Analysis of chemotactic bacterial distributions in population migration assays using a mathematical model applicable to steep or shallow attractant gradients

Abstract

The mathematical model developed by Rivero et al. (1989, Chem. Engng Sci. 44, 2881-2897) is applied to literature data measuring chemotactic bacterial population distributions in response to steep as well as shallow attractant gradients. This model is based on a fundamental picture of the sensing and response mechanisms of individual bacterial cells, and thus related individual cell properties such as swimming speed and tumbling frequency to population parameters such as the random motility coefficient and the chemotactic sensitivity coefficient. Numerical solution of the model equations generates predicted bacterial density and attractant concentration profiles for any given experimental assay. We have previously validated the mathematical model from experimental work involving a step change in the attractant gradient (Ford et al., 1991 Biotechnol. Bioengng, 37, 647-660; Ford and Lauffenburger, 1991, Biotechnol. Bioengng, 37, 661-672). Within the context of this experimental assay, effects of attractant diffusion and consumption, random motility, and chemotactic sensitivity on the shape of the profiles are explored to enhance our understanding of this complex phenomenon. We have applied this model to various other types of gradients with successful interpretation of data reported by Dalquist et al. (1972, Nature New Biol. 236, 120-123) for Salmonella typhimurium validating the mathematical model and supporting the involvement of high and low affinity receptors for serine chemotaxis by these cells.