Driven translocation of a polymer: Fluctuations at work

The impact of thermal fluctuations on the translocation dynamics of a polymer chain driven through a narrow pore has been investigated theoretically and by means of extensive molecular dynamics (MD) simulation. The theoretical consideration is based on the so-called velocity Langevin (V-Langevin) equation which determines the progress of the translocation in terms of the number of polymer segments, s(t), that have passed through the pore at time t due to a driving force f. The formalism is based only on the assumption that, due to thermal fluctuations, the translocation velocity v = s(t) is a Gaussian random process as suggested by our MD data. With this in mind we have derived the corresponding Fokker-Planck equation (FPE) which has a nonlinear drift term and diffusion term with a time-dependent diffusion coefficient D(t). Our MD simulation reveals that the driven translocation process follows a super diffusive law with a running diffusion coefficient D(t)alpha t(gamma) where < 1. This finding is then used in the numerical solution of the FPE which yields an important result: For comparatively small driving forces fluctuations facilitate the translocation dynamics. As a consequence, the exponent a which describes the scaling of the mean translocation time <iota > with the length N of the polymer, <iota > alpha N-alpha is found to diminish. Thus, taking thermal fluctuations into account, one can explain the systematic discrepancy between theoretically predicted duration of a driven translocation process, considered usually as a deterministic event, and measurements in computer simulations. In the nondriven case, f = 0, the translocation is slightly subdiffusive and can be treated within the framework of fractional Brownian motion (fBm).