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 ( X t ) t ≥ 0 with a changing reflection point ( R t ) t ≥ 0 . The rate of change of R t is γ ( X t − R t ) and the new reflection boundary is distributed uniformly between R t − and X t . The asymptotic speed of the ratchet scales with γ 1 / 3 and the asymptotic variance is independent of γ .