Analysis of the effects of immune cell motility and chemotaxis on target elimination dynamics.

White blood cells of the immune system must encounter specific targets such as bacteria, malignant cells, virus-infected cells or other cells of the immune response in order to carry out their function of protecting the host from infectious and malignant disease. To analyze the dynamics of this process, a mathematical model has been developed for elimination of proliferating targets by a constant population of motile immune system cells in two dimensions. Encounter is assumed to be the rate-limiting step for elimination. This model makes use of a previously derived analysis of single cell-target encounter times, which yields an encounter rate constant that is incorporated into a kinetic conservation equation for target number density. This paper focuses on the influence of directed cell movement, or chemotaxis, as well as other cell motility properties, such as cell speed and persistence, on target elimination dynamics. A particularly significant result is that a given relative decrease in chemotactic responsiveness leads to much more severe deficiencies in target clearance rates for low levels of baseline chemotactic responsiveness than for high levels of baseline responsiveness. The general model results are then applied to the particular example of bacterial clearance from the lung surface by alveolar macrophages. It is shown that moderate levels of macrophage chemotactic responsiveness, similar to those measured in vitro, can account for the experimentally observed rates of bacterial elimination from the lung for typical values of bacterial specific growth rate and alveolar macrophage number density.