# Asymptotics of Canonical and Saturated RNA Secondary Structures

* Auteur correspondant
4 ALGORITHMS - Algorithms
Inria Paris-Rocquencourt
Abstract : It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is $1.104366 n^{-3/2} 2.618034^n$. In this paper, we study combinatorial asymptotics for two special subclasses of RNA secondary structures - canonical and saturated structures. Canonical secondary structures were introduced by Bompfünewerer et al., who noted that the run time of Vienna RNA Package is substantially reduced when restricting computations to canonical structures. Here we provide an explanation for the speed-up. Saturated secondary structures have the property that no base pairs can be added without violating the definition of secondary structure (i.e. introducing a pseudoknot or base triple). Here we compute the asymptotic number of saturated structures, we show that the asymptotic expected number of base pairs is $0.337361 n$, and the asymptotic number of saturated stem-loop structures is $0.323954 1.69562^n$, in contrast to the number $2^{n-2}$ of (arbitrary) stem-loop structures as classically computed by Stein and Waterman. Finally, we show that the density of states for [all resp. canonical resp. saturated] secondary structures is asymptotically Gaussian. We introduce a stochastic greedy method to sample random saturated structures, called quasi-random saturated structures, and show that the expected number of base pairs of is $0.340633 n$.
Type de document :
Article dans une revue
Journal of Bioinformatics and Computational Biology, World Scientific Publishing, 2009, 22 p
Domaine :

Littérature citée [22 références]

https://hal.inria.fr/inria-00411277
Contributeur : Bruno Salvy <>
Soumis le : jeudi 27 août 2009 - 14:52:11
Dernière modification le : vendredi 25 mai 2018 - 12:02:05
Document(s) archivé(s) le : mardi 15 juin 2010 - 22:49:32

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• HAL Id : inria-00411277, version 1
• ARXIV : 0908.4003

### Citation

Peter Clote, Evangelos Kranakis, Danny Krizanc, Bruno Salvy. Asymptotics of Canonical and Saturated RNA Secondary Structures. Journal of Bioinformatics and Computational Biology, World Scientific Publishing, 2009, 22 p. 〈inria-00411277〉

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