Behavior of Active Polymer Knots

We investigate active polymer knots using Brownian dynamics simulations. We find the interplay of active force, chain connectivity, and knotting leads to several unexpected phenomena. First, active force significantly tightens knots through activity-induced stretching effect. The magnitude of the stretching effect differs greatly in and out of the knot core, probably because knotting modifies the arrangement of monomers and thus affects the stretching effect. We develop an approximate theory to quantify the dependence of the knot size on Péclet number Pe, which describes the activity strength. Second, active polymer knots significantly differ dynamically from nonactive polymer knots under tension. For example, active polymers exhibit knot breathing, i.e., switching between a very loose knot and a very tight knot, which is absent in nonactive knot under tension. Third, activity can shrink the conformations of very short chains, and knotting appears to enhance this activity-induced shrinkage. Fourth, in long knotted chains, activity-induced shrinkage vanishes because activity can reallocate segments from the knotted to the unknotted portion. This reallocation enlarges the overall conformation, counteracting the shrinkage effect. These results may have biological implications, considering that active force, chain connectivity, and knotting exist in biopolymers, such as DNA.