The effects of knot topology on the collapse of active polymers

Abstract: We use numerical simulations to study tangentially active flexible ring polymers with different knot topologies. Simple, unknotted active rings display a collapse transition upon increasing the degree of polymerization. We find that topology has a significant effect on the polymer size at which the collapse takes place, with twist knots collapsing earlier than torus knots. Increasing knot complexity further accentuates this difference, as the collapse point of torus knots grows linearly and that of twist knots shrinks, eventually canceling the actively stretched regime altogether. This behavior is a consequence of the ordered configuration of torus knots in their stretched active state, featuring an effective alignment for non-neighboring bonds which increases with the minimal crossing number. Twist knots do not feature ordered configurations or bond alignment, increasing the likelihood of collisions, leading to collapse. These results yield a degree of control on the collapse point of active ring polymers, as it can be tuned by changing the topology.