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

M. E. Cates, D. Marenduzzo, I. Pagonabarraga, J. Tailleur

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)11715-11720
Number of pages6
JournalProceedings of the National Academy of Sciences
Issue number26
Publication statusPublished - 29 Jun 2010


  • bacterial colonies
  • chemotactic patterns
  • non-Brownian diffusion
  • collective behavior
  • microbial aggregation


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