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Mathematical models and simulations of bacterial growth and chemotaxis in a diffusion gradient chamber. (English) Zbl 0988.92004

Summary: The diffusion gradient chamber (DGC) is a novel device developed to study the response of chemotactic bacteria to combinations of nutrients and attractants [D. Emerson et al., A diffusion gradient chamber for studying microbial behavior and separating micro-organisms. Appl. Environment. Microbiol. (1994)]. Its purpose is to characterize genetic variants that occur in many biological experiments. A mathematical model which describes the spatial distribution of a bacterial population within the DGC is developed. Mathematical analysis of the model concerning positivity and boundedness of the solutions are given. An ADI (Alternating Direction Implicit) method is constructed for finding numerical solutions of the model and carrying out computer simulations. The numerical results of the model successfully reproduced the patterns that were observed in the experiments using the DGC.

MSC:

92C17 Cell movement (chemotaxis, etc.)
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35K57 Reaction-diffusion equations
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