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Biased random walk models for chemotaxis and related diffusion approximations

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Summary

Stochastic models of biased random walk are discussed, which describe the behavior of chemosensitive cells like bacteria or leukocytes in the gradient of a chemotactic factor. In particular the turning frequency and turn angle distributions are derived from certain biological hypotheses on the background of related experimental observations. Under suitable assumptions it is shown that solutions of the underlying differential-integral equation approximately satisfy the well-known Patlak-Keller-Segel diffusion equation, whose coefficients can be expressed in terms of the microscopic parameters. By an appropriate energy functional a precise error estimation of the diffusion approximation is given within the framework of singular perturbation theory.

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  1. Institut für Angewandte Mathematik, Im Neuenheimer Feld 294, D-6900, Heidelberg, Federal Republic of Germany

    Wolgang Alt

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  1. Wolgang Alt
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Alt, W. Biased random walk models for chemotaxis and related diffusion approximations. J. Math. Biology 9, 147–177 (1980). https://doi.org/10.1007/BF00275919

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  • DOI: https://doi.org/10.1007/BF00275919

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