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

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


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.

    Research areas

  • bacterial colonies, chemotactic patterns, non-Brownian diffusion, collective behavior, microbial aggregation, GIANT NUMBER FLUCTUATIONS, ESCHERICHIA-COLI, HYDRODYNAMICS, MOTILITY, CELLS

ID: 1452158