LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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60 Francesco Bernardini, Marian Gheorghe, and Mike Holcombe 8. Gheorghe M (2000) Generalised stream X-machines and cooperating grammar systems, Formal Aspects of Computing 12:459-472 9. Holcombe M (1998) X-machines as a basis for dynamic system specification, Software Engineering Journal 3:69-76 10. Holcombe M, Ipate F (1998) Correct Systems Building a Business Process Solution. Springer, Berlin, Applied Computing Series 11. Krishna SN, Rama R (2001) P systems with replicated rewriting, Journal of Automata, Languages and Combinatorics 6:345-350 12. Păun Gh (1998) Computing with membranes, Journal of Computer System Sciences 61:108–143 (and Turku Center for Computer Science (1998) TUCS Report 208, http://www.tucs.fi) 13. Păun Gh (2002) Membrane computing. An Introduction, Springer, Berlin 14. Rozenberg G, Salomaa A (1980) The Mathematical Theory of L Systems, Academic Press. New York
Molecular Tiling and DNA Self-assembly Alessandra Carbone 1 and Nadrian C. Seeman 2 1 Institut des Hautes Études Scientifiques 35, route de Chartres, 91440 Bures-sur-Yvette, France carbone@ihes.fr 2 Department of Chemistry, New York University New York, NY 10003, USA ned.seeman@nyu.edu Abstract. We examine hypotheses coming from the physical world and address new mathematical issues on tiling. We hope to bring to the attention of mathematicians the way that chemists use tiling in nanotechnology, where the aim is to propose building blocks and experimental protocols suitable for the construction of 1D, 2D and 3D macromolecular assembly. We shall especially concentrate on DNA nanotechnology, which has been demonstrated in recent years to be the most effective programmable self-assembly system. Here, the controlled construction of supramolecular assemblies containing components of fixed sizes and shapes is the principal objective. We shall spell out the algorithmic properties and combinatorial constraints of “physical protocols”, to bring the working hypotheses of chemists closer to a mathematical formulation. 1 Introduction to Molecular Self-assembly Molecular self-assembly is the spontaneous organisation of molecules under thermodynamic equilibrium conditions into a structurally well-defined and rather stable arrangement through a number of non-covalent interactions [5,26,52]. It should not be forgotten that periodic self-assemblies of molecules lead to crystals in one, two or three dimensions; we often do not understand the interactions between the constituents of a crystal, but their presence in our world was an existence-proof for 3D self-assembly long before the notion was voiced. By a non-covalent interaction, we mean the formation of several non-covalent weak chemical bonds between molecules, including hydrogen bonds, ionic bonds and van der Waals interactions. These interactions (of the order of 1-5 kcal/mol) can be considered reversible at normal temperatures, while covalent interactions (typically > 50 kcal/mol) are regarded as irreversible. The self-association process leads the molecules to form stable hierarchical macroscopic structures. Even if the bonds themselves are rather weak, their collective interaction often results in very stable assemblies; think, for example, of an ice cube, held together by hydrogen bonds. Two important elements of molecular self-assembly are complementarity and self-stability, where both the size and the correct orientation of the molecules are crucial in order to have a complementary and compatible fitting. N. Jonoska et al. (Eds.): Molecular Computing (Head Festschrift), LNCS 2950, pp. 61–83, 2004. c○ Springer-Verlag Berlin Heidelberg 2004
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Lecture Notes in Computer Science 2
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Nata˘sa Jonoska Gheorghe Păun Grz
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Thomas J. Head
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VIII Preface portant to keep in min
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X Table of Contents Formal Properti
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Solving Graph Problems by P Systems
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Page 19 and 20: Solving Graph Problems by P Systems
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Page 37 and 38: Writing Information into DNA 27 Fig
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Page 41 and 42: 5 Results 5.1 DNA Code for the Engl
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Page 59 and 60: Eilenberg P Systems with Symbol-Obj
Page 61 and 62: 2 Definitions Definition 1. A strea
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Page 73 and 74: 3 Molecular Self-assembly Processes
Page 75 and 76: Molecular Tiling and DNA Self-assem
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Page 91 and 92: References Molecular Tiling and DNA
Page 95 and 96: On Some Classes of Splicing Languag
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The Power of Networks of Watson-Cri
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Fixed Point Approach to Commutation
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Here the last one holds if and only
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� � � � � Fixed Point App
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Remarks on Relativisations and DNA
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Splicing Test Tube Systems and Thei
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Splicing Test Tube Systems 141 the
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Splicing Test Tube Systems 143 to a
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Splicing Test Tube Systems 145 6. R
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Splicing Test Tube Systems 147 (c)
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I0 Ai i Splicing Test Tube Systems
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Splicing Test Tube Systems 151 4. J
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Digital Information Encoding on DNA
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DNA-based Cryptography Ashish Gehan
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DNA-based Cryptography 169 concern.
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DNA-based Cryptography 171 The one-
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DNA-based Cryptography 173 of DNA t
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DNA-based Cryptography 175 Fig. 3.
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DNA-based Cryptography 177 the comp
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DNA-based Cryptography 179 can be c
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DNA-based Cryptography 181 4.4 DNA-
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DNA-based Cryptography 183 Fig. 7.
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DNA-based Cryptography 185 offer li
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DNA-based Cryptography 187 30. C. M
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Splicing to the Limit Elizabeth Goo
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Splicing to the Limit 191 molecular
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Splicing to the Limit 193 Discussio
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Example 9. The splicing rules are S
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−2α � kNNk = −2αMN, k α
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Finally we define the limit languag
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6 Conclusion Splicing to the Limit
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Formal Properties of Gene Assembly
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(a) (b) Formal Properties of Gene A
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n-Insertion on Languages Masami Ito
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n-Insertion on Languages 215 3. ∀
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n-Insertion on Languages 217 Theore
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Transducers with Programmable Input
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1 01 s 0 Transducers with Programma
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order β l Transducers with Program
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start tile Transducers with Program
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Methods for Constructing Coded DNA
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u u Methods for Constructing Coded
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On the Universality of P Systems wi
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An Algorithm for Testing Structure
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Definition 1. Define the relation
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280 Manfred Kudlek Definition 5. Co
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On Languages of Cyclic Words 283 Th
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On Languages of Cyclic Words 285 No
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On Languages of Cyclic Words 287 Th
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A DNA Algorithm for the Hamiltonian
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Formal Languages Arising from Gene
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A Proof of Regularity for Finite Sp
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--- ◦ ❄ ⊗ γ ✲ A Proof of R
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The Duality of Patterning in Molecu
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The Duality of Patterning in Molecu
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Membrane Computing: Some Non-standa
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where: Membrane Computing: Some Non
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where: Membrane Computing: Some Non
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The P Versus NP Problem Through Cel
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Realizing Switching Functions Using
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Realizing Switching Functions Using
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AND Gate Realizing Switching Functi
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NOR Gate Realizing Switching Functi
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Plasmids to Solve #3SAT Rani Siromo
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Plasmids to Solve #3SAT 363 A comme
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Plasmids to Solve #3SAT 365 from th
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Communicating Distributed H Systems
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Proof Communicating Distributed H S
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Books: Publications by Thomas J. He
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Publications by Thomas J. Head 387
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Publications by Thomas J. Head 389
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LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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