  Polarons, introduced by Davydov to explain energy transport in
$\alpha$-helices, correspond to electrons localised on a few lattice sites
because of their interaction with phonons. While the static polaron field
configurations have been extensively studied, their displacement is more
difficult to explain. In this paper we show that, when the next to nearest
neighbour interactions are included, for physical values of the parameters,
polarons can spontaneously move, at T=0, on bent chains that exhibit a positive
gradient in their curvature. At room temperature polarons perform a random walk
but a curvature gradient can induce a non-zero average speed similar to the one
observed at zero temperature. We also show that at zero temperature a polaron
bounces on sharply kinked junctions. We interpret these results in light of the
energy transport by transmembrane proteins.
