Self-Trapping of Microorganisms Steering Toward their Own Trail

TL;DR

This paper investigates how self-propelled microorganisms leaving chemical trails can become trapped in their own paths due to an instability in chemotactic steering, revealing a universal trapping mechanism.

Contribution

It introduces a theoretical framework showing that self-trapping occurs for any chemotactic coupling strength, combining potential barrier and rare event analyses.

Findings

Particles transition to curved trajectories with size-scale radius.

Self-trapping occurs regardless of chemotactic strength.

The instability is explained through first-passage and rare event models.

Abstract

Active matter systems comprise self-propelled particles that move on a substrate while leaving chemical trails that influence other particles through chemotaxis (e.g., slime-depositing bacteria). Orientational chemotaxis manifests as a torque that steers the particle toward the chemical gradient. As each particle is coupled to its own trail, the dynamics exhibits an instability: when the particle gently diffuses, it abruptly transitions to trajectories with a radius of curvature comparable to its own size, becoming apparently trapped. We argue that, contrary to intuition, this trajectory instability occurs for any chemotactic coupling strength. Depending on the coupling regime, this arises either through a potential-barrier first-passage problem or from a rare event analysis.