Asymptotic distribution of motifs in a stochastic context-free grammar model of RNA folding

TL;DR

This paper proves that the distribution of various structural features in RNA secondary structures modeled by a stochastic context-free grammar is asymptotically Gaussian, providing insights into RNA folding patterns.

Contribution

It establishes the asymptotic Gaussian distribution of structural motifs in RNA models using singularity analysis, a novel application in this context.

Findings

Base pairs, helices, and loops follow a Gaussian distribution asymptotically.

The results apply to a generic set of grammar probabilities.

Discussion of model relevance to real ribosomal structures.

Abstract

We analyze the distribution of RNA secondary structures given by the Knudsen-Hein stochastic context-free grammar used in the prediction program Pfold. We prove that the distribution of base pairs, helices and various types of loops in RNA secondary structures in this probabilistic model is asymptotically Gaussian, for a generic choice of the grammar probabilities. Our proofs are based on singularity analysis of probability generating functions. Finally, we use our results to discuss how this model reflects the properties of some known ribosomal secondary structures.