Topological phase transition in a RNA model in the de Gennes regime

TL;DR

This paper investigates a simplified RNA model in a specific ionic environment, revealing a topological phase transition at a critical temperature where configurations shift from complex to simple topology.

Contribution

It identifies and analytically characterizes a topological phase transition in a simplified RNA model, linking configuration topology to temperature.

Findings

Critical temperature T_c separates two topological phases.

High-temperature phase has configurations with large genus.

Low-temperature phase has simple, spherical configurations.

Abstract

We study a simplified model of the RNA molecule proposed by G. Vernizzi, H. Orland and A. Zee in the regime of strong concentration of positive ions in solution. The model considers a flexible chain of equal bases that can pairwise interact with any other one along the chain, while preserving the property of saturation of the interactions. In the regime considered, we observe the emergence of a critical temperature T_c separating two phases that can be characterized by the topology of the predominant configurations: in the large temperature regime, the dominant configurations of the molecule have very large genera (of the order of the size of the molecule), corresponding to a complex topology, whereas in the opposite regime of low temperatures, the dominant configurations are simple and have the topology of a sphere. We determine that this topological phase transition is of first order and provide an analytic expression for T_c. The regime studied for this model exhibits analogies with that for the dense polymer systems studied by de Gennes