Combinatorics of RNA Structures with Pseudoknots

Abstract

In this paper, we derive the generating function of RNA structures with pseudoknots. We enumerate all k-noncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition, we enumerate pseudoknot structures over circular RNA. For 3-noncrossing RNA structures and RNA secondary structures we present a novel 4-term recursion formula and a 2-term recursion, respectively. Furthermore, we enumerate for arbitrary k all k-noncrossing, restricted RNA structures i.e. k-noncrossing RNA structures without 2-arcs i.e. arcs of the form (i,i+2), for 1≤in−2.

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Correspondence to Christian M. Reidys.

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Jin, E.Y., Qin, J. & Reidys, C.M. Combinatorics of RNA Structures with Pseudoknots. Bull. Math. Biol. 70, 45–67 (2008). https://doi.org/10.1007/s11538-007-9240-y

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Keywords

  • RNA secondary structure
  • Pseudoknot
  • Enumeration
  • Generating function
  • Reflection principle
  • Walks
  • Weyl-chamber