Forced translocation of a polymer: dynamical scaling vs. MD-simulation

TL;DR

This paper develops a theoretical model for polymer translocation through a nanopore under force, predicting different scaling regimes for translocation time, and validates these predictions with molecular dynamics simulations.

Contribution

The paper introduces a new theoretical framework based on tensile blob dynamics and propagating force fronts, extending understanding of force-driven polymer translocation.

Findings

Scaling law for translocation time changes with force

Simulation confirms increase of scaling exponent with force

Observed exponents are smaller than theoretical predictions

Abstract

We suggest a theoretical description of the force-induced translocation dynamics of a polymer chain through a nanopore. Our consideration is based on the tensile (Pincus) blob picture of a pulled chain and the notion of propagating front of tensile force along the chain backbone, suggested recently by T. Sakaue. The driving force is associated with a chemical potential gradient that acts on each chain segment inside the pore. Depending on its strength, different regimes of polymer motion (named after the typical chain conformation, "trumpet", "stem-trumpet", etc.) occur. Assuming that the local driving and drag forces are equal (i.e., in a quasi-static approximation), we derive an equation of motion for the tensile front position $X(t)$. We show that the scaling law for the average translocation time $<\tau>$ changes from $<\tau> \sim N^{2\nu}/f^{1/\nu}$ to $<\tau> \sim N^{1+\nu}/f$ (for the free-draining case) as the dimensionless force ${\widetilde f}_{R} = a N^{\nu}f /T$ (where $a$, $N$, $\nu$, $f$, $T$ are the Kuhn segment length, the chain length, the Flory exponent, the driving force, and the temperature, respectively) increases. These and other predictions are tested by Molecular Dynamics (MD) simulation. Data from our computer experiment indicates indeed that the translocation scaling exponent $\alpha$ grows with the pulling force ${\widetilde f}_{R}$) albeit the observed exponent $\alpha$ stays systematically smaller than the theoretically predicted value. This might be associated with fluctuations which are neglected in the quasi-static approximation.