The effect of chemotaxis and chemokinesis on leukocyte locomotion: a new interpretation of experimental results.

A mathematical model is developed to describe the motion of leukocytes through a Boyden chamber. The model is based on the Keller-Segel model of cell motion and comprises three partial differential equations which describe the evolution of the neutrophils, the chemoattractant, and a neutrophil-derived chemokinetic factor. Where other authors have concentrated on chemotaxis, here attention is focused on the manner in which the chemokinetic factor influences neutrophil locomotion. Numerical simulations show how the number of neutrophils initially placed on top of the chamber affects cellular motion through the system and reproduce the qualitative behaviour observed by Takeuchi & Persellin (Am. J. Physiol. 236, C22-C29). In particular, the simulations show how dense packing of the neutrophils increases the levels of the chemokinetic factor. This enhances random cell motion and increases the speed with which the neutrophils reach the source of chemoattractant. For a particular asymptotic limit of the system parameters, the model reduces to a nonlinear partial differential equation for the neutrophils. Similarity solutions of this caricature model yield algebraic expressions relating the speed with which the neutrophil front penetrates into the chamber to the number of neutrophils initially placed on top of it. The implications of the results are also discussed.