Combinatorial RNA Design: Designability and Structure-Approximating Algorithm in Watson-Crick and Nussinov-Jacobson Energy Models

Jozef Haleš 1 Alice Héliou 2, 3 Ján Maňuch 4, 1 Yann Ponty 2 Ladislav Stacho 1
2 AMIB - Algorithms and Models for Integrative Biology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France
Abstract : We consider the Combinatorial RNA Design problem, a minimal instance of RNA design where one must produce an RNA sequence that adopts a given secondary structure as its minimal free-energy structure. We consider two free-energy models where the contributions of base pairs are additive and independent: the purely combinatorial Watson-Crick model, which only allows equally-contributing A − U and C − G base pairs, and the real-valued Nussinov-Jacobson model, which associates arbitrary energies to A − U, C − G and G − U base pairs. We first provide a complete characterization of designable structures using restricted alphabets and, in the four-letter alphabet, provide a complete characterization for designable structures without unpaired bases. When unpaired bases are allowed, we characterize extensive classes of (non-)designable structures, and prove the closure of the set of designable structures under the stutter operation. Membership of a given structure to any of the classes can be tested in Θ(n) time, including the generation of a solution sequence for positive instances. Finally, we consider a structure-approximating relaxation of the design, and provide a Θ(n) algorithm which, given a structure S that avoids two trivially non-designable motifs, transforms S into a designable structure constructively by adding at most one base-pair to each of its stems.
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Jozef Haleš, Alice Héliou, Ján Maňuch, Yann Ponty, Ladislav Stacho. Combinatorial RNA Design: Designability and Structure-Approximating Algorithm in Watson-Crick and Nussinov-Jacobson Energy Models. Algorithmica, Springer Verlag, 2017, 79 (3), pp.835--856. ⟨10.1007/s00453-016-0196-x⟩. ⟨hal-01285499v2⟩

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