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Towards the Sequence Design Preventing Pseudoknot Formation

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Natural Computing

Part of the book series: Proceedings in Information and Communications Technology ((PICT,volume 1))

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Abstract

This paper addresses a pseudoknot-freeness problem of DNA and RNA sequences, motivated by biomolecular computing. Watson-Crick (WK) complementarity forces DNA strands to fold into themselves and form so-called secondary structures, which are usually undesirable for biomolecular computational purposes. This paper studies pseudoknot-bordered words, a mathematical formalization of a common secondary structure, the pseudoknot. We obtain several properties of WK-pseudoknot-bordered and -unbordered words. One of the main results of the paper is that a sufficient condition for a WK-pseudoknot-unbordered word u to result in all words in u  +  being WK-pseudoknot-unbordered is for u not to be a primitive word.

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References

  1. Adleman, L.: Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994)

    Article  Google Scholar 

  2. Daley, M., Kari, L.: DNA computing: Models and Implementations. Comments on Theoretical Biology 7(3), 177–198 (2002)

    Article  Google Scholar 

  3. McCaskill, J.S.: The equilibrium partition function and base pair binding probability for RNA secondary structure. Biopolymers 29, 1105–1119 (1990)

    Article  Google Scholar 

  4. 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)

    Google Scholar 

  5. Condon, A.E.: Problems on RNA secondary structure prediction and design. In: ICALP 2003. LNCS, vol. 2719, pp. 22–32. Springer, Heidelberg (2003)

    Google Scholar 

  6. Kari, L., Kitto, R., Thierrin, G.: Codes, involutions and DNA encodings. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds.) FNC 2002. LNCS, vol. 2300, pp. 376–393. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Kari, L., Konstantinidis, S., Losseva, E., Wozniak, G.: Sticky-free and overhang-free DNA languages. Acta Informatica 40, 119–157 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kari, L., Konstantinidis, S., Losseva, E., Sosík, P., Thierrin, G.: Hairpin structures in DNA words. In: Carbone, A., Pierce, N.A. (eds.) DNA 2005. LNCS, vol. 3892, pp. 158–170. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Kari, L., Mahalingam, K.: Involutively bordered words. International Journal of Foundations of Computer Science (2007)

    Google Scholar 

  10. Kobayashi, S.: Testing structure freeness of regular sets of biomolecular sequences (extended abstract). In: Ferretti, C., Mauri, G., Zandron, C. (eds.) DNA 2004. LNCS, vol. 3384, pp. 192–201. Springer, Heidelberg (2005)

    Google Scholar 

  11. Kari, L., Seki, S.: On pseudoknot words and their properties (submitted)

    Google Scholar 

  12. Jones, S.-G., Moxon, S., Marshall, M., Khanna, A., Eddy, S.R., Bateman, A.: Rfam: annotating non-coding RNAs in complete genomes. Nucleic Acid Research 33, 121–124 (2005)

    Article  Google Scholar 

  13. Grätzer, G.: Universal Algebra. Van Nostrand Princeton, NJ (1968)

    MATH  Google Scholar 

  14. Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Berlin (1997)

    MATH  Google Scholar 

  15. Lentin, A., Schützenberger, M.P.: A combinatorial problem in the theory of free monoids. In: Proceedings of Combinatorial Mathematics and its Applications, April 10-14, pp. 128–144 (1967)

    Google Scholar 

  16. Ehrenfeucht, A., Silberger, D.: Periodicity and unbordered segments of words. Discrete Mathematics 26(2), 101–109 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  17. Jonoska, N., Mahalingam, K., Chen, J.: Involution codes: with application to DNA coded languages. Natural Computing 4(2), 141–162 (2005)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Western Ontario, London, Ontario, Canada, N6A 5B7

    Lila Kari & Shinnosuke Seki

Authors
  1. Lila Kari
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  2. Shinnosuke Seki
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Editor information

Editors and Affiliations

  1. Nagoya University, Japan

    Y. Suzuki

  2. The University of Tokyo, Japan

    M. Hagiya

  3. Osaka Electro-Communication University, Japan

    H. Umeo

  4. University of West England, Bristol, UK

    A. Adamatzky

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© 2009 Springer Tokyo

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Kari, L., Seki, S. (2009). Towards the Sequence Design Preventing Pseudoknot Formation. In: Suzuki, Y., Hagiya, M., Umeo, H., Adamatzky, A. (eds) Natural Computing. Proceedings in Information and Communications Technology, vol 1. Springer, Tokyo. https://doi.org/10.1007/978-4-431-88981-6_9

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  • DOI: https://doi.org/10.1007/978-4-431-88981-6_9

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-88980-9

  • Online ISBN: 978-4-431-88981-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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