LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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240 Nataˇsa Jonoska, Shiping Liao, and Nadrian C. Seeman 18. P. Rothemund, N. Papadakis, E. Winfree, Algorithmic self-assembly of DNA sierpinski triangles (abstract) Preproceedings of the 9th International Meeting of DNA Based Computers, June 1-4, 2003. 19. P. Sa-Ardyen, N. Jonoska, N. Seeman, Self-assembling DNA graphs, Journal of Natural Computing (to appear). 20. N.C. Seeman, DNA junctions and lattices, J.Theor.Biol.99 (1982) 237-247. 21. N.C. Seeman, DNA nicks and nodes and nanotechnology, NanoLetters 1 (2001) 22-26. 22. P. Siwak, Soliton like dynamics of filtrons on cyclic automata, InverseProblems 17, Institute for Physics Publishing (2001) 897-918. 23. Y. Wang, J.E. Mueller, B. Kemper, N.C. Seeman, The assembly and characterization of 5-arm and 6-arm DNA junctions, Biochemistry 30 (1991) 5667-5674. 24. E. Winfree, X. Yang, N.C. Seeman, Universal computation via self-assembly of DNA: some theory and experiments, DNA computers II, (L. Landweber, E. Baum editors), AMS DIMACS series 44 (1998) 191-214. 25. E. Winfree, F. Liu, L.A. Wenzler, N.C. Seeman, Design and self-assembly of twodimensional DNA crystals, Nature394 (1998) 539-544. 26. H. Yan, X. Zhang, Z. Shen and N.C. Seeman, A robust DNA mechanical device controlled by hybridization topology, Nature415 (2002) 62-65. 27. H. Yan, N.C. Seeman, Edge-sharing motifs in DNA nanotechnology, Journal of Supramolecular Chemistry 1 (2003) 229-237. 28. B. Yurke, A.J. Turberfield, A.P. Mills, F.C. Simmel Jr., A DNA fueled molecular machine made of DNA, Nature406 (2000) 605-608. 29. Y. Zhang, N.C. Seeman, The construction of a DNA truncated octahedron, J.Am. Chem. Soc. 160 (1994) 1661-1669.
Methods for Constructing Coded DNA Languages Nataˇsa Jonoska and Kalpana Mahalingam Department of Mathematics University of South Florida, Tampa, FL 33620, USA jonoska@math.usf.edu, mahaling@helios.acomp.usf.edu Abstract. The set of all sequences that are generated by a biomolecular protocol forms a language over the four letter alphabet ∆ = {A, G, C, T }. This alphabet is associated with a natural involution mapping θ, A ↦→ T and G ↦→ C whichisanantimorphismof∆ ∗ . In order to avoid undesirable Watson-Crick bonds between the words (undesirable hybridization), the language has to satisfy certain coding properties. In this paper we build upon an earlier initiated study and give general methods for obtaining sets of code words with the same properties. We show that some of these code words have enough entropy to encode {0, 1} ∗ in a symbolto-symbol mapping. 1 Introduction In bio-molecular computing and in particular DNA based computations and DNA nanotechnology, one of the main problems is associated with the design of the oligonucleotides such that mismatched pairing due to the Watson-Crick complementarity is minimized. In laboratory experiments non-specific hybridizations pose potential problems for the results of the experiment. Many authors have addressed this problem and proposed various solutions. Common approach has been to use the Hamming distance as a measure for uniqueness [3,8,9,11,19]. Deaton et al. [8,11] used genetic algorithms to generate a set of DNA sequences that satisfy predetermined Hamming distance. Marathe et al. [20] also used Hamming distance to analyze combinatorial properties of DNA sequences, and they used dynamic programing for design of the strands used in [19]. Seeman’s program [23] generates sequences by testing overlapping subsequences to enforce uniqueness. This program is designed for producing sequences that are suitable for complex three-dimensional DNA structures, and the generation of suitable sequences is not as automatic as the other programs have proposed. Feldkamp et al. [10] also uses the test for uniqueness of subsequences and relies on tree structures in generating new sequences. Ruben at al. [22] use a random generator for initial sequence design, and afterwards check for unique subsequences with a predetermined properties based on Hamming distance. One of the first theoretical observations about number of DNA code words satisfying minimal Hamming distance properties was done by Baum [3]. Experimental separation of strands with “good” codes that avoid intermolecular cross hybridization was N. Jonoska et al. (Eds.): Molecular Computing (Head Festschrift), LNCS 2950, pp. 241–253, 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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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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Writing Information into DNA 29 Dea
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5 Results 5.1 DNA Code for the Engl
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Writing Information into DNA 33 3.
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Writing Information into DNA 35 101
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Balance Machines: Computing = Balan
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+ .. . + Balance Machines: Computin
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x Balance Machines: Computing = Bal
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1 Balance Machines: Computing = Bal
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Eilenberg P Systems with Symbol-Obj
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2 Definitions Definition 1. A strea
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5 Conclusions Eilenberg P Systems w
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Molecular Tiling and DNA Self-assem
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3 Molecular Self-assembly Processes
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8 Hierarchical Tiling Molecular Til
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References Molecular Tiling and DNA
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On Some Classes of Splicing Languag
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ˆxa ˆby ✬ ✩✬ ✩ a b x y
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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
Page 199 and 200: Splicing to the Limit Elizabeth Goo
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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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LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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