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

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.