A Formal Language Analysis of DNA Hairpin Structures

  • Authors:

  • L. Kari;E. Losseva;S. Konstantinidis;P. Sosík;G. Thierrin

  • Affiliations:

  • Department of Computer Science, The University of Western Ontario, London, ON, N6A 5B7, Canada. E-mail: {lila,elena}@csd.wuo.ca;Department of Computer Science, The University of Western Ontario, London, ON, N6A 5B7, Canada. E-mail: {lila,elena}@csd.wuo.ca;Dept. of Mathematics and Computing Science, Saint Mary's University, Halifax, Nova Scotia, B3H 3C3, Canada. E-mail: s.konstantinidis@smu.ca;Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo s/n, Boadilla del Monte 28660, Madrid, Spain and Institute of Computer Science, Silesian University, 74 ...;Department of Mathematics, The University of Western Ontario, London, ON, N6A 5B7, Canada. E-mail: thierrin@uwo.ca

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 2006

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Abstract

The concept of hairpin structures in formal languages is motivated from the biocomputing and bioinformatics fields. Hairpin (-free) DNA structures have numerous applications to DNA computing and molecular genetics in general. A word is called hairpin-free if it cannot be written in the form xuyθ(u)z, with certain additional conditions, for an involution θ (a function θ with the property that θ$^2$ equals the identity function). A particular involution, the so-called Watson-Crick involution, can characterize binding of two DNA strands. We study algebraic and decision properties, finiteness and descriptional complexity of hairpin (-free) languages. We show an existence of polynomial-time algorithms deciding hairpin-freeness of regular and context-free sets. Two related DNA secondary structures are considered, taking into the account imperfect bonds (bulges, mismatches) and multiple hairpins. Finally, effective methods for design of long hairpin-free DNA words are given.