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The impact of thermal fluctuations on the translocation dynamics of a polymerchain driven through a narrow pore has been investigated theoretically and bymeans of extensive Molecular-Dynamics (MD) simulation. The theoreticalconsideration is based on the so-called velocity Langevin (V-Langevin) equationwhich determines the progress of the translocation in terms of the number ofpolymer segments, $s(t)$, that have passed through the pore at time $t$ due toa driving force $f$. The formalism is based only on the assumption that, due tothermal fluctuations, the translocation velocity $v=\dot{s}(t)$ is a Gaussianrandom process as suggested by our MD data. With this in mind we have derivedthe corresponding Fokker-Planck equation (FPE) which has a nonlinear drift termand diffusion term with a {\em time-dependent} diffusion coefficient $D(t)$.Our MD simulation reveals that the driven translocation process follows a {\emsuper}diffusive law with a running diffusion coefficient $D(t) \proptot^{\gamma}$ where $\gamma < 1$. This finding is then used in the numericalsolution of the FPE which yields an important result: for comparatively smalldriving forces fluctuations facilitate the translocation dynamics. As aconsequence, the exponent $\alpha$ which describes the scaling of the meantranslocation time $<\tau>$ with the length $N$ of the polymer, $<\tau> \proptoN^{\alpha}$ is found to diminish. Thus, taking thermal fluctuations intoaccount, one can explain the systematic discrepancy between theoreticallypredicted duration of a driven translocation process, considered usually as adeterministic event, and measurements in computer simulations. In thenon-driven case, $f=0$, the translocation is slightly subdiffusive and can betreated within the framework of fractional Brownian motion (fBm).

Driven translocation of a polymer: fluctuations at work