A simple model of DNA denaturation and mutually avoiding walks statistics

TL;DR

This paper demonstrates that a DNA denaturation model with mutual avoidance exhibits a first order transition, supported by exact and numerical results, with a sharper transition than models including full excluded volume effects.

Contribution

The study provides an exact analysis of a DNA denaturation model with mutual avoidance, showing a first order transition driven by the reunion exponent of mutually avoiding walks.

Findings

First order denaturation transition confirmed by exact and numerical results.

Transition is sharper than in models with full excluded volume effects.

Probability distribution of base pair distances follows a power law at transition.

Abstract

Recently Garel, Monthus and Orland (Europhys. Lett. v 55, 132 (2001)) considered a model of DNA denaturation in which excluded volume effects within each strand are neglected, while mutual avoidance is included. Using an approximate scheme they found a first order denaturation. We show that a first order transition for this model follows from exact results for the statistics of two mutually avoiding random walks, whose reunion exponent is c > 2, both in two and three dimensions. Analytical estimates of c due to the interactions with other denaturated loops, as well as numerical calculations, indicate that the transition is even sharper than in models where excluded volume effects are fully incorporated. The probability distribution of distances between homologous base pairs decays as a power law at the transition.