Computational modeling of the bacterial self-organization in a rounded container: The effect of dimensionality - Baronas, Romas; Ledas, Žilvinas; Šimkus, Remigijus (Nonlinear Analysis: Modelling and Control, 2015)
A bacterial self-organization in a rounded container as detected by bioluminescence imaging is mathematically modeled by applying the the Keller–Segel approach with logistic growth. The pattern formation in a colony of luminous Escherichia coli is numerically simulated by the nonlinear reaction-advection-diffusion equations. In this work, the pattern formation is studied in 3D and the results are compared with previous and new 2D and 1D simulations. The numerical simulation at transition conditions was carried out using the finite difference technique. The simulation results showed that the developed 3D model captures fairly well the sophisticated patterns observed in the experiments. Since the numerical simulation based on the 3D model is very time-consuming, the reduction of spatial dimension of the model for simulating 1D spatiotemporal patterns is discussed. Due to the accumulation of luminous cells near the top three-phase contact line the experimental patterns of the bioluminescence can be qualitatively described by 1D and 2D models by adjusting values of the diffusion coefficient and/or chemotactic sensitivity.
Keywords: chemotaxis; reaction-diffusion; pattern formation; mathematical modelling