RNA substructure as a random matrix ensemble

TL;DR

This paper models RNA secondary structures using random matrix theory, deriving generating functions and analyzing their statistical properties to match experimental data.

Contribution

It introduces a novel random matrix model for RNA structures, providing analytical tools to study their statistical behavior.

Findings

Derived the generating function for RNA structures using Hermitian matrix models.

Analyzed the statistics of stems in RNA structures within a grand canonical ensemble.

Matched theoretical predictions with experimental statistical behavior of RNA structures.

Abstract

Combinatorial analysis of a certain abstract of RNA structures has been studied to investigate their statistics. Our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides, which can be described by random matrix model. We obtain the generating function of the structures using Hermitian matrix model with Chebyshev polynomial of the second kind and analyze the statistics with respect to the number of stems. To match the experimental findings of the statistical behavior, we consider the structures in a grand canonical ensemble and find a fugacity value corresponding to an appropriate number of stems.