title: Branching instability in expanding bacterial colonies.
abstract: 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 behaviour, 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, whereas 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, whereas the emergence of branching is favoured if the diffusion is dominant on the chemotaxis. The model is able to predict the experimental morphologies, confirming that compact (resp. branched) patterns arise for fast (resp. slow) expanding colonies. Such results, while providing new insights into pattern selection in bacterial colonies, may finally have important applications for designing controlled patterns.
authors: MOX, Politecnico di Milano, P.za Leonardo da Vinci, 32, 20133 Milan, Italy Fondazione CEN, P.za Leonardo da Vinci, 32, 20133 Milan, Italy.
authors: Chiara
authors: C
authors: Giverso
authors: MOX, Politecnico di Milano, P.za Leonardo da Vinci, 32, 20133 Milan, Italy.
authors: Marco
authors: M
authors: Verani
authors: Fondazione CEN, P.za Leonardo da Vinci, 32, 20133 Milan, Italy CNRS and Sorbonne Universités, Institut Jean le Rond d'Alembert, UPMC Univ Paris 06, UMR 7190, 4 place Jussieu case 162, 75005 Paris, France pasquale.ciarletta@upmc.fr.
authors: Pasquale
authors: P
authors: Ciarletta
mesh_terms: D000362:Agar / Q000737:chemistry; D001419:Bacteria / Q000254:growth & development*; D018407:Bacterial Physiological Phenomena; D002633:Chemotaxis; D003198:Computer Simulation; D004058:Diffusion; D016014:Linear Models; D008954:Models, Biological; D009024:Morphogenesis; D013997:Time Factors
chemical_list: D000362:Agar
keywords: bacterial colony growth; branching instability; pattern formation
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