Skip to main content
SpringerLink
Log in

Hairpin Structures Defined by DNA Trajectories

  • Published:
Theory of Computing Systems Aims and scope Submit manuscript

Abstract

We examine scattered hairpins, which are structures formed when a single strand of nucleotides folds into a partially hybridized stem and a loop. To specify different classes of hairpins, we use the concept of DNA trajectories, which allows precise descriptions of valid bonding patterns on the stem of the hairpin. DNA trajectories have previously been used to describe bonding between separate strands.

We are interested in the mathematical properties of scattered hairpins described by DNA trajectories. We examine the complexity of the set of hairpin-free words described by a set of DNA trajectories. In particular, we consider the closure properties of language classes under sets of DNA trajectories of differing complexity. We address decidability of recognition problems for hairpin structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cassaigne, J.: Motifs évitables et régularités dans les mots. Ph.D. thesis, Université Paris 6 (1994)

  2. Choffrut, C., Karhumäki, J.: Combinatorics on words. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, pp. 329–438. Springer, New York (1997)

    Google Scholar 

  3. Domaratzki, M.: Trajectory-based embedding relations. Fund. Inf. 59(4), 349–363 (2004)

    MATH  MathSciNet  Google Scholar 

  4. Domaratzki, M., Ibarra, O., Dang, Z.: Characterizing DNA bond shapes using trajectories. In: Developments in Language Theory. Lecture Notes in Computer Science, vol. 4036, pp. 180–191. Springer, New York (2006)

    Chapter  Google Scholar 

  5. Entringer, R., Jackson, D., Schatz, J.: On nonrepetitive sequences. J. Comb. Theory. Ser. A 16, 159–164 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fraenkel, A., Simpson, J.: How many squares must a binary sequence contain? Electon. J. Comb. 2, 2 (1995)

    MathSciNet  Google Scholar 

  7. Harju, T., Karhumäki, J.: Morphisms. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, pp. 439–510. Springer, New York (1997)

    Google Scholar 

  8. Jonoska, N., Mahalingam, K.: Languages of DNA based code words. In: Chen, J., Reif, J. (eds.) DNA Computing, 9th International Workshop on DNA Based Computers. Lecture Notes in Computer Science, vol. 2943, pp. 61–73. Springer, New York (2004)

    Google Scholar 

  9. Jonoska, N., Kephart, D., Mahalingam, K.: Generating DNA code words. Congr. Numer. 156, 99–110 (2002)

    MathSciNet  Google Scholar 

  10. Kari, L., Konstantinidis, S., Sosík, P.: On properties of bond-free DNA languages. Theor. Comput. Sci. 334, 131–159 (2005)

    Article  MATH  Google Scholar 

  11. Kari, L., Konstantinidis, S., Sosík, P., Thierrin, G.: On hairpin-free words and languages. In: Felice, C.D., Restivo, A. (eds.) Developments in Language Theory: 9th International Conference. Lecture Notes in Computer Science, vol. 3572, pp. 296–307. Springer, New York (2005)

    Google Scholar 

  12. Kari, L., Konstantinidis, S., Losseva, E., Sosík, P., Thierrin, G.: Hairpin structures in DNA words. In: Carbone, A., Pierce, N. (eds.) DNA Computing. Lecture Notes in Computer Science, vol. 3892, pp. 158–170. Springer, New York (2006)

    Chapter  Google Scholar 

  13. Kari, L., Losseva, E., Konstantinidis, S., Sosík, P., Thierrin, G.: A formal language analysis of DNA hairpin structures. Fund. Inf. 71, 453–475 (2006)

    MATH  Google Scholar 

  14. Lothaire, M.: Combinatorics on Words. Addison-Wesley, Reading (1983)

    MATH  Google Scholar 

  15. Mateescu, A., Rozenberg, G., Salomaa, A.: Shuffle on trajectories: syntactic constraints. Theor. Comput. Sci. 197, 1–56 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  16. Pǎun, G., Salomaa, A.: Thin and slender languages. Discrete Appl. Math. 61, 257–270 (1995)

    Article  MathSciNet  Google Scholar 

  17. Păun, G., Rozenberg, G., Salomaa, A.: DNA Computing: New Computing Paradigms. Springer, New York (1998)

    MATH  Google Scholar 

  18. Rampersad, N., Shallit, J.: Words avoiding reversed subwords. J. Comb. Math. Comb. Comput. 54, 157–164 (2005)

    MATH  MathSciNet  Google Scholar 

  19. Rampersad, N., Shallit, J., Wang, M.-W.: Avoiding large squares in infinite binary words. Theor. Comput. Sci. 339, 19–34 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  20. Rothemund, P., Papadakis, N., Winfree, E.: Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biol. 2(12), e424 (2004)

    Article  Google Scholar 

  21. Rozenberg, G., Salomaa, A.: Handbook of Formal Languages. Springer, New York (1997)

    MATH  Google Scholar 

  22. Shallit, J.: Numeration systems, linear recurrences, and regular sets. Inf. Comput. 113(2), 331–347 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  23. Szilard, A., Yu, S., Zhang, K., Shallit, J.: Characterizing regular languages with polynomial densities. In: Havel, I., Koubek, V. (eds.) Mathematical Foundations of Computer Science 1992. Lecture Notes in Computer Science, vol. 629, pp. 494–503. Springer, New York (1992)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Manitoba, Winipeg, MB, R3T 2T2, Canada

    Michael Domaratzki

Authors
  1. Michael Domaratzki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael Domaratzki.

Additional information

An earlier version of this paper without proofs appeared at DNA 12 (Lecture Notes in Computer Science, vol. 4287, pp. 182–194, 2006). Research conducted at the Jodrey School of Computer Science, Acadia University, and supported in part by a grant from NSERC.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Domaratzki, M. Hairpin Structures Defined by DNA Trajectories. Theory Comput Syst 44, 432–454 (2009). https://doi.org/10.1007/s00224-007-9086-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00224-007-9086-6

Keywords

Search

Navigation