Encounter dynamics of a small target by a polymer diffusing in a confined domain

TL;DR

This study investigates the first passage time of a polymer reaching a small target in a confined domain, revealing how polymer length and monomer position influence encounter times through simulations.

Contribution

It introduces a detailed simulation-based analysis of polymer encounter dynamics, highlighting the effects of polymer length and monomer position on first passage times.

Findings

NETP increases with polymer length up to a critical point, then decreases.

Long polymers exhibit exponential scaling of NETP with length.

Monomer position significantly affects encounter times in the second case.

Abstract

We study the first passage time for a polymer, that we call the narrow encounter time (NETP), to reach a small target located on the surface of a microdomain. The polymer is modeled as a Freely Joint Chain (beads connected by springs with a resting non zero length) and we use Brownian simulations to study two cases: when (i) any of the monomer or (ii) only one can be absorbed at the target window. Interestingly, we find that {in the first case} the NETP is an increasing function of the polymer length until a critical length, after which it decreases. Moreover, in the long polymer regime, we identified an exponential scaling law for the NETP as a function of the polymer length. {In the second case, the position of the absorbed monomer along the polymer chain strongly influences the NETP}. Our analysis can be applied to estimate the mean first time of a DNA fragment to a small target in the chromatin structure or for mRNA to find a small target.