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A Formal Language Analysis of DNA Hairpin Structures

Kari L., Losseva E., Konstantindis S., Sosik P., Thierrin G.

Fundamenta Informaticae

2006

Vol. 71, nr 4

453-475

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 xvyq(v)z, with certain additional conditions, for an involution q (a function q with the property that q2 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.