Swapping dynamics of composite knots in a stretched polymer under nanochannel confinement*

Abstract In this work, Langevin dynamics simulations were carried out to thoroughly investigate the swapping process of composite knots under tension in a cuboid nanochannel. From our analysis, the free energy profiles of knot swapping under different conditions were extracted from the overall probability distribution of the relative distance between the centers of composite knots. In addition, the impact of the stretching force, confinement size, and bending stiffness on the free energy profiles was directly identified. Especially, the influence of topology structure is for the first time reported. The increasing stretching force in a fixed confinement or the confinement size under a constant stretching force does not alter their respective equilibrium populations at the separate state and the entangled state. In contrast, a bending stiffness larger than 15 enhanced the formation of the entangled state. The topology structure of the 5 1 knot, which was different from the 5 2 knot, resulted in forming a metastable state in the free energy profiles. The increasing stretching forces yielded an enhancement of the following free energy barrier.