Simplified Langevin approach to the Peyrard-Bishop-Dauxois model of DNA

TL;DR

This paper introduces a simplified Langevin approach to analyze the Peyrard-Bishop-Dauxois DNA model, revealing insights into denaturation transitions and bubble formation, with implications for understanding DNA melting behavior.

Contribution

It presents a new simplified Langevin method to study the Peyrard-Bishop-Dauxois DNA model, highlighting an analogy with wetting transitions and effects of heterogeneity.

Findings

Second order transition in the order-parameter for homogeneous DNA.

Largest bubbles appear in adenine-thymine rich regions.

Possible non-local effects due to bubble merging.

Abstract

A simple Langevin approach is used to study stationary properties of the Peyrard-Bishop-Dauxois model for DNA, allowing known properties to be recovered in an easy way. Results are shown for the denaturation transition in homogeneous samples, for which some implications, so far overlooked, of an analogy with equilibrium wetting transitions are highlighted. This analogy implies that the order-parameter, asymptotically, exhibits a second order transition even if it may be very abrupt for non-zero values of the stiffness parameter. Not surprisingly, we also find that for heterogeneous DNA, within this model the largest bubbles in the pre-melting stage appear in adenine-thymine rich regions, while we suggest the possibility of some sort of not strictly local effects owing to the merging of bubbles.