Polymer Translocation out of Planar Confinements

TL;DR

This paper investigates polymer translocation out of planar confinements, revealing how dwell-time scales with polymer length under different confinement conditions through theoretical and simulation analysis.

Contribution

It provides a unified theoretical framework and high-precision simulations showing the scaling of translocation dwell-time in confined geometries, challenging previous bounds.

Findings

Dwell-time scales as N^{2+ν_2D} for symmetric confinement.

Dwell-time scales as N^{2ν_2D} for infinite confinement.

Results challenge earlier lower bounds on translocation time.

Abstract

Polymer translocation in three dimensions out of planar confinements is studied in this paper. Three membranes are located at $z=-h$, $z=0$ and $z=h_1$. These membranes are impenetrable, except for the middle one at $z=0$, which has a narrow pore. A polymer with length $N$ is initially sandwiched between the membranes placed at $z=-h$ and $z=0$ and translocates through this pore. We consider strong confinement (small $h$), where the polymer is essentially reduced to a two-dimensional polymer, with a radius of gyration scaling as $R^{\tinytext{(2D)}}_g \sim N^{\nu_{\tinytext{2D}}}$; here, $\nu_{\tinytext{2D}}=0.75$ is the Flory exponent in two dimensions. The polymer performs Rouse dynamics. Based on theoretical analysis and high-precision simulation data, we show that in the unbiased case $h=h_1$, the dwell-time $\tau_d$ scales as $N^{2+\nu_{\tinytext{2D}}}$, in perfect agreement with our previously published theoretical framework. For $h_1=\infty$, the situation is equivalent to field-driven translocation in two dimensions. We show that in this case $\tau_d$ scales as $N^{2\nu_{\tinytext{2D}}}$, in agreement with several existing numerical results in the literature. This result violates the earlier reported lower bound $N^{1+\nu}$ for $\tau_d$ for field-driven translocation. We argue, based on energy conservation, that the actual lower bound for $\tau_d$ is $N^{2\nu}$ and not $N^{1+\nu}$. Polymer translocation in such theoretically motivated geometries thus resolves some of the most fundamental issues that are the subjects of much heated debate in recent times.