Driven polymer translocation through a nanopore: a manifestation of anomalous diffusion

TL;DR

This paper demonstrates that polymer translocation through a nanopore under external force exhibits anomalous diffusion, characterized by a universal exponent, with analytical and simulation results confirming the non-standard dynamics.

Contribution

The study introduces a fractional Fokker-Planck framework to describe driven polymer translocation, revealing universal anomalous diffusion behavior and providing explicit analytical expressions.

Findings

Translocation number exhibits anomalous diffusion with a universal exponent.

Analytical probability distribution derived from fractional Fokker-Planck equation.

Monte Carlo simulations confirm the theoretical predictions.

Abstract

We study the translocation dynamics of a polymer chain threaded through a nanopore by an external force. By means of diverse methods (scaling arguments, fractional calculus and Monte Carlo simulation) we show that the relevant dynamic variable, the translocated number of segments $s(t)$, displays an {\em anomalous} diffusive behavior even in the {\em presence} of an external force. The anomalous dynamics of the translocation process is governed by the same universal exponent $\alpha = 2/(2\nu +2 - \gamma_1)$, where $\nu$ is the Flory exponent and $\gamma_1$ - the surface exponent, which was established recently for the case of non-driven polymer chain threading through a nanopore. A closed analytic expression for the probability distribution function $W(s, t)$, which follows from the relevant {\em fractional} Fokker - Planck equation, is derived in terms of the polymer chain length $N$ and the applied drag force $f$. It is found that the average translocation time scales as $\tau \propto f^{-1}N^{\frac{2}{\alpha} -1}$. Also the corresponding time dependent statistical moments, $< s(t) > \propto t^{\alpha}$ and $< s(t)^2 > \propto t^{2\alpha}$ reveal unambiguously the anomalous nature of the translocation dynamics and permit direct measurement of $\alpha$ in experiments. These findings are tested and found to be in perfect agreement with extensive Monte Carlo (MC) simulations.