Field Theory of the RNA Freezing Transition

TL;DR

This paper develops a field theory for the RNA freezing transition, demonstrating the phase transition's existence and calculating critical exponents, including the pairing probability exponent at the transition.

Contribution

It introduces a renormalizable field theory for the RNA freezing transition and confirms the phase transition through explicit calculations.

Findings

The phase transition exists and is renormalizable.

The pairing probability exponent at the transition is approximately 1.36.

Critical exponents for the denaturation transition are computed.

Abstract

Folding of RNA is subject to a competition between entropy, relevant at high temperatures, and the random, or random looking, sequence, determining the low- temperature phase. It is known from numerical simulations that for random as well as biological sequences, high- and low-temperature phases are different, e.g. the exponent rho describing the pairing probability between two bases is rho = 3/2 in the high-temperature phase, and approximatively 4/3 in the low-temperature (glass) phase. Here, we present, for random sequences, a field theory of the phase transition separating high- and low-temperature phases. We establish the existence of the latter by showing that the underlying theory is renormalizable to all orders in perturbation theory. We test this result via an explicit 2-loop calculation, which yields rho approximatively 1.36 at the transition, as well as diverse other critical exponents, including the response to an applied external force (denaturation transition).