Stochastic model of leukocyte chemosensory movement

Polymorphonuclear leukocyte (PMN) chemotaxis has been examined under conditions which allow phase microscope observations of cells responding to controlled gradients of chemotactic factors. With this visual assay, PMNs can be seen to orient rapidly and reversibly to gradients of N-formylmethionyl peptides. The level of orientation depends upon the mean concentration of peptide present as well as the concentration gradient. The response allows an estimation of the binding constant of the peptide to the cell. In optimal gradients, PMNs can detect a 1% difference in the concentration of peptide. At high cell densities, PMNs incubated with active peptides orient their locomotion away from the center of the cell population. This orientation appears to be due to inactivation of the peptides by the cells. Such inactivation in vivo could help to limit an inflammatory response. Show more

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 distribution 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. Show more