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We present a one-parameter family of mathematical models describing thedynamics of polarons in linear periodic structures such as polypeptides. Bytuning the parameter, we are able to recover the Davydov and the Scott models.We describe the physical significance of this parameter. In the continuumlimit, we derive analytical solutions which represent stationary polarons. On adiscrete lattice, we compute stationary polaron solutions numerically. Weinvestigate polaron propagation induced by several external forcing mechanisms.We show that an electric field consisting of a constant and a periodiccomponent can induce polaron motion with minimal energy loss. We also show thatthermal fluctuations can facilitate the onset of polaron motion. Finally, wediscuss the bio-physical implications of our results.

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