Mathematical analysis of cell-target encounter rates in two dimensions. The effect of chemotaxis

The process by which cells encounter their targets is the first step of a number of cell functions involved in the immune response, such as cell-mediated cytotoxicity and phagocytic ingestion of foreign material. In many instances, this encounter may be rate-limiting, and therefore it is important to understand what factors influence the encounter rate. One key aspect of cell-target encounter is the motility behavior of the cell in the vicinity of a target. This movement may be entirely random, or there may be a directed, or chemotactic, component to it. In this paper we focus on the effects of cell motility properties, and particularly the chemotactic directional bias, on the rate of cell-target encounter. Specifically, we derive an expression for the mean encounter time of cells that meet targets in two dimensions as a function of the cells' directional orientation bias. We show that a modest degree of bias can reduce the mean encounter time by orders of magnitude, while nearly perfect directional bias offers little additional benefit. We illustrate the application of these results to a particular example system: alveolar macrophages removing inhaled particles and bacteria from the lung surface.