Diffusion mechanisms of localised knots along a polymer

TL;DR

This paper investigates how localized knots diffuse along polymer chains, deriving the mean escape time considering chain self-reptation and local conformational changes, revealing mechanisms that influence knot mobility.

Contribution

It introduces a novel analysis of knot diffusion mechanisms, highlighting the impact of local breathing on escape times and chain length scaling.

Findings

Self-reptation leads to L^3 scaling of diffusion time.

Local breathing reduces escape time to L^2 scaling.

Knot mobility remains finite even in very long chains.

Abstract

We consider the diffusive motion of a localized knot along a linear polymer chain. In particular, we derive the mean diffusion time of the knot before it escapes from the chain once it gets close to one of the chain ends. Self-reptation of the entire chain between either end and the knot position, during which the knot is provided with free volume, leads to an L^3 scaling of diffusion time; for sufficiently long chains, subdiffusion will enhance this time even more. Conversely, we propose local ``breathing'', i.e., local conformational rearrangement inside the knot region (KR) and its immediate neighbourhood, as additional mechanism. The contribution of KR-breathing to the diffusion time scales only quadratically, L^2, speeding up the knot escape considerably and guaranteeing finite knot mobility even for very long chains.