Abstract
A spatially distributed mathematical model is developed to elucidate the effects of chemical diffusion and cell motility as well as cell growth, death, and substrate uptake on steady-state bacterial population growth in a finite, one-dimensional, nonmixed region. The situation considered is growth limited by a diffusing substrate from an adjacent phase not accessible to the bacteria. Chemotactic movement is not considered in this paper; we consider only "randomwalk"-type random motility behavior here. The following important general concepts are suggested by the results of our theoretical analysis: (a) The significance of random motility effects depends on the magnitude of the ratioμ/kL (2), whereμ is the bacterial random motility coefficient,k is the growth rate constant, andL is the linear dimension of the confined growth region. (b) In steady-state growth in a confined region, the bacterial population size decreases asμ increases. (c) The effect ofμ on population size can be great; in fact, sometimes relative population sizes of two species can be governed primarily by the relative values ofμ rather than by the relative values ofk.
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