On pseudoknot-bordered words and their properties

  • Authors:

  • Lila Kari;Shinnosuke Seki

  • Affiliations:

  • Department of Computer Science, University of Western Ontario, London, Ontario, Canada, N6A 5B7;Department of Computer Science, University of Western Ontario, London, Ontario, Canada, N6A 5B7

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2009

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Abstract

We study a generalization of the classical notions of bordered and unbordered words, motivated by biomolecular computing. DNA strands can be viewed as finite strings over the alphabet {A, G, C, T}, and are used in biomolecular computing to encode information. Due to the fact that A is Watson-Crick complementary to T and G to C, DNA single strands that are Watson-Crick complementary can bind to each other or to themselves forming so-called secondary structures. Most of these secondary structures are undesirable for biomolecular computational purposes since the strands they involve cannot further interact with other strands. This paper studies pseudoknot-bordered words, a mathematical formalization of pseudoknot-like inter- and intra-molecular structures. In this context, pseudoknot-unbordered words model DNA or RNA strands that will be free of such secondary structures. We obtain several properties of pseudoknot-bordered and -unbordered words. We also address following problem: Given a pseudoknot-unbordered word u, does {u}^+ consist of pseudoknot-unbordered words only? We show that this is not generally true. We find that a sufficient condition for {u}^+ to consist of pseudoknot-unbordered words only is that u be not primitive. All of our results hold for arbitrary antimorphic involutions, of which the DNA Watson-Crick complementarity function is a particular case.