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On the page number of RNA secondary structures with pseudoknots

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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.

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Authors and Affiliations

  1. Department of Biology, Boston College, Chestnut Hill, MA, 02467, USA

    Peter Clote & Ivan Dotu

  2. Institute of Mathematics, Slovak Academy of Sciences, Bratislava, Slovak Republic

    Stefan Dobrev

  3. School of Computer Science, Carleton University, Ottawa, ON, K1S 5B6, Canada

    Evangelos Kranakis

  4. Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT, 06459, USA

    Danny Krizanc

  5. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Jorge Urrutia

Authors
  1. Peter Clote
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  2. Stefan Dobrev
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  3. Ivan Dotu
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  4. Evangelos Kranakis
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  5. Danny Krizanc
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  6. Jorge Urrutia
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Correspondence to Peter Clote.

Additional information

P. Clote and I. Dotu: Research supported in part by National Science Foundation NSF grants DMS-1016618 and DMS-0817971, and by Digiteo Foundation; S. Dobrev: Supported in part by VEGA and APVV grants; and E. Kranakis: Research supported in part by NSERC and MITACS grants.

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Clote, P., Dobrev, S., Dotu, I. et al. On the page number of RNA secondary structures with pseudoknots. J. Math. Biol. 65, 1337–1357 (2012). https://doi.org/10.1007/s00285-011-0493-6

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  • DOI: https://doi.org/10.1007/s00285-011-0493-6

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