title: Arrested phase separation in reproducing bacteria creates a generic route to pattern formation.
abstract: We present a generic mechanism by which reproducing microorganisms, with a diffusivity that depends on the local population density, can form stable patterns. For instance, it is known that a decrease of bacterial motility with density can promote separation into bulk phases of two coexisting densities; this is opposed by the logistic law for birth and death that 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 predominates 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 some of those believed to result from chemotactic behavior.
authors.affiliation: School of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom.
authors.forename: M E
authors.initials: ME
authors.lastname: Cates
authors.forename: D
authors.initials: D
authors.lastname: Marenduzzo
authors.forename: I
authors.initials: I
authors.lastname: Pagonabarraga
authors.forename: J
authors.initials: J
authors.lastname: Tailleur
mesh_terms: D001422:Bacterial Adhesion / Q000502:physiology; D018407:Bacterial Physiological Phenomena; D055592:Biophysical Phenomena; D002633:Chemotaxis / Q000502:physiology; D004926:Escherichia coli / Q000254:growth & development / Q000502:physiology; D008954:Models, Biological; D012486:Salmonella typhimurium / Q000254:growth & development / Q000502:physiology