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Graph-Theoretic Formalization of Hybridization in DNA Sticker Complexes

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DNA Computing and Molecular Programming (DNA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6937))

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Abstract

Sticker complexes are a formal graph-based data model for a restricted class of DNA complexes, motivated by potential applications to databases. This data model allows for a purely declarative definition of hybridization. We introduce the notion of terminating hybridization, and characterize this notion in purely graph-theoretic terms. Terminating hybridization can still produce results of exponential size. We indicate a class of complexes where hybridization is guaranteed to be polynomially bounded.

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References

  1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)

    MATH  Google Scholar 

  2. Adleman, L.: Molecular computation of solutions to combinatorial problems. Science 226, 1021–1024 (1994)

    Article  Google Scholar 

  3. Amos, M.: Theoretical and Experimental DNA Computation. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  4. Arita, M., Hagiya, M., Suyama, A.: Joining and rotating data with molecules. In: Proceedings 1997 IEEE International Conference on Evolutionary Computation, pp. 243–248 (1997)

    Google Scholar 

  5. Benenson, Y., Gil, B., Ben-Dor, U., Adar, R., Shapiro, E.: An autonomous molecular computer for logical control of gene expression. Nature 429, 423–429 (2004)

    Article  Google Scholar 

  6. Boneh, D., Dunworth, C., Lipton, R., Sgall, J.: On the computational power of DNA. Discrete Applied Mathematics 71, 79–94 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cardelli, L.: Abstract machines of systems biology. In: Priami, C., Merelli, E., Gonzalez, P., Omicini, A. (eds.) Transactions on Computational Systems Biology III. LNCS (LNBI), vol. 3737, pp. 145–168. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Cardelli, L.: Strand algebras for DNA computing. In: Deaton and Suyama [12], pp. 12–24

    Google Scholar 

  9. Chen, H.L., Kao, M.Y.: Optimizing tile concentrations to minimize errors and time for DNA tile self-assembly systems. In: Sakakibara and Mi [28], pp. 13–24

    Google Scholar 

  10. Chen, J., Deaton, R., Wang, Y.Z.: A DNA-based memory with in vitro learning and associative recall. Natural Computing 4(2), 83–101 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Condon, A., Corn, R., Marathe, A.: On combinatorial DNA word design. Journal of Computational Biology 8(3), 201–220 (2001)

    Article  MATH  Google Scholar 

  12. Deaton, R., Suyama, A. (eds.): DNA 15. LNCS, vol. 5877. Springer, Heidelberg (2009)

    Google Scholar 

  13. Dimitrov, R., Zuker, M.: Prediction of hybridization and melting for double-stranded nucleic acids. Biophysical Journal 87, 215–226 (2004)

    Article  Google Scholar 

  14. Dirks, R., Pierce, N.: Triggered amplification by hybridization chain reaction. Proceedings of the National Academy of Sciences 101(43), 15275–15278 (2004)

    Article  Google Scholar 

  15. Garcia-Molina, H., Ullman, J., Widom, J.: Database Systems: The Complete Book. Prentice-Hall, Englewood Cliffs (2009)

    Google Scholar 

  16. Gillis, J., Van den Bussche, J.: A formal model of databases in DNA. In: Horimoto, K., Nakatsui, M., Popov, N. (eds.) Algebraic and Numeric Biology 2010. LNCS, Springer, Heidelberg (to appear, 2011) for a preprint, http://alpha.uhasselt.be/~vdbuss/dnaql.pdf

    Google Scholar 

  17. Hartmanis, J.: On the weight of computations. Bulletin of the EATCS 55, 136–138 (1995)

    MATH  Google Scholar 

  18. Hopcroft, J., Ullman, J.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)

    MATH  Google Scholar 

  19. Jonoska, N., McColm, G., Staninska, A.: On stoichiometry for the assembly of flexible tile DNA complexes. Natural Computing, January 23 (2010) (published online)

    Google Scholar 

  20. Majumder, U., Reif, J.: Design of a biomolecular device that executes process algebra. In: Deaton and Suyama [12], pp. 97–105

    Google Scholar 

  21. Paun, G., Rozenberg, G., Salomaa, A.: DNA Computing. Springer, Heidelberg (1998)

    Book  MATH  Google Scholar 

  22. Qian, L., Soloveichik, D., Winfree, E.: Efficient Turing-universal computation with DNA polymers. In: Sakakibara and Mi [28], pp. 123–140.

    Google Scholar 

  23. Reif, J.: Parallel biomolecular computation: models and simulations. Algorithmica 25(2-3), 142–175 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. Reif, J.H., LaBean, T.H., Pirrung, M., Rana, V.S., Guo, B., Kingsford, C., Wickham, G.S.: Experimental construction of very large scale DNA databases with associative search capability. In: Jonoska, N., Seeman, N.C. (eds.) DNA 2001. LNCS, vol. 2340, pp. 231–247. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  25. Rothemund, P.: A DNA and restriction enzyme implementation of Turing machines. In: Lipton, R., Baum, E. (eds.) DNA Based Computers: DIMACS Workshop, held April 4, pp. 75–120. American Mathematical Society, Providence (1996)

    Google Scholar 

  26. Roweis, S., Winfree, E., Burgoyne, R., Chelyapov, N., Goodman, M., Rothemund, P., Adleman, L.: A sticker-based model for DNA computation. Journal of Computational Biology 5(4), 615–629 (1998)

    Article  MATH  Google Scholar 

  27. Sager, J., Stefanovic, D.: Designing nucleotide sequences for computation: A survey of constraints. In: Carbone, A., Pierce, N.A. (eds.) DNA 2005. LNCS, vol. 3892, pp. 275–289. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  28. Sakakibara, Y., Mi, Y. (eds.): DNA 16 2010. LNCS, vol. 6518. Springer, Heidelberg (2011)

    MATH  Google Scholar 

  29. Sakamoto, K., et al.: State transitions by molecules. Biosystems 52, 81–91 (1999)

    Article  Google Scholar 

  30. Seelig, G., Soloveichik, D., Zhang, D., Winfree, E.: Enzyme-free nucleic acid logic circuits. Science 315(5805), 1585–1588 (2006)

    Article  Google Scholar 

  31. Shortreed, M., et al.: A thermodynamic approach to designing structure-free combinatorial DNA word sets. Nucleic Acids Research 33(15), 4965–4977 (2005)

    Article  Google Scholar 

  32. Soloveichik, D., Seelig, G., Winfree, E.: DNA as a universal substrate for chemical kinetics. In: PNAS 2010, March 4 (2010) (published online)

    Google Scholar 

  33. Soloveichik, D., Winfree, E.: The computational power of Benenson automata. Theor. Comput. Sci. 244(2–3), 279–297 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  34. Winfree, E., Yang, X., Seeman, N.: Universal computation via self-assembly of DNA: Some theory and experiments. In: Landweber, L., Baum, E. (eds.) DNA Based Computers II: DIMACS Workshop, held June 10-12, pp. 191–213. American Mathematical Society, Providence (1998)

    Google Scholar 

  35. Yamamoto, M., Kita, Y., Kashiwamura, S., Kameda, A., Ohuchi, A.: Development of DNA relational database and data manipulation experiments. In: Mao, C., Yokomori, T. (eds.) DNA12. LNCS, vol. 4287, pp. 418–427. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Hasselt University and transnational University of Limburg, Belgium

    Robert Brijder, Joris J. M. Gillis & Jan Van den Bussche

Authors
  1. Robert Brijder
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  2. Joris J. M. Gillis
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  3. Jan Van den Bussche
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Editor information

Editors and Affiliations

  1. Microsoft Research, 711 Thomson Avenue, CB3 0FB, Cambridge, UK

    Luca Cardelli

  2. Department of Biological Chemistry and Molecular Pharmacology, Dana-Farber Cancer Institute, 44 Binney Street, 02115, Boston, MA, USA

    William Shih

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Brijder, R., Gillis, J.J.M., Van den Bussche, J. (2011). Graph-Theoretic Formalization of Hybridization in DNA Sticker Complexes. In: Cardelli, L., Shih, W. (eds) DNA Computing and Molecular Programming. DNA 2011. Lecture Notes in Computer Science, vol 6937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23638-9_7

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  • DOI: https://doi.org/10.1007/978-3-642-23638-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23637-2

  • Online ISBN: 978-3-642-23638-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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