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Model and analysis of chemotactic bacterial patterns in a liquid medium |
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| Authors: | Rebecca Tyson S R Lubkin J D Murray |
| Institution: | (1) Department of Applied Mathematics, Box 352420, University of Washington, Seattle, WA 98195-2420, USA (rebecca@amath.washington.edu), US;(2) Biomathematics Program, Box 8203, North Carolina State University, Raleigh, NC 27695-8203, USA (lubkin@eos.ncsu.edu), US;(3) Department of Applied Mathematics, Box 352420, University of Washington, Seattle, WA 98195-2420, USA (murrayjd@amath.washington.edu)., US |
| Abstract: | A variety of spatial patterns are formed chemotactically by the bacteria Escherichia coli and Salmonella typhimurium. We focus in this paper on patterns formed by E. coli and S. typhimurium in liquid medium experiments. The dynamics of the bacteria, nutrient and chemoattractant are modeled mathematically and give rise to a nonlinear partial differential equation system. We present a simple and intuitively revealing analysis of the patterns generated by our model. Patterns arise from disturbances to a spatially uniform solution state. A linear analysis gives rise to a second order ordinary differential equation for the amplitude of each mode present in the initial disturbance. An exact solution to this equation can be obtained, but a more intuitive understanding of the solutions can be obtained by considering the rate of growth of individual modes over small time intervals. Received: 10 March 1998 / Revised version: 7 June 1998 |
| Keywords: | : Chemotaxis Partial differential equations Bacteria Mathematical Modeling Pattern formation |
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