Journal of Mathematical Biology

, Volume 9, Issue 2, pp 147–177 | Cite as

Biased random walk models for chemotaxis and related diffusion approximations

  • Wolgang Alt


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.

Key words

Chemotaxis Biased random walk Diffusion equations Singular perturbation 


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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Wolgang Alt
    • 1
  1. 1.Institut für Angewandte MathematikHeidelbergFederal Republic of Germany

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