Asymptotics of a Brownian ratchet for Protein Translocation

Abstract

Protein translocation in cells has been modelled by \emph{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 $(X_t{)}_{t\ge 0}$ with a changing reflection point $(R_t{)}_{t\ge 0}$. The rate of change of $R_t$ is $\gamma (X_t-R_t)$ and the new reflection boundary is distributed uniformly between $R_{t-}$ and $X_t$. The asymptotic speed of the ratchet scales with ${\gamma }^{1/3}$ and the asymptotic variance is independent of $\gamma$.

Replaced with revised version, 27 pages, 3 figures

References in corpus (1)

• Directed motion emerging from two coupled random processes: Translocation of a chain through a membrane nanopore driven by binding proteins