LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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80 Alessandra Carbone and Nadrian C. Seeman that form the template board. The coding will discriminate what are the tiles that will interact with new ones and what are those that will avoid interaction. In the example, a change in the programming of the board induces the formation of different shapes out of the same input set. This suggests that a formal notion of complexity describing self-assembly of molecular systems cannot be based merely on the variety of shapes that potentially can be assembled, but rather on the much larger variety of algorithms that allow their assembly. DNA computing. Last, we want to mention the effort in designing algorithms for DNA-computation. The landmark step is in [1], where DNA is used to solve an instance of the Hamiltonian Path problem, asking to establish whether there is a path between two cities, given an incomplete set of available roads. A set of strands of DNA is used to represent cities and roads (similar to the description of the 3-coloring problem in Section 6), and the coding is such that a strand representing a road would connect (according to the rules of base-pairing) to any two strands representing a city. By mixing together strands, joining the cities connected by roads, and weeding out any wrong answers, it has been shown that the strands could self-assemble to solve the problem. The first link between DNA-nanotechnology and DNA-computation was established in [54] with the suggestion that short branched DNA-molecules could be “programmed” to undergo algorithmic self-assembly and thus serve as the basis of computation. Other work has followed as [30,34,25]. 11 Discussion Most examples in this paper were based on Watson-Crick interactions of DNA molecules. Other kinds of interaction, usually referred to as tertiary interactions, can be used to lead a controlled behavior in the assembly of DNA molecules, for example, DNA triplexes [15], tecto-RNA [21] and G-quartet formation [42]. In the combinatorial DNA constructions that we presented, tertiary interactions were carefully avoided with the goal of maximizing control on the dynamics of the assembly. Tertiary interactions are not as readily controlled as Watson-Crick interactions. The next generation of structural DNA nanotechnologists will be likely to exploit this wider range of structural possibilities and it appears possible that new combinatorics might arise from these options. Acknowledgement The authors would like to thank Roberto Incitti and Natasha Jonoska for their comments on preliminary versions of this manuscript. This research has been supported by grants GM-29554 from the National Institute of General Medical Sciences, N00014-98-1-0093 from the Office of Naval Research, grants DMI-0210844, EIA-0086015, DMR-01138790, and CTS- 0103002 from the National Science Foundation, and F30602-01-2-0561 from DARPA/AFSOR.
References Molecular Tiling and DNA Self-assembly 81 1. L.M. Adleman. Molecular computation of solutions to combinatorial problems. Science, 266:1021-4, 1994. 2. L.M. Adleman. Toward a mathematical theory of self-assembly. Technical Report 00-722, Department of Computer Science, University of Southern California, 2000. 3. L.M.Adleman,Q.Cheng,A.Goel,M-D.Huang,D.Kempe,P.MoissetdeEspanés, P.W.K. Rothemund. Combinatorial optimisation problems in self-assembly. STOC’02 Proceedings, Montreal Quebec, Canada, 2002. 4. A. Aggeli, M. Bell, N. Boden, J.N. Keen, P.F. Knowles, T.C.B. McLeish, M. Pitkeathly, S.E. Radford. Responsive gels formed by the spontaneous selfassembly of peptides into polymeric beta-sheet tapes, Nature 386:259-62, 1997. 5. P. Ball Materials Science: Polymers made to measure, Nature, 367:323-4, 1994. 6. A. Carbone, M. Gromov. Mathematical slices of molecular biology, La Gazette des Mathématiciens, Numéro Spéciale, 88:11–80, 2001. 7. A. Carbone, N.C. Seeman. Circuits and programmable self-assembling DNA structures. Proceedings of the National Academy of Sciences USA, 99:12577-12582, 2002. 8. A. Carbone, N.C. Seeman. A route to fractal DNA-assembly, Natural Computing, 1:469-480, 2002. 9. A. Carbone, N.C. Seeman. Coding and geometrical shapes in nanostructures: a fractal DNA-assembly, Natural Computing, 2003. In press. 10. S.N. Cohen, A.C.Y. Chang, H.W. Boyer, R.B. Helling. Construction of biologically functional bacterial plasmids in vitro, Proceedings of the National Academy of Science USA, 70:3240-3244, 1973. 11. A.M. Diegelman, E.T. Kool. Generation of circular RNAs and trans-cleaving catalytic RNAs by rolling transcription of circular DNA oligonucleotides encoding hairpin ribozymes, Nucleic Acids Research, 26, 3235-3241, 1998. 12. S.M. Du, S. Zhang, N.C. Seeman. DNA Junctions, Antijunctions and Mesojunctions, Biochemistry, 31:10955-10963, 1992. 13. I. Duhnam, N. Shimizu, B.A. Roe et al. The DNA sequence of human chromosome 22, Nature, 402:489–95, 1999. 14. B.F. Eichman, J.M. Vargason, B.H.M. Mooers, P.S. Ho. The Holliday junction in an inverted repeat DNA sequence: Sequence effects on the structure of four-way junctions, Proceedings of the National Academy of Science USA, 97:3971-3976, 2000. 15. G. Felsenfeld, D.R. Davies, A. Rich. Formation of a three-stranded polynucleotide molecule, J. Am. Chem. Soc., 79:2023-2024, 1957. 16. T.-J. Fu, B. Kemper and N.C. Seeman. Endonuclease VII cleavage of DNA double crossover molecules, Biochemistry 33:3896-3905, 1994. 17. B. Grünbaum, G.C. Shephard. Tilings and Patterns, W.H. Freeman and Company, 1986. 18. J.D. Hartgerink, E. Beniash, and S.I. Stupp. Self-assembly and mineralization of peptide-amphiphile nanofibers, Science, 294:1684, 2001. 19. I. Huck, J.M. Lehn. Virtual combinatorial libraries: dynamic generation of molecular and supramolecular diversity by self-assembly, Proceedings of the National Academy of Sciences USA, 94:2106-10, 1997. 20. S. Hussini, L. Kari, S. Konstantinidis. Coding properties of DNA languages, Theoretical Computer Science, 290:1557-1579, 2003. 21. L. Jaeger, E. Westhof, N.B. Leontis. TectoRNA: modular assembly units for the construction of RNA nano-objects, Nucleic Acids Research, 29:455-463, 2001.
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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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where Solving Graph Problems by P S
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Writing Information into DNA Masano
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Writing Information into DNA 25 Ham
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Writing Information into DNA 27 Fig
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Fixed Point Approach to Commutation
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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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