Hairpin Structures in DNA Words

Abstract

Abstract. We formalize the notion of a DNA hairpin secondary structure, examining its mathematical properties. Two related secondary structures are also investigated, taking into the account imperfect bonds (bulges, mismatches) and multiple hairpins. We characterize maximal sets of hairpin-forming DNA sequences, as well as hairpin-free ones. We study their algebraic properties and their computational complexity. Related polynomial-time algorithms deciding hairpin-freedom of regular sets are presented. Finally, effective methods for design of long hairpinfree DNA words are given.

Hairpin Structures Defined by DNA Trajectories

“…This is similar to the work on bond-free properties [13] and hairpin-freeness [12,14]. In practice, an antimorphic involution yields results applicable to hairpin and scatteredhairpin structures, while morphic involutions yield structures where the scattered stem is bonded in a parallel, rather than an anti-parallel, orientation.…”

“…The definition of shp Σ (S, θ )-freeness is an extension of the notions of hairpin-freeness and scattered-hairpin-freeness, investigated by Kari et al [12,14].…”

“…The shape described by this set of trajectories is called scattered hairpins by Kari et al [12]. In particular, the condition is equivalent to the following: x ≤ e u and θ (x) ≤ e v imply |x| < k. An example of the shape of scattered hairpins described by S k when θ is an antimorphism is given in Figure 4.…”

Hairpin Structures Defined by DNA Trajectories

“…Note that Lemma 5.1 is in contrast to the case of hairpin languages and scattered hairpin languages, studied by Kari et al [12], where the associated languages are regular. Despite the fact that regularity is not preserved when using a set of DNA trajectories to describe hairpin trajectories, we can show that for all regular sets of trajectories S and all antimorphic involutions θ , the language shp Σ (S, θ ) is always context-free: Proof.…”

Towards the Sequence Design Preventing Pseudoknot Formation

“…On the other hand, in vitro biomolecular computing often considers them as disadvantages because it is very likely that the secondary structure formation of a DNA/RNA strand will prevent it from interacting with other DNA/RNA strands in the expected, pre-programmed way. Thence, many studies exist on how to free sequence sets from secondary structures [4], [5], [6], [7], [8], [9], [10].…”