Fractional Brownian motion approach to polymer translocation: The governing equation of motion

We suggest a governing equation that 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 subdiffusive increase of the distribution variance Delta(t) with elapsed time Delta(t) alpha t(alpha). The latter quantity measures the mean-squared number s of polymer segments that have passed through the pore Delta(t) = <[s(t) - s(t = 0)](2)>, and is known to grow with an anomalous diffusion exponent alpha < 1. Our main assumption [i.e., a Gaussian distribution of the translocation velocity upsilon(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 recently that the exponent a changes from 0.91 to 0.55 to 0.91 for short-, intermediate-, and long-time regimes, respectively.