Asymptotics of a Brownian ratchet for Protein Translocation
نویسندگان
چکیده
Protein translocation in cells has been modelled by Brownian ratchets. In such models, the protein diffuses through the nanopore by thermal fluctuations. On one side of the pore ratcheting molecules bind to the protein and hinder it to diffuse out of the pore. We study a simple 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 γ(Xt − Rt) and is distributed uniformly on [Rt;Xt]. We show that the asymptotic speed of the ratchet scales with γ and the asymptotic variance is independent of γ.
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