Issue No. 06 - November/December (2011 vol. 8)

ISSN: 1545-5963

pp: 1468-1482

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TCBB.2010.126

Anika Scheid , University of Kaiserslautern, Kaiserslautern

Markus E. Nebel , University of Kaiserslautern, Kaiserslautern

ABSTRACT

There are two custom ways for predicting RNA secondary structures: minimizing the free energy of a conformation according to a thermodynamic model and maximizing the probability of a folding according to a stochastic model. In most cases, stochastic grammars are used for the latter alternative applying the maximum likelihood principle for determining a grammar's probabilities. In this paper, building on such a stochastic model, we will analyze the expected minimum free energy of an RNA molecule according to Turner's energy rules. Even if the parameters of our grammar are chosen with respect to structural properties of native molecules only (and therefore, independent of molecules' free energy), we prove formulae for the expected minimum free energy and the corresponding variance as functions of the molecule's size which perfectly fit the native behavior of free energies. This gives proof for a high quality of our stochastic model making it a handy tool for further investigations. In fact, the stochastic model for RNA secondary structures presented in this work has, for example, been used as the basis of a new algorithm for the (nonuniform) generation of random RNA secondary structures.

INDEX TERMS

RNA folding, RNA secondary structure, RNA structure prediction, free energy, generating functions.

CITATION

Anika Scheid, Markus E. Nebel, "Analysis of the Free Energy in a Stochastic RNA Secondary Structure Model",

*IEEE/ACM Transactions on Computational Biology and Bioinformatics*, vol. 8, no. , pp. 1468-1482, November/December 2011, doi:10.1109/TCBB.2010.126