Topological signatures of globular polymers

TL;DR

This paper investigates how the minimal crossing number of knots influences the equilibrium behavior of globular ring polymers, revealing new topological effects on polymer segmentation and translocation through membranes.

Contribution

It introduces a novel analysis of how knot complexity affects globular polymer configurations and uncovers a topological effect impacting translocation through nanopores.

Findings

Minimal crossing number controls equilibrium statistics of globular rings.

Length distribution of unknotted loops shows a fast power law decay.

Topological effects interfere with surface tension during membrane translocation.

Abstract

Simulations in which a globular ring polymer with delocalized knots is separated in two interacting loops by a slipping link, or in two non-interacting globuli by a wall with a hole, show how the minimal crossing number of the knots controls the equilibrium statistics. With slipping link the ring length is divided between the loops according to a simple law, but with unexpectedly large fluctuations. These are suppressed only for unknotted loops, whose length distribution shows always a fast power law decay. We also discover and explain a topological effect interfering with that of surface tension in the globule translocation through a membrane nanopore.