On the page number of RNA secondary structures with pseudoknots

J Math Biol. 2012 Dec;65(6-7):1337-57. doi: 10.1007/s00285-011-0493-6. Epub 2011 Dec 10.

Abstract

Let S denote the set of (possibly noncanonical) base pairs {i, j } of an RNA tertiary structure; i.e. {i, j} ∈ S if there is a hydrogen bond between the ith and jth nucleotide. The page number of S, denoted π(S), is the minimum number k such that Scan be decomposed into a disjoint union of k secondary structures. Here, we show that computing the page number is NP-complete; we describe an exact computation of page number, using constraint programming, and determine the page number of a collection of RNA tertiary structures, for which the topological genus is known. We describe an approximation algorithm from which it follows that ω(S) ≤ π(S) ≤ ω(S) ・log n,where the clique number of S, ω(S), denotes the maximum number of base pairs that pairwise cross each other.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Base Pairing*
  • Hydrogen Bonding
  • Models, Chemical*
  • Models, Genetic
  • Models, Molecular
  • Nucleic Acid Conformation*
  • RNA / chemistry*
  • Thermodynamics

Substances

  • RNA