| Abstract: | A mathematical model is developed to elucidate the effects of biophysical transport processes (nutrient diffusion, cell motility, and chemotaxis) along with biochemical reaction processes (cell growth and death, nutrient uptake) upon steady-state bacterial population growth in a finite one-dimensional region. The particular situation considered is that of growth limitation by a nutrient diffusing from an adjacent phase not accessible to the bacteria. It is demonstrated that the cell motility and chemotaxis properties can have great influence on steady-state population size. In fact, motility effects can be as significant as growth kinetic effects, in a manner analogous to diffusion- and reaction-limited regimes in chemically reacting systems. In particular, the following conclusions can be drawn from our analysis for bacterial populations growing at steady-state in a confined, unmixed region: (a) Random motility may lead to decreased population density; (b) chemotaxis can allow increased population density if the chemotactic response is large enough; (c) a species with superior motility properties can outgrow a species with superior growth kinetic properties; (d) motility effects become greater as the size of the confined growth region increases; and (e) motility effects are diminished by significant mass-transfer limitation of the nutrient from the adjacent source phase. The relationships of these results for populations to previous conclusions for individual cells is discussed, and implications for microbial competition are suggested. |
