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.
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