Computational Studies of Bacterial Colony Model

Ondřej Pártl

Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic.

DOI: 10.4236/ajcm.2013.32023                

Abstract

Microbiological experiments show that the colonies of the bacterium bacillus subtilis placed on a dish filled with an agar medium and nutrient form varied spatial patterns while the individual cells grow, reproduce and migrate on the dish in clumps. In this paper, we discuss a system of reaction-diffusion equations that can be used with a view to modelling this phenomenon and we solve it numerically by means of the method of lines. For the spatial discretization, we use the finite difference method and Galerkin finite element method. We present how the spatial patterns obtained depend on the spatial discretization employed and we measure the experimental order of convergence of the numerical schemes used. Further, we present the numerical results obtained by solving the model in a cubic domain.

Keywords

Bacterial Colony Model; Reaction-Diffusion Equations; Method of Lines; Galerkin Finite Element Method

Conflicts of Interest

The authors declare no conflicts of interest.

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