Knotted globular ring polymers: how topology affects statistics and thermodynamics

TL;DR

This paper investigates how the topology of knotted globular ring polymers influences their statistical mechanics and thermodynamics, revealing a knot-dependent free-energy term and implications for entropic forces in macromolecular environments.

Contribution

It introduces a model showing that knot type affects free-energy and probabilities in long polymers, with simulations supporting the topological influence on polymer behavior.

Findings

Knot-dependent subleading free-energy term identified

Relative knot probabilities are temperature-independent for long chains

Topological effects induce entropic forces affecting polymer conformation

Abstract

The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter depending on the knot kind is an amplitude such that relative probabilities of knots do not vary with the temperature $T$, in the limit of long chains. We arrive at this conclusion by simulating interacting self-avoiding rings at low $T$ on the cubic lattice, both with unrestricted topology and with setups where the globule is divided by a slip link in two loops (preserving their topology) which compete for the chain length, either in contact or separated by a wall as for translocation through a membrane pore. These findings suggest that in macromolecular environments there may be entropic forces with a purely topological origin, whence portions of polymers holding complex knots should tend to expand at the expense of significantly shrinking other topologically simpler portions.