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Mathematical models and simulations of bacterial growth and chemotaxis in a diffusion gradient chamber |
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| Authors: | Chichia Chiu Frank C. Hoppensteadt |
| Affiliation: | (1) Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA. e-mail: chiu@mth.msu.edu, US;(2) Center for System Science and Engineering, Arizona State University, Tempe, Arizona 85287. e-mail: fchoppen@asu.edu, US |
| Abstract: | The diffusion gradient chamber (DGC) is a novel device developed to study the response of chemotactic bacteria to combinations of nutrients and attractants [7]. Its purpose is to characterize genetic variants that occur in many biological experiments. In this paper, 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. Received: 3 June 1997 / Revised version: 15 August 2000 / Published online: 20 December 2000 |
| Keywords: | : Mathematical models for bacterial cell populations – Reaction-diffusion-chemotaxis equations – ADI methods – Computer simulation |
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