Asymptotics of a Brownian ratchet for protein translocation

Protein translocation in cells has been modelled by Brownian ratchets. In such models, the protein diffuses through a nanopore. On one side of the pore, ratcheting molecules bind to the protein and hinder it to diffuse out of the pore. We study a Brownian ratchet by means of a reflected Brownian motion (Xt)t>=0 with a changing reflection point (Rt)t>=0. The rate of change of Rt is [gamma](Xt-Rt) and the new reflection boundary is distributed uniformly between Rt- and Xt. The asymptotic speed of the ratchet scales with [gamma]1/3 and the asymptotic variance is independent of [gamma].