Branching instability in expanding bacterial colonies

57/2014

Branching instability in expanding bacterial colonies

Friday 12th December 2014

Giverso, C.; Verani, M.; Ciarletta P.;

Self-organization in developing living organisms relies on the capability of cells to duplicate and perform a collective motion inside the surrounding environment. Chemical and mechanical interactions coordinate such a cooperative behavior, driving the dynamical evolution of the macroscopic system. In this work, we perform an analytical and computational analysis to study pattern formation during the spreading of an initially circular bacterial colony on a Petri dish. The continuous mathematical model addresses the growth and the chemotactic migration of the living monolayer, together with the diffusion and consumption of nutrients in the agar. The governing equations contain four dimensionless parameters, accounting for the interplay among the chemotactic response, the bacteria-substrate interaction and the experimental geometry. The spreading colony is found to be always linearly unstable to perturbations of the interface, whilst branching instability arises in finite-element numerical simulations. The typical length-scales of such fingers, which align in the radial direction and later undergo further branching, are controlled by the size parameters of the problem, whilst the emergence of branching is favored if the diffusion is dominant on the chemotaxis. The model is able to predict the experimental morphologies and their dynamical evolution, confirming that compact (resp. branched) patterns arise for fast (resp. slow) expanding colonies. Such results, while providing new insights on pattern selection in bacterial colonies, may finally have important applications for designing controlled patterns.

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Journal of the Royal Society Interface