Development of mathematical models for an in vitro-phagocytosis test system

Dependence of macrophage phagocytic efficacy on antibody concentration

Macrophages ingest the fungus Cryptococcus neoformans only in the presence of opsonins, and this provides a remarkably clean system for the detailed analysis of phagocytosis. This system is also unusual in that antibody-mediated phagocytosis involves ingestion through both Fc and complement receptors in the absence of complement. Mathematical modeling was used to analyze and explain the experimental data that the macrophage phagocytic index increased with increasing doses of antibody despite saturating concentrations and declined at high concentrations. A model was developed that explains the increase in phagocytic index with increasing antibody doses, differentiates among the contributions from Fc and complement receptors, and provides a tool for estimating antibody concentrations that optimize efficacy of phagocytosis. Experimental results and model calculations revealed that blocking of Fc receptors by excess antibody caused a reduction in phagocytic index but increased phagocytosis through complement receptors rapidly compensated for this effect. At high antibody concentrations, a further reduction in phagocytic index was caused by interference with complement receptor ingestion as a consequence of saturation of the fungal capsule. The ability of our model to predict the antibody dose dependence of the macrophage phagocytic efficacy for C. neoformans strongly suggest that the major variables that determine the efficacy of this process have been identified. The model predicts that the affinity constant of the opsonic antibody for the Fc receptor and the association-dissociation constant of antibody from the microbial antigen are critical parameters determining the efficacy of phagocytosis.