i = 1, 2) are positive c<strong>on</strong>stants, W1(t), W2(t) are two independent<br />

standard Wiener processes, X(t), Y (t) are stochastic processes which represent, respectively,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e first and <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d populati<strong>on</strong>. We c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>ree kinds <str<strong>on</strong>g>of</str<strong>on</strong>g> stochastic<br />

perturbati<strong>on</strong>s:<br />

(i) weakly correlated, i.e. ρ11ρ22 − ρ12ρ21 = 0;<br />

(ii) str<strong>on</strong>gly correlated, i.e. ρ11 > 0, ρ21 > 0, ρ12 = 0, ρ22 = 0;<br />

(iii) <strong>on</strong>ly <strong>on</strong>e populati<strong>on</strong> is stochastically perturbed, by symmetry we assume<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d populati<strong>on</strong> is perturbed, i.e. ρ11 = 0, ρ21 > 0, ρ12 = 0,<br />

ρ22 = 0.<br />

First we show <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence, uniqueness, positivity and n<strong>on</strong>-extincti<strong>on</strong> property <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> system (1) <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e assumpti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at b1b2 < c1c2. Next we prove <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e probability distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e process (X(t), Y (t)) are absolutely c<strong>on</strong>tinuous<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>e Lebesgue measure. Let U(x, y, t) be <str<strong>on</strong>g>th</str<strong>on</strong>g>e density <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> (X(t), Y (t)). We give a sufficient and a necessary c<strong>on</strong>diti<strong>on</strong> for asymptotic<br />

stability <str<strong>on</strong>g>of</str<strong>on</strong>g> system (1), i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>vergence <str<strong>on</strong>g>of</str<strong>on</strong>g> U(x, y, t) to an invariant density<br />

U∗(x, y). In <str<strong>on</strong>g>th</str<strong>on</strong>g>e case when <str<strong>on</strong>g>th</str<strong>on</strong>g>is system is not asymptotically stable, we prove <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

limt→∞ Y (t) = 0 a.e. We also show <str<strong>on</strong>g>th</str<strong>on</strong>g>at in <str<strong>on</strong>g>th</str<strong>on</strong>g>is case limt→∞ X(t) = 0 a.e. or <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

probability distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e process X(t) c<strong>on</strong>verge weakly to some probability<br />

measure. We give a biological interpretati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese results.<br />

References.<br />

[1] U. Skwara, A stochastic model <str<strong>on</strong>g>of</str<strong>on</strong>g> symbiosis Ann. Pol<strong>on</strong>. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.97.3 257–272 .<br />

[2] U. Skwara, A stochastic model <str<strong>on</strong>g>of</str<strong>on</strong>g> symbiosis wi<str<strong>on</strong>g>th</str<strong>on</strong>g> degenerate difussi<strong>on</strong> process Ann. Pol<strong>on</strong>.<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. 98.2 111–128.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cellular Systems Biology; Saturday, July 2, 11:00<br />

Jaroslaw Smieja<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Automatic C<strong>on</strong>trol, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: Jaroslaw.Smieja@polsl.pl<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Puszynski<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Automatic C<strong>on</strong>trol, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Coupled sensitivity and frequency analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> signalling<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> signalling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways has gained large popularity recently.<br />

The models <str<strong>on</strong>g>th</str<strong>on</strong>g>at have been developed describe dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> NFkB, JAK/STAT,<br />

p53/Mdm2 and many o<str<strong>on</strong>g>th</str<strong>on</strong>g>er pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways. One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most important advantages<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models in <str<strong>on</strong>g>th</str<strong>on</strong>g>is field is <str<strong>on</strong>g>th</str<strong>on</strong>g>eir flexibility and ability to<br />

check certain aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics if <str<strong>on</strong>g>th</str<strong>on</strong>g>e investigated systems before committing<br />

large resources into experimental work.<br />

Complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e models <str<strong>on</strong>g>th</str<strong>on</strong>g>at are under development varies, depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

particular goals <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling. Never<str<strong>on</strong>g>th</str<strong>on</strong>g>eless, regardless <str<strong>on</strong>g>of</str<strong>on</strong>g> model complexity, <strong>on</strong>e<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e key issues is proper choice <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters. As a result, in such work sensitivity<br />

analysis is a necessary stages in analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> simulati<strong>on</strong> results.<br />

Two main categories <str<strong>on</strong>g>of</str<strong>on</strong>g> sensitivity analysis me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods can be distinguished: local<br />

and global. Local sensitivity analysis provides informati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

small deviati<strong>on</strong> a single parameter from its nominal value <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system output.<br />

Global sensitivities, in turn, describe how <str<strong>on</strong>g>th</str<strong>on</strong>g>e system output changes when multiple<br />

parameters change in a relatively wide range.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work several sensitivity indices will be applied to find out which parameter<br />

subsets have <str<strong>on</strong>g>th</str<strong>on</strong>g>e greatest impact <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> several signaling<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways. However, instead <str<strong>on</strong>g>of</str<strong>on</strong>g> using <str<strong>on</strong>g>th</str<strong>on</strong>g>em wi<str<strong>on</strong>g>th</str<strong>on</strong>g> reference to steady states, which<br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most frequent approaches, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey will be coupled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> frequency<br />

analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e models dynamics. That way, it is possible to answer <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

most important questi<strong>on</strong>s c<strong>on</strong>cerning some signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways. There is an <strong>on</strong>going<br />

dispute about oscillati<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir importance in cellular resp<strong>on</strong>ses to external<br />

inputs. Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> sensitivity <str<strong>on</strong>g>of</str<strong>on</strong>g> main frequencies in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model outputs will push<br />

forward research in <str<strong>on</strong>g>th</str<strong>on</strong>g>is field. If it is <str<strong>on</strong>g>th</str<strong>on</strong>g>e oscillati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at are crucial for proper cell<br />

behavior, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese frequencies should be relatively insensitive to parameter changes.<br />

Moreover, sensitivity analysis will indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>e stages <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e signaling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

are <str<strong>on</strong>g>th</str<strong>on</strong>g>e most pr<strong>on</strong>e to disturbances, providing clues for experimental work.<br />

The work was partially supported by The Fundati<strong>on</strong> for Polish Science.<br />

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Neurosciences; Thursday, June 30, 11:30<br />

Mamiko Arai<br />

Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Program, Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina State Univ., Box 8203.Raleigh,<br />

NC 27695<br />

e-mail: marai@ncsu.edu<br />

Charles Eugene Smi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Statistics, Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Program, Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> Carolina State<br />

Univ., Box 8203.Raleigh, NC 27695<br />

e-mail: bmasmi<str<strong>on</strong>g>th</str<strong>on</strong>g>@ncsu.edu<br />

Distinguishing <str<strong>on</strong>g>th</str<strong>on</strong>g>e Type <str<strong>on</strong>g>of</str<strong>on</strong>g> Input Noise in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Fitzhugh-Nagumo Neur<strong>on</strong>al Model<br />

A n<strong>on</strong>linear system <str<strong>on</strong>g>of</str<strong>on</strong>g> differential equati<strong>on</strong>s known as <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fitzhugh-Nagumo (FN)<br />

is used to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e physiological state <str<strong>on</strong>g>of</str<strong>on</strong>g> a nerve membrane. Several different<br />

kinds <str<strong>on</strong>g>of</str<strong>on</strong>g> noise are added to <str<strong>on</strong>g>th</str<strong>on</strong>g>e FN model to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> noise <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e membrane. They are Gaussian white noise, O-U process and Poiss<strong>on</strong> noise.<br />

Gaussian white noise represents many small synaptic inputs and Poiss<strong>on</strong> noise represents<br />

a few large synaptic inputs. The n<strong>on</strong>-oscillatory regi<strong>on</strong> before and after <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

bifurcati<strong>on</strong> regi<strong>on</strong> is used to distinguish between Wiener vs. Poiss<strong>on</strong> inputs by a<br />

hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis test about <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean number <str<strong>on</strong>g>of</str<strong>on</strong>g> level crossings. The null hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e expected level crossings <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e equilibrium state by a time sampled linearized<br />

FN set <str<strong>on</strong>g>of</str<strong>on</strong>g> differential equati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Wiener input. The test performs well in rejecting<br />

n<strong>on</strong> Wiener inputs in simulati<strong>on</strong> studies, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e linearized and n<strong>on</strong>linear<br />

F-N model. A res<strong>on</strong>ance type phenomena was also observed.<br />

Key Words: Neur<strong>on</strong>; First passage time; level crossings; Poiss<strong>on</strong> process; stochastic<br />

differential equati<strong>on</strong><br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Recent advances in infectious disease modelling II; Saturday, July 2, 14:30<br />

Robert Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>?<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Ottawa<br />

e-mail: rsmi<str<strong>on</strong>g>th</str<strong>on</strong>g>43@uottawa.ca<br />

The impact <str<strong>on</strong>g>of</str<strong>on</strong>g> media coverage <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> human influenza<br />

There is an urgent need to understand how <str<strong>on</strong>g>th</str<strong>on</strong>g>e provisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> influences<br />

individual risk percepti<strong>on</strong> and how <str<strong>on</strong>g>th</str<strong>on</strong>g>is in turn shapes <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics.<br />

Individuals are influenced by informati<strong>on</strong> in complex and unpredictable<br />

ways. Emerging infectious diseases, such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e recent swine flu epidemic, may<br />

be particular hotspots for a media-fueled rush to vaccinati<strong>on</strong> c<strong>on</strong>versely, seas<strong>on</strong>al<br />

diseases may receive little media attenti<strong>on</strong>, despite <str<strong>on</strong>g>th</str<strong>on</strong>g>eir high mortality rate, due<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir perceived lack <str<strong>on</strong>g>of</str<strong>on</strong>g> newness. We formulate a deterministic transmissi<strong>on</strong> and<br />

vaccinati<strong>on</strong> model to invetigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> media coverage <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong><br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> influenza. The populati<strong>on</strong> is subdivided into different classes according<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir disease status. The compartmental model includes <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> media<br />

coverage <strong>on</strong> reporting <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> infecti<strong>on</strong>s as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals<br />

successfully vaccinated. A <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold parameter (<str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproductive ratio) is<br />

analytically derived and used to discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e local stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease-free steady<br />

state. The impact <str<strong>on</strong>g>of</str<strong>on</strong>g> costs <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be incurred, which include vaccinati<strong>on</strong>, educati<strong>on</strong>,<br />

implementati<strong>on</strong> and campaigns <strong>on</strong> media coverage, are also investigated using<br />

optimal c<strong>on</strong>trol <str<strong>on</strong>g>th</str<strong>on</strong>g>eory. A simplified versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> pulse vaccinati<strong>on</strong><br />

shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e media can trigger a vaccinating panic if <str<strong>on</strong>g>th</str<strong>on</strong>g>e vaccine is imperfect<br />

and simplified messages result in <str<strong>on</strong>g>th</str<strong>on</strong>g>e vaccinated mixing wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e infectives wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out<br />

regard to disease risk. The effects <str<strong>on</strong>g>of</str<strong>on</strong>g> media <strong>on</strong> an outbreak are complex. Simplified<br />

understandings <str<strong>on</strong>g>of</str<strong>on</strong>g> disease epidemiology, propogated <str<strong>on</strong>g>th</str<strong>on</strong>g>rough media soundbites,<br />

may make <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease significantly worse.<br />

911

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Oksana Sorokina<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Edinburgh<br />

e-mail: oksana.sorokina@ed.ac.uk<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Rule based modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular signalling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways in<br />

synapse.<br />

Synaptic transmissi<strong>on</strong> depends <strong>on</strong> a very well orchestrated sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> proteinprotein<br />

interacti<strong>on</strong>s <strong>on</strong> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> sides <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e neur<strong>on</strong>al synapse. The aggregati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

protein complexes <str<strong>on</strong>g>of</str<strong>on</strong>g> different sizes and compositi<strong>on</strong> underpins synapse functi<strong>on</strong>,<br />

and disrupti<strong>on</strong>s at <str<strong>on</strong>g>th</str<strong>on</strong>g>is level account for many neuropsychiatric and neurodegenerative<br />

diseases.<br />

The postsynaptic compartment <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e excitatory glutamatergic synapse c<strong>on</strong>tains<br />

hundreds <str<strong>on</strong>g>of</str<strong>on</strong>g> distinct polypeptides wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a wide range <str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong>s (signalling,<br />

trafficking, cell-adhesi<strong>on</strong>, etc). Structural dynamics in <str<strong>on</strong>g>th</str<strong>on</strong>g>e PSD (post synaptic density)<br />

are believed to resp<strong>on</strong>d for <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial steps <str<strong>on</strong>g>of</str<strong>on</strong>g> signalling cascades <str<strong>on</strong>g>th</str<strong>on</strong>g>at result in<br />

l<strong>on</strong>g-term synaptic plasticity. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough functi<strong>on</strong>ally and morphologically diverse,<br />

PSD proteins are generally enriched wi<str<strong>on</strong>g>th</str<strong>on</strong>g> specific domains, which precisely define<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e mode <str<strong>on</strong>g>of</str<strong>on</strong>g> clustering essential for signal processing.<br />

We apply a stochastic calculus <str<strong>on</strong>g>of</str<strong>on</strong>g> domain binding provided by <str<strong>on</strong>g>th</str<strong>on</strong>g>e rule-based<br />

modelling (e.g. Kappa) approach to formalise <str<strong>on</strong>g>th</str<strong>on</strong>g>e highly combinatorial signalling<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way in PSD and perform <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative distributi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> protein complexes and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir sizes (Danos and Schumacher, 2008, Danos et al,<br />

2009). We specify <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> PSD by rules, taking into account protein domain<br />

structure, specific domain affinity and relative protein availability. Resulting<br />

model has a hierarchical structure, composed <str<strong>on</strong>g>of</str<strong>on</strong>g> generic agents and generic rules<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir c<strong>on</strong>crete variants. This allows interrogate <str<strong>on</strong>g>th</str<strong>on</strong>g>e critical c<strong>on</strong>diti<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

protein aggregati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e large complexes al<strong>on</strong>g wi<str<strong>on</strong>g>th</str<strong>on</strong>g> simultaneous study <str<strong>on</strong>g>of</str<strong>on</strong>g> effect<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> presence <str<strong>on</strong>g>of</str<strong>on</strong>g> mutated polypeptides and protein splice variants <strong>on</strong> structure and<br />

relative stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ose complexes.<br />

912

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Dynamics; Saturday, July 2, 11:00<br />

Max O. Souza<br />

Departamento de Matemática Aplicada, Universidade Federal Fluminense,<br />

R. Mário Santos Braga, s/n, Niterói - RJ, 24020-140, Brazil<br />

e-mail: msouza@mat.uff.br<br />

Multiscaling Modelling in Evoluti<strong>on</strong>ary Dynamics<br />

We start from a family <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tinuous approximati<strong>on</strong>s to <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability density<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a frequency dependent Moran process studied by Chalub & Souza in [1]. These<br />

approximati<strong>on</strong>, depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e scalings, can be <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusive or n<strong>on</strong>-diffusive type,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e latter being equivalent to <str<strong>on</strong>g>th</str<strong>on</strong>g>e Replicator Dynamics. We <str<strong>on</strong>g>th</str<strong>on</strong>g>en study <str<strong>on</strong>g>th</str<strong>on</strong>g>e small<br />

diffusi<strong>on</strong> limit, and show how <str<strong>on</strong>g>th</str<strong>on</strong>g>e Replicator Dynamics can be c<strong>on</strong>sistenly fitted in<br />

a diffusive approximati<strong>on</strong>. Some additi<strong>on</strong>al results c<strong>on</strong>cerning <str<strong>on</strong>g>th</str<strong>on</strong>g>e fixati<strong>on</strong> probabilites<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>is limit are also presented. This is joint work wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Fabio Chalub.<br />

References.<br />

[1] Fabio A. C. C. Chalub & Max O. Souza, From discrete to c<strong>on</strong>tinuous evoluti<strong>on</strong> models: A<br />

unifying approach to drift-diffusi<strong>on</strong> and replicator dynamics, Theoretical Populati<strong>on</strong> Biology,<br />

76 (4) 268–277, 2009.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

E.N. Spanou<br />

Democritus University <str<strong>on</strong>g>of</str<strong>on</strong>g> Thrace, Xan<str<strong>on</strong>g>th</str<strong>on</strong>g>i, Greece<br />

e-mail: ispanou@ee.du<str<strong>on</strong>g>th</str<strong>on</strong>g>.gr<br />

A.G. Rigas<br />

Democritus University <str<strong>on</strong>g>of</str<strong>on</strong>g> Thrace, Xan<str<strong>on</strong>g>th</str<strong>on</strong>g>i, Greece<br />

e-mail: rigas@ee.du<str<strong>on</strong>g>th</str<strong>on</strong>g>.gr<br />

V.G. Vassiliadis<br />

Democritus University <str<strong>on</strong>g>of</str<strong>on</strong>g> Thrace, Xan<str<strong>on</strong>g>th</str<strong>on</strong>g>i, Greece<br />

e-mail: bvasil@ee.du<str<strong>on</strong>g>th</str<strong>on</strong>g>.gr<br />

Neurosciences; Friday, July 1, 14:30<br />

The identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a neuroelectric system in <str<strong>on</strong>g>th</str<strong>on</strong>g>e time and<br />

frequency domain when an alpha stimulati<strong>on</strong> is present<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work <str<strong>on</strong>g>th</str<strong>on</strong>g>e identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a neuroelectric system, called muscle spindle,<br />

is studied when it is affected by an alpha mot<strong>on</strong>eur<strong>on</strong> (alpha stimulati<strong>on</strong>). The<br />

muscle spindle is an element <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e neuromuscular system and plays an important<br />

role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e initiati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> movement and in <str<strong>on</strong>g>th</str<strong>on</strong>g>e maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e posture. The<br />

resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e muscle spindle and <str<strong>on</strong>g>th</str<strong>on</strong>g>e stimulus imposed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e mot<strong>on</strong>eur<strong>on</strong> are<br />

sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> acti<strong>on</strong> potentials and <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are c<strong>on</strong>sidered as realizati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

stati<strong>on</strong>ary point processes. A frequency and a time domain approach has been<br />

employed for <str<strong>on</strong>g>th</str<strong>on</strong>g>e identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e frequency domain, <str<strong>on</strong>g>th</str<strong>on</strong>g>e muscle spindle can be described by a Volterra<br />

- type model involving <strong>on</strong>e input and <strong>on</strong>e output. Spectral analysis techniques <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

stati<strong>on</strong>ary point processes are applied in order to estimate two important functi<strong>on</strong>s,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e coherence coefficient and <str<strong>on</strong>g>th</str<strong>on</strong>g>e impulse resp<strong>on</strong>se. The linear relati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system and <str<strong>on</strong>g>th</str<strong>on</strong>g>e input is described by <str<strong>on</strong>g>th</str<strong>on</strong>g>e estimate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e coherence<br />

coefficient, while <str<strong>on</strong>g>th</str<strong>on</strong>g>e estimate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e impulse resp<strong>on</strong>se functi<strong>on</strong> provides <str<strong>on</strong>g>th</str<strong>on</strong>g>e best<br />

linear predictor for <str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e input.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e time domain approach <str<strong>on</strong>g>th</str<strong>on</strong>g>e input and <str<strong>on</strong>g>th</str<strong>on</strong>g>e output <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system can<br />

also be c<strong>on</strong>sidered as binary time series and <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> generalized<br />

linear models (GLM) can be applied. The advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach is based <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at estimates <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system’s parameters can be obtained by using <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

maximum likelihood functi<strong>on</strong>. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is no c<strong>on</strong>vergence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximum<br />

likelihood estimates since <str<strong>on</strong>g>th</str<strong>on</strong>g>e phenomen<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> quasi-complete separati<strong>on</strong> occurs.<br />

To overcome <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem an approach based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e penalized likelihood functi<strong>on</strong><br />

is used, which provides an ideal soluti<strong>on</strong> and it is computati<strong>on</strong>ally much faster<br />

compared to <str<strong>on</strong>g>th</str<strong>on</strong>g>e M<strong>on</strong>te Carlo me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>th</str<strong>on</strong>g>at has been already used. The stochastic<br />

model which is proposed for <str<strong>on</strong>g>th</str<strong>on</strong>g>e descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system involves <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e summati<strong>on</strong> functi<strong>on</strong>. The estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e summati<strong>on</strong> functi<strong>on</strong> is <str<strong>on</strong>g>of</str<strong>on</strong>g> great<br />

interest as it describes whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e system is excitatory or inhibitory. A validity<br />

test for <str<strong>on</strong>g>th</str<strong>on</strong>g>e fitted model based <strong>on</strong> randomized quantile residuals is proposed. The<br />

validity test is transformed to a goodness <str<strong>on</strong>g>of</str<strong>on</strong>g> fit test and <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> Q-Q plot is also<br />

discussed.<br />

The estimate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e impulse resp<strong>on</strong>se functi<strong>on</strong> indicates <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e system accelerates<br />

for 1–2 ms shortly after <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e alpha mot<strong>on</strong>eur<strong>on</strong>, is blocked for<br />

about 30 ms and after <str<strong>on</strong>g>th</str<strong>on</strong>g>at does not change. Similar results are obtained by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

estimate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e summati<strong>on</strong> functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e GLM.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

References.<br />

[1] D.R. Brillinger, K.A. Lindsay, J.R. Rosenberg, 2009. Combining frequency and time domain<br />

approaches to systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multiple spike train input Biological Cybernetics 100 459–474.<br />

[2] D. Fir<str<strong>on</strong>g>th</str<strong>on</strong>g>, 1993. Bias reducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> maximum likelihood estimates Biometrika 80(1) 27–38.<br />

[3] G. Heinze, M. Schemper, 2003. A soluti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> separati<strong>on</strong> in logistic regressi<strong>on</strong><br />

Statistics in Medicine 21(16) 2409–2419.<br />

[4] V.K. Kotti, A.G. Rigas, 2003. Identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a complex neurophysiological system using <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

maximum likelihood J. Biological Systems 11(2) 189–243.<br />

[5] V.K. Kotti, A.G. Rigas, 2008. A M<strong>on</strong>te Carlo Me<str<strong>on</strong>g>th</str<strong>on</strong>g>od Used for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Muscle<br />

Spindle In: A. Deutsch et al. (Eds) Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Systems, Volume II,<br />

Birkhauser, Bost<strong>on</strong>, 237–243.<br />

[6] A.G. Rigas, P. Liatsis, 2000. Identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a neuroelectric system involving a single input<br />

and a single output Signal Processing 80(9) 1883–1894.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> physiological processes in patients <strong>on</strong> dialysis;<br />

Saturday, July 2, 11:00<br />

Joanna Stachowska-Piętka<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Biocybernetics and Biomedical Engineering<br />

e-mail: jstachowska@ibib.waw.pl<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> perit<strong>on</strong>eal dialysis<br />

Perit<strong>on</strong>eal dialysis (PD) is a treatment opti<strong>on</strong> for patients wi<str<strong>on</strong>g>th</str<strong>on</strong>g> kidney failure <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

is available in most countries around <str<strong>on</strong>g>th</str<strong>on</strong>g>e world. Its main goal is to remove waste<br />

metabolic product and excess water to <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluid infused into <str<strong>on</strong>g>th</str<strong>on</strong>g>e perit<strong>on</strong>eal cavity<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at is finally drained out. The increasing usage <str<strong>on</strong>g>of</str<strong>on</strong>g> PD required special tools <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

would allow for <str<strong>on</strong>g>th</str<strong>on</strong>g>e estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> treatment efficiency. In particular, ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

models allow for <str<strong>on</strong>g>th</str<strong>on</strong>g>e quantitative descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> bidirecti<strong>on</strong>al water and solute<br />

perit<strong>on</strong>eal transport.<br />

Three types <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models can be used for <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e perit<strong>on</strong>eal<br />

transport: <str<strong>on</strong>g>th</str<strong>on</strong>g>e classical membrane model, <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-pore model, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributed<br />

model. The first two models (typically applied in clinical and experimental<br />

research) use phenomenologically derived parameters <str<strong>on</strong>g>th</str<strong>on</strong>g>at characterize perit<strong>on</strong>eal<br />

transport. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>eir relative simplicity does not allow for <str<strong>on</strong>g>th</str<strong>on</strong>g>e derivati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e informati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fundamental physiological processes <str<strong>on</strong>g>th</str<strong>on</strong>g>at govern fluid and<br />

solute transport during perit<strong>on</strong>eal dialysis. Therefore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributed approach is<br />

used to provide detailed informati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e perit<strong>on</strong>eal physiology and more realistic<br />

descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e complexity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e perit<strong>on</strong>eal anatomy and transport system.<br />

This approach is based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e local tissue and microcirculatory physiology and its<br />

parameters are derived from <str<strong>on</strong>g>th</str<strong>on</strong>g>e local structure and properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue and<br />

microvasculature.<br />

In order to describe bidirecti<strong>on</strong>al fluid and solute transport, <str<strong>on</strong>g>th</str<strong>on</strong>g>e two-phase<br />

structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interstitium was taken into account, based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e previous experimental<br />

findings (Guyt<strong>on</strong> et al, 1969). The two-phase system c<strong>on</strong>tains a water-rich,<br />

colloid-poor regi<strong>on</strong> (Fluid Phase, F), where fluid transport is driven by <str<strong>on</strong>g>th</str<strong>on</strong>g>e hydrostatic<br />

pressure, and a colloid-rich, water-poor regi<strong>on</strong> (Colloid Phase, C). In general,<br />

Phase C corresp<strong>on</strong>ds to <str<strong>on</strong>g>th</str<strong>on</strong>g>e matrix <str<strong>on</strong>g>of</str<strong>on</strong>g> macromolecules <str<strong>on</strong>g>th</str<strong>on</strong>g>at makes up <str<strong>on</strong>g>th</str<strong>on</strong>g>e interstitial<br />

ground substance. The system <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear partial differential equati<strong>on</strong> was<br />

solved numerically for <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue layer <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e muscle <str<strong>on</strong>g>of</str<strong>on</strong>g> 1 cm wid<str<strong>on</strong>g>th</str<strong>on</strong>g> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> uniformly<br />

distributed capillary and lymphatic beds and an interstitial layer (0.015 cm) <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e perit<strong>on</strong>eal surface free from cells and blood vessels using a distributed model.<br />

The model parameters were adjusted to provide a descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a typical single<br />

exchange wi<str<strong>on</strong>g>th</str<strong>on</strong>g> hypert<strong>on</strong>ic glucose 3.86% soluti<strong>on</strong>. Diffusive and c<strong>on</strong>vective solute<br />

transport was analyzed <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e example <str<strong>on</strong>g>of</str<strong>on</strong>g> plasma protein (albumin) and glucose<br />

(osmotic agent).<br />

Numerical results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e developed model described <str<strong>on</strong>g>th</str<strong>on</strong>g>e bidirecti<strong>on</strong>al water and<br />

protein transport in agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e data about flows and clearances from clinical<br />

studies. Computer simulati<strong>on</strong> suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>at two-phase structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue<br />

allows for <str<strong>on</strong>g>th</str<strong>on</strong>g>e separati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> opposite fluid flows: fluid transport from <str<strong>on</strong>g>th</str<strong>on</strong>g>e perit<strong>on</strong>eal<br />

cavity into <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue (absorpti<strong>on</strong>) occurs mainly <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fluid Phase, whereas<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Colloid Phase is used for <str<strong>on</strong>g>th</str<strong>on</strong>g>e water transport in <str<strong>on</strong>g>th</str<strong>on</strong>g>e opposite directi<strong>on</strong> (ultrafiltrati<strong>on</strong>).<br />

Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model predicted <str<strong>on</strong>g>th</str<strong>on</strong>g>at glucose transport (mainly diffusive),<br />

916

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

occurs across bo<str<strong>on</strong>g>th</str<strong>on</strong>g> phases. In c<strong>on</strong>trast, <str<strong>on</strong>g>th</str<strong>on</strong>g>e perit<strong>on</strong>eal transport <str<strong>on</strong>g>of</str<strong>on</strong>g> albumin, which<br />

leaks by c<strong>on</strong>vecti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e perit<strong>on</strong>eal cavity, occurs mainly <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e Colloid<br />

Phase.<br />

917

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Developmental Biology; Saturday, July 2, 11:00<br />

Jörn Starruß<br />

Center for Infromati<strong>on</strong> Services and High Performance computing,<br />

TU-Dresden<br />

Fernando Peruani<br />

Max Planck Institute for Physics <str<strong>on</strong>g>of</str<strong>on</strong>g> Complex Systems, Dresden<br />

Andreas Deutsch<br />

Center for Infromati<strong>on</strong> Services and High Performance computing,<br />

TU-Dresden<br />

Collective migrati<strong>on</strong> in myxobacteria driven by adventurous<br />

motility and el<strong>on</strong>gated cell shape<br />

Myxococcus xan<str<strong>on</strong>g>th</str<strong>on</strong>g>us is a soil living bacterium <str<strong>on</strong>g>th</str<strong>on</strong>g>at is capable <str<strong>on</strong>g>of</str<strong>on</strong>g> forming multicellular<br />

fruiting bodies. Thus, M. xan<str<strong>on</strong>g>th</str<strong>on</strong>g>us may serve as an attractive model system<br />

for studying organizati<strong>on</strong>al principles <str<strong>on</strong>g>th</str<strong>on</strong>g>at allow individual cells to organize into<br />

and behave like a multicellular organism.<br />

I will present our latest experimental insights <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cluster formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> adventurous<br />

myxobacteria wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e main focus <strong>on</strong> statistical analysis [3]. Interestingly,<br />

initially unstructured col<strong>on</strong>ies restructure into collectively migrating clusters and<br />

finally c<strong>on</strong>verge into a characteristic distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cluster sizes.<br />

We envisage a simple mechanism for clustering based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristic<br />

rod cell shape and cell motility. We made use <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree modelling approaches,<br />

including a cellular Potts model, to elucidate <str<strong>on</strong>g>th</str<strong>on</strong>g>eir implicati<strong>on</strong>s <strong>on</strong> multicellular<br />

organizati<strong>on</strong> [1,2]. Recently we have shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at self-propelled rods interacting just<br />

by volume exclusi<strong>on</strong> exhibit a n<strong>on</strong>-equilibrium transiti<strong>on</strong> to clustering [1]. Using<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g>, statistical analysis and a mean field approach, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e models<br />

resemble <str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental cluster size distributi<strong>on</strong>s, including<br />

a clustering transiti<strong>on</strong> at a critical cell density.<br />

References.<br />

[1] Peruani, F., Deutsch, A., & Bär, M. (2006) N<strong>on</strong>-equilibrium clustering <str<strong>on</strong>g>of</str<strong>on</strong>g> self-propelled rods.<br />

Phys. Rev. E, 74(3), 030904.<br />

[2] Starruß, Jörn, Bley, Thomas, Søgaard-Andersen, Lotte and Deutsch, Andreas (2007) A new<br />

mechanism for collective migrati<strong>on</strong> in M. xan<str<strong>on</strong>g>th</str<strong>on</strong>g>us, in: J. Stat. Phys., 128, pp 269-286<br />

[3] Manuscript in preparati<strong>on</strong><br />

918

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Michał Startek<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw<br />

e-mail: michal.startek@duch.mimuw.edu.pl<br />

Anna Gambin<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw<br />

Dariusz Grzebelus<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Agriculture in Krakow<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e proliferati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> transpos<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

envir<strong>on</strong>mental stress<br />

Transposable elements (TEs) are DNA segments capable <str<strong>on</strong>g>of</str<strong>on</strong>g> changing <str<strong>on</strong>g>th</str<strong>on</strong>g>eir positi<strong>on</strong>s<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e genome. Until recently, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey have been c<strong>on</strong>sidered to be selfish,<br />

parasitic DNA. As <str<strong>on</strong>g>of</str<strong>on</strong>g> late, however, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey have been acknownledged to be a major<br />

driving force <str<strong>on</strong>g>of</str<strong>on</strong>g> genome evoluti<strong>on</strong>. The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> TE proliferati<strong>on</strong> in living<br />

organisms is not understood well. It is usually modelled wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e assumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

so-called ’transpositi<strong>on</strong>-selecti<strong>on</strong> equilibrium’ (TSE) a balance between <str<strong>on</strong>g>th</str<strong>on</strong>g>e TE’s<br />

selfish drive to multiply inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e host, increasing <str<strong>on</strong>g>th</str<strong>on</strong>g>eir numbers, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e deleterious<br />

influence <str<strong>on</strong>g>of</str<strong>on</strong>g> high TE copy number <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e host, causing selective pressure<br />

against hosts wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high TE counts. TSE models, however, fail to adequately explain<br />

certain behaviours observed in nature, such as explosive bursts <str<strong>on</strong>g>of</str<strong>on</strong>g> TE activity,<br />

dramatically varied TE counts between closely-related species, and increase <str<strong>on</strong>g>of</str<strong>on</strong>g> TE<br />

counts in domesticated variants <str<strong>on</strong>g>of</str<strong>on</strong>g> plants. I will present a n<strong>on</strong> TSE-based, stochastic<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> TE amplificati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at takes into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e stress exerted <strong>on</strong> host<br />

organisms by changing envir<strong>on</strong>ment. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>is model, I will show how <str<strong>on</strong>g>th</str<strong>on</strong>g>e various<br />

dynamics observed in nature (and not in TSE models) can be explained to be a<br />

result <str<strong>on</strong>g>of</str<strong>on</strong>g> interacti<strong>on</strong> between envir<strong>on</strong>mental pressure, <str<strong>on</strong>g>th</str<strong>on</strong>g>e organism’s phenotype,<br />

and TE-driven adaptati<strong>on</strong>.<br />

919

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Tracy Stepien<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Pittsburgh<br />

e-mail: tls52@pitt.edu<br />

David Swig<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Pittsburgh<br />

Cell and Tissue Biophysics; Thursday, June 30, 11:30<br />

Stretch-dependent proliferati<strong>on</strong> in a <strong>on</strong>e-dimensi<strong>on</strong>al elastic<br />

c<strong>on</strong>tinuum model <str<strong>on</strong>g>of</str<strong>on</strong>g> cell layer migrati<strong>on</strong><br />

Collective cell migrati<strong>on</strong> plays an important role in maintaining <str<strong>on</strong>g>th</str<strong>on</strong>g>e cohesi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cell layers and wound healing. Disrupti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell migrati<strong>on</strong> can cause<br />

disease such as necrotizing enterocolitis, an intestinal inflammatory disease <str<strong>on</strong>g>th</str<strong>on</strong>g>at is<br />

a major cause <str<strong>on</strong>g>of</str<strong>on</strong>g> dea<str<strong>on</strong>g>th</str<strong>on</strong>g> in premature infants. A recently developed ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> cell layer migrati<strong>on</strong> during experimental necrotizing enterocolitis based <strong>on</strong><br />

an assumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> elastic deformati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell layer leads to a generalized Stefan<br />

problem. The model is here extended to incorporate stretch-dependent proliferati<strong>on</strong>,<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting PDE system is solved analytically and numerically. The<br />

efficiency and accuracy <str<strong>on</strong>g>of</str<strong>on</strong>g> adaptive finite difference and MOL schemes for numerical<br />

soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem are compared. We find a large class <str<strong>on</strong>g>of</str<strong>on</strong>g> assumpti<strong>on</strong>s about<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> proliferati<strong>on</strong> <strong>on</strong> stretch <str<strong>on</strong>g>th</str<strong>on</strong>g>at lead to traveling wave soluti<strong>on</strong>s.<br />

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Stem cells and cancer; Wednesday, June 29, 14:30<br />

Thomas Stiehl<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Heidelberg<br />

e-mail: tstiehl@ix.urz.uni-heidelberg.de<br />

Models <str<strong>on</strong>g>of</str<strong>on</strong>g> stem cell differentiati<strong>on</strong> in hematopoiesis and<br />

leukemia<br />

Cancers and hematologic malignancies differ wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to interindividual symptomatology,<br />

course <str<strong>on</strong>g>of</str<strong>on</strong>g> disease, treatment susceptibility and prognosis. Over <str<strong>on</strong>g>th</str<strong>on</strong>g>e last<br />

decades <strong>on</strong>cological treatment strategies have been elaborated and optimized, never<str<strong>on</strong>g>th</str<strong>on</strong>g>eless<br />

important aspects remain unknown. A systematic ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical approach<br />

may help to better understand treatment failures and clinical heterogeneity <str<strong>on</strong>g>of</str<strong>on</strong>g> different<br />

cancers. Based <strong>on</strong> a model <str<strong>on</strong>g>of</str<strong>on</strong>g> cell differentiati<strong>on</strong> and signal feedback possible<br />

scenarios <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer development and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir impact <strong>on</strong> c<strong>on</strong>sequences for treatment<br />

c<strong>on</strong>cepts will be compared. A calibrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model to <str<strong>on</strong>g>th</str<strong>on</strong>g>e hematopoietic system<br />

will serve to transfer <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical results to <str<strong>on</strong>g>th</str<strong>on</strong>g>e understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> leukemias and<br />

myelodysplastic syndromes.<br />

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Bioengineering; Tuesday, June 28, 14:30<br />

Yv<strong>on</strong>ne Stokes<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Adelaide, SA<br />

5005, Australia.<br />

e-mail: Yv<strong>on</strong>ne.Stokes@adelaide.edu.au<br />

Alys Clark<br />

Auckland Bioengineering Institute, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Auckland, Auckland,<br />

New Zealand.<br />

e-mail: alys.clark@auckland.ac.nz<br />

Improving success rates <str<strong>on</strong>g>of</str<strong>on</strong>g> assisted reproducti<strong>on</strong> technology<br />

by ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling<br />

Assisted reproducti<strong>on</strong> technology (ART) involves support <str<strong>on</strong>g>of</str<strong>on</strong>g> oocytes (eggs) and<br />

embryos in <str<strong>on</strong>g>th</str<strong>on</strong>g>e laboratory for some period <str<strong>on</strong>g>of</str<strong>on</strong>g> time, and success rates are known to be<br />

highly dependent <strong>on</strong> laboratory c<strong>on</strong>diti<strong>on</strong>s. It is believed <str<strong>on</strong>g>th</str<strong>on</strong>g>at better reproducti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> normal in-vivo c<strong>on</strong>diti<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e laboratory will bring improved success rates. At<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e very least knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese c<strong>on</strong>diti<strong>on</strong>s provides valuable guidance for setting<br />

laboratory c<strong>on</strong>diti<strong>on</strong>s. Because measurement <str<strong>on</strong>g>of</str<strong>on</strong>g> in-vivo c<strong>on</strong>diti<strong>on</strong>s is difficult, if<br />

not impossible in some circumstances, ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling is a valuable tool<br />

for gaining understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> in-vivo envir<strong>on</strong>ments.<br />

We report <strong>on</strong> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling for gaining a better understanding <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e nutriti<strong>on</strong>al envir<strong>on</strong>ment <str<strong>on</strong>g>of</str<strong>on</strong>g> mammalian oocytes in antral follicles. In particular<br />

reacti<strong>on</strong>-diffusi<strong>on</strong> models have been used in c<strong>on</strong>juncti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experiments to investigate<br />

oxygen and glucose c<strong>on</strong>centrati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e bovine follicle. Unlike oxygen<br />

which diffuses readily <str<strong>on</strong>g>th</str<strong>on</strong>g>rough cell walls, glucose molecules pass <str<strong>on</strong>g>th</str<strong>on</strong>g>rough via facilitated<br />

transport mechanisms. The model for glucose transport must reflect <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

fact and is, c<strong>on</strong>sequently, more complicated <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>at for oxygen. Experimental<br />

validati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> our models is challenging and will be discussed.<br />

The ultimate aim <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is to improve <str<strong>on</strong>g>th</str<strong>on</strong>g>e developmental competence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> oocytes <str<strong>on</strong>g>th</str<strong>on</strong>g>at have been harvested at an immature stage and matured in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

laboratory, a procedure known as in-vitro maturati<strong>on</strong>. The ability to successfully<br />

use such oocytes in an IVF program reduces <str<strong>on</strong>g>th</str<strong>on</strong>g>e need for stimulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ovary<br />

to yield multiple mature oocytes for harvest and use in a traditi<strong>on</strong>al IVF program.<br />

This, in turn, makes ART available to women for whom ovarian stimulati<strong>on</strong> drugs,<br />

as used in traditi<strong>on</strong>al IVF me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods, are likely to cause life <str<strong>on</strong>g>th</str<strong>on</strong>g>reatening illnesses.<br />

Reducing <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese drugs also has <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential to reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e cost <str<strong>on</strong>g>of</str<strong>on</strong>g> IVF.<br />

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Mechanical Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Movement and Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cells and Tissues I;<br />

Wednesday, June 29, 14:30<br />

Magdalena A. Stolarska<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> St. Thomas, Saint Paul, MN, USA<br />

e-mail: mastolarska@st<str<strong>on</strong>g>th</str<strong>on</strong>g>omas.edu<br />

A mechanical model <str<strong>on</strong>g>of</str<strong>on</strong>g> cell motility and cell-subtrate<br />

interacti<strong>on</strong><br />

Mechanical interacti<strong>on</strong>s between a cell and <str<strong>on</strong>g>th</str<strong>on</strong>g>e substrate are vital for cell migrati<strong>on</strong><br />

and are involved in various cellular processes, such as wound healing, embry<strong>on</strong>ic<br />

development, a metastasis <str<strong>on</strong>g>of</str<strong>on</strong>g> cancerous tumors. In additi<strong>on</strong>, experiments<br />

have shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at inter-cellular and cell-substrate mechanical interacti<strong>on</strong>s affect signal<br />

transducti<strong>on</strong> pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. As a result, understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e nature<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> force generati<strong>on</strong> by single cells and mechanical interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a cell wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

substrate is extremely important.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e talk, I will present a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> cell motility and cellsubstrate<br />

interacti<strong>on</strong> where <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell and substrate are modeled as elastic twodimensi<strong>on</strong>al<br />

c<strong>on</strong>tinua. The spatially and temporally dynamics cell-substrate attachments<br />

are treated as discrete spring-dashpot systems. A finite element implementati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model <str<strong>on</strong>g>of</str<strong>on</strong>g> cell and substrate deformati<strong>on</strong> is coupled to <str<strong>on</strong>g>th</str<strong>on</strong>g>e equati<strong>on</strong>s<br />

governing <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e adhesi<strong>on</strong>s. The resulting simulati<strong>on</strong>s are used to better<br />

understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e oscillatory nature <str<strong>on</strong>g>of</str<strong>on</strong>g> amoeboid cell motility.<br />

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Epidemiology, Eco-Epidemiology and Evoluti<strong>on</strong>; Saturday, July 2, 11:00<br />

Nico Stollenwerk<br />

Centro de Matemática e Aplicações Fundamentais da Universidade de<br />

Lisboa,<br />

Avenida Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. Gama Pinto 2,1649-003 Lisboa, Portugal<br />

e-mail: nico@ptmat.fc.ul.pt<br />

Chaos and noise in populati<strong>on</strong> biology<br />

In several epidemiological and ecological case studies, <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>of</str<strong>on</strong>g>ten subtle interplay<br />

between typical n<strong>on</strong>-linear structures like co-existing attractors or dynamical saddles<br />

attracting in some state space directi<strong>on</strong>s and repelling in o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers and <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> noise in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese case will be investigated. Examples are dengue fever, seas<strong>on</strong>al<br />

influenza and retrospective measles studies as well as from classical predator-prey<br />

models. The findings in part come from empirical data analysis, here mainly from<br />

epidemiology due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e better data situati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>an in ecology, and also have impact<br />

<strong>on</strong> parameter estimati<strong>on</strong> in such epidemiological systems.<br />

References.<br />

[1] Drepper, F.R., Engbert, R., & Stollenwerk, N. (1994) N<strong>on</strong>linear time series analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> empirical<br />

populati<strong>on</strong> dynamics, Ecological Modelling 75/76, 171–181.<br />

[2] Aguiar, M., Kooi, B., & Stollenwerk, N. (2008) Epidemiology <str<strong>on</strong>g>of</str<strong>on</strong>g> dengue fever: A model wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

temporary cross-immunity and possible sec<strong>on</strong>dary infecti<strong>on</strong> shows bifurcati<strong>on</strong>s and chaotic<br />

behaviour in wide parameter regi<strong>on</strong>s, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Model. Nat. Phenom. 3, 48–70.<br />

[3] Aguiar, M., Stollenwerk, N., & Kooi, B. (2009) Torus bifurcati<strong>on</strong>s, isolas and chaotic attractors<br />

in a simple dengue fever model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> ADE and temporary cross immunity, Intern. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Computer Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics 86, 1867–77.<br />

[4] S. van Noort, N. Stollenwerk and L. St<strong>on</strong>e, “Analytic likelihood functi<strong>on</strong> for data analysis in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

starting phase <str<strong>on</strong>g>of</str<strong>on</strong>g> an influenza outbreak”, Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g> 9<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Computati<strong>on</strong>al and<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in Science and Engineering, CMMSE 2009, ISBN 978-84-612-9727-6,<br />

edited by Jesus Vigo Aguiar et al., Salamanca, 2009, pp. 1072–1080.<br />

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Modelling dengue fever epidemiology; Saturday, July 2, 08:30<br />

Nico Stollenwerk<br />

CMAF, Universidade de Lisboa, Portugal<br />

e-mail: nico@ptmat.fc.ul.pt<br />

Maira Aguiar<br />

Sebastien Ballesteros<br />

Bob W. Kooi<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>e origin <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e irregularity <str<strong>on</strong>g>of</str<strong>on</strong>g> DHF epidemics<br />

By using an estimated parameter set for <str<strong>on</strong>g>th</str<strong>on</strong>g>e minimalistic multi-strain dengue model<br />

we analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model investigating <str<strong>on</strong>g>th</str<strong>on</strong>g>e interplay between<br />

stochasticity, seas<strong>on</strong>ality and import.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Beatriz Stransky<br />

Centre <str<strong>on</strong>g>of</str<strong>on</strong>g> Engineering, Modelling and Applied Social Sciences - Federal<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> ABC, Brazil<br />

e-mail: beatriz.stransky@ufabc.edu.br<br />

Lucas Amaral da Silva<br />

Federal University od ABC<br />

Luana Regina Aff<strong>on</strong>so<br />

Federal University od ABC<br />

Luiz Rozante<br />

Centre <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Cogniti<strong>on</strong> and Computati<strong>on</strong> - Federal University<br />

od ABC<br />

Fabiana Santana<br />

Centre <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Cogniti<strong>on</strong> and Computati<strong>on</strong> - Federal University<br />

od ABC<br />

Modelling populati<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> human epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cell<br />

lines: <str<strong>on</strong>g>th</str<strong>on</strong>g>e differential expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> c-erbB2 <strong>on</strong>cogene and<br />

breast tumour development<br />

The comprehensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanisms underlying cancer development depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> processes underlying tissue formati<strong>on</strong>. In physiological c<strong>on</strong>diti<strong>on</strong>,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e tissues are maintained in a dynamic equilibrium, called homeostasis, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cell number is kept essentially c<strong>on</strong>stant and is regulated based <strong>on</strong> reproducti<strong>on</strong>,<br />

dea<str<strong>on</strong>g>th</str<strong>on</strong>g> and half-life rates <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular populati<strong>on</strong>. Molecular alterati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at disturb<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e homeostasis can be potentially dangerous. Mutati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at would permit selective<br />

advantages, like a faster cell divisi<strong>on</strong>, could lead to <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a cl<strong>on</strong>e<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tinuous grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. Repeated cycles <str<strong>on</strong>g>of</str<strong>on</strong>g> mutati<strong>on</strong>, competiti<strong>on</strong> and natural selecti<strong>on</strong><br />

form <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer development. The c-erbB2 <strong>on</strong>cogene is a membrane<br />

receptor wi<str<strong>on</strong>g>th</str<strong>on</strong>g> tyrosine kinase activity <str<strong>on</strong>g>th</str<strong>on</strong>g>at bel<strong>on</strong>gs to <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidermal grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factor<br />

receptor family. C-erbB2 over-expressi<strong>on</strong> is observed in 25-30% <str<strong>on</strong>g>of</str<strong>on</strong>g> breast tumours<br />

and is an adverse prognostic factor. To study <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> c-erbB2,<br />

Harris at al. (1999) developed a model <str<strong>on</strong>g>of</str<strong>on</strong>g> c-erbB2 over-expressi<strong>on</strong> in c<strong>on</strong>diti<strong>on</strong>ally<br />

immortalized mammary luminal epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells. Two new lines, HB4a-C3.6<br />

and HB4a-C5.2, expressing different levels <str<strong>on</strong>g>of</str<strong>on</strong>g> c-erbB2, were derived from <str<strong>on</strong>g>th</str<strong>on</strong>g>e immortalized<br />

cell line HB4a. This work presents a computati<strong>on</strong>al model designed to<br />

mimic <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental data obtained from <str<strong>on</strong>g>th</str<strong>on</strong>g>e in vitro culture <str<strong>on</strong>g>of</str<strong>on</strong>g> HB4a-C3.6 and<br />

HB4a-C5.2 lineages. A discrete agent-based model, c<strong>on</strong>trolled by a dynamic system<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at represents c-erbB2 expressi<strong>on</strong>, simulates <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell culture dynamics. In order<br />

to validate <str<strong>on</strong>g>th</str<strong>on</strong>g>e results, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey were compared to experimental data, regarding cell<br />

cycle and populati<strong>on</strong> dynamics. The model will be applied to evaluate differential<br />

expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> 4 transcripts positively regulated by c-erbB2 tumours, evaluated by<br />

Real Time PCR in HB4a and HB4a-C5.2 cell lines. Their functi<strong>on</strong>al characterizati<strong>on</strong><br />

will allow a better understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular mechanisms behind c-erbB2<br />

over-expressi<strong>on</strong> and breast tumour development.<br />

926<br />

References.

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[1] R.A. Harris, T.J. Eichholtz, I.D. Hiles, M.J. Page, M.J. Ohare. New model <str<strong>on</strong>g>of</str<strong>on</strong>g> erbB-2 overexpressi<strong>on</strong><br />

in human mammary luminal epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells. Int. J. Cancer: 80, 477484 (1999).<br />

927

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling viral hepatitis dynamics in-vivo and in-vitro in <str<strong>on</strong>g>th</str<strong>on</strong>g>e era <str<strong>on</strong>g>of</str<strong>on</strong>g> direct<br />

anti-viral agents I; Tuesday, June 28, 17:00<br />

Lior Strauss<br />

Bar-Ilan University, Ramat-Gan, Israel<br />

e-mail: liorstr1@gmail.com<br />

Avidan U. Neumann<br />

Bar-Ilan University, Ramat-Gan, Israel<br />

Distributed Intra-Cellular Model <str<strong>on</strong>g>of</str<strong>on</strong>g> Hepatitis C Viral<br />

Replicati<strong>on</strong> and Resistance Evoluti<strong>on</strong><br />

The new generati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> direct acting anti-viral (DAA) drugs for HCV led to <str<strong>on</strong>g>th</str<strong>on</strong>g>e need<br />

for ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>th</str<strong>on</strong>g>at take in c<strong>on</strong>siderati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intra-cellular drug effects<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in clinical virology data. We have recently introduced <str<strong>on</strong>g>th</str<strong>on</strong>g>e ICCI model <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

integrated <str<strong>on</strong>g>th</str<strong>on</strong>g>e intra-cellular level <str<strong>on</strong>g>of</str<strong>on</strong>g> replicati<strong>on</strong> and resistance evoluti<strong>on</strong> processes<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular infecti<strong>on</strong> level (Guedj and Neumann, 2010). However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e ICCI<br />

model used a mean-field approach to treat all infected cell as <str<strong>on</strong>g>th</str<strong>on</strong>g>e same dynamics,<br />

which we know is not accurate. Here, we present a new model (DIC) <str<strong>on</strong>g>th</str<strong>on</strong>g>at describes<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e intra-cellular level dynamics integrated into <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell infecti<strong>on</strong> level whle taking<br />

into c<strong>on</strong>siderati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> infected cells as functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

replicati<strong>on</strong> complexes in each cell. The DIC model shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at main novel findings<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ICCI model hold even when <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean-field assumpti<strong>on</strong> is released. Most<br />

importantly, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model allows for 2 modes <str<strong>on</strong>g>of</str<strong>on</strong>g> viral decline: ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e delta model,<br />

where l<strong>on</strong>g term viral decline slope is governed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e loss <str<strong>on</strong>g>of</str<strong>on</strong>g> infected cells, or <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

gamma mode, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral decline is more rapid and related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e intra-cellular<br />

loss <str<strong>on</strong>g>of</str<strong>on</strong>g> replicati<strong>on</strong> complexes. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, <str<strong>on</strong>g>th</str<strong>on</strong>g>e DIC model shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at while <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

delta mode <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different number <str<strong>on</strong>g>of</str<strong>on</strong>g> replicati<strong>on</strong> complexes<br />

is held stable, <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e gamma mode <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells is shifting towards<br />

intra-cellular clearance. We have also established <str<strong>on</strong>g>th</str<strong>on</strong>g>e properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e infected cell<br />

distributi<strong>on</strong> at steady state. The model was able to show a good fit for a wide<br />

range <str<strong>on</strong>g>of</str<strong>on</strong>g> results observed in real patients treated ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> IFN based <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy<br />

or DAA combinati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy. In a sec<strong>on</strong>d part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e work we have established<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e various resistance evoluti<strong>on</strong> patterns observed wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ICCI model hold also<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out <str<strong>on</strong>g>th</str<strong>on</strong>g>e mean-field assumpti<strong>on</strong>. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we show how <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different number and identity, wild-type versus resistant, <str<strong>on</strong>g>of</str<strong>on</strong>g> replicati<strong>on</strong><br />

complexes follows specific patterns during evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance. These results<br />

are important for our understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e DAA <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy effect and allowing us to<br />

optimize treatment and prevent resistance evoluti<strong>on</strong>.<br />

928

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective phenomena in biological systems; Saturday, July 2,<br />

08:30<br />

Zbigniew Struzik<br />

The University <str<strong>on</strong>g>of</str<strong>on</strong>g> Tokyo<br />

e-mail: zbigniew.struzik@p.u-tokyo.ac.jp<br />

Measures <str<strong>on</strong>g>of</str<strong>on</strong>g> heart rate complexity<br />

For nearly <str<strong>on</strong>g>th</str<strong>on</strong>g>ree decades, human heart rate variability (HRV) has been c<strong>on</strong>sistently<br />

shown to display intriguing and puzzling characteristics, to a large degree defying<br />

satisfactory explanati<strong>on</strong> and posing challenges for bo<str<strong>on</strong>g>th</str<strong>on</strong>g> modelling and clinical<br />

treatment. Recent findings c<strong>on</strong>firm <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e HRV regulatory system represents a<br />

prominent example <str<strong>on</strong>g>of</str<strong>on</strong>g> a biological complex system and remains a benchmark <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

biocomplexity.<br />

C<strong>on</strong>tinued <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical and experimental effort is required to achieve a <str<strong>on</strong>g>th</str<strong>on</strong>g>orough<br />

understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is systems complexity. From <str<strong>on</strong>g>th</str<strong>on</strong>g>e point <str<strong>on</strong>g>of</str<strong>on</strong>g> view <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>trol<br />

engineering, such an understanding should be capable <str<strong>on</strong>g>of</str<strong>on</strong>g> explaining regulatory<br />

mechanisms. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a physics approach, it should reveal striking properties <str<strong>on</strong>g>of</str<strong>on</strong>g> universality.<br />

From a clinical perspective, it should dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>e utility <str<strong>on</strong>g>of</str<strong>on</strong>g> prognostic<br />

and predictive algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms.<br />

In my talk, I will provide a review <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e measures <str<strong>on</strong>g>of</str<strong>on</strong>g> complexity utilised in<br />

various aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> HRV signal processing, focusing <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ose providing a unifying<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>read for <str<strong>on</strong>g>th</str<strong>on</strong>g>e challenges above. Particular stress will be laid <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most up-to-date<br />

multi-time and multiscale evaluati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-Gaussian properties <str<strong>on</strong>g>of</str<strong>on</strong>g> HRV.<br />

929

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Mechanics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> and cortical actin at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular level;<br />

Saturday, July 2, 08:30<br />

Wanda Strychalski<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> California, Davis<br />

e-mail: wanda@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ucdavis.edu<br />

Robert D. Guy<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> California, Davis<br />

Computati<strong>on</strong>al explorati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular blebbing<br />

Blebbing occurs when <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> detaches from <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell membrane, resulting<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e pressure-driven flow <str<strong>on</strong>g>of</str<strong>on</strong>g> cytosol towards <str<strong>on</strong>g>th</str<strong>on</strong>g>e area <str<strong>on</strong>g>of</str<strong>on</strong>g> detachment and <str<strong>on</strong>g>th</str<strong>on</strong>g>e local<br />

expansi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell membrane. Recent interest has focused <strong>on</strong> cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at use<br />

blebbing for migrating <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>ree dimensi<strong>on</strong>al fibrous matrices. In particular,<br />

metastatic cancer cells have been shown to use blebs for motility. A dynamic<br />

computati<strong>on</strong>al model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell is presented <str<strong>on</strong>g>th</str<strong>on</strong>g>at includes mechanics <str<strong>on</strong>g>of</str<strong>on</strong>g> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

interacti<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>e intracellular fluid, <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell membrane, <str<strong>on</strong>g>th</str<strong>on</strong>g>e actin cortex,<br />

and internal cytoskelet<strong>on</strong>. The Immersed Boundary Me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is modified to account<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative moti<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e fluid. The computati<strong>on</strong>al<br />

model is used to explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative roles in bleb formati<strong>on</strong> time <str<strong>on</strong>g>of</str<strong>on</strong>g> cytoplasmic<br />

viscosity and drag between <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytosol. A regime <str<strong>on</strong>g>of</str<strong>on</strong>g> values for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e drag coefficient and cytoplasmic viscosity values <str<strong>on</strong>g>th</str<strong>on</strong>g>at match bleb formati<strong>on</strong> time<br />

scales is presented. The model results are used to predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e Darcy permeability<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e volume fracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cortex. Applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model to blebbing-based<br />

cell motility are discussed.<br />

930

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Student Sebastian<br />

Biosystems Group, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Automatic C<strong>on</strong>trol, Silesian University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, 44-100 Gliwice, Poland<br />

e-mail: sebastian.student@polsl.pl<br />

Cichońska Anna<br />

Student <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Faculty Of Automatic C<strong>on</strong>trol, Electr<strong>on</strong>ics And Computer<br />

Science, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Gliwice, Poland<br />

e-mail: anna.cich<strong>on</strong>ska@gmail.com<br />

Sk<strong>on</strong>ieczna Magdalena<br />

Biosystems Group, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Automatic C<strong>on</strong>trol, Silesian University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, 44-100 Gliwice, Poland<br />

e-mail: magdalena.sk<strong>on</strong>ieczna@polsl.pl<br />

Joanna Rzeszowska-Wolny<br />

Biosystems Group, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Automatic C<strong>on</strong>trol, Silesian University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, 44-100 Gliwice, Poland<br />

e-mail: jrzeszowskawolny@yahoo.com<br />

Microarray gene expressi<strong>on</strong> studies and real time RT-PCR<br />

validati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e DNA damage and repair pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way<br />

Different low-level preprocessing me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for Affymetrix microarrays data were<br />

evaluated based <strong>on</strong> c<strong>on</strong>cordance wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a real time RT-PCR me<str<strong>on</strong>g>th</str<strong>on</strong>g>od. The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> lowlevel<br />

analysis is to measure gene expressi<strong>on</strong> levels, and to allow comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

results from more <str<strong>on</strong>g>th</str<strong>on</strong>g>an <strong>on</strong>e array. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper <str<strong>on</strong>g>th</str<strong>on</strong>g>ree <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most popular preprocessing<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods: MAS5, RMA and GCRMA, were used. Expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genes from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e DNA damage and repair pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way were analyzed <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e MAS5 - single<br />

array analysis algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m, <str<strong>on</strong>g>th</str<strong>on</strong>g>e GCRMA - probe-specific background correcti<strong>on</strong> and<br />

multiple array analysis, or RMA - mismatch probes ignored and multiple array<br />

analysis.<br />

The data were derived from experiments c<strong>on</strong>ducted wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Affymetrix platform<br />

U133A. For biological testing <str<strong>on</strong>g>th</str<strong>on</strong>g>e colorectal carcinoma HCT 116 cell line was chosen.<br />

The cells were irradiated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> 4 Gy <str<strong>on</strong>g>of</str<strong>on</strong>g> i<strong>on</strong>izing radiati<strong>on</strong>, and n<strong>on</strong>-irradiated<br />

cells used as a c<strong>on</strong>trol group. After microarray data analysis, real time RT-PCR<br />

was c<strong>on</strong>ducted. As an indicator for c<strong>on</strong>cordance between microarray experiments<br />

and real time RT-PCR, <str<strong>on</strong>g>th</str<strong>on</strong>g>e percentage <str<strong>on</strong>g>of</str<strong>on</strong>g> genes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same directi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> changes<br />

in irradiated and n<strong>on</strong>-irradiated cells was used. The computati<strong>on</strong>al analysis was<br />

finished wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e PLS-based (partial least squares-based) gene selecti<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od,<br />

which enables assignment <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological meanings for <str<strong>on</strong>g>th</str<strong>on</strong>g>e genes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e highest<br />

weights in <str<strong>on</strong>g>th</str<strong>on</strong>g>e PLS model. The PLS me<str<strong>on</strong>g>th</str<strong>on</strong>g>od, in c<strong>on</strong>trast to <str<strong>on</strong>g>th</str<strong>on</strong>g>e PCA (principal<br />

comp<strong>on</strong>ent analysis) criteri<strong>on</strong> based <strong>on</strong> maximizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e variance <str<strong>on</strong>g>of</str<strong>on</strong>g> a linear<br />

combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genes, extracts comp<strong>on</strong>ents by maximizing <str<strong>on</strong>g>th</str<strong>on</strong>g>e sample covariance<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e class variable and linear combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> genes. The informati<strong>on</strong> for<br />

genes included in comp<strong>on</strong>ents described by PLS can be directly related to <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological<br />

meaning <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is analysis.<br />

The results show <str<strong>on</strong>g>th</str<strong>on</strong>g>at data preprocessed wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e RMA me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for microarray data<br />

has <str<strong>on</strong>g>th</str<strong>on</strong>g>e best c<strong>on</strong>cordance wi<str<strong>on</strong>g>th</str<strong>on</strong>g> real time RT-PCR assays. The biological validati<strong>on</strong><br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e best 10 genes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e highest weights in <str<strong>on</strong>g>th</str<strong>on</strong>g>e PLS model proved its applicability<br />

in systems biology. Some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese genes (MSH2, RAD9A, XP) are sensors<br />

for nucleic acid damage, and o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers (NTHL1, TDP1 DCLRE1A, ERCC2, POLI,<br />

MPG, TREX2) are engaged in mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> DNA repair. Obviously, <str<strong>on</strong>g>th</str<strong>on</strong>g>e best<br />

score was obtained for genes resp<strong>on</strong>sible for signaling cellular stress after i<strong>on</strong>izing<br />

radiati<strong>on</strong>.<br />

This work was supported by grants No. N N 518497639 from <str<strong>on</strong>g>th</str<strong>on</strong>g>e Polish Ministry<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Educati<strong>on</strong> and Science and BK 221/Rau1/20 from <str<strong>on</strong>g>th</str<strong>on</strong>g>e Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Technology<br />

References.<br />

[1] Affymetrix, New Statistical Algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms for M<strong>on</strong>itoring Gene Expressi<strong>on</strong> <strong>on</strong> GeneChip Probe<br />

Arrays2001.<br />

[2] R. Irizarry et al, Explorati<strong>on</strong>, normalizati<strong>on</strong>, and summaries <str<strong>on</strong>g>of</str<strong>on</strong>g> high density olig<strong>on</strong>ucleotide<br />

array probe level data Biostatistics 4 249-264.<br />

[3] Z. Wu et al, A Model Based Background Adjustment for Olig<strong>on</strong>ucleotide Expressi<strong>on</strong> Arrays<br />

Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e American Statistical Associati<strong>on</strong> 99 909-917.<br />

[4] A. Boulesteix, PLS dimensi<strong>on</strong> reducti<strong>on</strong> for classificati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> microarray data. Statistical<br />

Applicati<strong>on</strong>s in Genetics and Molecular Biology 3 Article33.<br />

932

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Marc Sturrock<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee<br />

e-mail: msturrock@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.dundee.ac.uk<br />

Cancer; Tuesday, June 28, 11:00<br />

Spatio-temporal modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Hes1 and p53 pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways<br />

The correct localisati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong> factors is vitally important for <str<strong>on</strong>g>th</str<strong>on</strong>g>e proper<br />

functi<strong>on</strong>ing <str<strong>on</strong>g>of</str<strong>on</strong>g> many intracellular signalling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways. Experimental data has revealed<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at many pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways exhibit oscillati<strong>on</strong>s, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> temporally and spatially, in<br />

resp<strong>on</strong>se to certain external stimuli. Negative feedback loops are important comp<strong>on</strong>ents<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese oscillati<strong>on</strong>s, providing fine regulati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e factors involved. In<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> two such pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways–Hes1 and p53–are presented.<br />

Building <strong>on</strong> previous ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling approaches, we derive systems <str<strong>on</strong>g>of</str<strong>on</strong>g> partial<br />

differential equati<strong>on</strong>s to capture <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> in space and time <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e variables<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Hes1 and p53 systems. Through computati<strong>on</strong>al simulati<strong>on</strong>s we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at our<br />

reacti<strong>on</strong>-diffusi<strong>on</strong> models are able to produce sustained oscillati<strong>on</strong>s bo<str<strong>on</strong>g>th</str<strong>on</strong>g> spatially<br />

and temporally, accurately reflecting experimental evidence and advancing previous<br />

models. The simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> our models also allow us to calculate a diffusi<strong>on</strong> coefficient<br />

range for <str<strong>on</strong>g>th</str<strong>on</strong>g>e variables in each mRNA and protein system, as well as ranges<br />

for o<str<strong>on</strong>g>th</str<strong>on</strong>g>er key parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e models, where sustained oscillati<strong>on</strong>s are observed.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, by exploiting <str<strong>on</strong>g>th</str<strong>on</strong>g>e explicitly spatial nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e partial differential<br />

equati<strong>on</strong>s, we are also able to manipulate ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial locati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e ribosomes, <str<strong>on</strong>g>th</str<strong>on</strong>g>us c<strong>on</strong>trolling where <str<strong>on</strong>g>th</str<strong>on</strong>g>e proteins are syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esized wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoplasm.<br />

The results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese simulati<strong>on</strong>s predict an optimal distance outside <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

nucleus where protein syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis should take place in order to generate sustained<br />

oscillati<strong>on</strong>s.<br />

Using partial differential equati<strong>on</strong> models, new informati<strong>on</strong> can be gained about <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

precise spatio-temporal dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> mRNA and proteins. The ability to determine<br />

spatial localisati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> proteins wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell is likely to yield fresh insight into a<br />

range <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular diseases such as diabetes and cancer.<br />

References.<br />

[1] M. Sturrock, A. J. Terry, D. P. Xirodimas, A. M. Thomps<strong>on</strong>, M. A. J. Chaplain, Spatiotemporal<br />

modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Hes1 and p53-Mdm2 intracellular signalling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways Journal <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Theoretical Biology 273 15–31.<br />

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Lisa Sundqvist<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Marine Ecology<br />

e-mail: lisa.sundqvist@gu.se<br />

Measures <str<strong>on</strong>g>of</str<strong>on</strong>g> generati<strong>on</strong> time problems and clarificati<strong>on</strong>s<br />

Generati<strong>on</strong> time is a frequently used term in biology it is for example used in<br />

estimates <str<strong>on</strong>g>of</str<strong>on</strong>g> rate <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong>. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er it is an important parameter for evaluati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> extincti<strong>on</strong> risks <str<strong>on</strong>g>of</str<strong>on</strong>g> species and populati<strong>on</strong>s in c<strong>on</strong>servati<strong>on</strong> biology. Generati<strong>on</strong><br />

time is used by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Internati<strong>on</strong>al Uni<strong>on</strong> for C<strong>on</strong>servati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Nature (IUCN) to<br />

scale time based-measures <str<strong>on</strong>g>of</str<strong>on</strong>g> extincti<strong>on</strong> risk in species where <str<strong>on</strong>g>th</str<strong>on</strong>g>ree generati<strong>on</strong>s<br />

is l<strong>on</strong>ger <str<strong>on</strong>g>th</str<strong>on</strong>g>en 10 years. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e term is frequently used <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is no clear<br />

definiti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ree main ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods to estimate generati<strong>on</strong> time<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong>s are incoherent. Which leads to c<strong>on</strong>fusi<strong>on</strong> when generati<strong>on</strong> time is<br />

to be calculated for <str<strong>on</strong>g>th</str<strong>on</strong>g>reatened species. A number <str<strong>on</strong>g>of</str<strong>on</strong>g> papers have pointed out <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ambiguity c<strong>on</strong>nected to generati<strong>on</strong> time. However an overview <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e definiti<strong>on</strong>s<br />

and usage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e term is lacking in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature. This work aims to bring some<br />

clarity into <str<strong>on</strong>g>th</str<strong>on</strong>g>e measures <str<strong>on</strong>g>of</str<strong>on</strong>g> generati<strong>on</strong> time especially in <str<strong>on</strong>g>th</str<strong>on</strong>g>e area <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>servati<strong>on</strong>.<br />

It is <str<strong>on</strong>g>of</str<strong>on</strong>g> great c<strong>on</strong>cern <str<strong>on</strong>g>th</str<strong>on</strong>g>at already <str<strong>on</strong>g>th</str<strong>on</strong>g>reatened species are not disfavored according<br />

to inadequate calculati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e system meant to save <str<strong>on</strong>g>th</str<strong>on</strong>g>em.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Moving Organisms: From Individuals to Populati<strong>on</strong>s; Wednesday, June 29, 17:00<br />

Christina Surulescu<br />

ICAM, WWU Münster, Einsteinstr. 62, 48149 Münster, Germany<br />

e-mail: christina.surulescu@uni-muenster.de<br />

Nico Surulescu<br />

IMS, WWU Münster, Einsteinstr. 62, 48149 Münster, Germany<br />

e-mail: nicolae.surulescu@uni-muenster.de<br />

Cell dispersal: some n<strong>on</strong>parametric and multiscale aproaches<br />

We provide a short overview <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e current approaches to modeling cell moti<strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>rough various media, <str<strong>on</strong>g>th</str<strong>on</strong>g>ereby focussing <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model scales, ranging from <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic,<br />

intracellular level <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e mesoscale <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint acti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong><br />

c<strong>on</strong>stituents toward <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire populati<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic level.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>text we propose and analyze a multiscale model for bacterial motility<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e framework <str<strong>on</strong>g>of</str<strong>on</strong>g> partial differential equati<strong>on</strong>s. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er we present an alternative<br />

approach which relies <strong>on</strong> stochastic processes accounting for <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying moti<strong>on</strong><br />

phenotype and uses a n<strong>on</strong>parametric statistical technique in order to directly assess<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscpic cell populati<strong>on</strong> density from data (if available) or numerical<br />

simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell trajectories. This n<strong>on</strong>parametric approach allows to handle<br />

detailed multiscale models in a complexity which in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> PDEs is still<br />

prohibitive for <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerics.<br />

We will also provide an outlook <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

interesting biomedical problems.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Tuesday, June 28, 14:30<br />

Maciej Swat<br />

Biocomplexity Institute, Indiana University, Bloomingt<strong>on</strong> ,IN, USA<br />

e-mail: mswat@indiana.edu<br />

Abbas Shirinifard<br />

Biocomplexity Institute, Indiana University, Bloomingt<strong>on</strong> ,IN, USA<br />

Multi-Cell Tumor Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> Modeling Using CompuCell3D<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and computer simulati<strong>on</strong> have become crucial to biological<br />

fields from genomics to ecology. However, multi-cell, tissue-level simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

development and disease have lagged behind o<str<strong>on</strong>g>th</str<strong>on</strong>g>er areas because <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically<br />

more complex and lacked easy-to-use s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware tools <str<strong>on</strong>g>th</str<strong>on</strong>g>at allow building<br />

and running in-silico experiments wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out requiring in-dep<str<strong>on</strong>g>th</str<strong>on</strong>g> knowledge <str<strong>on</strong>g>of</str<strong>on</strong>g> programming.<br />

Recent advances in development <str<strong>on</strong>g>of</str<strong>on</strong>g> multi-scale, multi-cell simulati<strong>on</strong><br />

envir<strong>on</strong>ments allow broad range <str<strong>on</strong>g>of</str<strong>on</strong>g> researchers to develop relatively easily sophisticated<br />

simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> development or disease. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I will present Glazier<br />

Graner Hogeweg (GGH) model, its extensi<strong>on</strong>s to support subcellular Reacti<strong>on</strong>-<br />

Kinetics(RK) models and CompuCell3D a simulati<strong>on</strong> envir<strong>on</strong>ment supporting GGH<br />

and RK modeling. To dem<strong>on</strong>strate CompuCell3D [1] capabilities I will present a<br />

3D multi-cell simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a generic simplificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> [2]<br />

which can be easily extended and adapted to describe more specific vascular tumor<br />

types and host tissues. Initially, tumor cells proliferate as <str<strong>on</strong>g>th</str<strong>on</strong>g>ey take up <str<strong>on</strong>g>th</str<strong>on</strong>g>e oxygen<br />

which <str<strong>on</strong>g>th</str<strong>on</strong>g>e pre-existing vasculature supplies. The tumor grows exp<strong>on</strong>entially. When<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e oxygen level drops below a <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold, <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor cells become hypoxic and start<br />

secreting pro-angiogenic factors. At <str<strong>on</strong>g>th</str<strong>on</strong>g>is stage, <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor reaches a maximum diameter<br />

characteristic <str<strong>on</strong>g>of</str<strong>on</strong>g> an avascular tumor spheroid. The endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

pre-existing vasculature resp<strong>on</strong>d to <str<strong>on</strong>g>th</str<strong>on</strong>g>e pro-angiogenic factors bo<str<strong>on</strong>g>th</str<strong>on</strong>g> by chemotaxing<br />

towards higher c<strong>on</strong>centrati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> pro-angiogenic factors and by forming new blood<br />

vessels via angiogenesis. The tumor-induced vasculature increases <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting vascularized solid tumor compared to an avascular tumor, allowing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor to grow bey<strong>on</strong>d <str<strong>on</strong>g>th</str<strong>on</strong>g>e spheroid in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese linear-grow<str<strong>on</strong>g>th</str<strong>on</strong>g> phases. In c<strong>on</strong>trast<br />

to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er simulati<strong>on</strong>s in which avascular tumors remain spherical, our simulated<br />

avascular tumors form cylinders following <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood vessels, leading to a different<br />

distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> hypoxic cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor. Our simulati<strong>on</strong>s cover time periods<br />

which are l<strong>on</strong>g enough to produce a range <str<strong>on</strong>g>of</str<strong>on</strong>g> biologically reas<strong>on</strong>able complex morphologies,<br />

allowing us to study how tumor-induced angiogenesis affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

rate, size and. morphology <str<strong>on</strong>g>of</str<strong>on</strong>g> simulated tumors. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>clusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e talk I will<br />

show a live demo (5-10 minutes) <str<strong>on</strong>g>of</str<strong>on</strong>g> CompuCell3D and dem<strong>on</strong>strate how, starting<br />

from relatively simple toy-models <str<strong>on</strong>g>of</str<strong>on</strong>g> cell-sorting, c<strong>on</strong>tact-inhibited chemotaxis and<br />

nutrient-dependent cell grow<str<strong>on</strong>g>th</str<strong>on</strong>g>/cell divisi<strong>on</strong>, we can build a fairly realistic simulati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> vascularized tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. Such simulati<strong>on</strong> can be fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er improved to<br />

produce simulati<strong>on</strong> equivalent to <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>e published in [2].<br />

References.<br />

[1] Multi-Cell Simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> Development and Disease Using <str<strong>on</strong>g>th</str<strong>on</strong>g>e CompuCell3D Simulati<strong>on</strong> Envir<strong>on</strong>ment,<br />

Maciej Swat, Susan D. Hester, Randy W. Heiland, Benjamin L. Zaitlen, James<br />

A. Glazier. In Ivan V. Maly ed., Systems Biology Series: Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in Molecular Biology, pp.<br />

138-190<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[2] 3D Multi-Cell Simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Tumor Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and Angiogenesis, Abbas Shirinifard, John S.<br />

Gens, Benjamin L. Zaitlen, Nikodem J. Poplawski, Maciej Swat, James A. Glazier, PLoS<br />

ONE 4: e7190, doi:10.1371/journal.p<strong>on</strong>e.0007190 (2009).<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Computati<strong>on</strong>al toxicology and pharmacology - in silico drug activity and<br />

safety assessment; Saturday, July 2, 11:00<br />

Maciej Swat<br />

Medical Biochemistry Academic Medical Center University <str<strong>on</strong>g>of</str<strong>on</strong>g> Amsterdam<br />

e-mail: m.j.swat@amc.uva.nl<br />

Systems Biology driven Pharmacokinetics and<br />

Pharmacodynamics<br />

Pharmacokinetics is probably <str<strong>on</strong>g>th</str<strong>on</strong>g>e most neglected field in <str<strong>on</strong>g>th</str<strong>on</strong>g>e medically relevant<br />

biosimulati<strong>on</strong>s. It is a science about <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug fate in a living organism and embraces<br />

in broader sense four main domains: absorpti<strong>on</strong>, distributi<strong>on</strong>, metabolism,<br />

and excreti<strong>on</strong>, in short ADME. It is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten combined and c<strong>on</strong>sidered toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

pharmacodynamics, a science branch dealing wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>th</str<strong>on</strong>g>e drug has <strong>on</strong><br />

its target and eventually <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole body and disease progressi<strong>on</strong>. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e same<br />

time, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanism based but in most cases drugfree models and simulati<strong>on</strong>s<br />

are highly appreciated and developed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Systems Biology community. There<br />

is no doubt <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e full understanding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying phenomena like physiological<br />

regulati<strong>on</strong> and c<strong>on</strong>trol, phenotypes, mutati<strong>on</strong>s and in general diseases is<br />

essential for <str<strong>on</strong>g>th</str<strong>on</strong>g>e progress in medicine. However, much has been achieved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

last decades wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out sophisticated algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms and supercomputers. Semimechanistic<br />

models or even simple phenomenological formulas and models are in use since<br />

beginning <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e 20<str<strong>on</strong>g>th</str<strong>on</strong>g> century providing useful insights in e.g. physiology and pharmacokinetics<br />

related issues. We are c<strong>on</strong>vinced, <str<strong>on</strong>g>th</str<strong>on</strong>g>at parallel applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

two seemingly unc<strong>on</strong>nected approaches can eventually c<strong>on</strong>verge into more effective<br />

treatments me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods now or in near future. We are making an attempt to introduce<br />

a new platform combining standard phenomenological models used in <str<strong>on</strong>g>th</str<strong>on</strong>g>e PK/PD<br />

field wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mechanistically based Systems Biology models and approaches. There<br />

are many examples <str<strong>on</strong>g>of</str<strong>on</strong>g> wellknown 1, 2 or more compartmental models providing<br />

valuable initial guesses and insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolism, and ADME processes<br />

in general, <str<strong>on</strong>g>of</str<strong>on</strong>g> a particular drug. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>eir use is limited due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>mechanistic<br />

nature <str<strong>on</strong>g>of</str<strong>on</strong>g> such models. We c<strong>on</strong>sider Systems Biology driven models<br />

as complementary to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir phenomenological counterparts. The ultimate goal <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

wholebody full mechanistic model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e combined PKPDADME is doable <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

scale <str<strong>on</strong>g>of</str<strong>on</strong>g> next few decades, but to support modern drug development now, we need<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e imperfect but useful phenomenological models in combinati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mechanistic<br />

models under development.<br />

938

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bioinformatics and System Biology; Wednesday, June 29, 17:00<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Świder<br />

Rzeszow University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: kswider@prz-rzeszow.pl<br />

Bartosz Jędrzejec<br />

Rzeszow University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Modeling and Integrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Networks wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

BiNArr<br />

The investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biological networks for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir better understanding and making<br />

available for practical use is currently an important task in systems biology.<br />

The au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors developed an integrated envir<strong>on</strong>ment BiNArr (Biological Network Arranger)<br />

aimed to perform a number <str<strong>on</strong>g>of</str<strong>on</strong>g> practically useful operati<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network<br />

data stored in biological databases. Dissimilar to <str<strong>on</strong>g>th</str<strong>on</strong>g>e existing tools like Cytoscape<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong>ality <str<strong>on</strong>g>of</str<strong>on</strong>g> our applicati<strong>on</strong> is ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er limited and strictly oriented for transforming<br />

structured data from real databases into graphs. This allows its fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

processing e.g. wi<str<strong>on</strong>g>th</str<strong>on</strong>g> use <str<strong>on</strong>g>of</str<strong>on</strong>g> graph mining algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms. We proposed <str<strong>on</strong>g>th</str<strong>on</strong>g>e unified<br />

graph representati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e structures extracted from original resources and developed<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e modules for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir visualizati<strong>on</strong> and editi<strong>on</strong>. Ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er wor<str<strong>on</strong>g>th</str<strong>on</strong>g>y features are:<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e automatic coding <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting graphs in several formats, <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability to generate<br />

graphic files for presentati<strong>on</strong> purposes and an open architecture enabling to<br />

cooperate wi<str<strong>on</strong>g>th</str<strong>on</strong>g> number <str<strong>on</strong>g>of</str<strong>on</strong>g> existing biological databases. In order to present capabilities<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> BiNArr we used <str<strong>on</strong>g>th</str<strong>on</strong>g>e biological structures representing metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways<br />

extracted from KEGG (Kyoto Encyclopedia <str<strong>on</strong>g>of</str<strong>on</strong>g> Genes and Genomes) as well as<br />

protein-protein interacti<strong>on</strong>s provided in DIP (Database <str<strong>on</strong>g>of</str<strong>on</strong>g> Interacting Proteins).<br />

939

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Structure and Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemical Reacti<strong>on</strong> Networks I; Tuesday, June<br />

28, 14:30<br />

David Swig<strong>on</strong><br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Pittsburgh<br />

e-mail: swig<strong>on</strong>@pitt.edu<br />

Decompositi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chemical reacti<strong>on</strong> networks<br />

I will outline <str<strong>on</strong>g>th</str<strong>on</strong>g>e ideas behind a novel <str<strong>on</strong>g>th</str<strong>on</strong>g>eory for analyzing <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g term dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> chemical reacti<strong>on</strong> networks wi<str<strong>on</strong>g>th</str<strong>on</strong>g> mass acti<strong>on</strong> kinetics based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e combinati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Deficiency Theory <str<strong>on</strong>g>of</str<strong>on</strong>g> Horn, Johns<strong>on</strong>, and Feinberg, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e decompositi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

networks into extreme subnetworks, pi<strong>on</strong>eered by Clarke. This is a work in progress,<br />

but am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e results <str<strong>on</strong>g>th</str<strong>on</strong>g>at have been obtained are <str<strong>on</strong>g>th</str<strong>on</strong>g>e formulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> new sufficient<br />

c<strong>on</strong>diti<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e existence <str<strong>on</strong>g>of</str<strong>on</strong>g> a unique asymptotically stable positive equilibrium<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at generalize <str<strong>on</strong>g>th</str<strong>on</strong>g>e Deficiency Zero Theorem.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Structure and Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Biochemical Reacti<strong>on</strong> Networks I; Tuesday, June<br />

28, 14:30<br />

Gábor Szederkényi<br />

Computer and Automati<strong>on</strong> Research Institute, Hungarian Acad. Sci.<br />

Kende u. 13-17, H-1111 Budapest, Hungary<br />

e-mail: szeder@scl.sztaki.hu<br />

Dynamically equivalent reacti<strong>on</strong> networks: a computati<strong>on</strong>al<br />

point <str<strong>on</strong>g>of</str<strong>on</strong>g> view<br />

It has been known from <str<strong>on</strong>g>th</str<strong>on</strong>g>e ’fundamental dogma <str<strong>on</strong>g>of</str<strong>on</strong>g> chemical kinetics’ <str<strong>on</strong>g>th</str<strong>on</strong>g>at different<br />

mass acti<strong>on</strong> type reacti<strong>on</strong> networks can give rise to <str<strong>on</strong>g>th</str<strong>on</strong>g>e same ordinary differential<br />

equati<strong>on</strong>s describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e time evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> specie c<strong>on</strong>centrati<strong>on</strong>s. Finding<br />

dynamically equivalent network structures wi<str<strong>on</strong>g>th</str<strong>on</strong>g> preferred properties can significantly<br />

enhance <str<strong>on</strong>g>th</str<strong>on</strong>g>e applicati<strong>on</strong> range <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e known and c<strong>on</strong>tinuously developing<br />

str<strong>on</strong>g results <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong> between network structure and qualitative dynamical<br />

properties (deficiency <str<strong>on</strong>g>th</str<strong>on</strong>g>eorems, structural c<strong>on</strong>diti<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility <str<strong>on</strong>g>of</str<strong>on</strong>g> multiple<br />

steady states, Global Attractor and Persistency C<strong>on</strong>jectures etc.). It is also known<br />

primarily from systems and c<strong>on</strong>trol <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical feasibility <str<strong>on</strong>g>of</str<strong>on</strong>g> many<br />

existence and design problems can <str<strong>on</strong>g>of</str<strong>on</strong>g>ten be checked via appropriately formulated<br />

optimizati<strong>on</strong> tasks even if <str<strong>on</strong>g>th</str<strong>on</strong>g>e original problem is algebraically complex to treat.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, an overview <str<strong>on</strong>g>of</str<strong>on</strong>g> linear programming (LP) and mixed integer linear<br />

programming (MILP) techniques will be given for <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong> networks<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> prescribed properties. This includes <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> structures wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e minimal/maximal number <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong>s/complexes, detailed/complex balanced,<br />

and fully/weakly reversible realizati<strong>on</strong>s.<br />

941

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling III; Wednesday, June 29,<br />

17:00<br />

Piotr Szopa<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research<br />

Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warsaw<br />

e-mail: pszopa@ippt.gov.pl<br />

Bogdan Kazmierczak<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research<br />

Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warsaw<br />

e-mail: bkazmier@ippt.gov.pl<br />

Bifurcati<strong>on</strong> phenomena in spatially extended kinase-receptor<br />

interacti<strong>on</strong> model<br />

We c<strong>on</strong>sider a reacti<strong>on</strong>-diffusi<strong>on</strong> model <str<strong>on</strong>g>of</str<strong>on</strong>g> mutual interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> membrane receptors<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> kinases proposed in [1]. It is assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at membrane receptors and<br />

cytosolic kinases activate each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er, which establishes <str<strong>on</strong>g>th</str<strong>on</strong>g>e positive feedback. The<br />

kinases and <str<strong>on</strong>g>th</str<strong>on</strong>g>e receptors are dephosphorylated by uniformly distributed phosphatases.<br />

The existence <str<strong>on</strong>g>of</str<strong>on</strong>g> positive feedback leads to bifurcati<strong>on</strong> at which <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

positive stable soluti<strong>on</strong> appears.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is study we c<strong>on</strong>sider, unlike <str<strong>on</strong>g>th</str<strong>on</strong>g>e au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors in [1], <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>uniformly<br />

distributed membrane receptors. We apply <str<strong>on</strong>g>th</str<strong>on</strong>g>e Steklov eigenproblem <str<strong>on</strong>g>th</str<strong>on</strong>g>eory [2] to<br />

analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e linearized model and find <str<strong>on</strong>g>th</str<strong>on</strong>g>e analytic form <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s. This approach<br />

allows us to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e critical value <str<strong>on</strong>g>of</str<strong>on</strong>g> phospahatase activity at which cell<br />

activati<strong>on</strong> is possible as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> kinase diffusi<strong>on</strong> coeffcient and anisotropy <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

receptor distributi<strong>on</strong> using <strong>on</strong>ly algebraic me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods.<br />

We showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at cell sensitivity grows wi<str<strong>on</strong>g>th</str<strong>on</strong>g> decreasing kinase diffusi<strong>on</strong> and increasing<br />

polarity <str<strong>on</strong>g>of</str<strong>on</strong>g> receptor distributi<strong>on</strong>. Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two effects are cooperating.<br />

The soluti<strong>on</strong>s to <str<strong>on</strong>g>th</str<strong>on</strong>g>e original n<strong>on</strong>linear system close to <str<strong>on</strong>g>th</str<strong>on</strong>g>e bifurcati<strong>on</strong><br />

point can be approximated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e soluti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e linearized <strong>on</strong>e. Moreover <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

approximati<strong>on</strong> can be improved by using <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <str<strong>on</strong>g>of</str<strong>on</strong>g> successive approximati<strong>on</strong>s.<br />

References.<br />

[1] B. Kazmierczak, T. Lipniacki Regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> kinase activity by diffusi<strong>on</strong> and feedback J. Theor.<br />

Biol. 259 291–296.<br />

[2] G. Auchmuty Steklov eigenproblems and <str<strong>on</strong>g>th</str<strong>on</strong>g>e representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> elliptic boundary<br />

value problems Numer. Funct. Anal. Optim. 25 321–348 .<br />

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Developmental Biology; Saturday, July 2, 11:00<br />

Joanna Szymanowska-Pułka<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biophysics and Plant Morphogenesis, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Silesia, Katowice<br />

e-mail: jsp@us.edu.pl<br />

Jerzy Karczewski<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biophysics and Plant Morphogenesis, University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Silesia, Katowice<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Lateral Root Morphology wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Use <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Fast Fourier Transform<br />

During <str<strong>on</strong>g>th</str<strong>on</strong>g>e lateral root (LR) development bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e size and <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e organ<br />

change c<strong>on</strong>tinuously since <str<strong>on</strong>g>th</str<strong>on</strong>g>e moment <str<strong>on</strong>g>of</str<strong>on</strong>g> its initiati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e pericycle <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mo<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

root until it reaches its mature form. Subsequent stages <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e LR formati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

typical changes <str<strong>on</strong>g>of</str<strong>on</strong>g> its form and cell pattern are known [1]. However, our observati<strong>on</strong>s<br />

[2] prove <str<strong>on</strong>g>th</str<strong>on</strong>g>at in <str<strong>on</strong>g>th</str<strong>on</strong>g>e early stages, when <str<strong>on</strong>g>th</str<strong>on</strong>g>e LR promordia push <str<strong>on</strong>g>th</str<strong>on</strong>g>rough<br />

tissues <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mo<str<strong>on</strong>g>th</str<strong>on</strong>g>er root, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey show a great diversity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir surface morphology.<br />

Most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e forms are repeatable, few occur as single cases. From mechanical point<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> view <str<strong>on</strong>g>th</str<strong>on</strong>g>e LR formati<strong>on</strong> may be interpreted as a bucling and <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed changes<br />

in shape as local deflecti<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e root apex surface resulting from a pressure <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding tissues <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mo<str<strong>on</strong>g>th</str<strong>on</strong>g>er root. This irregularity in form may suggest<br />

changeable mechanical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e surface <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e LR apex.<br />

The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> our study is to analyze atypicaly formed LRs in comparis<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

apices <str<strong>on</strong>g>of</str<strong>on</strong>g> typical morhology as well as to estimate mechanical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e LR<br />

apex basing <strong>on</strong> deflecti<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir structures. The LR primordia forming in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Arabidopsis <str<strong>on</strong>g>th</str<strong>on</strong>g>aliana roots were photographed in Nomarski c<strong>on</strong>trast microscopic<br />

technique in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir axial secti<strong>on</strong>s. The outlines <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e chosen LRs showing typical<br />

and atypical shapes were digitized. The coordinates were introduced as initial data<br />

to a program analyzing <str<strong>on</strong>g>th</str<strong>on</strong>g>e shapes <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e apices. The basic assumti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> our model<br />

were <str<strong>on</strong>g>th</str<strong>on</strong>g>e following: (i) a surface <str<strong>on</strong>g>of</str<strong>on</strong>g> a typicaly shaped LR is a circular paraboloid<br />

[3]; (ii) trajectories <str<strong>on</strong>g>of</str<strong>on</strong>g> principal directi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> stress form a pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> paraboloids<br />

[3]; (iii) deflecti<strong>on</strong>s (irregularities) <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e organ surface are local and small in comparis<strong>on</strong><br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e apex size. The LR formati<strong>on</strong> was analyzed in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanical<br />

buckling. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e model we applied <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fast Fourier Transform me<str<strong>on</strong>g>th</str<strong>on</strong>g>od a standard<br />

tool adopted to descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> buckling [4, 5]. This allowed determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e deflecti<strong>on</strong><br />

curves <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e trig<strong>on</strong>ometric series. Our results show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e outline <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

each LR apex <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e unchanged geometry (independently <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stage <str<strong>on</strong>g>of</str<strong>on</strong>g> development)<br />

may be described by <strong>on</strong>e parabolic curve, which in <str<strong>on</strong>g>th</str<strong>on</strong>g>e parabolic coordinates<br />

refers <str<strong>on</strong>g>th</str<strong>on</strong>g>e line 1.2. Thus <str<strong>on</strong>g>th</str<strong>on</strong>g>e curves representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e outlines <str<strong>on</strong>g>of</str<strong>on</strong>g> atypicaly formed<br />

LRs where in <str<strong>on</strong>g>th</str<strong>on</strong>g>e first step adjusted to <str<strong>on</strong>g>th</str<strong>on</strong>g>at line. For each studied curve <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fourier<br />

spectrum (amplitude and phase) was calculated . On <str<strong>on</strong>g>th</str<strong>on</strong>g>is basis we were able to<br />

classify atypicaly shaped LR apices. Then applying <str<strong>on</strong>g>th</str<strong>on</strong>g>e Euler formula to <str<strong>on</strong>g>th</str<strong>on</strong>g>e elastic<br />

buckling we estimated basic mechanical moduli for <str<strong>on</strong>g>th</str<strong>on</strong>g>e studied cases. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e results <str<strong>on</strong>g>th</str<strong>on</strong>g>e following c<strong>on</strong>nclusi<strong>on</strong>s can be drawn: (i) <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fourier Transform<br />

may be a useful tool to a shape annalisys <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e living structures; (ii) mechanical<br />

moduli <str<strong>on</strong>g>of</str<strong>on</strong>g> a growing plant organ tissues can be estimated <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e organ<br />

shape and its deformati<strong>on</strong>s; (iii) <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical properties <str<strong>on</strong>g>of</str<strong>on</strong>g> growing plant tissues<br />

943

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may be regulated by biological factors like plant grow<str<strong>on</strong>g>th</str<strong>on</strong>g> horm<strong>on</strong>es as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

cell wall achitecture. The last needs additi<strong>on</strong>al studies.<br />

References.<br />

[1] J.E. Malamy, P.N. Benfey, 1997. Organizati<strong>on</strong> and cell differentiati<strong>on</strong> in lateral roots <str<strong>on</strong>g>of</str<strong>on</strong>g> Arabidopsis<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>aliana. Development, 124, 33-44.<br />

[2] J. Szymanowska-Pułka, I. Potocka, L. Feldman, J. Karczewski. Principal directi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir manifestati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> a developing lateral root in Arabidopsis <str<strong>on</strong>g>th</str<strong>on</strong>g>aliana<br />

poster. The EMBO Meeting 2010, Barcel<strong>on</strong>a Sept 27, 2010.<br />

[3] Z. Hejnowicz, 1984. Trajectories <str<strong>on</strong>g>of</str<strong>on</strong>g> principal directi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, natural coordinate system<br />

in growing plant organ. Acta Soc. Bot. Pol., 53(1), 29-42.<br />

[4] S.P.Timoshenko, J.M Gere, 1985. Theory <str<strong>on</strong>g>of</str<strong>on</strong>g> elastic stability. McGraw-Hill Int. Book Com,<br />

1-45.<br />

[5] R. Vandiver , A. Goriely, 2009. Differential grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and residual stress in cylindrical elastic<br />

structures. Phil. Trans. R. Soc. A, 367, 3607-3630.<br />

944

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling IV; Saturday, July 2, 08:30<br />

Paulina Szymanska<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics and Mechanics<br />

e-mail: p.szymanska@gmail.com<br />

Jacek Miekisz<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Informatics and Mechanics<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> self-regulating gene<br />

We study <str<strong>on</strong>g>th</str<strong>on</strong>g>e variance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> proteins produced in a self-regulating<br />

gene in a steady state wi<str<strong>on</strong>g>th</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <strong>on</strong>e and two copies <str<strong>on</strong>g>of</str<strong>on</strong>g> gene. Master equati<strong>on</strong>s and<br />

differential equati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e first and sec<strong>on</strong>d moments <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e variable describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> proteins are formulated in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> models. Various approximati<strong>on</strong> schemes<br />

are used in order to close <str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e moments. Specifically, we<br />

examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e variance <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e adiabaticity parameter measuring<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e relative rate <str<strong>on</strong>g>of</str<strong>on</strong>g> DNA-protein unbinding and protein degradati<strong>on</strong>. We compare<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e variance obtained in models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <strong>on</strong>e and two gene copies.<br />

945

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Zuzanna Szymańska<br />

ICM, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw<br />

e-mail: Z.Szymanska@icm.edu.pl<br />

Mark A. J. Chaplain<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Dundee<br />

Mirosław Lachowicz<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw<br />

Dariusz Wrzosek<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw<br />

Cancer; Tuesday, June 28, 17:00<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer invasi<strong>on</strong>: distinguishing<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative importance <str<strong>on</strong>g>of</str<strong>on</strong>g> cell-cell adhesi<strong>on</strong> and<br />

cell-matrix adhesi<strong>on</strong><br />

The process <str<strong>on</strong>g>of</str<strong>on</strong>g> invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tissue by cancer cells is crucial for metastasis – <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> sec<strong>on</strong>dary tumours – which is <str<strong>on</strong>g>th</str<strong>on</strong>g>e main cause <str<strong>on</strong>g>of</str<strong>on</strong>g> mortality in patients<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> cancer. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong> process itself, adhesi<strong>on</strong>, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> cell-cell and cell-matrix,<br />

plays an extremely important role. In our talk we present a novel ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cell invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular matrix taking into account cellcell<br />

adhesi<strong>on</strong> as well as cell-matrix adhesi<strong>on</strong>. C<strong>on</strong>sidering <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s between<br />

cancer cells, extracellular matrix and matrix degrading enzymes, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model c<strong>on</strong>sists<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a system <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong>-diffusi<strong>on</strong> partial integro-differential equati<strong>on</strong>s, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> n<strong>on</strong>-local<br />

(integral) terms describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e adhesive interacti<strong>on</strong>s between cancer cells and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

host tissue, i.e. cell-cell adhesi<strong>on</strong> and cell-matrix adhesi<strong>on</strong>. We first describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

main results <str<strong>on</strong>g>th</str<strong>on</strong>g>at we obtained from a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

existence and uniqueness <str<strong>on</strong>g>of</str<strong>on</strong>g> global in time classical soluti<strong>on</strong>s which are uniformly<br />

bounded. Then, using computati<strong>on</strong>al simulati<strong>on</strong>s we investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

relative importance <str<strong>on</strong>g>of</str<strong>on</strong>g> cell-cell adhesi<strong>on</strong> and cell-matrix adhesi<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong><br />

process. In particular we examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e roles <str<strong>on</strong>g>of</str<strong>on</strong>g> cell-cell adhesi<strong>on</strong> and cell-matrix<br />

adhesi<strong>on</strong> in generating heterogeneous spatio-temporal soluti<strong>on</strong>s.<br />

References.<br />

[1] M. A. J. Chaplain, M. Lachowicz, Z. Szymańska and D. Wrzosek (2011) Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> cancer invasi<strong>on</strong>: <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> cell-cell adhesi<strong>on</strong> and cell-matrix adhesi<strong>on</strong>, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

Models Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods Appl. Sci., 21, 1-25.<br />

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Medical Physiology; Saturday, July 2, 08:30<br />

Masoomeh Taghipoor 1<br />

e-mail: masoomeh.taghipoor@lmpt.univ-tours.fr<br />

Philippe Lescoat 2<br />

e-mail: Philippe.Lescoat@tours.inra.fr<br />

Jean-René Licois 1<br />

e-mail: licois@lmpt.univ-tours.fr<br />

Christine Georgelin 1<br />

e-mail: Christine.Georgelin@lmpt.univ-tours.fr<br />

Guy Barles 1<br />

e-mail: barles@lmpt.univ-tours.fr<br />

1 Laboratoire de Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ématiques et Physique Théorique (CNRS UMR-<br />

6083), Denis Poiss<strong>on</strong> Federati<strong>on</strong> (CNRS FR-2964), François Rabelais<br />

University, Parc de Grandm<strong>on</strong>t, 37200 Tours, France<br />

2 INRA, UR83 Recherches Avicoles, 37380 Nouzilly, France,<br />

A New Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Model for combining Transport and<br />

Degradati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Small Intestine<br />

The small intestine is resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>e major part <str<strong>on</strong>g>of</str<strong>on</strong>g> feedstuffs digesti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

gastrointestinal tract. Several models have been developed for representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

digesti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a bolus in <str<strong>on</strong>g>th</str<strong>on</strong>g>e small intestine ([1], [2], [3]). This work tries to go fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

in modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>ese phenomena by representing a simultaneous model for degradati<strong>on</strong><br />

and absorpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> feedstuffs and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir transport in <str<strong>on</strong>g>th</str<strong>on</strong>g>e intestinal lumen. Specifically,<br />

we determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e positi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bolus and <str<strong>on</strong>g>th</str<strong>on</strong>g>e proporti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>stituents at<br />

each time. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e first part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is study, we present four successive models which<br />

reflect <str<strong>on</strong>g>th</str<strong>on</strong>g>e modeling process at its different stages wi<str<strong>on</strong>g>th</str<strong>on</strong>g> our attempts to make it more<br />

realistic by inclusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> more relevant biological phenomena. The small intestine is<br />

assumed to be a <strong>on</strong>e-dimensi<strong>on</strong>al interval and <str<strong>on</strong>g>th</str<strong>on</strong>g>e bolus moves <str<strong>on</strong>g>th</str<strong>on</strong>g>rough its lumen due<br />

to migrating myoelectric complex. The bolus is treated as a homogeneous cylinder<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a fixed leng<str<strong>on</strong>g>th</str<strong>on</strong>g> ℓ and variable radius R(t). The degradati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> feedstuffs is <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

result <str<strong>on</strong>g>of</str<strong>on</strong>g> volumic and surfacic transformati<strong>on</strong>s. This model is based <strong>on</strong> a system <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

coupled ordinary differential equati<strong>on</strong>s. These equati<strong>on</strong>s are solved by a classical<br />

numerical integrati<strong>on</strong> using Runge-Kutta me<str<strong>on</strong>g>th</str<strong>on</strong>g>od. The results <str<strong>on</strong>g>of</str<strong>on</strong>g> simulati<strong>on</strong> are<br />

c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental works in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature (e.g. in <str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> purified<br />

starch [5]), al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough more analysis and experimentati<strong>on</strong>s are needed to represent<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e reality more closely.<br />

The sec<strong>on</strong>d part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work c<strong>on</strong>sists in using <str<strong>on</strong>g>th</str<strong>on</strong>g>e homogenizati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od to<br />

simplify <str<strong>on</strong>g>th</str<strong>on</strong>g>e transport equati<strong>on</strong> and justify <str<strong>on</strong>g>th</str<strong>on</strong>g>e choice <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> absorpti<strong>on</strong> by<br />

intestinal wall [4].<br />

The transport <str<strong>on</strong>g>of</str<strong>on</strong>g> bolus inside <str<strong>on</strong>g>th</str<strong>on</strong>g>e small intestine is induced by high frequency<br />

pulses. These pulses cause rapid variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e bolus’ velocity in <str<strong>on</strong>g>th</str<strong>on</strong>g>e small intestine.<br />

We show ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematically <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e pulses can be averaged out in an appropriate<br />

way <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore <str<strong>on</strong>g>th</str<strong>on</strong>g>e rapidly varying velocity can be replaced by a slowly varying <strong>on</strong>e.<br />

Because <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lack <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> about <str<strong>on</strong>g>th</str<strong>on</strong>g>e properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e small intestine<br />

wall, <str<strong>on</strong>g>th</str<strong>on</strong>g>e local absorpti<strong>on</strong> rate is not precisely defined. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough, an effective or<br />

averaged rate <str<strong>on</strong>g>of</str<strong>on</strong>g> absorpti<strong>on</strong> is determined by help <str<strong>on</strong>g>of</str<strong>on</strong>g> homogenizati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods [6].<br />

To <str<strong>on</strong>g>th</str<strong>on</strong>g>is aim, a 3-D transport-diffusi<strong>on</strong> PDE in <str<strong>on</strong>g>th</str<strong>on</strong>g>e domain Ωɛ wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a Neumann<br />

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boundary c<strong>on</strong>diti<strong>on</strong> (reflecting <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fourier’s law) is defined. The domain Ωɛ describes<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e small intestine. It is a 3-D domain wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a small radius rɛ and a highly<br />

oscillating boundary. The oscillati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> its boundary is justified by <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fingerlike villi which cover <str<strong>on</strong>g>th</str<strong>on</strong>g>e inner surface <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e small intestine. The unknown<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem being <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>e absorbable nutrients, <str<strong>on</strong>g>th</str<strong>on</strong>g>e boundary c<strong>on</strong>diti<strong>on</strong><br />

represents <str<strong>on</strong>g>th</str<strong>on</strong>g>e absorpti<strong>on</strong> rate by intestinal wall. To justify <str<strong>on</strong>g>th</str<strong>on</strong>g>e choice <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>stant<br />

absorpti<strong>on</strong> rate, our me<str<strong>on</strong>g>th</str<strong>on</strong>g>od c<strong>on</strong>sists in a passage to <str<strong>on</strong>g>th</str<strong>on</strong>g>e limit from <str<strong>on</strong>g>th</str<strong>on</strong>g>is equati<strong>on</strong><br />

to obtain a 1-D transport equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a c<strong>on</strong>stant averaged rate <str<strong>on</strong>g>of</str<strong>on</strong>g> absorpti<strong>on</strong> .<br />

References.<br />

[1] J.D. Logan, A. Joern, W. Wolesensky , Locati<strong>on</strong>, Time, and Temperature Dependence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Digesti<strong>on</strong> in Simple Animal Tracts, J. Theoretical Biology, (2002), Issue 1, 216 5–18.<br />

[2] D. Bastianelli, D. Sauvant, A. Rerat, A Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> digesti<strong>on</strong> and nutrient<br />

absorpti<strong>on</strong> in pigs, J. Anim. Sci. (1996) Issue 8, 74 1873–1887.<br />

[3] R. Miftah<str<strong>on</strong>g>of</str<strong>on</strong>g>, N. Akhmadeev, Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> intestinal propulsi<strong>on</strong>, J. Theoretical Biology, (2007),<br />

Issue 2, 246 377–393.<br />

[4] Piccinini, Livio C. Homogenizati<strong>on</strong> problems for ordinary differential equati<strong>on</strong>s, Rend. Circ.<br />

Mat. Palermo (2), (1978),27 no. 1, 95–112.<br />

[5] B. Darcy, J.P. Laplace, P.A. Villiers, Digesti<strong>on</strong> dans l’intestin grele chez le porc, Ann.zootech,<br />

(1981), 30 31–62.<br />

[6] G. Barles, F.Da Lio, P-L Li<strong>on</strong>s, P. E. SouganidisErgodic problems and periodic homogenizati<strong>on</strong><br />

for fully n<strong>on</strong>linear equati<strong>on</strong>s in half-space type domains wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Neumann boundary c<strong>on</strong>diti<strong>on</strong>s,<br />

Indiana University Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Journal, (2008), 57 5 2355–2376<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Takenori Takada<br />

Hokkaido University<br />

e-mail: takada@ees.hokudai.ac.jp<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Derivati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> yearly transiti<strong>on</strong> matrix <str<strong>on</strong>g>of</str<strong>on</strong>g> land-use dynamics<br />

and its applicati<strong>on</strong>s<br />

Transiti<strong>on</strong> matrices have <str<strong>on</strong>g>of</str<strong>on</strong>g>ten been used in landscape ecology and GIS studies <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

land-use to quantitatively estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> change. When transiti<strong>on</strong> matrices<br />

for different observati<strong>on</strong> periods are compared, <str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong> intervals <str<strong>on</strong>g>of</str<strong>on</strong>g>ten differ<br />

because satellite images or photographs <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e research site taken at c<strong>on</strong>stant<br />

time intervals may not be available. For such calculati<strong>on</strong>, several previous studies<br />

have utilized a linear algebra formula <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e power root <str<strong>on</strong>g>of</str<strong>on</strong>g> matrices. However,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ree difficulties may arise when applying <str<strong>on</strong>g>th</str<strong>on</strong>g>is formula to a practical dataset from<br />

photographs <str<strong>on</strong>g>of</str<strong>on</strong>g> a research site. We examined <str<strong>on</strong>g>th</str<strong>on</strong>g>e first difficulty, namely <str<strong>on</strong>g>th</str<strong>on</strong>g>at plural<br />

soluti<strong>on</strong>s could exist for a yearly transiti<strong>on</strong> matrix, which implies <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere could<br />

be multiple scenarios for <str<strong>on</strong>g>th</str<strong>on</strong>g>e same transiti<strong>on</strong> in land-use change. Using data for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Abukuma Mountains in Japan, we <str<strong>on</strong>g>th</str<strong>on</strong>g>en looked at <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d difficulty, in which we<br />

may obtain no positive Markovian matrix and <strong>on</strong>ly a matrix partially c<strong>on</strong>sisting<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> negative numbers. We propose a way to calibrate a matrix wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some negative<br />

transiti<strong>on</strong> elements and to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e predicti<strong>on</strong> error. Finally, we discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ird difficulty <str<strong>on</strong>g>th</str<strong>on</strong>g>at arises when a new land-use category appears at <str<strong>on</strong>g>th</str<strong>on</strong>g>e end <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong> period and how to solve it. We developed a computer program to<br />

calculate and calibrate <str<strong>on</strong>g>th</str<strong>on</strong>g>e yearly matrices and to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e predicti<strong>on</strong> error.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Daisuke Takahashi<br />

Center for Ecological Research, Kyoto University, Japan<br />

e-mail: dtakahashi@ecology.kyoto-u.ac.jp<br />

Åke Brännström<br />

Evoluti<strong>on</strong> and Ecology Program, Internati<strong>on</strong>al Institute for Applied<br />

Systems Analysis, Austria<br />

e-mail: brnstrom@iiasa.ac.at<br />

Rupert Mazzucco<br />

Evoluti<strong>on</strong> and Ecology Program, Internati<strong>on</strong>al Institute for Applied<br />

Systems Analysis, Austria<br />

e-mail: mazzucco@iiasa.ac.at<br />

Atsushi Yamauchi<br />

Center for Ecological Research, Kyoto University, Japan<br />

e-mail: a-yama@ecology.kyoto-u.ac.jp<br />

Ulf Dieckmann<br />

Evoluti<strong>on</strong> and Ecology Program, Internati<strong>on</strong>al Institute for Applied<br />

Systems Analysis, Austria<br />

e-mail: dieckmann@iiasa.ac.at<br />

Meta-stable states and macro-evoluti<strong>on</strong>ary transiti<strong>on</strong>s in an<br />

eco-evoluti<strong>on</strong>ary food-web model<br />

Eco-evoluti<strong>on</strong>ary food-web models help elucidate <str<strong>on</strong>g>th</str<strong>on</strong>g>e processes resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

emergence and maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> complex community structures. However, most existing<br />

community-evoluti<strong>on</strong> models are based <strong>on</strong> random speciati<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>us do<br />

not c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e gradual evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> trophic traits. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, intermittent<br />

bursts <str<strong>on</strong>g>of</str<strong>on</strong>g> evoluti<strong>on</strong> associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> punctuated equilibria highlight <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> describing not <strong>on</strong>ly an evolved community’s structure, but also <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying<br />

evoluti<strong>on</strong>ary dynamics. While models based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> self-organized criticality<br />

help understand n<strong>on</strong>-equilibrium community dynamics, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey have so far been<br />

based <strong>on</strong> str<strong>on</strong>gly simplified assumpti<strong>on</strong>s about ecological interacti<strong>on</strong>s. Using an<br />

individual-based model, here we incorporate <str<strong>on</strong>g>th</str<strong>on</strong>g>e gradual evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> key traits for<br />

foraging and interference interacti<strong>on</strong> into a model <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>-equilibrium community<br />

evoluti<strong>on</strong>. We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at our model communities quickly diversify into autotrophs<br />

(plants) and c<strong>on</strong>sumers (herbvivores), wi<str<strong>on</strong>g>th</str<strong>on</strong>g> distinctive phenotypic clusters resulting<br />

from successive speciati<strong>on</strong> driven by plant-herbivore coevoluti<strong>on</strong>. Occasi<strong>on</strong>ally, all<br />

herbivores go extinct in sudden macroevoluti<strong>on</strong>ary transiti<strong>on</strong>s, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e remaining<br />

community primarily featuring plants. Our findings <str<strong>on</strong>g>th</str<strong>on</strong>g>us reveal a pattern <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

community macroevoluti<strong>on</strong> involving two meta-stable states, corresp<strong>on</strong>ding to a<br />

plant–herbivore community and a plant community, respectively. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary<br />

timescale, our model community switches stochastically and rapidly between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese two alternative community states. We explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e processes resp<strong>on</strong>sible for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e breakdown <str<strong>on</strong>g>of</str<strong>on</strong>g> plant–herbivore communities in our model, as well as for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

subsequent reestablishment <str<strong>on</strong>g>of</str<strong>on</strong>g> herbivore diversity. Our model <str<strong>on</strong>g>th</str<strong>on</strong>g>us helps us understand<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e eco-evoluti<strong>on</strong>ary mechanisms underlying <str<strong>on</strong>g>th</str<strong>on</strong>g>ese recurrent dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

rapid community breakdown and regenerati<strong>on</strong>, which terminate intermittent periods<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> near-stasis or punctuated equilibrium.<br />

950

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Genetics; Wednesday, June 29, 14:30<br />

Satoshi Takahashi<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Informati<strong>on</strong> and Computer Sciences, Nara Women’s<br />

University<br />

e-mail: takahasi@lisboa.ics.nara-wu.ac.jp<br />

Rika Okamoto, Sayaka Noguchi, Yumiko Inoue, Tomoko Kawasaki<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Informati<strong>on</strong> and Computer Sciences, Nara Women’s<br />

University<br />

Michio Hori<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Zoology, Kyoto University<br />

e-mail: hori@terra.zool.kyoto-u.ac.jp<br />

From Populati<strong>on</strong> Dynamics to Evoluti<strong>on</strong>: Oscillati<strong>on</strong> in<br />

Lateral Asymmetry <str<strong>on</strong>g>of</str<strong>on</strong>g> Fish Induces <str<strong>on</strong>g>th</str<strong>on</strong>g>e Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Homozygote Incompatibility<br />

Lateral asymmetry, originally found in scale eating cichlid fish in Lake Tanganyika,<br />

was first c<strong>on</strong>sidered to follow <str<strong>on</strong>g>th</str<strong>on</strong>g>e simple Mendelian genetics. Later, more c<strong>on</strong>trolled<br />

mating experiments <strong>on</strong> scale eaters and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er fish reveal <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey lack lefty<br />

(dominant) homozygote. Le<str<strong>on</strong>g>th</str<strong>on</strong>g>ality <str<strong>on</strong>g>of</str<strong>on</strong>g> lefty homozygote explains F1 ratio, but not<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e high hatchability <str<strong>on</strong>g>of</str<strong>on</strong>g> lefty pairs. We c<strong>on</strong>struct models <str<strong>on</strong>g>of</str<strong>on</strong>g> incompatibilities <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

lefty homozygote and investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e invasi<strong>on</strong> and fixati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

incompatibility gene. Laterality morph frequencies in many fish oscillate due to<br />

cross-predati<strong>on</strong> am<strong>on</strong>g prey and predators: predators feed <strong>on</strong> prey <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same<br />

laterality wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em more <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>ose <str<strong>on</strong>g>of</str<strong>on</strong>g> different laterality. Incompatibility gene,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at prevents eggs <str<strong>on</strong>g>of</str<strong>on</strong>g> lefty gene from fertilizing sperm <str<strong>on</strong>g>of</str<strong>on</strong>g> lefty gene, spreads in case<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> group spawning, as l<strong>on</strong>g as laterality morph frequencies oscillates. Under pair<br />

spawning c<strong>on</strong>diti<strong>on</strong>, however, incompatibility gene does not spread, as incompatibility<br />

gene prevents part <str<strong>on</strong>g>of</str<strong>on</strong>g> eggs to fertilize in some genotype combinati<strong>on</strong>s. We<br />

c<strong>on</strong>sider partial incompatibility where eggs <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e incompatibility gene and <str<strong>on</strong>g>th</str<strong>on</strong>g>e lefty<br />

gene fertilize wi<str<strong>on</strong>g>th</str<strong>on</strong>g> sperm <str<strong>on</strong>g>of</str<strong>on</strong>g> lefty gene in smaller ratio <str<strong>on</strong>g>th</str<strong>on</strong>g>an sperm <str<strong>on</strong>g>of</str<strong>on</strong>g> righty gene.<br />

The incompatibility gene spreads even under pair spawning c<strong>on</strong>diti<strong>on</strong> if its incompatibility<br />

is partial. We also study <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> incompatibility<br />

by simulating <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> frequencies <str<strong>on</strong>g>of</str<strong>on</strong>g> two incompatibility genes <str<strong>on</strong>g>of</str<strong>on</strong>g> different<br />

incompatibility levels bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in prey and predator. Str<strong>on</strong>ger cross predati<strong>on</strong>, large<br />

predati<strong>on</strong> coefficient, as well as larger survival rate lead to larger level <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e lefty<br />

homozygote incompatibility.<br />

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Recent developments in <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> Lotka-Volterra and Kolmogorov<br />

systems; Saturday, July 2, 14:30<br />

Yasuhiro Takeuchi<br />

Graduate School <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Technology, Shizuoka University<br />

e-mail: takeuchi@sys.eng.shizuoka.ac.jp<br />

Global stability <str<strong>on</strong>g>of</str<strong>on</strong>g> Lotka-Volterra equati<strong>on</strong>s<br />

This presentati<strong>on</strong> will review some c<strong>on</strong>diti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> global stability <str<strong>on</strong>g>of</str<strong>on</strong>g> Lotka-Volterra<br />

equati<strong>on</strong>s and discuss <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship between <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability and <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e systems.<br />

Y. Takeuchi; Global Dynamical Properties <str<strong>on</strong>g>of</str<strong>on</strong>g> Lotka-Volterra Systems, World Scientific<br />

1996.<br />

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Neurosciences; Friday, July 1, 14:30<br />

Massimiliano Tamborrino<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Copenhagen, Universitetsparken<br />

5, DK 2100, Copenhagen, Denmark.<br />

e-mail: mt@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ku.dk<br />

Susanne Ditlevsen<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Copenhagen, Universitetsparken<br />

5, DK 2100, Copenhagen, Denmark.<br />

e-mail: susanne@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ku.dk<br />

Petr Lansky<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physiology, Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Czech Republic,<br />

142 20 Prague 4, Czech Republic<br />

e-mail: lansky@biomed.cas.cz<br />

Detecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e first-spike latency<br />

Resp<strong>on</strong>se latency is <str<strong>on</strong>g>th</str<strong>on</strong>g>e durati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e delivery <str<strong>on</strong>g>of</str<strong>on</strong>g> a stimulus and <str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>se.<br />

In neurosciences, it is <str<strong>on</strong>g>of</str<strong>on</strong>g> interest to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e first-spike latency, i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

intertime between <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>set <str<strong>on</strong>g>of</str<strong>on</strong>g> a stimulus and <str<strong>on</strong>g>th</str<strong>on</strong>g>e first-resp<strong>on</strong>se spike. However,<br />

when sp<strong>on</strong>taneous activity is observed, <str<strong>on</strong>g>th</str<strong>on</strong>g>is task becomes more complicated. To<br />

deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is problem, we apply <str<strong>on</strong>g>th</str<strong>on</strong>g>e statistical me<str<strong>on</strong>g>th</str<strong>on</strong>g>od introduced recently by Lansky<br />

et al. [1]. Some preliminary analysis <strong>on</strong> real data as well as some <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical<br />

results <strong>on</strong> Wiener processes are here presented.<br />

References.<br />

[1] P. Lansky et al. (2010), First-spike latency in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> sp<strong>on</strong>taneous activity, Neural<br />

Computati<strong>on</strong> 22, 1675–1697.<br />

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Developmental Biology; Saturday, July 2, 11:00<br />

S<str<strong>on</strong>g>of</str<strong>on</strong>g>ia Tapani<br />

Dep. <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Statistics,<br />

Chalmers University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology and Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg University<br />

e-mail: s<str<strong>on</strong>g>of</str<strong>on</strong>g>ia.tapani@chalmers.se<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> pr<strong>on</strong>uclei migrati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

mammalian egg<br />

At <str<strong>on</strong>g>th</str<strong>on</strong>g>is time it remains unanswered how <str<strong>on</strong>g>th</str<strong>on</strong>g>e embry<strong>on</strong>ic-abembry<strong>on</strong>ic axis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

mouse blastocyst is first established. Cell-fate is flexible in <str<strong>on</strong>g>th</str<strong>on</strong>g>e sense <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

development can recover from perturbati<strong>on</strong>s. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e early mouse embryo is<br />

not merely a uniform ball. The cells show some preferences for adopting certain<br />

positi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at will in turn govern <str<strong>on</strong>g>th</str<strong>on</strong>g>eir developmental decisi<strong>on</strong>s. Our main questi<strong>on</strong><br />

is: When are <str<strong>on</strong>g>th</str<strong>on</strong>g>ese preferences established? Cell-fates could be decided completely<br />

at random but it is also possible <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese decisi<strong>on</strong>s are guided by even as early<br />

c<strong>on</strong>tributing factors as <str<strong>on</strong>g>th</str<strong>on</strong>g>e first cleavage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e egg. The orientati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e opposing<br />

pr<strong>on</strong>uclei plays most likely a decisive role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e polarity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e developing embryo.<br />

Earlier studies <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mouse embryo development show deviating results <str<strong>on</strong>g>of</str<strong>on</strong>g> when<br />

patterning is initiated in <str<strong>on</strong>g>th</str<strong>on</strong>g>e egg, [1]-[4], [6], [7]. Some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese studies <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>clude<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e pattern formati<strong>on</strong> starts later in <str<strong>on</strong>g>th</str<strong>on</strong>g>e embryo have however been c<strong>on</strong>ducted<br />

in 2D. We <str<strong>on</strong>g>th</str<strong>on</strong>g>ink it is important to see <str<strong>on</strong>g>th</str<strong>on</strong>g>is as a <str<strong>on</strong>g>th</str<strong>on</strong>g>ree dimensi<strong>on</strong>al problem to reduce<br />

bias in <str<strong>on</strong>g>th</str<strong>on</strong>g>e results. The purpose <str<strong>on</strong>g>of</str<strong>on</strong>g> introducing our model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong> is to<br />

easier visualize <str<strong>on</strong>g>th</str<strong>on</strong>g>e fertilizati<strong>on</strong> process to answer <str<strong>on</strong>g>th</str<strong>on</strong>g>ese questi<strong>on</strong>s. The usefulness<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong> is not <strong>on</strong>ly a case for visualizati<strong>on</strong>, but<br />

could also be used to predict outcomes by simulating different scenarios, such as<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e point <str<strong>on</strong>g>of</str<strong>on</strong>g> sperm entry. Also, values <str<strong>on</strong>g>of</str<strong>on</strong>g> model parameters can<br />

be used to quantify <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> standard treatment or measurements <str<strong>on</strong>g>of</str<strong>on</strong>g> fertilized<br />

eggs in <str<strong>on</strong>g>th</str<strong>on</strong>g>e lab. From <str<strong>on</strong>g>th</str<strong>on</strong>g>e model we can make simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong> process<br />

and plot <str<strong>on</strong>g>th</str<strong>on</strong>g>e meeting positi<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e pr<strong>on</strong>uclei. As data we use stacks <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>focal<br />

microscopy time-lapse images <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pr<strong>on</strong>uclei migrati<strong>on</strong>, and realistic parameters in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e models are identified by statistical me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods. Given different distances between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e sperm entry and <str<strong>on</strong>g>th</str<strong>on</strong>g>e positi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d polar body, <str<strong>on</strong>g>th</str<strong>on</strong>g>e estimated models are<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>en used to produce distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> orientati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e meeting plane between <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

pr<strong>on</strong>uclei. Parameter values corresp<strong>on</strong>ding to <str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese forces are estimated<br />

from data <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> eggs treated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a microtubule inhibitor and untreated eggs.<br />

The centralizati<strong>on</strong> force is modelled by two mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> pushing and pulling <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e microtubule exerted forces. The model is essentially based <strong>on</strong> two forces <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

attracti<strong>on</strong>, a general migrati<strong>on</strong> directed towards <str<strong>on</strong>g>th</str<strong>on</strong>g>e centre <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell, and a sec<strong>on</strong>d<br />

attracti<strong>on</strong> force towards <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er pr<strong>on</strong>ucleus. From <str<strong>on</strong>g>th</str<strong>on</strong>g>is we have for example an<br />

indicati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e pulling mechanism is more significant <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>e pushing.<br />

References.<br />

[1] Hiiragi, T., Solter, D. , (2005). Mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> first cleavage specificati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mouse egg. Is<br />

our body plan set at day 0? Cell Cycle 4 661–664.<br />

[2] Motosugi, N., Bauer, T., Polanski, Z., Solter, D., Hiiragi, T. (2005). Polarity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mouse<br />

embryo is established at blastocyst and is not prepatterned Genes Dev. 19 1081–1092.<br />

954

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[3] Plusa B, Hadjant<strong>on</strong>akis AK, Gray D, Piotrowska-Nitsche K, Jedrusik A, Papaioannou VE,<br />

Glover DM, Zernicka-Goetz M, (2005). The first cleavage <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mouse zygote predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

blastocyst axis. Nature 434 391–5.<br />

[4] Schatten G., D<strong>on</strong>ovan P., (2004). Embryology: Plane talk Nature 430 301–2.<br />

[5] Tapani, S., Udagawa, J., Plusa, B., Zernicka-Goetz, M., Lundh, T., (2008). Three dimensi<strong>on</strong>al<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> pr<strong>on</strong>uclei migrati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e mouse. <str<strong>on</strong>g>European</str<strong>on</strong>g> C<strong>on</strong>gress <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Stereology and Image Analysis, Nor<str<strong>on</strong>g>th</str<strong>on</strong>g> America.<br />

[6] Zernicka-Goetz M. (2006). The first cell-fate decisi<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mouse embryo: destiny is a<br />

matter <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> chance and choice. Curr Opin Genet Dev. 16(4) 406–12.<br />

[7] Zernicka-Goetz M. (2005). Developmental cell biology: cleavage pattern and emerging asymmetry<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mouse embryo. Nat Rev Mol Cell Biol. 6 919–28.<br />

955

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemic models: Networks and stochasticity II; Thursday, June 30, 11:30<br />

Michael Taylor<br />

Universuty <str<strong>on</strong>g>of</str<strong>on</strong>g> Sussex<br />

e-mail: mt264@sussex.ac.uk<br />

From Markovian to pairwise epidemic models and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

performance <str<strong>on</strong>g>of</str<strong>on</strong>g> moment closure approximati<strong>on</strong>s<br />

Many if not all models <str<strong>on</strong>g>of</str<strong>on</strong>g> disease transmissi<strong>on</strong> <strong>on</strong> networks can be linked to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

exact state-based Markovian formulati<strong>on</strong>. However <str<strong>on</strong>g>th</str<strong>on</strong>g>e large number <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s<br />

for any system <str<strong>on</strong>g>of</str<strong>on</strong>g> realistic size limits <str<strong>on</strong>g>th</str<strong>on</strong>g>eir applicability to small populati<strong>on</strong>s. As<br />

a result, most modelling work relies <strong>on</strong> simulati<strong>on</strong> and pairwise models. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

paper, for a simple SIS dynamics <strong>on</strong> an arbitrary network, we formalise <str<strong>on</strong>g>th</str<strong>on</strong>g>e link<br />

between a well known pairwise model and <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact Markovian formulati<strong>on</strong>. This<br />

involves <str<strong>on</strong>g>th</str<strong>on</strong>g>e rigorous derivati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact ODE model at <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> pairs in<br />

terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e expected number <str<strong>on</strong>g>of</str<strong>on</strong>g> pairs and triples. The exact system is <str<strong>on</strong>g>th</str<strong>on</strong>g>en closed<br />

using two different closures, <strong>on</strong>e well established and <strong>on</strong>e <str<strong>on</strong>g>th</str<strong>on</strong>g>at has been recently<br />

proposed. A new interpretati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> closures is presented, which explains several<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir previously observed properties. The closed dynamical systems are solved<br />

numerically and <str<strong>on</strong>g>th</str<strong>on</strong>g>e results are compared to output from individual-based stochastic<br />

simulati<strong>on</strong>s. This is d<strong>on</strong>e for a range <str<strong>on</strong>g>of</str<strong>on</strong>g> networks wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same average degree and<br />

clustering coefficient but generated using different algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms. It is shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

ability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e pairwise system to accurately model an epidemic is fundamentally<br />

dependent <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying large-scale network structure. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

existing pairwise models are a good t for certain types <str<strong>on</strong>g>of</str<strong>on</strong>g> network but have to<br />

be used wi<str<strong>on</strong>g>th</str<strong>on</strong>g> cauti<strong>on</strong> as higher-order network structures may compromise <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

effectiveness.<br />

956

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Mickael Teixeira Alves<br />

UR880 - URIH / INRA Sophia Antipolis FRANCE<br />

e-mail: mteixeira@sophia.inra.fr<br />

Ludovic Mailleret<br />

UR880 - URIH / INRA Sophia Antipolis FRANCE<br />

e-mail: ludovic.mailleret@sophia.inra.fr<br />

Frédéric Grognard<br />

BIOCORE / INRIA Sophia Antipolis FRANCE<br />

e-mail: frederic.grognard@inria.fr<br />

Populati<strong>on</strong> Dynamics; Tuesday, June 28, 14:30<br />

Optimal foraging predators in Leslie Gower models wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

alternative prey<br />

Optimal foraging <str<strong>on</strong>g>th</str<strong>on</strong>g>eory defines <str<strong>on</strong>g>th</str<strong>on</strong>g>e diet choice <str<strong>on</strong>g>of</str<strong>on</strong>g> a predator by imposing <str<strong>on</strong>g>th</str<strong>on</strong>g>at it<br />

chooses <str<strong>on</strong>g>th</str<strong>on</strong>g>e prey <str<strong>on</strong>g>th</str<strong>on</strong>g>at is instantaneously <str<strong>on</strong>g>th</str<strong>on</strong>g>e most beneficial for him [1]. It has been<br />

shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is phenomen<strong>on</strong> leads to a switching diet and to <str<strong>on</strong>g>th</str<strong>on</strong>g>e persistence <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

prey and predators in generalized Lokta-Volterra models [2, 3]. This framework can<br />

be useful to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> an introduced alternative prey <strong>on</strong> a <strong>on</strong>e-prey<strong>on</strong>e-predator<br />

system. In a Lokta-Volterra model, <str<strong>on</strong>g>th</str<strong>on</strong>g>is introducti<strong>on</strong> can enhance<br />

predator grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and have negative effects <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e main prey, which is called apparent<br />

competiti<strong>on</strong> [4].<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, we focus <strong>on</strong> a Leslie-Gower model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> two dynamic prey, where<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e preyed populati<strong>on</strong> determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e carrying capacity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e predator populati<strong>on</strong>.<br />

Optimal foraging aiming at <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e per capita grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

predator populati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>en leads to <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> its instantaneous carrying<br />

capacity. This optimizati<strong>on</strong> defines two main regi<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> state space,<br />

separated by a dividing plane, and <str<strong>on</strong>g>th</str<strong>on</strong>g>us <str<strong>on</strong>g>th</str<strong>on</strong>g>ree diet strategies. The predator populati<strong>on</strong><br />

will have <str<strong>on</strong>g>th</str<strong>on</strong>g>e choice between eating <strong>on</strong>ly <str<strong>on</strong>g>th</str<strong>on</strong>g>e main prey, or <strong>on</strong>ly <str<strong>on</strong>g>th</str<strong>on</strong>g>e alternative<br />

prey, or following a mixed diet. In each <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese <str<strong>on</strong>g>th</str<strong>on</strong>g>ree regi<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics which<br />

are relevant to <str<strong>on</strong>g>th</str<strong>on</strong>g>e predator reduce to a Leslie-Gower model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a stable positive<br />

equilibrium.<br />

Depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system, different global behaviors arise.<br />

However, in all cases, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is <strong>on</strong>ly a single positive stable equilibrium, which can<br />

potentially lie <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dividing plane; <str<strong>on</strong>g>th</str<strong>on</strong>g>e equilibrium is such <str<strong>on</strong>g>th</str<strong>on</strong>g>at its predator populati<strong>on</strong><br />

is larger or equal <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>at in <str<strong>on</strong>g>th</str<strong>on</strong>g>e absence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e alternative prey. Also,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> an alternative prey is never detrimental to <str<strong>on</strong>g>th</str<strong>on</strong>g>e main prey; so <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

apparent competiti<strong>on</strong> does not hold.<br />

References.<br />

[1] W. W. Murdoch, Switching in General Predators: Experiments <strong>on</strong> Predator Specificity and<br />

Stability <str<strong>on</strong>g>of</str<strong>on</strong>g> Prey Populati<strong>on</strong>s Ecological M<strong>on</strong>ographs 1969 335–354.<br />

[2] M. van Baalen, V. Krivan, P. C.J. van Rijn and M. W. Sabelis, Alternative food, switching<br />

predators, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e persistence <str<strong>on</strong>g>of</str<strong>on</strong>g> predator-prey systems. The American Naturalist 2001 512–<br />

524.<br />

[3] V. Krivan and J. Eisner, Optimal Foraging and predator-prey dynamics III Theoretical Populati<strong>on</strong><br />

Biology 2003 269–279.<br />

[4] R. D. Holt, Predati<strong>on</strong>, Apparent Competiti<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Structure <str<strong>on</strong>g>of</str<strong>on</strong>g> Prey Communities Theoretical<br />

Populati<strong>on</strong> Biology 1977 197–229.<br />

957

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Atsushi Tero<br />

Kyusyu University<br />

e-mail: tero.atsushi@gmail.com<br />

Toshiyuki Nakagaki<br />

Future University Hakodate<br />

Ryo Kobayashi<br />

Hiroshima University<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Adaptive Network <str<strong>on</strong>g>of</str<strong>on</strong>g> True Slime Mold<br />

We describe here a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptive dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> a transport<br />

network <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e true slime mold Physarum polycephalum, an amoeboid organism<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at exhibits pa<str<strong>on</strong>g>th</str<strong>on</strong>g>-finding behavior in a maze. This organism possesses a network<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tubular elements, by means <str<strong>on</strong>g>of</str<strong>on</strong>g> which nutrients and signals circulate <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Physarum. When <str<strong>on</strong>g>th</str<strong>on</strong>g>e organism is put in a maze, <str<strong>on</strong>g>th</str<strong>on</strong>g>e network changes its shape<br />

to c<strong>on</strong>nect two exits by <str<strong>on</strong>g>th</str<strong>on</strong>g>e shortest pa<str<strong>on</strong>g>th</str<strong>on</strong>g>. By reproducing <str<strong>on</strong>g>th</str<strong>on</strong>g>is phenomen<strong>on</strong> we<br />

introduce new me<str<strong>on</strong>g>th</str<strong>on</strong>g>od to solve shortest pa<str<strong>on</strong>g>th</str<strong>on</strong>g> problem. In additi<strong>on</strong>, Physarum<br />

makes various optimal network for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>. It is similar to<br />

human transportati<strong>on</strong> network. We will talk about <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Physarum which can apply to various adaptive network.<br />

References.<br />

[1] A. Tero, S. Takagi, T. Saigusa, K. Ito, D. P. Bebber, M. D. Fricker, K. Yumiki, R. Kobayashi,<br />

T. Nakagaki, Rules for Biologically Inspired Adaptive Network Design. Science 2010/1/22 Vol.<br />

327, No.5964 P.439-442<br />

[2] A. Tero, R. Kobayashi, T. Nakagaki, A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for adaptive transport network<br />

in pa<str<strong>on</strong>g>th</str<strong>on</strong>g> finding by <str<strong>on</strong>g>th</str<strong>on</strong>g>e true slime mold. J. Theor. Biol, ELSEVIER 244(2007)553-564<br />

958

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

B and T cell immune resp<strong>on</strong>ses; Wednesday, June 29, 11:00<br />

Emmanuelle Terry<br />

Institut Camille Jordan, UMR CNRS 5208, Université Claude Bernard<br />

Ly<strong>on</strong> 1, 21 avenue Claude Bernard, 69622 Villeurbanne Cedex, France;<br />

INRIA Team Dracula, INRIA Center Grenoble Rhône-Alpes<br />

e-mail: terry@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.univ-ly<strong>on</strong>1.fr<br />

Modelling CD8 T-Cell Immune Resp<strong>on</strong>se<br />

This work has been made in collaborati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Christophe Arpin (IN-<br />

SERM U851, Ly<strong>on</strong>), Fabien Crauste (Univ. Ly<strong>on</strong> 1), Clarisse Dubois<br />

(INSERM U851, Ly<strong>on</strong>), Olivier Gandrill<strong>on</strong> (Univ. Ly<strong>on</strong> 1), Stéphane<br />

Genieys (Univ. Ly<strong>on</strong> 1), Isabelle Lemercier (INSERM U851, Ly<strong>on</strong>),<br />

Jacqueline Marvel (INSERM U851, Ly<strong>on</strong>)<br />

The primary CD8 T-cell resp<strong>on</strong>se, due to a first encounter wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen,<br />

happens in two phases: an expansi<strong>on</strong> phase, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a fast increase <str<strong>on</strong>g>of</str<strong>on</strong>g> T-cell count,<br />

followed by a c<strong>on</strong>tracti<strong>on</strong> phase. This c<strong>on</strong>tracti<strong>on</strong> phase is followed by <str<strong>on</strong>g>th</str<strong>on</strong>g>e generati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> memory cells. These latter are specific <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e antigen and will allow a<br />

faster and str<strong>on</strong>ger resp<strong>on</strong>se when encountering <str<strong>on</strong>g>th</str<strong>on</strong>g>e antigen for <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d time.<br />

Several works recently proposed models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e CD8 immune resp<strong>on</strong>se [1, 2, 3, 4].<br />

Some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese works do not c<strong>on</strong>sider any regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune resp<strong>on</strong>se [1, 2,<br />

4], whereas o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers propose very detailed and complex models [3].<br />

We will present two models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e primary resp<strong>on</strong>se, in which n<strong>on</strong>linearities account<br />

for molecular regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell dynamics. The first <strong>on</strong>e, inspired by [2], is<br />

based <strong>on</strong> ordinary differential equati<strong>on</strong>s. The sec<strong>on</strong>d <strong>on</strong>e, inspired by [1], is based<br />

<strong>on</strong> partial delay differential equati<strong>on</strong>s, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e delay takes into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e time<br />

cells take to differentiate from <strong>on</strong>e state to <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er <strong>on</strong>e. We will discuss in particular<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e roles and relevance <str<strong>on</strong>g>of</str<strong>on</strong>g> feedback c<strong>on</strong>trols <str<strong>on</strong>g>th</str<strong>on</strong>g>at could regulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e resp<strong>on</strong>se.<br />

Then, we will show some simulati<strong>on</strong>s we can get from <str<strong>on</strong>g>th</str<strong>on</strong>g>e models and c<strong>on</strong>fr<strong>on</strong>t <str<strong>on</strong>g>th</str<strong>on</strong>g>em<br />

to experimental data. Finally, we will c<strong>on</strong>sider <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem at <str<strong>on</strong>g>th</str<strong>on</strong>g>e molecular scale,<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a model describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e network <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular regulati<strong>on</strong>s in a T-cell during <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

immune resp<strong>on</strong>se.<br />

References.<br />

[1] R. Antia, V.V. Ganusov and R. Ahmed, The role <str<strong>on</strong>g>of</str<strong>on</strong>g> models in understanding CD8+ T-cell<br />

memory Nature Reviews 5 101–111.<br />

[2] R.J. De Boer, M. Oprea, R. Antia, K. Murali-Krishna, R. Ahmed and A.S. Perels<strong>on</strong>, Recruitment<br />

Times, Proliferati<strong>on</strong>, and Apoptosis Rates during <str<strong>on</strong>g>th</str<strong>on</strong>g>e CD8 T-Cell Resp<strong>on</strong>se to<br />

Lymphocytic Choriomeningitis Virus J. Virology 75 10663–10669.<br />

[3] P.S. Kim, P.P. Lee and D. Levy, Modeling regulati<strong>on</strong> mechanisms in <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune system J.<br />

Theor. Biol. 246 33–69.<br />

[4] I.M. Rouzine, K. Murali-Krishna and R. Ahmed, Generals die in friendly fire, or modeling<br />

immune resp<strong>on</strong>se to HIV J. Computati<strong>on</strong>al and Appl. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. 184 258–274.<br />

959

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Jeremy Thibodeaux<br />

Loyola University New Orleans<br />

e-mail: <str<strong>on</strong>g>th</str<strong>on</strong>g>ibodea@loyno.edu<br />

Timo<str<strong>on</strong>g>th</str<strong>on</strong>g>y P. Schlittenhardt<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Central Oklahoma<br />

Populati<strong>on</strong> Dynamics; Wednesday, June 29, 14:30<br />

Optimal Treatment Strategies for Malaria Infecti<strong>on</strong><br />

We develop a numerical me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for estimating optimal parameters in a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-host dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> malaria infecti<strong>on</strong>. The model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a quasilinear system <str<strong>on</strong>g>of</str<strong>on</strong>g> partial differential equati<strong>on</strong>s. We present several numerical<br />

simulati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at periodic treatments <str<strong>on</strong>g>th</str<strong>on</strong>g>at are in synchr<strong>on</strong>izati<strong>on</strong><br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e periodic bursting rate <str<strong>on</strong>g>of</str<strong>on</strong>g> infected ery<str<strong>on</strong>g>th</str<strong>on</strong>g>rocytes are <str<strong>on</strong>g>th</str<strong>on</strong>g>e most productive<br />

strategies.<br />

960

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Semigroups <str<strong>on</strong>g>of</str<strong>on</strong>g> Operators in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology I; Wednesday, June 29, 08:30<br />

Horst Thieme<br />

Ariz<strong>on</strong>a State University<br />

e-mail: <str<strong>on</strong>g>th</str<strong>on</strong>g>ieme@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.asu.edu<br />

Iterative approximati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spectral radius <str<strong>on</strong>g>of</str<strong>on</strong>g> a positive<br />

operator<br />

In populati<strong>on</strong> models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> infinite dimensi<strong>on</strong>al structure, <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic reproducti<strong>on</strong><br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g>ten is <str<strong>on</strong>g>th</str<strong>on</strong>g>e spectral radius <str<strong>on</strong>g>of</str<strong>on</strong>g> an appropriate positive linear operator <strong>on</strong> an<br />

infinite-dimensi<strong>on</strong>al ordered Banach space. This operator is called next generati<strong>on</strong><br />

operator in case a biological interpretati<strong>on</strong> is available. Since a closed expressi<strong>on</strong> for<br />

its spectral radius can <strong>on</strong>ly be obtained in special cases, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is renewed interest<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e approximati<strong>on</strong> and estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spectral radius. Quite a few results are<br />

available in <str<strong>on</strong>g>th</str<strong>on</strong>g>e operator <str<strong>on</strong>g>th</str<strong>on</strong>g>eory and and computati<strong>on</strong>al/numerical literature. It is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e purpose <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk to review some <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese and give <str<strong>on</strong>g>th</str<strong>on</strong>g>em a new twist.<br />

961

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bioimaging; Tuesday, June 28, 11:00<br />

K<strong>on</strong>stantin Thierbach<br />

Institute for Medical Informatics and Biometry , Medical Faculty<br />

Carl Gustav Carus, Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: k<strong>on</strong>stantin.phil@googlemail.com<br />

Nico Scherf<br />

IMB, Medical Faculty, Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Ingmar Glauche<br />

IMB, Medical Faculty, Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Ingo Roeder<br />

IMB, Medical Faculty, Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> variati<strong>on</strong>al shape models in single cell<br />

tracking<br />

The analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> single cells provides valuable insights into ex vivo cell assays. This<br />

is achieved by taking time series <str<strong>on</strong>g>of</str<strong>on</strong>g> images <str<strong>on</strong>g>of</str<strong>on</strong>g> cell cultures and analyzing <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e individual cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to migrati<strong>on</strong>, divisi<strong>on</strong>, mitosis and cell-cell<br />

interacti<strong>on</strong>.<br />

However, due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e large amount <str<strong>on</strong>g>of</str<strong>on</strong>g> data complete manual rec<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cell trajectories is not feasible, which indicates a urgent need for automated<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods. As computerized approaches lack <str<strong>on</strong>g>th</str<strong>on</strong>g>e highly optimized features <str<strong>on</strong>g>of</str<strong>on</strong>g> human<br />

percepti<strong>on</strong>, it is especially <str<strong>on</strong>g>th</str<strong>on</strong>g>e reliability <str<strong>on</strong>g>of</str<strong>on</strong>g> cell detecti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e tracking in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

presence <str<strong>on</strong>g>of</str<strong>on</strong>g> object occlusi<strong>on</strong> and large displacements between single images which<br />

represent <str<strong>on</strong>g>th</str<strong>on</strong>g>e major difficulties for individual cell tracking.<br />

We present an essentially novel approach to mitigate <str<strong>on</strong>g>th</str<strong>on</strong>g>ese problems using recently<br />

developed me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods in image processing incorporating prior shape knowledge<br />

into <str<strong>on</strong>g>th</str<strong>on</strong>g>e detecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> objects. In particular, <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> object occlusi<strong>on</strong>s and<br />

blurry object outlines due to noise in <str<strong>on</strong>g>th</str<strong>on</strong>g>e data can be handled by <str<strong>on</strong>g>th</str<strong>on</strong>g>is extensi<strong>on</strong>. We<br />

adapted <str<strong>on</strong>g>th</str<strong>on</strong>g>e active c<strong>on</strong>tour framework wi<str<strong>on</strong>g>th</str<strong>on</strong>g> prior shape informati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> robust cell detecti<strong>on</strong>. The me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is able to detect cell shapes more accurately<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>us allows for <str<strong>on</strong>g>th</str<strong>on</strong>g>e utilizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> refined tracking algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms using more robust<br />

object features for <str<strong>on</strong>g>th</str<strong>on</strong>g>e mapping <str<strong>on</strong>g>of</str<strong>on</strong>g> cells between images. We fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er present a direct<br />

applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e active c<strong>on</strong>tour models to <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint detecti<strong>on</strong> and tracking <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

moving, deformable cells.<br />

962

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Stochastic models in computati<strong>on</strong>al neuroscience I; Wednesday, June 29, 14:30<br />

Michele Thieullen<br />

Universite Pierre et Marie Curie<br />

e-mail: michele.<str<strong>on</strong>g>th</str<strong>on</strong>g>ieullen@upmc.jussieu.fr<br />

Piecewise Deterministic Markov Processes and detailed<br />

neur<strong>on</strong> models.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I will introduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e family <str<strong>on</strong>g>of</str<strong>on</strong>g> Piecewise Deterministic Markov Processes.<br />

Systems described by <str<strong>on</strong>g>th</str<strong>on</strong>g>ese processes undergo deterministic evoluti<strong>on</strong> <strong>on</strong><br />

random intervals. I will present some results about <str<strong>on</strong>g>th</str<strong>on</strong>g>ese processes including limit<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eorems and diffusi<strong>on</strong> approximati<strong>on</strong>. Models <str<strong>on</strong>g>of</str<strong>on</strong>g> neur<strong>on</strong>s taking into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

stochasticity <str<strong>on</strong>g>of</str<strong>on</strong>g> i<strong>on</strong> channels make a natural example.<br />

963

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Bi<str<strong>on</strong>g>of</str<strong>on</strong>g>luids, Solute Transport, and Hemodynamics; Wednesday, June 29, 11:00<br />

S. Randall Thomas<br />

IR4M UMR8081 CNRS, France<br />

e-mail: stephen-randall.<str<strong>on</strong>g>th</str<strong>on</strong>g>omas@u-psud.fr<br />

Robert G. Moss<br />

IR4M UMR8081 CNRS, France<br />

Thibault Grosse<br />

IR4M UMR8081 CNRS, France<br />

François Gueyffier<br />

Université Ly<strong>on</strong> 1; CNRS, UMR 5558; INSERM, CIC 201; Service de<br />

Pharmacologie Clinique, L. Pradel Hospital, Ly<strong>on</strong>, France<br />

Na<str<strong>on</strong>g>th</str<strong>on</strong>g>alie Lassau<br />

IR4M UMR8081 CNRS, France<br />

Patrick Hannaert<br />

Inserm U927, CHU La Milétrie, Poitiers, France<br />

Towards integrative multiscale models <str<strong>on</strong>g>of</str<strong>on</strong>g> whole kidney<br />

structure and functi<strong>on</strong><br />

Existing models <str<strong>on</strong>g>of</str<strong>on</strong>g> renal functi<strong>on</strong> have generally focused <strong>on</strong> open questi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> ’local’<br />

(i.e., intrarenal) physiology ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an <strong>on</strong> providing an overall descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

renal functi<strong>on</strong> relevant to its role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e body and incorporating sufficient detail<br />

to address <str<strong>on</strong>g>th</str<strong>on</strong>g>e roles <str<strong>on</strong>g>of</str<strong>on</strong>g> transporters and channels in each nephr<strong>on</strong> segment We will<br />

present our current efforts towards a multi-organ systems model <str<strong>on</strong>g>of</str<strong>on</strong>g> blood pressure<br />

regulati<strong>on</strong>. The resulting open-source platform will be oriented towards interactive<br />

explorati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> targeted pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ologies and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir pharmacology. Our approach will<br />

be: (1) to complete an integrated endocrine/paracrine RAAS (renin-angiotensinaldoster<strong>on</strong>e<br />

system) model, (2) to build a whole-kidney model representing essential<br />

nephrovascular relati<strong>on</strong>ships in <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ree kidney z<strong>on</strong>es and operati<strong>on</strong>al descripti<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> specific transport processes in each nephr<strong>on</strong> segment and to build up a multinephr<strong>on</strong><br />

model capable <str<strong>on</strong>g>of</str<strong>on</strong>g> addressing progressive renal failure, (3) to combine <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

renal and RAAS models in our modular core-model (based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e classic Guyt<strong>on</strong><br />

model), (4) to calibrate and validate <str<strong>on</strong>g>th</str<strong>on</strong>g>e models <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> pre-clinical and<br />

clinical data related to physiological and pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ological c<strong>on</strong>diti<strong>on</strong>s, and finally (5)<br />

to produce a large populati<strong>on</strong> (>100 000) <str<strong>on</strong>g>of</str<strong>on</strong>g> ’virtual individuals’ wi<str<strong>on</strong>g>th</str<strong>on</strong>g> randomized<br />

model parameters (analogous to genetic polymorphisms) for comparis<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> data<br />

from cohorts <str<strong>on</strong>g>of</str<strong>on</strong>g> real patients from our partner clinicians (and published clinical<br />

trials). These new tools, based <strong>on</strong> virtual physiopa<str<strong>on</strong>g>th</str<strong>on</strong>g>ological models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e kidney<br />

and RAAS, will be useful to investigate dysfuncti<strong>on</strong>s at <str<strong>on</strong>g>th</str<strong>on</strong>g>e clinical level as well as<br />

at <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> scientific research and educati<strong>on</strong>.<br />

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling V; Saturday, July 2, 11:00<br />

Ruediger Thul<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Nottingham<br />

e-mail: ruediger.<str<strong>on</strong>g>th</str<strong>on</strong>g>ul@nottingham.ac.uk<br />

Calcium alternans in a piecewise linear model <str<strong>on</strong>g>of</str<strong>on</strong>g> cardiac<br />

myocytes<br />

Cardiac alternans is a beat-to-beat alternati<strong>on</strong> in acti<strong>on</strong> potential durati<strong>on</strong> and<br />

intracellular calcium cycling seen in cardiac myocytes under rapid pacing <str<strong>on</strong>g>th</str<strong>on</strong>g>at is<br />

believed to be a precursor to fibrillati<strong>on</strong>. The cellular mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e coupling between cellular calcium and voltage dynamics have been extensively<br />

studied leading to <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> a class <str<strong>on</strong>g>of</str<strong>on</strong>g> physiologically detailed<br />

models, which are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten expressed as coupled n<strong>on</strong>linear differential equati<strong>on</strong>s. Here<br />

we establish <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e key dynamical behaviours <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model developed by Shiferaw<br />

and Karma are arranged around a set <str<strong>on</strong>g>of</str<strong>on</strong>g> switches. Exploiting <str<strong>on</strong>g>th</str<strong>on</strong>g>is observati<strong>on</strong> we<br />

show <str<strong>on</strong>g>th</str<strong>on</strong>g>at a piecewise linear caricature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Shiferaw-Karma model can be c<strong>on</strong>structed<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at preserves <str<strong>on</strong>g>th</str<strong>on</strong>g>e physiological interpretati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e original model whilst<br />

being amenable to a systematic ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis. We compute <str<strong>on</strong>g>th</str<strong>on</strong>g>e properties<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> periodic orbits wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out approximati<strong>on</strong> and show <str<strong>on</strong>g>th</str<strong>on</strong>g>at alternans emerge via a<br />

period-doubling instability. We also dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at when coupled to a spatially<br />

extended descripti<strong>on</strong> for calcium transport <str<strong>on</strong>g>th</str<strong>on</strong>g>e model supports spatially varying<br />

patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> alternans. We analyse <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>set <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is instability wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a generalisati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e master stability approach to accommodate <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>-smoo<str<strong>on</strong>g>th</str<strong>on</strong>g> nature <str<strong>on</strong>g>of</str<strong>on</strong>g> our<br />

system.<br />

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling V; Saturday, July 2, 11:00<br />

Kevin Thurley<br />

Max-Delbrück-Center Berlin<br />

e-mail: kevin.<str<strong>on</strong>g>th</str<strong>on</strong>g>urley@mdc-berlin.de<br />

Martin Falcke<br />

Max-Delbrück-Center Berlin<br />

Hierachic stochastic modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> intracellular Ca(2+)<br />

signals - a new c<strong>on</strong>cept based <strong>on</strong> emergent behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

biomolecules<br />

Biological systems <str<strong>on</strong>g>of</str<strong>on</strong>g>ten exhibit complex spatio-temporal dynamics and are stochastic<br />

at <str<strong>on</strong>g>th</str<strong>on</strong>g>e same time. That is a challenge for ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling, since<br />

standard techniques <str<strong>on</strong>g>th</str<strong>on</strong>g>en ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er apply rude assumpti<strong>on</strong>s like mean-field <str<strong>on</strong>g>th</str<strong>on</strong>g>eories, or<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ey lead to astr<strong>on</strong>omic numbers <str<strong>on</strong>g>of</str<strong>on</strong>g> system states. As a new c<strong>on</strong>cept, we formulate<br />

a <str<strong>on</strong>g>th</str<strong>on</strong>g>eory in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> interevent interval distributi<strong>on</strong>s describing mesoscopic cluster<br />

states.<br />

Here we c<strong>on</strong>sider intracellular Ca(2+) dynamics, where channel clusters are<br />

known to evoke local Ca(2+) release events <str<strong>on</strong>g>th</str<strong>on</strong>g>at eventually induce cellular c<strong>on</strong>centrati<strong>on</strong><br />

spikes by diffusive coupling. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e new modeling framework<br />

can potentially also be applied to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er systems c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled clusters <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

biomolecules, like T cell receptor clusters or chemotaxis. Describing system dynamics<br />

in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> probability distributi<strong>on</strong>s instead <str<strong>on</strong>g>of</str<strong>on</strong>g> rate-laws implies <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

model becomes n<strong>on</strong>-Markovian, but it has <str<strong>on</strong>g>th</str<strong>on</strong>g>e advantage <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e shape <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

distributi<strong>on</strong>s reflects <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscopic dynamics wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out c<strong>on</strong>sidering <str<strong>on</strong>g>th</str<strong>on</strong>g>em in detail.<br />

Moreover, probability distributi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> cluster state-changes can <str<strong>on</strong>g>of</str<strong>on</strong>g>ten be measured<br />

in vivo or calculated from known c<strong>on</strong>straints, in c<strong>on</strong>trast to kinetic parameters <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

state-changes <str<strong>on</strong>g>of</str<strong>on</strong>g> individual proteins.<br />

Despite <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er complicated integral equati<strong>on</strong>s appearing in <str<strong>on</strong>g>th</str<strong>on</strong>g>e complete<br />

descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics, we arrive at simple expressi<strong>on</strong>s for stati<strong>on</strong>ary statistics<br />

at regular cluster arrangements, and stochastic simulati<strong>on</strong>s run quite efficiently.<br />

For Ca(2+) dynamics, we verify data input and output by fluorescence microscopy<br />

in HEK cells and <str<strong>on</strong>g>th</str<strong>on</strong>g>us provide str<strong>on</strong>g support for <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed stochastic model.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we find valuable robustness properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic mechanism,<br />

which might be <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reas<strong>on</strong>s for ubiquity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ca(2+) signalling toolkit in<br />

cell signalling.<br />

Publicati<strong>on</strong>s: Thurley and Falcke, PNAS 108:427-32 (2011); Thul, Thurley and<br />

Falcke, Chaos 19:037108 (2009).<br />

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Cell and Tissue Biophysics; Thursday, June 30, 11:30<br />

Sara Tiburtius<br />

TU Darmstadt<br />

e-mail: tiburtius@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematik.tu-darmstadt.de<br />

Quentin Grimal<br />

Laboratoire d’Imagerie Paramétrique, Université Paris 6<br />

e-mail: quentin.grimal@upmc.fr<br />

Ferenc Molnar<br />

Charité - Universitätsmedizin Berlin<br />

e-mail: ferenc-lajos.molnar@charite.de<br />

Kay Raum<br />

Charité - Universitätsmedizin Berlin<br />

e-mail: kay.raum@charite.de<br />

Alf Gerisch<br />

TU Darmstadt<br />

e-mail: gerisch@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematik.tu-darmstadt.de<br />

A multiscale model <str<strong>on</strong>g>of</str<strong>on</strong>g> mineralized fibril bundles - a<br />

homogenizati<strong>on</strong> approach<br />

Modeling complex biological tissues like musculoskeletal mineralized tissues (e.g<br />

b<strong>on</strong>e or tend<strong>on</strong>) is a challenging task. These tissues are characterized by <strong>on</strong>e comm<strong>on</strong><br />

building block, <str<strong>on</strong>g>th</str<strong>on</strong>g>e so called mineralized collagen fibril (MCF). Depending<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue type <str<strong>on</strong>g>th</str<strong>on</strong>g>e fibrils are organized in different pattern across many leng<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

scales. One important aim is to predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e elastic behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue at a coarser<br />

leng<str<strong>on</strong>g>th</str<strong>on</strong>g> scale (effective stiffness) based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure and <str<strong>on</strong>g>th</str<strong>on</strong>g>e material properties<br />

at a finer scale. This can be achieved using homogenizati<strong>on</strong>.<br />

Most homogenizati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e effective stiffness based <strong>on</strong> different<br />

structural assumpti<strong>on</strong>s at <str<strong>on</strong>g>th</str<strong>on</strong>g>e finer scale and achieve hence different estimates. The<br />

choice <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods is <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore a crucial part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model definiti<strong>on</strong>. We analyze<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g> different homogenizati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods, i.e. self-c<strong>on</strong>sistent me<str<strong>on</strong>g>th</str<strong>on</strong>g>od,<br />

Mori-Tanaka and asymptotic homogenizati<strong>on</strong>, <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e effective stiffness estimates<br />

using a simple collagen-mineral material. Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese results we build up a<br />

multiscale model for mineralized fibril bundles as present in mineralized tend<strong>on</strong>.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>ese fibril bundles <str<strong>on</strong>g>th</str<strong>on</strong>g>e MCFs are aligned in parallel and additi<strong>on</strong>al stiffness is<br />

achieved by extrafibrillar mineralizati<strong>on</strong>. We apply <str<strong>on</strong>g>th</str<strong>on</strong>g>is model to experimental data<br />

from circumferential tissue <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mineralized turkey leg tend<strong>on</strong> (MTLT) assessed<br />

by Scanning Acoustic Microscopy.<br />

Our stiffness estimates are in very good agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental data.<br />

The experimental studies <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e MTLT also revealed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is tissue exhibits (besides<br />

circumferential tissue) ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er fine structure: loosely packed fibril bundles<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> high porosity (interstitial tissue). Its specific porous structure needs to be<br />

incorporated in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er homogenizati<strong>on</strong> step.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Marcus Tindall<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Reading<br />

e-mail: m.tindall@reading.ac.uk<br />

B.S. Bhattacharya<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Reading<br />

P.K. Sweby<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Reading<br />

A. Minihane<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> East Anglia<br />

K.G. Jacks<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Reading<br />

Cellular Systems Biology; Thursday, June 30, 11:30<br />

Genetic Regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cholesterol Biosyn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis<br />

The regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cholesterol producti<strong>on</strong> is fundamental to maintaining good human<br />

heal<str<strong>on</strong>g>th</str<strong>on</strong>g>. Sterol regulatory element binding protein (SREBP) is a key regulatory<br />

transcripti<strong>on</strong> factor for lipid syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we present a n<strong>on</strong>linear ordinary<br />

differential equati<strong>on</strong> model <str<strong>on</strong>g>of</str<strong>on</strong>g> SREBP transcripti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e HMGR<br />

cholesterol biosyn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way. SREBP transcripti<strong>on</strong> is regulated by forming an<br />

inactive complex wi<str<strong>on</strong>g>th</str<strong>on</strong>g> its end product, cholesterol, to c<strong>on</strong>trol homeostatic c<strong>on</strong>centrati<strong>on</strong><br />

levels <str<strong>on</strong>g>of</str<strong>on</strong>g> cholesterol wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical<br />

system <str<strong>on</strong>g>of</str<strong>on</strong>g> equati<strong>on</strong>s shows it admits <str<strong>on</strong>g>th</str<strong>on</strong>g>ree distinct types <str<strong>on</strong>g>of</str<strong>on</strong>g> behaviour: (i) oscillati<strong>on</strong>s<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mRNA, HMGR protein and cholesterol expressi<strong>on</strong> levels; (ii) oscillati<strong>on</strong>s in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e mRNA, HMGR protein and cholesterol expressi<strong>on</strong> levels which decay in time;<br />

and (iii) n<strong>on</strong>-oscillatory soluti<strong>on</strong>s. The number <str<strong>on</strong>g>of</str<strong>on</strong>g> binding sites between cholesterol<br />

and SREBP and SREBP and <str<strong>on</strong>g>th</str<strong>on</strong>g>e genes are shown to be crucial factors in determining<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e system behaviour. We discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sequences <str<strong>on</strong>g>of</str<strong>on</strong>g> our work and show how<br />

our results provide a receipe for syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic biology in <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>text <str<strong>on</strong>g>of</str<strong>on</strong>g> homeostasis.<br />

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Jaakko Toiv<strong>on</strong>en<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Helsinki<br />

e-mail: jaakko.toiv<strong>on</strong>en@helsinki.fi<br />

Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 14:30<br />

An adaptive trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f between seed size and germinati<strong>on</strong><br />

time<br />

I c<strong>on</strong>sider a model <str<strong>on</strong>g>of</str<strong>on</strong>g> an annual plant where seedlings compete for patches <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

are just big enough to support <strong>on</strong>e plant each. The seeds are characterized by two<br />

qualities, <str<strong>on</strong>g>th</str<strong>on</strong>g>eir size and <str<strong>on</strong>g>th</str<strong>on</strong>g>e time <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir germinati<strong>on</strong>. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> qualities affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e competitive<br />

ability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e seedlings: big seeds produce more competitive seedlings and<br />

early seedlings are more competitive <str<strong>on</strong>g>th</str<strong>on</strong>g>an seedlings <str<strong>on</strong>g>th</str<strong>on</strong>g>at emerge later. I do not assume<br />

any physiological trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f between seed size and germinati<strong>on</strong> time. However,<br />

I show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a Nash equilibrium strategy such <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere emerges never<str<strong>on</strong>g>th</str<strong>on</strong>g>eless<br />

a correlati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e two. If we assume a large resident populati<strong>on</strong> and<br />

an initially rare mutant populati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e Nash equilibrium is also an Evoluti<strong>on</strong>arily<br />

Stable Strategy (ESS).<br />

References.<br />

[1] Bishop, T.D. and Cannings, C. (1978) A generalized war <str<strong>on</strong>g>of</str<strong>on</strong>g> attriti<strong>on</strong> Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical<br />

Biology 70 85–124.<br />

[2] Geritz, S. A. H. (1995) Evoluti<strong>on</strong>ary stable seed polymorphism and small-scale spatial variati<strong>on</strong><br />

in seedling density The American Naturalist 146 685–707.<br />

[3] Maynard-Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>, J. (1974) The <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> games and <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> animal c<strong>on</strong>flicts Journal<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology 47 209–221.<br />

[4] Norden, N., Daws, M.I., Antoine, C., G<strong>on</strong>zalez, M.A., Garwood, N.C. and Chave, J. (2009)<br />

The relati<strong>on</strong>ship between seed mass and mean time to germinati<strong>on</strong> for 1037 tree species across<br />

five tropical forests Functi<strong>on</strong>al Ecology 23 203–210.<br />

[5] Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>, C. C. and Fretwell, S. D. (1974) The optimal balance between size and number <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g>fspring American Naturalist 108 499–506.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

C. Tokarski 1 , S. Hummert 1,2 , A. Schroeter 1 , S. Schuster 1<br />

1 Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioinformatics, Friedrich Schiller University Jena, Ernst-<br />

Abbe-Platz 2, D-07743 Jena<br />

2 Leibniz Institute for Natural Product Research and Infecti<strong>on</strong> Biology<br />

- Hans-Knöll-Institute (HKI), Beutenbergstr. 11a, D-07745 Jena<br />

e-mail: {christian.tokarski, sabine.hummert, an.schroeter, stefan.schu}<br />

@uni-jena.de<br />

Interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> opportunistic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenic fungi and human<br />

phagocytes: A multi-agent-based modeling approach<br />

The fungal pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen Aspergillus fumigatus causes severe systemic diseases in<br />

immunocompromised patients [1,2]. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>is fungus is found worldwide and<br />

its small c<strong>on</strong>idia are present in air and food [2] it is almost harmless to heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y<br />

people, since inhaled c<strong>on</strong>idia are phagocytosed by macrophages and neutrophil<br />

granulocytes [1]. However, nei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular dynamics, <str<strong>on</strong>g>th</str<strong>on</strong>g>e per-cell efficiency, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

outcome <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is interacti<strong>on</strong>, nor <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>mental impact <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is process are known<br />

[3]. Live imaging shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> phagocytes and fungal c<strong>on</strong>idia is a<br />

dynamic process <str<strong>on</strong>g>of</str<strong>on</strong>g> touching, dragging and phagocytosis [3].<br />

Using multi-agent-based modeling, <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> human neutrophil granulocytes<br />

and Aspergillus fumigatus are simulated to gain knowledge about different<br />

behavioral strategies by optimizing parameter settings such as velocity <str<strong>on</strong>g>of</str<strong>on</strong>g> cells,<br />

dragging and phagocytosis efficiency as well as movement directi<strong>on</strong>s. Behavior <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

simulated cells is compared to <str<strong>on</strong>g>th</str<strong>on</strong>g>ose <str<strong>on</strong>g>of</str<strong>on</strong>g> living cells in liquid cultures gained by live<br />

imaging data.<br />

Implemented in <str<strong>on</strong>g>th</str<strong>on</strong>g>e multi-agent modeling envir<strong>on</strong>ment NetLogo [4], neutrophil<br />

granulocytes and c<strong>on</strong>idia <str<strong>on</strong>g>of</str<strong>on</strong>g> Aspergillus fumigatus are modeled as distinct agents,<br />

whose individual behavior is determined by spatial settings, e. g., density <str<strong>on</strong>g>of</str<strong>on</strong>g> cells,<br />

communicati<strong>on</strong> between cells, individual states and is influenced by random effects.<br />

Moreover, chemotaxis and random movement <str<strong>on</strong>g>of</str<strong>on</strong>g> immune cells are compared to get<br />

insight into advantages in regard to phagocytosis efficiency.<br />

References.<br />

[1] Richards<strong>on</strong>, Changing patterns and trends in systemic fungal infecti<strong>on</strong>s. J Antimicrob<br />

Chemo<str<strong>on</strong>g>th</str<strong>on</strong>g>er 56 Suppl 1 i5–i11. 2005.<br />

[2] Karkowska-Kuleta et al., Fungi pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenic to humans: molecular bases <str<strong>on</strong>g>of</str<strong>on</strong>g> virulence <str<strong>on</strong>g>of</str<strong>on</strong>g> Candida<br />

albicans, Cryptococcus ne<str<strong>on</strong>g>of</str<strong>on</strong>g>ormans and Aspergillus fumigatus. Acta Biochim Pol 56 211–224.<br />

2009.<br />

[3] Behnsen et al., Envir<strong>on</strong>mental dimensi<strong>on</strong>ality c<strong>on</strong>trols <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> phagocytes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogenic fungi Aspergillus fumigatus and Candida albicans PLoS Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>og 3 e13. 2007.<br />

[4] Wilensky, NetLogo http://ccl.nor<str<strong>on</strong>g>th</str<strong>on</strong>g>western.edu/netlogo/. Center for C<strong>on</strong>nected Learning and<br />

Computer-Based Modeling, Nor<str<strong>on</strong>g>th</str<strong>on</strong>g>western University. Evanst<strong>on</strong>, IL. 1999.<br />

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Cell and Tissue Biophysics; Friday, July 1, 14:30<br />

Alina Toma<br />

Andreas Mang<br />

Tina A. Schütz<br />

Stefan Becker<br />

Thorsten M. Buzug<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Engineering, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Luebeck, Ratzeburger<br />

Allee 160, 23538 Lübeck, Germany<br />

e-mail: {toma,buzug}@imt.uni-luebeck.de<br />

Philipp-Niclas Pfenning, Wolfgang Wick<br />

Clinical Cooperati<strong>on</strong> Unit Neuro<strong>on</strong>cology, German Cancer Research<br />

Center Heidelberg and Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Neuro<strong>on</strong>cology, University<br />

Hospital Heidelberg, Germany<br />

A Nutrient-Quided Chemotaxis-Haptotaxis Approach for<br />

Modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e Invasi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Tumor Cells<br />

We propose a hybrid c<strong>on</strong>tinuum-discrete model to simulate nutrient-guided malignant<br />

brain tumor cell invasi<strong>on</strong>. The lattice-based spatio-temporal model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ree reacti<strong>on</strong>–diffusi<strong>on</strong> equati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at describe interacti<strong>on</strong>s between cancer cells,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular matrix (ECM) and nutrients. In additi<strong>on</strong> to random diffusi<strong>on</strong> and<br />

haptotactic movement, <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells is directed towards <str<strong>on</strong>g>th</str<strong>on</strong>g>e gradient<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusible nutrients as oxygen and glucose [3], which is referred to as<br />

chemotaxis. As for <str<strong>on</strong>g>th</str<strong>on</strong>g>e descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial migratory resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial<br />

cells to <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor angiogenic factors and <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular matrix macromolecule<br />

fibr<strong>on</strong>ectin [2], we model a system <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear partial differential equati<strong>on</strong>s. While<br />

[1] focuses <strong>on</strong> tumor cell adhesi<strong>on</strong>, we model bo<str<strong>on</strong>g>th</str<strong>on</strong>g>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e migrati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cells by <str<strong>on</strong>g>th</str<strong>on</strong>g>e ECM and, additi<strong>on</strong>ally, by <str<strong>on</strong>g>th</str<strong>on</strong>g>e attracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> higher nutrient<br />

c<strong>on</strong>centrati<strong>on</strong>s. Moreover, we assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at every cell is able to push a neighboring<br />

cell <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same size towards an empty site.<br />

Simulati<strong>on</strong> studies show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental invitro<br />

invasi<strong>on</strong> results as regards <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor interacting<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ECM. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>e flexibility <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model realizing<br />

simulati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> varying arrangements <str<strong>on</strong>g>of</str<strong>on</strong>g> nutrient delivering blood vessels.<br />

References.<br />

[1] A.R.A. Anders<strong>on</strong>, A hybrid ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> solid tumour invasi<strong>on</strong>: <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cell adhesi<strong>on</strong>, 2005 Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Med. and Biol. 22(2) 163–186.<br />

[2] A.R.A. Anders<strong>on</strong>, M.A.J. Chaplain, C<strong>on</strong>tinuous and Discrete Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Tumour-Induced Angiogenesis, 1998 Bull. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol. 60 857–899.<br />

[3] Y. Mansury, M. Kimura, J. Lobo, T.S. Deisboeck, Emerging Patterns in Tumor Systems:<br />

Simulating <str<strong>on</strong>g>th</str<strong>on</strong>g>e Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Multicellular Clusters wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an Agent-based Spatial Agglomerati<strong>on</strong><br />

Model, 2002 J. <str<strong>on</strong>g>th</str<strong>on</strong>g>eor. Biol. 219 343–370.<br />

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Stem cells and cancer; Wednesday, June 29, 14:30<br />

Cristian Tomasetti<br />

Harvard University & Dana-Farber Cancer Institute<br />

e-mail: cristian@jimmy.harvard.edu<br />

The role <str<strong>on</strong>g>of</str<strong>on</strong>g> symmetric and asymmetric divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer<br />

stem cells in developing drug resistance for various types <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Often, resistance to drugs is an obstacle to a successful treatment <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer. Many<br />

attempts to study drug resistance have been made in <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling<br />

literature. Clearly, in order to understand drug resistance, it is imperative to have a<br />

good model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells. One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e main ingredients<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at has been recently introduced into <str<strong>on</strong>g>th</str<strong>on</strong>g>e rapidly growing pool <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

cancer models is stem cells. Surprisingly, <str<strong>on</strong>g>th</str<strong>on</strong>g>is all-so-important subset <str<strong>on</strong>g>of</str<strong>on</strong>g> cells has<br />

not been fully integrated into existing ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> drug resistance. In<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is work we incorporate <str<strong>on</strong>g>th</str<strong>on</strong>g>e various possible ways in which a stem cell may divide<br />

into <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> drug resistance. We derive a new estimate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

developing drug resistance by <str<strong>on</strong>g>th</str<strong>on</strong>g>e time a tumor is detected, and calculate <str<strong>on</strong>g>th</str<strong>on</strong>g>e expected<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> resistant cancer stem cells at <str<strong>on</strong>g>th</str<strong>on</strong>g>e time <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor detecti<strong>on</strong>. We<br />

are also able to obtain analytical results for cases where <str<strong>on</strong>g>th</str<strong>on</strong>g>e average exp<strong>on</strong>ential<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer has been replaced by o<str<strong>on</strong>g>th</str<strong>on</strong>g>er, arguably more realistic types <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. Finally, to dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>e significance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach, we combine our<br />

new ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical estimates wi<str<strong>on</strong>g>th</str<strong>on</strong>g> clinical data to show <str<strong>on</strong>g>th</str<strong>on</strong>g>at leukemic stem cells<br />

must tend to renew symmetrically as opposed to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir heal<str<strong>on</strong>g>th</str<strong>on</strong>g>y counterparts <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

predominantly appear to divide asymmetrically. (Part <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is work is joint wi<str<strong>on</strong>g>th</str<strong>on</strong>g> D.<br />

Levy, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Maryland)<br />

References.<br />

[1] C. Tomasetti, On <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability <str<strong>on</strong>g>of</str<strong>on</strong>g> random genetic mutati<strong>on</strong>s for various types <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, submitted.<br />

[2] C. Tomasetti & D. Levy, Role <str<strong>on</strong>g>of</str<strong>on</strong>g> symmetric and asymmetric divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> stem cells in developing<br />

drug resistance, Proc Natl Acad Sci USA, 107(39):16766–16771.<br />

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Mechanical Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Movement and Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cells and Tissues II;<br />

Wednesday, June 29, 17:00<br />

Paweł Topa<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Geological Sciences, Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science, AGH University <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Technology<br />

e-mail: topa@agh.edu.pl<br />

Jarosław Tyszka<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Geological Science, Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

e-mail: ndtyszka@cyf-kr.edu.pl<br />

The particle-based model <str<strong>on</strong>g>of</str<strong>on</strong>g> foraminiferal morphogenesis<br />

Foraminifera are a large group <str<strong>on</strong>g>of</str<strong>on</strong>g> single cellular organisms. About 275,000<br />

species are recognized, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> living and fossil. They produce shells made <str<strong>on</strong>g>of</str<strong>on</strong>g> calcium<br />

carb<strong>on</strong>ate, agglutinated sediment grains and/or organic compounds. Shells<br />

are typically built from several chambers organized in very elaborated way. The<br />

questi<strong>on</strong> what govern <str<strong>on</strong>g>th</str<strong>on</strong>g>eir morphology to produce such great weal<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> forms was<br />

unanswered for decades. Early suggesti<strong>on</strong>s come from D’Arcy Thoms<strong>on</strong> (1919) who<br />

rec<strong>on</strong>gnised <str<strong>on</strong>g>th</str<strong>on</strong>g>at simple physical forces associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> fluid dynamics are resp<strong>on</strong>sible<br />

for cell morphogenesis. First <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical morphospace was defined over 40 year<br />

ago by Berger. His model included <strong>on</strong>ly simple geometrical operati<strong>on</strong> (rotati<strong>on</strong>,<br />

translati<strong>on</strong>) and produced simple spiral form. Subsequent models used a similar<br />

approach and were able reproduce <strong>on</strong>ly narrow group <str<strong>on</strong>g>of</str<strong>on</strong>g> forms.<br />

We showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at diversed shell patterns forms can be produced by using a simple<br />

optimizati<strong>on</strong> process. It is assumed <str<strong>on</strong>g>th</str<strong>on</strong>g>at foraminifera locally optimizes <str<strong>on</strong>g>th</str<strong>on</strong>g>e way <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

intracellular transport between <str<strong>on</strong>g>th</str<strong>on</strong>g>e chambers. When every new chamber is formed,<br />

a new aperture is located at <str<strong>on</strong>g>th</str<strong>on</strong>g>e shortest distance from <str<strong>on</strong>g>th</str<strong>on</strong>g>e previous aperture. This<br />

simple formula produced several diversed forms. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model works well<br />

<strong>on</strong>ly for spheroidal chambers, it does not work for o<str<strong>on</strong>g>th</str<strong>on</strong>g>er shapes <str<strong>on</strong>g>of</str<strong>on</strong>g> chambers.<br />

The next stage in research <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> foraminiferal shells is to build a<br />

low-level emergent model <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be able explained why “local optimizati<strong>on</strong> rule”<br />

was so accurate. We are searching for a model <str<strong>on</strong>g>of</str<strong>on</strong>g> processes <str<strong>on</strong>g>th</str<strong>on</strong>g>at occur just before a<br />

new chamber is formed. Foraminifera create a “bubble” <str<strong>on</strong>g>of</str<strong>on</strong>g> cytoplasm attached to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

shell which is mineralized preserving its shape. The ”bubble” is not <strong>on</strong>ly deformed<br />

by external factors but mainly by internal organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong>. We<br />

want to reflect <str<strong>on</strong>g>th</str<strong>on</strong>g>is processes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e computer model and present its impact <strong>on</strong> final<br />

shapes <str<strong>on</strong>g>of</str<strong>on</strong>g> chambers. The cytoplasmic ”bubble” is sourrounded by <str<strong>on</strong>g>th</str<strong>on</strong>g>in membrane<br />

made <str<strong>on</strong>g>of</str<strong>on</strong>g> lipid bilayer.<br />

Lipid bilayer is an example <str<strong>on</strong>g>of</str<strong>on</strong>g> complex fluid phenomena so we employed <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

DPD (Dissipative Particle Dynamics) me<str<strong>on</strong>g>th</str<strong>on</strong>g>od. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is simulati<strong>on</strong> technique a set<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> interacting particles is c<strong>on</strong>sidered and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir time evoluti<strong>on</strong> is governed by Newt<strong>on</strong>’s<br />

equati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> moti<strong>on</strong>. In our model lipid bilayer is modelled by two types <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

DPD particles: “A” which reflects hydrophilic heads and “B” for hydrophobic tails.<br />

Additi<strong>on</strong>al two types <str<strong>on</strong>g>of</str<strong>on</strong>g> particles denote extracellular fluid (water) and intracellular<br />

fluid (cytoplasm). Particles “A” and “B” are arranged into chained amphiphilic<br />

molecules by establishing c<strong>on</strong>stant “spring” c<strong>on</strong>necti<strong>on</strong>s. In order to avoid bending<br />

in chains <str<strong>on</strong>g>of</str<strong>on</strong>g> particles we apply force <str<strong>on</strong>g>th</str<strong>on</strong>g>at streighten each triplet <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>nected “A”<br />

973

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and “B“ particles. Depending <strong>on</strong> types <str<strong>on</strong>g>of</str<strong>on</strong>g> particles <str<strong>on</strong>g>th</str<strong>on</strong>g>at interact in pair we choose<br />

different potentials <str<strong>on</strong>g>of</str<strong>on</strong>g> interacti<strong>on</strong>. In our simulati<strong>on</strong> we study <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

planar membranes affected by external forces.<br />

Acknowldgements This research is supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Polish Ministry <str<strong>on</strong>g>of</str<strong>on</strong>g> Science<br />

and Higher Educati<strong>on</strong>, project no. 0573/B/P01/2008/34.<br />

References.<br />

[1] J. Tyszka, P. Topa, A new approach to modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> morphogenesis <str<strong>on</strong>g>of</str<strong>on</strong>g> foraminiferal shells,<br />

Paleobiology, vol. 31, nr 3, pp. 526-541, Pale<strong>on</strong>tological Society, 2005.<br />

[2] P. Topa, J. Tyszka, Local Minimizati<strong>on</strong> Paradigm in Numerical Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> Foraminiferal<br />

Shells, LNCS 2329, vol I, pp. 97-106, Springer-Verlag, 2002.<br />

[3] L. Gao, J. Shilcock, R. Lipowsky, Improved dissipative particle dynamics simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> lipid<br />

bilayers, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Chemical Physics 126, 2007.<br />

[4] S. Yamamoto, Y. Maruyama, Sh. Hyodo, Dissipative particle dynamics study <str<strong>on</strong>g>of</str<strong>on</strong>g> sp<strong>on</strong>tanous<br />

vesicle formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> amphiphilic molecules, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Chemical Physics, vol. 116, no. 13,<br />

2002.<br />

974

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Nadine Töpfer<br />

Zoran Nikoloski<br />

Systems Biology and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling<br />

Max-Planck-Institute for Molecular Plant Physiology<br />

Am Mühlenberg 1<br />

14476 Potsdam, Germany<br />

e-mail: toepfer@mpimp-golm.mpg.de<br />

e-mail: nikoloski@mpimp-golm.mpg.de<br />

Time-resolved integrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Flux Balance Analysis,<br />

Elementary Flux Modes, and transcriptomics data for<br />

characterizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e temporal metabolic resp<strong>on</strong>se to<br />

temperature stress in S. cerevisiae<br />

The increased availability <str<strong>on</strong>g>of</str<strong>on</strong>g> large-scale metabolic network models and <str<strong>on</strong>g>th</str<strong>on</strong>g>e improved<br />

quality <str<strong>on</strong>g>of</str<strong>on</strong>g> high-<str<strong>on</strong>g>th</str<strong>on</strong>g>roughput data provide <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis for system-wide network<br />

analysis. Flux Balance Analysis (FBA) [2] and its extensi<strong>on</strong>s have been successfully<br />

applied to determine steady-state systemic characteristics from <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>stituent elements.<br />

In additi<strong>on</strong>, FBA has recently been extended to facilitate <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

transient behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic networks. While FBA-based me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods, due to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical programming formulati<strong>on</strong>, can readily be applied to large-scale metabolic<br />

networks, <str<strong>on</strong>g>th</str<strong>on</strong>g>e applicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> approaches relying <strong>on</strong> Elementary Flux Modes<br />

(EFMs) [1] is hindered by large computati<strong>on</strong>al demands. Here we address <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> time-resolved integrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> FBA and EFMs based <strong>on</strong> transcriptomics data<br />

capturing <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic networks to stress c<strong>on</strong>diti<strong>on</strong>s.<br />

Our approach integrates time-resolved transcriptomics data wi<str<strong>on</strong>g>th</str<strong>on</strong>g> large-scale<br />

metabolic networks to identify active subnetworks by using a novel FBA-based<br />

optimizati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od. To perform <str<strong>on</strong>g>th</str<strong>on</strong>g>e integrati<strong>on</strong>, <str<strong>on</strong>g>th</str<strong>on</strong>g>e results from a statistical<br />

analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> differential gene expressi<strong>on</strong>, translated into carefully tailored weights, are<br />

employed to extract temporal subnetworks <str<strong>on</strong>g>th</str<strong>on</strong>g>at not <strong>on</strong>ly show significant changes<br />

in expressi<strong>on</strong> values in resp<strong>on</strong>se to stress c<strong>on</strong>diti<strong>on</strong>s, but also represent a minimal<br />

subset <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole metabolic network. We present <str<strong>on</strong>g>th</str<strong>on</strong>g>ree possible ways in which<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e extracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> such minimal active temporal subnetworks can be achieved. The<br />

found subnetworks are <str<strong>on</strong>g>th</str<strong>on</strong>g>en used to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> EFMs for each time point,<br />

reflecting <str<strong>on</strong>g>th</str<strong>on</strong>g>e temporal stress resp<strong>on</strong>se. We show empirically <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e objective <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

minimality allows <str<strong>on</strong>g>th</str<strong>on</strong>g>e identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> all EFMs for each time point in a feasible<br />

time frame. Finally, <str<strong>on</strong>g>th</str<strong>on</strong>g>e sets <str<strong>on</strong>g>of</str<strong>on</strong>g> EFMs are used in a comparative analysis based <strong>on</strong><br />

set-similarity measures to identify putative transiti<strong>on</strong>s.<br />

We apply <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed approach to time-resolved transcriptomics data sets<br />

from temperature shock experiments in S. cerevisiae. The results dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

FBA-based optimizati<strong>on</strong> approaches can be used in c<strong>on</strong>juncti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> EFMs-based<br />

analysis and high-<str<strong>on</strong>g>th</str<strong>on</strong>g>roughput data to reveal <str<strong>on</strong>g>th</str<strong>on</strong>g>e temporal behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> large-scale<br />

networks in an integrative and systematic manner.<br />

References.<br />

[1] C. Trinh, A. Wlaschin, F. Srienc, Elementary mode analysis: a useful metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way<br />

analysis tool for characterizing cellular metabolism. Applied Microbiology and Biotechnology<br />

81 (5) 813–826.<br />

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[2] J. Or<str<strong>on</strong>g>th</str<strong>on</strong>g>, I. Thiele, B. Palss<strong>on</strong>, What is flux balance analysis? Nature Biotechnology 28 (3)<br />

245–248.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Crowd Dynamics: Modeling, Analysis and Simulati<strong>on</strong> (Part 1); Wednesday,<br />

June 29, 11:00<br />

Andrea Tosin<br />

INDAM-Compagnia di San Paolo postdoctoral fellow<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Politecnico di Torino – Torino, Italy<br />

e-mail: andrea.tosin@polito.it<br />

A multiscale look at crowd dynamics by time-evolving<br />

measures<br />

The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> particle-like living systems, such as human crowds, are mainly<br />

ruled by mutual interacti<strong>on</strong>s am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e individuals. This is because <str<strong>on</strong>g>th</str<strong>on</strong>g>e latter have<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e ability to express different behavioral strategies depending <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

o<str<strong>on</strong>g>th</str<strong>on</strong>g>er individuals in <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment. For instance, pedestrians heading for a certain<br />

destinati<strong>on</strong> deviate from <str<strong>on</strong>g>th</str<strong>on</strong>g>eir preferred pa<str<strong>on</strong>g>th</str<strong>on</strong>g>s when encountering o<str<strong>on</strong>g>th</str<strong>on</strong>g>er pedestrians.<br />

Remarkably, interacti<strong>on</strong>s are usually n<strong>on</strong>-cooperative, i.e., walkers do not pursue a<br />

goal collectively.<br />

Due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e intrinsic granularity (discreteness) <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system (<str<strong>on</strong>g>th</str<strong>on</strong>g>e number N <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

pedestrians is possibly large, yet <str<strong>on</strong>g>th</str<strong>on</strong>g>e approximati<strong>on</strong> N → ∞ may not be acceptable),<br />

interacti<strong>on</strong>s are better described at an individual-based level. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

hand, an ensemble representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e crowd is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten preferable over an agentbased<br />

<strong>on</strong>e, in order to catch <str<strong>on</strong>g>th</str<strong>on</strong>g>e average group behavior sp<strong>on</strong>taneously emerging<br />

from interacti<strong>on</strong>s (self-organizati<strong>on</strong>) and also in view <str<strong>on</strong>g>of</str<strong>on</strong>g> fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er analysis, numerics,<br />

and optimizati<strong>on</strong> issues. Measure-<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretic stochastic approaches, such as <str<strong>on</strong>g>th</str<strong>on</strong>g>ose<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at will be discussed in <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, <str<strong>on</strong>g>of</str<strong>on</strong>g>fer useful c<strong>on</strong>ceptual tools to <str<strong>on</strong>g>th</str<strong>on</strong>g>is purpose.<br />

Indeed, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey make possible an Eulerian particle-free representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e crowd,<br />

in which single pedestrians are blurred into <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir<br />

spatial positi<strong>on</strong>s. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e same time, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey allow <str<strong>on</strong>g>th</str<strong>on</strong>g>e descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s<br />

to stem from (stochastic) individual-based reas<strong>on</strong>ings. Finally, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey enable <strong>on</strong>e to<br />

treat discrete and c<strong>on</strong>tinuous models under a comm<strong>on</strong> framework, as well as to<br />

deduce models at intermediate scales wi<str<strong>on</strong>g>th</str<strong>on</strong>g> interesting implicati<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e predicted<br />

dynamics.<br />

References.<br />

[1] L. Bruno, A. Tosin, P. Tricerri, F. Venuti. N<strong>on</strong>-local first-order modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> crowd dynamics:<br />

A multidimensi<strong>on</strong>al framework wi<str<strong>on</strong>g>th</str<strong>on</strong>g> applicati<strong>on</strong>s, Appl. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Model., 35, 426–445, 2011.<br />

[2] E. Cristiani, B. Piccoli, A. Tosin. Multiscale modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> granular flows wi<str<strong>on</strong>g>th</str<strong>on</strong>g> applicati<strong>on</strong> to<br />

crowd dynamics, Multiscale Model. Simul., 9, 155–182, 2011.<br />

[3] B. Piccoli, A. Tosin. Time-evolving measures and macroscopic modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> pedestrian flow,<br />

Arch. Rati<strong>on</strong>. Mech. Anal., 199, 707–738, 2011.<br />

[4] A. Tosin, P. Frasca. Existence and approximati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> probability measure soluti<strong>on</strong>s to models<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> collective behaviors, Netw. Heterog. Media, 2011 (to appear).<br />

[5] E. Cristiani, B. Piccoli, A. Tosin. Modeling self-organizati<strong>on</strong> in pedestrians and animal groups<br />

from macroscopic and microscopic viewpoints, in G. Naldi, L. Pareschi, G. Toscani (Eds.),<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> Collective Behavior in Socio-Ec<strong>on</strong>omic and Life Sciences, 337–364,<br />

Brikäuser, 2010.<br />

[6] B. Piccoli, A. Tosin. Pedestrian flows in bounded domains wi<str<strong>on</strong>g>th</str<strong>on</strong>g> obstacles, C<strong>on</strong>tin. Mech. Termodyn.,<br />

21, 85–107, 2009.<br />

977

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Suzanne Touzeau<br />

UR341 MIA, INRA, F-78350 Jouy-en-Josas, France<br />

e-mail: Suzanne.Touzeau@jouy.inra.fr<br />

Caroline Bidot<br />

UR341 MIA, INRA, F-78350 Jouy-en-Josas, France<br />

e-mail: Caroline.Bidot@jouy.inra.fr<br />

Epidemics; Wednesday, June 29, 17:00<br />

Estimating scrapie epidemiological parameters: comparis<strong>on</strong><br />

between a populati<strong>on</strong> dynamic model and an<br />

individual-based model<br />

Classical scrapie is a transmissible sp<strong>on</strong>giform encephalopa<str<strong>on</strong>g>th</str<strong>on</strong>g>y <str<strong>on</strong>g>th</str<strong>on</strong>g>at affects small<br />

ruminants (pri<strong>on</strong> disease) and is submitted to eradicati<strong>on</strong> measures. Transmissi<strong>on</strong><br />

mechanisms are still incompletely understood and difficult to quantify. Scrapie is<br />

characterised in sheep by a genetic susceptibility factor. Its l<strong>on</strong>g infectious and undetectable<br />

incubati<strong>on</strong> period makes direct data analyses difficult, hence <str<strong>on</strong>g>th</str<strong>on</strong>g>e interest<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a modelling approach to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemiological parameters.<br />

Two models were developed to represent <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a<br />

sheep flock: a realistic structured populati<strong>on</strong> model (PDE) and an individual-based<br />

model. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> take into account <str<strong>on</strong>g>th</str<strong>on</strong>g>e same epidemiological processes, based <strong>on</strong> similar<br />

assumpti<strong>on</strong>s, including seas<strong>on</strong>ality in transmissi<strong>on</strong>, genetic and age-dependent<br />

susceptibilities, l<strong>on</strong>g and variable incubati<strong>on</strong> periods. To focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemiological parameters, demographic processes c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> seas<strong>on</strong>al lambings,<br />

routine culling and reform, directly derive from <str<strong>on</strong>g>th</str<strong>on</strong>g>e flock data. The data used<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>is study originate from <str<strong>on</strong>g>th</str<strong>on</strong>g>e Langlade experimental sheep flock (SAGA, INRA,<br />

Toulouse, France), in which a natural scrapie outbreak occured.<br />

The criteri<strong>on</strong> implemented to estimate <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemiological parameters is based<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e scrapie incidence observed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Langlade data and simulated by <str<strong>on</strong>g>th</str<strong>on</strong>g>e two<br />

models. As <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are quite many parameters to estimate (23, <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be reduced<br />

to 11 wi<str<strong>on</strong>g>th</str<strong>on</strong>g> simplifying assumpti<strong>on</strong>s), an optimisati<strong>on</strong> me<str<strong>on</strong>g>th</str<strong>on</strong>g>od based <strong>on</strong> a randomsearch<br />

minimisati<strong>on</strong> algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m was chosen.<br />

The parameter values obtained for bo<str<strong>on</strong>g>th</str<strong>on</strong>g> models are comparable and realistic,<br />

i.e. c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g> what is known from <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease and expert opini<strong>on</strong>. The<br />

robustness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese results was tested by a sensitivity analysis, which showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

some parameters are highly sensitive and need to be identified wi<str<strong>on</strong>g>th</str<strong>on</strong>g> care.<br />

978

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Hiroshi Toyoizumi<br />

Waseda University<br />

e-mail: toyoizumi@waseda.jp<br />

Jeremy Field<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sussex<br />

e-mail: j.field@sussex.ac.uk<br />

Populati<strong>on</strong> Dynamics; Thursday, June 30, 11:30<br />

The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> social queues<br />

A wide variety <str<strong>on</strong>g>of</str<strong>on</strong>g> animals are known to form simple hierarchical groups called<br />

social queues, where individuals inherit resources or social status in a predictable<br />

order. Queues are <str<strong>on</strong>g>of</str<strong>on</strong>g>ten age-based, so <str<strong>on</strong>g>th</str<strong>on</strong>g>at a new individual joins <str<strong>on</strong>g>th</str<strong>on</strong>g>e end <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

queue <strong>on</strong> reaching adul<str<strong>on</strong>g>th</str<strong>on</strong>g>ood, and must wait for older individuals to die in order<br />

to reach <str<strong>on</strong>g>th</str<strong>on</strong>g>e fr<strong>on</strong>t <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e queue. While waiting, an individual may work for her<br />

group, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g>ten risking her own survival and hence her chance <str<strong>on</strong>g>of</str<strong>on</strong>g> inheritance.<br />

Eventually, she may survive to reach <str<strong>on</strong>g>th</str<strong>on</strong>g>e head <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e queue and becomes<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e dominant <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e group. Queueing has been particularly well-studied in hover<br />

wasps (Hymenoptera: Stenogastrinae). In hover wasp social groups, <strong>on</strong>ly <strong>on</strong>e female<br />

lays eggs, and <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a strict, age-based queue to inherit <str<strong>on</strong>g>th</str<strong>on</strong>g>e reproductive<br />

positi<strong>on</strong>. While <str<strong>on</strong>g>th</str<strong>on</strong>g>e dominant individual (queen) c<strong>on</strong>centrates <strong>on</strong> breeding, subordinate<br />

helpers risk dea<str<strong>on</strong>g>th</str<strong>on</strong>g> by foraging outside <str<strong>on</strong>g>th</str<strong>on</strong>g>e nest, but have a slim chance<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> eventually inheriting dominance. Some explanati<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>is altruistic behavior<br />

and for <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability <str<strong>on</strong>g>of</str<strong>on</strong>g> social queues have been proposed and analyzed [1, 2]. Since<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e productivity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nest and <str<strong>on</strong>g>th</str<strong>on</strong>g>e chance to inherit <str<strong>on</strong>g>th</str<strong>on</strong>g>e dominant positi<strong>on</strong><br />

depend critically <strong>on</strong> group size, queueing dynamics are crucial for understanding<br />

social queues, but detailed analysis is lacking. Here, using hover wasps as an example,<br />

we dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at some basic queueing <str<strong>on</strong>g>th</str<strong>on</strong>g>eory[3] and n<strong>on</strong>-homogeneous<br />

bir<str<strong>on</strong>g>th</str<strong>on</strong>g> and dea<str<strong>on</strong>g>th</str<strong>on</strong>g> processes are useful for analyzing queueing dynamics and <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong><br />

demographics <str<strong>on</strong>g>of</str<strong>on</strong>g> social queues. Our work leads to better understanding <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

how envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s and strategic decisi<strong>on</strong>-making by individuals interact<br />

to produce <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed group dynamics; and in turn, how group dynamics affects<br />

individual decisi<strong>on</strong>-making.<br />

References.<br />

[1] J. Field, A. Cr<strong>on</strong>in, and C. Bridge. Future fitness and helping in social queues. Nature, 441:214–<br />

217, 2006.<br />

[2] H. Kokko and R. A. Johnst<strong>on</strong>e. Social queuing in animal societies: a dynamic model <str<strong>on</strong>g>of</str<strong>on</strong>g> reproductive<br />

skew. Proc. R. Soc. L<strong>on</strong>d. B, 266:571–578, 1999.<br />

[3] H. Toyoizumi. Sample pa<str<strong>on</strong>g>th</str<strong>on</strong>g> analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tributi<strong>on</strong> and reward in cooperative groups. Journal<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology, 2008.<br />

979

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cancer; Saturday, July 2, 14:30<br />

Arne Traulsen<br />

Evoluti<strong>on</strong>ary Theory Group, Max Planck Institute for Evoluti<strong>on</strong>ary<br />

Biology, Plön, Germany<br />

e-mail: traulsen@evolbio.mpg.de<br />

Jorge M. Pacheco<br />

Departamento de Matemática e Aplicações, Universidade do Minho,Braga,<br />

Portugal<br />

David Dingli<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Hematology, Mayo Clinic, Rochester, MN, USA<br />

Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> blood diseases and <str<strong>on</strong>g>th</str<strong>on</strong>g>e hierarchy <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

hematopoiesis<br />

Hematopoiesis is a process <str<strong>on</strong>g>th</str<strong>on</strong>g>at is based <strong>on</strong> a hierarchical organizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell<br />

types, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> stem cells at <str<strong>on</strong>g>th</str<strong>on</strong>g>e very basis <str<strong>on</strong>g>th</str<strong>on</strong>g>at differentiate into more specialized<br />

cells. A simple ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>is process has been proposed<br />

[1]. This hierarchical structure has important effects <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> diseases,<br />

including blood cancers [2]. For example, it is becoming increasingly clear <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

our bodies harbor numerous mutant cl<strong>on</strong>es <str<strong>on</strong>g>th</str<strong>on</strong>g>at do not give rise to no disease at<br />

all, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutati<strong>on</strong>s are typically associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> diseases. The fate <str<strong>on</strong>g>of</str<strong>on</strong>g> any<br />

mutant cl<strong>on</strong>e will depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e target cell and <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fitness advantage, if any,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutati<strong>on</strong> c<strong>on</strong>fers <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell [3]. In general, we can expect <str<strong>on</strong>g>th</str<strong>on</strong>g>at <strong>on</strong>ly a<br />

mutati<strong>on</strong> in a hematopoietic stem cell will give l<strong>on</strong>g-term disease; <str<strong>on</strong>g>th</str<strong>on</strong>g>e same mutati<strong>on</strong><br />

taking place in a cell located more downstream may produce just a ripple in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

hematopoietic ocean [4].<br />

References.<br />

[1] D. Dingli, A. Traulsen, and J.M. Pacheco, Compartmental Architecture and Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Hematopoiesis PLoS One 4 345 (2007).<br />

[2] T. Lenaerts, J.M. Pacheco, A. Traulsen, and D. Dingli, Tyrosine kinase inhibitor <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy can<br />

cure chr<strong>on</strong>ic myeloid leukemia wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out hitting leukemic stem cells Haematologica 95, 900-907<br />

(2010).<br />

[3] A. Traulsen, J.M. Pacheco, D. Dingli, Reproductive fitness advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> BCR-ABL expressing<br />

leukemia cells, Cancer Letters 294 43-48 (2010).<br />

[4] A. Traulsen, J.M. Pacheco, L. Luzzatto, D. Dingli, Somatic mutati<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>e hierarchy <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

hematopoiesis, BioEssays 32 1003-1008 (2010).<br />

980

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling III; Wednesday, June 29,<br />

17:00<br />

Je-Chiang Tsai<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Nati<strong>on</strong>al Chung Cheng University, 168,<br />

University Road, Min-Hsiung, Chia-Yi 621, Taiwan<br />

e-mail: tsaijc@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ccu.edu.tw<br />

Traveling Waves in <str<strong>on</strong>g>th</str<strong>on</strong>g>e Buffered FitzHugh-Nagumo Model<br />

In many physiologically important excitable systems, such as intracellular calcium<br />

dynamics, <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusing variable is highly buffered. In additi<strong>on</strong>, all physiological<br />

buffered excitable systems c<strong>on</strong>tain multiple buffers, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different affinities.<br />

We will discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e properties <str<strong>on</strong>g>of</str<strong>on</strong>g> wave soluti<strong>on</strong>s in excitable systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multiple<br />

buffers, and how multiple buffers interact.<br />

981

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> Macromolecules and Molecular Aggregates;<br />

Saturday, July 2, 14:30<br />

Reidun Twarock<br />

York Centre for Complex Systems Analysis, University <str<strong>on</strong>g>of</str<strong>on</strong>g> York, UK<br />

e-mail: rt507@york.ac.uk<br />

Eric Dykeman<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> York<br />

Nick Grays<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> York<br />

Tom Keef<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> York<br />

Jess Wardman<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> York<br />

Neil Rans<strong>on</strong> and Peter Stockley<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Leeds<br />

Genome Organisati<strong>on</strong> and Assembly <str<strong>on</strong>g>of</str<strong>on</strong>g> RNA Viruses:<br />

Where Geometry Meets Functi<strong>on</strong><br />

Cryo-electr<strong>on</strong> microscopy and X-ray crystallography have revealed ordered features<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e genome organisati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a number <str<strong>on</strong>g>of</str<strong>on</strong>g> ssRNA viruses. These include a dodecahedral<br />

RNA cage in Pariacoto virus and a double-shell organisati<strong>on</strong> in bacteriophage<br />

MS2. We show here <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese ordered features are due to symmetry c<strong>on</strong>straints<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e overall organisati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese particles.<br />

We moreover show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical results can be used to better understand<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms underlying <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> (assembly) <str<strong>on</strong>g>of</str<strong>on</strong>g> viruses. In particular,<br />

we dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e geometric c<strong>on</strong>straints <strong>on</strong> genome organisati<strong>on</strong> result in a<br />

str<strong>on</strong>g reducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e combinatorially possible pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways <str<strong>on</strong>g>of</str<strong>on</strong>g> assembly and hence<br />

c<strong>on</strong>tribute to <str<strong>on</strong>g>th</str<strong>on</strong>g>e remarkable assembly efficiency <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese viruses. Since assembly<br />

efficiency is important for viruses in order to outcompete <str<strong>on</strong>g>th</str<strong>on</strong>g>eir hosts immune system,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese results provide important insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e strategies and mechanisms<br />

underlying <str<strong>on</strong>g>th</str<strong>on</strong>g>e viral infecti<strong>on</strong> process.<br />

References.<br />

[1] T. Keef, J. Wardman, N. A. Rans<strong>on</strong>, P.G. Stockley & R. Twarock (2010) Viruses measure up<br />

to ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical predicti<strong>on</strong> 3D Geometry imposes fundamental c<strong>on</strong>straints <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e structures<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> simple viruses, submitted to Current Biology<br />

[2] Twarock R, Keef T (2010) Viruses and geometry where symmetry meets functi<strong>on</strong>, Micobiology<br />

Today 37: 24-27.<br />

[3] Dykeman EC, Stockley PG, Twarock R (2010) Dynamic allostery c<strong>on</strong>trols coat protein c<strong>on</strong>former<br />

switching during MS2 phage assembly, J Mol. Biol. 395: 916-23<br />

[4] Dykeman EC, Twarock R (2010) All-atom normal-mode analysis reveals a dynamic RNAinduced<br />

allostery in a bacteriophage coat protein, Physical Review E. 81, 031908.<br />

[5] ElSawy KM, Caves L, Twarock R (2010) The impact <str<strong>on</strong>g>of</str<strong>on</strong>g> viral RNA <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e associati<strong>on</strong> rates <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

capsid protein assembly: bacteriophage MS2 as a case study, J. Mol. Biol. 400(4):935-47.<br />

[6] Victoria L. Mort<strong>on</strong>, Eric C. Dykeman, Nicola J. St<strong>on</strong>ehouse, Alis<strong>on</strong> E. Ashcr<str<strong>on</strong>g>of</str<strong>on</strong>g>t, Reidun<br />

Twarock and Peter G. Stockley (2010) The Impact <str<strong>on</strong>g>of</str<strong>on</strong>g> Viral RNA <strong>on</strong> Assembly Pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way Selecti<strong>on</strong>,<br />

J. Mol. Biol. 401(2):298-308.<br />

[7] E.C. Dykeman, N. Grays<strong>on</strong>, N. A. Rans<strong>on</strong>, P.G.Stockley & R. Twarock, Simple rules for<br />

efficient assembly predict <str<strong>on</strong>g>th</str<strong>on</strong>g>e layout <str<strong>on</strong>g>of</str<strong>on</strong>g> a packaged viral RNA (2011), to appear in J. Mol.<br />

Biol. (selected as research highlight)<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Z. Burda<br />

Jagiell<strong>on</strong>ian University, Marian Smoluchowski Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics<br />

and Mark Kac Complex System Research Center<br />

e-mail: zdzislaw.burda@uj.edu.pl<br />

J. Kornelsen<br />

Nati<strong>on</strong>al Research Council <str<strong>on</strong>g>of</str<strong>on</strong>g> Canada, Institute for Biodiagnostics,<br />

Winnipeg, Calgary, Canada<br />

e-mail: Jennifer.Kornelsen@nrc-cnrc.gc.ca<br />

M. A. Nowak<br />

Jagiell<strong>on</strong>ian University, Marian Smoluchowski Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics<br />

and Mark Kac Complex System Research Center<br />

e-mail: nowak@<str<strong>on</strong>g>th</str<strong>on</strong>g>.if.uj.edu.pl<br />

U. Sboto-Frankenstein<br />

Nati<strong>on</strong>al Research Council <str<strong>on</strong>g>of</str<strong>on</strong>g> Canada, Institute for Biodiagnostics,<br />

Winnipeg, Calgary, Canada<br />

e-mail: Uta.Sboto-Frankenstein@nrc-cnrc.gc.ca<br />

B. Tomanek<br />

Nati<strong>on</strong>al Research Council <str<strong>on</strong>g>of</str<strong>on</strong>g> Canada, Institute for Biodiagnostics,<br />

Winnipeg, Calgary, Canada<br />

e-mail: Boguslaw.Tomanek@nrc-cnrc.gc.ca<br />

J. Tyburczyk<br />

Jagiell<strong>on</strong>ian University, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics, Astr<strong>on</strong>omy and Applied<br />

Computer Science<br />

e-mail: jacek.tyburczyk@uj.edu.pl<br />

Random Matrix approach to fMRI data<br />

We apply random matrix techniques to analyse correlati<strong>on</strong>s in Human Brain<br />

fMRI data. We rec<strong>on</strong>struct correlati<strong>on</strong>s between different regi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> brain. These<br />

regi<strong>on</strong>s are selected ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er by purely geometrical voxel positi<strong>on</strong> or by physiological<br />

a classificati<strong>on</strong> given by Brodmann’s areas. We analyse spectral properties for<br />

covariance matrices and compare <str<strong>on</strong>g>th</str<strong>on</strong>g>e results to some classical results from random<br />

matrix <str<strong>on</strong>g>th</str<strong>on</strong>g>eory including Marcenko-Pastur eigenvalue density for Wishart matrices.<br />

These result provide us wi<str<strong>on</strong>g>th</str<strong>on</strong>g> reference points - a sort <str<strong>on</strong>g>of</str<strong>on</strong>g> a null hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis. We<br />

also perform graph <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> correlati<strong>on</strong> matrices applying ideas <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>reshold graphs. Such graphs are c<strong>on</strong>structed using <str<strong>on</strong>g>th</str<strong>on</strong>g>e idea <str<strong>on</strong>g>of</str<strong>on</strong>g> metric space <str<strong>on</strong>g>th</str<strong>on</strong>g>at is<br />

c<strong>on</strong>structed from <str<strong>on</strong>g>th</str<strong>on</strong>g>e correlati<strong>on</strong> matrix for <str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> vertices representing different<br />

voxels or Bordmann’s areas. A <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold graph is a graph between vertices whose<br />

distance in <str<strong>on</strong>g>th</str<strong>on</strong>g>is metric space is smaller <str<strong>on</strong>g>th</str<strong>on</strong>g>an a given <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold.<br />

983

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Michelle D. Leach 1∗ , Katarzyna Tyc 2∗ , Rebecca S. Shapiro 3 , Leah E.<br />

Cowen 3 , Edda Klipp 2 and Alistair J.P. Brown 1<br />

1. School <str<strong>on</strong>g>of</str<strong>on</strong>g> Medical Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Aberdeen, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Medical Sciences, Foresterhill, Aberdeen AB25 2ZD, United Kingdom;<br />

2. Theoretische Biophysik, Humboldt-Universität zu Berlin, Invalidenstraße<br />

42, 10115 Berlin, Germany; 3. Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Molecular<br />

Genetics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Tor<strong>on</strong>to, Tor<strong>on</strong>to, ON M5S 1A8, Canada<br />

e-mail: edda.klipp@rz.hu-berlin.de<br />

e-mail: al.brown@abdn.ac.uk<br />

Modelling <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ermal adaptati<strong>on</strong> by Hsf1 and<br />

Hsp90 in Candida albicans, a major fungal pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen <str<strong>on</strong>g>of</str<strong>on</strong>g> humans<br />

The heat shock resp<strong>on</strong>se is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e most highly c<strong>on</strong>served and well studied networks<br />

in eukaryotic cells. Up<strong>on</strong> sensing a sudden temperature upshift, <str<strong>on</strong>g>th</str<strong>on</strong>g>e heat<br />

shock transcripti<strong>on</strong> factor is rapidly activated, leading to <str<strong>on</strong>g>th</str<strong>on</strong>g>e inducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> numerous<br />

genes <str<strong>on</strong>g>th</str<strong>on</strong>g>at mediate <str<strong>on</strong>g>th</str<strong>on</strong>g>ermal adaptati<strong>on</strong>, including heat shock genes <str<strong>on</strong>g>th</str<strong>on</strong>g>at encode<br />

molecular chaper<strong>on</strong>es. We have shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e major fungal pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen <str<strong>on</strong>g>of</str<strong>on</strong>g> humans,<br />

Candida albicans, has retained a b<strong>on</strong>a fide heat shock resp<strong>on</strong>se even <str<strong>on</strong>g>th</str<strong>on</strong>g>ough it is<br />

obligatorily associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> warm blooded mammals [1]. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, <str<strong>on</strong>g>th</str<strong>on</strong>g>is <str<strong>on</strong>g>th</str<strong>on</strong>g>ermal<br />

adaptati<strong>on</strong> is essential for <str<strong>on</strong>g>th</str<strong>on</strong>g>e virulence <str<strong>on</strong>g>of</str<strong>on</strong>g> C. albicans. We have predicted <str<strong>on</strong>g>th</str<strong>on</strong>g>at interacti<strong>on</strong>s<br />

between Hsf1 and <str<strong>on</strong>g>th</str<strong>on</strong>g>e essential chaper<strong>on</strong>e Heat shock protein 90 (Hsp90)<br />

play critical roles in <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ermal adaptati<strong>on</strong> in C. albicans [2]. We<br />

have now tested <str<strong>on</strong>g>th</str<strong>on</strong>g>is predicti<strong>on</strong> using a combinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling and<br />

experimental dissecti<strong>on</strong>. Our model predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>at chr<strong>on</strong>ic exposure to heat leads to<br />

protein unfolding, which in turn sequesters Hsp90, <str<strong>on</strong>g>th</str<strong>on</strong>g>ereby releasing Hsf1 from inactive<br />

Hsp90-Hsf1 complexes. This allows Hsf1 to become activated leading to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

transcripti<strong>on</strong>al activati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> heat shock genes including HSP90. Our model, which<br />

predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamic molecular resp<strong>on</strong>ses <str<strong>on</strong>g>of</str<strong>on</strong>g> C. albicans wi<str<strong>on</strong>g>th</str<strong>on</strong>g> reas<strong>on</strong>able accuracy,<br />

has yielded a number <str<strong>on</strong>g>of</str<strong>on</strong>g> novel predicti<strong>on</strong>s. For example, Hsf1 activati<strong>on</strong> appears to<br />

be acutely sensitive to <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> unfolded proteins. Also, Hsp90 levels<br />

appear to be regulated at post-transcripti<strong>on</strong>al as well as transcripti<strong>on</strong>al levels. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore,<br />

our model provides an explanati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e observati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at C. albicans<br />

cells retain a ‘molecular memory’, rendering <str<strong>on</strong>g>th</str<strong>on</strong>g>em more resistant to subsequent heat<br />

shocks. Therefore our ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling has provided novel insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is evoluti<strong>on</strong>arily c<strong>on</strong>served envir<strong>on</strong>mental resp<strong>on</strong>se.<br />

References.<br />

[1] S. Nicholls, M.D. Leach, C.L. Priest, A.J. Brown, Role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heat shock transcripti<strong>on</strong> factor,<br />

Hsf1, in a major fungal pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen <str<strong>on</strong>g>th</str<strong>on</strong>g>at is obligately associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> warm-blooded animals Mol<br />

Microbiol. 74 844–61.<br />

[2] A.J. Brown, M.D. Leach, S. Nicholls, The relevance <str<strong>on</strong>g>of</str<strong>on</strong>g> heat shock regulati<strong>on</strong> in fungal pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogens<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> humans Virulence 1 330–2.<br />

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Regulatory Networks; Saturday, July 2, 11:00<br />

Elpida Tzafestas<br />

Cognitive Science Lab., Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Hist. & Philosophy <str<strong>on</strong>g>of</str<strong>on</strong>g> Science, Univ.<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> A<str<strong>on</strong>g>th</str<strong>on</strong>g>ens, GREECE<br />

e-mail: etzafestas@phs.uoa.gr<br />

Modeling horm<strong>on</strong>ally dependent genetic networks<br />

Usual approaches to regulatory genetic network modeling follow a feed-forward<br />

me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology, where <str<strong>on</strong>g>th</str<strong>on</strong>g>e network represents a black-box wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell. The operati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e black box is modeled as an input-output relati<strong>on</strong> and research tries<br />

to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e proper relati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at holds for several observed cases; <str<strong>on</strong>g>th</str<strong>on</strong>g>is relati<strong>on</strong><br />

may be expressed in various formalisms (typically boolean networks [1], but also<br />

Bayesian networks, etc.).<br />

Our proposal follows a developmental perspective and borrows <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretically<br />

from modern accounts <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene as an informati<strong>on</strong>-carrier and as a complex entity<br />

and c<strong>on</strong>cept [2-5]. These <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical developments bel<strong>on</strong>g to <str<strong>on</strong>g>th</str<strong>on</strong>g>e broad evo-devo<br />

trend and attempt to use <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene as a functi<strong>on</strong>al biological entity or as a developmental<br />

molecular process instead <str<strong>on</strong>g>of</str<strong>on</strong>g> a well-delimited structural entity encoding for<br />

a specific trait.<br />

Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>is <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical c<strong>on</strong>text, it is wor<str<strong>on</strong>g>th</str<strong>on</strong>g>while to study enhanced relati<strong>on</strong>s<br />

between genetic network and cellular behavior <str<strong>on</strong>g>th</str<strong>on</strong>g>at include c<strong>on</strong>trol in <str<strong>on</strong>g>th</str<strong>on</strong>g>e loop in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> memory : in regulatory networks wi<str<strong>on</strong>g>th</str<strong>on</strong>g> memory, subsequent activati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e same input vector will yield different output vectors, i.e.<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e transfer functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole network will be itself dynamic. From an external<br />

point <str<strong>on</strong>g>of</str<strong>on</strong>g> view, <str<strong>on</strong>g>th</str<strong>on</strong>g>is may be seen as <str<strong>on</strong>g>th</str<strong>on</strong>g>e network prefering some inputs already seen, or<br />

dismissing <str<strong>on</strong>g>th</str<strong>on</strong>g>em, or in general specializing to certain activity pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways. We expect<br />

a cell to behave in such a way so as to resist to abrupt changes and to external<br />

manipulati<strong>on</strong>, for example by viruses. In a medium term, a genetic network wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

memory will behave in a more aut<strong>on</strong>omous and prudent manner and it will be less<br />

dependent <strong>on</strong> quick changes in its envir<strong>on</strong>ment.<br />

From a technical point <str<strong>on</strong>g>of</str<strong>on</strong>g> view, <strong>on</strong>e way to introduce a sort <str<strong>on</strong>g>of</str<strong>on</strong>g> memory is to<br />

define individual gene functi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at are not uniquely defined but <str<strong>on</strong>g>th</str<strong>on</strong>g>at vary for<br />

different envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s. One such c<strong>on</strong>trolling c<strong>on</strong>diti<strong>on</strong> may be <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

level <str<strong>on</strong>g>of</str<strong>on</strong>g> an horm<strong>on</strong>e [6]. This model represents <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> various genes<br />

<strong>on</strong> external factors <str<strong>on</strong>g>th</str<strong>on</strong>g>at change slowly in comparis<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e time scale <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene. We have studied gene functi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at differ according to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

level <str<strong>on</strong>g>of</str<strong>on</strong>g> an external horm<strong>on</strong>e <str<strong>on</strong>g>th</str<strong>on</strong>g>at follows its own dynamics. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is case, l<strong>on</strong>g<br />

complex (irregular) attractors emerge wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic network. We have also<br />

studied genetic networks <str<strong>on</strong>g>th</str<strong>on</strong>g>at interact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e horm<strong>on</strong>e in <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e following<br />

ways: <str<strong>on</strong>g>th</str<strong>on</strong>g>e horm<strong>on</strong>e does not have intrinsic dynamics but its producti<strong>on</strong> is triggered<br />

or hindered ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er by each <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene functi<strong>on</strong>s per horm<strong>on</strong>al level, or by each <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e genes <str<strong>on</strong>g>th</str<strong>on</strong>g>at may be in <strong>on</strong> or <str<strong>on</strong>g>of</str<strong>on</strong>g>f state. In bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cases, <str<strong>on</strong>g>th</str<strong>on</strong>g>e networks reach<br />

a co-attractor wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e horm<strong>on</strong>e (<str<strong>on</strong>g>th</str<strong>on</strong>g>at is, <str<strong>on</strong>g>th</str<strong>on</strong>g>e network state and <str<strong>on</strong>g>th</str<strong>on</strong>g>e horm<strong>on</strong>al level<br />

reach coupled attractors). In <str<strong>on</strong>g>th</str<strong>on</strong>g>e first case, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese attractors are very <str<strong>on</strong>g>of</str<strong>on</strong>g>ten irregular<br />

and l<strong>on</strong>ger <str<strong>on</strong>g>th</str<strong>on</strong>g>at usual attractors <str<strong>on</strong>g>of</str<strong>on</strong>g> RBNs, while in <str<strong>on</strong>g>th</str<strong>on</strong>g>e sec<strong>on</strong>d case <str<strong>on</strong>g>th</str<strong>on</strong>g>ey resemble<br />

more <str<strong>on</strong>g>th</str<strong>on</strong>g>e short point and periodic attractors <str<strong>on</strong>g>of</str<strong>on</strong>g> RBNs. A few higher c<strong>on</strong>nectivity<br />

studies (K = number <str<strong>on</strong>g>of</str<strong>on</strong>g> inputs per gene > 2) and perturbati<strong>on</strong> studies have been<br />

985

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performed, <str<strong>on</strong>g>th</str<strong>on</strong>g>at are indicative <str<strong>on</strong>g>of</str<strong>on</strong>g> enhanced robustness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models: for example<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic-horm<strong>on</strong>al systems appear robust to <str<strong>on</strong>g>th</str<strong>on</strong>g>e exact ranges <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e horm<strong>on</strong>al<br />

levels c<strong>on</strong>sidered per gene but not to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir number.<br />

References.<br />

[1] S.A.Kauffman. The origins <str<strong>on</strong>g>of</str<strong>on</strong>g> order: Self-organizati<strong>on</strong> and selecti<strong>on</strong> in evoluti<strong>on</strong>, Oxford University<br />

Press, 1993.<br />

[2] P.Beurt<strong>on</strong>, R.Falk, H-J.Rheinberger. The c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene in development and evoluti<strong>on</strong>,<br />

Cambridge University Press, 2000.<br />

[3] P.Portin. Historical development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine and Philosophy,<br />

27(3):257-286, 2002.<br />

[4] J.Marks, R.B.Lyles. Re<str<strong>on</strong>g>th</str<strong>on</strong>g>inking genes, Evoluti<strong>on</strong>ary An<str<strong>on</strong>g>th</str<strong>on</strong>g>ropology, 3(4):139-146, 1994.<br />

[5] D.Cassill. The social gene, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Bioec<strong>on</strong>omics, 7(1):73-84, 2005.<br />

[6] A.Q.Chen, S.D.Yu, Z.G.Wang, Z.R.Hu, Z.G.Yang. Stage-specific expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> b<strong>on</strong>e morphogenetic<br />

protein type I and type II receptor genes: Effects <str<strong>on</strong>g>of</str<strong>on</strong>g> follicle-stimulating horm<strong>on</strong>e <strong>on</strong><br />

ovine antral follicles, Animal Reproducti<strong>on</strong> Science, 111:391-399, 2009.<br />

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Applicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>negative Rad<strong>on</strong> measure spaces wi<str<strong>on</strong>g>th</str<strong>on</strong>g> metric structure<br />

to populati<strong>on</strong> dynamic models; Wednesday, June 29, 17:00<br />

Agnieszka Ulikowska<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw<br />

e-mail: aulikowska@mimuw.edu.pl<br />

Two-sex, age-structured populati<strong>on</strong> model<br />

The subject <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e presentati<strong>on</strong> is a two-sex, age-structured populati<strong>on</strong> model introduced<br />

first by A.Fredricks<strong>on</strong> and F.Hoppensteadt. The model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> a system<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree PDE’s describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> males and females populati<strong>on</strong>s and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

process <str<strong>on</strong>g>of</str<strong>on</strong>g> couples formati<strong>on</strong>. The age structure plays here a crucial role, because<br />

individuals <str<strong>on</strong>g>of</str<strong>on</strong>g> different ages usually have different preferences for entering into a<br />

marriage. Also envir<strong>on</strong>mental limitati<strong>on</strong>s and influences are taken into c<strong>on</strong>siderati<strong>on</strong><br />

- a bir<str<strong>on</strong>g>th</str<strong>on</strong>g> rate, dea<str<strong>on</strong>g>th</str<strong>on</strong>g> rate, divorce rate and marriage functi<strong>on</strong> depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

state <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e whole system.<br />

Existence and uniqueness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e weak soluti<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e space <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>negative<br />

finite Rad<strong>on</strong> measures equipped wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a flat metric is proved. The pro<str<strong>on</strong>g>of</str<strong>on</strong>g> bases <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e operator splitting algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m. Splitting transport terms (which describe aging<br />

and dea<str<strong>on</strong>g>th</str<strong>on</strong>g>) and boundary terms (which describe an influx <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e new individuals)<br />

allows for obtaining necessary estimates. Hence, <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>tinuous dependence wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

respect to time, initial data and model coefficients is proved.<br />

References.<br />

[1] R.M. Colombo G. Guerra, Differential equati<strong>on</strong>s in metric spaces wi<str<strong>on</strong>g>th</str<strong>on</strong>g> applicati<strong>on</strong>s, Discrete<br />

C<strong>on</strong>tin. Dyn. Syst., 23 733–753, 2009.<br />

[2] A. Fredricks<strong>on</strong>, A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> age structure in sexual populati<strong>on</strong>s: random mating<br />

and m<strong>on</strong>ogamous models, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci., 10 117–143, 1971.<br />

[3] F. Hoppensteadt, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Theory <str<strong>on</strong>g>of</str<strong>on</strong>g> Populati<strong>on</strong>s: Demographics, Genetics and Epidemics,<br />

Society for Industrial and Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Philadelphia, 1975.<br />

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Evoluti<strong>on</strong>ary Ecology; Thursday, June 30, 11:30<br />

Margarete Utz<br />

Ludwig-Maximilians-University Munich, Department Biology II, Evoluti<strong>on</strong>ary<br />

Ecology<br />

e-mail: utz@bio.lmu.de<br />

Eva Kisdi, Mats Gyllenberg<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Helsinki, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics<br />

e-mail: eva.kisdi@helsinki.fi, mats.gyllenberg@helsinki.fi<br />

Body C<strong>on</strong>diti<strong>on</strong> Dependent Dispersal in a Heterogeneous<br />

Envir<strong>on</strong>ment<br />

Body c<strong>on</strong>diti<strong>on</strong> dependent dispersal is a widely evident but barely understood<br />

phenomen<strong>on</strong>. Empirical data display diverse relati<strong>on</strong>ships between individual body<br />

c<strong>on</strong>diti<strong>on</strong> and dispersal between as well as wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in species.<br />

I develop models <str<strong>on</strong>g>th</str<strong>on</strong>g>at study <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal strategies <str<strong>on</strong>g>th</str<strong>on</strong>g>at depend<br />

<strong>on</strong> individual body c<strong>on</strong>diti<strong>on</strong>. In a patchy envir<strong>on</strong>ment where patches differ in<br />

envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s, individuals born in rich (e.g. nutritious) patches are <strong>on</strong><br />

average str<strong>on</strong>ger <str<strong>on</strong>g>th</str<strong>on</strong>g>an <str<strong>on</strong>g>th</str<strong>on</strong>g>eir c<strong>on</strong>specifics <str<strong>on</strong>g>th</str<strong>on</strong>g>at are born in poorer patches. Body c<strong>on</strong>diti<strong>on</strong><br />

(streng<str<strong>on</strong>g>th</str<strong>on</strong>g>) determines competitive ability such <str<strong>on</strong>g>th</str<strong>on</strong>g>at str<strong>on</strong>ger individuals win<br />

competiti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> higher probability <str<strong>on</strong>g>th</str<strong>on</strong>g>an weak individuals. Individuals compete for<br />

patches such <str<strong>on</strong>g>th</str<strong>on</strong>g>at kin competiti<strong>on</strong> selects for dispersal. Survival probability during<br />

dispersal may depend <strong>on</strong> body c<strong>on</strong>diti<strong>on</strong>.<br />

I determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>arily stable strategy (ESS) for different ecological<br />

scenarios. In a fixed envir<strong>on</strong>ment, patches are aband<strong>on</strong>ed <str<strong>on</strong>g>th</str<strong>on</strong>g>at are too unsafe or <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

would not produce enough successful dispersers in <str<strong>on</strong>g>th</str<strong>on</strong>g>e future so <str<strong>on</strong>g>th</str<strong>on</strong>g>at all <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring<br />

disperse from <str<strong>on</strong>g>th</str<strong>on</strong>g>ese patches. In a fluctuating envir<strong>on</strong>ment where patch qualities<br />

change randomly from year to year, all patches are equally wor<str<strong>on</strong>g>th</str<strong>on</strong>g> keeping so <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

all families keep <str<strong>on</strong>g>th</str<strong>on</strong>g>e same competitive weight in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir natal patch and disperse <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

rest.<br />

From families <str<strong>on</strong>g>th</str<strong>on</strong>g>at invest in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> retaining <str<strong>on</strong>g>th</str<strong>on</strong>g>eir natal patch and gaining o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

patches <str<strong>on</strong>g>th</str<strong>on</strong>g>rough successful dispersers, <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e highest survival probability<br />

during dispersal disperse whereas individuals <str<strong>on</strong>g>th</str<strong>on</strong>g>at are less suitable for dispersal<br />

defend <str<strong>on</strong>g>th</str<strong>on</strong>g>eir natal patch. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>is clear wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in-family pattern is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten not<br />

reflected in <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong>-wide body c<strong>on</strong>diti<strong>on</strong> distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> dispersers or n<strong>on</strong>dispersers.<br />

This may be an explanati<strong>on</strong> why empirical data do not show any general<br />

relati<strong>on</strong>ship between body c<strong>on</strong>diti<strong>on</strong> and dispersal.<br />

When all individuals are equally good dispersers, <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>ere exist equivalence<br />

classes <str<strong>on</strong>g>of</str<strong>on</strong>g> dispersal strategies <str<strong>on</strong>g>th</str<strong>on</strong>g>at are defined by <str<strong>on</strong>g>th</str<strong>on</strong>g>e competitive weight <str<strong>on</strong>g>th</str<strong>on</strong>g>at remains<br />

in a patch. An equivalence class c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> infinitely many dispersal strategies<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at are selectively neutral. This provides an explanati<strong>on</strong> why very diverse<br />

patterns found in body c<strong>on</strong>diti<strong>on</strong> dependent dispersal data can all be equally evoluti<strong>on</strong>arily<br />

stable.<br />

References.<br />

[1] M. Gyllenberg, E. Kisdi, M. Utz, Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>diti<strong>on</strong>-dependent dispersal under kin competiti<strong>on</strong><br />

Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology 57 258–307.<br />

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[2] M. Gyllenberg, E. Kisdi, M. Utz, Variability wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in families and <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> body c<strong>on</strong>diti<strong>on</strong><br />

dependent dispersal Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Dynamics (in press).<br />

[3] M. Gyllenberg, E. Kisdi, M. Utz, Body c<strong>on</strong>diti<strong>on</strong> dependent dispersal in a heterogeneous envir<strong>on</strong>ment<br />

(submitted).<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Asher Uziel<br />

Tel-Aviv University, BioMa<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Unit<br />

e-mail: asher.uziel@gmail.com<br />

Lewi St<strong>on</strong>e<br />

Tel-Aviv University, BioMa<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Unit<br />

Epidemics; Wednesday, June 29, 11:00<br />

Predicting <str<strong>on</strong>g>th</str<strong>on</strong>g>e period in seas<strong>on</strong>ally driven epidemics<br />

Seas<strong>on</strong>ality str<strong>on</strong>gly affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e transmissi<strong>on</strong> and spatio-temporal dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> many<br />

infectious diseases, and is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten an important cause for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir recurrence. However,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ere are many open questi<strong>on</strong>s regarding <str<strong>on</strong>g>th</str<strong>on</strong>g>e intricate relati<strong>on</strong>ship between seas<strong>on</strong>ality<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases it gives rise to. For example, in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> l<strong>on</strong>g-term time-series <str<strong>on</strong>g>of</str<strong>on</strong>g> childhood diseases, it is not clear why <str<strong>on</strong>g>th</str<strong>on</strong>g>ere<br />

are transiti<strong>on</strong>s from regimes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> regular annual dynamics, to regimes in which<br />

epidemics occur every two or more years, and vice-versa. The classical seas<strong>on</strong>allyforced<br />

SIR epidemic model gives insights into <str<strong>on</strong>g>th</str<strong>on</strong>g>is phenomena but due to its intrinsic<br />

n<strong>on</strong>linearity and complex dynamics, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is rarely amenable to detailed<br />

ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical analysis. Making sensible approximati<strong>on</strong>s we analytically study <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>reshold (bifurcati<strong>on</strong>) point <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e forced SIR model where <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a switch from<br />

annual to biennial epidemics. We derive, for <str<strong>on</strong>g>th</str<strong>on</strong>g>e first time, a simple equati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

predicts <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong>ship between key epidemiological parameters near <str<strong>on</strong>g>th</str<strong>on</strong>g>e bifurcati<strong>on</strong><br />

point. The relati<strong>on</strong>ship makes clear <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic period will decrease if<br />

ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e bir<str<strong>on</strong>g>th</str<strong>on</strong>g>-rate () or basic reproductive ratio (R0) is increased sufficiently, or if<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> seas<strong>on</strong>ality () is reduced sufficiently. These effects are c<strong>on</strong>firmed in<br />

simulati<strong>on</strong> studies and are also in accord wi<str<strong>on</strong>g>th</str<strong>on</strong>g> empirical observati<strong>on</strong>s. For example,<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e pre-vaccinati<strong>on</strong> era, <str<strong>on</strong>g>th</str<strong>on</strong>g>e increase in bir<str<strong>on</strong>g>th</str<strong>on</strong>g>-rate in <str<strong>on</strong>g>th</str<strong>on</strong>g>e United States and in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e United Kingdom was <str<strong>on</strong>g>th</str<strong>on</strong>g>e factor resp<strong>on</strong>sible for driving measles dynamics from<br />

biennial to annual oscillati<strong>on</strong>s. Moreover, it is argued <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e str<strong>on</strong>g seas<strong>on</strong>ality in<br />

India (high ) may be resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>e erratic polio outbreaks. Corresp<strong>on</strong>dingly,<br />

our equati<strong>on</strong> identifies <str<strong>on</strong>g>th</str<strong>on</strong>g>e first bifurcati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e expected period-doubling route<br />

to chaos <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>tinues as seas<strong>on</strong>ality increases.<br />

990

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cellular Systems Biology; Thursday, June 30, 11:30<br />

Milan J.A. van Hoek<br />

Centrum Wiskunde & Informatica<br />

and Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands C<strong>on</strong>sortium for Systems Biology<br />

Science Park 123, 1098 XG, Amsterdam, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

e-mail: Milan.van.Hoek@cwi.nl<br />

Roeland M.H. Merks<br />

Centrum Wiskunde & Informatica<br />

and Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands C<strong>on</strong>sortium for Systems Biology<br />

Science Park 123, 1098 XG, Amsterdam, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

e-mail: Roeland.Merks@cwi.nl<br />

Protein Cost and Metabolic Network Structure Underlie<br />

Different Modes <str<strong>on</strong>g>of</str<strong>on</strong>g> Metabolic Efficiency<br />

When grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate increases, many unicellular organisms shift from an energetically<br />

efficient to an energetically inefficient metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way to break down<br />

glucose. An example is baker’s yeast Saccharomyces cerivisiae, which ferments glucose<br />

to e<str<strong>on</strong>g>th</str<strong>on</strong>g>anol if <str<strong>on</strong>g>th</str<strong>on</strong>g>e glucose c<strong>on</strong>centrati<strong>on</strong> is high, even in aerobic envir<strong>on</strong>ments<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at allow for more efficient catabolism <str<strong>on</strong>g>of</str<strong>on</strong>g> glucose [1]. Recently, a new explanati<strong>on</strong><br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>is paradoxical behaviour has been proposed: because cells can <strong>on</strong>ly pack a limited<br />

volume <str<strong>on</strong>g>of</str<strong>on</strong>g> metabolic enzymes, inefficient metabolism can maximise <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

rate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell, because efficient metabolic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways require more enzymes <str<strong>on</strong>g>th</str<strong>on</strong>g>an<br />

inefficient pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways [2,3]. Indeed, Vazquez et al. [2] explained <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>current use <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e efficient and inefficient pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way by Escherichia coli in <str<strong>on</strong>g>th</str<strong>on</strong>g>is way. However, it is<br />

unknown why, at high grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rates, some microbes <strong>on</strong>ly use efficient metabolism,<br />

while o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers <strong>on</strong>ly use inefficient metabolism and again o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers use bo<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>currently.<br />

Here we apply Vazquez’ me<str<strong>on</strong>g>th</str<strong>on</strong>g>od <strong>on</strong> genome-scale metabolic models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree<br />

organisms <str<strong>on</strong>g>th</str<strong>on</strong>g>at use different modes <str<strong>on</strong>g>of</str<strong>on</strong>g> inefficient metabolism, E. coli, S. cerevisiae<br />

and Lactococcus lactis: E. coli does not downregulate its efficient pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way at high<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rates, while S. cerevisiae and L. lactis do. The Vazquez me<str<strong>on</strong>g>th</str<strong>on</strong>g>od incorporates<br />

a protein cost for each reacti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e genome-scale metabolic network. This<br />

cost is proporti<strong>on</strong>al to enzyme volume divided by enzyme turnover number (kcat).<br />

Because <str<strong>on</strong>g>th</str<strong>on</strong>g>ese protein costs are not known for each reacti<strong>on</strong> individually, we created<br />

1000 networks, each wi<str<strong>on</strong>g>th</str<strong>on</strong>g> protein costs for each reacti<strong>on</strong> drawn randomly from an<br />

experimentally-obtained distributi<strong>on</strong>. For <strong>on</strong>ly a subset <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese networks inefficient<br />

metabolism is <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal strategy. This allowed us to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein costs <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is inefficient subset in more detail.<br />

We found <str<strong>on</strong>g>th</str<strong>on</strong>g>at for cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> low glycolytic protein cost, inefficient metabolism<br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal strategy, in all <str<strong>on</strong>g>th</str<strong>on</strong>g>ese organisms. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, for S. cerevisiae and<br />

L. lactis optimal grow<str<strong>on</strong>g>th</str<strong>on</strong>g> yield is bimodally distributed over <str<strong>on</strong>g>th</str<strong>on</strong>g>ese 1000 networks:<br />

metabolism is ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er efficient or inefficient. In c<strong>on</strong>trast, for E. coli we observed<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at optimal grow<str<strong>on</strong>g>th</str<strong>on</strong>g> yield varies c<strong>on</strong>tinuously over <str<strong>on</strong>g>th</str<strong>on</strong>g>ese 1000 networks. This could<br />

explain why S. cerevisiae and L. lactis truly switch <str<strong>on</strong>g>of</str<strong>on</strong>g>f efficient metabolism, while<br />

E. coli uses inefficient and efficient metabolism c<strong>on</strong>currently. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at differences<br />

in metabolic network structure underlie <str<strong>on</strong>g>th</str<strong>on</strong>g>is qualitative difference between<br />

991

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E. coli <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>e hand and S. cerevisiae and L. lactis <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand. C<strong>on</strong>cluding,<br />

protein costs determine whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er inefficient metabolism is optimal, while<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolic network structure determines <str<strong>on</strong>g>th</str<strong>on</strong>g>e mode <str<strong>on</strong>g>of</str<strong>on</strong>g> inefficient metabolism.<br />

References.<br />

[1] Hoek PV, Dijken JPV, Pr<strong>on</strong>k JT (1998). Effect <str<strong>on</strong>g>of</str<strong>on</strong>g> specific grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate <strong>on</strong> fermentative capacity<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> baker’s yeast. Appl Envir<strong>on</strong> Microbiol 64 4226–4233.<br />

[2] Vazquez A, Beg QK, Demenezes MA, Ernst J, Bar-Joseph Z, et al (2008). Impact <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e solvent<br />

capacity c<strong>on</strong>straint <strong>on</strong> E. coli metabolism. BMC Syst Biol 2: 7.<br />

[3] Molenaar D, van Berlo R, de Ridder D, Teusink B (2009). Shifts in grow<str<strong>on</strong>g>th</str<strong>on</strong>g> strategies reflect<br />

trade<str<strong>on</strong>g>of</str<strong>on</strong>g>fs in cellular ec<strong>on</strong>omics. Mol Syst Biol5: 323.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Regulatory Networks; Saturday, July 2, 11:00<br />

Sim<strong>on</strong> van Mourik<br />

Kerstin Kaufmann<br />

Richard Immink<br />

Gerco Angenent<br />

Jaap Molenaar<br />

Wageningen University, Wageningen, The Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

e-mail: Sim<strong>on</strong>.vanmourik@wur.nl<br />

Quantitative modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong> in Arabidopsis<br />

flowers<br />

Flowers have a complex structure in which tissues and organs obtain <str<strong>on</strong>g>th</str<strong>on</strong>g>eir identities<br />

and arrangements in a very special way. According to <str<strong>on</strong>g>th</str<strong>on</strong>g>e so-called ABC(DE) model<br />

[1], <str<strong>on</strong>g>th</str<strong>on</strong>g>e different floral organs in Arabidopsis are specified by <str<strong>on</strong>g>th</str<strong>on</strong>g>e expressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> five<br />

types <str<strong>on</strong>g>of</str<strong>on</strong>g> MADS box genes. During development, <str<strong>on</strong>g>th</str<strong>on</strong>g>e floral meristem gets divided<br />

into four c<strong>on</strong>centric areas (whorls) in which different combinati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> MADS gene<br />

expressi<strong>on</strong>s are observed: A+E in <str<strong>on</strong>g>th</str<strong>on</strong>g>e sepal whorl, A+B+E in <str<strong>on</strong>g>th</str<strong>on</strong>g>e petal whorl,<br />

B+C+E in <str<strong>on</strong>g>th</str<strong>on</strong>g>e stamen whorl, and C+E in <str<strong>on</strong>g>th</str<strong>on</strong>g>e carpel whorl.<br />

In [2] we proposed an ODE model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e gene regulatory network<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at underlies <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e MADS domain proteins. We showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

model type is well suited for testing hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses <strong>on</strong> formati<strong>on</strong> and functi<strong>on</strong>ing <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

higher order complexes, transcripti<strong>on</strong> activati<strong>on</strong> and DNA binding.<br />

For <str<strong>on</strong>g>th</str<strong>on</strong>g>e predictive power <str<strong>on</strong>g>of</str<strong>on</strong>g> such a model, accurate estimati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> parameter values<br />

plays an essential role. To <str<strong>on</strong>g>th</str<strong>on</strong>g>is end, we developed a spatiotemporal data set <str<strong>on</strong>g>of</str<strong>on</strong>g> in<br />

vivo protein c<strong>on</strong>centrati<strong>on</strong>s, using a state <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e art protein tagging procedure. We<br />

used a novel image analysis technique to estimate relative protein c<strong>on</strong>centrati<strong>on</strong>s<br />

from <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting c<strong>on</strong>focal images [3].<br />

We also developed a novel parameter estimati<strong>on</strong> procedure <str<strong>on</strong>g>th</str<strong>on</strong>g>at explicitly incorporates<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e temporal expressi<strong>on</strong> development, as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e measured standard<br />

deviati<strong>on</strong>s. The estimati<strong>on</strong> results will give a direct feedback <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses,<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>ey will be presented at <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>ference.<br />

References.<br />

[1] Causier B, Schwarz-Sommer Z, Davies B: Floral organ identity: 20 years <str<strong>on</strong>g>of</str<strong>on</strong>g> ABCs. Seminars<br />

in Cell & Developmental Biology 2010, 21(1):73-79.<br />

[2] van Mourik S, van Dijk AD, de Gee M, Immink RG, Kaufmann K, Angenent GC, van Ham<br />

RC, Molenaar J: C<strong>on</strong>tinuous-time modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> cell fate determinati<strong>on</strong> in Arabidopsis flowers.<br />

BMC Syst Biol 2010, 4:101.<br />

[3] Quelhas P, Mend<strong>on</strong>ca, A, Campilho, A: 3D cell nuclei fluorescence quantificati<strong>on</strong> using sliding<br />

band filter. In: Internati<strong>on</strong>al <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Pattern Recogniti<strong>on</strong>: 2010: IEEE Press -<br />

Computer Society; 2010: 2508-2511.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biomechanical regulati<strong>on</strong> in b<strong>on</strong>e tissue (Sessi<strong>on</strong><br />

I); Wednesday, June 29, 08:30<br />

Bert van Rietbergen<br />

Eindhoven Universty <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Eindhoven, Ne<str<strong>on</strong>g>th</str<strong>on</strong>g>erlands<br />

e-mail: b.v.rietbergen@tue.nl<br />

A <str<strong>on</strong>g>th</str<strong>on</strong>g>eory for load-adaptive b<strong>on</strong>e remodeling at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular<br />

level<br />

It is well known <str<strong>on</strong>g>th</str<strong>on</strong>g>at b<strong>on</strong>e tissue can adapt its shape and density to <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanical<br />

demands it is subjected to. However, how, exactly, <str<strong>on</strong>g>th</str<strong>on</strong>g>is process is regulated is not<br />

well known. Over <str<strong>on</strong>g>th</str<strong>on</strong>g>e last decade we have developed a <str<strong>on</strong>g>th</str<strong>on</strong>g>eory for load adaptive b<strong>on</strong>e<br />

remodeling <str<strong>on</strong>g>th</str<strong>on</strong>g>at is based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>th</str<strong>on</strong>g>at osteocyte cells in <str<strong>on</strong>g>th</str<strong>on</strong>g>e b<strong>on</strong>e tissue can<br />

sense local loading c<strong>on</strong>diti<strong>on</strong>s and based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is informati<strong>on</strong> regulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e activity <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

b<strong>on</strong>e forming cells (osteoblast) and b<strong>on</strong>e resorbing cell (osteoclasts) [1]. We tested<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis using computati<strong>on</strong>al models <str<strong>on</strong>g>th</str<strong>on</strong>g>at included finite element models<br />

to represent trabecular b<strong>on</strong>e architectures and to calculate loading c<strong>on</strong>diti<strong>on</strong>s at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e locati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> osteocytes, In <str<strong>on</strong>g>th</str<strong>on</strong>g>e earlier <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese studies [2], <strong>on</strong>ly <str<strong>on</strong>g>th</str<strong>on</strong>g>e net result <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

b<strong>on</strong>e formati<strong>on</strong> and resorpti<strong>on</strong> was represented by changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model geometry.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>ese studies we dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is <str<strong>on</strong>g>th</str<strong>on</strong>g>eory can explain many aspects <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

b<strong>on</strong>e remodeling <str<strong>on</strong>g>th</str<strong>on</strong>g>at could not be explained before. First, it was shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eory can explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> typical trabecular architectures (osteogenesis).<br />

Sec<strong>on</strong>d, it was shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory can explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptati<strong>on</strong> and alignment <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

trabecular b<strong>on</strong>e as <str<strong>on</strong>g>th</str<strong>on</strong>g>e result <str<strong>on</strong>g>of</str<strong>on</strong>g> a local adaptati<strong>on</strong> process. Third, it was shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory could explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> osteoporosis as <str<strong>on</strong>g>th</str<strong>on</strong>g>e result <str<strong>on</strong>g>of</str<strong>on</strong>g> changes in<br />

cell activity or loading magnitude. In later studies [3] we increased <str<strong>on</strong>g>th</str<strong>on</strong>g>e resoluti<strong>on</strong> to<br />

also represent individual cells. In <str<strong>on</strong>g>th</str<strong>on</strong>g>ese studies we dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>eory can<br />

explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e coupling between osteoclast and osteoblast cells in basic multicellular<br />

units as <str<strong>on</strong>g>th</str<strong>on</strong>g>e result <str<strong>on</strong>g>of</str<strong>on</strong>g> changes in local loading c<strong>on</strong>diti<strong>on</strong> sensed by osteocytes. It<br />

could also explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> oste<strong>on</strong>s in cortical b<strong>on</strong>e and why <str<strong>on</strong>g>th</str<strong>on</strong>g>ese are<br />

oriented in <str<strong>on</strong>g>th</str<strong>on</strong>g>e loading directi<strong>on</strong>. Finally, al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough <str<strong>on</strong>g>th</str<strong>on</strong>g>e biochemical pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way by<br />

which <str<strong>on</strong>g>th</str<strong>on</strong>g>e osteocytes regulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er cells was never specified, we were ble to<br />

dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at bo<str<strong>on</strong>g>th</str<strong>on</strong>g> a stimulatory pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way, in which inicreased loading leads to<br />

increased stimulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> osteoblast, and an inhibitory pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way, in which increased<br />

loading leads to decreased inhibiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> osteoblast (typically for sclerostin) could<br />

work. Presently it is investigated if <str<strong>on</strong>g>th</str<strong>on</strong>g>is <str<strong>on</strong>g>th</str<strong>on</strong>g>eory can be transformed into a clinical<br />

tool to predict b<strong>on</strong>e remodeling in patients as expected due to changes in cell<br />

metabolism or loading c<strong>on</strong>diti<strong>on</strong>s.<br />

References.<br />

[1] Huiskes R, Ruimerman R, van Len<str<strong>on</strong>g>th</str<strong>on</strong>g>e GH, Janssen JD. Effects <str<strong>on</strong>g>of</str<strong>on</strong>g> mechanical forces <strong>on</strong> maintenance<br />

and adaptati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> form in trabecular b<strong>on</strong>e. Nature. 2000 Jun 8;405(6787):704-6.<br />

[2] Ruimerman R, Hilbers PAJ, van Rietbergen B, Huiskes R. A <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical ramework for strainrelated<br />

trabecular b<strong>on</strong>e maintenance and adaptati<strong>on</strong>. J Biomech,2005;38:931-41.<br />

[3] van Oers RFM, Ruimerman R, Tanck E, Hilbers PAJ, Huiskes R. A unified <str<strong>on</strong>g>th</str<strong>on</strong>g>eory for oste<strong>on</strong>al<br />

and hemi-oste<strong>on</strong>al remodeling. B<strong>on</strong>e 2008;42:250-9.<br />

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Informati<strong>on</strong>, human behaviour and disease; Saturday, July 2, 11:00<br />

Raffaele Vardavas<br />

RAND Corporati<strong>on</strong><br />

e-mail: Raffaele_Vardavas@rand.org<br />

Modeling Adaptive Behavior in Influenza Vaccinati<strong>on</strong><br />

Decisi<strong>on</strong>s<br />

Classic game-<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretic approaches, whereby individuals are assumed to evaluate<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir opti<strong>on</strong>s deductively based up<strong>on</strong> available informati<strong>on</strong> and percepti<strong>on</strong>s, have<br />

previously been used to model vaccinati<strong>on</strong>-related decisi<strong>on</strong> making. However, for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> influenza, individuals may rely <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir memories and past experiences<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> having vaccinated. They <str<strong>on</strong>g>th</str<strong>on</strong>g>us use adaptati<strong>on</strong> by evaluating <str<strong>on</strong>g>th</str<strong>on</strong>g>eir vaccinati<strong>on</strong><br />

opti<strong>on</strong>s inductively. We explore <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>cept by c<strong>on</strong>structing an individual-level<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> adaptive-decisi<strong>on</strong> making. Here, individuals are characterized by two<br />

biological attributes (memory and adaptability) <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey use when making vaccinati<strong>on</strong><br />

decisi<strong>on</strong>s. We couple <str<strong>on</strong>g>th</str<strong>on</strong>g>is model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a populati<strong>on</strong>-level model <str<strong>on</strong>g>of</str<strong>on</strong>g> influenza<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at includes vaccinati<strong>on</strong> dynamics. The coupled models allow individual-level decisi<strong>on</strong>s<br />

to influence influenza epidemiology and, c<strong>on</strong>versely, influenza epidemiology<br />

to influence individual-level decisi<strong>on</strong>s. By including <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> adaptive-decisi<strong>on</strong><br />

making wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in an epidemic model we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at severe influenza epidemics could<br />

occur due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavioral dynamics in vaccinati<strong>on</strong> uptake wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a pandemic strain. These severe epidemics can be prevented if vaccinati<strong>on</strong> programs<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g>fer incentives. We find <str<strong>on</strong>g>th</str<strong>on</strong>g>at when a family-based incentive is <str<strong>on</strong>g>of</str<strong>on</strong>g>fered, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

frequency <str<strong>on</strong>g>of</str<strong>on</strong>g> severe epidemics is increased. Instead, <str<strong>on</strong>g>th</str<strong>on</strong>g>is frequency could be reduced<br />

if programs provide several years <str<strong>on</strong>g>of</str<strong>on</strong>g> free vaccines to individuals who pay for <strong>on</strong>e<br />

year <str<strong>on</strong>g>of</str<strong>on</strong>g> vaccinati<strong>on</strong>. We c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at individuals memories and flexibility in adaptive<br />

decisi<strong>on</strong>-making can be extremely important factors in influenza and voluntary<br />

vaccinati<strong>on</strong> determining <str<strong>on</strong>g>th</str<strong>on</strong>g>e success <str<strong>on</strong>g>of</str<strong>on</strong>g> influenza vaccinati<strong>on</strong> programs. Finally, we<br />

discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e implicati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> our results in success <str<strong>on</strong>g>of</str<strong>on</strong>g> a universal flu vaccine and for<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> a pandemic, and discuss some extensi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model.<br />

References.<br />

[1] Raffaele Vardavas, Romulus Breban, and Sally Blower. Can influenza epidemics be prevented<br />

by voluntary vaccinati<strong>on</strong>? PLoS Comput Biol, 3(5):e85, May 2007.<br />

[2] Romulus Breban, Raffaele Vardavas, and Sally Blower. Mean-field analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> an inductive reas<strong>on</strong>ing<br />

game: Applicati<strong>on</strong> to influenza vaccinati<strong>on</strong>. Physical Review E (Statistical, N<strong>on</strong>linear,<br />

and S<str<strong>on</strong>g>of</str<strong>on</strong>g>t Matter Physics), 76(3):031127, 2007.<br />

[3] Raffaele Vardavas, Romulus Breban, and Sally Blower. A universal l<strong>on</strong>g-term flu vaccine may<br />

not prevent severe epidemics. BMC Res Notes, 3:92, 2010.<br />

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Ecosystems Dynamics; Tuesday, June 28, 17:00<br />

M. Vela-Pérez<br />

Departamento de Arquitectura, IE University, C/ Zúñiga 12, 40003<br />

Segovia, Spain<br />

e-mail: mvp_es@yahoo.es<br />

M. A. F<strong>on</strong>telos and J. J. L. Velázquez<br />

Instituto de Ciencias Matemáticas, (ICMAT, CSIC-UAM-UC3M-UCM),<br />

C/ Nicolás Cabrera 15, 28049 Madrid, Spain<br />

e-mail: marco.f<strong>on</strong>telos@icmat.es, jj_velazquez@icmat.es<br />

Geodesic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>s in simple graphs for some social insects<br />

Social insects are an important example <str<strong>on</strong>g>of</str<strong>on</strong>g> complex collective behavior. In particular,<br />

ant col<strong>on</strong>ies develop different tasks as foraging, building and allocati<strong>on</strong> [1].<br />

While <str<strong>on</strong>g>th</str<strong>on</strong>g>ey search for food <str<strong>on</strong>g>th</str<strong>on</strong>g>ey deposit a pherom<strong>on</strong>e <str<strong>on</strong>g>th</str<strong>on</strong>g>at it is c<strong>on</strong>sidered as a<br />

crucial element in <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanism for finding minimal pa<str<strong>on</strong>g>th</str<strong>on</strong>g>s. The experimental<br />

observati<strong>on</strong>s suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e model should include <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> pherom<strong>on</strong>e and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e persistence (tendency to follow straight pa<str<strong>on</strong>g>th</str<strong>on</strong>g>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e absence <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er effects).<br />

In our study, we will c<strong>on</strong>sider ants as random walkers where <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability to<br />

move in <strong>on</strong>e or ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er directi<strong>on</strong> is influenced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> pherom<strong>on</strong>e<br />

near <str<strong>on</strong>g>th</str<strong>on</strong>g>em (reinforced random walks). We are mainly interested not in an individual<br />

random walker but ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <strong>on</strong> a large number <str<strong>on</strong>g>of</str<strong>on</strong>g> random walkers, <str<strong>on</strong>g>th</str<strong>on</strong>g>eir collective<br />

behavior, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e possibility for <str<strong>on</strong>g>th</str<strong>on</strong>g>em to aggregate forming geodesic pa<str<strong>on</strong>g>th</str<strong>on</strong>g>s between<br />

two points in some simple networks.<br />

We investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> ants in a two node network and in a <str<strong>on</strong>g>th</str<strong>on</strong>g>ree node<br />

network (wi<str<strong>on</strong>g>th</str<strong>on</strong>g> and wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out directi<strong>on</strong>ality c<strong>on</strong>straint). Our analytical and computati<strong>on</strong>al<br />

results show <str<strong>on</strong>g>th</str<strong>on</strong>g>at in order for <str<strong>on</strong>g>th</str<strong>on</strong>g>e ants to follow shortest pa<str<strong>on</strong>g>th</str<strong>on</strong>g>s between nest<br />

and food, it is necessary to superimpose to <str<strong>on</strong>g>th</str<strong>on</strong>g>e ants’ random walk <str<strong>on</strong>g>th</str<strong>on</strong>g>e chemotactic<br />

reinforcement. It is also needed a certain degree <str<strong>on</strong>g>of</str<strong>on</strong>g> persistence so <str<strong>on</strong>g>th</str<strong>on</strong>g>at ants tend<br />

to move preferably wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out changing <str<strong>on</strong>g>th</str<strong>on</strong>g>eir directi<strong>on</strong> much. Ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er important fact<br />

is <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> ants, since we will show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e speed for finding minimal pa<str<strong>on</strong>g>th</str<strong>on</strong>g>s<br />

increases very fast wi<str<strong>on</strong>g>th</str<strong>on</strong>g> it.<br />

References.<br />

[1] B. Hölldobler and K. Wils<strong>on</strong>, The ants, Berlin: Springer, 1990<br />

[2] M. Vela-Pérez, M. A. F<strong>on</strong>telos and J. J. L. Velázquez,Ant foraging and minimal pa<str<strong>on</strong>g>th</str<strong>on</strong>g>s in<br />

simple graphs, Submitted for publicati<strong>on</strong><br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemiology, Eco-Epidemiology and Evoluti<strong>on</strong>; Saturday, July 2, 11:00<br />

Ezio Venturino, Alessandro Castellazzo, Andrea Mauro, Claudia Volpe<br />

Dipartimento di Matematica “Giuseppe Peano”,<br />

Università di Torino, Italy.<br />

e-mail: ezio.venturino@unito.it<br />

On an age- and stage-dependent epidemic model.<br />

A very general epidemic model will be introduced in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease spreads<br />

by c<strong>on</strong>tact am<strong>on</strong>g a populati<strong>on</strong> which is age-dependent. A stage structure is introduced<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease, to describe its progressi<strong>on</strong>. The model formulati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>us hinges<br />

<strong>on</strong> a system <str<strong>on</strong>g>of</str<strong>on</strong>g> highly n<strong>on</strong>linear hyperbolic partial differential equati<strong>on</strong>s. The wellposedness<br />

is discussed. Numerical simulati<strong>on</strong>s reveal <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> recurrent<br />

epidemic outbreaks, under suitable circumstances.<br />

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models in Eco-epidemiology I; Wednesday, June 29, 08:30<br />

Ezio Venturino, Fabio Roman, Federica Rossotto<br />

Dipartimento di Matematica “Giuseppe Peano”,<br />

Università di Torino, Italy.<br />

e-mail: ezio.venturino@unito.it<br />

A two-strain ecoepidemic model<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we present a model in which two strains are c<strong>on</strong>sidered. In a<br />

predator-prey demographic model, two c<strong>on</strong>tagious diseases are assumed to spread<br />

am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e predators. Under <str<strong>on</strong>g>th</str<strong>on</strong>g>e relatively str<strong>on</strong>g assumpti<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at <strong>on</strong>e individual<br />

cannot be affected by bo<str<strong>on</strong>g>th</str<strong>on</strong>g>, we analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e system to determine its l<strong>on</strong>g term<br />

behavior. While in some o<str<strong>on</strong>g>th</str<strong>on</strong>g>er already published models bo<str<strong>on</strong>g>th</str<strong>on</strong>g> populati<strong>on</strong>s have<br />

been c<strong>on</strong>sidered subject to a disease, or <str<strong>on</strong>g>th</str<strong>on</strong>g>e same disease is able to cross <str<strong>on</strong>g>th</str<strong>on</strong>g>e species<br />

barrier, to our knowledge <str<strong>on</strong>g>th</str<strong>on</strong>g>is is <str<strong>on</strong>g>th</str<strong>on</strong>g>e first ecoepidemic model accounting for two<br />

diseases affecting <str<strong>on</strong>g>th</str<strong>on</strong>g>e same populati<strong>on</strong>.<br />

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Undergraduate Bioma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Educati<strong>on</strong> Bey<strong>on</strong>d BIO 2010 (Part II);<br />

Saturday, July 2, 08:30<br />

Paola Vera-Lic<strong>on</strong>a<br />

Institut Curie<br />

e-mail: paola.vera-lic<strong>on</strong>a@curie.fr<br />

Ana Martins<br />

Virginia Bioinformatics Institute<br />

Reinhard Laubenbacher<br />

Virginia Bioinformatics Institute<br />

Computati<strong>on</strong>al Systems Biology: Discrete Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Gene<br />

Regulatory Networks<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we will describe a hands-<strong>on</strong> project in computati<strong>on</strong>al systems biology for<br />

students and <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be used in a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> settings, from high school to college,<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a particular focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> discrete ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics. The biological focus is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Escherichia coli lactose oper<strong>on</strong>, <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e first known intracellular regulatory<br />

networks. The modeling approach uses <str<strong>on</strong>g>th</str<strong>on</strong>g>e framework <str<strong>on</strong>g>of</str<strong>on</strong>g> Boolean networks and<br />

tools from discrete ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics for model simulati<strong>on</strong> and analysis.<br />

The talk is based <strong>on</strong> materials from a workshop for high school teachers described<br />

in Martins et al. [1] and c<strong>on</strong>ducted as a collaborati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e Virginia<br />

Bioinformatics Institute (VBI) at Virginia Tech and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Institute for Advanced<br />

Learning & Research (IALR) in Danville, VA. The workshop structure simulated<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e team science approach comm<strong>on</strong> in today practice in computati<strong>on</strong>al molecular<br />

biology and <str<strong>on</strong>g>th</str<strong>on</strong>g>us represents a social case study in collaborative research.<br />

During <str<strong>on</strong>g>th</str<strong>on</strong>g>e workshop <str<strong>on</strong>g>th</str<strong>on</strong>g>e participants were provided wi<str<strong>on</strong>g>th</str<strong>on</strong>g> all <str<strong>on</strong>g>th</str<strong>on</strong>g>e necessary background<br />

in molecular biology and discrete ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics required to complete <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

project, and developed activities intended to show students <str<strong>on</strong>g>th</str<strong>on</strong>g>e value <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

modeling in understanding biochemical network mechanisms and dynamics.<br />

References.<br />

[1] A. Martins, P. Vera Lic<strong>on</strong>a, R. Laubenbacher. Computati<strong>on</strong>al systems biology: Discrete models<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> gene regulati<strong>on</strong> networks. To appear in MAA Notes volume: Undergraduate Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Life Sciences: Processes, Models, Assessment, and Directi<strong>on</strong>s. 2011.<br />

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Bioinformatics and System Biology; Wednesday, June 29, 11:00<br />

Maurício Vieira Kritz<br />

LNCC/MCT, Av. Getúlio Vargas 333, 25651-075 Petrópolis, Brazil<br />

e-mail: kritz@lncc.br<br />

Biological Informati<strong>on</strong>, Biological Interacti<strong>on</strong> and<br />

Anticipati<strong>on</strong><br />

Understanding biological organisati<strong>on</strong>s and interacti<strong>on</strong>s is becoming ever more<br />

important. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, a c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> designed to handle informati<strong>on</strong><br />

c<strong>on</strong>veyed by organizati<strong>on</strong>s is introduced. This c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> may be used<br />

at all biological scales: from molecular and intracellular to multi-cellular organisms<br />

and human beings, and fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er <strong>on</strong> into collectivities, societies and culture.<br />

This c<strong>on</strong>cept is based <strong>on</strong> whole-part graphs, a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for biological<br />

organizati<strong>on</strong> introduced earlier [1]. This model supports <str<strong>on</strong>g>th</str<strong>on</strong>g>e formal investigati<strong>on</strong><br />

about properties <str<strong>on</strong>g>of</str<strong>on</strong>g> biological organisati<strong>on</strong>s, allowing for ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical pro<str<strong>on</strong>g>of</str<strong>on</strong>g>s and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e definiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> organisati<strong>on</strong> transformati<strong>on</strong>s [2].<br />

Ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er c<strong>on</strong>cept, necessary for developing <str<strong>on</strong>g>th</str<strong>on</strong>g>e definiti<strong>on</strong>, will also be introduced.<br />

It is <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> synexi<strong>on</strong>s, or organisati<strong>on</strong>s immersed in space-time.<br />

The definiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> also formalizes percepti<strong>on</strong>, observers and interpretati<strong>on</strong>;<br />

al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough observers appear just as acknowledgers <str<strong>on</strong>g>of</str<strong>on</strong>g> changes. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is setting,<br />

informati<strong>on</strong> and interpretati<strong>on</strong> stand as seminal elements <str<strong>on</strong>g>of</str<strong>on</strong>g> (biological) interacti<strong>on</strong><br />

and <str<strong>on</strong>g>of</str<strong>on</strong>g> transformati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> organisati<strong>on</strong>s. Some aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese c<strong>on</strong>cepts will be<br />

clarified while arguing why <str<strong>on</strong>g>th</str<strong>on</strong>g>e immersi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> whole-part graphs in (<str<strong>on</strong>g>th</str<strong>on</strong>g>e physical)<br />

space-time is needed. This immersi<strong>on</strong> c<strong>on</strong>nects <str<strong>on</strong>g>th</str<strong>on</strong>g>e definiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> to<br />

issues related to anticipati<strong>on</strong>.<br />

Me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for identifying organisati<strong>on</strong>s in biological data may be derived based<br />

<strong>on</strong> whole-part graphs. However, me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for inspecting and identifying organisati<strong>on</strong>s<br />

in bio-chemical networks grounded solely <strong>on</strong> network informati<strong>on</strong> and not<br />

c<strong>on</strong>sidering interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment do not work satisfactorily [4] for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

following reas<strong>on</strong>. It can be proved <str<strong>on</strong>g>th</str<strong>on</strong>g>at de-organizing <str<strong>on</strong>g>th</str<strong>on</strong>g>ings into <str<strong>on</strong>g>th</str<strong>on</strong>g>eir interc<strong>on</strong>nected<br />

parts is a deterministic process, while re-organizing associated parts into<br />

wholes is a n<strong>on</strong>-deterministic process. This implies <str<strong>on</strong>g>th</str<strong>on</strong>g>at raw relati<strong>on</strong>al data [6],<br />

like bio-chemical networks, is insufficient to determine <str<strong>on</strong>g>th</str<strong>on</strong>g>eir natural organisati<strong>on</strong><br />

and how biological organisati<strong>on</strong>s come to be, indicating <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> neatly<br />

c<strong>on</strong>sidering interacti<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e organisati<strong>on</strong> process.<br />

It has been suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>at informati<strong>on</strong> exchange is <str<strong>on</strong>g>th</str<strong>on</strong>g>e distinctive mode <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

interacti<strong>on</strong> in biological phenomena [5]. The arguments presented in support to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is claim are grounded <strong>on</strong> Shann<strong>on</strong>’s informati<strong>on</strong>, what keeps informati<strong>on</strong> more<br />

as an investigatory aid <str<strong>on</strong>g>th</str<strong>on</strong>g>an as some<str<strong>on</strong>g>th</str<strong>on</strong>g>ing intrinsically entailing <str<strong>on</strong>g>th</str<strong>on</strong>g>e phenomen<strong>on</strong>.<br />

Shann<strong>on</strong> himself called attenti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at his definiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong>c<strong>on</strong>tend<br />

precludes meaning and interpretati<strong>on</strong>, addressing <strong>on</strong>ly <str<strong>on</strong>g>th</str<strong>on</strong>g>e communicati<strong>on</strong><br />

(signal transmissi<strong>on</strong>) aspect <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> exchange [7].<br />

The present definiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> informati<strong>on</strong> ties interpretati<strong>on</strong> to changes in organisati<strong>on</strong><br />

[3]. Therefore, informati<strong>on</strong>-grounded biological interacti<strong>on</strong>s mold organisati<strong>on</strong>s.<br />

The fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e definiti<strong>on</strong> is grounded <strong>on</strong> synexi<strong>on</strong>s ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an whole-part<br />

graphs intertwines anticipati<strong>on</strong> to informati<strong>on</strong> recogniti<strong>on</strong>. Indeed, <str<strong>on</strong>g>th</str<strong>on</strong>g>e percepti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> an interpretati<strong>on</strong> event relies <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e violati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e anticipati<strong>on</strong> by an observer<br />

1000

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

about propensities in <str<strong>on</strong>g>th</str<strong>on</strong>g>e behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interpreter <str<strong>on</strong>g>of</str<strong>on</strong>g> a signal. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is sense, biological<br />

informati<strong>on</strong> and anticipati<strong>on</strong> are at <str<strong>on</strong>g>th</str<strong>on</strong>g>e very core <str<strong>on</strong>g>of</str<strong>on</strong>g> biological interacti<strong>on</strong>s<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>sequent formati<strong>on</strong> and transformati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biological organisati<strong>on</strong>s.<br />

References.<br />

[1] M.V. Kritz, Biological Organizati<strong>on</strong>. In Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e IV Brazilian Symposium <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

and Computati<strong>on</strong>al Biology — BIOMAT IV, R. Modaini, ed. e-papers Editora, Rio<br />

de Janeiro, 2005.<br />

[2] M.V. Kritz, Organizing biological observati<strong>on</strong>s: a model and some properties. Book<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>Abstracts</str<strong>on</strong>g>. ECMTB08, Edinburg, June 29<str<strong>on</strong>g>th</str<strong>on</strong>g> – July 4<str<strong>on</strong>g>th</str<strong>on</strong>g>. Available <strong>on</strong>line at<br />

http://www.ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.dundee.ac.uk/ecmtb08, last access <strong>on</strong> .<br />

[3] M. V. Kritz, Biological informati<strong>on</strong> and knowledge. P&D Report #23/2009, LNCC/MCT,<br />

Petrópolis, December 2009.<br />

[4] M. V. Kritz, M. T. dos Santos, S. Urrutia and J.-M. Schwartz, Organizing metabolic networks:<br />

Cycles in flux distributi<strong>on</strong>. Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology, 265(3):250–260, August 2010.<br />

doi:10.1016/j.jtbi.2010.04.026<br />

[5] J. G. Roederer, The Role <str<strong>on</strong>g>of</str<strong>on</strong>g> Informati<strong>on</strong> in Nature. The Fr<strong>on</strong>tiers Collecti<strong>on</strong>. Springer Verlag,<br />

Berlin, 2005.<br />

[6] R. Rosen, Life Itself: A Comprehesive Inquiry into <str<strong>on</strong>g>th</str<strong>on</strong>g>e Nature, Origin, and Fabricati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Life. Complexity in Ecological Systems Series. Columbia University Press, New York, NY,<br />

1991.<br />

[7] C. E. Shann<strong>on</strong> and W. Weaver, The Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Theory <str<strong>on</strong>g>of</str<strong>on</strong>g> Communicati<strong>on</strong>. University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Illinois Press, Urbana, 1949.<br />

1001

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Irene Vign<strong>on</strong>-Clementel<br />

INRIA Paris-Rocquencourt, France<br />

e-mail: irene.vign<strong>on</strong>-clementel@inria.fr<br />

G. Troiwanowski<br />

Stanford University, USA<br />

W. Yang<br />

UCSD, USA<br />

J. Feinstein<br />

Stanford University, USA<br />

A. Marsden<br />

UCSD, USA<br />

F. Migliavacca<br />

Politecnico Di Milano, Italy<br />

Medical Physiology; Tuesday, June 28, 11:00<br />

Towards predictive modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> patient-specific<br />

Glenn-to-F<strong>on</strong>tan c<strong>on</strong>versi<strong>on</strong>s: boundary c<strong>on</strong>diti<strong>on</strong>s and<br />

design issues.<br />

Single-ventricle defects are a class <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>genital heart diseases <str<strong>on</strong>g>th</str<strong>on</strong>g>at leave <str<strong>on</strong>g>th</str<strong>on</strong>g>e child<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <strong>on</strong>ly <strong>on</strong>e operati<strong>on</strong>al pump, requiring <str<strong>on</strong>g>th</str<strong>on</strong>g>e systemic and <str<strong>on</strong>g>th</str<strong>on</strong>g>e pulm<strong>on</strong>ary circulati<strong>on</strong>s<br />

to be placed in series <str<strong>on</strong>g>th</str<strong>on</strong>g>rough several operati<strong>on</strong>s performed during young<br />

childhood. The last procedure (<str<strong>on</strong>g>th</str<strong>on</strong>g>e F<strong>on</strong>tan palliati<strong>on</strong>) artificially c<strong>on</strong>nects bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

venae cavae to <str<strong>on</strong>g>th</str<strong>on</strong>g>e pulm<strong>on</strong>ary arteries, which improves oxygenerati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e baby<br />

at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cost <str<strong>on</strong>g>of</str<strong>on</strong>g> blood flowing passively into <str<strong>on</strong>g>th</str<strong>on</strong>g>e lungs. Numerical simulati<strong>on</strong>s may<br />

be used to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e flow and its c<strong>on</strong>necti<strong>on</strong> to post-operative<br />

failures and sources <str<strong>on</strong>g>of</str<strong>on</strong>g> morbidity. However <str<strong>on</strong>g>th</str<strong>on</strong>g>ey heavily rely <strong>on</strong> boundary c<strong>on</strong>diti<strong>on</strong><br />

prescripti<strong>on</strong>. We present our recent work <strong>on</strong> predictive patient-specific modeling<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Glenn-to-F<strong>on</strong>tan c<strong>on</strong>versi<strong>on</strong>. Three-dimensi<strong>on</strong>al patient-specific preoperative<br />

models are developed based <strong>on</strong> clinical data. Results include a sensitivity analysis <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

several hemodynamics factors to <str<strong>on</strong>g>th</str<strong>on</strong>g>e input data. In additi<strong>on</strong>, previous studies have<br />

dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e geometry plays an important role in F<strong>on</strong>tan hemodynamics.<br />

A novel Y-shaped design was recently proposed to improve up<strong>on</strong> traditi<strong>on</strong>al designs,<br />

and results showed promising hemodynamics. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is study, we show how geometry<br />

and boundary c<strong>on</strong>diti<strong>on</strong>s affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e performance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese virtual surgical designs.<br />

In particular, we investigate if and how <str<strong>on</strong>g>th</str<strong>on</strong>g>e inferior vena cava flow (which c<strong>on</strong>tains<br />

an important biological hepatic factor) can be optimally distributed amoung bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

lungs. Finally, we present a multiscale (<str<strong>on</strong>g>th</str<strong>on</strong>g>ree-dimensi<strong>on</strong>al to reduced model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

entire circulati<strong>on</strong>) predictive framework for <str<strong>on</strong>g>th</str<strong>on</strong>g>is Glenn-to-F<strong>on</strong>tan c<strong>on</strong>versi<strong>on</strong>, which<br />

provides a means to relate global resp<strong>on</strong>se to local changes in geometry and hemodynamics<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e circulatory system. Results illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e local graft geometry<br />

plays essentially no role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e workload <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e heart. While <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>of</str<strong>on</strong>g>fset and Y-graft<br />

designs result in reduced energy loss, <str<strong>on</strong>g>th</str<strong>on</strong>g>is does not appear to have any significant<br />

impact <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cardiac dynamics. This result suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at future work should focus<br />

not just <strong>on</strong> energy loss, but <strong>on</strong> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er clinical relevant parameters, such as hepatic<br />

flow distributi<strong>on</strong>.<br />

1002

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Fernão Vistulo de Abreu<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Aveiro<br />

e-mail: fva@ua.pt<br />

Patricia Mostardinha<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Aveiro<br />

Immunology; Saturday, July 2, 08:30<br />

Self-N<strong>on</strong>self discriminati<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> Costimulati<strong>on</strong><br />

and Anergy<br />

The problem <str<strong>on</strong>g>of</str<strong>on</strong>g> self-n<strong>on</strong>self discriminati<strong>on</strong> is a l<strong>on</strong>g standing problem in immunology.<br />

So far, it has been unclear whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er T cells can perform perfect and efficient<br />

self-n<strong>on</strong>self discriminati<strong>on</strong>, in populati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> arbitrary diversity. I will discuss a<br />

mechanism <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows performing perfect self-n<strong>on</strong>self discriminati<strong>on</strong> if bo<str<strong>on</strong>g>th</str<strong>on</strong>g> positive<br />

and negative repertoire educati<strong>on</strong> processes are used, and fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore if costimulati<strong>on</strong><br />

and anergy mechanisms are afterwards c<strong>on</strong>sidered during cellular activati<strong>on</strong>.<br />

These results provide compiling evidence <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e main driving force shaping <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

adaptive immune could be <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability to perform prompt and accurate self-n<strong>on</strong>self<br />

discriminati<strong>on</strong>. They also provide insights <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e possible role <str<strong>on</strong>g>of</str<strong>on</strong>g> positive selecti<strong>on</strong>,<br />

costimulati<strong>on</strong> and anergy in <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptive immune system.<br />

1003

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Mechanical Models <str<strong>on</strong>g>of</str<strong>on</strong>g> Movement and Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> Cells and Tissues I;<br />

Wednesday, June 29, 14:30<br />

Guido Vitale<br />

Politecnico di Torino<br />

e-mail: guido.vitale@polito.it<br />

Cellular Tracti<strong>on</strong> as an Optimal C<strong>on</strong>trol Problem<br />

Force Tracti<strong>on</strong> Microscopy is <str<strong>on</strong>g>th</str<strong>on</strong>g>e determinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stress exerted by a cell <strong>on</strong><br />

a planar deformable substrate <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> pointwise measured displacement.<br />

This classical inverse problem in biophysics is typically addressed inverting <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

displacement field using <str<strong>on</strong>g>th</str<strong>on</strong>g>e Green functi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> linear elasticity, under suitable<br />

regularizing c<strong>on</strong>diti<strong>on</strong>s.<br />

An alternative me<str<strong>on</strong>g>th</str<strong>on</strong>g>od formulates an adjoint problem for <str<strong>on</strong>g>th</str<strong>on</strong>g>e direct two-dimensi<strong>on</strong>al<br />

plain stress operator by minimizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>venient functi<strong>on</strong>al. The resulting coupled<br />

systems <str<strong>on</strong>g>of</str<strong>on</strong>g> elliptic partial dfferential equati<strong>on</strong>s (<str<strong>on</strong>g>th</str<strong>on</strong>g>e forward and <str<strong>on</strong>g>th</str<strong>on</strong>g>e adjoint<br />

problem) can <str<strong>on</strong>g>th</str<strong>on</strong>g>en be solved by a finite element me<str<strong>on</strong>g>th</str<strong>on</strong>g>od. One advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> such<br />

an approach is <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be extended to <str<strong>on</strong>g>th</str<strong>on</strong>g>ree dimensi<strong>on</strong>al case, including inhomogeneity<br />

and anisotropy and even finite displacements <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e material.<br />

This work deals wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e rigorous statement <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e inverse problem Some results<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> well posedness for <str<strong>on</strong>g>th</str<strong>on</strong>g>e linear case are first given, using standard techniques.<br />

The <str<strong>on</strong>g>th</str<strong>on</strong>g>eory is <str<strong>on</strong>g>th</str<strong>on</strong>g>en extended to <str<strong>on</strong>g>th</str<strong>on</strong>g>e less trivial case <str<strong>on</strong>g>of</str<strong>on</strong>g> pointwise observati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

boundary c<strong>on</strong>trol in 2D and 3D. The model is numerically approximated in 2D and a<br />

critical discussi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e results is addressed. Early results <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e major biophysical<br />

problem <str<strong>on</strong>g>of</str<strong>on</strong>g> pointiwise observati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> boundary c<strong>on</strong>trol will be shown.<br />

item Ambrosi D. et al. em Tracti<strong>on</strong> pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cells, J Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Biol (2007)<br />

item Ambrosi D. em Cellular tracti<strong>on</strong> as an inverse problem, SIAM J Appl Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> 66:<br />

2049-2060 (2006) item Li<strong>on</strong>s J.L. em Optimal c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> systems, Springer Verlag<br />

(1971) item Casas E. em Boundary C<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> a Semilinear Elliptic Equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

Pointwise state C<strong>on</strong>straint, SIAM J. Opt. C<strong>on</strong>tr. (1996)<br />

1004

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cellular Systems Biology; Thursday, June 30, 11:30<br />

Evgenii Volkov<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Physics, Lebedev Physical Inst., Leninskii<br />

53, Moscow, Russia<br />

e-mail: volkov@td.lpi.ru<br />

Ilya Potapov<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Signal Processing, Tampere University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology,<br />

Korkeakoulunkatu 10, Tampere, Finland and Biophysics Department,<br />

Lom<strong>on</strong>osov Moscow State University, GSP-1, Leninskie Gory, Moscow,<br />

Russia<br />

e-mail: ilya.potapov@tut.fi<br />

Alexey Kuznetsov<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences and Center for Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

Biosciences, IUPUI, 402 N. Blackford St., Indianapolis, IN 46202, USA.<br />

e-mail: alexey@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.iupui.edu<br />

Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> coupled repressilators: <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> mRNA<br />

kinetics and transcripti<strong>on</strong> cooperativity<br />

Regulatory molecular networks are collecti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting molecules in a cell.<br />

One particular kind, oscillatory networks, has been discovered in many pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ways.<br />

Well-known examples are <str<strong>on</strong>g>th</str<strong>on</strong>g>e circadian clock [1] and <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell cycle [2], where <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

oscillatory nature <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e process plays a central role.<br />

These natural regulatory networks are very complex and include many types<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> molecules, from genes to small messengers. It is necessary to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulatory<br />

mechanisms by means <str<strong>on</strong>g>of</str<strong>on</strong>g> highly simplified models. These models are particularly<br />

valuable because artificial regulatory networks can be engineered experimentally<br />

[3, 4, 5]. Our computati<strong>on</strong>al study [6] suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e oscillatory mechanisms<br />

implemented in regulatory oscillators are qualitatively different. Comparing various<br />

artificial networks helps revealing general principles <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular regulati<strong>on</strong>.<br />

We study an artificial oscillatory network called <str<strong>on</strong>g>th</str<strong>on</strong>g>e repressilator [4], which<br />

borrows <str<strong>on</strong>g>th</str<strong>on</strong>g>e idea <str<strong>on</strong>g>of</str<strong>on</strong>g> a ring oscillator coming from engineering. The oscillatory<br />

mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e repressilator is based <strong>on</strong> c<strong>on</strong>necting an odd number <str<strong>on</strong>g>of</str<strong>on</strong>g> inverters<br />

(negative c<strong>on</strong>trol elements) in a ring. Its genetic implementati<strong>on</strong> uses <str<strong>on</strong>g>th</str<strong>on</strong>g>ree proteins<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at cyclically repress <str<strong>on</strong>g>th</str<strong>on</strong>g>e syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>e ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er by inhibiti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> corresp<strong>on</strong>ding<br />

mRNA producti<strong>on</strong>.<br />

A challenging area <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e research is communicati<strong>on</strong> am<strong>on</strong>g cells in a populati<strong>on</strong><br />

or organism. It has been proposed <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretically to design artificial interacti<strong>on</strong><br />

am<strong>on</strong>g cellular oscillators using quorum sensing [7, 8]. A small molecule, autoinducer<br />

(AI), carries out <str<strong>on</strong>g>th</str<strong>on</strong>g>e coupling functi<strong>on</strong>. Synchr<strong>on</strong>izati<strong>on</strong> is <strong>on</strong>ly <strong>on</strong>e and<br />

simplest outcome <str<strong>on</strong>g>of</str<strong>on</strong>g> such interacti<strong>on</strong>. It is suggested <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e outcome depends<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network. A phase-attractive (synchr<strong>on</strong>izing) and phaserepulsive<br />

coupling structures were distinguished for regulatory oscillators. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

paper, we questi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is separati<strong>on</strong>.<br />

We study an example <str<strong>on</strong>g>of</str<strong>on</strong>g> two interacting repressilators. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at increasing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cooperativity <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong> repressi<strong>on</strong> (Hill coefficient) and changing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

reacti<strong>on</strong> time-scales dramatically alter synchr<strong>on</strong>izati<strong>on</strong> properties. The network<br />

1005

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

dem<strong>on</strong>strates in- and anti-phase oscillatory regimes and can be birhy<str<strong>on</strong>g>th</str<strong>on</strong>g>mic, choosing<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>ose two types <str<strong>on</strong>g>of</str<strong>on</strong>g> synchr<strong>on</strong>izati<strong>on</strong>, in a wide range <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters. In<br />

some regi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> parametric space <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are whole cascades <str<strong>on</strong>g>of</str<strong>on</strong>g> complex anti-phase<br />

oscillatory soluti<strong>on</strong>s, which coexist wi<str<strong>on</strong>g>th</str<strong>on</strong>g> in-phase regime. Thus, <str<strong>on</strong>g>th</str<strong>on</strong>g>e type <str<strong>on</strong>g>of</str<strong>on</strong>g> synchr<strong>on</strong>izati<strong>on</strong><br />

is not characteristic for <str<strong>on</strong>g>th</str<strong>on</strong>g>e network structure. However, we c<strong>on</strong>clude<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e specific scenario <str<strong>on</strong>g>of</str<strong>on</strong>g> emergence and stabilizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> synchr<strong>on</strong>ous soluti<strong>on</strong>s<br />

is much more characteristic.<br />

In particular, anti-phase oscillati<strong>on</strong>s emerge at elevated cooperativity values.<br />

We choose <str<strong>on</strong>g>th</str<strong>on</strong>g>e maximal syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis rate for <str<strong>on</strong>g>th</str<strong>on</strong>g>e mRNA as <str<strong>on</strong>g>th</str<strong>on</strong>g>e main c<strong>on</strong>trol parameter<br />

for our analysis. We calculate bifurcati<strong>on</strong> diagrams wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to <str<strong>on</strong>g>th</str<strong>on</strong>g>is parameter<br />

and study how regimes found in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese diagrams depend <strong>on</strong> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er parameters. At<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e initial cooperativity value <str<strong>on</strong>g>of</str<strong>on</strong>g> 2.0, <str<strong>on</strong>g>th</str<strong>on</strong>g>e in-phase synchr<strong>on</strong>izati<strong>on</strong> remains stable<br />

and anti-phase remains unstable at any syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis rate. When <str<strong>on</strong>g>th</str<strong>on</strong>g>e cooperativity is<br />

elevated <strong>on</strong>ly to 2.6, <str<strong>on</strong>g>th</str<strong>on</strong>g>e anti-phase soluti<strong>on</strong> becomes stable at a sufficiently high<br />

syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis rate. In c<strong>on</strong>trast, <str<strong>on</strong>g>th</str<strong>on</strong>g>e in-phase soluti<strong>on</strong> loses its stability at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese elevated<br />

cooperativity and high syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis rate.<br />

Additi<strong>on</strong>ally, fast mRNA kinetics provides birhy<str<strong>on</strong>g>th</str<strong>on</strong>g>micity in a wide range <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis rate. Initially, <str<strong>on</strong>g>th</str<strong>on</strong>g>e time-scales <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e protein and mRNA kinetics were<br />

identical. We make mRNA kinetics much faster <str<strong>on</strong>g>th</str<strong>on</strong>g>an protein, which is a more<br />

natural case. The sequence in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e oscillatory soluti<strong>on</strong>s emerge from Hopf<br />

bifurcati<strong>on</strong>s changes — <str<strong>on</strong>g>th</str<strong>on</strong>g>e anti-phase emerges first. As a result, <str<strong>on</strong>g>th</str<strong>on</strong>g>e anti-phase<br />

soluti<strong>on</strong> emerges stable, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e in-phase emerges unstable. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e birhy<str<strong>on</strong>g>th</str<strong>on</strong>g>mic<br />

parameter regime, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> soluti<strong>on</strong>s must be stable. Three bifurcati<strong>on</strong>s always precede<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e birhy<str<strong>on</strong>g>th</str<strong>on</strong>g>mic parameter regime when <str<strong>on</strong>g>th</str<strong>on</strong>g>e syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis rate increases. The in-phase<br />

soluti<strong>on</strong> becomes stable as a result <str<strong>on</strong>g>of</str<strong>on</strong>g> a repelling invariant torus emanating from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e limit cycle. The o<str<strong>on</strong>g>th</str<strong>on</strong>g>er two bifurcati<strong>on</strong>s are unexpected: The anti-phase limit<br />

cycle first loses its stability, and <str<strong>on</strong>g>th</str<strong>on</strong>g>en regains it. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> transiti<strong>on</strong>s are pitchfork<br />

bifurcati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> limit cycles. The sec<strong>on</strong>d bifurcati<strong>on</strong> cancels <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e first<br />

<strong>on</strong>e <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e anti-phase soluti<strong>on</strong>. Thus, bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in-phase and anti-phase<br />

soluti<strong>on</strong>s are stable in a very wide range <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis rate.<br />

Our work presents a novel scenario <str<strong>on</strong>g>of</str<strong>on</strong>g> emerging birhy<str<strong>on</strong>g>th</str<strong>on</strong>g>micity and switching<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e in- and anti-phase soluti<strong>on</strong>s in regulatory oscillators. Since <str<strong>on</strong>g>th</str<strong>on</strong>g>e types <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

synchr<strong>on</strong>izati<strong>on</strong> coexist in <strong>on</strong>e network, <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are not characteristic for <str<strong>on</strong>g>th</str<strong>on</strong>g>e network<br />

structure. However, <str<strong>on</strong>g>th</str<strong>on</strong>g>e bifurcati<strong>on</strong> scenario may be much more characteristic. This<br />

may help to address a central questi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> regulatory networks —<br />

how to c<strong>on</strong>nect structural characteristics to dynamical and functi<strong>on</strong>al properties <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

a network.<br />

References.<br />

[1] J. Dunlap, Molecular bases for circadian clocks Cell 96 271–290.<br />

[2] P. Nurse, A l<strong>on</strong>g twentie<str<strong>on</strong>g>th</str<strong>on</strong>g> century <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell cycle and bey<strong>on</strong>d Cell 100 71–78.<br />

[3] T.S. Gardner, C.R. Cantor and J.J. Collins, C<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a genetic toggle switch in Escherichia<br />

coli Nature 403 339–342.<br />

[4] M. Elowitz and S. Leibler, A syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic oscillatory network <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong>al regulators Nature<br />

403 335–338.<br />

[5] M. Atkins<strong>on</strong>, M. Savageau, J. Myers and A. Ninfa, Development <str<strong>on</strong>g>of</str<strong>on</strong>g> genetic circuitry exhibiting<br />

toggle switch or oscillatory behavior in Escherichia coli Cell 113 597–607.<br />

[6] D. Yang, Y. Li and A. Kuznetsov, Characterizati<strong>on</strong> and merger <str<strong>on</strong>g>of</str<strong>on</strong>g> oscillatory mechanisms in<br />

an artificial genetic regulatory network Chaos 19 033115.<br />

[7] D. McMillen, N. Kopell, J. Hasty and J. Collins, Synchr<strong>on</strong>izing genetic relaxati<strong>on</strong> oscillators<br />

by intercell signalling Proc. Natl. Acad. Sci. U.S.A. 99 679–684.<br />

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[8] J. García-Ojalvo, M. Elowitz and S. Strogatz, Modeling a syn<str<strong>on</strong>g>th</str<strong>on</strong>g>etic multicellular clock: Repressilators<br />

coupled by quorum sensing Proc. Natl. Acad. Sci. U.S.A. 101 10955–10960.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> biological systems: from physical tools to<br />

applicati<strong>on</strong>s in cancer modeling I; Saturday, July 2, 08:30<br />

Vitaly Volpert<br />

CNRS, University Ly<strong>on</strong> 1, France<br />

e-mail: volpert@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.univ-ly<strong>on</strong>1.fr<br />

Hybrid models <str<strong>on</strong>g>of</str<strong>on</strong>g> normal and leukemic hematopoiesis<br />

We develop hybrid models <str<strong>on</strong>g>of</str<strong>on</strong>g> cell populati<strong>on</strong> dynamics where cells are c<strong>on</strong>sidered as<br />

individual objects, intracellular regulatory networks are described by ordinary differential<br />

equati<strong>on</strong>s while biochemical species in <str<strong>on</strong>g>th</str<strong>on</strong>g>e extracellular matrix by partial<br />

differential equati<strong>on</strong>s. We use <str<strong>on</strong>g>th</str<strong>on</strong>g>is approach to various biological and medical applicati<strong>on</strong>.<br />

In particular, to model normal and leukemic hematopoiesis and leukemia<br />

treatment.<br />

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Plants, grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and transport processes II; Tuesday, June 28, 14:30<br />

Vitaly Volpert<br />

CNRS, UNiversity Ly<strong>on</strong> 1<br />

e-mail: volpert@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.univ-ly<strong>on</strong>1.fr<br />

N<strong>on</strong>linear dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> plant grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

We model plant grow<str<strong>on</strong>g>th</str<strong>on</strong>g> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> free boundary problems where <str<strong>on</strong>g>th</str<strong>on</strong>g>e moving boundary<br />

corresp<strong>on</strong>ds to <str<strong>on</strong>g>th</str<strong>on</strong>g>e mersitem, a narrow layer <str<strong>on</strong>g>of</str<strong>on</strong>g> proliferating cells. Cell cycle<br />

progressi<strong>on</strong> and transport <str<strong>on</strong>g>of</str<strong>on</strong>g> nutrient and metabolites are taken into account. N<strong>on</strong>linear<br />

dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> plant grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, endogeneous rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>ms and branching patterns are<br />

discussed.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Epidemics; Wednesday, June 29, 11:00<br />

Max v<strong>on</strong> Kleist<br />

Freie Universität Berlin, Germany<br />

e-mail: vkleist@zedat.fu-berlin.de<br />

M<strong>on</strong>ika Frank<br />

Martin-Lu<str<strong>on</strong>g>th</str<strong>on</strong>g>er Universität Halle-Wittenberg, Germany<br />

Charlotte Kl<str<strong>on</strong>g>of</str<strong>on</strong>g>t<br />

Martin-Lu<str<strong>on</strong>g>th</str<strong>on</strong>g>er Universität Halle-Wittenberg, Germany<br />

Christ<str<strong>on</strong>g>of</str<strong>on</strong>g> Schütte<br />

Freie Universität Berlin, Germany<br />

A Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling Framework to Assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e Impact<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Antiviral Strategies <strong>on</strong> HIV Transmissi<strong>on</strong><br />

Stopping <str<strong>on</strong>g>th</str<strong>on</strong>g>e AIDS epidemic c<strong>on</strong>stitutes a major challenge to mankind. Up to now,<br />

HIV infected individuals cannot be cured. However, <strong>on</strong>e possible way <str<strong>on</strong>g>of</str<strong>on</strong>g> stopping<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic is to disrupt its transmissi<strong>on</strong>. In 2009, approximately 370,000 infants<br />

became infected wi<str<strong>on</strong>g>th</str<strong>on</strong>g> HIV during pregnancy, delivery and breastfeeding [1]. A single<br />

dose <str<strong>on</strong>g>of</str<strong>on</strong>g> nevirapine (NVP) can reduce HIV transmissi<strong>on</strong> by half, when administered<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e mo<str<strong>on</strong>g>th</str<strong>on</strong>g>ers before bir<str<strong>on</strong>g>th</str<strong>on</strong>g> and to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir newborns shortly after bir<str<strong>on</strong>g>th</str<strong>on</strong>g>. This simple<br />

and cost-efficient me<str<strong>on</strong>g>th</str<strong>on</strong>g>od is widely applied in resource-c<strong>on</strong>strained settings.<br />

Based <strong>on</strong> a ugandan program for <str<strong>on</strong>g>th</str<strong>on</strong>g>e preventi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> mo<str<strong>on</strong>g>th</str<strong>on</strong>g>er-to-child transmissi<strong>on</strong>,<br />

we assessed <str<strong>on</strong>g>th</str<strong>on</strong>g>e pharmacokinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> NVP in HIV infected pregnant women<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir newborns. The derived pharmacokinetic parameters were used in a stochastic<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV dynamics and -transmissi<strong>on</strong>. Subsequently, we used <str<strong>on</strong>g>th</str<strong>on</strong>g>e model<br />

to predict HIV transmissi<strong>on</strong> rates during <str<strong>on</strong>g>th</str<strong>on</strong>g>e first two years after bir<str<strong>on</strong>g>th</str<strong>on</strong>g> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different<br />

alterati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basic NVP scheme. The model predicti<strong>on</strong>s were in excellent<br />

agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> data from seven independent HIV preventi<strong>on</strong> trials. We found <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e maternal NVP c<strong>on</strong>stitutes a major risk for resistance development and subsequent<br />

treatment success in <str<strong>on</strong>g>th</str<strong>on</strong>g>e HIV infected mo<str<strong>on</strong>g>th</str<strong>on</strong>g>er [2]. However, maternal NVP<br />

decreases HIV transmissi<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e newborn substantially. Our model revealed a<br />

perplexing mechanism: Maternal NVP does not reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> viral particles<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at come into c<strong>on</strong>tact wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e child during bir<str<strong>on</strong>g>th</str<strong>on</strong>g>. Instead, maternal NVP<br />

reduces HIV transmissi<strong>on</strong> by providing NVP trans-placental to <str<strong>on</strong>g>th</str<strong>on</strong>g>e child, so <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

protective NVP levels are available at <str<strong>on</strong>g>th</str<strong>on</strong>g>e moment <str<strong>on</strong>g>of</str<strong>on</strong>g> viral c<strong>on</strong>tact during delivery.<br />

Our model also revealed, <str<strong>on</strong>g>th</str<strong>on</strong>g>at extended newborn NVP administrati<strong>on</strong> can protect<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e infant from acquiring HIV during <str<strong>on</strong>g>th</str<strong>on</strong>g>e breastfeeding period wi<str<strong>on</strong>g>th</str<strong>on</strong>g>out fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er risk<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> resistance selecti<strong>on</strong>.<br />

Extended newborn NVP, as well as single-dose maternal NVP protect <str<strong>on</strong>g>th</str<strong>on</strong>g>e newborn<br />

from HIV acquisiti<strong>on</strong> by a mechanism, which could best be termed ’preexposure<br />

prophylaxis’ (PrEP). In view <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e predictive power <str<strong>on</strong>g>of</str<strong>on</strong>g> our model, we<br />

are encouraged <str<strong>on</strong>g>th</str<strong>on</strong>g>at a very similar modeling framework may be useful to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

impact <str<strong>on</strong>g>of</str<strong>on</strong>g> PrEP <strong>on</strong> sexual transmissi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> HIV, which could become a central tool<br />

to curb <str<strong>on</strong>g>th</str<strong>on</strong>g>e HIV epidemic in <str<strong>on</strong>g>th</str<strong>on</strong>g>e near future [3].<br />

References.<br />

[1] UNAIDS. Report <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e global aids epidemic. http://www.unaids.org/globalreport/ (2010).<br />

[2] Jourdain, G. et al. Intrapartum exposure to nevirapine and subsequent maternal resp<strong>on</strong>ses to<br />

nevirapine-based antiretroviral <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy. N Engl J Med 351, 229–240 (2004).<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[3] Grant, R. M. et al. Preexposure chemoprophylaxis for HIV preventi<strong>on</strong> in men who have sex<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> men. N Engl J Med 363, 2587–2599 (2010).<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Genetics; Friday, July 1, 14:30<br />

Ute v<strong>on</strong> Wangenheim<br />

Technische Fakultät, Universität Bielefeld, 335011 Bielefeld<br />

e-mail: uv<strong>on</strong>wang@techfak.uni-bielefeld.de<br />

Single–crossover recombinati<strong>on</strong> and ancestral recombinati<strong>on</strong><br />

trees<br />

Modeling <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong>s under recombinati<strong>on</strong> leads to a large coupled<br />

n<strong>on</strong>-linear dynamical system <str<strong>on</strong>g>th</str<strong>on</strong>g>at is notoriously difficult to treat. In my talk, I will<br />

present a model <str<strong>on</strong>g>th</str<strong>on</strong>g>at describes recombinati<strong>on</strong> in an ’infinite‘ populati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> single<br />

crossovers <strong>on</strong>ly.<br />

The comm<strong>on</strong> way to solve <str<strong>on</strong>g>th</str<strong>on</strong>g>ese systems relies <strong>on</strong> a certain n<strong>on</strong>linear transformati<strong>on</strong><br />

from (gamete or haplotype) frequencies to suitable correlati<strong>on</strong> functi<strong>on</strong>s.<br />

This provides an elegant soluti<strong>on</strong> in principle, but <str<strong>on</strong>g>th</str<strong>on</strong>g>e price to be paid is <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e coefficients<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transformati<strong>on</strong> must be c<strong>on</strong>structed via recursi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at involve <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e recombinati<strong>on</strong> model [1], i.e. an explicit soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics<br />

cannot be stated.<br />

I will describe a new approach to infer an explicit soluti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics. To<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is end, I use <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying stochastic process to trace recombinati<strong>on</strong> backwards<br />

in time, i.e. by backtracking <str<strong>on</strong>g>th</str<strong>on</strong>g>e ancestry <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e various independent segments each<br />

type is composed <str<strong>on</strong>g>of</str<strong>on</strong>g>. This results in binary tree structures, which can be used as a<br />

tool to formulate an explicit soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics.<br />

References.<br />

[1] v<strong>on</strong> Wangenheim, U., Baake, E., Baake, M. Single–crossover recombinati<strong>on</strong> in discrete time<br />

J. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biol 60 727–760 (2010).<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting cell systems: from intercellular interacti<strong>on</strong><br />

to tissue-level traits II; Wednesday, June 29, 17:00<br />

Anja Voss-Boehme<br />

Technical University Dresden, Center for High Performance Computing,<br />

01062 Dresden, Germany<br />

e-mail: anja.voss-boehme@tu-dresden.de<br />

Interacting cell system models for cell sorting and collective<br />

moti<strong>on</strong><br />

Biological structure and functi<strong>on</strong> in cell populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g>ten result from <str<strong>on</strong>g>th</str<strong>on</strong>g>e complex<br />

interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a large number <str<strong>on</strong>g>of</str<strong>on</strong>g> comp<strong>on</strong>ents. In particular when cells <str<strong>on</strong>g>th</str<strong>on</strong>g>at are in<br />

direct physical c<strong>on</strong>tact or located close to each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er are known to interact, possibly<br />

in a type-specific manner, <strong>on</strong>e is interested in c<strong>on</strong>cluding characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

global, collective behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell c<strong>on</strong>figurati<strong>on</strong>s from <str<strong>on</strong>g>th</str<strong>on</strong>g>e individual properties<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells and <str<strong>on</strong>g>th</str<strong>on</strong>g>e details <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e intercellular interacti<strong>on</strong>. To understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

determinants <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese processes and to c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue level traits, it is necessary<br />

to design and analyze appropriate ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models.<br />

It is argued <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e model class <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting particle systems is well-suited<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>is task. For two exemplary problems, cell sorting and collective moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

oriented cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> ferromagnetic alignment, cell based lattice models are developed<br />

which describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e major details <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e respective intercellular interacti<strong>on</strong>.<br />

If suitably simplified, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese models are analytically tractable. Several results c<strong>on</strong>cerning<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g-time behavior and <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> structure are presented and<br />

interpreted in biological terms. Challenging ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical problems <str<strong>on</strong>g>th</str<strong>on</strong>g>at require<br />

fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical developments are identified.<br />

1013

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Joe Yuichiro Wakano<br />

Meiji University<br />

e-mail: joe@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.meiji.ac.jp<br />

Kota Ikeda<br />

Meiji University<br />

Takeshi Miki<br />

Nati<strong>on</strong>al Taiwan University<br />

Masayasu Mimura<br />

Meiji University<br />

Ecosystems Dynamics; Tuesday, June 28, 14:30<br />

Reducti<strong>on</strong> from reacti<strong>on</strong>-diffusi<strong>on</strong> model to two-patch<br />

compartment model<br />

Two-patch compartment models have been explored to understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial<br />

processes <str<strong>on</strong>g>th</str<strong>on</strong>g>at promote species coexistence. However, a phenomenological definiti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e inter-patch dispersal rate has limited <str<strong>on</strong>g>th</str<strong>on</strong>g>e quantitative predictability <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ese models to community dynamics in spatially c<strong>on</strong>tinuous habitats. Here, we<br />

mechanistically rederived a two-patch Lotka-Volterra competiti<strong>on</strong> model for a spatially<br />

c<strong>on</strong>tinuous reacti<strong>on</strong>-diffusi<strong>on</strong> system where a narrow corridor c<strong>on</strong>nects two<br />

large habitats. We provide a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical formula <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dispersal rate appearing<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e two-patch compartment model as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> habitat size, corridor shape<br />

(ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> its wid<str<strong>on</strong>g>th</str<strong>on</strong>g> to its leng<str<strong>on</strong>g>th</str<strong>on</strong>g>), and organism diffusi<strong>on</strong> coefficients. For most<br />

reas<strong>on</strong>able settings, <str<strong>on</strong>g>th</str<strong>on</strong>g>e two-patch compartment model successfully approximated<br />

not <strong>on</strong>ly <str<strong>on</strong>g>th</str<strong>on</strong>g>e steady states, but also <str<strong>on</strong>g>th</str<strong>on</strong>g>e transient dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e reacti<strong>on</strong>-diffusi<strong>on</strong><br />

model. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er numerical simulati<strong>on</strong>s indicated <str<strong>on</strong>g>th</str<strong>on</strong>g>e general applicability <str<strong>on</strong>g>of</str<strong>on</strong>g> our formula<br />

to o<str<strong>on</strong>g>th</str<strong>on</strong>g>er types <str<strong>on</strong>g>of</str<strong>on</strong>g> community dynamics, e.g. driven by resource-competiti<strong>on</strong>, in<br />

spatially homogeneous and heterogeneous envir<strong>on</strong>ments. Our results suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial c<strong>on</strong>figurati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> habitats plays a central role in community dynamics<br />

in space. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, our new framework will help to improve experimental designs<br />

for quantitative test <str<strong>on</strong>g>of</str<strong>on</strong>g> metacommunity <str<strong>on</strong>g>th</str<strong>on</strong>g>eories and reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e gaps am<strong>on</strong>g<br />

modeling, empirical studies, and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir applicati<strong>on</strong> to landscape management.<br />

1014

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Fractals and Complexity I; Wednesday, June 29, 14:30<br />

Przemyslaw Waliszewski<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Urology, Philipps University, Baldingerstrasse 1, 35043<br />

Marburg, Germany<br />

e-mail: complexityresearch@yahoo.com<br />

On dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> prostate cancer; Towards <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

objective fractal system <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor grading<br />

Cellular grow<str<strong>on</strong>g>th</str<strong>on</strong>g> is <str<strong>on</strong>g>th</str<strong>on</strong>g>e fundamental biological phenomen<strong>on</strong>. A ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model<br />

shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> simplistic macroscopic dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, such as<br />

Gompertzian dynamics results from a coupling <str<strong>on</strong>g>of</str<strong>on</strong>g> a number <str<strong>on</strong>g>of</str<strong>on</strong>g> events at <str<strong>on</strong>g>th</str<strong>on</strong>g>e microscale<br />

level. The coupling is associated wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> at least <str<strong>on</strong>g>th</str<strong>on</strong>g>ree<br />

features, i.e. fractal structure <str<strong>on</strong>g>of</str<strong>on</strong>g> space-time, in which grow<str<strong>on</strong>g>th</str<strong>on</strong>g> occurs, c<strong>on</strong>diti<strong>on</strong>al<br />

probability <str<strong>on</strong>g>of</str<strong>on</strong>g> events, which eliminates sensitivity to <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial c<strong>on</strong>diti<strong>on</strong>s, and a<br />

temporal functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> entropy. The latter <strong>on</strong>e is dependent <strong>on</strong> macroscopic dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, and determines a capability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e supramolecular system for coding<br />

or transfer <str<strong>on</strong>g>of</str<strong>on</strong>g> biologically relevant informati<strong>on</strong>. Indeed, experiments wi<str<strong>on</strong>g>th</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> prostate cancer spheroids suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at bo<str<strong>on</strong>g>th</str<strong>on</strong>g> intra- and intercellular interacti<strong>on</strong>s<br />

play a significant role in fractal dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

The pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> during tumor angiogenesis changes. Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> in space<br />

results in formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial fractal tissue structures as reflected by <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial<br />

fractal dimensi<strong>on</strong>. The spatial fractal dimensi<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e normal-appearing prostate<br />

epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elium was 1.451 (018) (n=18 cases), for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Gleas<strong>on</strong> 3 pattern 1.469 (022)<br />

(n = 15 cases), for <str<strong>on</strong>g>th</str<strong>on</strong>g>e Gleas<strong>on</strong> 4 pattern 1.601 (019) (n=18 cases), and for <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Gleas<strong>on</strong> 5 pattern 1.769 (011) (n=10 cases). In additi<strong>on</strong>, different areas <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

same tumor possessed a similar value <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial fractal dimensi<strong>on</strong>. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g> regards<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e morphometric cell analysis, <str<strong>on</strong>g>th</str<strong>on</strong>g>e minimal cell radius, aspect ratio, cell<br />

roundness and compactness were all statistically different across all Gleas<strong>on</strong> score<br />

cases (ANOVA p<br />

0.95 and <str<strong>on</strong>g>th</str<strong>on</strong>g>e Poiss<strong>on</strong> probability distributi<strong>on</strong>, in which p(t) stands for PSA c<strong>on</strong>centrati<strong>on</strong>,<br />

p0 is <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial PSA c<strong>on</strong>centrati<strong>on</strong> in time t0, b stands for <str<strong>on</strong>g>th</str<strong>on</strong>g>e coefficient,<br />

t denotes scalar time. Such evoluti<strong>on</strong> suggests a decay <str<strong>on</strong>g>of</str<strong>on</strong>g> intercellular interacti<strong>on</strong>s.<br />

Those results define clinically relevant prostate cancer as <str<strong>on</strong>g>th</str<strong>on</strong>g>e first order dynamic<br />

system. The novel approach based up<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parameters p0, p’ and b can be used to<br />

compare objectively dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> different prostate cancers or to identify<br />

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cancer recurrence. The spatial fractal dimensi<strong>on</strong> allows <str<strong>on</strong>g>th</str<strong>on</strong>g>e objective and numerical<br />

grading <str<strong>on</strong>g>of</str<strong>on</strong>g> prostate cancer.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Doro<str<strong>on</strong>g>th</str<strong>on</strong>g>y Wallace<br />

Dartmou<str<strong>on</strong>g>th</str<strong>on</strong>g> College, USA<br />

e-mail: doro<str<strong>on</strong>g>th</str<strong>on</strong>g>y.wallace@dartmou<str<strong>on</strong>g>th</str<strong>on</strong>g>.edu<br />

Erin Daus<strong>on</strong><br />

Dartmou<str<strong>on</strong>g>th</str<strong>on</strong>g> College<br />

Ca<str<strong>on</strong>g>th</str<strong>on</strong>g>erine Pini<strong>on</strong><br />

Dartmou<str<strong>on</strong>g>th</str<strong>on</strong>g> College<br />

Evoluti<strong>on</strong>ary Ecology; Friday, July 1, 14:30<br />

Sexually differentiated dea<str<strong>on</strong>g>th</str<strong>on</strong>g> rates in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> an<br />

efficient mating strategy<br />

Darwin noted <str<strong>on</strong>g>th</str<strong>on</strong>g>at some sexually differentiated genetic traits, such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e bright<br />

plumage <str<strong>on</strong>g>of</str<strong>on</strong>g> male birds <str<strong>on</strong>g>th</str<strong>on</strong>g>at seems to make <str<strong>on</strong>g>th</str<strong>on</strong>g>em more visible to predators, appear<br />

to c<strong>on</strong>tradict <str<strong>on</strong>g>th</str<strong>on</strong>g>e main assumpti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> natural selecti<strong>on</strong>. Darwin proposed <str<strong>on</strong>g>th</str<strong>on</strong>g>e noti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> sexual selecti<strong>on</strong> to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>is phenomen<strong>on</strong>, and o<str<strong>on</strong>g>th</str<strong>on</strong>g>er explanati<strong>on</strong>s have<br />

been <str<strong>on</strong>g>of</str<strong>on</strong>g>fered. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is study, we use a system <str<strong>on</strong>g>of</str<strong>on</strong>g> four n<strong>on</strong>linear ordinary differential<br />

equati<strong>on</strong>s to model male and female populati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> two species <str<strong>on</strong>g>th</str<strong>on</strong>g>at have identical,<br />

efficient mating strategies but do not interbreed. One species has a higher dea<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

rate for males <str<strong>on</strong>g>th</str<strong>on</strong>g>an for females. These o<str<strong>on</strong>g>th</str<strong>on</strong>g>erwise identical species are placed in competiti<strong>on</strong>,<br />

resulting in a system wi<str<strong>on</strong>g>th</str<strong>on</strong>g> multiple fixed points and str<strong>on</strong>g dependence <strong>on</strong><br />

initial c<strong>on</strong>diti<strong>on</strong>s. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> some choices <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters, increasing <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

dea<str<strong>on</strong>g>th</str<strong>on</strong>g> rate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e male in <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two species enlarges <str<strong>on</strong>g>th</str<strong>on</strong>g>e basin <str<strong>on</strong>g>of</str<strong>on</strong>g> attracti<strong>on</strong> in<br />

which <str<strong>on</strong>g>th</str<strong>on</strong>g>at species survives and <str<strong>on</strong>g>th</str<strong>on</strong>g>e competitor is driven to extincti<strong>on</strong>, and <str<strong>on</strong>g>th</str<strong>on</strong>g>us is<br />

an adaptive resp<strong>on</strong>se. We also <str<strong>on</strong>g>of</str<strong>on</strong>g>fer a heuristic argument as to why <str<strong>on</strong>g>th</str<strong>on</strong>g>is should be<br />

so.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Georg R. Wal<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

Computati<strong>on</strong>al and Systems Biology, John Innes Centre, Norwich Research<br />

Park, Norwich NR4 7UH, UK<br />

e-mail: georg.wal<str<strong>on</strong>g>th</str<strong>on</strong>g>er@bbsrc.ac.uk<br />

Verônica A. Grieneisen<br />

Computati<strong>on</strong>al and Systems Biology, John Innes Centre, Norwich Research<br />

Park, Norwich NR4 7UH, UK<br />

e-mail: ver<strong>on</strong>ica.grieneisen@bbsrc.ac.uk<br />

A<str<strong>on</strong>g>th</str<strong>on</strong>g>anasius F. M. Marée<br />

Computati<strong>on</strong>al and Systems Biology, John Innes Centre, Norwich Research<br />

Park, Norwich NR4 7UH, UK<br />

e-mail: stan.maree@bbsrc.ac.uk<br />

Leah Edelstein-Keshet<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Department, The University <str<strong>on</strong>g>of</str<strong>on</strong>g> British Columbia, Vancouver,<br />

BC V6T 1Z2, Canada<br />

e-mail: keshet@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.ubc.ca<br />

Cell Polarizati<strong>on</strong> by Wave-Pinning: C<strong>on</strong>diti<strong>on</strong>s, Stochastic<br />

Behaviour, and Relevance to Plant Development<br />

Cell polarizati<strong>on</strong> is an important resp<strong>on</strong>se <str<strong>on</strong>g>of</str<strong>on</strong>g> eukaryotic cells to external cues, which<br />

allow cells to sense and react to signals in <str<strong>on</strong>g>th</str<strong>on</strong>g>eir envir<strong>on</strong>ment.<br />

Members <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e family <str<strong>on</strong>g>of</str<strong>on</strong>g> Rho GTPases have emerged as important comp<strong>on</strong>ents<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e polarizati<strong>on</strong> machinery <str<strong>on</strong>g>of</str<strong>on</strong>g> cells: <str<strong>on</strong>g>th</str<strong>on</strong>g>ese switch-like proteins have a distinct<br />

active (membrane-bound, low diffusivity) and inactive form (mostly cytoplasmic,<br />

high diffusivity), and localizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e active form (accumulati<strong>on</strong> in a small porti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell) has been shown to act as a necessary cue for cell polarizati<strong>on</strong> (e.g.<br />

rearrangement <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cytoskelet<strong>on</strong>). To <str<strong>on</strong>g>th</str<strong>on</strong>g>is end, Rho localizati<strong>on</strong> (short timescale)<br />

signals <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell where its fr<strong>on</strong>t and back are and <str<strong>on</strong>g>th</str<strong>on</strong>g>is informati<strong>on</strong> is usually imprinted<br />

in more committed processes such as cytoskelet<strong>on</strong> remodelling (l<strong>on</strong>g timescale).<br />

Mori et al. [1] established a reacti<strong>on</strong>-diffusi<strong>on</strong> system as a model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Rho GTPases and derived c<strong>on</strong>diti<strong>on</strong>s under which <str<strong>on</strong>g>th</str<strong>on</strong>g>eir model predicts Rho<br />

localizati<strong>on</strong>. These c<strong>on</strong>diti<strong>on</strong>s include mass c<strong>on</strong>servati<strong>on</strong>, uniformity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e inactive<br />

form, and an invasi<strong>on</strong> criteri<strong>on</strong> <strong>on</strong> a local pulse in <str<strong>on</strong>g>th</str<strong>on</strong>g>e active form. Mori et al.<br />

named <str<strong>on</strong>g>th</str<strong>on</strong>g>is mechanism wave-pinning due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e nature <str<strong>on</strong>g>of</str<strong>on</strong>g> how <str<strong>on</strong>g>th</str<strong>on</strong>g>e Rho localizati<strong>on</strong><br />

pattern forms over time.<br />

We provide a short overview <str<strong>on</strong>g>of</str<strong>on</strong>g> Rho localizati<strong>on</strong> due to wave-pinning, c<strong>on</strong>dti<strong>on</strong>s<br />

for wave-pinning, and discuss biological properties and phenomena <str<strong>on</strong>g>th</str<strong>on</strong>g>at wavepinning<br />

is capable <str<strong>on</strong>g>of</str<strong>on</strong>g> reproducing. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we introduce local pulse analysis<br />

(LPA) as a useful tool for determining c<strong>on</strong>diti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at meet an invasi<strong>on</strong> criteri<strong>on</strong><br />

necessary for wave-pinning.<br />

In a recent effort, [4], we studied a stochastic versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e wave-pinning mechanism<br />

(spatial Gillespie algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m, [2], [3]) which models Rho localizati<strong>on</strong> in a low<br />

copy-number regime <str<strong>on</strong>g>of</str<strong>on</strong>g> Rho: <str<strong>on</strong>g>th</str<strong>on</strong>g>is model includes biologically relevant stochastic<br />

noise, and behaves markedly different from <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic model established by<br />

Mori et al. We discuss differences between <str<strong>on</strong>g>th</str<strong>on</strong>g>e determinstic model, [1], and our<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

stochastic model, and reas<strong>on</strong> about c<strong>on</strong>diti<strong>on</strong>s under which wave-pinning is lost in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e latter.<br />

Relevant to plant science, our current work focuses <strong>on</strong> plant homologues <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Rho GTPase family, Rho <str<strong>on</strong>g>of</str<strong>on</strong>g> Plants (ROP), and a model <str<strong>on</strong>g>of</str<strong>on</strong>g> ROP localizati<strong>on</strong> due<br />

to wave-pinning established by Grieneisen et al. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is effort we attempt to find<br />

links between ROP localizati<strong>on</strong> as a result <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin gradients (external signal), and<br />

localizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> auxin efflux carriers (PINOID, PIN) as a readout <str<strong>on</strong>g>of</str<strong>on</strong>g> cell polarizati<strong>on</strong>.<br />

We hope <str<strong>on</strong>g>th</str<strong>on</strong>g>at linking short-timescale ROP localizati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> l<strong>on</strong>g-timescale PIN<br />

localizati<strong>on</strong> will reveal biologically relevant feedback loops between external auxin<br />

gradients, internal cell polarizati<strong>on</strong>, and eventual modificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e external auxin<br />

gradient. We argue <str<strong>on</strong>g>th</str<strong>on</strong>g>at feedback loops <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is kind may be relevant for <str<strong>on</strong>g>th</str<strong>on</strong>g>e development<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e plant embryo and establishment <str<strong>on</strong>g>of</str<strong>on</strong>g> biological phenomena such as <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

auxin maximum in <str<strong>on</strong>g>th</str<strong>on</strong>g>e quiescent centre <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e root.<br />

References.<br />

[1] Y. Mori, A. Jilkine, and L. Edelstein-Keshet Wave-pinning and cell polarity from a bistable<br />

reacti<strong>on</strong>-diffusi<strong>on</strong> system Biophysical Journal, 2008, 94 3684–97<br />

[2] D. T. Gillespie, A general me<str<strong>on</strong>g>th</str<strong>on</strong>g>od for numerically simulating <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic time evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

coupled chemical reacti<strong>on</strong>s, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Computati<strong>on</strong>al Physics, 1976, 22 403–434<br />

[3] R. Erban, J. Chapman, and P. Maini, A practical guide to stochastic simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong>diffusi<strong>on</strong><br />

processes, http://arxiv.org/abs/0704.1908, 2007<br />

[4] G.R. Wal<str<strong>on</strong>g>th</str<strong>on</strong>g>er, A.F.M. Marée, V.A. Grieneisen, and L. Edelstein-Keshet, Deterministic Versus<br />

Stochastic Cell Polarizati<strong>on</strong> by Wave Pinning Submitted for Publicati<strong>on</strong>, 2011<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Xiaojing Wang<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Science, Beijing University <str<strong>on</strong>g>of</str<strong>on</strong>g> Civil Engineering and Architecture<br />

e-mail: wangxj857@sohu.com<br />

Guohua S<strong>on</strong>g<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Science, Beijing University <str<strong>on</strong>g>of</str<strong>on</strong>g> Civil Engineering and Architecture<br />

Junqing Li<br />

Key Laboratory for Silviculture and C<strong>on</strong>servati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Ministry <str<strong>on</strong>g>of</str<strong>on</strong>g> Educati<strong>on</strong><br />

Stability Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> a Kind <str<strong>on</strong>g>of</str<strong>on</strong>g> Three-Species Food System<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Time Delay<br />

A kind <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree-dimensi<strong>on</strong>al model <str<strong>on</strong>g>of</str<strong>on</strong>g> food system including Giant Panda , bamboo<br />

and arbor wi<str<strong>on</strong>g>th</str<strong>on</strong>g> delay is c<strong>on</strong>sidered. Absolute stability and Hopf bifurcati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

model are studied by using systematic analysis me<str<strong>on</strong>g>th</str<strong>on</strong>g>od. Sufficient c<strong>on</strong>diti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

absolute stability are obtained, it is shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e delay is locally harmless. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore,<br />

it is proved <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e time delay may destabilize <str<strong>on</strong>g>th</str<strong>on</strong>g>e positive equilibrium,<br />

and Hopf bifurcati<strong>on</strong> occurs under certain c<strong>on</strong>diti<strong>on</strong>s.<br />

1020

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

John Ward<br />

Loughborough University<br />

e-mail: john.ward@lboro.ac.uk<br />

Najida Begum<br />

Loughborough University<br />

e-mail: nbegum@pharmerit.com<br />

Medical Physiology; Tuesday, June 28, 11:00<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> wound healing and <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

development <str<strong>on</strong>g>of</str<strong>on</strong>g> chr<strong>on</strong>ic wounds<br />

Epidermal wound healing is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten described in broad terms as a 3 stage process,<br />

1) inflammati<strong>on</strong> (initial resp<strong>on</strong>ses to <str<strong>on</strong>g>th</str<strong>on</strong>g>e trauma), 2) granulati<strong>on</strong> and reepi<str<strong>on</strong>g>th</str<strong>on</strong>g>eliasati<strong>on</strong><br />

(leading to wound closure) and 3) remodelling (streng<str<strong>on</strong>g>th</str<strong>on</strong>g>ening <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

new skin at <str<strong>on</strong>g>th</str<strong>on</strong>g>e wound site). Progressi<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e granulati<strong>on</strong> phase is crucial<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e wound healing process and it is <str<strong>on</strong>g>th</str<strong>on</strong>g>is stage <str<strong>on</strong>g>th</str<strong>on</strong>g>at is typically arrested in chr<strong>on</strong>ic<br />

wounds. Factors <str<strong>on</strong>g>th</str<strong>on</strong>g>at can lead to such an arrest include locally poor circulati<strong>on</strong><br />

(particularly for ulcers and pressure sores in <str<strong>on</strong>g>th</str<strong>on</strong>g>e elderly and diabetic patients) and<br />

bacterial infecti<strong>on</strong>. The costs involved in patient care is a significant burden to<br />

heal<str<strong>on</strong>g>th</str<strong>on</strong>g> services <str<strong>on</strong>g>th</str<strong>on</strong>g>roughout <str<strong>on</strong>g>th</str<strong>on</strong>g>e world.<br />

Presented in <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk is a spatio-temporal model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e healing processes during<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e granulati<strong>on</strong> phase, <str<strong>on</strong>g>th</str<strong>on</strong>g>at incorporates tissue grow<str<strong>on</strong>g>th</str<strong>on</strong>g> (granular and epi<str<strong>on</strong>g>th</str<strong>on</strong>g>elial)<br />

and migrati<strong>on</strong>, immune resp<strong>on</strong>se, fibroblast activity and angiogenesis, all <str<strong>on</strong>g>of</str<strong>on</strong>g> which<br />

dependent <strong>on</strong> nutrients and grow<str<strong>on</strong>g>th</str<strong>on</strong>g> factor levels. Simulati<strong>on</strong>s highlighting <str<strong>on</strong>g>th</str<strong>on</strong>g>e key<br />

factors <str<strong>on</strong>g>th</str<strong>on</strong>g>at influence normal and abnormal healing will be presented. For larger<br />

wounds, normal healing is characterised by <str<strong>on</strong>g>th</str<strong>on</strong>g>e formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> travelling wave soluti<strong>on</strong>s<br />

towards wound closure. Results assessing <str<strong>on</strong>g>th</str<strong>on</strong>g>e effectiveness <str<strong>on</strong>g>of</str<strong>on</strong>g> a range <str<strong>on</strong>g>of</str<strong>on</strong>g> bolus<br />

and topical <str<strong>on</strong>g>th</str<strong>on</strong>g>erapies will also be discussed.<br />

1021

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Michael Wats<strong>on</strong><br />

Heriot-Watt University, Edinburgh<br />

e-mail: michael.wats<strong>on</strong>@pet.hw.ac.uk<br />

Dr Steven McDougall<br />

Heriot-Watt University, Edinburgh<br />

Developmental Biology; Wednesday, June 29, 17:00<br />

Development <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Murine Retinal Vasculature:<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Modelling and Numerical Simulati<strong>on</strong><br />

Tumour-induced angiogenesis has been extensively explored by <str<strong>on</strong>g>th</str<strong>on</strong>g>e ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

community. However, despite <str<strong>on</strong>g>th</str<strong>on</strong>g>e availability <str<strong>on</strong>g>of</str<strong>on</strong>g> animal models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimentally<br />

accesible and highly ordered vascular topologies, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere have been few attempts to<br />

model angiogenesis during normal development. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we present a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e developing retinal vasculature, based <strong>on</strong> a coupled experimental<br />

program <str<strong>on</strong>g>of</str<strong>on</strong>g> investigati<strong>on</strong> in ne<strong>on</strong>atal mice. Formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e superficial retinal<br />

vascular plexus (RVP) occurs in a spatio-temporally defined pattern. Prior to bir<str<strong>on</strong>g>th</str<strong>on</strong>g>,<br />

astrocytes migrate away from <str<strong>on</strong>g>th</str<strong>on</strong>g>e optic nerve over <str<strong>on</strong>g>th</str<strong>on</strong>g>e surface <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e inner retina<br />

in resp<strong>on</strong>se to a chemotactic gradient. Astrocytes express fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er chemotactic, and<br />

haptotactic, signals which induce endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cell sprouting and grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e RVP.<br />

Adopting a hybrid PDE-discrete approach, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model allows tracking <str<strong>on</strong>g>of</str<strong>on</strong>g> individual<br />

astrocytes and endo<str<strong>on</strong>g>th</str<strong>on</strong>g>elial cells in resp<strong>on</strong>se to <str<strong>on</strong>g>th</str<strong>on</strong>g>ese migratory cues. The simulati<strong>on</strong>s<br />

provide an excellent correlati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e extent and pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> astrocyte<br />

migrati<strong>on</strong> and vascular network formati<strong>on</strong> observed in vivo. The model is extended<br />

to include simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> blood flow <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e nascent vessel networks, and oxygen<br />

delivery to <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding tissues. Dynamic remodelling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vasculature is <str<strong>on</strong>g>th</str<strong>on</strong>g>en<br />

performed, again producing excellent agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental observati<strong>on</strong>s.<br />

1022

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Agata Wawrzkiewicz<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Physical Chemistry and Technology <str<strong>on</strong>g>of</str<strong>on</strong>g> Polymers, Secti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Physics and Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology,<br />

44-100 Gliwice, Ks. M. Strzody 9, Poland<br />

e-mail: agata.wawrzkiewicz@gmail.com<br />

K. Pawelek<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Physical Chemistry and Technology <str<strong>on</strong>g>of</str<strong>on</strong>g> Polymers, Secti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Physics and Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology,<br />

44-100 Gliwice, Ks. M. Strzody 9, Poland<br />

P Borys<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Physical Chemistry and Technology <str<strong>on</strong>g>of</str<strong>on</strong>g> Polymers, Secti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Physics and Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology,<br />

44-100 Gliwice, Ks. M. Strzody 9, Poland<br />

Z. J. Grzywna<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Physical Chemistry and Technology <str<strong>on</strong>g>of</str<strong>on</strong>g> Polymers, Secti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Physics and Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology,<br />

44-100 Gliwice, Ks. M. Strzody 9, Poland<br />

The random walk and Langevin approaches to diffusive<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e BKCa i<strong>on</strong> channel kinetics.<br />

Up to date, several different <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical approaches were introduced to describe<br />

open and closed states <str<strong>on</strong>g>of</str<strong>on</strong>g> i<strong>on</strong> channels. They describe correctly dwell-time distributi<strong>on</strong>s,<br />

however many <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em are incapable <str<strong>on</strong>g>of</str<strong>on</strong>g> predicting and explaining l<strong>on</strong>g-term<br />

correlati<strong>on</strong>s between <str<strong>on</strong>g>th</str<strong>on</strong>g>e dwelling times <str<strong>on</strong>g>of</str<strong>on</strong>g> subsequent states <str<strong>on</strong>g>of</str<strong>on</strong>g> a channel, found<br />

in experimental patch clamp time series. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work, we have proposed a new<br />

diffusive model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinetics <str<strong>on</strong>g>of</str<strong>on</strong>g> voltage and Ca2+-activated potassium channels<br />

(BKCa). We have c<strong>on</strong>sidered and compared two <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical approaches towards<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> modeled states: <str<strong>on</strong>g>th</str<strong>on</strong>g>e random walk and Langevin <strong>on</strong>es. Our<br />

results show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinetic properties <str<strong>on</strong>g>of</str<strong>on</strong>g> experimental time series and <str<strong>on</strong>g>th</str<strong>on</strong>g>e corresp<strong>on</strong>ding<br />

simulated data obtained from <str<strong>on</strong>g>th</str<strong>on</strong>g>e model, turn out to be quite c<strong>on</strong>current.<br />

Moreover, <str<strong>on</strong>g>th</str<strong>on</strong>g>e rescaled range analysis (R/S analysis, Hurst analysis), which in our<br />

investigati<strong>on</strong>s measures <str<strong>on</strong>g>th</str<strong>on</strong>g>e correlati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e time series <str<strong>on</strong>g>of</str<strong>on</strong>g> adjacent openings and<br />

closings dwell times <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e BK channel, gives close results for experimental and<br />

modeled data.<br />

1023

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical modeling and simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis I; Wednesday, June 29,<br />

08:30<br />

Rafał Wcisło<br />

AGH University <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Technology<br />

e-mail: wcislo@agh.edu.pl<br />

Witold Dźwinel<br />

AGH University <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Technology<br />

e-mail: dzwinel@agh.edu.pl<br />

Complex Cellular Automata based <strong>on</strong> particle dynamics as a<br />

framework for modeling solid tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and angiogenesis<br />

To simulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> its avascular and angiogenic<br />

phases we propose a novel computati<strong>on</strong>al paradigm based <strong>on</strong>, so called, complex<br />

automata approach (CxA). It combines <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular automata modeling (CA) wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g>f-grid particle dynamics coupled by c<strong>on</strong>tinuum reacti<strong>on</strong>-diffusi<strong>on</strong> equati<strong>on</strong>s. The<br />

particles represent bo<str<strong>on</strong>g>th</str<strong>on</strong>g> tissue cells and fragments <str<strong>on</strong>g>of</str<strong>on</strong>g> vascular network. They interact<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir closest neighbors via semi-harm<strong>on</strong>ic central forces simulating mechanical<br />

resistance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell walls. The particle dynamics is governed by bo<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e Newt<strong>on</strong>ian laws <str<strong>on</strong>g>of</str<strong>on</strong>g> moti<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular automata rules. The rules represent<br />

cell life-cycle stimulated by various biological processes such as carcinogenesis and<br />

diffusi<strong>on</strong>-reacti<strong>on</strong> processes involving nutrients and tumor angiogenic factors. We<br />

discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e main advantage <str<strong>on</strong>g>of</str<strong>on</strong>g> CxA model such as its ability <str<strong>on</strong>g>of</str<strong>on</strong>g> simulating mechanical<br />

interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e rest <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tissue. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at our model can<br />

reproduce realistic 3-D dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e entire system c<strong>on</strong>sisting <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor, normal<br />

tissue cells, blood vessels and blood flow. We c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e CxA paradigm<br />

can serve as an efficient and elegant general framework <str<strong>on</strong>g>of</str<strong>on</strong>g> more advanced multiplescale<br />

models <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor coupling microscopic in-cell processes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> its macroscopic<br />

evoluti<strong>on</strong>. Finally, we discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e main requirements and design comp<strong>on</strong>ents <str<strong>on</strong>g>of</str<strong>on</strong>g> an<br />

interactive visualizati<strong>on</strong> engine based <strong>on</strong> CxA paradigm. Such <str<strong>on</strong>g>th</str<strong>on</strong>g>e system can be<br />

used as a valuable tool for educati<strong>on</strong>al purposes and, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e nearest future, for in<br />

silico experiments, which can play <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> angiogenesis assays in planning cancer<br />

treatment.<br />

1024

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

William Weens<br />

INRIA<br />

e-mail: william.weens@inria.fr<br />

Sabine Colnot<br />

INSERM<br />

Dirk Drasdo<br />

INRIA<br />

Jan G. Hengstler<br />

IFADO<br />

Stefan Hoehme<br />

IZBI<br />

Bioinformatics and System Biology; Wednesday, June 29, 08:30<br />

Modeling tumor development in liver<br />

As recently dem<strong>on</strong>strated for liver regenerati<strong>on</strong> after drug-induced damage, organizati<strong>on</strong><br />

and grow<str<strong>on</strong>g>th</str<strong>on</strong>g> processes can be systematically analysed by a process chain <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

experiments, image analysis and modeling [1]. In <str<strong>on</strong>g>th</str<strong>on</strong>g>at paper our group was able to<br />

quantitatively characterize <str<strong>on</strong>g>th</str<strong>on</strong>g>e architecture <str<strong>on</strong>g>of</str<strong>on</strong>g> liver lobules, <str<strong>on</strong>g>th</str<strong>on</strong>g>e repetitive functi<strong>on</strong>al<br />

building blocks <str<strong>on</strong>g>of</str<strong>on</strong>g> liver, and turn <str<strong>on</strong>g>th</str<strong>on</strong>g>is into a quantitative ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model capable<br />

to predict a previously unrecognized order mechanism. The model predicti<strong>on</strong><br />

could subsequently be experimentally validated. Here, we extend <str<strong>on</strong>g>th</str<strong>on</strong>g>is model to <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

multi-lobular scale and study, guided by experimental findings, cancerogenesis in<br />

liver. We explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e possible scenarios leading to <str<strong>on</strong>g>th</str<strong>on</strong>g>e different tumor phenotypes<br />

experimentally observed in mouse. Our model c<strong>on</strong>siders <str<strong>on</strong>g>th</str<strong>on</strong>g>e hepatocytes, <str<strong>on</strong>g>th</str<strong>on</strong>g>e main<br />

cell type in liver, as individual units wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a single cell based model and <str<strong>on</strong>g>th</str<strong>on</strong>g>e blood<br />

vessel system as a network <str<strong>on</strong>g>of</str<strong>on</strong>g> extensible objects. The model is parameterized by<br />

measurable values <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell and tissue scale and its results are directly compared<br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental findings.<br />

References.<br />

[1] Hoehme, et al. (2010) Predicti<strong>on</strong> and validati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cell alignment al<strong>on</strong>g microvessels as order<br />

principle to restore tissue architecture in liver regenerati<strong>on</strong>. Proc. Natl. Acad. Sci (USA) vol.<br />

107 no. 23 10371-10376<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Dynamics; Wednesday, June 29, 17:00<br />

Sebastian Weitz<br />

Richard Fournier<br />

Stéphane Blanco<br />

Laboratoire Plasma et C<strong>on</strong>versi<strong>on</strong> d’Energie, UMR-CNRS 5213, Université<br />

Paul Sabatier, Bât 3R1, 118 Route de Narb<strong>on</strong>ne, F-31062 Toulouse<br />

cedex 9, France<br />

e-mail: weitz@laplace.univ-tlse.fr<br />

Jacques Gautrais<br />

Christian Jost<br />

Guy Theraulaz<br />

Centre de Recherches sur la Cogniti<strong>on</strong> Animale, UMR-CNRS 5169,<br />

Université Paul Sabatier, Bât 4R3, 118 Route de Narb<strong>on</strong>ne, F-31062<br />

Toulouse cedex 9, France<br />

A model <str<strong>on</strong>g>of</str<strong>on</strong>g> self-induced <str<strong>on</strong>g>th</str<strong>on</strong>g>igmotactism in ants<br />

Ants display <str<strong>on</strong>g>th</str<strong>on</strong>g>igmotactic behaviour which is a tendency to align wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a border<br />

and move al<strong>on</strong>g it for some time. In many cases, ants’ activity results in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> envir<strong>on</strong>mental heterogeneities <str<strong>on</strong>g>th</str<strong>on</strong>g>at in turn modify <str<strong>on</strong>g>th</str<strong>on</strong>g>e moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ants<br />

and trigger a <str<strong>on</strong>g>th</str<strong>on</strong>g>igmotactic behaviour as <str<strong>on</strong>g>th</str<strong>on</strong>g>ey reach a critical size. We have analyzed<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is phenomen<strong>on</strong> during object clustering experiments in <str<strong>on</strong>g>th</str<strong>on</strong>g>e ant Messor Sanctus.<br />

The experimental investigati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ants in presence <str<strong>on</strong>g>of</str<strong>on</strong>g> objects (Casellas<br />

et al. [1] and subsequent experimental work) leads to a new <str<strong>on</strong>g>th</str<strong>on</strong>g>igmotactic random<br />

walk model, in which ants tend to walk around <str<strong>on</strong>g>th</str<strong>on</strong>g>e emerging piles ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an<br />

crossing <str<strong>on</strong>g>th</str<strong>on</strong>g>em. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is c<strong>on</strong>tributi<strong>on</strong> we analyze <str<strong>on</strong>g>th</str<strong>on</strong>g>e properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model and show<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at its predicti<strong>on</strong>s are in quantitive agreement wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental observati<strong>on</strong>s.<br />

We <str<strong>on</strong>g>th</str<strong>on</strong>g>en show <str<strong>on</strong>g>th</str<strong>on</strong>g>e essential role played by <str<strong>on</strong>g>th</str<strong>on</strong>g>e coupling between <str<strong>on</strong>g>th</str<strong>on</strong>g>e clustering<br />

dynamics and <str<strong>on</strong>g>th</str<strong>on</strong>g>e moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ants in <str<strong>on</strong>g>th</str<strong>on</strong>g>e object clustering experiments. We<br />

finally discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e implicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e nest building<br />

process in ants, and for understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e shape transiti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e clustered items<br />

observed when ants are facing low-speed air currents.<br />

References.<br />

[1] E. Casellas, J. Gautrais, R. Fournier, S. Blanco, M. Combe, V. Fourcassié, G. Theraulaz, and<br />

C. Jost, From individual to collective displacements in heterogeneous envir<strong>on</strong>ments Journal<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology 250 424–434.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Evoluti<strong>on</strong>ary Ecology; Friday, July 1, 14:30<br />

Bernt Wennberg<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical sciences, Chalmers university <str<strong>on</strong>g>of</str<strong>on</strong>g> technolgy<br />

and<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg<br />

e-mail: wennberg@chalmers.se<br />

Philip Gerlee<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical sciences, Chalmers university <str<strong>on</strong>g>of</str<strong>on</strong>g> technolgy<br />

and<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg<br />

e-mail: gerlee@chalmers.se<br />

Johan Henrikss<strong>on</strong><br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biosciences at Novum, Karolinska Institutet<br />

e-mail: johan.henrikss<strong>on</strong>@ki.se<br />

Torbjörn Lundh<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical sciences, Chalmers university <str<strong>on</strong>g>of</str<strong>on</strong>g> technolgy<br />

and<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Go<str<strong>on</strong>g>th</str<strong>on</strong>g>enburg<br />

e-mail: torbjorn.lundh@chalmers.se<br />

Sympatric speciati<strong>on</strong> and its dependence <strong>on</strong> competiti<strong>on</strong> and<br />

streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> reinforcement<br />

Sympatric speciati<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary split <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>e species into two or more<br />

species in <str<strong>on</strong>g>th</str<strong>on</strong>g>e same envir<strong>on</strong>ment. We c<strong>on</strong>sider a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for <str<strong>on</strong>g>th</str<strong>on</strong>g>is phenomen<strong>on</strong>,<br />

in which reinforcement plays an important role. By reinforcement we<br />

mean a phenotypic trait <str<strong>on</strong>g>th</str<strong>on</strong>g>at influences <str<strong>on</strong>g>th</str<strong>on</strong>g>e choice <str<strong>on</strong>g>of</str<strong>on</strong>g> mating partner, but has no<br />

impact <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment. The model is individual based,<br />

implemented as a discrete time Markov process in a space Z N , where Z is <str<strong>on</strong>g>th</str<strong>on</strong>g>e phenotype<br />

space <str<strong>on</strong>g>of</str<strong>on</strong>g> an individual and N is <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals. Reproducti<strong>on</strong> is<br />

modelled as <str<strong>on</strong>g>th</str<strong>on</strong>g>e result <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> pairs <str<strong>on</strong>g>of</str<strong>on</strong>g> individuals, but does not involve<br />

different genders, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>of</str<strong>on</strong>g>fspring depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parents’s adaptati<strong>on</strong><br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment. The basic model is presented in [1], where simulati<strong>on</strong>s simulati<strong>on</strong><br />

results are presented <str<strong>on</strong>g>th</str<strong>on</strong>g>at show <str<strong>on</strong>g>th</str<strong>on</strong>g>at reinforcement is essential for speciati<strong>on</strong><br />

to take place. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper <str<strong>on</strong>g>th</str<strong>on</strong>g>e model is fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er developed, and in particular we<br />

investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact <str<strong>on</strong>g>of</str<strong>on</strong>g> specializati<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>ment <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e rate <str<strong>on</strong>g>of</str<strong>on</strong>g> speciati<strong>on</strong><br />

events, and <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g term survival <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e decendants <str<strong>on</strong>g>of</str<strong>on</strong>g> a species.<br />

References.<br />

[1] J. Henrikss<strong>on</strong>, T. Lundh and B. Wennberg, A model <str<strong>on</strong>g>of</str<strong>on</strong>g> sympatric speciati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>rough reinforcement,<br />

Kinetic and related models 3 no 1, 143–163.<br />

1027

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Statistical Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Signals II; Saturday, July 2, 11:00<br />

Aleksander Wer<strong>on</strong><br />

Wroclaw University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: aleksander.wer<strong>on</strong>@pwr.wroc.pl<br />

Identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> fracti<strong>on</strong>al subdiffusive dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> mRNA<br />

molecules<br />

Identificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> fracti<strong>on</strong>al subdiffusive dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> mRNA molecules<br />

Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g> Burnecki and Aleksander Wer<strong>on</strong><br />

Hugo Steinhaus Center, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science, Wroclaw<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we propose a statistical me<str<strong>on</strong>g>th</str<strong>on</strong>g>odology how to distinguish between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>ree mechanisms leading to single molecule subdiffusi<strong>on</strong>, [1-2]. Namely, fracti<strong>on</strong>al<br />

Brownian moti<strong>on</strong>, fracti<strong>on</strong>al Levy stable moti<strong>on</strong> and Fracti<strong>on</strong>al Fokker-Planck<br />

equati<strong>on</strong>. We illustrate step by step <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> sample mean-squared<br />

displacement and p-variati<strong>on</strong> can be successfully applied for infinite and c<strong>on</strong>fined<br />

systems. We already identified fracti<strong>on</strong>al subdiffusive dynamics <strong>on</strong> biological data<br />

describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e moti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individual fluorescently labeled mRNA molecules inside<br />

live E. coli cells [3-5], but it may c<strong>on</strong>cern also many o<str<strong>on</strong>g>th</str<strong>on</strong>g>er biological experimental<br />

data.<br />

References.<br />

[1] I. Golding and E.C. Cox, Phys. Rev. Lett. 96, 098102 (2006).<br />

[2] G. Guigas, C. Kalla, and M. Weiss, Biophys. J. 93, 316 (2007).<br />

[3] M. Magdziarz, A. Wer<strong>on</strong>, K. Burnecki, and J. Klafter, Phys Rev. Lett. 103, 180602 (2009).<br />

[4] K. Burnecki, A. Wer<strong>on</strong>, Phys. Rev. E 82, 021130 (2010).<br />

[5] M. Magdziarz and J. Klafter, Phys. Rev. E 82, 011129 (2010).<br />

1028

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Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Sergiusz Wesolowski<br />

Dept. <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Computer Science, Mechanics; Warsaw University,<br />

Poland<br />

e-mail: wesserg@gmail.com<br />

Piotr Kraj<br />

Cancer Center, Medical College <str<strong>on</strong>g>of</str<strong>on</strong>g> Georgia, Georgia Heal<str<strong>on</strong>g>th</str<strong>on</strong>g> Science<br />

University, USA<br />

e-mail: pkraj@georgiaheal<str<strong>on</strong>g>th</str<strong>on</strong>g>.edu<br />

Improving statistical models for discovering cell type specific<br />

genes<br />

Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong> is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fundamental me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> characterizing<br />

cell populati<strong>on</strong>s. One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e major cells in <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune system are "helper" T cells<br />

expressing CD4 surface marker. The majority <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese cells c<strong>on</strong>stitutes a populati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>venti<strong>on</strong>al CD4+ T cells which supports functi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> o<str<strong>on</strong>g>th</str<strong>on</strong>g>er cells <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e adaptive<br />

and innate immune system. A smaller populati<strong>on</strong>, called regulatory CD4+ T cells<br />

(Treg), has opposite functi<strong>on</strong> and suppresses immune resp<strong>on</strong>se and is resp<strong>on</strong>sible<br />

for <str<strong>on</strong>g>th</str<strong>on</strong>g>e homeostasis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune system. The most characteristic gene expressed<br />

by Treg cells is a transcripti<strong>on</strong> factor Foxp3. Bo<str<strong>on</strong>g>th</str<strong>on</strong>g> c<strong>on</strong>venti<strong>on</strong>al and Treg cells are<br />

generated in <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ymus from b<strong>on</strong>e marrow-derived progenitors. Treg cells produced<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ymus are called natural Treg cells. Under certain c<strong>on</strong>diti<strong>on</strong>s, c<strong>on</strong>venti<strong>on</strong>al<br />

CD4 T cells can express Foxp3 and acquire suppressor functi<strong>on</strong>. These Treg cells<br />

are called adaptive Treg.<br />

One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> investigating different subsets <str<strong>on</strong>g>of</str<strong>on</strong>g> CD4 T cells is to compare<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir gene expressi<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles. This approach allows insight into cellular functi<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> individual cell subsets and allows for analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> functi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> differentially<br />

expressed genes. Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e global expressi<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles is comm<strong>on</strong>ly d<strong>on</strong>e using<br />

microarrays.<br />

To reveal genetic c<strong>on</strong>trol <str<strong>on</strong>g>of</str<strong>on</strong>g> various subsets <str<strong>on</strong>g>of</str<strong>on</strong>g> CD4 T cells we compared gene<br />

expressi<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles <str<strong>on</strong>g>of</str<strong>on</strong>g> resting and activated c<strong>on</strong>venti<strong>on</strong>al CD4 T cells, resting and<br />

activated natural Treg cells and adaptive Treg cells. RNA was isolated from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

respective T cell populati<strong>on</strong>s and hybridized to Affymetrix GeneChip M430 2.0<br />

Plus microarrays. Three individual samples <str<strong>on</strong>g>of</str<strong>on</strong>g> each kind were processed.<br />

In order to make our data set more representative, followin a similar approach<br />

described in [1], we included microarrays from <str<strong>on</strong>g>th</str<strong>on</strong>g>e respective CD4 T cell subsets<br />

from o<str<strong>on</strong>g>th</str<strong>on</strong>g>er laboratories. These data were obtained from <str<strong>on</strong>g>th</str<strong>on</strong>g>e GEO database:<br />

www.ncbi.nlm.nih.gov/geo.<br />

To deal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem we produced a framework combined from several<br />

available statistical approaches: Linear models for Microarray data, Bayesian approach,<br />

N<strong>on</strong>-Negative Matrix Factorisati<strong>on</strong> [2].<br />

Comparis<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> data from multiple laboratories introduces additi<strong>on</strong>al levels <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

variability which need to be accounted for during data normalizati<strong>on</strong>.<br />

Normalizati<strong>on</strong> attempts <str<strong>on</strong>g>th</str<strong>on</strong>g>at adjusted mean values and standard deviati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

gene expressi<strong>on</strong> resulted in <str<strong>on</strong>g>th</str<strong>on</strong>g>e sets <str<strong>on</strong>g>of</str<strong>on</strong>g> differentially expressed genes <str<strong>on</strong>g>th</str<strong>on</strong>g>at differed<br />

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between laboratories instead <str<strong>on</strong>g>of</str<strong>on</strong>g> between different T cell populati<strong>on</strong>s. Our computati<strong>on</strong>s<br />

indicated <str<strong>on</strong>g>th</str<strong>on</strong>g>at lab origin has more influence <strong>on</strong> gene expressi<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>en<br />

investigated cell types am<strong>on</strong>g laboratories.<br />

To account for multi-dimensi<strong>on</strong>ality <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e normalizati<strong>on</strong> problem we developed<br />

a heuristic approach.<br />

References.<br />

[1] Jean-Philippe Brunet, Pablo Tamayo, Todd R. Golub, Jill P. Mesirov, Metagenes and molecular<br />

pattern discovery using matrix factorizati<strong>on</strong> PNAS 12 4164–4169.<br />

[2] Franz-Josef Müller, Louise C. Laurent, Dennis Kostka, Igor Ulitsky, Roy Williams, Christina<br />

Lu, In-Hyun Park, Mahendra S. Rao, R<strong>on</strong> Shamir, Philip H. Schwartz, Nils O. Schmidt Loring,<br />

Jeanne F. Loring, Regulatory networks define phenotypic classes <str<strong>on</strong>g>of</str<strong>on</strong>g> human stem cell lines<br />

Nature (18 September 2008) 455 401–405.<br />

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Fractals and Complexity I; Wednesday, June 29, 14:30<br />

Bruce J. West<br />

Informati<strong>on</strong> Science Directorate, US Army Research Office<br />

e-mail: bruce.j.west@us.army.mil<br />

Origins <str<strong>on</strong>g>of</str<strong>on</strong>g> Allometric Grow<str<strong>on</strong>g>th</str<strong>on</strong>g>: A C<strong>on</strong>temporary Perspective<br />

The <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical allometry relati<strong>on</strong> (AR) between <str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> an organism Y<br />

and <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>of</str<strong>on</strong>g> an organ wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e organism X is <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e form X = aY b and has<br />

been known for nearly two centuries. The allometry coefficient a and allometry<br />

exp<strong>on</strong>ent b have been fit by various data sets over <str<strong>on</strong>g>th</str<strong>on</strong>g>at time. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e last century<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e phenomenological field <str<strong>on</strong>g>of</str<strong>on</strong>g> allometry has found its way into almost every scientific<br />

discipline and <str<strong>on</strong>g>th</str<strong>on</strong>g>e ARs have been reinterpreted wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Y still being <str<strong>on</strong>g>th</str<strong>on</strong>g>e size <str<strong>on</strong>g>of</str<strong>on</strong>g> a host<br />

network and X a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network. For example, in biology <str<strong>on</strong>g>th</str<strong>on</strong>g>e measure <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

size is <str<strong>on</strong>g>of</str<strong>on</strong>g>ten taken to be <str<strong>on</strong>g>th</str<strong>on</strong>g>e total body mass and <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong> is <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolic rate,<br />

or heart rate, brea<str<strong>on</strong>g>th</str<strong>on</strong>g>ing rate, or l<strong>on</strong>gevity <str<strong>on</strong>g>of</str<strong>on</strong>g> animals. Most <str<strong>on</strong>g>th</str<strong>on</strong>g>eories purporting to<br />

explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e origin <str<strong>on</strong>g>of</str<strong>on</strong>g> ARs focus <strong>on</strong> establishing <str<strong>on</strong>g>th</str<strong>on</strong>g>e proper value <str<strong>on</strong>g>of</str<strong>on</strong>g> b entailed by<br />

reducti<strong>on</strong>ist models, whereas a few o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers use statistical arguments to emphasize<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> a.<br />

On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er hand, statistical data analysis indicates <str<strong>on</strong>g>th</str<strong>on</strong>g>at empirical ARs are<br />

obtained wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e replacements X → 〈X〉 and Y → 〈Y 〉 and <str<strong>on</strong>g>th</str<strong>on</strong>g>e brackets denote an<br />

average over an ensemble <str<strong>on</strong>g>of</str<strong>on</strong>g> realizati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network and its functi<strong>on</strong>. Networks<br />

in which <str<strong>on</strong>g>th</str<strong>on</strong>g>ese empirical ARs are established include <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolism <str<strong>on</strong>g>of</str<strong>on</strong>g> animals,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e grow<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> plants, species abundance in ec<strong>on</strong>etworks, <str<strong>on</strong>g>th</str<strong>on</strong>g>e geomorphology <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

rivers, and many more. The resulting empirical AR can <strong>on</strong>ly be derived from <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical <strong>on</strong>e by averaging under c<strong>on</strong>diti<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at are incompatible wi<str<strong>on</strong>g>th</str<strong>on</strong>g> real data.<br />

C<strong>on</strong>sequently ano<str<strong>on</strong>g>th</str<strong>on</strong>g>er strategy for finding <str<strong>on</strong>g>th</str<strong>on</strong>g>e origin <str<strong>on</strong>g>of</str<strong>on</strong>g> ARs is required and for <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

we turn to <str<strong>on</strong>g>th</str<strong>on</strong>g>e probability calculus and fracti<strong>on</strong>al derivatives.<br />

We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e statistics <str<strong>on</strong>g>of</str<strong>on</strong>g> living networks can be described by fracti<strong>on</strong>al<br />

diffusi<strong>on</strong> equati<strong>on</strong>s (FDEs) and hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esize <str<strong>on</strong>g>th</str<strong>on</strong>g>at FDEs can explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e origin <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

ARs. We obtain <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fourier-Laplace transform <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e general soluti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>e FDE<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>tains bo<str<strong>on</strong>g>th</str<strong>on</strong>g> historical informati<strong>on</strong> and n<strong>on</strong>local influences <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamic<br />

variables, <str<strong>on</strong>g>th</str<strong>on</strong>g>at is, fracti<strong>on</strong>al derivatives in bo<str<strong>on</strong>g>th</str<strong>on</strong>g> time and phase space, complexity<br />

comm<strong>on</strong>ly found in living networks. The scaling properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting soluti<strong>on</strong><br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e FDE enable us to interrelate <str<strong>on</strong>g>th</str<strong>on</strong>g>e network’s size and functi<strong>on</strong> by means <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanism <str<strong>on</strong>g>of</str<strong>on</strong>g> str<strong>on</strong>g anticipati<strong>on</strong>. The analysis shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at str<strong>on</strong>g anticipati<strong>on</strong><br />

and scaling taken toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er support <str<strong>on</strong>g>th</str<strong>on</strong>g>e hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis and is sufficient to explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

origin <str<strong>on</strong>g>of</str<strong>on</strong>g> empirical ARs.<br />

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Ecology and evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> infectious diseases; Friday, July 1, 14:30<br />

Andy White<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Heriot Watt University, Edinburgh, EH14 4AS.<br />

e-mail: A.R.White@hw.ac.uk<br />

Alex Best<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sheffield<br />

Eva Kisdi<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Helsinki<br />

Janis Ant<strong>on</strong>ovics<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Virginia<br />

Mike Brockhurst<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Liverpool<br />

Mike Boots<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Sheffield<br />

The evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> host-parasite range<br />

Understanding <str<strong>on</strong>g>th</str<strong>on</strong>g>e coevoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> hosts and parasites is <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e key challenges<br />

for evoluti<strong>on</strong>ary biology. Adaptive dynamics techniques have examined coevoluti<strong>on</strong>ary<br />

outcomes in classical infectious disease model frameworks in which<br />

infecti<strong>on</strong> depends <strong>on</strong> absolute rates <str<strong>on</strong>g>of</str<strong>on</strong>g> transmissi<strong>on</strong> and defence [1]. These models<br />

typically predict ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>at <strong>on</strong>e strain dominates or <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is evoluti<strong>on</strong>ary<br />

branching, where disruptive selecti<strong>on</strong> around a fitness minimum causes <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> two distinct strains. This may <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore provide insight into <str<strong>on</strong>g>th</str<strong>on</strong>g>e <strong>on</strong>set <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

diversity but does not fully explain <str<strong>on</strong>g>th</str<strong>on</strong>g>e generati<strong>on</strong> and maintenance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e wide<br />

range <str<strong>on</strong>g>of</str<strong>on</strong>g> variati<strong>on</strong> in host and parasite strains observed in natural systems. Here<br />

we present a fully coevoluti<strong>on</strong>ary host-parasite model using <str<strong>on</strong>g>th</str<strong>on</strong>g>e assumpti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

adaptive dynamics, but ra<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>an assuming <str<strong>on</strong>g>th</str<strong>on</strong>g>at transmissibility and defence are<br />

absolute we approximate an ‘all or no<str<strong>on</strong>g>th</str<strong>on</strong>g>ing’ infecti<strong>on</strong> process where <str<strong>on</strong>g>th</str<strong>on</strong>g>e success <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

infecti<strong>on</strong> depends up<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e relative ‘range’ <str<strong>on</strong>g>of</str<strong>on</strong>g> host resistance and parasite infectivity.<br />

A parasite <str<strong>on</strong>g>th</str<strong>on</strong>g>at can infect a wide range <str<strong>on</strong>g>of</str<strong>on</strong>g> host strains will pay a cost in<br />

terms <str<strong>on</strong>g>of</str<strong>on</strong>g> disease transmissi<strong>on</strong> compared to parasites <str<strong>on</strong>g>th</str<strong>on</strong>g>at infect a narrower range <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

hosts. A similar trade-<str<strong>on</strong>g>of</str<strong>on</strong>g>f exists in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> parasite strains a host can<br />

resist and <str<strong>on</strong>g>th</str<strong>on</strong>g>e host reproductive rate. Infecti<strong>on</strong> success <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore depends <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

specific characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e parasite and <str<strong>on</strong>g>th</str<strong>on</strong>g>e host. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at c<strong>on</strong>siderable<br />

diversity can be generated and maintained due to epidemiological feedbacks, wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

strains differing in <str<strong>on</strong>g>th</str<strong>on</strong>g>e range <str<strong>on</strong>g>of</str<strong>on</strong>g> host and parasite types <str<strong>on</strong>g>th</str<strong>on</strong>g>ey can respectively infect<br />

or resist [2]. The patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> resistance and infectivity are also in close agreement<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> laboratory results <str<strong>on</strong>g>th</str<strong>on</strong>g>at assess <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary behaviour in a bacteria-phage<br />

system.<br />

References.<br />

[1] Best, A., White, A. and Boots, M. 2009. The implicati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> coevoluti<strong>on</strong>ary dynamics to<br />

host-parasite interacti<strong>on</strong>s. American Naturalist, 173: 779-791.<br />

[2] Best, A., White, A., Kisdi, E., Ant<strong>on</strong>ovics, J., Brockhurst, M. A. and Boots, M. 2010. The<br />

evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> host-parasite range. American Naturalist, 176: 63-71.<br />

1032

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Reports from US - African BioMa<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Initiative: C<strong>on</strong>servati<strong>on</strong><br />

Biology; Saturday, July 2, 14:30<br />

Ruscena Wiederholt<br />

USGS Patuxent Wildlife Research Center<br />

e-mail: rpw143@psu.edu<br />

Chris Guerney<br />

University California Berkeley<br />

L<strong>on</strong>gt<strong>on</strong>g Turshak<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Jos<br />

Adel Ferchichi<br />

Tunis University<br />

The effects <str<strong>on</strong>g>of</str<strong>on</strong>g> disturbance, fire, and elephants <strong>on</strong> savanna<br />

woodlands<br />

The extent to which ecological systems are experiencing disturbance and change in<br />

functi<strong>on</strong> and structure is critical for <str<strong>on</strong>g>th</str<strong>on</strong>g>e l<strong>on</strong>g-term c<strong>on</strong>servati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> biological diversity.<br />

The savanna, <str<strong>on</strong>g>th</str<strong>on</strong>g>e dominant ecosystem <str<strong>on</strong>g>of</str<strong>on</strong>g> sub-Saharan Africa, is characterized<br />

by <str<strong>on</strong>g>th</str<strong>on</strong>g>e coexistence <str<strong>on</strong>g>of</str<strong>on</strong>g> a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> woody plants and grasses. Vegetati<strong>on</strong> modificati<strong>on</strong><br />

from woodland to grassland has most <str<strong>on</strong>g>of</str<strong>on</strong>g>ten been attributed to <str<strong>on</strong>g>th</str<strong>on</strong>g>e coupled effects<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> elephant herbivory and fire. Therefore, to better inform management strategies<br />

for woodland savanna ecosystems, <str<strong>on</strong>g>th</str<strong>on</strong>g>e objective <str<strong>on</strong>g>of</str<strong>on</strong>g> our study was to model <str<strong>on</strong>g>th</str<strong>on</strong>g>e impact<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> fire and herbivory <strong>on</strong> tree survival. We used density-dependent, stochastic<br />

Lefkovitch matrix models to simulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong> dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> woody plants in<br />

Kruger Nati<strong>on</strong>al Park, Mpumalanga, Sou<str<strong>on</strong>g>th</str<strong>on</strong>g> Africa. Our model was run <strong>on</strong> biannual<br />

time steps, including wet and dry seas<strong>on</strong>s, for 50 years. Elephant herbivory was<br />

assumed to occur every dry seas<strong>on</strong>, while <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> fire was stochastic. We<br />

tested different frequencies and intensities <str<strong>on</strong>g>of</str<strong>on</strong>g> fire and herbivory in our model, and<br />

also altered <str<strong>on</strong>g>th</str<strong>on</strong>g>e variance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e fire parameters. Preliminary results indicated an<br />

average fire return interval <str<strong>on</strong>g>of</str<strong>on</strong>g> 3-4 years produced an approximately stable populati<strong>on</strong><br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. Our sensitivity analysis showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at under baseline c<strong>on</strong>diti<strong>on</strong>s adult<br />

tree survival was <str<strong>on</strong>g>th</str<strong>on</strong>g>e most important factor affecting populati<strong>on</strong> grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rates. We<br />

also found <str<strong>on</strong>g>th</str<strong>on</strong>g>at different fire regimes, varying intensities <str<strong>on</strong>g>of</str<strong>on</strong>g> disturbance, and even<br />

altering <str<strong>on</strong>g>th</str<strong>on</strong>g>e variance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese parameters can pr<str<strong>on</strong>g>of</str<strong>on</strong>g>oundly affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e pattern <str<strong>on</strong>g>of</str<strong>on</strong>g> savanna<br />

structure over time. Therefore, our results indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>at savanna woodland<br />

structure is sensitive to bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e frequency and intensity <str<strong>on</strong>g>of</str<strong>on</strong>g> disturbance which has<br />

important management implicati<strong>on</strong>s.<br />

1033

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Ka<str<strong>on</strong>g>th</str<strong>on</strong>g>leen Wilkie and Philip Hahnfeldt<br />

Center <str<strong>on</strong>g>of</str<strong>on</strong>g> Cancer Systems Biology<br />

Steward St. Elizabe<str<strong>on</strong>g>th</str<strong>on</strong>g>’s Medical Center,<br />

Tufts University School <str<strong>on</strong>g>of</str<strong>on</strong>g> Medicine, Bost<strong>on</strong>, MA 02135 USA<br />

e-mail: ka<str<strong>on</strong>g>th</str<strong>on</strong>g>leen.wilkie@steward.org<br />

Modelling Immunomodulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Tumor Grow<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

The physical presence and activities <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells elicit an immune resp<strong>on</strong>se<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e host. In turn, <str<strong>on</strong>g>th</str<strong>on</strong>g>is immune resp<strong>on</strong>se has been shown to be bo<str<strong>on</strong>g>th</str<strong>on</strong>g> stimulatory<br />

and inhibitory to tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. This interplay <str<strong>on</strong>g>th</str<strong>on</strong>g>erefore has complex implicati<strong>on</strong>s<br />

for tumor development. To explore <str<strong>on</strong>g>th</str<strong>on</strong>g>ese, we have developed a system <str<strong>on</strong>g>of</str<strong>on</strong>g> differential<br />

equati<strong>on</strong>s to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune resp<strong>on</strong>se in tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. The<br />

two-compartment model c<strong>on</strong>sists <str<strong>on</strong>g>of</str<strong>on</strong>g> bo<str<strong>on</strong>g>th</str<strong>on</strong>g> cancer and immune cells: <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer cells<br />

proliferate <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir own and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir grow<str<strong>on</strong>g>th</str<strong>on</strong>g> can ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er be inhibited or stimulated by<br />

immune cells in a manner dependent <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e states <str<strong>on</strong>g>of</str<strong>on</strong>g> each, while <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune cells<br />

are recruited to <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor site by ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer cells or by <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune cells. Cancer cells, innate immune cells (such as<br />

platelets, dendritic cells, macrophages, and natural killer cells) and adaptive immune<br />

cells (such as T and B lymphocytes) communicate wi<str<strong>on</strong>g>th</str<strong>on</strong>g> each o<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>rough<br />

cytokine and chemokine producti<strong>on</strong> which c<strong>on</strong>trols and shapes tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>. The<br />

cummulative result <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interacti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese diverse cells determines whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

tumor-promoting inflammati<strong>on</strong> or antitumor immunity occurs, and it is <str<strong>on</strong>g>th</str<strong>on</strong>g>is wholistic<br />

resp<strong>on</strong>se <str<strong>on</strong>g>th</str<strong>on</strong>g>at we attempt to capture in our model. Most ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune resp<strong>on</strong>se to cancer focus <strong>on</strong> single immune cells and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir specific<br />

functi<strong>on</strong> in cancer cell killing. One <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e main advantages <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is model is <str<strong>on</strong>g>th</str<strong>on</strong>g>at it<br />

combines <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> all immune cell types and <str<strong>on</strong>g>th</str<strong>on</strong>g>e physical process <str<strong>on</strong>g>of</str<strong>on</strong>g> inflammati<strong>on</strong><br />

into <strong>on</strong>e quantitative model setting. Thus, it is better positi<strong>on</strong>ed to predict<br />

immunomodulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, and to assist in <str<strong>on</strong>g>th</str<strong>on</strong>g>e design <str<strong>on</strong>g>of</str<strong>on</strong>g> novel treatment<br />

approaches <str<strong>on</strong>g>th</str<strong>on</strong>g>at exploit immune resp<strong>on</strong>se to improve tumor suppressi<strong>on</strong>.<br />

References.<br />

[1] S.I. Grivennikov, F.R. Greten, M. Karin, Immunity, Inflammati<strong>on</strong>, and Cancer Cell 2010 140<br />

883–899.<br />

[2] V.A. Kuznetsov, I.A. Makalkin, M.A. Taylor, A.S. Perels<strong>on</strong>, N<strong>on</strong>linear Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Immunogenic<br />

Tumors: Parameter Estimati<strong>on</strong> and Global Bifurcati<strong>on</strong> Analysis Bull Ma<str<strong>on</strong>g>th</str<strong>on</strong>g> Biol 1994<br />

56(2) 295–321.<br />

[3] R.T. Prehn The Immune Reacti<strong>on</strong> as a Stimulator <str<strong>on</strong>g>of</str<strong>on</strong>g> Tumor Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> Science 1972 176 170–<br />

171.<br />

1034

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Lisa Willis<br />

CoMPLEX, University College L<strong>on</strong>d<strong>on</strong><br />

e-mail: l.willis@ucl.ac.uk<br />

Developmental Biology; Saturday, July 2, 11:00<br />

Biosilica nanoscale pattern formati<strong>on</strong> in diatoms<br />

Over <str<strong>on</strong>g>th</str<strong>on</strong>g>e last 200 milli<strong>on</strong> years, a number <str<strong>on</strong>g>of</str<strong>on</strong>g> aquatic unicellular eukaryotic organisms<br />

have evolved mechanisms to sequester and assemble biominerals into exogenous<br />

structures. The results seen today are high-fidelity, mineralized shells featuring patterned<br />

complex nanoscale ornamentati<strong>on</strong>s <str<strong>on</strong>g>th</str<strong>on</strong>g>at defy syn<str<strong>on</strong>g>th</str<strong>on</strong>g>esis in vitro. Am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

organisms, diatoms are topical owing to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir fundamental role in <str<strong>on</strong>g>th</str<strong>on</strong>g>e carb<strong>on</strong> cycle,<br />

in food chains ascending to fish, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e potential uses <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir biosilica shells in<br />

developing nanotechnologies. Their species-specific mineralized shells have diverse<br />

morphologies, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> structures <str<strong>on</strong>g>th</str<strong>on</strong>g>at span scales from 5 nm to 0.5 mm. At <str<strong>on</strong>g>th</str<strong>on</strong>g>e finest<br />

scale are structures called pore occlusi<strong>on</strong>s, which in a matter <str<strong>on</strong>g>of</str<strong>on</strong>g> minutes assemble<br />

and solidify under ambient physiological c<strong>on</strong>diti<strong>on</strong>s into roughly deterministic<br />

patterns <str<strong>on</strong>g>th</str<strong>on</strong>g>at are c<strong>on</strong>served wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in species, but which vary between species. Very<br />

little is known about <str<strong>on</strong>g>th</str<strong>on</strong>g>e physical processes governing <str<strong>on</strong>g>th</str<strong>on</strong>g>is biosilica patterned assembly.<br />

In an attempt to identify <str<strong>on</strong>g>th</str<strong>on</strong>g>e physical processes governing pore occlusi<strong>on</strong><br />

formati<strong>on</strong>, we are investigating new pattern forming probabilistic (spin-like) lattice<br />

models in coordinati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> diatom culturing experiments, which have produced<br />

some promising results.<br />

1035

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Dynamics; Wednesday, June 29, 14:30<br />

Christian Winkel<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Analysis and Numerical Simulati<strong>on</strong> · University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Stuttgart · Pfaffenwaldring 57 · D-70569 Stuttgart<br />

e-mail: christian.winkel@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematik.uni-stuttgart.de<br />

Christina Surulescu<br />

Institut <str<strong>on</strong>g>of</str<strong>on</strong>g> Numerical and Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics · University <str<strong>on</strong>g>of</str<strong>on</strong>g> Münster<br />

· Einsteinstraße 62 · D-48149 Münster<br />

e-mail: christina.surulescu@uni-muenster.de<br />

Peter Scheurich<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Cell Biology and Immunology · University <str<strong>on</strong>g>of</str<strong>on</strong>g> Stuttgart<br />

· Allmandring 31 · D-70569 Stuttgart<br />

e-mail: peter.scheurich@izi.uni-stuttgart.de<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model(s) for <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> (TNF-)<br />

Receptor Clustering<br />

Resp<strong>on</strong>ses <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e immune system are coordinated by immune horm<strong>on</strong>es, called<br />

cytokines. Tumor necrosis factor (TNF) is a cytokine regulating <str<strong>on</strong>g>th</str<strong>on</strong>g>e innate immune<br />

system, including cells like dendritic cells, macrophages and neutrophils.<br />

Disregulated TNF has been recognized as <str<strong>on</strong>g>th</str<strong>on</strong>g>e main factor in progressi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> many<br />

autoimmune diseases, like Rheumatoid Ar<str<strong>on</strong>g>th</str<strong>on</strong>g>ritis and Morbus Crohn. TNF is a homotrimeric<br />

protein capable to bind <str<strong>on</strong>g>th</str<strong>on</strong>g>ree receptors. But also unligated receptors<br />

occur <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell surface as homomultimers due to a homophilic interacti<strong>on</strong> domain.<br />

Based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese two interacti<strong>on</strong> motivs (ligand/receptor and receptor/receptor) we<br />

present two different modelling and simulati<strong>on</strong> strategies.<br />

Firstly, we use a mass acti<strong>on</strong> kinetics approach to propose an ordinary differential<br />

equati<strong>on</strong>s model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> subsequent formati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> signal clusters <strong>on</strong><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cell membrane. Thereby, we focus our attenti<strong>on</strong> <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e essential comp<strong>on</strong>ents <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e system <str<strong>on</strong>g>of</str<strong>on</strong>g> elementary ligand/receptor complexes <str<strong>on</strong>g>th</str<strong>on</strong>g>at can initiate intracellular<br />

signaling processes eventually leading to caspase mediated cell dea<str<strong>on</strong>g>th</str<strong>on</strong>g>. Therefore we<br />

develop our model in a way <str<strong>on</strong>g>th</str<strong>on</strong>g>at not <strong>on</strong>ly receptor cross-linking by ligand but also<br />

homophilic interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> receptors leading to homodimer formati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e absence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> ligand is encompassed.<br />

It turns out <str<strong>on</strong>g>th</str<strong>on</strong>g>at using parameter values for binding affinities c<strong>on</strong>sistent wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

experimentally determined values <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> our model suggests <str<strong>on</strong>g>th</str<strong>on</strong>g>at in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

case <str<strong>on</strong>g>of</str<strong>on</strong>g> high ligand and low receptor c<strong>on</strong>centrati<strong>on</strong> no substrate inhibiti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

receptor cross-linking can be observed. In c<strong>on</strong>trast, our model shows <str<strong>on</strong>g>th</str<strong>on</strong>g>at an increasing<br />

ligand c<strong>on</strong>centrati<strong>on</strong> leads to a saturati<strong>on</strong> in receptor cross-linking and<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>erewi<str<strong>on</strong>g>th</str<strong>on</strong>g> illustrating <str<strong>on</strong>g>th</str<strong>on</strong>g>e persistence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e downstream signaling events even in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e case <str<strong>on</strong>g>of</str<strong>on</strong>g> ligand excess. These results are underlined by numerical simulati<strong>on</strong>s,<br />

which are c<strong>on</strong>firmed by experimental data.<br />

Sec<strong>on</strong>dly, we apply a populati<strong>on</strong> balance model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> simultaneous grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and<br />

breakage processes in order to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e forming <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e signaling clusters al<strong>on</strong>g<br />

1036

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cluster sizes and couple <str<strong>on</strong>g>th</str<strong>on</strong>g>is wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er equati<strong>on</strong> characterising<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> free receptors. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e numerical soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is system<br />

in its integro-differential form we use several discretizati<strong>on</strong> techniques including<br />

finite differences and semi-discrete moment preserving finite volume schemes which<br />

can be extended to incorporate fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er spatial effects <strong>on</strong> cell surfaces. Thereby we<br />

examine <str<strong>on</strong>g>th</str<strong>on</strong>g>e results obtained not <strong>on</strong>ly wi<str<strong>on</strong>g>th</str<strong>on</strong>g> regard to biological relevance but also<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to stability and robustness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e discretizati<strong>on</strong>.<br />

1037

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Annelene Wittenfeld, Martin Bock and Wolfgang Alt<br />

Universität B<strong>on</strong>n, IZMB, Theoretische Biologie, Kirschallee 1–3, 53115<br />

B<strong>on</strong>n, Germany<br />

e-mail: a.wittenfeld@uni-b<strong>on</strong>n.de<br />

Surfactant dynamics in lung alveoli<br />

During brea<str<strong>on</strong>g>th</str<strong>on</strong>g>ing, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mammalian lung exchanges oxygen and carb<strong>on</strong> dioxide in<br />

bubble-like structures called lung alveoli. Their interior is covered by a <str<strong>on</strong>g>th</str<strong>on</strong>g>in film<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> water <strong>on</strong> which lipids act as surfactant. The surfactant ensures <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e inner<br />

surface <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e alveoli remains wetted in spite <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>tinuing expansi<strong>on</strong> and compressi<strong>on</strong>.<br />

Atomic force microscopy has revealed, <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e lipid surfactant undergoes<br />

phase seperati<strong>on</strong> into a high- and a low-density phase. In order to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial<br />

separati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two lipid phases, we have c<strong>on</strong>structed a phase field c<strong>on</strong>tinuum<br />

model. Thereby, <str<strong>on</strong>g>th</str<strong>on</strong>g>e free energy <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system seperates <str<strong>on</strong>g>th</str<strong>on</strong>g>e two phases by a barrier<br />

depending <strong>on</strong> overall lipid density and volume fracti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e low-density phase.<br />

The equati<strong>on</strong>s for transiti<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles and resulting interface speed can be reduced<br />

to a set <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear degenerated ODEs, which we solve numerically. For fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

insights elucidating <str<strong>on</strong>g>th</str<strong>on</strong>g>e microsopic scale, we additi<strong>on</strong>ally perform computer simulati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> rod-like lipids <strong>on</strong> a rigid water surface. The lipid-water interacti<strong>on</strong> arises<br />

from a varying submersi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> hydrophilic head- and hydrophobic tail-parts <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

model lipids. Toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> explicit, polar interacti<strong>on</strong> forces between pairs <str<strong>on</strong>g>of</str<strong>on</strong>g> lipid<br />

rods, we obtain phases seperati<strong>on</strong> and spatial cluster aggregates.<br />

References.<br />

[1] H. W. Alt and W. Alt, Phase boundary dynamics: transiti<strong>on</strong> between ordered and disordered<br />

lipid m<strong>on</strong>olayer, Interfaces and Free Boundaries 11, 1–36 (2009).<br />

[2] J. Ding, D. Y. Takamoto, A. v<strong>on</strong> Nahmen, M. M. Lipp, K. Y. C. Lee A. J. Waning and<br />

J. A. Zasadzinski, Effects <str<strong>on</strong>g>of</str<strong>on</strong>g> lung surfactant proteins, SP-B and SP-C, and palmitic acid <strong>on</strong><br />

m<strong>on</strong>olayer stability, Biophys. J. 80, 2262–2272 (2001).<br />

[3] A. Wittenfeld, Order phenomena wi<str<strong>on</strong>g>th</str<strong>on</strong>g> polar rods, manuscript (2011).<br />

1038

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Genetics; Wednesday, June 29, 14:30<br />

Meike Wittmann<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology II, Ludwig-Maximilians University Munich<br />

e-mail: wittmann@bio.lmu.de<br />

Wilfried Gabriel<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology II, Ludwig-Maximilians University Munich<br />

e-mail: wilfried.gabriel@lmu.de<br />

Dirk Metzler<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biology II, Ludwig-Maximilians University Munich<br />

e-mail: metzler@bio.lmu.de<br />

Genetic effects <str<strong>on</strong>g>of</str<strong>on</strong>g> introduced species <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir native<br />

competitors in habitats wi<str<strong>on</strong>g>th</str<strong>on</strong>g> different spatial structures<br />

When a new species is introduced to a habitat where it did not occur before, it<br />

interacts wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e members <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e local community and influences <str<strong>on</strong>g>th</str<strong>on</strong>g>em in many<br />

ways. Most empirical and <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical work so far has focused <strong>on</strong> how introduced<br />

species cause changes in populati<strong>on</strong> sizes <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting native species. However, little<br />

is known <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic effect <str<strong>on</strong>g>of</str<strong>on</strong>g> introduced species <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>eir native competitors,<br />

predators, or prey species. Using analytical arguments and computer simulati<strong>on</strong>s,<br />

we aim to understand how <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount and spatial structure <str<strong>on</strong>g>of</str<strong>on</strong>g> genetic variati<strong>on</strong> in<br />

a native species changes after <str<strong>on</strong>g>th</str<strong>on</strong>g>e introducti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> an ecologically similar competitor.<br />

Genetic variati<strong>on</strong> measured in terms <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e expected heterozygosity at a neutral locus<br />

declines after <str<strong>on</strong>g>th</str<strong>on</strong>g>e introducti<strong>on</strong> event, reaches a minimum, and eventually rises<br />

again provided <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e native species does not go extinct. The severity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>is<br />

reducti<strong>on</strong> as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e time scale <strong>on</strong> which it occurs depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

introduced individuals, <str<strong>on</strong>g>th</str<strong>on</strong>g>e size, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e native populati<strong>on</strong>.<br />

The expected impacts differ between single homogeneous populati<strong>on</strong>s, subdivided<br />

populati<strong>on</strong>s, and metapopulati<strong>on</strong>s subject to local extincti<strong>on</strong> and recol<strong>on</strong>izati<strong>on</strong>.<br />

These results for neutral loci suggest <str<strong>on</strong>g>th</str<strong>on</strong>g>at also variati<strong>on</strong> at loci for ecologically<br />

important traits may be affected by competiti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> introduced species, <str<strong>on</strong>g>th</str<strong>on</strong>g>us influencing<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e species ability to adapt to new envir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>s.<br />

1039

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Carsten Wiuf<br />

Bioinformatics Research Centre<br />

e-mail: wiuf@cs.au.dk<br />

Cancer; Wednesday, June 29, 11:00<br />

Stochastic Modeling and Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> DNA Sequence Data<br />

from Heterogeneous Tumors<br />

Many cancers are believed to have cl<strong>on</strong>al origin, starting from a single cell wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

a defining mutati<strong>on</strong> and fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er acquiring <strong>on</strong>e or more additi<strong>on</strong>al mutati<strong>on</strong>s before<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e first cancerous cell is established. For example, in Follicular Lymphoma, a blood<br />

cancer, <str<strong>on</strong>g>th</str<strong>on</strong>g>e total number <str<strong>on</strong>g>of</str<strong>on</strong>g> required mutati<strong>on</strong>s M is believed to be two <str<strong>on</strong>g>of</str<strong>on</strong>g> which<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e first is a translocati<strong>on</strong> called t(14;18).<br />

A populati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cancer cells evolves fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er over time and accumulates genetic<br />

changes, many <str<strong>on</strong>g>of</str<strong>on</strong>g> which are random and o<str<strong>on</strong>g>th</str<strong>on</strong>g>ers potentially beneficial for <str<strong>on</strong>g>th</str<strong>on</strong>g>e cancer.<br />

C<strong>on</strong>sequently, cells in different parts <str<strong>on</strong>g>of</str<strong>on</strong>g> a tumor might show differences in<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>eir genomes, or DNA. This phenomen<strong>on</strong> is referred to as genetic tumor heterogeneity<br />

and is comparable to <str<strong>on</strong>g>th</str<strong>on</strong>g>e genetic heterogeneity observed in individuals in a<br />

populati<strong>on</strong>.<br />

Here, I address <str<strong>on</strong>g>th</str<strong>on</strong>g>e problem <str<strong>on</strong>g>of</str<strong>on</strong>g> modeling how <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor evolves over time and<br />

accumulates changes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e DNA, starting from <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial cell wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e defining<br />

mutati<strong>on</strong>. The model is stochastic and relies <strong>on</strong> bir<str<strong>on</strong>g>th</str<strong>on</strong>g>-dea<str<strong>on</strong>g>th</str<strong>on</strong>g> processes; it allows <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

first required M mutati<strong>on</strong>s to be under selective pressure, while <str<strong>on</strong>g>th</str<strong>on</strong>g>e subsequent mutati<strong>on</strong>s<br />

are neutral. I show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a simple descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> how <str<strong>on</strong>g>th</str<strong>on</strong>g>e (stochastic)<br />

number <str<strong>on</strong>g>of</str<strong>on</strong>g> tumor cells in <str<strong>on</strong>g>th</str<strong>on</strong>g>e system changes over time and <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e model imposes<br />

c<strong>on</strong>straints <strong>on</strong> parameters <str<strong>on</strong>g>th</str<strong>on</strong>g>at determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e reproducibility and <str<strong>on</strong>g>th</str<strong>on</strong>g>e survival <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cells; <str<strong>on</strong>g>th</str<strong>on</strong>g>us <str<strong>on</strong>g>th</str<strong>on</strong>g>e model leads to biological insight.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model leads to a simple way <str<strong>on</strong>g>of</str<strong>on</strong>g> simulating tumor evoluti<strong>on</strong>. Based<br />

<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>is, I show how a sample <str<strong>on</strong>g>of</str<strong>on</strong>g> DNA sequences taken from distinct parts <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

heterogeneous tumor might be used to draw inference <strong>on</strong> model parameters and<br />

date <str<strong>on</strong>g>th</str<strong>on</strong>g>e origin <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tumor, as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e defining and subsequent mutati<strong>on</strong>s.<br />

The latter might have clinical importance as it provides an estimate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e time<br />

from tumor initiati<strong>on</strong> to diagnosis.<br />

Finally, I show a simple applicati<strong>on</strong> to DNA sequence data from Follicular<br />

Lymphoma patients and outlining some fur<str<strong>on</strong>g>th</str<strong>on</strong>g>er ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and statistical work<br />

to be d<strong>on</strong>e.<br />

1040

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Tomasz Wojdyla<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: tpwojdyla@polsl.pl<br />

Marek Kimmel<br />

Rice University and Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

e-mail: kimmel@stat.rice.edu<br />

Adam Bobrowski<br />

Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences and Technical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Lublin<br />

e-mail: a.bobrowski@pollub.pl<br />

Computati<strong>on</strong>al Model <str<strong>on</strong>g>of</str<strong>on</strong>g> Genetic Demographic Networks<br />

Demographic network is defined as a set <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong>s evolving from a single<br />

ancestral populati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a beginning at <str<strong>on</strong>g>th</str<strong>on</strong>g>e time 0. The structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e network is<br />

described by two types <str<strong>on</strong>g>of</str<strong>on</strong>g> events: split <str<strong>on</strong>g>of</str<strong>on</strong>g> a single populati<strong>on</strong> into two populati<strong>on</strong>s<br />

and merger <str<strong>on</strong>g>of</str<strong>on</strong>g> two populati<strong>on</strong>s. Additi<strong>on</strong>ally, we incorporate migrati<strong>on</strong> between<br />

populati<strong>on</strong>s coexisting in <str<strong>on</strong>g>th</str<strong>on</strong>g>e model.<br />

There are several models available in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature <str<strong>on</strong>g>th</str<strong>on</strong>g>at can be used to analyze<br />

data from such demographic networks. Most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>em are based <strong>on</strong> backward-time<br />

coalescent simulati<strong>on</strong>s and require c<strong>on</strong>siderable computati<strong>on</strong>al power. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is paper<br />

we introduce a forward-time and time-c<strong>on</strong>tinuous model <str<strong>on</strong>g>th</str<strong>on</strong>g>at allows to calculate <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

exact values <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e entries <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e infinite matrixes Rij(t) being <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint distributi<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> pairs <str<strong>on</strong>g>of</str<strong>on</strong>g> alleles sampled at <str<strong>on</strong>g>th</str<strong>on</strong>g>e time t from populati<strong>on</strong>s i (first allele from a<br />

pair) and j (sec<strong>on</strong>d allele). We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at individuals in each populati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

network are described by <str<strong>on</strong>g>th</str<strong>on</strong>g>e same allelic space model and we introduce mutati<strong>on</strong><br />

to <str<strong>on</strong>g>th</str<strong>on</strong>g>e model using intensity matrices Qi <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Markov chain <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e mutati<strong>on</strong> process<br />

in populati<strong>on</strong> i. Mutati<strong>on</strong> model is assumed unchanged between two adjacent<br />

demographic events. Populati<strong>on</strong> size grow<str<strong>on</strong>g>th</str<strong>on</strong>g> can be specified for each populati<strong>on</strong>.<br />

Evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint distributi<strong>on</strong>s between network events is described by Lyapunov<br />

differential equati<strong>on</strong>s.<br />

In our work we present ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical details <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model and a computer<br />

program implementing <str<strong>on</strong>g>th</str<strong>on</strong>g>is model al<strong>on</strong>g wi<str<strong>on</strong>g>th</str<strong>on</strong>g> several applicati<strong>on</strong>s. We also discuss<br />

some improvements to our model, such as optimizati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e computati<strong>on</strong>al complexity<br />

for some comm<strong>on</strong> mutati<strong>on</strong> models and calculating <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint distributi<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a sample <str<strong>on</strong>g>of</str<strong>on</strong>g> size greater <str<strong>on</strong>g>th</str<strong>on</strong>g>at 2.<br />

References.<br />

[1] Bobrowski A., Kimmel M., Arino O. and Chakraborty R., A Semigroup Representati<strong>on</strong> and<br />

Asymptotic Behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> Certain Statistics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fisher-Wright-Moran Coalescent Handbook<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Statistics, Vol. 19, 2001.<br />

[2] Gajic Z. and Qureshi MTJ, Lyapunov Matrix Equati<strong>on</strong> in System Stability and C<strong>on</strong>trol Academic<br />

Press New York 1995.<br />

1041

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Carina Wollnik and Wolfgang Alt<br />

Theoretische Biologie, Universität B<strong>on</strong>n<br />

Kirschallee 1-3<br />

53115 B<strong>on</strong>n<br />

Germany<br />

e-mail: cwollnik@uni-b<strong>on</strong>n.de<br />

Poster Sessi<strong>on</strong>; Friday, July 1, 20:00<br />

Qualitative analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> lamella and cell body shape during<br />

cell migrati<strong>on</strong><br />

The aim <str<strong>on</strong>g>of</str<strong>on</strong>g> our work is to investigate migrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> single cells <strong>on</strong> two-dimensi<strong>on</strong>al<br />

substrata. To <str<strong>on</strong>g>th</str<strong>on</strong>g>is end, we label adhesi<strong>on</strong> sites and <str<strong>on</strong>g>th</str<strong>on</strong>g>e interior keratinocyte cell<br />

body by staining vinculin and tubulin wi<str<strong>on</strong>g>th</str<strong>on</strong>g> fluorescence dyes. This enables us to<br />

reliably distinguish between cell body and <str<strong>on</strong>g>th</str<strong>on</strong>g>e surrounding lamella.<br />

For time-lapse image processing we quantitatively determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e lamella edge<br />

as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell body outline by an adaptive stochastic chain algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m [1], also<br />

known as active c<strong>on</strong>tour model [2, 3]. The stochastic chain adapts to <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell<br />

outline by interpreting <str<strong>on</strong>g>th</str<strong>on</strong>g>e informati<strong>on</strong> given by phase c<strong>on</strong>trast micrographs or<br />

corresp<strong>on</strong>ding fluorescence images. Chain adapti<strong>on</strong> follows from different “image<br />

forces”, which involve (i) chain stiffness, (ii) retrograde centripetal pulling and (iii)<br />

gradients in picture brightness. The evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e chain stops when <str<strong>on</strong>g>th</str<strong>on</strong>g>e stochastic<br />

fluctuati<strong>on</strong>s have become stati<strong>on</strong>ary.<br />

Our statistical analysis investigates cell body and lamella shape, which are<br />

independently quantified by <str<strong>on</strong>g>th</str<strong>on</strong>g>e positi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e interior body chain and <str<strong>on</strong>g>th</str<strong>on</strong>g>e exterior<br />

edge chain, respectively. Spatio-temperal auto- and cross-correlati<strong>on</strong>s reveal<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e time-lag relati<strong>on</strong> between mean protrusi<strong>on</strong> vector and cell migrati<strong>on</strong> velocity.<br />

Moreover, we find <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell body has an elliptic shape during forward migrati<strong>on</strong>,<br />

whereas up<strong>on</strong> turning it becomes almost circular. The overall lamella dynamics is<br />

mainly influenced by <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying cell body shape. Significant deviati<strong>on</strong>s from<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>is protrusi<strong>on</strong> pattern appear, particularly when <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell changes its migrati<strong>on</strong><br />

directi<strong>on</strong>.<br />

References.<br />

[1] Wolfgang Alt, Oana Brosteanu, Boris Hinz and Hans Wilhelm Kaiser, Patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> sp<strong>on</strong>taneous<br />

motility in videomicrographs <str<strong>on</strong>g>of</str<strong>on</strong>g> human epidermal keratinocytes (HEK) Biochemistry and Cell<br />

Biology (1995) 73 441–459<br />

[2] Frederic Leymarie and Martin D. Levine, Tracking deformable objects in <str<strong>on</strong>g>th</str<strong>on</strong>g>e plane using an<br />

active c<strong>on</strong>tour model IEEE Transacti<strong>on</strong>s <strong>on</strong> Pattern Analysis and Machine Intelligence (1993)<br />

15 617–633.<br />

[3] K. Zhang, H. Xi<strong>on</strong>g, X. Zhou, L. Yang, Y. L. Wang and S. T. C. W<strong>on</strong>g, A c<strong>on</strong>fident scalespace<br />

shape reprensentati<strong>on</strong> framework for cell migrati<strong>on</strong> detecti<strong>on</strong> Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Microscopy<br />

(2008) 231 395–407<br />

1042

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Semigroups <str<strong>on</strong>g>of</str<strong>on</strong>g> Operators in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Biology I; Wednesday, June 29, 08:30<br />

Dariusz Wrzosek<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Mechanics,<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw<br />

e-mail: darekw@mimuw.edu.pl<br />

Do <str<strong>on</strong>g>th</str<strong>on</strong>g>e aggregating cells attain a tight packing state?<br />

We c<strong>on</strong>sider models <str<strong>on</strong>g>of</str<strong>on</strong>g> chemotaxis which take into account volume-filling effects<br />

such <str<strong>on</strong>g>th</str<strong>on</strong>g>at an a priori <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold for <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell density corresp<strong>on</strong>ding to a tight packing<br />

state is taken into account (for more informati<strong>on</strong> we refer to a survey [2]). Our study<br />

c<strong>on</strong>cerns quasilinear parabolic systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> singular or degenerate diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells<br />

which include recent models by Wang and Hillen(2007) and Lushnikov (2008). It is<br />

proved in [3] <str<strong>on</strong>g>th</str<strong>on</strong>g>at for some range <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e relati<strong>on</strong> between <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

diffusive and <str<strong>on</strong>g>th</str<strong>on</strong>g>e taxis part <str<strong>on</strong>g>of</str<strong>on</strong>g> a cell flux <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are global-in-time classical soluti<strong>on</strong>s<br />

which in some cases are separated from <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold uniformly in time. Existence<br />

and uniqueness <str<strong>on</strong>g>of</str<strong>on</strong>g> global in time weak soluti<strong>on</strong>s as well as <str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> stati<strong>on</strong>ary<br />

states are studied as well. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e recent preprint [1] it is proved for parabolicelliptic<br />

versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e model <str<strong>on</strong>g>th</str<strong>on</strong>g>at if <str<strong>on</strong>g>th</str<strong>on</strong>g>e taxis force is str<strong>on</strong>g enough wi<str<strong>on</strong>g>th</str<strong>on</strong>g> respect to<br />

self-diffusi<strong>on</strong> and <str<strong>on</strong>g>th</str<strong>on</strong>g>e initial data are chosen properly <str<strong>on</strong>g>th</str<strong>on</strong>g>en <str<strong>on</strong>g>th</str<strong>on</strong>g>ere exists a classical<br />

soluti<strong>on</strong> which reaches <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold in finite time provided <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> cells is<br />

n<strong>on</strong>-degenerate.<br />

References.<br />

[1] Z.-A. Wang, M. Winkler and D.Wrzosek Singularity formati<strong>on</strong> in chemotaxis systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

volume-filling effect submitted.<br />

[2] D. Wrzosek. Volume filling effect in modelling chemotaxis. Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Model. Nat. Phenom., 5,<br />

123-147 (2010).<br />

[3] D. Wrzosek. Model <str<strong>on</strong>g>of</str<strong>on</strong>g> chemotaxis wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>reshold density and singular diffusi<strong>on</strong>. N<strong>on</strong>linear<br />

Anal. TMA.,73, 338-349 (2010).<br />

1043

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Cell migrati<strong>on</strong> during development: modelling and experiment; Saturday,<br />

July 2, 08:30<br />

Michelle Wynn<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Michigan Medical School<br />

e-mail: mlwynn@umich.edu<br />

Paul M. Kulesa<br />

Stowers Institute for Medical Research<br />

Santiago Schnell<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Michigan Medical School<br />

A computati<strong>on</strong>al model <str<strong>on</strong>g>of</str<strong>on</strong>g> neural crest chain migrati<strong>on</strong><br />

provides mechanistic insight into cellular follow-<str<strong>on</strong>g>th</str<strong>on</strong>g>e-leader<br />

behavior<br />

Follow-<str<strong>on</strong>g>th</str<strong>on</strong>g>e-leader chain migrati<strong>on</strong> is a striking cell migratory behavior observed<br />

during vertebrate development, adult neurogenesis, and some cancer metastases.<br />

An example <str<strong>on</strong>g>of</str<strong>on</strong>g> chain migrati<strong>on</strong> is found in <str<strong>on</strong>g>th</str<strong>on</strong>g>e embry<strong>on</strong>ic neural crest (NC), a<br />

multipotent, invasive cell populati<strong>on</strong>. Al<str<strong>on</strong>g>th</str<strong>on</strong>g>ough some aspects <str<strong>on</strong>g>of</str<strong>on</strong>g> chain migrati<strong>on</strong><br />

have been well described, <str<strong>on</strong>g>th</str<strong>on</strong>g>e mechanisms involved in <str<strong>on</strong>g>th</str<strong>on</strong>g>e persistence <str<strong>on</strong>g>of</str<strong>on</strong>g> NC cell<br />

chain migrati<strong>on</strong> are unclear. We developed a quantitative agent based modeling<br />

framework to investigate <str<strong>on</strong>g>th</str<strong>on</strong>g>ree distinct model mechanisms <str<strong>on</strong>g>of</str<strong>on</strong>g> chain migrati<strong>on</strong>. The<br />

models relied <strong>on</strong> biological data from <str<strong>on</strong>g>th</str<strong>on</strong>g>e NC and involved extracellular matrix and<br />

cell c<strong>on</strong>tact mediated promoti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> chain migrati<strong>on</strong>. Sensitivity analysis revealed<br />

specific criteria for high chain migrati<strong>on</strong> persistence and suggested possible mechanism<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at may sustain follow-<str<strong>on</strong>g>th</str<strong>on</strong>g>e-leader behavior. Our approach <str<strong>on</strong>g>of</str<strong>on</strong>g>fers a means<br />

to test mechanistic hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>eses <str<strong>on</strong>g>of</str<strong>on</strong>g> collective NC cell chain migrati<strong>on</strong> in an in silico<br />

framework <str<strong>on</strong>g>th</str<strong>on</strong>g>at is applicable to studying collective chain migrati<strong>on</strong> in o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

biological systems.<br />

1044

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Norio Yamamura<br />

Research Institute for Humanity and Nature<br />

e-mail: yamamura@chikyu.ac.jp<br />

Ecosystems Dynamics; Tuesday, June 28, 17:00<br />

Different Social-ecological Networks in Grassland and Forest<br />

SystemsImplicati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>eir sustainable management<br />

Many ecosystems have been seriously degraded by human activities in <str<strong>on</strong>g>th</str<strong>on</strong>g>e world.<br />

In order to c<strong>on</strong>sider management <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ose systems, we should grasp <str<strong>on</strong>g>th</str<strong>on</strong>g>e systems as<br />

social-ecological networks as a whole. Remarking specially <str<strong>on</strong>g>th</str<strong>on</strong>g>e network structure<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> social-ecological systems, we are executing a project titled Collapse and Restorati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Ecosystem Networks wi<str<strong>on</strong>g>th</str<strong>on</strong>g> Human Activity (http//www.chikyu.ac.jp/rihn<br />

e/project/D-04.html) in Research Institute for Humanity and Nature (http//www.chikyu.ac.jp/index<br />

e.html).<br />

We found <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e networks have remarkable difference between grassland<br />

and forest systems, by analyzing data from grassland in M<strong>on</strong>golia and forests in<br />

Sarawak, Malaysia. In M<strong>on</strong>golia, <str<strong>on</strong>g>th</str<strong>on</strong>g>e vegetati<strong>on</strong> itself (grasses) has no direct value<br />

for humans <str<strong>on</strong>g>th</str<strong>on</strong>g>e value is stored in livestock <str<strong>on</strong>g>th</str<strong>on</strong>g>at feeds <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e grasses. Therefore,<br />

global ec<strong>on</strong>omy affects <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> inhabitants, leading to overuse <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e vegetati<strong>on</strong><br />

and degradati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e grassland. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is case, <str<strong>on</strong>g>th</str<strong>on</strong>g>e effective soluti<strong>on</strong> to<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e problem should involve changing <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> inhabitants. On <str<strong>on</strong>g>th</str<strong>on</strong>g>e o<str<strong>on</strong>g>th</str<strong>on</strong>g>er<br />

hand, in Sarawak, <str<strong>on</strong>g>th</str<strong>on</strong>g>e ec<strong>on</strong>omic value is stored in <str<strong>on</strong>g>th</str<strong>on</strong>g>e vegetati<strong>on</strong> (trees). Therefore,<br />

enterprises and governments tend to severely develop <str<strong>on</strong>g>th</str<strong>on</strong>g>e forests, causing bo<str<strong>on</strong>g>th</str<strong>on</strong>g> reducti<strong>on</strong>s<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>e amount <str<strong>on</strong>g>of</str<strong>on</strong>g> forest available to inhabitants and biodiversity loss. The<br />

effective soluti<strong>on</strong> here should involve regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> enterprises and governments.<br />

We here explore <str<strong>on</strong>g>th</str<strong>on</strong>g>e model representing <str<strong>on</strong>g>th</str<strong>on</strong>g>e difference <str<strong>on</strong>g>of</str<strong>on</strong>g> networks, and examine<br />

effective strategies for sustainable management <str<strong>on</strong>g>of</str<strong>on</strong>g> each type <str<strong>on</strong>g>of</str<strong>on</strong>g> systems, using<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e model. In M<strong>on</strong>golian social-ecological system, <str<strong>on</strong>g>th</str<strong>on</strong>g>e equilibrium is always stable<br />

even if price <str<strong>on</strong>g>of</str<strong>on</strong>g> livestock products increases because <str<strong>on</strong>g>of</str<strong>on</strong>g> negative feedback between<br />

grassland quality and livestock biomass. However, c<strong>on</strong>sidering climate fluctuati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> grassland quality, <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk <str<strong>on</strong>g>of</str<strong>on</strong>g> system collapse is lower for <str<strong>on</strong>g>th</str<strong>on</strong>g>e higher equilibrium<br />

value. In Sarawak social-ecological system, when logging rate reflecting global<br />

ec<strong>on</strong>omy exceeds a critical level, usable forests for habitants rapidly decreases to 0<br />

because <str<strong>on</strong>g>of</str<strong>on</strong>g> positive feedback between decreases <str<strong>on</strong>g>of</str<strong>on</strong>g> such forests and inhabitant utilizati<strong>on</strong><br />

activity for forests. The system has <str<strong>on</strong>g>th</str<strong>on</strong>g>e essential nature <str<strong>on</strong>g>of</str<strong>on</strong>g> instability. We<br />

discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>at general social-ecological systems wi<str<strong>on</strong>g>th</str<strong>on</strong>g> envir<strong>on</strong>mental problems can be<br />

placed at some positi<strong>on</strong>s between two types <str<strong>on</strong>g>of</str<strong>on</strong>g> M<strong>on</strong>golia and Sarawak networks.<br />

1045

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Evoluti<strong>on</strong>ary Ecology; Wednesday, June 29, 14:30<br />

Atsushi Yamauchi<br />

Center for Ecological Research, Kyoto University<br />

e-mail: a-yama@ecology.kyoto-u.ac.jp<br />

Yutaka Kobayashi<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Biological Science, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Tokyo<br />

Joint evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> sex ratio and reproductive group size<br />

under local mate competiti<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> inbreeding depressi<strong>on</strong><br />

Local mate competiti<strong>on</strong> (LMC) may involve some amount <str<strong>on</strong>g>of</str<strong>on</strong>g> inbreeding between<br />

siblings. Because sib-mating is generally accompanied by inbreeding depressi<strong>on</strong>,<br />

natural selecti<strong>on</strong> may favor a reduced rate <str<strong>on</strong>g>of</str<strong>on</strong>g> sib-mating, possibly affecting <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> sex ratio and reproductive group size. The present study <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretically<br />

investigated <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese traits under LMC in <str<strong>on</strong>g>th</str<strong>on</strong>g>e presence <str<strong>on</strong>g>of</str<strong>on</strong>g> inbreeding<br />

depressi<strong>on</strong>. When <str<strong>on</strong>g>th</str<strong>on</strong>g>e reproductive group size evolves, <str<strong>on</strong>g>th</str<strong>on</strong>g>e determinati<strong>on</strong> mechanism<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> sex ratio is important because <str<strong>on</strong>g>th</str<strong>on</strong>g>e time scale <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sex ratio resp<strong>on</strong>se to<br />

reproductive group size can affect <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>ary process. We c<strong>on</strong>sider a spectrum<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> sex ratio determinati<strong>on</strong> mechanisms from purely unc<strong>on</strong>diti<strong>on</strong>al to purely<br />

c<strong>on</strong>diti<strong>on</strong>al, including intermediate modes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> various relative streng<str<strong>on</strong>g>th</str<strong>on</strong>g>s <str<strong>on</strong>g>of</str<strong>on</strong>g> unc<strong>on</strong>diti<strong>on</strong>al<br />

and c<strong>on</strong>diti<strong>on</strong>al effects. This analysis revealed <str<strong>on</strong>g>th</str<strong>on</strong>g>at bo<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong>arily<br />

stable reproductive group size and ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> males increase wi<str<strong>on</strong>g>th</str<strong>on</strong>g> higher inbreeding<br />

depressi<strong>on</strong> and wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a larger relative streng<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> an unc<strong>on</strong>diti<strong>on</strong>al effect in sex ratio<br />

determinati<strong>on</strong>. Unexpectedly, when <str<strong>on</strong>g>th</str<strong>on</strong>g>e sex ratio is c<strong>on</strong>trolled purely c<strong>on</strong>diti<strong>on</strong>ally,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e reproductive group size cannot exceed <str<strong>on</strong>g>th</str<strong>on</strong>g>ree even under <str<strong>on</strong>g>th</str<strong>on</strong>g>e severest level <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

inbreeding depressi<strong>on</strong> (i.e., le<str<strong>on</strong>g>th</str<strong>on</strong>g>al effect). The present study reveals <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>diti<strong>on</strong>s<br />

for LMC to evolve <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e joint evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> reproductive group<br />

size and sex ratio.<br />

1046

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ecosystems Dynamics; Tuesday, June 28, 17:00<br />

Mats Gyllenberg<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Helsinki<br />

e-mail: mats.gyllenberg@helsinki.fi<br />

Yi Wang<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Technology<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> China<br />

e-mail: wangyi@ustc.edu.cn<br />

Ping Yan<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Statistics, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Helsinki<br />

e-mail: ping.yan@helsinki.fi<br />

Global asymptotic stability <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>aut<strong>on</strong>omous<br />

master equati<strong>on</strong>s<br />

We discuss <str<strong>on</strong>g>th</str<strong>on</strong>g>e master equati<strong>on</strong> dx<br />

dt = A(t)x, here A(t) is an nxn matrix whose<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g>f-diag<strong>on</strong>al entries are <str<strong>on</strong>g>th</str<strong>on</strong>g>e transiti<strong>on</strong> rates aij(t) and whose columns sum to zero.<br />

These c<strong>on</strong>diti<strong>on</strong>s ensure <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e sum <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e entries <str<strong>on</strong>g>of</str<strong>on</strong>g> a soluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e master<br />

equati<strong>on</strong> is c<strong>on</strong>served and <str<strong>on</strong>g>th</str<strong>on</strong>g>at n<strong>on</strong>negative soluti<strong>on</strong>s remain n<strong>on</strong>negative. Such<br />

matrices are called W-matrices by van Kampen. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk, we give some new<br />

results for <str<strong>on</strong>g>th</str<strong>on</strong>g>e master equati<strong>on</strong> c<strong>on</strong>cerning Earnshaw and Keener’s c<strong>on</strong>jecture.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Dynamics; Friday, July 1, 14:30<br />

Xuxin Yang<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Helsinki (visiting) and Hunan First Normal University<br />

e-mail: xuxin.yang@helsinki.fi<br />

Permanence <str<strong>on</strong>g>of</str<strong>on</strong>g> a logistic type impulsive equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

infinite delay<br />

Many evoluti<strong>on</strong> processes are characterized by <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at at certain moments<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> time <str<strong>on</strong>g>th</str<strong>on</strong>g>ey experience a change <str<strong>on</strong>g>of</str<strong>on</strong>g> state abruptly. Theses processes are subject to<br />

short-time perturbati<strong>on</strong>s whose durati<strong>on</strong> is negligible in comparis<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e durati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e process. C<strong>on</strong>sequently, it is natural to assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ese perturbati<strong>on</strong>s<br />

act instantaneously, <str<strong>on</strong>g>th</str<strong>on</strong>g>at is, in <str<strong>on</strong>g>th</str<strong>on</strong>g>e form <str<strong>on</strong>g>of</str<strong>on</strong>g> impulses. It is known, for example,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at many biological phenomena involving <str<strong>on</strong>g>th</str<strong>on</strong>g>resholds, bursting rhy<str<strong>on</strong>g>th</str<strong>on</strong>g>m models in<br />

medicine and biology, optimal c<strong>on</strong>trol models in ec<strong>on</strong>omics, pharmacokinetics and<br />

frequency modulated systems, do exhibit impulsive effects.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is presentati<strong>on</strong> we give an introducti<strong>on</strong> to <str<strong>on</strong>g>th</str<strong>on</strong>g>eory <str<strong>on</strong>g>of</str<strong>on</strong>g> impulsive differential<br />

equati<strong>on</strong>s. Impulsive differential equati<strong>on</strong>s, <str<strong>on</strong>g>th</str<strong>on</strong>g>at is, differential equati<strong>on</strong>s involving<br />

impulse effects, appear as a natural descripti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> observed evoluti<strong>on</strong> phenomena<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> several real world problems. We investigate a n<strong>on</strong>-aut<strong>on</strong>omous Logistic type<br />

impulsive equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> infinite delay. For <str<strong>on</strong>g>th</str<strong>on</strong>g>e general n<strong>on</strong>-aut<strong>on</strong>omous case, some<br />

sufficient c<strong>on</strong>diti<strong>on</strong>s which guarantee <str<strong>on</strong>g>th</str<strong>on</strong>g>e permanence <str<strong>on</strong>g>of</str<strong>on</strong>g> soluti<strong>on</strong>s are obtained.<br />

Our results extend a known result <str<strong>on</strong>g>of</str<strong>on</strong>g> Seifert [1]. This presentati<strong>on</strong> is based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

paper [2].<br />

References.<br />

[1] G. Seifert, Almost periodic soluti<strong>on</strong>s for delay Logistic equati<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> almost periodic time<br />

dependence Differential and Integral Equati<strong>on</strong>s 9 (2) (1996) 335–342.<br />

[2] X. Yang, W. Wang and J. Shen, Permanence <str<strong>on</strong>g>of</str<strong>on</strong>g> a logistic type impulsive equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> infinite<br />

delay Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Letters 24 (2011) 420–427.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Populati<strong>on</strong> Dynamics; Wednesday, June 29, 14:30<br />

Je<strong>on</strong>g-Mi Yo<strong>on</strong><br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Houst<strong>on</strong>-Downtown<br />

e-mail: yo<strong>on</strong>j@uhd.edu<br />

Lisa Morano<br />

Vlad Hrynkiv<br />

Anh Tuan Nguyen ∗<br />

Sara Wilder ∗<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Houst<strong>on</strong>-Downtown; *: undergraduate students<br />

e-mail: Moranol@uhd.edu,Hrynkivv@uhd.edu<br />

Populati<strong>on</strong> Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> Glassy-winged Sharpshooter in<br />

Texas Vineyards<br />

Pierce’s Disease (PD) is a bacterial disease <str<strong>on</strong>g>of</str<strong>on</strong>g> grapevines wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e capacity to kill an<br />

entire vineyard in <strong>on</strong>e year. Outbreaks <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e disease <str<strong>on</strong>g>th</str<strong>on</strong>g>reaten California vineyards<br />

and are a chr<strong>on</strong>ic problem in Texas, particularly al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e Gulf Coast. The disease<br />

is caused by a bacterium, Xylella fastidiosa and is transmitted by xylem-feeding<br />

insects comm<strong>on</strong>ly called sharpshooters. To understand <str<strong>on</strong>g>th</str<strong>on</strong>g>e role <str<strong>on</strong>g>of</str<strong>on</strong>g> sharpshooter<br />

ecology <strong>on</strong> PD epidemiology, <str<strong>on</strong>g>th</str<strong>on</strong>g>e USDA-APHIS has funded sharpshooter trap data<br />

from 50 Texas vineyards from 2003-to present under <str<strong>on</strong>g>th</str<strong>on</strong>g>e directi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Dr. Forrest<br />

Mitchell, Texas A&M University. Am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e insects m<strong>on</strong>itored, Homolodisca<br />

vitripennis (Glassy-winged sharpshooter-GWSS) is <str<strong>on</strong>g>th</str<strong>on</strong>g>e most abundant insect captured<br />

across all vineyards in Texas. Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e enormous GWSS data set is<br />

an excellent opportunity to have bo<str<strong>on</strong>g>th</str<strong>on</strong>g> biology and ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics students and apply<br />

modeling techniques to temporal changes in insect populati<strong>on</strong>s in order to predict<br />

future PD risk and determine <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal management protocols.<br />

This collaborative research has been funded by <str<strong>on</strong>g>th</str<strong>on</strong>g>e NSF Grant: The Interdisciplinary<br />

Training for Undergraduates in Biology and Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Sciences (UBM).<br />

During year 2009-2010, our group has developed a populati<strong>on</strong> model based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

time-delayed logistic equati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e dominant single species in <str<strong>on</strong>g>th</str<strong>on</strong>g>e central Texas<br />

hill regi<strong>on</strong>s (Ecoregi<strong>on</strong> 7: Edwards Plateau) for <str<strong>on</strong>g>th</str<strong>on</strong>g>e years 2003-2009. The chosen<br />

model was transformed as <strong>on</strong>e-parameter delayed equati<strong>on</strong> by <str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>-dimensi<strong>on</strong>al<br />

technique. The existence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e periodic cyclic soluti<strong>on</strong> was explained by <str<strong>on</strong>g>th</str<strong>on</strong>g>e local<br />

stability analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e linear model near <str<strong>on</strong>g>th</str<strong>on</strong>g>e carrying capacity analytically. Undergraduate<br />

students worked <strong>on</strong> obtaining <str<strong>on</strong>g>th</str<strong>on</strong>g>e optimal values <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters which<br />

could guarantee <str<strong>on</strong>g>th</str<strong>on</strong>g>e periodic soluti<strong>on</strong> numerically using s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware, MATLAB and<br />

compared it to <str<strong>on</strong>g>th</str<strong>on</strong>g>e experimental histogram. From <str<strong>on</strong>g>th</str<strong>on</strong>g>e fall <str<strong>on</strong>g>of</str<strong>on</strong>g> 2010 we have been<br />

working <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e revisi<strong>on</strong> model wi<str<strong>on</strong>g>th</str<strong>on</strong>g> harvesting and immigrati<strong>on</strong> terms which could<br />

include <str<strong>on</strong>g>th</str<strong>on</strong>g>e envir<strong>on</strong>mental factors such as insecticide use, informati<strong>on</strong> campaigns,<br />

weeds cleaning, and temperature changes. We will test <str<strong>on</strong>g>th</str<strong>on</strong>g>e aut<strong>on</strong>omous and also<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e n<strong>on</strong>-aut<strong>on</strong>omous harvesting terms. In <str<strong>on</strong>g>th</str<strong>on</strong>g>e future, <str<strong>on</strong>g>th</str<strong>on</strong>g>e model will be extended<br />

to a spatio-temporal model based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fisher’s equati<strong>on</strong> wi<str<strong>on</strong>g>th</str<strong>on</strong>g> delayed logistic<br />

populati<strong>on</strong> grow<str<strong>on</strong>g>th</str<strong>on</strong>g>.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Developmental Biology; Thursday, June 30, 11:30<br />

Hiroshi Yoshida<br />

Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Kyushu University, Itou, Motouoka 744, Nishiku,<br />

FUKUOKA 819-0395 Japan.<br />

e-mail: youshida.p@gmail.com<br />

A c<strong>on</strong>diti<strong>on</strong> for regenerati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a cell chain based <strong>on</strong><br />

Dachsous:Fat heterodimer system<br />

Regenerati<strong>on</strong> phenomena have been studied <str<strong>on</strong>g>th</str<strong>on</strong>g>rough various models. Taking<br />

cockroach leg regenerati<strong>on</strong> for instance, it has been studied <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e positi<strong>on</strong>al<br />

informati<strong>on</strong> model [6], <str<strong>on</strong>g>th</str<strong>on</strong>g>e polar coordinate model [3], and <str<strong>on</strong>g>th</str<strong>on</strong>g>e boundary model [5].<br />

Bey<strong>on</strong>d <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical models, recent studies have led to models at <str<strong>on</strong>g>th</str<strong>on</strong>g>e single<br />

cellular level [1]. Wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in a cell, Dachsous (Ds) and Fat molecules, and between<br />

cells, Ds:Fat heterodimers, are c<strong>on</strong>sidered to facilitate regenerati<strong>on</strong>. The Ds:Fat<br />

signaling system looks like an entity to realize <str<strong>on</strong>g>th</str<strong>on</strong>g>e steepness hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis where <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

leg size and regenerati<strong>on</strong> are regulated <str<strong>on</strong>g>th</str<strong>on</strong>g>rough a gradient across cells [4].<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is work we modeled a cell chain based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ds:Fat system. It has been<br />

said <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e heterodimer is produced from free active Ds and Fat molecules wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in<br />

cells. Ds and Fat molecules are redistributed when a cell divides into two, so <str<strong>on</strong>g>th</str<strong>on</strong>g>at<br />

Ds:Fat heterodimers become redistributed accordingly. Little is, however, known<br />

about <str<strong>on</strong>g>th</str<strong>on</strong>g>e way <str<strong>on</strong>g>th</str<strong>on</strong>g>ey are redistributed because <str<strong>on</strong>g>th</str<strong>on</strong>g>e metabolism <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Ds:Fat signaling<br />

and heterodimers remains obscure [2]. We hence modeled <str<strong>on</strong>g>th</str<strong>on</strong>g>is redistributi<strong>on</strong> and<br />

calculated a c<strong>on</strong>diti<strong>on</strong> for regenerati<strong>on</strong>. The derived equati<strong>on</strong>s show <str<strong>on</strong>g>th</str<strong>on</strong>g>at some degenerated<br />

redistributi<strong>on</strong> ratio <str<strong>on</strong>g>of</str<strong>on</strong>g> heterodimers provides a cell chain wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e ability<br />

to regenerate.<br />

References.<br />

[1] Agata, K. et al. (2003) Intercalary regenerati<strong>on</strong> in Planarians. Dev. Dyn., 226 308–316.<br />

[2] Bando, T. et al. (2009) Regulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> leg size and shape by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Dachsous/Fat signalling pa<str<strong>on</strong>g>th</str<strong>on</strong>g>way<br />

during regenerati<strong>on</strong>. Development, 136(13) 2235–2245.<br />

[3] French, V. et al. (1976) Pattern regulati<strong>on</strong> in epimorphic fields. Science, 193 969–981.<br />

[4] Lawrence, P. A. et al. (2008) Do <str<strong>on</strong>g>th</str<strong>on</strong>g>e protocadherins fat and dachsous link up to determine<br />

bo<str<strong>on</strong>g>th</str<strong>on</strong>g> planar cell polarity and <str<strong>on</strong>g>th</str<strong>on</strong>g>e dimensi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> organs? Nat. Cell. Biol., 10(12) 1379–1382.<br />

[5] Meinhardt, H. (1983) A boundary model for pattern formati<strong>on</strong> in vertebrate limbs. J. Embryol.<br />

Exp. Morph., 76 115–137.<br />

[6] Wolpert, L. (1994) Positi<strong>on</strong>al informati<strong>on</strong> and pattern formati<strong>on</strong> in development. Dev. Genet.,<br />

15 485–490.<br />

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<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Marcin Zagórski<br />

Jagiell<strong>on</strong>ian University, Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics<br />

e-mail: marcin.zagorski@uj.edu.pl<br />

Regulatory Networks; Saturday, July 2, 11:00<br />

Model gene regulatory networks under mutati<strong>on</strong>-selecti<strong>on</strong><br />

balance<br />

Gene regulatory networks typically have low in-degrees, whereby any given gene<br />

is regulated by few <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e genes in <str<strong>on</strong>g>th</str<strong>on</strong>g>e network. They also tend to have broad<br />

distributi<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e out-degree. What mechanisms might be resp<strong>on</strong>sible for <str<strong>on</strong>g>th</str<strong>on</strong>g>ese<br />

degree distributi<strong>on</strong>s? Starting wi<str<strong>on</strong>g>th</str<strong>on</strong>g> an accepted framework <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e binding <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong><br />

factors to DNA, we c<strong>on</strong>sider a simple model <str<strong>on</strong>g>of</str<strong>on</strong>g> gene regulatory dynamics.<br />

There, we show <str<strong>on</strong>g>th</str<strong>on</strong>g>at selecti<strong>on</strong> for a target expressi<strong>on</strong> pattern leads to <str<strong>on</strong>g>th</str<strong>on</strong>g>e emergence<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> minimum c<strong>on</strong>nectivities compatible wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e selective c<strong>on</strong>straint. As a<br />

c<strong>on</strong>sequence, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese gene networks have low in-degree, and “functi<strong>on</strong>ality” is parsim<strong>on</strong>ious,<br />

i.e., is c<strong>on</strong>centrated <strong>on</strong> a sparse number <str<strong>on</strong>g>of</str<strong>on</strong>g> interacti<strong>on</strong>s as measured for<br />

instance by <str<strong>on</strong>g>th</str<strong>on</strong>g>eir essentiality. Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore, we find <str<strong>on</strong>g>th</str<strong>on</strong>g>at mutati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e transcripti<strong>on</strong><br />

factors drive <str<strong>on</strong>g>th</str<strong>on</strong>g>e networks to have broad out-degrees. Finally, <str<strong>on</strong>g>th</str<strong>on</strong>g>ese classes <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

models are evolvable, i.e., significantly different genotypes can emerge gradually<br />

under mutati<strong>on</strong>-selecti<strong>on</strong> balance.<br />

1051

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> collective phenomena in biological systems; Saturday, July 2,<br />

08:30<br />

M. Zagorski<br />

Marian Smoluchowski Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics and Mark Kac Complex<br />

Systems Research Centre, Jagell<strong>on</strong>ian University, Reym<strong>on</strong>ta 4, 30-059<br />

Krakow, Poland<br />

e-mail: Marcin.Zagorskii@gmail.com<br />

Z. Burda<br />

Marian Smoluchowski Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Physics and Mark Kac Complex<br />

Systems Research Centre, Jagell<strong>on</strong>ian University, Reym<strong>on</strong>ta 4, 30-059<br />

Krakow, Poland<br />

e-mail: zdzislaw.burda@uj.edu.pl<br />

A. Krzywicki<br />

Univ Paris-Sud, LPT ; CNRS, UMR8627, Orsay, F-91405, France<br />

e-mail: Andre.Krzywicki@<str<strong>on</strong>g>th</str<strong>on</strong>g>.u-psud.fr<br />

O.C. Martin<br />

Univ Paris-Sud, LPTMS ; CNRS, UMR8626, F-91405, Orsay, France,<br />

INRA, CNRS, UMR0320 / UMR 8120 Génétique Végétale, F-91190 Gifsur-Yvette,<br />

France<br />

e-mail: olivier.martin@u-psud.fr<br />

Emergence <str<strong>on</strong>g>of</str<strong>on</strong>g> sparsity and motifs in gene regulatory<br />

networks<br />

We c<strong>on</strong>sider a simple model <str<strong>on</strong>g>of</str<strong>on</strong>g> gene regulatory dynamics derived from <str<strong>on</strong>g>th</str<strong>on</strong>g>e statistical<br />

framework describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e binding <str<strong>on</strong>g>of</str<strong>on</strong>g> transcripti<strong>on</strong> factors to DNA. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

networks representing essential interacti<strong>on</strong>s in gene regulati<strong>on</strong> have a minimal c<strong>on</strong>nectivity<br />

compatible wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a given functi<strong>on</strong>. We discuss statistical properties using<br />

M<strong>on</strong>te Carlo sampling. We show <str<strong>on</strong>g>th</str<strong>on</strong>g>at functi<strong>on</strong>al networks have a specific motifs statistics.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e case where <str<strong>on</strong>g>th</str<strong>on</strong>g>e regulatory networks are to exhibit multi-stability, we<br />

find a high frequency <str<strong>on</strong>g>of</str<strong>on</strong>g> gene pairs <str<strong>on</strong>g>th</str<strong>on</strong>g>at are mutually inhibitory and self-activating.<br />

In c<strong>on</strong>trast, networks having periodic gene expressi<strong>on</strong> patterns (mimicking for instance<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e cell cycle) have a high frequency <str<strong>on</strong>g>of</str<strong>on</strong>g> bifan-like motifs involving four genes<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g> at least <strong>on</strong>e activating and <strong>on</strong>e inhibitory interacti<strong>on</strong>.<br />

1052

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The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> interacting cell systems: from intercellular interacti<strong>on</strong><br />

to tissue-level traits II; Wednesday, June 29, 17:00<br />

Thomas Zerjatke, Nico Scherf, Ingmar Glauche, Ingo Roeder<br />

Institute for Medical Informatics and Biometry<br />

Medical Faculty C. G. Carus, Dresden University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology<br />

Fetscherstrasse 74, D-01307 Dresden, Germany<br />

e-mail: <str<strong>on</strong>g>th</str<strong>on</strong>g>omas.zerjatke@tu-dresden.de<br />

Knowing <str<strong>on</strong>g>th</str<strong>on</strong>g>eir neighbours - correlati<strong>on</strong> structures in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

development <str<strong>on</strong>g>of</str<strong>on</strong>g> related stem cells<br />

Time lapse video microscopy enables <str<strong>on</strong>g>th</str<strong>on</strong>g>e tracking <str<strong>on</strong>g>of</str<strong>on</strong>g> stem cell development in bioengineered<br />

culture c<strong>on</strong>diti<strong>on</strong>s <strong>on</strong> a single cell level. The resulting cellular genealogies<br />

retain informati<strong>on</strong> <strong>on</strong> cellular characteristics, divisi<strong>on</strong>al history, and differentiati<strong>on</strong>.<br />

Analysing <str<strong>on</strong>g>th</str<strong>on</strong>g>e topology, <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamical features, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e correlati<strong>on</strong> structure<br />

wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese pedigree-like genealogies provides informati<strong>on</strong> about underlying processes<br />

such as migrati<strong>on</strong>, cell grow<str<strong>on</strong>g>th</str<strong>on</strong>g>, and differentiati<strong>on</strong>.<br />

For a systematic analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular genealogies we compare experimental data<br />

for different hematopoietic stem cell cultures wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a single- cell based, ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical<br />

model <str<strong>on</strong>g>of</str<strong>on</strong>g> hematopoietic stem cell organisati<strong>on</strong>. In particular we illustrate how<br />

ancestral relati<strong>on</strong> between cells influences <str<strong>on</strong>g>th</str<strong>on</strong>g>eir current behaviour and decisi<strong>on</strong> making.<br />

Fur<str<strong>on</strong>g>th</str<strong>on</strong>g>ermore we derive emerging c<strong>on</strong>tact networks based <strong>on</strong> spatial positi<strong>on</strong>ing<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cells wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e time lapse video data. In particular we analyse whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er ancestral<br />

informati<strong>on</strong> is c<strong>on</strong>served wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e community structure <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ese networks and<br />

whe<str<strong>on</strong>g>th</str<strong>on</strong>g>er <str<strong>on</strong>g>th</str<strong>on</strong>g>ese mutual interacti<strong>on</strong>s between cells correlate wi<str<strong>on</strong>g>th</str<strong>on</strong>g> sec<strong>on</strong>dary read-outs<br />

such as cell cycle distributi<strong>on</strong> or <str<strong>on</strong>g>th</str<strong>on</strong>g>e occurrence <str<strong>on</strong>g>of</str<strong>on</strong>g> cell dea<str<strong>on</strong>g>th</str<strong>on</strong>g> events.<br />

The presented framework for a comprehensive descripti<strong>on</strong> and analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular<br />

development <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e level <str<strong>on</strong>g>of</str<strong>on</strong>g> individual cells and <str<strong>on</strong>g>th</str<strong>on</strong>g>eir progeny is an important<br />

advancement to support experimental single cell tracking approaches. By combining<br />

experimental and modeling data our results dem<strong>on</strong>strate <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e analysis <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

cellular genealogies and corresp<strong>on</strong>ding interacti<strong>on</strong> networks can provide valuable<br />

insights into processes <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular development and differentiati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at can not be<br />

obtained <strong>on</strong> a populati<strong>on</strong> level.<br />

References.<br />

[1] N. Scherf, JP. Kuska et al. (2009) Spatio-temporal Analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> Unstained Cells in vitro Proceedings<br />

BVM 2009, 292- 296.<br />

[2] N. Scherf, I. Roeder, and I. Glauche (2008) Correlati<strong>on</strong> patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular genealogies Proceedings<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Fif<str<strong>on</strong>g>th</str<strong>on</strong>g> Internati<strong>on</strong>al Workshop <strong>on</strong> Computati<strong>on</strong>al Systems Biology, WCSB 2008,<br />

Leipzig, Germany, 161-164.<br />

1053

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Populati<strong>on</strong> Dynamics; Wednesday, June 29, 11:00<br />

Lai Zhang<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Technical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Denmark<br />

e-mail: L.Zhang@mat.dtu.dk<br />

K.H. Andersen<br />

Nati<strong>on</strong>al Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Aquatic Resources, Technical University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Denmark<br />

U.H. Thygesen<br />

Nati<strong>on</strong>al Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Aquatic Resources, Technical University <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Denmark<br />

K. Knudsen<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Technical University <str<strong>on</strong>g>of</str<strong>on</strong>g> Denmark<br />

Trait diversity promotes to stabilize community dynamics<br />

The dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> marine communities are generally modeled <str<strong>on</strong>g>th</str<strong>on</strong>g>rough <str<strong>on</strong>g>th</str<strong>on</strong>g>e McKendrickv<strong>on</strong><br />

Foerster equati<strong>on</strong>s describing <str<strong>on</strong>g>th</str<strong>on</strong>g>e biomass flow al<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e size spectrum. This<br />

modeling disregards <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individual grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate am<strong>on</strong>g different<br />

species due to <str<strong>on</strong>g>th</str<strong>on</strong>g>e ignorance <str<strong>on</strong>g>of</str<strong>on</strong>g> species identities. The potential c<strong>on</strong>sequence is<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>at predicti<strong>on</strong>s from <str<strong>on</strong>g>th</str<strong>on</strong>g>is model might deviate from <str<strong>on</strong>g>th</str<strong>on</strong>g>e reality by ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er being<br />

overestimated or underestimated. Using <str<strong>on</strong>g>th</str<strong>on</strong>g>e novel size- and trait-based species<br />

model where <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> individual grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate is explicitly included, <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

community size spectrum can be represented as an output <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e total species size<br />

spectra. A significant stabilizing mechanism is recognized for <str<strong>on</strong>g>th</str<strong>on</strong>g>e first time. It is<br />

dem<strong>on</strong>strated <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e distributed individual grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate tends to smoo<str<strong>on</strong>g>th</str<strong>on</strong>g>en out <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

fluctuati<strong>on</strong>s in <str<strong>on</strong>g>th</str<strong>on</strong>g>e resulting community spectrum and <str<strong>on</strong>g>th</str<strong>on</strong>g>us individual experiences<br />

less variable prey and predator fields. Effectively, trophic waves are smoo<str<strong>on</strong>g>th</str<strong>on</strong>g>ed out<br />

due to different grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rates am<strong>on</strong>g <str<strong>on</strong>g>th</str<strong>on</strong>g>e individuals at a given point in <str<strong>on</strong>g>th</str<strong>on</strong>g>e wave.<br />

The finding infers <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e traditi<strong>on</strong>al community modeling is to some extent oversimplified.<br />

1054

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Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models in Eco-epidemiology I; Wednesday, June 29, 08:30<br />

Qingguo Zhang<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Anhui Agricultural University, Hefei,<br />

Anhui 230036, China<br />

e-mail: qgzhang@ahau.edu.cn<br />

Li Xu<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics, Anhui Agricultural University, Hefei,<br />

Anhui 230036, China<br />

Cellular automata modeling applied in eco-epidemiology -<br />

Simulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial spread <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics wi<str<strong>on</strong>g>th</str<strong>on</strong>g> individual<br />

c<strong>on</strong>tact<br />

The spread <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics should be complex phenomena. As <str<strong>on</strong>g>th</str<strong>on</strong>g>e exchange <str<strong>on</strong>g>of</str<strong>on</strong>g> ec<strong>on</strong>omics<br />

and culture am<strong>on</strong>g different countries and areas become much closer in recent<br />

years, it has been an ecological issue <str<strong>on</strong>g>th</str<strong>on</strong>g>at influences public heal<str<strong>on</strong>g>th</str<strong>on</strong>g> for invading<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics to new areas. Generally, <str<strong>on</strong>g>th</str<strong>on</strong>g>ere are two types <str<strong>on</strong>g>of</str<strong>on</strong>g> ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models<br />

to describe <str<strong>on</strong>g>th</str<strong>on</strong>g>e spread <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics, determinate models and network dynamics<br />

models. Most <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e existing ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical models <str<strong>on</strong>g>of</str<strong>on</strong>g> simulating epidemics are<br />

built <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> ordinary and partial differential equati<strong>on</strong>s traditi<strong>on</strong>ally. These<br />

determinate models have an obviously weakness <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e local characteristics <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

transmissi<strong>on</strong> were neglected. In particularly ,<str<strong>on</strong>g>th</str<strong>on</strong>g>ey could not simulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e problems<br />

properly as following: <str<strong>on</strong>g>th</str<strong>on</strong>g>e process <str<strong>on</strong>g>of</str<strong>on</strong>g> individual c<strong>on</strong>tact<str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e individual<br />

behavior<str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial problems <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemical transmissi<strong>on</strong><str<strong>on</strong>g>th</str<strong>on</strong>g>e effects <str<strong>on</strong>g>of</str<strong>on</strong>g> mixed pattern<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> individual.<br />

As a typical representative <str<strong>on</strong>g>of</str<strong>on</strong>g> network dynamics models, cellular automata<br />

model has provided a useful and powerful tool for <str<strong>on</strong>g>th</str<strong>on</strong>g>e research <str<strong>on</strong>g>of</str<strong>on</strong>g> complex systems.<br />

According to <str<strong>on</strong>g>th</str<strong>on</strong>g>e definite <str<strong>on</strong>g>of</str<strong>on</strong>g> cellular automata model, it can be represented<br />

as an array <str<strong>on</strong>g>of</str<strong>on</strong>g> four elements, A=(Ld,S,N,f),where A is <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular automata system;<br />

Ld is <str<strong>on</strong>g>th</str<strong>on</strong>g>e cellular space; S is set <str<strong>on</strong>g>of</str<strong>on</strong>g> states; N is <str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> neighbors <str<strong>on</strong>g>of</str<strong>on</strong>g> cell,<br />

N=(S1,S2,S3„Sn),n is <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> neighbors <str<strong>on</strong>g>of</str<strong>on</strong>g> cell; f is <str<strong>on</strong>g>th</str<strong>on</strong>g>e map <str<strong>on</strong>g>of</str<strong>on</strong>g> state transfer<br />

from Sn to S. Based <strong>on</strong> cellular automata, a simple <str<strong>on</strong>g>th</str<strong>on</strong>g>eoretical model was presented<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>is work to simulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial spread <str<strong>on</strong>g>of</str<strong>on</strong>g> epidemics wi<str<strong>on</strong>g>th</str<strong>on</strong>g> individual c<strong>on</strong>tact.<br />

Populati<strong>on</strong> is divided into <str<strong>on</strong>g>th</str<strong>on</strong>g>ree classes: infected, immunized and susceptible. Each<br />

state <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell stands for <strong>on</strong>e class <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e populati<strong>on</strong>s. The epidemic model wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e characteristic <str<strong>on</strong>g>of</str<strong>on</strong>g> vertical transmissi<strong>on</strong> and c<strong>on</strong>tact was c<strong>on</strong>sidered particularly.<br />

The model, moreover, is extended to include <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> vaccinati<strong>on</strong>.<br />

This kind <str<strong>on</strong>g>of</str<strong>on</strong>g> effect can reduce <str<strong>on</strong>g>th</str<strong>on</strong>g>e epidemic propagati<strong>on</strong>. The proposed model can<br />

serve as a basis for <str<strong>on</strong>g>th</str<strong>on</strong>g>e development <str<strong>on</strong>g>of</str<strong>on</strong>g> algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms to simulate <str<strong>on</strong>g>th</str<strong>on</strong>g>e spatial spread <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

epidemics using real data.<br />

Keywords: Cellular Automata; Epidemics; Spatial Spread; Computer Simulati<strong>on</strong><br />

References.<br />

[1] G.C.Sirakoulis, I.Karafyllidis, and A.Thanailakis, A cellular automat<strong>on</strong> model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e effects<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> populati<strong>on</strong> movement and vaccinati<strong>on</strong> <strong>on</strong> epidemic propagati<strong>on</strong>. Ecological Modelling, 2000,<br />

133(3):209-223<br />

[2] A.Johansen, A simple model <str<strong>on</strong>g>of</str<strong>on</strong>g> recurrent epidemics, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Theoretical Biology, 1996,<br />

178(1):45-51<br />

1055

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

[3] C.Beauchemin, J.Samuel, and J.Tuszynski, A simple cellular automat<strong>on</strong> models for influenza<br />

A viral infecti<strong>on</strong>s. Theoretical Biology, 2005, 232:223-234<br />

[4] R.Willox, B.Grammaticos, A.S.Carstea, and A.Ramani, Epidemic dynamics: discrete-time<br />

and cellular automat<strong>on</strong> models, Physica A, 2003, 328:13-22<br />

1056

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Bioinformatics and System Biology; Wednesday, June 29, 17:00<br />

Michał Zientek<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology. Faculty Of Automatic C<strong>on</strong>trol,<br />

Electr<strong>on</strong>ics And Computer Science. Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science<br />

e-mail: michal.zientek@gmail.com<br />

Paweł Foszner<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology. Faculty Of Automatic C<strong>on</strong>trol,<br />

Electr<strong>on</strong>ics And Computer Science. Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science<br />

Andrzej Polański<br />

Silesian University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology. Faculty Of Automatic C<strong>on</strong>trol,<br />

Electr<strong>on</strong>ics And Computer Science. Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Computer Science<br />

Improving functi<strong>on</strong>al coherence <str<strong>on</strong>g>of</str<strong>on</strong>g> gene signatures by using<br />

Gene Ontology terms<br />

Molecular classifiers based <strong>on</strong> gene expressi<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles obtained in DNA microarray<br />

expreriments are very extensively studied due to <str<strong>on</strong>g>th</str<strong>on</strong>g>eir potential to be apllied in a<br />

variety <str<strong>on</strong>g>of</str<strong>on</strong>g> areas, such as diagnosis, predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>erapy results etc. The secific<br />

property <str<strong>on</strong>g>of</str<strong>on</strong>g> classificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> gene expressi<strong>on</strong> pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iles is <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e feature<br />

selecti<strong>on</strong> step. This stems from <str<strong>on</strong>g>th</str<strong>on</strong>g>e fact <str<strong>on</strong>g>th</str<strong>on</strong>g>at in DNA microarray experiments very<br />

large numbers <str<strong>on</strong>g>of</str<strong>on</strong>g> values <str<strong>on</strong>g>of</str<strong>on</strong>g> genes expressi<strong>on</strong>s are obtained for relatively small number<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> samples.<br />

Therefore in recent years significant effort has been paid to development <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

feature selecti<strong>on</strong> algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms leading to choosing appropriate subsets <str<strong>on</strong>g>of</str<strong>on</strong>g> genes, called<br />

gene signatures, which are <str<strong>on</strong>g>th</str<strong>on</strong>g>en used as arguments for discriminant functi<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

molecular classifier.<br />

Am<strong>on</strong>g me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods for gene selecti<strong>on</strong>, proposed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature, an interesting<br />

group are algori<str<strong>on</strong>g>th</str<strong>on</strong>g>ms using <str<strong>on</strong>g>th</str<strong>on</strong>g>e idea <str<strong>on</strong>g>of</str<strong>on</strong>g> combining <str<strong>on</strong>g>th</str<strong>on</strong>g>e informati<strong>on</strong> <strong>on</strong> expressi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

genes wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e informati<strong>on</strong> <strong>on</strong> functi<strong>on</strong>al coherence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e set <str<strong>on</strong>g>of</str<strong>on</strong>g> selected genes. Several<br />

papers in <str<strong>on</strong>g>th</str<strong>on</strong>g>e literature showed <str<strong>on</strong>g>th</str<strong>on</strong>g>at such an approach can lead to improvement<br />

in classificati<strong>on</strong> quality.<br />

In our study we propose an algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Steiner tree metrics, which<br />

was recently proposed as a tool for measuring functi<strong>on</strong>al coherence <str<strong>on</strong>g>of</str<strong>on</strong>g> subsets <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

genes. The proposed me<str<strong>on</strong>g>th</str<strong>on</strong>g>od uses a recursive procedure for signature slimming<br />

by removing least coherent genes. The obtained signature has largest measures <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

functi<strong>on</strong>al coherence. We present <str<strong>on</strong>g>th</str<strong>on</strong>g>e use <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e proposed algoritm for classificati<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> several publicly available DNA microarra datasets.<br />

This work was financially supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Polish Ministry <str<strong>on</strong>g>of</str<strong>on</strong>g> Science under<br />

Grant No. N516 441938 Efficient me<str<strong>on</strong>g>th</str<strong>on</strong>g>ods <str<strong>on</strong>g>of</str<strong>on</strong>g> genome browsing based <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Burrows<br />

Wheeler Transform.<br />

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Bioinformatics and System Biology; Wednesday, June 29, 17:00<br />

Ulyana Zubairova<br />

The Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Cytology and Genetics The Siberian Branch <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

Russian Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences<br />

e-mail: ulyanochka@bi<strong>on</strong>et.nsc.ru<br />

The Cell Grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and Divisi<strong>on</strong> Can Destroy Stem Cell Niche<br />

in a Reacti<strong>on</strong>-Diffusi<strong>on</strong> Model<br />

A minimal 1D-model <str<strong>on</strong>g>of</str<strong>on</strong>g> stem cell niche structure regulati<strong>on</strong> al<strong>on</strong>g vertical axis <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e SAM was developed <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e basis <str<strong>on</strong>g>of</str<strong>on</strong>g> a qualitative hypo<str<strong>on</strong>g>th</str<strong>on</strong>g>esis <str<strong>on</strong>g>of</str<strong>on</strong>g> interplay between<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e CLV and WUS genes. Previously it was shown <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ere is a set <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters<br />

supplying a stati<strong>on</strong>ary soluti<strong>on</strong> in qualitative corresp<strong>on</strong>dence wi<str<strong>on</strong>g>th</str<strong>on</strong>g> experimental<br />

observati<strong>on</strong>s. But <str<strong>on</strong>g>th</str<strong>on</strong>g>e questi<strong>on</strong> arises what will be <str<strong>on</strong>g>th</str<strong>on</strong>g>e model dynamics under cell<br />

grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and divisi<strong>on</strong>.<br />

Using DL-system formalism we developed a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model <str<strong>on</strong>g>of</str<strong>on</strong>g> stem cell<br />

niche structure regulati<strong>on</strong> <strong>on</strong> 1D-array <str<strong>on</strong>g>of</str<strong>on</strong>g> growing and dividing cells. A number <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

computer simulati<strong>on</strong>s were performed to study <str<strong>on</strong>g>th</str<strong>on</strong>g>e model dynamics.<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>e issue <str<strong>on</strong>g>th</str<strong>on</strong>g>e dependence <str<strong>on</strong>g>of</str<strong>on</strong>g> probability <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stem cell niche destructi<strong>on</strong><br />

<strong>on</strong> cell cycle durati<strong>on</strong> relative to diffusi<strong>on</strong> time scale was obtained. Increase <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e specific cell grow<str<strong>on</strong>g>th</str<strong>on</strong>g> rate results in m<strong>on</strong>ot<strong>on</strong>ic increase <str<strong>on</strong>g>of</str<strong>on</strong>g> system destructi<strong>on</strong><br />

probability and in decrease <str<strong>on</strong>g>of</str<strong>on</strong>g> its mean lifetime.<br />

Cell divisi<strong>on</strong>s account for relevant perturbati<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e SAM structure and may<br />

result in destructi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> it. The stem cell niche survivability depends <strong>on</strong> relati<strong>on</strong>s<br />

between model parameters.<br />

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Vladimir Zubkov<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: vladimir.s.zubkov@gmail.com<br />

Chris Breward<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

Eam<strong>on</strong>n Gaffney<br />

University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

Cell and Tissue Biophysics; Thursday, June 30, 11:30<br />

Hyperosmolarity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e tear film in dry eye syndrom.<br />

The biophysical factors <str<strong>on</strong>g>th</str<strong>on</strong>g>at dictate hyperosmolarity and <str<strong>on</strong>g>th</str<strong>on</strong>g>e observed patterns<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> tear film break-up in dry eye are poorly understood and are difficult to interrogate<br />

experimentally, highlighting <str<strong>on</strong>g>th</str<strong>on</strong>g>e need for ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and computati<strong>on</strong>al<br />

modelling in <str<strong>on</strong>g>th</str<strong>on</strong>g>is field. We have examined a model incorporating <str<strong>on</strong>g>th</str<strong>on</strong>g>e influence <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

polar lipids overlying an aqueous layer, while tracking <str<strong>on</strong>g>th</str<strong>on</strong>g>e evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> osmolarity.<br />

Our strategic objective was to identify factors which may influence <str<strong>on</strong>g>th</str<strong>on</strong>g>e risk<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> developing or exacerbating dry eye as well as exploring how such factors differ<br />

between evaporative dry eye and aqueous tear deficient dry eye. In particular, we<br />

focus <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e solute c<strong>on</strong>centrati<strong>on</strong> for <str<strong>on</strong>g>th</str<strong>on</strong>g>e durati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a single blink<br />

and interblink. Our ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model tracks <str<strong>on</strong>g>th</str<strong>on</strong>g>e <str<strong>on</strong>g>th</str<strong>on</strong>g>ickness <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e aqueous layer,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e polar lipid, toge<str<strong>on</strong>g>th</str<strong>on</strong>g>er wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e solute.<br />

Firstly, we have observed <str<strong>on</strong>g>th</str<strong>on</strong>g>at tear film osmolarity is very sensitive to <str<strong>on</strong>g>th</str<strong>on</strong>g>e evaporati<strong>on</strong><br />

rate, wi<str<strong>on</strong>g>th</str<strong>on</strong>g> salt c<strong>on</strong>centrati<strong>on</strong>s readily exceeding irritati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>resholds when using<br />

dry eye parameters. The results also highlight <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> diffusi<strong>on</strong> in reducing<br />

osmolar stress in <str<strong>on</strong>g>th</str<strong>on</strong>g>e vicinity <str<strong>on</strong>g>of</str<strong>on</strong>g> black lines during <str<strong>on</strong>g>th</str<strong>on</strong>g>e interblink. N<strong>on</strong>e<str<strong>on</strong>g>th</str<strong>on</strong>g>eless,<br />

in <str<strong>on</strong>g>th</str<strong>on</strong>g>ese regi<strong>on</strong>s diffusi<strong>on</strong> is not sufficient to prevent potentially damaging osmolarities,<br />

especially as <str<strong>on</strong>g>th</str<strong>on</strong>g>e evaporati<strong>on</strong> rate is increased (c<strong>on</strong>stituting evaporative dry<br />

eye) or <str<strong>on</strong>g>th</str<strong>on</strong>g>e tear volume is decreased (i.e. aqueous deficient dry eye). Simulati<strong>on</strong>s<br />

also indicate <str<strong>on</strong>g>th</str<strong>on</strong>g>at saccades (rapid eye movements) could have a positive effect <strong>on</strong><br />

osmolarities in <str<strong>on</strong>g>th</str<strong>on</strong>g>e vicinity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e black lines.<br />

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Modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> immune resp<strong>on</strong>ses and calcium signaling II; Wednesday, June 29,<br />

14:30<br />

Paweł Żuk<br />

College <str<strong>on</strong>g>of</str<strong>on</strong>g> Inter-Faculty Individual Studies in Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Natural<br />

Sciences, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Warsaw, Poland<br />

e-mail: pzuk@ippt.gov.pl<br />

Marek Kochańczyk<br />

Jagiell<strong>on</strong>ian University, Krakow, Poland<br />

e-mail: marek.kochanczyk@uj.edu.pl<br />

Tomasz Lipniacki<br />

Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Fundamental Technological Research, Warsaw, Poland<br />

e-mail: tlipnia@ippt.gov.pl<br />

Stochastic switching in a spatially extended,<br />

bistable kinase autoactivati<strong>on</strong> model<br />

In <str<strong>on</strong>g>th</str<strong>on</strong>g>is study we c<strong>on</strong>sider a spatially extended kinase autoactivati<strong>on</strong> model wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />

underlying bistability. We assume <str<strong>on</strong>g>th</str<strong>on</strong>g>at kinases may diffuse <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e cell membrane<br />

(or its restricted domain) and can be in <strong>on</strong>e <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>ree states: unphosphorylated,<br />

single or doubly phosphorylated. Catalitic activity <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e kinase is regulated by its<br />

phosphorylati<strong>on</strong> level; unphosphorylated kinases have <str<strong>on</strong>g>th</str<strong>on</strong>g>e lowest activity, doubly<br />

phosphorylated – <str<strong>on</strong>g>th</str<strong>on</strong>g>e highest. The emerging reacti<strong>on</strong>s are following:<br />

d<br />

d<br />

Kp −→ K, Kpp −→ Kp – dephosphorylati<strong>on</strong>,<br />

K + K c1<br />

c1<br />

−→ K + Kp, K + Kp −→ K + Kpp – phosphorylati<strong>on</strong> by K,<br />

Kp + K c2<br />

c2<br />

−→ Kp + Kp, Kp + Kp −→ Kp + Kpp – phosphorylati<strong>on</strong> by Kp,<br />

Kpp + K c3<br />

c3<br />

−→ Kpp + Kp, Kpp + Kp −→ Kpp + Kpp – phosphorylati<strong>on</strong> by Kpp,<br />

where d and c3 > c2 > c1 are dephosphorylati<strong>on</strong> and phosphorylati<strong>on</strong>s coefficients.<br />

Let us notice <str<strong>on</strong>g>th</str<strong>on</strong>g>at for c1 = 0 <str<strong>on</strong>g>th</str<strong>on</strong>g>e state in which all kinases are unphosphorylated is<br />

absorbing.<br />

We c<strong>on</strong>sider two limits:<br />

(1) infinite diffusi<strong>on</strong> for which <str<strong>on</strong>g>th</str<strong>on</strong>g>e system can be c<strong>on</strong>sidered as perfectly mixed<br />

and its dynamics is described by <str<strong>on</strong>g>th</str<strong>on</strong>g>e two-dimensi<strong>on</strong>al Markov process, and<br />

simulated using <str<strong>on</strong>g>th</str<strong>on</strong>g>e Gillespie algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m,<br />

(2) c<strong>on</strong>tinuous limit in which evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>centrati<strong>on</strong>s is given by <str<strong>on</strong>g>th</str<strong>on</strong>g>e system<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> partial differential equati<strong>on</strong>s.<br />

We numerically investigated <str<strong>on</strong>g>th</str<strong>on</strong>g>e activati<strong>on</strong> process in <str<strong>on</strong>g>th</str<strong>on</strong>g>e original model in<br />

SpatKin, a program designed to simulate reacti<strong>on</strong>-diffusi<strong>on</strong> processes <strong>on</strong> a triangular<br />

lattice. We observed <str<strong>on</strong>g>th</str<strong>on</strong>g>at for biologically justified values <str<strong>on</strong>g>of</str<strong>on</strong>g> parameters <str<strong>on</strong>g>th</str<strong>on</strong>g>e behavior<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e system cannot be described in any <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e two limits even qualitatively. In<br />

particular, we found <str<strong>on</strong>g>th</str<strong>on</strong>g>at probability density distributi<strong>on</strong>s depend <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e diffusi<strong>on</strong><br />

coefficient: bimodal distributi<strong>on</strong>s observed in <str<strong>on</strong>g>th</str<strong>on</strong>g>e infinite diffusi<strong>on</strong> limit become<br />

unimodal wi<str<strong>on</strong>g>th</str<strong>on</strong>g> decreasing diffusivity. We also found <str<strong>on</strong>g>th</str<strong>on</strong>g>at in <str<strong>on</strong>g>th</str<strong>on</strong>g>e bistable case <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

expected extincti<strong>on</strong> time (i.e. <str<strong>on</strong>g>th</str<strong>on</strong>g>e time in which <str<strong>on</strong>g>th</str<strong>on</strong>g>e absorbing state is reached when<br />

c1 = 0) grows wi<str<strong>on</strong>g>th</str<strong>on</strong>g> diffusivity and <strong>on</strong>ly in <str<strong>on</strong>g>th</str<strong>on</strong>g>e infinite diffusi<strong>on</strong> limit it becomes<br />

exp<strong>on</strong>entially proporti<strong>on</strong>al to <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> molecules.<br />

1060

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

We c<strong>on</strong>clude <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>e original Gillespie algori<str<strong>on</strong>g>th</str<strong>on</strong>g>m is not appropriate for simulati<strong>on</strong>s<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> spatially extended systems.<br />

This study was supported by <str<strong>on</strong>g>th</str<strong>on</strong>g>e Polish Ministry <str<strong>on</strong>g>of</str<strong>on</strong>g> Science and Higher Educati<strong>on</strong><br />

grant N N501 132936 and Foundati<strong>on</strong> for Polish Science grant TEAM/2009-<br />

3/6.<br />

1061

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Plants, grow<str<strong>on</strong>g>th</str<strong>on</strong>g> and transport processes I; Tuesday, June 28, 11:00<br />

K<strong>on</strong>stantinos Zygalakis<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Institute, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: zygalakis@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

G.J.D. Kirk<br />

Nati<strong>on</strong>al Soil Resources Institute, Cranfield University<br />

D.L. J<strong>on</strong>es<br />

School <str<strong>on</strong>g>of</str<strong>on</strong>g> Envir<strong>on</strong>ment, Natural Resources & Geography, Bangor<br />

University<br />

M. Wissuwa<br />

Crop Producti<strong>on</strong> and Envir<strong>on</strong>ment Divisi<strong>on</strong>, Japan Internati<strong>on</strong>al Research<br />

Center for Agricultural Sciences<br />

T. Roose<br />

Bioengineering, Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Engineering and Envir<strong>on</strong>ment, University<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> Sou<str<strong>on</strong>g>th</str<strong>on</strong>g>ampt<strong>on</strong><br />

A dual porosity model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e uptake <str<strong>on</strong>g>of</str<strong>on</strong>g> nutrients by root<br />

hairs<br />

Root hairs are <str<strong>on</strong>g>th</str<strong>on</strong>g>ought to play an important role in mediating nutrient uptake by<br />

plants. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we develop a ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical model for <str<strong>on</strong>g>th</str<strong>on</strong>g>e nutrient transport<br />

and uptake <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e scale <str<strong>on</strong>g>of</str<strong>on</strong>g> a single root. We treat soil as a double porous material,<br />

since nutrients are assumed to diffuse bo<str<strong>on</strong>g>th</str<strong>on</strong>g> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e soil fluid phase and wi<str<strong>on</strong>g>th</str<strong>on</strong>g>in <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

soil particles, while <str<strong>on</strong>g>th</str<strong>on</strong>g>ey can also bind to <str<strong>on</strong>g>th</str<strong>on</strong>g>e soil particle surfaces by reversible<br />

reacti<strong>on</strong>s. Using homogenizati<strong>on</strong> techniques we derive a macroscopic model for<br />

nutrient diffusi<strong>on</strong> and reacti<strong>on</strong> in <str<strong>on</strong>g>th</str<strong>on</strong>g>e soil which includes <str<strong>on</strong>g>th</str<strong>on</strong>g>e effect <str<strong>on</strong>g>of</str<strong>on</strong>g> all root hair<br />

surfaces. Various numerical simulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> a simplified versi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e macroscopic<br />

model highlight <str<strong>on</strong>g>th</str<strong>on</strong>g>e importance <str<strong>on</strong>g>of</str<strong>on</strong>g> root hairs for <str<strong>on</strong>g>th</str<strong>on</strong>g>e uptake <str<strong>on</strong>g>of</str<strong>on</strong>g> nutrients by <str<strong>on</strong>g>th</str<strong>on</strong>g>e<br />

plant in a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> different soil moisture scenarios.<br />

1062

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Multiscale modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> reacti<strong>on</strong> kinetics in biology; Tuesday, June 28, 14:30<br />

K<strong>on</strong>stantinos Zygalakis<br />

Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Institute, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

e-mail: zygalakis@ma<str<strong>on</strong>g>th</str<strong>on</strong>g>s.ox.ac.uk<br />

K. Burrage<br />

Computing Laboratory, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Oxford<br />

B. Melykuti<br />

Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Mechanical Engineering, University <str<strong>on</strong>g>of</str<strong>on</strong>g> California, Santa<br />

Barbara<br />

Alternative formulati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e Chemical Langevin Equati<strong>on</strong><br />

The Chemical Langevin Equati<strong>on</strong> is a Stochastic Differential Equati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>at describes<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>e time evoluti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> molecular counts <str<strong>on</strong>g>of</str<strong>on</strong>g> reacting chemical species D. Gillespie,<br />

Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Chemical Physics, 113(1), pp 297-306 (2000)). It stands as a bridge<br />

between <str<strong>on</strong>g>th</str<strong>on</strong>g>e deterministic ODE model and <str<strong>on</strong>g>th</str<strong>on</strong>g>e discrete probabilistic chemical Master<br />

equati<strong>on</strong>.<br />

Suppose n chemical species react <str<strong>on</strong>g>th</str<strong>on</strong>g>rough m reacti<strong>on</strong> channels, and <str<strong>on</strong>g>th</str<strong>on</strong>g>e n x<br />

m stoichiometry matrix is denoted by S. Gillespie formulated <str<strong>on</strong>g>th</str<strong>on</strong>g>e CLE wi<str<strong>on</strong>g>th</str<strong>on</strong>g> m<br />

independent standard Brownian moti<strong>on</strong>s. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk we describe an alternative<br />

formulati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e CLE which in general leads to a SDE wi<str<strong>on</strong>g>th</str<strong>on</strong>g> a smaller number <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

Brownian moti<strong>on</strong>s. For example if r is <str<strong>on</strong>g>th</str<strong>on</strong>g>e number <str<strong>on</strong>g>of</str<strong>on</strong>g> pairs <str<strong>on</strong>g>of</str<strong>on</strong>g> reversible reacti<strong>on</strong>s,<br />

<str<strong>on</strong>g>th</str<strong>on</strong>g>en in Gillespie’s formulati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ere would be 2r Brownian moti<strong>on</strong>s for <str<strong>on</strong>g>th</str<strong>on</strong>g>e reversible<br />

reacti<strong>on</strong>s, while in our formulati<strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>ere would <strong>on</strong>ly be r. We illustrate <str<strong>on</strong>g>th</str<strong>on</strong>g>at such<br />

a reacti<strong>on</strong> leads to significant computati<strong>on</strong>al savings.<br />

1063

Abreu, Fernão Vistulo de, 678, 1003<br />

Achim, Cristian V., 24<br />

Adachi, Taiji, 470<br />

Adams, Ben, 25, 26, 393, 734<br />

Afenya, Evans, 27<br />

Aff<strong>on</strong>so, Luana Regina, 926<br />

Af<strong>on</strong>nikov, Dmitry, 238<br />

Agaranovich, Alexandra, 595<br />

Aguiar, Maíra, 28<br />

Aguiar, Maira, 925<br />

Ahammer, Helmut, 30<br />

Ajelli, Marco, 31<br />

Akberdin, Ilya, 32<br />

Akerman, Ada, 33, 141<br />

Akhmetzhanov, Andrei R., 372<br />

Akhobadze, Vladimer, 494<br />

Akiyama, Masakazu, 34<br />

Akutsu, T., 690<br />

Alam-Nazki, Aiman, 539<br />

Alarcón, Tomás, 768, 770<br />

Alarc<strong>on</strong>, Tomas, 36<br />

Alber, Mark, 457<br />

Albert, Steven M., 893<br />

Alf<strong>on</strong>so, Juan Carlos López, 588<br />

Al-husari, Maym<strong>on</strong>a, 37<br />

Aliz<strong>on</strong>, Samuel, 38<br />

Allgower, Frank, 863<br />

Al<strong>on</strong>so, Juan Ant<strong>on</strong>io, 854<br />

Alt, Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. Wolfgang, 76<br />

Alt, Wolfgang, 39, 106, 1038, 1042<br />

Alvarez, Juan Manuel Cordovez, 53<br />

Alvarez-Martinez, Teresa, 414<br />

Amaku, Marcos, 637<br />

Amann, Ant<strong>on</strong>, 499<br />

Ambroch, Krystyna, 40<br />

Amigó, Jose, 41<br />

Ammunét, Tea, 42<br />

Anandanadesan, Anan<str<strong>on</strong>g>th</str<strong>on</strong>g>i, 44<br />

Anazawa, Masahiro, 46<br />

Ancliff, Mark, 755<br />

Andersen, K.H., 1054<br />

Anders<strong>on</strong>, Alexandar R. A., 833<br />

Anders<strong>on</strong>, Alexander, 47, 880<br />

Anders<strong>on</strong>, Alexander R. A., 330, 496<br />

Index <str<strong>on</strong>g>of</str<strong>on</strong>g> au<str<strong>on</strong>g>th</str<strong>on</strong>g>ors<br />

1065<br />

Anders<strong>on</strong>, Alexander R. M., 307<br />

Anders<strong>on</strong>, A. R. A., 830<br />

Anders<strong>on</strong>, Matt S., 689<br />

André, N., 428<br />

Andreasen, Viggo, 48<br />

Andriv<strong>on</strong>, Didier, 156<br />

Andrzej, pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. dr hab. inż. Polaski, 621<br />

Angenent, Gerco, 993<br />

Anguelov, Roumen, 49<br />

Angulo, O., 590<br />

Antes, Iris, 50<br />

Ant<strong>on</strong>ovics, Janis, 1032<br />

Apreutesei, Narcisa, 51<br />

Apri, Mochamad, 52<br />

Arai, Mamiko, 910<br />

Arbelaez Alvarado, Daniel, 53<br />

Argasinski, Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g>, 54<br />

Arnaud, Jacques-Damien, 414<br />

Arndts, Julian, 55<br />

Arnold, Anne, 56<br />

Artalejo, Jesus R., 57<br />

Artzy-Randrup, Yael, 58<br />

Asakawa, Takeshi, 59<br />

Ascolani, Gianluca, 60<br />

Astola, Laura, 62<br />

Atac, Irem, 63<br />

Avilov, K.K., 64<br />

Azevedo, Franciane, 66<br />

Bachar, Mostafa, 67<br />

Back, Walter de, 215<br />

Badoual, M., 344<br />

Badoual, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ilde, 224<br />

Baeumer, Boris, 334<br />

Baigent, S., 713<br />

Baigent, Stephen, 68, 426<br />

Baird, Austin, 387<br />

Bajpai, Archana, 69<br />

Baker, Ru<str<strong>on</strong>g>th</str<strong>on</strong>g>, 70, 71, 258, 550<br />

Baker, Ru<str<strong>on</strong>g>th</str<strong>on</strong>g> E., 688<br />

Baklouti, Melika, 284<br />

Bakshi, Suruchi, 71<br />

Bal, Wojciech, 359<br />

Balbus, Joanna, 72

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ballesta, Annabelle, 73<br />

Ballesteros, Sebastien, 28, 925<br />

Banaji, Murad, 74<br />

Band, Leah, 686<br />

Band, L. R., 75<br />

Bandura, Jörg, 76<br />

Banerjee, Malay, 77, 237<br />

Banks, H. T., 474<br />

Baranowski, R., 351<br />

Baranowski, Rafał, 773<br />

Barbarossa, Maria, 78<br />

Barbolosi, D., 428<br />

Barbosa, Susana, 79<br />

Barles, Guy, 947<br />

Barreira, Raquel, 613<br />

Barreto, F.R., 301<br />

Barry, J. D., 356<br />

Bartl, M., 517<br />

Bartoszek, Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g>, 80, 544<br />

Bartoszek, Wojciech, 81<br />

Barua, Dipak, 582<br />

Baruch-Mordo, Shar<strong>on</strong>, 413<br />

Basanta, David, 47, 82, 83, 496, 880<br />

Basler, K<strong>on</strong>rad, 203<br />

Bate, Andrew, 84<br />

Batel, Jerry, 85<br />

Bauer, Robert, 87<br />

Beauchemin, Ca<str<strong>on</strong>g>th</str<strong>on</strong>g>erine, 439<br />

Becker, S., 88<br />

Becker, Stefan, 971<br />

Becskei, Attila, 221<br />

Begum, Najida, 1021<br />

Belm<strong>on</strong>te, Julio, 90<br />

Belm<strong>on</strong>te-Beitia, J., 764<br />

Benabdallah, A., 428<br />

Bennett, Malcolm, 686<br />

Bennett, M. J., 75<br />

Benoit, Eric, 813<br />

Benzekry, S., 91, 428<br />

Berbert, Juliana Militão, 92<br />

Berec, Luděk, 93<br />

Beretta, Edoardo, 152<br />

Berezovskaya, Faina, 475<br />

Bergmann, Sven, 203<br />

Berkhout, Jan, 122<br />

Bernard, Samuel, 95, 303<br />

Bernhard, Pierre, 372<br />

Bertolusso, Roberto, 97<br />

Bertrand, Maury, 641<br />

Bertuzzi, Alessandro, 293<br />

Berven, Kei<str<strong>on</strong>g>th</str<strong>on</strong>g> A., 49<br />

Besl<strong>on</strong>, Guillaume, 303<br />

Best, Alex, 98, 1032<br />

Best, Janet, 867<br />

Be<str<strong>on</strong>g>th</str<strong>on</strong>g>ge, Anja, 99<br />

Beyer, Andreas, 898<br />

Bhattacharya, B.S., 968<br />

Bhinder, Arvinder, 449<br />

1066<br />

Bidot, Caroline, 978<br />

Bielczyk, N., 111<br />

Bielecki, Andrzej, 100<br />

Bier, Ben, 208<br />

Binder, Hans, 331<br />

Binder, Sebastian, 102<br />

Bisseling, T., 218<br />

Blair, Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ew W., 189<br />

Blanco, Stéphane, 1026<br />

Błażej, Paweł, 103<br />

Bley, Th., 573<br />

Bloomfield, Jenny, 104<br />

Blumberg, Mark S., 867<br />

Bobrowski, Adam, 105, 112, 1041<br />

Bock, Martin, 39, 106, 1038<br />

Bode, Nikolai, 107<br />

Bodenstein, C., 108<br />

Bodnar, M., 109, 111<br />

Bodyl, Andrzej, 326<br />

Bogucki, Radosław, 112<br />

Bohmann, Ansgar, 113<br />

Bohn, Andreas, 114, 205<br />

Bois, Justin, 694<br />

Boldin, Barbara, 115, 501<br />

Bolz<strong>on</strong>i, Luca, 837<br />

B<strong>on</strong>, Dimitra, 116<br />

B<strong>on</strong>ewald, Lynda, 779<br />

B<strong>on</strong>ino, Ferruccio, 182<br />

Boots, Mike, 98, 1032<br />

Boová, Katarína, 119, 521<br />

Borina, Maria Yu., 787<br />

Borkowski, Wojciech, 120<br />

Borowska, Marta, 121, 726<br />

Borys, P, 1023<br />

Borys, P., 377<br />

Bosch, Frank van den, 892<br />

Bosdriesz, Evert, 122<br />

Boudaoud, Arezki, 541<br />

Bowers, Roger, 123<br />

Bradham, Cyn<str<strong>on</strong>g>th</str<strong>on</strong>g>ia, 390<br />

Brainard, Diana M., 689<br />

Brännström, Åke, 580, 715, 950<br />

Brasier, Allan, 97<br />

Bratus, Alexander S., 124<br />

Braumann, Carlos A., 126<br />

Breban, Romulus, 127, 128<br />

Breindl, Christian, 863<br />

Breña–Medina, Víctor F., 129<br />

Breward, Chris, 1059<br />

Briët, Olivier, 173<br />

Brites, Nuno M., 126<br />

Britt<strong>on</strong>, Nicholas F., 130<br />

Britt<strong>on</strong>, Tom, 131<br />

Brockhurst, Mike, 1032<br />

Brook, B.S., 197, 417<br />

Brooks-Pollock, Ellen, 132<br />

Broom, dr Mark, 54<br />

Broom, Mark, 133, 384

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Brown, Alistair J.P., 984<br />

Brown, Ian H., 849<br />

Brown, Sam, 335<br />

Bruggeman, Frank, 122<br />

Brulport, Marc, 243<br />

Brunetto, Maurizia Rossana, 182<br />

Brusch, Lutz, 134, 135, 159, 215<br />

Buchner, Teodor, 137<br />

Buenzli, Pascal, 779<br />

Bunimovich, Svetlana, 138<br />

Bu<strong>on</strong>omo, Bruno, 139<br />

Burda, Z., 140, 983<br />

Bürger, Reinhard, 33, 141<br />

Burie, J.-B., 142<br />

Burke, D<strong>on</strong>ald S., 893<br />

Burrage, K., 1063<br />

Bushmelev, Eugene, 846<br />

Buske, Peter, 144<br />

Buszko, K., 145<br />

Buzug, Thorsten M., 971<br />

Buzug, T.M., 88<br />

Byrne, Helen, 241, 245, 448, 686<br />

Byrne, Helen M., 768, 770<br />

Byrne, Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. Helen, 184<br />

Cai, Anna, 146<br />

Cai, Yin, 147<br />

Callard, Robin, 895<br />

Calle, Eusebi, 827<br />

Callender, Hannah, 148<br />

Calvo, G. F., 635, 647, 764<br />

Camara, Baba Issa, 149<br />

Campanella, Mario, 150<br />

Capasso, Vincenzo, 152, 153<br />

Cardoso, M.Z., 646<br />

Carlos, Clara, 126<br />

Carrillo, Jose A., 155<br />

Carroll, David, 519<br />

Castel, Magda, 156, 616<br />

Castellazzo, Alessandro, 997<br />

Castillo-Chavez, Carlos, 222, 709<br />

Catterall, Stephen, 634<br />

Cebrat, Stanisław, 103, 606<br />

Cer<strong>on</strong>e, Luca, 703<br />

Chairez Hernández, Isaias, 157<br />

Chalub, Fabio, 158<br />

Champneys, Alan R., 129<br />

Chandrashaker, Akhila, 468<br />

Chaplain, Mark, 44, 792, 864<br />

Chaplain, Mark A. J., 946<br />

Chara, Osvaldo, 159<br />

Charles, Sandrine, 175<br />

Chauviere, Arnaud, 160, 162<br />

Chavarría-Krauser, Andrés, 163<br />

Chavarría-Krauser, Andres, 802<br />

Chaves, Luis Fernando, 165<br />

Chaves, Madalena, 365<br />

Cheddadi, Ibrahim, 166<br />

Cheng, Yiming, 230<br />

Cherniha, Roman, 167<br />

Cherstvy, Andrey, 168<br />

Chettaoui, Chadha, 170<br />

Chiam, Keng-Hwee, 171<br />

Chiam, K.-H., 558<br />

Chickarmane, Vijay, 543<br />

Chisholm, Ryan, 172<br />

Chitnis, Nakul, 173, 602, 629<br />

Choi, Ye<strong>on</strong>taek, 174<br />

Ch<strong>on</strong>, Tae-Soo, 174<br />

Choserot, Victoria, 62<br />

Chowell, Gerardo, 709<br />

Christodoulou, Zoe, 711<br />

Chrobak, Joanna M. Rodríguez, 836<br />

Ciccorossi, Pietro, 182<br />

Cichońska, Anna, 931<br />

Cieutat, P., 267<br />

Ciffroy, Philippe, 175<br />

Ciribilli, Yari, 685<br />

Ciric, Catalina, 175<br />

Ciupe, Stanca, 310<br />

Ciupe, Stanca M., 177<br />

Civitano, Luigi, 182<br />

Clairambault, Jean, 178<br />

Clark, Alys, 922<br />

Clarke, James, 179<br />

Clement, J., 298<br />

Clenden<strong>on</strong>, Sherry, 90<br />

Clint<strong>on</strong>, Steven, 449<br />

Cobbold, Christina, 180<br />

Cobbold, Christina A., 356<br />

Colijn, Caroline, 666<br />

Collinet, Claudio, 468<br />

Colnot, Sabine, 1025<br />

Colombatto, Piero, 182<br />

Cominetti, Ornella, 184<br />

Commenges, Daniel, 895<br />

C<strong>on</strong>de, Ignacio Ramis, 245<br />

C<strong>on</strong>duit, Paul, 71<br />

C<strong>on</strong>radi, Carsten, 185<br />

C<strong>on</strong>way, Jessica, 186<br />

C<strong>on</strong>way, Jessica M., 526<br />

Cook, Alex R., 634<br />

Coolen, A. C. C., 828<br />

Coombes, S., 197<br />

Coombs, Daniel, 526<br />

Coombs, Dr. Daniel, 186<br />

Cordoleani, Flora, 187<br />

Cordovez, Juan, 94<br />

Cornell, Stephen, 188, 272<br />

Cornish, J., 298<br />

Corso, G., 646<br />

Cortes, Andres, 189<br />

Coster, Adelle, 190<br />

Cotter, Sim<strong>on</strong>, 191<br />

Coutinho, Francisco Ant<strong>on</strong>io Bezerra, 637<br />

Coutinho, R. M., 535<br />

1067

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Coutinho, 646<br />

Covert, Markus, 192<br />

Cowen, Leah E., 984<br />

Craciun, Gheorghe, 193<br />

Crauste, Fabien, 95, 194<br />

Cressman, Ross, 540<br />

Cristini, Vittorio, 160, 162, 196, 609, 611<br />

Croisier, H., 197<br />

Crowell, Valerie, 173<br />

Cruz-Pacheco, Gustavo, 279<br />

Csikasz-Nagy, A., 69<br />

Csikasz-Nagy, Attila, 198, 685<br />

Cui, Jing-an, 199<br />

Cummings, Peter, 200<br />

Curk, Tine, 640<br />

Czarnołęski, Macrin, 265<br />

Czirok, Andras, 201<br />

Daamen, Winnie, 150<br />

Dads, E.Ait, 267<br />

Dahari, Harel, 202, 379<br />

Dahmen, Uta, 824<br />

Dalessi, Sascha, 203<br />

Damineli, Daniel, 205<br />

Danek, Agnieszka, 206<br />

Das, R., 298<br />

Daus<strong>on</strong>, Erin, 208, 1017<br />

Davids<strong>on</strong>, Fordyce A., 209, 210<br />

Davids<strong>on</strong>, Ross, 211<br />

Davis, Lisa, 337<br />

Dawidowicz, Ant<strong>on</strong>i Le<strong>on</strong>, 212<br />

Day, Troy, 213<br />

Deakin, Niall, 214<br />

Debowska, Malgorzata, 216<br />

Dehghany, Jaber, 217<br />

Deinum, E.E., 218<br />

Delgado-Eckert, Edgar, 219<br />

de los Reyes V, Aurelio, 221<br />

Delsanto, Pier Paolo, 380<br />

Dengel, Bernd-Sim<strong>on</strong>, 223<br />

de Oliveira, Paulo Murilo Castro, 606<br />

de Oliveira, Suzana Moss, 606<br />

Deroulers, C., 344<br />

Deroulers, Christophe, 224<br />

Deutsch, Andreas, 135, 159, 215, 225, 226,<br />

420, 651, 918<br />

Dhirasakdan<strong>on</strong>, Thanate, 227<br />

Díaz Herrera, Edgar, 228<br />

Dieckmann, Ulf, 580, 950<br />

Diego, D., 647, 764<br />

Diekman, Casey O., 312<br />

Dillilngham, Mark, 484<br />

Dimitriu, Gabriel, 229<br />

Dingli, David, 980<br />

Dirsch, Olaf, 824<br />

Diserens, Gaelle, 230<br />

Ditlevsen, Susanne, 231, 852, 953<br />

Dixit, Narendra, 232<br />

1068<br />

Doblare, Manuel, 591<br />

Dobnikar, Jure, 640<br />

Dobrescu, Radu, 233<br />

Dobrota, Dušan, 615<br />

Dolfin, Marina, 234<br />

Domijan, Mirela, 235<br />

Domingo, Esteban, 437<br />

D<strong>on</strong>nelly, Ruairi, 489<br />

d’On<str<strong>on</strong>g>of</str<strong>on</strong>g>rio, Alberto, 236, 237, 333<br />

Doroshkov, Alexey, 238<br />

Drake, Christiana, 240<br />

Drasdo, Dirk, 166, 170, 241, 243, 245, 419,<br />

447, 1025<br />

Drossel, Barbara, 338<br />

Drubi, Fátima, 247<br />

Drulis-Kawa, Zuzanna, 608<br />

Dshalalow, Eugene, 519<br />

Du, Yejie, 163<br />

Duan, Wen, 248<br />

Duarte, Jorge, 249<br />

Ducray, François, 823<br />

Ducrot, A., 142<br />

Dufourd, Claire, 250<br />

Dulla, G., 766<br />

Dum<strong>on</strong>t, Yves, 250, 252<br />

Dunn, Sara-Jane, 254<br />

Dunt<strong>on</strong>, Thomas A., 255<br />

Dup<strong>on</strong>t, Geneviève, 256<br />

Düring, Bertram, 257<br />

Dushek, Omer, 71<br />

Dykeman, Eric, 982<br />

Dys<strong>on</strong>, Louise, 258, 550<br />

Dys<strong>on</strong>, R. J., 75<br />

Dys<strong>on</strong>, R.J., 259<br />

Dyzma, Michal, 260<br />

Dźwinel, Witold, 1024<br />

Eames, Ken, 261<br />

Ebenhöh, Oliver, 906<br />

Eberl, Hermann, 262<br />

Edelstein-Keshet, Leah, 1018<br />

Edgert<strong>on</strong>, Mary E., 609, 611<br />

Edmunds, W.J., 459<br />

Eftimie, Raluca, 263<br />

Eid, Rasha Abu, 22<br />

Eisenberg, Marisa, 264<br />

Ejsm<strong>on</strong>d, Maciej Jan, 265<br />

Elaiw, A. M., 266<br />

Elbert, Benjamin, 464<br />

Elias Wolff, Federico, 269<br />

Ellert, J., 270<br />

Elliott, Charlie M., 613<br />

Elliott, Elizabe<str<strong>on</strong>g>th</str<strong>on</strong>g>, 272<br />

Ellner, Steve, 758<br />

Enciso, German A., 274<br />

Enderling, Heiko, 275, 276<br />

Erban, Radek, 277, 396<br />

Erikss<strong>on</strong>, Anders, 269

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Erikss<strong>on</strong>, Olivia, 444, 626<br />

Erm<strong>on</strong>, Stefano, 278<br />

Escobar, Adriana Bernal, 94<br />

Essen, Steve C., 849<br />

Esteva, L., 301<br />

Esteva, Lourdes, 279<br />

Esteve, François, 574<br />

Eunok, Jung, 280<br />

Evans, Roger, 281<br />

Evers, Joep, 283<br />

Eynaud, Yoan, 284<br />

Fackeldey, K<strong>on</strong>stantin, 286<br />

Faeder, James R., 287<br />

Fae<str<strong>on</strong>g>th</str<strong>on</strong>g>, Stanley H., 227<br />

Falcke, Martin, 289, 290, 966<br />

Fang, Chun, 291<br />

Farkas, József Z., 416<br />

Farkas, Jozsef, 292<br />

Fasano, A., 406<br />

Fasano, Ant<strong>on</strong>io, 293<br />

Fauci, Lisa, 731<br />

Fedorenko, Inna, 307<br />

Fedotov, Sergei, 295<br />

Feinstein, J., 1002<br />

Feliu, Elisenda, 296, 511<br />

Ferchichi, Adel, 1033<br />

Fernandez, J., 298<br />

Ferreira, C.P., 301<br />

Ferreira Jr., Wils<strong>on</strong>, 302<br />

Field, Jeremy, 979<br />

Filipe, Patrícia A., 126<br />

Findeisen, Rolf, 623<br />

Fischer, Stephan, 303<br />

Fister, K. Renee, 305<br />

Fitzpatrick, Ben, 306<br />

Flach, Edward H., 307<br />

Fleck, Christian, 660<br />

Flegg, Jennifer, 872<br />

Fletcher, Dr Alexander, 308<br />

Flint, Harry, 489<br />

Flockerzi, Dietrich, 185<br />

F<strong>on</strong>telos, M. A., 996<br />

F<strong>on</strong>tes, Pascaline, 414<br />

Foo, Jasmine, 309<br />

Forde, J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an, 310, 311<br />

Forger, Daniel, 312<br />

Fornasier, Massimo, 395<br />

Fortmann-Roe, Scott, 313<br />

Foryś, U., 111<br />

Foryś, Urszula, 786<br />

Foryś, Urszula, 777<br />

Foszner, Pawel, 314<br />

Foszner, Paweł, 1057<br />

Fournier, Richard, 1026<br />

Fozard, John, 316<br />

Frank, M<strong>on</strong>ika, 1010<br />

Franz, Benjamin, 317<br />

Franz<strong>on</strong>e, P. Colli, 859<br />

Fricker, Mark, 723<br />

Friedman, Avner, 318, 319, 449, 587<br />

Fuhrmann, Jan, 320<br />

Fujita Yashima, Hisao, 386<br />

Funk, Sebastian, 321<br />

Gabriel, Wilfried, 1039<br />

Gaff, Holly, 322, 323, 845<br />

Gaffney, Eam<strong>on</strong>n, 71, 1059<br />

Gaffney, Eam<strong>on</strong>n A., 325<br />

Gagat, Przemyslaw, 326<br />

Gajecka-Mirek, Elżbieta, 327<br />

Galach, Magda, 328<br />

Gallaher, Jill, 330<br />

Galle, Jörg, 798<br />

Galle, Joerg, 144, 245, 331<br />

Gallenberger, Martina, 332<br />

Galliot, Brigitte, 159<br />

Galvez, Thierry, 468<br />

Gambin, Anna, 919<br />

Gandolfi, Alberto, 293, 333<br />

Ganesh, Ayalvadi, 666<br />

García, José A., 334<br />

Garcia Lopez, Diana, 335<br />

Gardiner, Bruce S., 281<br />

Gasselhuber, Astrid, 336<br />

Gatenby, R. A., 830<br />

Gauduch<strong>on</strong>, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ias, 187<br />

Gautrais, Jacques, 1026<br />

Gavaghan, David, 723<br />

Gavaghan, David J., 255<br />

Gede<strong>on</strong>, Tomas, 337<br />

Gee, Maarten de, 52<br />

Gehrmann, Eva, 338<br />

Gejji, Richard, 339, 601<br />

Genaev, Mikhail, 238<br />

Gens, J. Scott, 90<br />

George, Uduak, 340<br />

Georgelin, Christine, 947<br />

Gerdes, Sebastian, 342<br />

Gerin, C., 344<br />

Gerisch, Alf, 967<br />

Gerlee, Philip, 345, 1027<br />

Gerrish, Philip, 346<br />

Gerstner, Wulfram, 347<br />

Getto, Philipp, 348, 697<br />

Getz, Wayne, 313<br />

Getz, Wayne M., 349<br />

Geurts, R., 218<br />

Ghosh, Atiyo, 350<br />

Gierałtowski, J., 351<br />

Gillies, R. J., 830<br />

Gilliland, D. Gary, 385<br />

Gillot-From<strong>on</strong>t, E., 560<br />

Gin, Elan, 134<br />

Giorgakoudi, Kyriaki, 353<br />

Giverso, Chiara, 355<br />

1069

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Gjini, Erida, 356<br />

Glauche, Ingmar, 342, 962, 1053<br />

Glazier, James, 357<br />

Glazier, James A., 90<br />

Glimm, Tilmann, 358<br />

Glinka, Anna, 649<br />

Gliozzi, Ant<strong>on</strong>io S., 380<br />

Goch, Wojciech, 359<br />

Gog, Julia, 360, 547<br />

Gog, Julia R., 849<br />

Gölgeli, Meltem, 362<br />

Goman, Mikhail, 676<br />

Gomes, Gabriela, 363<br />

G<strong>on</strong>zález, M., 679<br />

G<strong>on</strong>ze, Didier, 364<br />

Gopi, D., 593<br />

Gouzé, Jean-Luc, 365<br />

Graf, Isabell, 366<br />

Graff, Beata, 367, 465<br />

Graff, Grzegorz, 367, 465<br />

Grammaticos, B., 344<br />

Grammaticos, Basile, 224<br />

Gramotnev, Dmitri K., 368<br />

Gramotnev, Galina, 368<br />

Grau, Vicente, 723<br />

Grays<strong>on</strong>, Nick, 982<br />

Greenman, J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an, 369<br />

Greenwood, Priscilla, 231, 370, 842<br />

Grefenstette, John, 893<br />

Grenfell, Bryan T., 849<br />

Grieneisen, Verônica A., 1018<br />

Grieneisen, Ver<strong>on</strong>ica, 853<br />

Grill, Stephan W., 694<br />

Grima, Ram<strong>on</strong>, 660<br />

Grimal, Quentin, 967<br />

Grizzi, Fabio, 371<br />

Groenenboom, Marian, 62<br />

Grognard, Frédéric, 372, 957<br />

Groh, C. M., 373<br />

Grosse, Thibault, 964<br />

Gruca, Aleksandra, 314<br />

Grün, S<strong>on</strong>ja, 375<br />

Grüning, Dr André, 803<br />

Grzebelus, Dariusz, 919<br />

Grzywna, Z. J., 1023<br />

Grzywna, Z.J., 377<br />

Guaraldo, Irene, 371<br />

Gubbins, Sim<strong>on</strong>, 353<br />

Gubernov, Vladimir V., 522<br />

Gudowska-Nowak, Ewa, 584<br />

Guedj, Jeremie, 379<br />

Guerney, Chris, 1033<br />

Gueyffier, François, 964<br />

Guillomot, Michel, 170<br />

Guiot, Caterina, 380, 381<br />

Gutiérrez, C., 679<br />

Guy, Robert D., 930<br />

Guzik, P., 270, 778<br />

1070<br />

Gwiazda, Piotr, 382, 383<br />

Gyllenberg, Mats, 291, 988, 1047<br />

Haccou, Patsy, 247<br />

Hadeler, Karl P., 227<br />

Hadjichrysan<str<strong>on</strong>g>th</str<strong>on</strong>g>ou, Christ<str<strong>on</strong>g>of</str<strong>on</strong>g>oros, 384<br />

Haemmerich, Dieter, 336<br />

Haeno, Hiroshi, 385<br />

Hahnfeldt, Philip, 1034<br />

Hall, I., 417<br />

Hall, I.P., 197<br />

Hamant, Olivier, 541<br />

Hamdous, Saliha, 386<br />

Hamelin, Frédéric, 616<br />

Hamelin, Frederic M., 156<br />

Hamlet, Christina, 387<br />

Handelman, Samuel, 388<br />

Hänel, Sven-Erik, 599<br />

Hanin, Le<strong>on</strong>id, 389<br />

Hanke, Thomas, 559<br />

Hannaert, Patrick, 964<br />

Hansen, Thomas, 80<br />

Hardway, Hea<str<strong>on</strong>g>th</str<strong>on</strong>g>er, 390<br />

Hardy, Diggory, 173<br />

Harel, Roi, 313<br />

Harezlak, Jaroslaw, 391<br />

Harigua, Emna, 692<br />

Harris, Andrew, 392<br />

Harris<strong>on</strong>, Eleanor, 393<br />

Hashemi, S.Naser, 394<br />

Haskovec, Jan, 395, 396<br />

Hat-Plewinska, Beata, 397<br />

Hatzikirou, Haralambos, 160, 162<br />

Hatzikirou, Haralampos, 398, 674<br />

Hatzopoulos, Vasilis, 502<br />

Hayashida, M., 690<br />

Hayd<strong>on</strong>, Daniel T., 356<br />

Hbid, M.L., 399<br />

Head<strong>on</strong>, Denis, 400<br />

Heil, Ca<str<strong>on</strong>g>th</str<strong>on</strong>g>leen, 135<br />

Heiland, Ines, 862<br />

Heimburger, Ol<str<strong>on</strong>g>of</str<strong>on</strong>g>, 328<br />

Heinemann, Sascha, 559<br />

Heise, Robert, 401<br />

Heisler, Marcus, 541<br />

Hellander, Andreas, 592<br />

Hellander, Stefan, 592<br />

Hellmich, Christian, 402, 779<br />

Hengstler, Jan, 419<br />

Hengstler, Jan G., 241, 243, 1025<br />

Henkel, Annett, 684<br />

Henrikss<strong>on</strong>, Johan, 1027<br />

Hense, B. A., 766<br />

Hense, Burkhard A., 332, 362<br />

Herbis<strong>on</strong>, Allan E., 248<br />

Herman, Dorota, 403<br />

Hermiss<strong>on</strong>, Joachim, 404<br />

Hernandez, Ana, 405

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Herrera, Alejandra, 526<br />

Herrero, Dr. Miguel A., 588<br />

Herrero, Henar, 836<br />

Herrero, Miguel A., 406, 407<br />

Herrmann, Eva, 116, 408<br />

Hertz, John, 409<br />

Hester, Susan D., 90<br />

He<str<strong>on</strong>g>th</str<strong>on</strong>g>cote, Herbert W., 222<br />

Hicks<strong>on</strong>, R.I., 411<br />

Hilhorst, Danielle, 412<br />

Himes Boor, Gina, 413<br />

Hingant, Erwan, 414<br />

Hinow, 416<br />

Hiorns, J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an E., 417<br />

Hirt, Bar<str<strong>on</strong>g>th</str<strong>on</strong>g>olomäus, 418<br />

Hlavacek, Wiliam, 582<br />

Hoefer, Thomas, 873<br />

Hoehme, Stefan, 241, 243, 419, 1025<br />

Hoek, Milan J.A. van, 991<br />

Hoeng, Julia, 230<br />

Höfer, Thomas, 147<br />

Hogan, Thea, 895<br />

Hohmann, Nadine, 420<br />

Holmes, William, 421<br />

Holst, Klaus Kähler, 422<br />

Holstein-Ra<str<strong>on</strong>g>th</str<strong>on</strong>g>lou, Niels-Henrik, 423<br />

Holtrop, Grietje, 489<br />

Holzhuetter, Hermann-Georg, 424<br />

Hoogendoorn, Serge, 150<br />

Hori, Michio, 951<br />

Horn, Mary Ann, 425<br />

Hössjer, Ola, 626<br />

Hou, Zhanyuan, 426<br />

House, Thomas, 427<br />

Hoyle, Andy, 123, 825<br />

Hrynkiv, Vlad, 1049<br />

Hu, Bei, 319<br />

Hubbard, M. E., 373<br />

Hubbard, Steven, 44<br />

Hubert, F., 428<br />

Huds<strong>on</strong>, Andrew, 484<br />

Hue, Isabelle, 170<br />

Hui, C., 811<br />

Hulme, Philip E., 634<br />

Hulsh<str<strong>on</strong>g>of</str<strong>on</strong>g>, J., 714<br />

Hunt, C. An<str<strong>on</strong>g>th</str<strong>on</strong>g><strong>on</strong>y, 430<br />

Hunter, P., 298<br />

Hunter, Peter, 431<br />

Hurtado, Paul, 432<br />

Hustedt, Thiemo, 433<br />

Hutchings, Mike, 211<br />

Hyman, James M., 222<br />

Hyman, Mac, 629<br />

Iber, Dagmar, 434<br />

Iftikhar, Afifa, 492<br />

Igarashi, Tatsuhiko, 439<br />

Iino, Satomi, 435<br />

Ikeda, Kota, 1014<br />

Immink, Richard, 993<br />

Imran, Mudassar, 492<br />

Indelicato, Giuliana, 436<br />

Inga, Alberto, 685<br />

Innocentini, Guilherme, 808<br />

Inoue, Yumiko, 951<br />

Iranzo, Jaime, 437<br />

Ito, Kentaro, 480<br />

Iwami, Shingo, 439<br />

Iwanaszko, Marta, 440<br />

Iwasa, Yoh, 848<br />

Jabbari, Sara, 441<br />

Jabłoński, Jędrzej, 442<br />

Jacks<strong>on</strong>, Ian J., 748<br />

Jacks<strong>on</strong>, K.G., 968<br />

Jaeger, Johannes, 443<br />

Jafari-Mamaghani, Mehrdad, 444<br />

Jaffar, Mai, 209<br />

Jagers, Peter, 446<br />

Jagiella, Nick, 447<br />

Jagodič, Marko, 640<br />

Jain, Harsh, 448, 449<br />

Jain, Kavita, 756<br />

Jaksik, Roman, 314, 450, 632<br />

Jalan, R., 713<br />

Jalilzadeh, Aidin, 334<br />

Jamróz, Grzegorz, 452<br />

Janies, D. A., 388<br />

Janoušová, Eva, 789<br />

Jaroszewska, Joanna, 453<br />

Jaruszewicz, Joanna, 454<br />

Jarząb, Barbara, 775<br />

Jarząb, Michał, 775<br />

Jelinek, Herbert, 455<br />

Jensen, O. E., 75<br />

Jensen, O.E., 417<br />

Jensen, Ole Nørregaard, 875<br />

Je<strong>on</strong>, W<strong>on</strong>ju, 456<br />

Jiang, Yi, 457<br />

Jędrzejec, Bartosz, 939<br />

Joanny, Jean-François, 458<br />

Johns<strong>on</strong>*, H.C., 459<br />

J<strong>on</strong>es, D.L., 1062<br />

J<strong>on</strong>es, P. F., 373<br />

J<strong>on</strong>es, Z<str<strong>on</strong>g>of</str<strong>on</strong>g>ia, 461<br />

J<strong>on</strong>ss<strong>on</strong>, Henrik, 541<br />

Jordan, F., 69<br />

Jost, Christian, 1026<br />

Jr., Daniel C<str<strong>on</strong>g>of</str<strong>on</strong>g>field, 181<br />

Jung, Eunok, 568<br />

Just, Winfried, 463, 464<br />

Kaczkowska, Agnieszka, 367, 465<br />

Kahm, Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ias, 466<br />

Kaiser, Dale, 457<br />

Kalaidzidis, Yannis, 468<br />

Kaleta, C., 517<br />

1071

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Kalita, Piotr, 100<br />

Kamei, Hiroko, 469<br />

Kameo, Yoshitaka, 470<br />

Kamimura, Atsushi, 472, 707<br />

Kamp, Christel, 473<br />

Kapan, Durrell D., 25<br />

Kaper, Tasso, 390<br />

Kappel, Franz, 67, 474<br />

Kapustka, Filip, 265<br />

Karczewski, Jerzy, 943<br />

Karev, Georgy, 475<br />

Kareva, Irina, 475<br />

Karkach, Arseny S., 476<br />

Karley, Alis<strong>on</strong>, 44<br />

Kar<strong>on</strong>en, Ilmari, 477<br />

Karperien, Audrey, 455<br />

Kassa, Semu Mitiku, 744<br />

Kassara, Khalid, 478<br />

Katauskis, Pranas, 905<br />

Kaufmann, Kerstin, 993<br />

Kawasaki, Tomoko, 951<br />

Kawka, Joanna, 479<br />

Kazama, Toshiya, 480<br />

Kazantsev, Fedor, 32<br />

Kazmierczak, Bogdan, 260, 397, 481, 942<br />

Keef, T., 482<br />

Keef, Tom, 982<br />

Kelkel, Jan, 483<br />

Kelly, David, 484<br />

Kelly, Hea<str<strong>on</strong>g>th</str<strong>on</strong>g>, 653<br />

Kempf, Harald, 485, 659<br />

Kerner, Richard, 487<br />

Kettle, Helen, 489<br />

Khain, Evgeniy, 490, 491<br />

Khan, Adnan, 492<br />

Khan, Amjad, 493<br />

Khan, Rahmat Ali, 493<br />

Khatiashvili, Nino, 494<br />

Khayyeri, Hanifeh, 495<br />

Khlebodarova, Tamara M., 32<br />

Kieber, Joseph, 686<br />

Kim, Do-Wan, 568<br />

Kim, Eunjung, 496<br />

Kim, Jaejik, 820<br />

Kim, Yangjin, 497, 498<br />

Kim, Yung Sam, 280<br />

Kimmel, Marek, 97, 747, 1041<br />

King, John, 686<br />

King, J. R., 75<br />

King, Julian, 499<br />

Kirk, G.J.D., 1062<br />

Kisdi, Eva, 501, 988, 1032<br />

Kiss, István, 427<br />

Kiss, Istvan, 502<br />

Kitlas, Agnieszka, 503, 726<br />

Kleczkowski, Adam, 505, 730<br />

Kleessen, Sabrina, 506<br />

Klemola, Tero, 42<br />

1072<br />

Klepac, Kristen, 578<br />

Klika, Václav, 507<br />

Klipp, Edda, 984<br />

Kl<str<strong>on</strong>g>of</str<strong>on</strong>g>t, Charlotte, 1010<br />

Kl<strong>on</strong>owski, Wlodzimierz, 508<br />

Klu<str<strong>on</strong>g>th</str<strong>on</strong>g>, Sandra, 509<br />

Knappitsch, Markus P., 510<br />

Knibbe, Carole, 303<br />

Knudsen, K., 1054<br />

Knudsen, Michael, 511<br />

Kobayashi, Ryo, 34, 480, 958<br />

Kobayashi, Ryota, 512<br />

Kobayashi, Tetsuya J., 472, 513<br />

Kobayashi, Yutaka, 1046<br />

Koç, Helin, 499<br />

Kochańczyk, Marek, 514, 1060<br />

Kocieniewski, Pawel, 516<br />

Koetzing, M., 517<br />

K<str<strong>on</strong>g>of</str<strong>on</strong>g>f, David, 531<br />

Kohandel, Mohammad, 890<br />

Kohda, Masanori, 435<br />

Köhn-Luque, Alvaro, 518<br />

Koinuma, Satoshi, 59<br />

Koksal, Semen, 519<br />

Kolev, Mikhail, 520<br />

Kollár, Richard, 119, 521<br />

Kolobov, Andrey V., 522<br />

Kolomeisky, A., 168<br />

Komorowski, Michał 523<br />

K<strong>on</strong>, Ryusuke, 524<br />

K<strong>on</strong>do, Shigeru, 525<br />

K<strong>on</strong>rad, Bernhard, 526<br />

K<strong>on</strong>rad, Wilfried, 527, 838<br />

Kooi, Bob W., 28, 925<br />

Korb, Mas<strong>on</strong>, 464<br />

Kornelsen, J., 983<br />

Kornyshev, A., 168<br />

Kostal, Lubomir, 529<br />

Kotanko, Peter, 67<br />

Koumoutsakos, Petros, 664<br />

Kowalik-Urbaniak, Il<strong>on</strong>a Anna, 531<br />

Kozłowski, Jan, 265<br />

Kozubowski, T., 533<br />

Kraenkel, R.A., 646<br />

Kraenkel, Roberto, 534, 535<br />

Kraj, Piotr, 1029<br />

Krasowska, M., 377<br />

Krauze, T., 270<br />

Kravchuk, K.G., 536<br />

Krinner, Axel, 245, 537<br />

Krishnan, J., 539<br />

Kritz, Maurício Vieira, 1000<br />

Krivan, Vlastimil, 540<br />

Kropinski, Andrew M., 608<br />

Krug, Joachim, 756<br />

Krupinski, Pawel, 541, 543<br />

Krzemiński, Michał 544<br />

Krzywicki, A., 140

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Krzyzanski, Wojciech, 545<br />

Kschischo, Maik, 466<br />

Kuang, Yang, 311<br />

Kubo, Akisato, 546<br />

Kucharski, Adam, 360, 547<br />

Kücken, Michael, 548<br />

Kühl, Peter, 549<br />

Kulesa, Paul, 258, 550<br />

Kulesa, Paul M., 1044<br />

Kumar, S. B., 388<br />

Kuniya, Toshikazu, 551<br />

Kuttler, C., 766<br />

Kuttler, Christina, 78, 332, 362, 552<br />

Kuznetsov, Alexey, 1005<br />

Kwiek, J. J., 388<br />

Kyes, Sue A., 711<br />

Kzhyshkowska, Julia, 553<br />

L., Hannah, 425<br />

Lachapelle, Aitana Mort<strong>on</strong> de, 203<br />

Lachor, Paweł, 554<br />

Lachowicz, Mirosław, 556, 557, 946<br />

Lai, Tanny, 558<br />

Landini, Gabriel, 22<br />

Landsberg, Christoph, 559<br />

Langlais, Michel, 560<br />

Lansky, Petr, 529, 561, 784, 953<br />

Lapin, A., 562<br />

Lapin, Alexei, 768<br />

Laporta, G. Z., 535<br />

Lassau, Na<str<strong>on</strong>g>th</str<strong>on</strong>g>alie, 964<br />

Laubenbacher, Reinhard, 999<br />

Laudański, Tadeusz, 503<br />

Lavrova, Anastasia, 563<br />

Layt<strong>on</strong>, Anita, 564<br />

Layt<strong>on</strong>, Anita T., 565<br />

Layt<strong>on</strong>, Harold E., 565<br />

Leach, Michelle D., 984<br />

LeDuc, Philip R., 558<br />

Ledzewicz, Urszula, 566, 861<br />

Lee, Chang Hye<strong>on</strong>g, 567<br />

Lee, Junggul, 568<br />

Lee, Kiho, 248<br />

Lee, Nam-Kyung, 569<br />

Lee, Sang-Hee, 174, 456<br />

Lee, S. Seirin, 570<br />

Lee, Wanho, 280<br />

Leiderman, Karin, 572<br />

Lélu, M., 560<br />

Lenk, Felix, 573<br />

Lesart, Anne-Cécile, 574<br />

Lescoat, Philippe, 947<br />

Leśkow, Jacek, 575<br />

Levine, Ross L., 385<br />

Leviyang, Sivan, 576<br />

Lhachimi, L., 267<br />

Li, H. L., 752<br />

Li, J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an F., 577<br />

Li, Junqing, 1020<br />

Liautard, Jean-Pierre, 414<br />

Lichius, Alexander, 723<br />

Licois, Jean-René, 947<br />

Liddell, Chelsea, 578<br />

Liebscher, Volkmar, 579<br />

Likhoshvai, Vitaly, 670, 717<br />

Likhoshvai, Vitaly A., 32<br />

Lim, F<strong>on</strong>g Yin, 171<br />

Lin, Y. T., 490<br />

Lindh, Magnus, 580<br />

Lindholm, Bengt, 328<br />

Lio, Pietro, 581<br />

Li<strong>on</strong>, Sébastien, 38<br />

Lipniacki, Tomasz, 97, 397, 454, 514, 516,<br />

582, 761, 1060<br />

Lisowski, Bartosz, 584<br />

Lloyd, Alun, 586<br />

Loadman, P. M., 373<br />

Lock, John, 444, 626<br />

Loeffler, Markus, 144<br />

Löffler, Markus, 798<br />

Lokuge, K.M., 411<br />

Lolas, Georgios, 587<br />

Lopez, Luis F., 300<br />

Lopez-Herrero, M. J., 589<br />

López-Marcos, J. C., 590<br />

López-Marcos, M. A., 590<br />

Lopez-Menendez, Horacio, 591<br />

Lötstedt, Per, 592<br />

Louis, Kavi<str<strong>on</strong>g>th</str<strong>on</strong>g>a, 593<br />

Louis, Petra, 489<br />

Lourenço, José, 594<br />

Loux, Travis, 240<br />

Louzoun, Yoram, 595<br />

Lowengrub, John, 160, 162, 577, 596, 597,<br />

674<br />

Lozoya, Oswaldo, 598<br />

Lubkin, Shar<strong>on</strong>, 598<br />

Lundh, Torbjörn, 599, 1027<br />

Lunelli, Ant<strong>on</strong>ella, 804<br />

Luo, Jamie, 600<br />

Lutambi, Angelina Mageni, 602<br />

Lutter, Petra, 682<br />

Maciaszczyk-Dziubinska, Ewa, 608<br />

Maciejewski, Wes, 603<br />

Mackey, Michael C., 604, 605<br />

Mackiewicz, Dorota, 606<br />

Mackiewicz, Paweł, 103, 326, 608<br />

Macklin, Paul, 609, 611<br />

Madriñán, Santiago, 189<br />

Madzvamuse, Anotida, 340, 613<br />

Magnus, Carsten, 614<br />

Mahadevan, L., 171<br />

Maharaj, Savi, 505<br />

Mahmood, 615<br />

Mahmood, Silvia, 615<br />

1073

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Mailleret, Ludovic, 156, 372, 616, 957<br />

Maini, Philip, 71, 258, 550<br />

Maini, Philip K., 688, 768, 770<br />

Maini, Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. Philip, 184<br />

Maire, Nicolas, 173<br />

Makowiec, Danuta, 617, 619<br />

Makuchowski, Adam, 621<br />

Makuchowski, mgr Adam, 621<br />

Malchow, Horst, 622<br />

Mald<strong>on</strong>ado, Solvey, 623<br />

Malmros, Jens, 626<br />

Małogrosz, Marcin, 627<br />

Maman, Yaacov, 595<br />

Manca, Luigi, 386<br />

Manfredi, Piero, 628<br />

Mang, A., 88<br />

Mang, Andreas, 971<br />

Manore, Carrie, 629<br />

Manrubia, Susanna C., 437<br />

Manzano, Marc, 827<br />

Marciniak-Czochra, Anna, 630, 631<br />

Marczyk, Michał, 450, 632<br />

Marée, A<str<strong>on</strong>g>th</str<strong>on</strong>g>anasius F. M., 1018<br />

Maree, Stan, 853<br />

Marhl, M., 108<br />

Marinovic, Axel B<strong>on</strong>acic, 118<br />

Mari<strong>on</strong>, Glenn, 211, 489, 634<br />

Marlewski, A., 593<br />

Marsden, A., 1002<br />

Marsh, D<strong>on</strong>ald J., 423<br />

Martin, Clyde, 208<br />

Martin, O.C., 140<br />

Martínez, R., 679<br />

Martínez-G<strong>on</strong>zález, A., 647<br />

Martínez-G<strong>on</strong>zález, A., 635<br />

Martínez-Rodríguez, J., 590<br />

Martins, Ana, 999<br />

Martins, Nuno, 249<br />

Maršík, František, 507<br />

Marzantowicz, Wacław, 897<br />

Massad, Eduardo, 300, 637<br />

Massey, Susan, 833<br />

Massey, Susan Christine, 638<br />

Masumoto, Koh-hei, 59<br />

Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>äus, Franziska, 640<br />

Mauro, Andrea, 997<br />

Maxin, Daniel, 93<br />

Mayer, Jiří, 789<br />

Mazzucco, Rupert, 950<br />

McCauley, John W., 849<br />

McDougall, Dr Steven, 1022<br />

McElwain, D.L.S., 872<br />

McGillen, Jessica B., 642<br />

McKane, Alan, 335, 643<br />

McLennan, Rebecca, 550<br />

McPhers<strong>on</strong>, Nicola, 644<br />

Mehlig, Bernhard, 269<br />

Melgar, P., 647<br />

1074<br />

Melnichenko, O.A., 645<br />

Melykuti, B., 1063<br />

Mendoza-Juez, B., 647<br />

Mendyk, Aleksander, 649<br />

Mensi, Skander, 347<br />

Mente, Carsten, 651<br />

Meral, Gülnihal, 652<br />

Mercer, Ge<str<strong>on</strong>g>of</str<strong>on</strong>g>fry N., 653<br />

Mercer, G.N., 411<br />

Merelli, Emanuela, 581<br />

Merks, Roeland M. H., 654, 655<br />

Merks, Roeland M.H., 751, 991<br />

Merler, Stefano, 31<br />

Meszéna, Géza, 656<br />

Metze, K<strong>on</strong>radin, 657<br />

Metzler, Dirk, 1039<br />

Meyer-Hermann, Michael, 102, 217, 485,<br />

659, 866<br />

Meyerowitz, Elliot, 541<br />

Meyers, Rachel, 468<br />

Michor, Franziska, 385<br />

Middlet<strong>on</strong>, Alistair, 660<br />

Middlet<strong>on</strong>, A. M., 75<br />

Miekisz, Jacek, 661, 662, 945<br />

Mierczyński, Janusz, 663<br />

Migliavacca, F., 1002<br />

Miki, Takeshi, 1014<br />

Milde, Florian, 664<br />

Miller, Judi<str<strong>on</strong>g>th</str<strong>on</strong>g>, 665<br />

Miller, Laura, 758<br />

Miller, Laura A., 387<br />

Mills, Harriet, 666<br />

Milosevic, Nebojsa, 455, 667<br />

Mimura, Masayasu, 412, 1014<br />

Mincheva, Maya, 668<br />

Minihane, A., 968<br />

Mir<strong>on</strong>, Rachelle, 669<br />

Mir<strong>on</strong>ova, Victoria, 670, 717<br />

Mittag, Maria, 862<br />

Miura, Tomoyuki, 439<br />

Moldovan, Nicanor, 448<br />

Molenaar, Douwe, 122<br />

Molenaar, Jaap, 52, 62, 993<br />

Molenda, Mariola, 672<br />

Molnar, Ferenc, 967<br />

Mommer, Mario S., 640<br />

M<strong>on</strong>daini, Rubem P., 673<br />

M<strong>on</strong>serrate, Fredy, 189<br />

M<strong>on</strong>teiro, M. Teresa T., 835<br />

Moobedmehdiabadi, Shabnam, 674<br />

Morale, Daniela, 153<br />

Morano, Lisa, 1049<br />

Morishita, Yoshihiro, 675<br />

Moroz, Adam, 676<br />

Morozov, Andrew, 187<br />

Morozova, Nadya, 152<br />

Mort, Richard L., 748<br />

Mort<strong>on</strong>, Charles, 677

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Moss, Robert G., 964<br />

Mostad, Petter, 80<br />

Mostardinha, Patricia, 678, 1003<br />

Mota, M., 679<br />

Mou, Chunyan, 400<br />

Mourik, Sim<strong>on</strong> van, 993<br />

Moustafid, Amine, 478<br />

Moustaid, Fadoua El, 273<br />

Mroz, Iw<strong>on</strong>a, 681<br />

Mrozek, Kalina, 682<br />

Mrugala, Maciej M., 833<br />

Mueller, Thomas, 230<br />

Mueller–Roeber, Bernd, 735<br />

Mulder, B.M., 218<br />

Müller, Benedikt, 447<br />

Müller, J., 766<br />

Müller, Johannes 684<br />

Müller, Johannes, 362<br />

Müller, Margareta, 447<br />

Munir, M., 474<br />

Muniyappan, A., 593<br />

Munoz-Garcia, Javier, 703<br />

Muppirisetty, Sreeharish, 685<br />

Muraro, Daniele, 686<br />

Murray, Philip J., 688<br />

Nachbar, Robert B., 689<br />

Nacher, J.C., 690<br />

Nadolny, Robyn, 692<br />

Naef, Felix, 693<br />

Nagana<str<strong>on</strong>g>th</str<strong>on</strong>g>an, Sundar, 694<br />

Nagano, Mamoru, 59<br />

Nagy, John, 885<br />

Nakabayashi, Jun, 695<br />

Nakagaki, Toshiyuki, 480, 958<br />

Nakamura, Tetsuya, 696<br />

Nakata, Yukihiko, 697<br />

Namba, Toshiyuki, 698<br />

Na<str<strong>on</strong>g>th</str<strong>on</strong>g>an, Ran, 313<br />

Naud, Richard, 347<br />

Navarrete, Clara, 466<br />

Nawrot, Martin Paul, 700<br />

Nedorezov, L.V., 701<br />

Nedorezova, Bakhyt, 701<br />

Neigenfind, Jost, 702<br />

Nelander, Sven, 345<br />

Nerini, David, 187<br />

Neufeld, Zoltan, 703<br />

Neuhauser, Claudia, 704<br />

Neumann, Avidan U., 705, 928<br />

Newbold, Chris I., 711<br />

Nguyen, Anh Tuan, 1049<br />

Nguyen, H., 411<br />

Nie, Qing, 146<br />

Niehaus, Karsten, 682<br />

Nikolaev, Sergey, 706<br />

Nikoloski, Zoran, 56, 401, 506, 702, 735,<br />

850, 975<br />

Nishi, Ryosuke, 707<br />

Nishinari, Katsuhiro, 707<br />

Nishiura, Hiroshi, 709<br />

Noble, Robert, 711<br />

Noguchi, Sayaka, 951<br />

Noiret, L., 713<br />

Nolet, Robert, 714<br />

N<strong>on</strong>aka, Etsuko, 715<br />

Norman, Dr. Rachel, 644<br />

Norman, Rachel, 728, 825<br />

Nosek, Jozef, 119, 521<br />

Nosova, Ekaterina A., 716<br />

Novoselova, Ekaterina, 670<br />

Novoselova, Ka<str<strong>on</strong>g>th</str<strong>on</strong>g>erine, 717<br />

Novozhilov, Artem S., 124, 719<br />

Nowak, Ewa Gudowska -, 730<br />

Nowak, M.A., 983<br />

Nowakowski, A., 720<br />

Nunes, Ana, 363<br />

Nunez, Dr. Luis, 588<br />

Nurmi, Tuomas, 722<br />

Obara, Boguslaw, 723<br />

Ochab-Marcinek, Anna, 725<br />

O’C<strong>on</strong>nor, Paul M., 281<br />

Oczeretko, Edward, 121, 503, 726<br />

Oczko-Wojciechowska, Małgorzata, 775<br />

O’Dea, Reuben, 727<br />

Oduro, Bismark, 464<br />

Oelz, Dietmar, 733, 889<br />

Ogg, Eryll, 728<br />

Ohira, Toru, 707<br />

Ohno, Carolyn, 541<br />

Okamoto, Rika, 951<br />

Okuno, Takuya, 480<br />

Olczak, Łukasz, 729<br />

Oleś, Katarzyna, 730<br />

Olshak, Tal, 705<br />

Ols<strong>on</strong>, Sarah, 731<br />

Olufsen, Mette, 732<br />

Omelyanchuk, Nadezda, 717<br />

Omelyanchuk, Nadya, 670<br />

Omori, Ryosuke, 734<br />

Omranian, Nooshin, 735<br />

Orita, Natsuki, 737<br />

Osborne, Dr James, 739<br />

Osborne, James M., 255<br />

Otake, Yo-Hey, 740<br />

Otani, Hiroki, 599<br />

O<str<strong>on</strong>g>th</str<strong>on</strong>g>mer, Hans G, 742<br />

O<str<strong>on</strong>g>th</str<strong>on</strong>g>mer, Hans G., 741<br />

Ottesen, Johnny, 743<br />

Ouhinou, A., 811<br />

Ouhinou, Aziz, 744<br />

Ouhinou, Dr. Aziz, 273, 810<br />

Overgaard, Niels Chr, 745<br />

Owen, Markus R., 768, 770<br />

Owusu-Brackett, Nicci, 578<br />

1075

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Pacheco, Jorge M., 980<br />

Pacholczyk, Marcin, 747<br />

Packer, Aar<strong>on</strong>, 311<br />

Padmanabhan, Pranesh, 232<br />

Painter, Kevin, 400, 748, 749<br />

Palk, Laurence, 750<br />

Pallud, J., 344<br />

Palm, Margriet M., 751<br />

Pamuk, Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. Dr. Serdal, 63<br />

Pang, Peter, 752<br />

Panorchan, Paul, 689<br />

Panorska, A., 753<br />

Pantea, Casian, 754<br />

Paoletti, Nicola, 581<br />

Paraiso, Kim, 307<br />

Parisi, Andrea, 363<br />

Park, Je<strong>on</strong>g-Man, 755<br />

Park, Su-Chan, 756<br />

Parvinen, Kalle, 42, 715, 757, 885<br />

Pasour, Virginia, 369, 758<br />

Paszek, Pawel, 759<br />

Pásztor, Liz, 656<br />

Pavarino, L. F., 859<br />

Pavlík, Tomáš, 789<br />

Pawelek, K., 1023<br />

Pawelek, Kasia, 760<br />

Pawełek, P., 377<br />

Pawlas, Zbynek, 561<br />

Payan, Esteban, 94<br />

Pekalski, Jakub, 761<br />

Penny, Melissa, 173, 602<br />

Pepper, Michael, 587<br />

Peradzynski, Zbigniew, 763<br />

Perales, Celia, 437<br />

Perc, M., 108<br />

Perels<strong>on</strong>, Alan, 177, 379<br />

Pérez-García, Víctor M., 764<br />

Pérez-García, V. M., 647<br />

Pérez-García, V. M., 635<br />

Pérez-Velázquez, J., 766<br />

Perfahl, Holger, 223, 768, 770<br />

Periasamy, N., 373<br />

Perminov, Valeriy, 771<br />

Per<str<strong>on</strong>g>th</str<strong>on</strong>g>ame, Benoît, 166<br />

Peruani, Fernando, 772, 918<br />

Petelczyc, M<strong>on</strong>ika, 773<br />

Peters<strong>on</strong>, Carsten, 543<br />

Pfeifer, Aleksandra, 775<br />

Pfenning, Philipp-Niclas, 971<br />

Pham, Kara, 160<br />

Phillips, R. M., 373<br />

Pienaar, Jas<strong>on</strong>, 80<br />

Pieruschka, Roland, 776<br />

Pierzchalski, Michal, 508<br />

Pinches, Robert, 711<br />

Pinho, S.T.R., 301<br />

Pini<strong>on</strong>, Ca<str<strong>on</strong>g>th</str<strong>on</strong>g>erine, 1017<br />

Piotrowska, M<strong>on</strong>ika, 777<br />

1076<br />

Piotrowska, M<strong>on</strong>ika Joanna, 786<br />

Pirumova, Christina, 494<br />

Piskorski, J., 270, 778<br />

Piv<strong>on</strong>ka, P., 298<br />

Piv<strong>on</strong>ka, Peter, 779<br />

Płatkowski, T., 111<br />

Pluciński, Mateusz M., 780<br />

Podgorski, Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g>, 533<br />

Podziemski, Piotr, 781<br />

Poggi, Sylvain, 156<br />

Poggiale, J.-C., 783<br />

Poggiale, Jean-Christophe, 187, 284<br />

Pokora, Ondrej, 529, 784<br />

Pokrzywa, Rafał, 206<br />

Pokrzywa, Rafał, 729<br />

Polak, Miłosz, 649<br />

Polak, Sebastian, 649, 785<br />

Polanska, Joanna, 314<br />

Polańska, Joanna, 450, 632<br />

Polański, Andrzej, 554, 1057<br />

Polanski, Andrzej, 314<br />

Polański, Andrzej, 632<br />

Polaski, Andrzej, 729<br />

Poleszczuk, J., 111<br />

Poleszczuk, Jan, 786<br />

Poletti, Piero, 31<br />

Polezhaev, Andrey A., 522, 787<br />

Popa, A., 720<br />

Porter, Rosalyn, 788<br />

Poskrobko, Anna, 212<br />

Pospíšil, Zdeněk, 789<br />

Posvyanskii, Vladimir P., 124<br />

Potapov, Ilya, 790, 1005<br />

Pötzsche, Christian, 684<br />

Powa<str<strong>on</strong>g>th</str<strong>on</strong>g>il, Gibin, 792<br />

Pozzorini, Christian, 347<br />

Prado, P. I., 535<br />

Praetorius, Sim<strong>on</strong>, 793<br />

Pra<str<strong>on</strong>g>th</str<strong>on</strong>g>er, Kate, 550<br />

Prendergast, Patrick J., 495<br />

Prentice, Jamie, 794<br />

Preusser, Tobias, 877<br />

Preziosi, Luigi, 795<br />

Priano, Lorenzo, 381<br />

Prokert, G., 714<br />

Proulx, Stephen, 797<br />

Przybilla, Jens, 798<br />

Przymus, Piotr, 799, 843<br />

Pshenichnikova, Tatyana, 238<br />

Psiuk-Maksymowicz, Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g>, 801<br />

Ptashnyk, Mariya, 802<br />

Puddicombe, Robert, 803<br />

Pugliese, Andrea, 804, 837<br />

Pujo-Menjouet, Laurent, 414<br />

Pułka, Małgorzata, 805<br />

Puszyński, Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g>, 554<br />

Puszynski, Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g>, 909<br />

Přiklopil, Tadeáš, 796

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Pyrzowski, Jan, 806<br />

Quigley, Ben, 335<br />

Quintanilla, Rodrigo Huerta, 405<br />

Qutub, Amina, 807<br />

Radszuweit, Markus, 245<br />

Radtke, Kelly, 146<br />

Radulescu, Ovidiu, 808<br />

Rafajlovic, Marina, 809<br />

Rafał, dr inż. Pokrzywa, 621<br />

Raff, Jordan, 71<br />

Raharinirina, Nomenjanahary Alexia, 810<br />

Rajkovic, Katarina, 667<br />

Ramanantoanina, A., 811<br />

Ramis-C<strong>on</strong>de, Ignacio, 864<br />

Ramos, José, 466<br />

Rans<strong>on</strong>, Neil, 982<br />

Rault, J<strong>on</strong>a<str<strong>on</strong>g>th</str<strong>on</strong>g>an, 813<br />

Raum, Kay, 967<br />

Read, Nick, 723<br />

Recker, Mario, 594, 711, 814<br />

Regoes, Roland R., 614<br />

Reichhardt, Charles, 815<br />

Reimann, Peter, 865<br />

Rejniak, Katarzyna, 816<br />

Rejniak, Katarzyna A., 817, 818<br />

Reluga, Timo<str<strong>on</strong>g>th</str<strong>on</strong>g>y, 819<br />

Rempala, Grzegorz A., 820<br />

Repsys, Sarunas, 821<br />

Reuss, M., 562<br />

Reuss, Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ias, 223, 768, 770<br />

Reynolds, Jennifer, 822<br />

Ri, Maxim, 32<br />

Ri, Natalya, 32<br />

Ribba, Benjamin, 823<br />

Ribeiro, Ruy, 177<br />

Ricken, Tim, 824<br />

Rider, Rachel, 825<br />

Rieger, Heiko, 826<br />

Rietbergen, Bert van, 994<br />

Rigas, A.G., 914<br />

Ripoll, Jordi, 827<br />

Ristanovic, Dusan, 667<br />

Rizzoli, Annapaola, 837<br />

Roberts, E. S., 828<br />

Roberts, Mick, 829<br />

Roberts<strong>on</strong>-Tessi, Mark, 830<br />

Robeva, Raina, 831<br />

Röblitz, Susanna, 832<br />

Rockne, Russell, 638, 833<br />

Rodrigo, M. R., 406<br />

Rodrigues, Helena S<str<strong>on</strong>g>of</str<strong>on</strong>g>ia, 835<br />

Rodriguez, Jose Felix, 591<br />

Rodriguez, Terry, 387<br />

Roeder, Ingo, 342, 537, 962, 1053<br />

Romagnoli, Ver<strong>on</strong>ica, 182<br />

Roman, Fabio, 998<br />

Romanyukha, Alexei A., 476, 716<br />

Roose, T., 1062<br />

Roquete, Carlos J., 126<br />

Rosà, Roberto, 837<br />

Ross, Amanda, 173<br />

Rosso, Fausta, 837<br />

Rossotto, Federica, 998<br />

Rost, Fabian, 135<br />

Ro<str<strong>on</strong>g>th</str<strong>on</strong>g>-Nebelsick, Anita, 527, 838<br />

Roto, Elina, 840<br />

Roudi, Yasser, 409<br />

Rovetti, Robert, 841<br />

Rowat, Peter, 370, 842<br />

Rozante, Luiz, 926<br />

Ryan, Sadie, 323, 845<br />

Rychtar, Jan, 133, 384<br />

Rykaczewski, Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g>, 799, 843<br />

Rynkiewicz, A., 619<br />

Rzeszowska-Wolny, Joanna, 931<br />

Sacerdote, Laura, 844<br />

Sadovsky, Michael, 846<br />

Saeki, Koichi, 848<br />

Saenz, Roberto, 849<br />

Sajitz-Hermstein, Max, 850<br />

Saku, Takashi, 22<br />

Sala<str<strong>on</strong>g>th</str<strong>on</strong>g>é, Marcel, 321<br />

Salbreux, Guillaume, 694, 851<br />

Sal<str<strong>on</strong>g>th</str<strong>on</strong>g>ouse, D., 482<br />

Saltzman, Jeffrey S., 689<br />

Sams<strong>on</strong>, Adeline, 852<br />

Sanchez Corrales, Yara Elena, 853<br />

Sanchez-Prieto, P., 647<br />

Sander, Le<strong>on</strong>ard, 491<br />

Sander, L. M., 490<br />

Sander, Martin, 135<br />

Sanogo, Chata, 278<br />

Sansom, Mark S.P., 255<br />

Santana, Fabiana, 926<br />

Sanz, Luis, 854<br />

Sapoukhina, Natalia, 149<br />

Sardanyés, Josep, 249<br />

Sasaki, Akira, 856<br />

Satake, Akiko, 857<br />

Savory, Andrew, 858<br />

Sawair, Faleh, 22<br />

Sboto-Frankenstein, U., 983<br />

Scacchi, S., 859<br />

Schadschneider, Andreas, 860<br />

Schaettler, Heinz, 566, 861<br />

Schäuble, Sascha, 862<br />

Scheiner, Stefan, 779<br />

Scherf, Nico, 962, 1053<br />

Scheurich, Peter, 1036<br />

Schilling, Thomas F., 146<br />

Schimansky-Geier, L., 563<br />

Schittler, Daniella, 863<br />

Schley, David, 353<br />

Schlicht, R., 766<br />

1077

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Schlitt, T., 828<br />

Schlittenhardt, Timo<str<strong>on</strong>g>th</str<strong>on</strong>g>y P., 960<br />

Schlüter, Daniela, 864<br />

Schmal, Christoph, 865<br />

Schmeiser, Christian, 889<br />

Schmeitz, Christine, 866<br />

Schmidt, Deena, 867<br />

Schneditz, Daniel, 328, 868<br />

Schneider, Kristan, 870<br />

Schnell, Santiago, 871, 1044<br />

Schoell, Eckehard, 245<br />

Sch<str<strong>on</strong>g>of</str<strong>on</strong>g>ield, Pietá, 44<br />

Scholz, Markus, 537<br />

Schroeter, A., 970<br />

Schugart, Richard, 872<br />

Schulze, Anna, 873<br />

Schuster, S., 108, 517, 862, 970<br />

Schütte, Christ<str<strong>on</strong>g>of</str<strong>on</strong>g>, 1010<br />

Schütte, Moritz, 906<br />

Schütz, T.A., 88<br />

Schütz, Tina A., 971<br />

Schwämmle, Veit, 875<br />

Schwank, Gerald, 203<br />

Schwartz, Elissa, 876<br />

Schwen, Lars Ole, 877<br />

Scianna, Marco, 878<br />

Scott, Jacob, 880<br />

Sedd<strong>on</strong>, Bennedict, 895<br />

Sedivy, Roland, 30<br />

Selbach-Allen, Megan, 881<br />

Sella, Lorenzo, 882<br />

Seno, Hiromi, 884<br />

Seppänen, Anne, 885<br />

Seri, Raffaello, 886<br />

Service, Robert, 887<br />

Seyfried, Armin, 888<br />

Sfakianakis, Nikolaos, 889<br />

Shahbandi, Nazgol, 890<br />

Shapiro, Michael, 219<br />

Shapiro, Rebecca S., 984<br />

Sharkey, Dr. Kieran, 881<br />

Sharkey, Kieran, 891<br />

Sharp, Ryan, 892<br />

Sheikh-Bahaei, Shahab, 430<br />

Shifflet, Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. Angela, 184<br />

Shifflet, Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. George, 184<br />

Shigeyoshi, Yasufumi, 59<br />

Shillor, Meir, 49<br />

Shim, Eunha, 893<br />

Shinomoto, Shigeru, 512, 894<br />

Shirinifard, Abbas, 357, 936<br />

Shuvaev, Andrey, 895<br />

Sieber, Michael, 896<br />

Signerska, Justyna, 897<br />

Sikora-Wohlfeld, Wer<strong>on</strong>ika, 898<br />

Silva, Lucas Amaral da, 926<br />

Silva, V.C.M., 301<br />

Sime<strong>on</strong>i, Luca, 873<br />

1078<br />

Sim<strong>on</strong>, Peter, 900<br />

Sim<strong>on</strong>, Peter L., 502<br />

Simps<strong>on</strong>, Dr Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ew, 70<br />

Simps<strong>on</strong>, Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ew, 901, 902<br />

Sinden, Richard, 519<br />

Sinisgalli, Carmela, 293<br />

Sirl, David, 903<br />

Sirovich, Roberta, 904<br />

Skakauskas, Vladas, 821, 905<br />

Sk<strong>on</strong>ieczna, Magdalena, 931<br />

Skupin, Alexander, 906, 907<br />

Skvortsov, Alex, 905<br />

Skwara, Urszula, 908<br />

Sleeman, B. D., 373<br />

Smalley, Keiran S., 496<br />

Smalley, Keiran S. M., 307<br />

Smieja, Jaroslaw, 909<br />

Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>, Charles Eugene, 910<br />

Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>, David W., 281, 779<br />

Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>?, Robert, 911<br />

Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>, Thomas, 173<br />

Smi<str<strong>on</strong>g>th</str<strong>on</strong>g>, Tom, 602<br />

S.M.Salehi, Fazeleh, 394<br />

Smye, S. W., 373<br />

Sneppen, Kim, 875<br />

Sneyd, James, 248<br />

S<strong>on</strong>g, Guohua, 199, 1020<br />

Sorokina, Oksana, 912<br />

Sosnovtseva, Olga, 423<br />

Souai, Oussama, 692<br />

Souza, Max, 158<br />

Souza, Max O., 913<br />

Spanou, E.N., 914<br />

Spiegel, Orr, 313<br />

Stachowska-Piętka, Joanna, 916<br />

Staiger, Doro<str<strong>on</strong>g>th</str<strong>on</strong>g>ee, 865<br />

Stanley-Wall, Nicola, 210<br />

Starruß, Jörn, 918<br />

Startek, Michał, 919<br />

Stefański, K., 145<br />

Steiner, Lydia, 331<br />

Steingroewer, J., 573<br />

Stekel, Dov J., 403<br />

Stéphanou, Angélique, 340<br />

Stephanou, Angélique, 574<br />

Stepien, Pawel, 508<br />

Stepien, Robert, 508<br />

Stepien, Tracy, 920<br />

Stevens, Angela, 113, 320<br />

Stiehl, Thomas, 921<br />

Stockley, Peter, 982<br />

Stokes, Yv<strong>on</strong>ne, 922<br />

Stolarska, Magdalena A., 923<br />

Stollenwerk, Nico, 28, 924, 925<br />

St<strong>on</strong>e, Lewi, 990<br />

Stransky, Beatriz, 926<br />

Strauss, Lior, 928<br />

Strömblad, Staffan, 444

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Struzik, Zbigniew, 929<br />

Strychalski, Wanda, 930<br />

Student, Sebastian, 931<br />

Stura, Ilaria, 381<br />

Sturrock, Marc, 933<br />

Suarez, Susan, 731<br />

Sumpter, David J. T., 715<br />

Sundqvist, Lisa, 934<br />

Surulescu, Christina, 652, 935, 1036<br />

Surulescu, Nico, 935<br />

Suzuki, Sayaki U., 856<br />

Swans<strong>on</strong>, Kristin R., 638, 833<br />

Swat, Maciej, 936, 938<br />

Sweby, P.K., 968<br />

Świątek, Michał, 584<br />

Świder, Krzyszt<str<strong>on</strong>g>of</str<strong>on</strong>g>, 939<br />

Świerniak, Michał, 775<br />

Swig<strong>on</strong>, David, 920, 940<br />

Szederkényi, Gábor, 941<br />

Szilágyi, András, 656<br />

Szlęk, Jakub, 649<br />

Szopa, Piotr, 260, 942<br />

Szymanowska-Pułka, Joanna, 943<br />

Szymanska, Paulina, 945<br />

Szymańska, Zuzanna, 946<br />

Tabaka, Marcin, 725<br />

Tada, Tetsuko, 439<br />

Taghipoor, Masoomeh, 947<br />

Takada, Takenori, 493, 949<br />

Takahashi, Daisuke, 950<br />

Takahashi, Lucy T., 302<br />

Takahashi, Satoshi, 435, 951<br />

Takasu, Fugo, 737<br />

Takeuchi, Yasuhiro, 952<br />

Talikka, Marja, 230<br />

Tamborrino, Massimiliano, 844, 953<br />

Tanaka, Elly M., 134<br />

Tanase, Mihai, 233<br />

Tang, Min, 166<br />

Tapani, S<str<strong>on</strong>g>of</str<strong>on</strong>g>ia, 954<br />

Tay, Savas, 761<br />

Taylor, Michael, 502, 956<br />

Taylor, Nick, 728<br />

Teixeira, M.G.L., 301<br />

Teixeira Alves, Mickael, 957<br />

Telschow, Arndt, 102<br />

Terada, Ayaka, 884<br />

Tero, Atsushi, 34, 958<br />

Terry, Emmanuelle, 959<br />

Teschl, Gerald, 499<br />

Teschl, Susanne, 499<br />

Teusink, Bas, 122<br />

Thanh, Ngo van, 174<br />

Theraulaz, Guy, 1026<br />

Thibodeaux, Jeremy, 960<br />

Thiébaut, Rodolphe, 895<br />

Thieme, Horst, 961<br />

Thieme, Horst R., 227<br />

Thierbach, K<strong>on</strong>stantin, 962<br />

Thieullen, Michele, 963<br />

Thober, Stephan, 579<br />

Thomas, Christopher M., 403<br />

Thomas, D., 298<br />

Thomas, S. R., 713<br />

Thomas, S. Randall, 964<br />

Thul, R., 197<br />

Thul, Ruediger, 965<br />

Thurley, Kevin, 289, 290, 966<br />

Thygesen, U.H., 1054<br />

Tiburtius, Sara, 967<br />

Tim<strong>on</strong>ov, Vladimir, 32<br />

Tindall, Marcus, 968<br />

Tobin, Frank, 230<br />

Toiv<strong>on</strong>en, Jaakko, 969<br />

Tokarski, C., 970<br />

Toma, A., 88<br />

Toma, Alina, 971<br />

Tomanek, B., 983<br />

Tomas, Susana Ubeda, 686<br />

Tomasetti, Cristian, 972<br />

Tomáška,<br />

[Pleaseinsertintopreamble]ubomír, 119<br />

Tomáška, Ľubomír, 521<br />

Tomba, Gianpaolo Scalia, 804<br />

Topa, Paweł, 973<br />

Töpfer, Nadine, 975<br />

Torres, Delfim F. M., 835<br />

Tosin, Andrea, 977<br />

Touzeau, Suzanne, 978<br />

Toyoizumi, Hiroshi, 979<br />

Traas, Jan, 541<br />

Tracht, Saman<str<strong>on</strong>g>th</str<strong>on</strong>g>a M., 222<br />

Traulsen, Arne, 980<br />

Traulsen, Chaitanya S. Gokhale and Arne,<br />

361<br />

Trněný, Marek, 789<br />

Troiwanowski, G., 1002<br />

Trubuil, Alain, 170<br />

Tsaban, Lea, 595<br />

Tsai, Je-Chiang, 981<br />

Tsubo, Yasuhiro, 512<br />

Turner, Dr. Katy, 179<br />

Turner, Mat<str<strong>on</strong>g>th</str<strong>on</strong>g>ew, 600<br />

Turshak, L<strong>on</strong>gt<strong>on</strong>g, 1033<br />

Twarock, R., 482<br />

Twarock, Reidun, 982<br />

Tyburczyk, J., 983<br />

Tyc, Katarzyna, 984<br />

Tyran-Kamińska, Marta, 605<br />

Tyrcha, Joanna, 409, 444, 626<br />

Tyszka, Jarosław, 973<br />

Tzafestas, Elpida, 985<br />

Úbeda-Tomás, S., 75<br />

Udagawa, Jun, 599<br />

1079

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Ulikowska, Agnieszka, 987<br />

Unterk<str<strong>on</strong>g>of</str<strong>on</strong>g>ler, Karl, 499<br />

Utz, Margarete, 988<br />

Uys, Dr. Lafras, 273, 810<br />

Uyttewaal, Magalie, 541<br />

Uziel, Asher, 990<br />

Vaggi, F., 69<br />

Vaggi, Federico, 685<br />

Valentine, Jack L., 689<br />

Valle, Sara Y. Del, 222<br />

van der Sanden, Boudewijn, 574<br />

Vardavas, Raffaele, 995<br />

Vargas, Cristobal, 279<br />

Vassilevska, Tanya Kostova, 530<br />

Vassiliadis, V.G., 914<br />

Vauchelet, Nicolas, 166<br />

Vela-Pérez, M., 996<br />

Velázquez, J. J. L., 996<br />

Velazquez, J.J.L., 109<br />

Venturino, Ezio, 381, 997, 998<br />

Vera-Lic<strong>on</strong>a, Paola, 999<br />

Verducci, J. S., 388<br />

Vider, Tal, 595<br />

Vidybida, A.K., 536<br />

Vign<strong>on</strong>-Clementel, Irene, 447, 1002<br />

Vign<strong>on</strong>-Clémentel, Irène, 166<br />

Vitale, Guido, 795, 1004<br />

Volkov, Evgenii, 790, 1005<br />

Volpe, Claudia, 997<br />

Volpert, Vitaly, 1008, 1009<br />

v<strong>on</strong> Kleist, Max, 1010<br />

Voß, Ute, 686<br />

Voss-Boehme, Anja, 1013<br />

Voß-Böhme, Anja, 420<br />

Voytsekh, Olga, 862<br />

Vrscay, Edward R., 531<br />

Vuillaume, Gregory, 230<br />

Vybiral, Jan, 395<br />

Wakano, Joe Yuichiro, 1014<br />

Waliszewski, Przemyslaw, 22, 1015<br />

Wallace, Doro<str<strong>on</strong>g>th</str<strong>on</strong>g>y, 578, 1017<br />

Wal<str<strong>on</strong>g>th</str<strong>on</strong>g>er, Georg R., 1018<br />

Wang, Juhui, 170<br />

Wang, M. X., 752<br />

Wang, Xiaojing, 1020<br />

Wang, Yi, 291, 1047<br />

Wang, Zhou, 531<br />

Wangenheim, Ute v<strong>on</strong>, 1012<br />

Waniewski, Jacek, 167, 216, 328<br />

Ward, John, 353, 1021<br />

Wardman, Jess, 982<br />

Wats<strong>on</strong>, Michael, 1022<br />

Wawrzkiewicz, Agata, 1023<br />

Wcisło, Rafał, 1024<br />

Wdowczyk-Szulc, J., 619<br />

Webb, Dr Steven, 37<br />

Webb, Steve, 98<br />

1080<br />

Weens, William, 1025<br />

Weitz, Sebastian, 1026<br />

Welter, Michael, 826<br />

Wennberg, Bernt, 1027<br />

Wer<strong>on</strong>, Aleksander, 1028<br />

Werynski, Andrzej, 328<br />

Wesolowski, Sergiusz, 1029<br />

West, Bruce J., 1031<br />

White, Andy, 98, 123, 1032<br />

White, Dr. K.A. Jane, 179<br />

White, Pr<str<strong>on</strong>g>of</str<strong>on</strong>g>. Michael, 759<br />

White, R.G., 459<br />

Wick, Wolfgang, 971<br />

Wiederholt, Ruscena, 1033<br />

Wiesner, Karoline, 484<br />

Wilder, Sara, 1049<br />

Wilkie, Ka<str<strong>on</strong>g>th</str<strong>on</strong>g>leen, 1034<br />

Willis, Lisa, 1035<br />

Wimpenny, David I., 676<br />

Winkel, Christian, 1036<br />

Wiśniowska, Barbara, 649, 785<br />

Wissuwa, M., 1062<br />

Wittenfeld, Annelene, 1038<br />

Wittmann, Meike, 1039<br />

Wiuf, Carsten, 296, 511, 1040<br />

Woesik, Robert van, 519<br />

Wojdyla, Tomasz, 1041<br />

Wollnik, Carina, 1042<br />

Wrzosek, Dariusz, 946, 1043<br />

Wu, Yilin, 457<br />

Wylie, Karen, 692<br />

Wynn, Michelle, 1044<br />

Xu, Li, 1055<br />

Yamamura, Norio, 1045<br />

Yamauchi, Atsushi, 950, 1046<br />

Yan, Ping, 1047<br />

Yanchukov, Alexey, 797<br />

Yang, W., 1002<br />

Yang, Xuxin, 1048<br />

Yi, Chung-Se<strong>on</strong>, 210<br />

Yo<strong>on</strong>, Je<strong>on</strong>g-Mi, 1049<br />

Yoshida, Hiroshi, 1050<br />

Young, Todd R., 464<br />

Yvinec, Romain, 605<br />

Żabicki, Michał, 584<br />

Zagorski, M., 140<br />

Zagórski, Marcin, 1051<br />

Zalasiński, Jerzy Leszek, 212<br />

Żarczyńska-Buchowiecka, M., 619<br />

Zdravković, S., 593<br />

Żebrowski, Jan Jacek, 773<br />

Zebrowski, Jan J. ˙ , 781<br />

Żebrowski, J. J., 351<br />

Zeng, Yukai, 558<br />

Zerial, Marino, 468<br />

Zerjatke, Thomas, 1053

<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />

Zhang, Lai, 1054<br />

Zhang, Qingguo, 1055<br />

Zhang, Zhid<strong>on</strong>g, 353<br />

Zientek, Michał, 1057<br />

Zijerveld, Leo, 211<br />

Zubairova, Ulyana, 1058<br />

Zubik-Kowal, Barbara, 520<br />

Zubkov, Vladimir, 1059<br />

Żuk, Paweł, 1060<br />

Żuk, Paweł, 761<br />

Zuk, Pawel, 454<br />

Zygalakis, K<strong>on</strong>stantinos, 1062, 1063<br />

1081

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