  Chaperone-assisted translocation through a nanopore embedded in membrane
holds a prominent role in the transport of biopolymers. Inspired by classical
Brownian ratchet, we develop a theoretical framework characterizing such
translocation process through a master equation approach. In this framework,
the polymer chain, provided with reversible binding of chaperones, undergoes
forward/backward diffusion, which is rectified by chaperones. We drop the
assumption of timescale separation and keep the length of a polymer chain
finite, both of which happen to be the key points in most of the previous
studies. Our framework makes it accessible to derive analytical expressions for
mean translocation velocity and effective diffusion constant in stationary
state, which is the basis of a comprehensive understanding towards the dynamics
of such process. Generally, the translocation of polymer chain across membrane
consists of three subprocesses: initiation, termination, and translocation of
the main body part of a polymer chain, where the translocation of the main body
part depends on the binding/unbinding kinetics of chaperones. That is the main
concern of this study. Our results show that the increase of forward/backward
diffusion rate of a polymer chain and the binding/unbinding ratio of chaperones
both raise the mean translocation velocity of a polymer chain, and roughly
speaking, the dependence of effective diffusion constant on these two factors
achieves similar behavior.
