Hairpin Structures Defined by DNA Trajectories

  • Michael Domaratzki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4287)


We examine scattered hairpins, which are structures formed when a single strand 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 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.


Hairpin Structure Regular Language Closure Property Language Class Input Word 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Domaratzki, M.: Hairpin structures defined by dna trajectories. Technical Report TR-2006-001, Jodrey School of Computer Science, Acadia University (2006)Google Scholar
  2. 2.
    Kari, L., Konstantinidis, S., Losseva, E., Sosík, P., Thierrin, G.: Hairpin structures in DNA words. In: Carbone, A., Daley, M., Kari, L., McQuillan, I., Pierce, N. (eds.) The 11th International Meeting on DNA Computing: DNA 11, Preliminary Proceedings, pp. 267–277 (2005)Google Scholar
  3. 3.
    Kari, L., Konstantinidis, S., Sosík, P., Thierrin, G.: On Hairpin-Free Words and Languages. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 296–307. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Rothemund, P., Papadakis, N., Winfree, E.: Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biol. 2(12), e424 (2004)CrossRefGoogle Scholar
  5. 5.
    Kari, L., Konstantinidis, S., Sosík, P.: On properties of bond-free DNA languages. Theor. Comp. Sci. 334, 131–159 (2005)MATHCrossRefGoogle Scholar
  6. 6.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Heidelberg (1997)MATHGoogle Scholar
  7. 7.
    Păun, G., Rozenberg, G., Salomaa, A.: DNA Computing: New Computing Paradigms. Springer, Heidelberg (1998)MATHGoogle Scholar
  8. 8.
    Mateescu, A., Rozenberg, G., Salomaa, A.: Shuffle on trajectories: Syntactic constraints. Theor. Comp. Sci. 197, 1–56 (1998)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Domaratzki, M.: Trajectory-based embedding relations. Fund. Inf. 59(4), 349–363 (2004)MATHMathSciNetGoogle Scholar
  10. 10.
    Jonoska, N., Kephart, D., Mahalingam, K.: Generating DNA code words. Congressus Numerantium 156, 99–110 (2002)MathSciNetGoogle Scholar
  11. 11.
    Jonoska, N., Mahalingam, K.: Languages of DNA based code words. In: Chen, J., Reif, J.H. (eds.) DAN 2003. LNCS, vol. 2943, pp. 61–73. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Szilard, A., Yu, S., Zhang, K., Shallit, J.: Characterizing regular languages with polynomial densities. In: Havel, I.M., Koubek, V. (eds.) MFCS 1992. LNCS, vol. 629, pp. 494–503. Springer, Heidelberg (1992)Google Scholar
  13. 13.
    Domaratzki, M.: Characterizing DNA Bond Shapes Using Trajectories. In: H. Ibarra, O., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 180–191. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Rampersad, N., Shallit, J.: Words avoiding reversed subwords. J. Combin. Math. and Combin. Comput. 54, 157–164 (2005)MATHMathSciNetGoogle Scholar
  15. 15.
    Cassaigne, J.: Motifs évitables et régularités dans les mots. PhD thesis, Université Paris 6 (1994)Google Scholar
  16. 16.
    Entringer, R., Jackson, D., Schatz, J.: On nonrepetitive sequences. J. Combin. Theory. Ser. A 16, 159–164 (1974)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Michael Domaratzki
    • 1
  1. 1.Department of Computer ScienceUniversity of ManitobaWinnipegCanada

Personalised recommendations