Length-dependent residence time of contacts in simple polymeric models

TL;DR

This study investigates how the residence time of contacts in simple polymer models depends on polymer length, revealing a power-law relationship and conditions under which it aligns with Arrhenius predictions, supported by theoretical and simulation analysis.

Contribution

It provides a theoretical framework for understanding length-dependent contact residence times in polymers, including explicit expressions applicable to experimental scenarios.

Findings

Residence time follows a power-law with length, exponent -1.

Strong interactions and short range lead to Arrhenius-like residence times.

Theoretical predictions align with molecular dynamics simulations.

Abstract

Starting from the reported experimental evidence that the residence time of contacts between the ends of biopolymers is length dependent, we investigate the kinetics of contact breaking in simple polymer models from a theoretical point of view. We solved Kramers equation first for an ideal chain and then for a polymer with attracting ends, and compared the predictions with the results of molecular dynamics simulations. We found that the mean residence time always shows a power--law dependence on the length of the polymer with exponent $-1$, although is significantly smaller when obtained from the analysis of a single trajectory than when calculated from independent initial conformations. Only when the interaction is strong (>>kT) and the interaction range is small (of the order of the distance between consecutive monomers) does the residence time converge to that of the Arrhenius equation, independent of the length. We are able to provide expressions of the mean residence time for cases when the exact definition of contact is not available a priori, expressions that can be useful in typical cases of microscopy experiments.