Asymptotics of RNA Shapes

13 years 4 months ago

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Abstract. RNA shapes, introduced by Giegerich et al. (17), provide a useful classification of the branching complexity for RNA secondary structures. In this paper, we derive an exact value for the asymptotic number of RNA shapes, by relying on an elegant relation between non-ambiguous, context-free grammars and generating functions. Our results provide a theoretical upper bound on the length of RNA sequences amenable to probabilistic shape analysis (37; 41), under the assumption that any base can basepair with any other base. Since the relation between context-free grammars and asymptotic enumeration is simple yet not well-known in bioinformatics, we give a self-contained presentation with illustrative examples. Additionally, we prove a surprising 1-to-1 correspondence between -shapes and Motzkin numbers. Key words and phrases. enumerative combinatorics, RNA secondary structure, generating functions, RNA shapes. This research was supported by National Science Foundation Grant DBI054350...

W. A. Lorenz, Yann Ponty, Peter Clote

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