Arrested phase separation in reproducing bacteria: a generic route to pattern formation?

TL;DR

This paper introduces a generic mechanism where density-dependent motility in reproducing bacteria leads to stable, patterned structures through arrested phase separation, without requiring chemotaxis.

Contribution

It develops a mathematical model showing how density-dependent diffusivity causes stable pattern formation in bacteria, independent of chemotactic signaling.

Findings

Formation of stable droplets and rings in bacterial populations

Pattern characteristics depend on diffusivity gradients

Model predicts patterns similar to chemotactic behavior

Abstract

We present a generic mechanism by which reproducing microorganisms, with a diffusivity that depends on the local population density, can form stable patterns. It is known that a decrease of swimming speed with density can promote separation into bulk phases of two coexisting densities; this is opposed by the logistic law for birth and death which allows only a single uniform density to be stable. The result of this contest is an arrested nonequilibrium phase separation in which dense droplets or rings become separated by less dense regions, with a characteristic steady-state length scale. Cell division mainly occurs in the dilute regions and cell death in the dense ones, with a continuous flux between these sustained by the diffusivity gradient. We formulate a mathematical model of this in a case involving run-and-tumble bacteria, and make connections with a wider class of mechanisms for density-dependent motility. No chemotaxis is assumed in the model, yet it predicts the formation of patterns strikingly similar to those believed to result from chemotactic behavior.