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.
Read more at Macromolecules:
https://pubs.acs.org/doi/10.1021/acs.macromol.5c01381
Photo caption:
Simulation model. (a) Illustration of a knotted polymer ring. The arrows represent the active force fact on beads. (b) A simulation snapshot of our simulation with the chain length of L = 200 and Pe = 0, i.e., activity turned off. The colored beads indicate the region of the knot core. (c) A simulation snapshot of our simulation with the same chain length but at Pe = 120. The knot core is shrunk into a small region indicated by red beads. The knot type here is 31 using the Alexander-Briggs notation, where 3 is the minimum crossing number and 1 is an index to distinguish the knot types with the same minimum crossing number.
07 Oct 2025
