Model and analysis of chemotactic bacterial patterns in a liquid medium

A variety of spatial patterns are formed chemotactically by the bacteria Es cherichia coli and Salmonella typhimurium. We focus in this paper on patter ns formed by E. coli and S. typhimurium in liquid medium experiments. The d ynamics of the bacteria, nutrient and chemoattractant are modeled mathemati cally and give rise to a nonlinear partial differential equation system. We present a simple and intuitively revealing analysis of the patterns gene rated by our model. Patterns arise from disturbances to a spatially uniform solution state. A linear analysis gives rise to a second order ordinary di fferential equation for the amplitude of each mode present in the initial d isturbance. 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.