Advertisement

Methods for Constructing Coded DNA Languages

  • Nataša Jonoska
  • Kalpana Mahalingam
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2950)

Abstract

The set of all sequences that are generated by a biomolecular protocol forms a language over the four letter alphabet Δ={A,G,C,T}. This alphabet is associated with a natural involution mapping θ, AT and GC which is an antimorphism of Δ*. 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 symbol-to-symbol mapping.

Keywords

Adjacency Matrix Code Word Closure Property Cross Hybridization Reverse Complement 
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.
    Adler, R.L., Coppersmith, D., Hassner, M.: Algorithms for sliding block codes -an application of symbolic dynamics to information theory. IEEE Trans. Inform. Theory 29, 5–22 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Arita, M., Kobayashi, S.: DNA sequence design using templates. New Generation Comput. 20(3), 263–277 (2002), Available as a sample paper at http://www.ohmsha.co.jp/ngc/index.htm
  3. 3.
    Baum, E.B.: DNA Sequences useful for computation unpublished article (1996), available at http://www.neci.nj.nec.com/homepages/eric/seq.ps
  4. 4.
    Braich, R.S., et al.: Solution of a 20-variable 3-SAT problem on a DNA computer. Science 296, 499–502 (2002)CrossRefGoogle Scholar
  5. 5.
    Berstel, J., Perrin, D.: Theory of codes. Academis Press, Inc., Orlando (1985)Google Scholar
  6. 6.
    Lind, D., Marcus, B.: An introduction to Symbolic Dynamics and Coding. Cambridge University Press, Inc., Cambridge (1999)Google Scholar
  7. 7.
    Deaton, R., et al.: A PCR-based protocol for in vitro selection of non-crosshybridizing oligonucleotides. In: Hagiya, M., Ohuchi, A. (eds.) DNA 2002. LNCS, vol. 2568, pp. 196–204. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Deaton, R., et al.: A DNA based implementation of an evolutionary search for good encodings for DNA computation. In: Proc. IEEE Conference on Evolutionary Computation ICEC 1997, pp. 267–271 (1997)Google Scholar
  9. 9.
    Faulhammer, D., Cukras, A.R., Lipton, R.J., Landweber, L.F.: Molecular Computation: RNA solutions to chess problems. Proceedings of the National Academy of Sciences 97(4), 1385–1389 (2000)CrossRefGoogle Scholar
  10. 10.
    Feldkamp, U., Saghafi, S., Rauhe, H.: DNASequenceGenerator - A program for the construction of DNA sequences. In: Jonoska, N., Seeman, N.C. (eds.) DNA 2001. LNCS, vol. 2340, pp. 23–32. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Garzon, M., Deaton, R., Reanult, D.: Virtual test tubes: a new methodology for computing. In: Proc. 7th. Int. Symposium on String Processing and Information retrieval, A Corun̆a, Spain, pp. 116–121. IEEE Computing Society Press, Los Alamitos (2000)CrossRefGoogle Scholar
  12. 12.
    Head, T.: Relativised code properties and multi-tube DNA dictionaries in Finite vs. Infinite. In: Calude, C., Paun, G. (eds.), pp. 175–186. Springer, Heidelberg (2000)Google Scholar
  13. 13.
    Hussini, S., Kari, L., Konstantinidis, S.: Coding properties of DNA languages. In: Jonoska, N., Seeman, N.C. (eds.) DNA 2001. LNCS, vol. 2340, pp. 57–69. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Jonoska, N., Mahalingam, K.: Languages of DNA based code words Preliminary. In: Proceedings of the 9th International Meeting on DNA Based Computers, Madison, Wisconsin, June 1-4, pp. 58–68 (2003)Google Scholar
  15. 15.
    Jonoska, N., Kephart, D., Mahalingam, K.: Generating DNA code words. Congressus Numernatium 156, 99–110 (2002)MathSciNetGoogle Scholar
  16. 16.
    Kari, L., Konstantinidis, S., Losseva, E., Wozniak, G.: Sticky-free and overhang-free DNA languages (preprint)Google Scholar
  17. 17.
    Keane, M.S.: Ergodic theory an subshifts of finite type. In: Edford, T., et al. (eds.) Ergodic theory, symbolic dynamics and hyperbolic spaces, pp. 35–70. Oxford Univ. Press, Oxford (1991)Google Scholar
  18. 18.
    Li, Z.: Construct DNA code words using backtrack algorithm (preprint)Google Scholar
  19. 19.
    Liu, Q., et al.: DNA computing on surfaces. Nature 403, 175–179 (2000)CrossRefGoogle Scholar
  20. 20.
    Marathe, A., Condon, A.E., Corn, R.M.: On combinatorial word design. In: Preliminary Preproceedings of the 5th International Meeting on DNA Based Computers, Boston, pp. 75–88 (1999)Google Scholar
  21. 21.
    Paun, G., Rozenberg, G., Salomaa, A.: DNA Computing, New computing paradigms. Springer, Heidelberg (1998)zbMATHGoogle Scholar
  22. 22.
    Ruben, A.J., Freeland, S.J., Landweber, L.F.: PUNCH: An evolutionary algorithm for optimizing bit set selection. In: Jonoska, N., Seeman, N.C. (eds.) DNA 2001. LNCS, vol. 2340, pp. 150–160. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  23. 23.
    Seeman, N.C.: De Novo design of sequences for nucleic acid structural engineering. J. of Biomolecular Structure & Dynamics 8(3), 573–581 (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Nataša Jonoska
    • 1
  • Kalpana Mahalingam
    • 1
  1. 1.Department of MathematicsUniversity of South FloridaTampaUSA

Personalised recommendations