Asymptotics of a Brownian ratchet for protein translocation

摘要

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 gamma(X-t - R-t) and the new reflection boundary is distributed uniformly between Rt- and X-t. The asymptotic speed of the ratchet scales with gamma(1/3) and the asymptotic variance is independent of gamma. (C) 2010 Elsevier B.V. All rights reserved.