Polymer dynamics under tension: mean first passage time for looping

TL;DR

This paper investigates the dynamics of polymer looping under tension using the FJC model, deriving an analytical expression for looping probability and validating it with simulations, ultimately challenging traditional barrier escape methods.

Contribution

It introduces a new analytical approach for predicting polymer looping times under tension and demonstrates its superiority over barrier escape methods through simulations.

Findings

Looping time is inversely proportional to looping probability.

Traditional barrier escape methods do not accurately predict looping dynamics.

The inverse scaling law provides a more reliable prediction for polymer looping times.

Abstract

This study deals with polymer looping, an important process in many chemical and biological systems. We investigate basic questions on the looping dynamics of a polymer under tension using the freely-jointed chain (FJC) model. Previous theoretical approaches to polymer looping under tension have relied on barrier escape methods, which assume local equilibrium, an assumption that may not always hold. As a starting point we use an analytical expression for the equilibrium looping probability as a function of the number of monomers and applied force, predicting an inverse relationship between looping time and looping probability. Using molecular dynamics simulations the predictions of this theoretical approach are validated within the numerical precision achieved. We compare our predictions to those of the barrier escape approach, by way of a calculation of the mean first passage time (MFPT) for the ends of a polymer to cross. For this purpose, we derive the exact free energy landscape, but resulting temporal predictions do not agree with the observed inverse scaling. We conclude that the traditional barrier escape approach does not provide satisfactory predictions for polymer looping dynamics and that the inverse scaling with looping probability offers a more reliable alternative.