Fractional Brownian motion approach to polymer translocation: the governing equation of motion
Abstract
We suggest a governing equation which describes the process of polymer chain translocation through a narrow pore and reconciles the seemingly contradictory features of such dynamics: (i) a Gaussian probability distribution of the translocated number of polymer segments at time t after the process has begun, and (ii) a sub-diffusive increase of the distribution variance (t) with elapsed time, (t) tα. The latter quantity measures the mean-squared number s of polymer segments which have passed through the pore, (t) = <[s(t)-s(t=0)]2>, and is known to grow with an anomalous diffusion exponent α < 1. Our main assumption - a Gaussian distribution of the translocation velocity v(t) - and some important theoretical results, derived recently, are shown to be supported by extensive Brownian dynamics simulation which we performed in 3D. We also numerically confirm the predictions made in ref.Kantor3, that the exponent α changes from 0.91 to 0.55, to 0.91, for short, intermediate and long time regimes, respectively.