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

## TL;DR

This paper introduces a flexible mathematical model for polarons in linear peptide chains, unifying previous models and exploring their dynamics under various external influences with potential biological implications.

## Contribution

It develops a one-parameter family of models that generalize Davydov and Scott models, providing analytical and numerical solutions for polaron behavior.

## Key findings

- Electric fields can induce low-loss polaron motion.
- Thermal fluctuations facilitate polaron mobility.
- Analytical stationary solutions derived in the continuum limit.

## Abstract

We present a one-parameter family of mathematical models describing the dynamics of polarons in linear periodic structures such as polypeptides. By tuning the parameter, we are able to recover the Davydov and the Scott models. We describe the physical significance of this parameter. 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.