Graph-Theoretic Formalization of Hybridization in DNA Sticker Complexes

  • Robert Brijder
  • Joris J. M. Gillis
  • Jan Van den Bussche
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6937)

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.

Keywords

Relational Algebra Undirected Edge Free Node Negative Strand Positive Strand 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)MATHGoogle Scholar
  2. 2.
    Adleman, L.: Molecular computation of solutions to combinatorial problems. Science 226, 1021–1024 (1994)CrossRefGoogle Scholar
  3. 3.
    Amos, M.: Theoretical and Experimental DNA Computation. Springer, Heidelberg (2005)MATHGoogle Scholar
  4. 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. 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)CrossRefGoogle Scholar
  6. 6.
    Boneh, D., Dunworth, C., Lipton, R., Sgall, J.: On the computational power of DNA. Discrete Applied Mathematics 71, 79–94 (1996)MathSciNetCrossRefMATHGoogle Scholar
  7. 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)CrossRefGoogle Scholar
  8. 8.
    Cardelli, L.: Strand algebras for DNA computing. In: Deaton and Suyama [12], pp. 12–24Google Scholar
  9. 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. 13–24Google Scholar
  10. 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)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Condon, A., Corn, R., Marathe, A.: On combinatorial DNA word design. Journal of Computational Biology 8(3), 201–220 (2001)CrossRefMATHGoogle Scholar
  12. 12.
    Deaton, R., Suyama, A. (eds.): DNA 15. LNCS, vol. 5877. Springer, Heidelberg (2009)Google Scholar
  13. 13.
    Dimitrov, R., Zuker, M.: Prediction of hybridization and melting for double-stranded nucleic acids. Biophysical Journal 87, 215–226 (2004)CrossRefGoogle Scholar
  14. 14.
    Dirks, R., Pierce, N.: Triggered amplification by hybridization chain reaction. Proceedings of the National Academy of Sciences 101(43), 15275–15278 (2004)CrossRefGoogle Scholar
  15. 15.
    Garcia-Molina, H., Ullman, J., Widom, J.: Database Systems: The Complete Book. Prentice-Hall, Englewood Cliffs (2009)Google Scholar
  16. 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. 17.
    Hartmanis, J.: On the weight of computations. Bulletin of the EATCS 55, 136–138 (1995)MATHGoogle Scholar
  18. 18.
    Hopcroft, J., Ullman, J.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)MATHGoogle Scholar
  19. 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. 20.
    Majumder, U., Reif, J.: Design of a biomolecular device that executes process algebra. In: Deaton and Suyama [12], pp. 97–105Google Scholar
  21. 21.
    Paun, G., Rozenberg, G., Salomaa, A.: DNA Computing. Springer, Heidelberg (1998)CrossRefMATHGoogle Scholar
  22. 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. 23.
    Reif, J.: Parallel biomolecular computation: models and simulations. Algorithmica 25(2-3), 142–175 (1999)MathSciNetCrossRefMATHGoogle Scholar
  24. 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)CrossRefGoogle Scholar
  25. 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. 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)CrossRefMATHGoogle Scholar
  27. 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)CrossRefGoogle Scholar
  28. 28.
    Sakakibara, Y., Mi, Y. (eds.): DNA 16 2010. LNCS, vol. 6518. Springer, Heidelberg (2011)MATHGoogle Scholar
  29. 29.
    Sakamoto, K., et al.: State transitions by molecules. Biosystems 52, 81–91 (1999)CrossRefGoogle Scholar
  30. 30.
    Seelig, G., Soloveichik, D., Zhang, D., Winfree, E.: Enzyme-free nucleic acid logic circuits. Science 315(5805), 1585–1588 (2006)CrossRefGoogle Scholar
  31. 31.
    Shortreed, M., et al.: A thermodynamic approach to designing structure-free combinatorial DNA word sets. Nucleic Acids Research 33(15), 4965–4977 (2005)CrossRefGoogle Scholar
  32. 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. 33.
    Soloveichik, D., Winfree, E.: The computational power of Benenson automata. Theor. Comput. Sci. 244(2–3), 279–297 (2005)MathSciNetCrossRefMATHGoogle Scholar
  34. 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. 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)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Robert Brijder
    • 1
  • Joris J. M. Gillis
    • 1
  • Jan Van den Bussche
    • 1
  1. 1.Hasselt University and transnational University of LimburgBelgium

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