RNAlike polymer model: exact calculation on the Bethe lattice

TL;DR

This paper presents an exact solution for a lattice polymer model on the Bethe lattice, capturing phase transitions relevant to RNA-like molecules, including coil, molten, and paired states, influenced by stacking effects.

Contribution

It introduces an exactly solvable Bethe lattice model for RNA-like polymers, incorporating stacking effects and phase transitions in a grand-canonical framework.

Findings

Identifies two phase transitions: coil to molten and molten to paired.

Stacking effects change the transition from second to first order.

Provides an exact phase diagram for the model.

Abstract

We consider a lattice polymer model (random walk), in which the walk is allowed to visit lattice bonds at most twice. Such a model might have some relevance to describe statistical properties of RNA molecules. In order to mimic base pairing, we assign an attractive energy term to each doubly-visited bond, and a further contribution to each pair of consecutive doubly-visited bonds. The latter term is expected to mimic the stacking effect, whereas no effect of sequence, that is, of chemical specificity, is taken into account. The phase diagram is worked out exactly on a Bethe lattice, in a grand-canonical formulation. In the dilute solution (single molecule) limit, the system undergoes two different phase transitions, upon decreasing temperature: a Thetalike collapse from a swollen "coil" state to a "molten" state, with a low fraction of doubly-visited bonds, and subsequently to a "paired" state, with empty or doubly-visited bonds only. The stacking effect drives the latter transition from second to first order.