Field Theory of the RNA Freezing Transition
François David1, Kay Jörg Wiese2
1SPhT-Service de Physique Théorique, CEA/Saclay - 91191 Gif-sur-Yvette Cedex, France
2CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France
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 ρ describing the pairing probability between two bases is ρ = 3/2 in the high-temperature phase, and ρ ≈ 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 ρ ≈ 1.36 at the transition, as well as diverse other critical exponents, including the response to an applied external force (denaturation transition).
arXiv:0906.1472 (q-bio.BM) [pdf]
J. Stat. Mech. (2009) P10019 [pdf]
Copyright (C) by Kay Wiese. Last edited June 2, 2009.