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

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Abstract

The mathematical model developed by Riveroet 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 relates 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 (Fordet al., 1991Biotechnol. Bioengng.37, 647–660; For 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 intepretation of data reported by Dalquistet al. (1972,Nature New Biol. 236, 120–123) forSalmonella typhimurum validating the mathematical model and supportin the involvement of high and low affinity receptors for serine chemotaxis by these cells.

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Author notes

  1. Roseanne M. Ford

    Present address: Department of Chemical Engineering, University of Virginia, 22903, Charlottesville, VA, USA

  2. Douglas A. Lauffenburger

    Present address: Department of Chemical Engineering, University of Illinois, 61801, Urbana, IL, USA

Authors and Affiliations

  1. Department of Chemical Engineering, University of Pennsylvania, 19104, Philadelphia, PA, USA

    Roseanne M. Ford & Douglas A. Lauffenburger

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  1. Roseanne M. Ford
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  2. Douglas A. Lauffenburger
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Ford, R.M., Lauffenburger, D.A. Analysis of chemotactic bacterial distributions in population migration assays using a mathematical model applicable to steep or shallow attractant gradients. Bltn Mathcal Biology 53, 721–749 (1991). https://doi.org/10.1007/BF02461551

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