Enumeration of RNA structures by Matrix Models

TL;DR

This paper uses matrix models to exactly enumerate RNA contact structures by genus, revealing how pseudoknot complexity varies with RNA length, advancing understanding of RNA topology.

Contribution

It introduces a matrix model approach to enumerate RNA structures by genus, providing exact results for flexible backbone scenarios.

Findings

Exact enumeration of RNA contact structures by genus.

Distribution of pseudoknot genus as a function of RNA length.

Insights into RNA topology complexity.

Abstract

We enumerate the number of RNA contact structures according to their genus, i.e. the topological character of their pseudoknots. By using a recently proposed matrix model formulation for the RNA folding problem, we obtain exact results for the simple case of an RNA molecule with an infinitely flexible backbone, in which any arbitrary pair of bases is allowed. We analyze the distribution of the genus of pseudoknots as a function of the total number of nucleotides along the phosphate-sugar backbone.