Chemotaxis and chemokinesis in eukaryotic cells: the Keller-Segel equations as an approximation to a detailed model.

More than 20 years after its proposal, Keller and Segel's model (1971, J. theor. Biol., 30, 235-248) remains by far the most popular model for chemical control of cell movement. However, before the Keller-Segel equations can be applied to a particular system, appropriate functional forms must be specified for the dependence on chemical concentration of the cell transport coefficients and the chemical degradation rate. In the vast majority of applications, these functional forms have been chosen using simple intuitive criteria. We focus on the particular case of eukaryotic cell movement, and derive an approximation to the detailed model of Sherratt et al. (1993, J. theor. Biol., 162, 23-40). The approximation consists of the Keller-Segel equations, with specific forms predicted for the cell transport coefficients and chemical degradation rate. Moreover, the parameter values in these functional forms can be directly measured experimentally. In the case of the much studied neutrophil-peptide system, we test our approximation using both the Boyden chamber and under-agarose assays. Finally, we show that for other cell-chemical interactions, a simple comparison of time scales provides a rapid check on the validity of our Keller-Segel approximation.