Spontaneous knotting and unknotting of flexible linear polymers: equilibrium and kinetic aspects

TL;DR

This study uses computational simulations to analyze the equilibrium properties and dynamic processes of spontaneous knotting and unknotting in long flexible linear polymers, revealing insights into their entanglement behavior.

Contribution

It provides the first systematic characterization of spontaneous knotting and unknotting in linear homopolymers through unbiased dynamics simulations.

Findings

High knotting probability in long chains

Knot formation and disappearance occur away from chain ends

Spontaneous knotting dynamics observed over long simulations

Abstract

We report on a computational study of the statics and dynamics of long flexible linear polymers that spontaneously knot and unknot. Specifically, the equilibrium self-entanglement properties, such as the knotting probability, knot length and position, are investigated with extensive Monte Carlo sampling of chains of up to 15,000 beads. Tens of such equilibrated chains of up to 4, 096 beads are next used as starting points for Langevin dynamics simulations. The complex interplay of chain dynamics and self-knotting is addressed by monitoring the time evolution of various metric and entanglement properties. In particular, the extensive duration of the simulations allows for observing the spontaneous formation and disappearance of prime and composite physical knots in linear chains. Notably, a sizeable fraction of self-knotting and unknotting events is found to involve regions that are far away from the chain termini. To the best of our knowledge this represents the first instance where spontaneous changes in knotting for linear homopolymers are systematically characterized using unbiased dynamics simulations.