Eur. Phys. J. B (2017) 90: 155
https://doi.org/10.1140/epjb/e2017-80209-2

Regular Article

A generalised Davydov-Scott model for polarons in linear peptide chains

Department of Mathematical Sciences, Durham University, Lower Mountjoy, Stockton Road, Durham DH1 3LE, UK

^a e-mail: b.m.a.g.piette@durham.ac.uk

Received: 10 April 2017
Published online: 16 August 2017

Abstract

We present a one-parameter family of mathematical models describing the dynamics of polarons in periodic structures, such as linear polypeptides, which, by tuning the model parameter, can be reduced to the Davydov or the Scott model. We describe the physical significance of this parameter and, in the continuum limit, we derive analytical solutions which represent stationary polarons. On a discrete lattice, we compute stationary polaron solutions numerically. We investigate polaron propagation induced by several external forcing mechanisms. We show that an electric field consisting of a constant and a periodic component can induce polaron motion with minimal energy loss. We also show that thermal fluctuations can facilitate the onset of polaron motion. Finally, we discuss the bio-physical implications of our results.