Advertisement

Efficient Algorithm for Testing Structure Freeness of Finite Set of Biomolecular Sequences

  • Atsushi Kijima
  • Satoshi Kobayashi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3892)

Abstract

In this paper we will focus on the structure freeness test problem of finite sets of sequences. The result is an extension of Andronescu’s algorithm which can be applied to the sequence design of various DNA computing experiments. We will first give a general algorithm for this problem which runs in O(n 5) time. Then, we will give an evaluation method for sequence design system, which requires O(n 5) time for precomputation, and O(n 4) time and O(n 5) space for each evaluation of sequence sets. The authors believe that this result will give an important progress of efficient sequence design systems.

Keywords

Minimum Free Energy Regular Language Loop Length Stochastic Local Search Structure String 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adleman, L.: Molecular Computation of Solutions to Combinatorial Problems. Science 266, 1021–1024 (1994)CrossRefGoogle Scholar
  2. 2.
    Andronescu, M., Dees, D., Slaybaugh, L., Zhao, Y., Condon, A., Cohen, B., Skiena, S.: Algorithms for Testing That Sets of DNA Words Concatenate without Secondary Structure. In: Hagiya, M., Ohuchi, A. (eds.) DNA 2002. LNCS, vol. 2568, pp. 182–195. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Arita, M., Kobayashi, S.: DNA sequence design using templates. New Generation Computing 20, 263–277 (2002)CrossRefMATHGoogle Scholar
  4. 4.
    Arita, M., Nishikawa, A., Hagiya, M., Komiya, K., Gouzu, H., Sakamoto, K.: Improving sequence design for DNA computing. In: Proc. of Genetic and Evolutionary Computation Conference 2000, pp. 875–882 (2000)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.
    Brenneman, A., Condon, A.E.: Strand Design for Bio-Molecular Computation. Theoretical Computer Science 287, 39–58 (2002)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Carbone, A., Seeman, N.C.: Circuits and programmable self-assembling DNA structures. Proc. Natl. Acad. Sci. USA 99, 12577–12582 (2002)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Condon, A.E.: Problems on RNA Secondary Structure Prediction and Design. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 22–32. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Dirks, R.M., Pierce, N.A.: An algorithm for computing nucleic acid base-pairing probabilities including pseudoknots. Journal of Computational Chemistry 25, 1295–1304 (2004)CrossRefGoogle Scholar
  10. 10.
    D’yachkov, A.G., Macula, A.J., Pogozelski, W.K., Renz, T.E., Rykov, V.V., Torney, D.C.: A weighted insertion-deletion stacked pair thermodynamic metric for DNA codes. In: Ferretti, C., Mauri, G., Zandron, C. (eds.) DNA 2004. LNCS, vol. 3384, pp. 142–151. Springer, Heidelberg (2005)Google Scholar
  11. 11.
    Hofacker, I.L., Fontana, W., Stadler, P.F., Bonhoeffer, L.S., Tacker, M., Schuster, P.: Fast Folding and Comparison of RNA Secondary Structures (The Vienna RNA Package). Monatshefte für Chemie 125, 167–188 (1994)CrossRefGoogle Scholar
  12. 12.
    Kari, L., Konstantinidis, S., Sosík, P.: Bond-free languages: Formalizations, maximality and construction methods. In: Ferretti, C., Mauri, G., Zandron, C. (eds.) DNA 2004. LNCS, vol. 3384, pp. 16–25. Springer, Heidelberg (2005)Google Scholar
  13. 13.
    Kobayashi, S.: Testing structure freeness of regular sets of biomolecular sequence. In: Ferretti, C., Mauri, G., Zandron, C. (eds.) DNA 2004. LNCS, vol. 3384, pp. 395–404. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Kobayashi, S., Yokomori, T., Sakakibara, Y.: An Algorithm for Testing Structure Freeness of Biomolecular Sequences. In: Aspects of Molecular Computing. LNCS, vol. 2950, pp. 266–277. Springer, Heidelberg (2004)Google Scholar
  15. 15.
    Mao, C., LaBean, T.H., Reif, J.H., Seeman, N.C.: Logical computation using algorithmic self-assembly of DNA triple-crossover molecules. Nature 407, 493–496 (2000)CrossRefGoogle Scholar
  16. 16.
    McCaskill, J.S.: The equilibrium partition function and base pair binding probabilities for RNA secondary structure. Biopolymers 29, 1105–1119 (1990)CrossRefGoogle Scholar
  17. 17.
    Sankoff, D., Kruskal, J.B., Mainville, S., Cedergen, R.J.: Fast Algorithms to Determine RNA Secondary Structures Containing Multiple Loops. In: Sankoff, D., Kruskal, J. (eds.) Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, ch. 3, pp. 93–120 (1983)Google Scholar
  18. 18.
    Tulpan, D.C., Hoos, H.H., Condon, A.E.: Stochastic local search algorithms for DNA word design. In: Hagiya, M., Ohuchi, A. (eds.) DNA 2002. LNCS, vol. 2568, pp. 229–241. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  19. 19.
    Winfree, E., Liu, F., Wenzler, L.A., Seeman, N.C.: Design self-assembly of two-dimensional DNA crystals. Nature 394, 539–544 (1998)CrossRefGoogle Scholar
  20. 20.
    Zuker, M.: On finding all suboptimal foldings of an RNA molecule. Science 244, 48–52 (1989)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Atsushi Kijima
    • 1
  • Satoshi Kobayashi
    • 1
  1. 1.Graduate School of University of Electro-CommunicationsTokyoJapan

Personalised recommendations