Topological Self-Entanglement in Growing, Confined Bacterial Filaments

Topological self-entanglement in growing filaments presents a fundamental problem in nonequilibrium soft matter: how can slow, extensile forcing alone generate micron-scale knots? We address this question in filament-forming bacteria, using Trichococcous flocculiformis as a model non-motile active filament whose length increases through growth while experiencing confinement and intermittent shear from bulk agitation. We combine static-media microfluidic imaging with long-timescale shape tracking to capture filament conformations over many doubling times. Image-based topological analysis (crossing number, loop geometry, and temporal stability) enables us to identify knotted states and reconstruct the discrete geometric events that generate them. Our observations indicate that growth-driven loop capture, together with confinement-enhanced self-contact and shear-assisted threading, serve as the dominant pathways for knot initiation. By mapping these outcomes as a function of nutrient-controlled filament length and external agitation, and by comparing with filamentous cyanobacteria, we isolate geometry-driven features that generalize across systems from organism-specific behaviors. These results establish a physical framework for knot formation in non-motile active filaments and clarify how topological complexity can emerge and persist in growing, confined cellular collectives.