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

We develop a kinetic Monte Carlo scheme for polymer chains on the 3d FCC lattice which takes into account the possibility for pairs of polymer strands to perform strand crossing at a given tunable rate. We apply this method to melts of ring polymers and we characterize their structure and dynamics. We focus on the complex topology arising during the relaxation process by looking, in particular, at the formation of knots, links and higher order topological structures. As for the dynamics, we show that strand crossing makes polymers to diffuse faster with respect to melts of unknotted and non-concatenated rings provided that the time-scale of the process is smaller respect to the relaxation time of the unperturbed state, in agreement with recent experiments employing solutions of DNA rings in the presence of the type II topoisomerase enzyme. In contrast, at slow rates the melt is shown to become slower, and this prediction may be easily validated experimentally.