Simplifying Topological Entanglements by Entropic Competition of Slip-Links

TL;DR

This paper explores how diffusing slip-links can entropically compete with and localize knots in polymeric systems, simplifying their topology and offering strategies to control material properties.

Contribution

It introduces a theoretical framework showing slip-links can localize and simplify knots, with the efficiency depending on slip-link network topology.

Findings

Slip-links can entropically compete with knots to facilitate simplification.

The efficiency of knot localization depends on slip-link network topology.

Potential strategies for controlling topology in biological and synthetic materials are discussed.

Abstract

Topological entanglements are abundant, and often detrimental, in polymeric systems in biology and materials science. Here we theoretically investigate the topological simplification of knots by diffusing slip-links (SLs), which may represent biological or synthetic molecules, such as proteins on the genome or cyclodextrines in slide-ring gels. We find that SLs entropically compete with knots and can localise them, greatly facilitating their downstream simplification by transient strand-crossing. We further show that the efficiency of knot localisation strongly depends on the topology of the SL network and, informed by our findings, discuss potential strategies to control the topology of biological and synthetic materials.