Controlling Knot Interactions through Confinement

We investigate how confinement affects the mutual interactions between knots tied on a single polymer chain using extensive coarse-grained molecular dynamics simulations. We introduce a novel model of an infinite chain that prevents knots from escaping while allowing for the exploration of knot interactions along seemingly infinite channels free from finite-size effects. Our simulations encompass 54 different settings, examining interactions between knots with varying chirality: +3₁# + 3₁, +3₁# – 3₁, and −3₁#4₁. We also explore the effects of tension on knot interactions and its interplay with confinement strength, using six unconfined chain settings as a reference to compare with previous studies. Furthermore, we investigate three channel geometries: achiral cylindrical channels and left-handed and right-handed helical channels. By utilizing these helical channels, we simulate left- and right-handed chirality, providing insight into how chirality influences knot behavior under confinement. We monitor several geometrical, topological, and thermodynamic properties throughout these simulations. Our findings reveal complex behaviors in the probability of knot intertwining, with a novel observation that confinement in chiral channels significantly enhances knot intertwining, reaching the highest probabilities reported to date.