NDLI: Combinatorics of locally optimal RNA secondary structures

Content Provider	Springer Nature Link
Author	Fusy, Éric Clote, Peter
Copyright Year	2012
Abstract	It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is $$1.104366 \cdot n^{-3/2} \cdot 2.618034^n$$ . Motivated by the kinetics of RNA secondary structure formation, we are interested in determining the asymptotic number of secondary structures that are locally optimal, with respect to a particular energy model. In the Nussinov energy model, where each base pair contributes $$-1$$ towards the energy of the structure, locally optimal structures are exactly the saturated structures, for which we have previously shown that asymptotically, there are $$1.07427\cdot n^{-3/2} \cdot 2.35467^n$$ many saturated structures for a sequence of length $$n$$ . In this paper, we consider the base stacking energy model, a mild variant of the Nussinov model, where each stacked base pair contributes $$-1$$ toward the energy of the structure. Locally optimal structures with respect to the base stacking energy model are exactly those secondary structures, whose stems cannot be extended. Such structures were first considered by Evers and Giegerich, who described a dynamic programming algorithm to enumerate all locally optimal structures. In this paper, we apply methods from enumerative combinatorics to compute the asymptotic number of such structures. Additionally, we consider analogous combinatorial problems for secondary structures with annotated single-stranded, stacking nucleotides (dangles).
Ending Page	375
Page Count	35
Starting Page	341
File Format	PDF
ISSN	03036812
e-ISSN	14321416
Journal	Journal of Mathematical Biology
Issue Number	1-2
Volume Number	68
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2012-12-22
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Statistical thermodynamics General biology and biomathematics Mathematical and Computational Biology Applications of Mathematics Asymptotic enumeration
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation

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