Topological localisation and motility of active knots

TL;DR

This study reveals how the topology of active ring polymers influences their nonequilibrium behavior, localizing, inflating, or tightening based on knot type, and demonstrates their potential as programmable chiral particles.

Contribution

It uncovers the topological dependence of active polymer dynamics and introduces the concept of knots as deformable topological quasiparticles with controllable motility.

Findings

Torus knots delocalise and inflate under activity.

Twist knots tighten and stay localised.

Active torus knots exhibit persistent chiral motion.

Abstract

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.