Kinetic Catalysis of Spontaneous Knotting: How Free Particles Modulate Filament Entanglement

Abstract

Entangled knots form spontaneously in flexible filaments, yet the influence of the surrounding environment on this process is poorly understood. Here we demonstrate that free-moving particles act as kinetic catalysts for spontaneous knotting. Through controlled agitation experiments, we find that a small number of inert beads substantially enhance the probability and accelerate the rate of knot formation. This catalytic effect is non-monotonic: an optimal particle size and concentration that maximizes entanglement, while an excess of particles suppresses knotting by impeding the filament's dynamics. We develop a stochastic model that quantitatively reproduces this behavior, attributing it to a competition between entanglement-promoting collisions and motion-suppressing drag. Our findings reveal a mechanism for tuning topological complexity, whereby adjusting these environmental agitators can either promote rapid self-assembly or inhibit unwanted entanglement. This work suggests new strategies for controlling filament topology in settings ranging from crowded biological environments to advanced materials processing.

13 pages, 4 figures