Dynamics of end-pulled polymer translocation through a nanopore

TL;DR

This paper extends the iso-flux tension propagation theory to include trans side friction, providing a detailed analysis of polymer translocation dynamics through nanopores, with exact scaling laws validated by simulations.

Contribution

The authors develop a generalized IFTP theory that accounts for trans side friction and derive exact scaling laws for translocation time under high driving forces.

Findings

Scaling exponent for translocation time: α=2

Scaling exponent for force dependence: β=-1

Good agreement with molecular dynamics simulations

Abstract

We consider the translocation dynamics of a polymer chain forced through a nanopore by an external force on its head monomer on the trans side. For a proper theoretical treatment we generalize the iso-flux tension propagation (IFTP) theory to include friction arising from the trans side subchain. The theory reveals a complicated scenario of multiple scaling regimes depending on the configurations of the cis and the trans side subchains. In the limit of high driving forces $f$ such that the trans subchain is strongly stretched, the theory is in excellent agreement with molecular dynamics simulations and allows an exact analytic solution for the scaling of the translocation time ${\tau}$ as a function of the chain length $N_0$ and $f$. In this regime the asymptotic scaling exponents for ${\tau} \sim N_0^{\alpha} f^{\beta}$ are $\alpha=2$, and $\beta =-1$. The theory reveals significant correction-to-scaling terms arising from the cis side subchain and pore friction, which lead to a very slow approach to $\alpha =2$ from below as a function of increasing $N_0$.