Genus Distributions For Extended Matrix Models Of RNA

TL;DR

This paper introduces an extended random matrix model for RNA folding that incorporates a perturbation distinguishing between paired and unpaired bases, revealing a structural transition and differences in genus distributions.

Contribution

It develops a novel extended matrix model for RNA that captures structural transitions and genus distribution changes due to a perturbation affecting base pairing.

Findings

Genus distributions differ between the original and extended models.

A structural transition occurs as the perturbation strength approaches a critical value.

The model predicts a phase with only fully paired bases at certain parameters.

Abstract

We construct and study an extended random matrix model of RNA (polymer) folding. A perturbation which acts on all the nucleotides in the chain is added to the action of the RNA partition function. The effect of this perturbation on the partition function and the Genus Distributions is studied. This perturbation distinguishes between the paired and unpaired bases. For example, for $\alpha = 1$ (where $\alpha$ is the ratio of the strengths of the original and perturbed term in the action) the partition function and genus distribution for odd lengths vanish completely. This partition function and the genus distribution is non-zero for even lengths where structures with fully paired bases only remain. This implies that (i). the genus distributions are different and (ii). there is a ``structural transition'' (from an ``unpaired-paired base phase'' to a ``completely paired base phase'') as $\alpha$ approaches 1 in the extended matrix models. We compare the results of the extended RNA model with the results of G. Vernizzi, H. Orland and A. Zee in PRL 94, 168103(2005).