Computer simulations of melts of ring polymers with non-conserved topology: A dynamic Monte Carlo lattice model

TL;DR

This paper introduces a Monte Carlo lattice simulation method to study how topological strand crossings affect the structure and dynamics of ring polymer melts, revealing conditions that fluidize or slow the melt.

Contribution

It develops a novel dynamic Monte Carlo algorithm explicitly modeling strand crossing in ring polymers, linking crossing rates to melt fluidity and dynamics.

Findings

Fast strand crossing rates fluidize the melt.

Slow crossing rates slow down the melt.

Simulation results align with DNA enzyme experiments.

Abstract

We present computer simulations of a dynamic Monte Carlo algorithm for polymer chains on the FCC lattice which takes explicitly into account the possibility to overcome topological constraints by controlling the rate at which nearby polymer strands may cross through each other. By applying the method to systems of interacting ring polymers at melt conditions, we characterize their structure and dynamics by measuring, in particular, the amounts of knots and links which are formed during the relaxation process. In comparison to standard melts of unknotted and unconcatenated rings, our simulations demonstrate that the mechanism of strand crossing is responsible for fluidizing the melt provided the time scale of the process is faster than the internal relaxation of the chain, in agreement with recent experiments employing solutions of DNA rings in the presence of the type II topoisomerase enzyme. In the opposite case of slow rates the melt is shown to become slower, and this prediction may be easily validated experimentally.