Measurement of bacterial random motility and chemotaxis coefficients: II. Application of single‐cell‐based mathematical model

Abstract

A quantitative description of bacterial chemotaxis is necessary for making predictions about the migratory behavior of bacterial populations in applications such as biofilm development, release of genetically engineered bacteria into the environment, and in situ bioremediation technologies. The bacterial chemotactic response is characterized by a mathematical model which relates individual cell properties such as swimming speed and tumbling frequency to population parameters, specifically the random motility coefficient and the chemotactic sensitivity coefficient. Our model includes a nonlinear dependence of the chemotactic velocity on the attractant gradient as well as a dependence of the random motility coefficient on the temporal and spatial attractant gradients, both of which previous analyses have neglected. As we will show, these aspects are critical for interpreting the results from experiments like those performed in the stopped-flow diffusion chamber (SFDC) because the initial temporal and spatial gradients are very steep. Our analysis demonstrates that values for the random motility coefficient and chemotactic sensitivity coefficient can be obtained from experimental plots of net cell redistribution from initial conditions versus the square root of time. Values for these parameters are determined from experimental measurements of bacterial population distributions in the SFDC as described in the companion article. Using parameter values determined from independent experiments, μ = 1.1 ± 0.4 ± 10⁻⁵ cm²/s and χ₀ = 8 ± 3 ± 10⁻⁵ cm²/s, excellent agreement is found between theoretically predicted bacterial density profiles and actual experimental profiles for Escherichia coli K12 responding to fucose over two orders of magnitude in initial attractant concentration. Thus, our model captures the concentration dependence of this behavioral response satisfactorily in terms of cell population parameters which are derived from individual cell properties and will therefore be useful for making predictions about the migratory behavior of bacterial populations in the environment.