Algorithmica

, Volume 79, Issue 3, pp 835–856 | Cite as

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

  • Jozef Haleš
  • Alice Héliou
  • Ján Maňuch
  • Yann Ponty
  • Ladislav Stacho
Article

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 \(\mathsf{A}\)\(\mathsf{U}\) and \(\mathsf{C}\)\(\mathsf{G}\) base pairs, and the real-valued Nussinov–Jacobson model, which associates arbitrary energies to \(\mathsf{A}\)\(\mathsf{U}\), \(\mathsf{C}\)\(\mathsf{G}\) and \(\mathsf{G}\)\(\mathsf{U}\) 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 \(\varTheta (n)\) time, including the generation of a solution sequence for positive instances. Finally, we consider a structure-approximating relaxation of the design, and provide a \(\varTheta (n)\) 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.

Keywords

RNA structure Inverse combinatorial optimization String design 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Jozef Haleš
    • 2
  • Alice Héliou
    • 1
  • Ján Maňuch
    • 2
    • 3
  • Yann Ponty
    • 1
  • Ladislav Stacho
    • 2
  1. 1.LIX (CNRS UMR 7161) Ecole Polytechnique & Inria SaclayPalaiseauFrance
  2. 2.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  3. 3.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada

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