A Formal Language Analysis of DNA Hairpin Structures

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.