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Journal of Mathematical Biology

, Volume 65, Issue 6–7, pp 1337–1357 | Cite as

On the page number of RNA secondary structures with pseudoknots

  • Peter CloteEmail author
  • Stefan Dobrev
  • Ivan Dotu
  • Evangelos Kranakis
  • Danny Krizanc
  • Jorge Urrutia
Article

Abstract

Let \({\mathcal {S}}\) denote the set of (possibly noncanonical) base pairs {i, j} of an RNA tertiary structure; i.e. \({\{i, j\} \in \mathcal {S}}\) if there is a hydrogen bond between the ith and jth nucleotide. The page number of \({\mathcal {S}}\), denoted \({\pi(\mathcal {S})}\), is the minimum number k such that \({\mathcal {S}}\) can 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 \({\omega(\mathcal {S}) \leq \pi(\mathcal {S}) \leq \omega(\mathcal {S}) \cdot \log n}\), where the clique number of \({\mathcal {S}, \omega(\mathcal {S})}\), denotes the maximum number of base pairs that pairwise cross each other.

Mathematics Subject Classification (2000)

92B05 68W25 05C85 62F30 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Peter Clote
    • 1
    Email author
  • Stefan Dobrev
    • 2
  • Ivan Dotu
    • 1
  • Evangelos Kranakis
    • 3
  • Danny Krizanc
    • 4
  • Jorge Urrutia
    • 5
  1. 1.Department of BiologyBoston CollegeChestnut HillUSA
  2. 2.Institute of MathematicsSlovak Academy of SciencesBratislavaSlovak Republic
  3. 3.School of Computer ScienceCarleton UniversityOttawaCanada
  4. 4.Department of Mathematics and Computer ScienceWesleyan UniversityMiddletownUSA
  5. 5.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMexico CityMexico

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