Symmetry-Breaking Motility

TL;DR

This paper develops a phenomenological model for active motility of beads and bacteria, linking shape symmetry to motion transitions, and analyzes universal phase behavior and velocity fluctuations.

Contribution

It introduces a new model connecting shape symmetry to motility transitions and provides analytical and simulation insights into phase behavior.

Findings

Shape symmetry influences the transition between stationary and moving states.

Velocity fluctuations are non-Maxwellian and shape-dependent.

Universal phase behavior is analytically characterized.

Abstract

Locomotion of bacteria by actin polymerization, and in vitro motion of spherical beads coated with a protein catalyzing polymerization, are examples of active motility. Starting from a simple model of forces locally normal to the surface of a bead, we construct a phenomenological equation for its motion. The singularities at a continuous transition between moving and stationary beads are shown to be related to the symmetries of its shape. Universal features of the phase behavior are calculated analytically and confirmed by simulations. Fluctuations in velocity are shown to be generically non-Maxwellian and correlated to the shape of the bead.