Eur. Phys. J. E (2010) 32: 209-216
https://doi.org/10.1140/epje/i2010-10618-y

Regular Article

Stationary solutions for a modified Peyrard-Bishop DNA model with up to third-neighbor interactions

Department of Mathematics, University of Illinois at Urbana-Champaign, 61801-2975, Urbana, IL, USA

^* e-mail: zrapti@illinois.edu

Received: 8 February 2010
Accepted: 10 May 2010
Published online: 17 June 2010

Abstract

We investigate a DNA model that takes into account stacking interactions with neighbors up to three bases away. The model is a generalization of the well-known Peyrard-Bishop (PB) model and is motivated by studies that suggest that nearest-neighbor models for base-pair interaction in a DNA chain might not be enough to capture the mechanism and dynamics of DNA base-pair opening. We study stationary solutions of the modified model and investigate their stability. A comparison with the PB model reveals that under a wide range of parameter values the main characteristics of the original model --such as the hyperbolicity of the equilibrium at the origin-- are preserved, but new types of stationary solutions emerge.