Ring Polymers: Threadings, Knot Electrophoresis and Topological Glasses

TL;DR

This paper reviews how topological interactions, especially inter-ring threadings, influence the physical behavior of ring polymer systems, leading to phenomena like topologically-driven glasses and patterns in DNA knot electrophoresis.

Contribution

It highlights the significance of inter-ring threadings in determining the physical properties of ring polymers and connects these topological features to observable behaviors.

Findings

Threadings increase with ring size.

Threadings induce topologically-driven glassy behavior.

Explain patterns in DNA knot electrophoresis.

Abstract

Elucidating the physics of a concentrated suspension of ring polymers, or of an ensemble of ring polymers in a complex environment, is an important outstanding question in polymer physics. Many of the characteristic features of these systems arise due to topological interactions between polymers, or between the polymers and the environment, and it is often challenging to describe this quantitatively. Here we review recent research which suggests that a key role is played by inter-ring threadings (or penetrations), which become more abundant as the ring size increases. As we discuss, the physical consequences of such threadings are far-reaching: for instance, they lead to a topologically-driven glassy behaviour of ring polymer melts under pinning perturbations, while they can also account for the shape of experimentally observed patterns in two-dimensional gel electrophoresis of DNA knots.