Topological localisation and motility of active knots

Nonequilibrium active polymers provide a minimal framework to investigate biopolymers such as DNA and chromatin under the action of molecular motors. Here we study active ring polymers with controlled topology and show that knot type qualitatively determines their nonequilibrium behaviour. We find that activity induces opposite localisation responses in different topological families: torus knots systematically delocalise and inflate, whereas twist knots tighten and remain localised. We trace this divergent behaviour to the distinct symmetry properties of their tangent fields, which control the alignment of active forces along the chain. We show that topology also governs internal and emergent dynamics. Active torus knots behave as soft chiral self-propelled particles exhibiting persistent motion with a well-defined handedness fixed by their topological chirality. In contrast, achiral knots show no net handedness. The knot thus acts as a deformable topological quasiparticle whose morphology and propulsion are selected by topology. These results suggest potential routes toward programmable soft chiral particles with controllable morphology and emergent motility modes.