On the behavior of random RNA secondary structures near the glass transition

TL;DR

This paper investigates the phase transition in random RNA secondary structures between glassy and molten states, using numerical methods and order parameters to understand the underlying mechanisms of this transition.

Contribution

It introduces new order parameters for the glass and molten phases and numerically studies the RNA glass transition inspired by field theory insights.

Findings

Identified critical behavior at the glass transition point.

Defined order parameters that vanish at the critical point.

Explored the mechanisms driving the phase transition.

Abstract

RNA forms elaborate secondary structures through intramolecular base pairing. These structures perform critical biological functions within each cell. Due to the availability of a polynomial algorithm to calculate the partition function over these structures, they are also a suitable system for the statistical physics of disordered systems. In this model, below the denaturation temperature, random RNA secondary structures exist in one of two phases: a strongly disordered, low-temperature glass phase, and a weakly disordered, high-temperature molten phase. The probability of two bases to pair decays with their distance with an exponent 3/2 in the molten phase, and about 4/3 in the glass phase. Inspired by previous results from a renormalized field theory of the glass transition separating the two phases, we numerically study this transition. We introduce distinct order parameters for each phase, that both vanish at the critical point. We finally explore the driving mechanism behind this transition.