Dependence of macrophage phagocytic efficacy on antibody concentration

Abstract

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.

FIG. 1.

Experimental counts of the number of phagocytized microbes (per 100 macrophages) as a function of antibody concentration (A) and in the setting of blocked complement (C3R) receptors (B). Error bars represent standard deviations.

FIG. 2.

Experimental counts of the number of phagocytized microbes (per 100 macrophages) as a function of time for antibody concentrations of 10 and 100 μg/ml (A) and 0, 250, 500, and 100 μg/ml (B). Error bars represent standard deviations.

FIG. 3.

Graphs of the antibody binding to the microbe capsule: the amount bound after 2 h as a function of the initial concentration (A) and the dynamics of binding (B).

FIG. 4.

Experimental counts of the number of phagocytized microbes, P_I (per 100 macrophages), as a function of the initial antibody concentration c₀. IgG1 was incubated with C. neoformans cells for 1 h to obtain near-saturation occupancy of the binding sites on the C. neoformans capsule. C. neoformans cells were then separated from antibody and added to a macrophage monolayer in the fresh medium (see Materials and Methods). The two sets of results represent experiments without and with blocking of complement receptors. The results of experiments with blocking represented in panel A were obtained with partial blocking of complement receptors, and those in panel B were obtained with complement receptors fully blocked. Error bars represent standard deviations.

FIG. 5.

Experimental counts of the number of phagocytized microbes, P_I (per 100 macrophages), as a function of the initial antibody concentration, c₀. IgG1 was incubated with C. neoformans cells for an hour and a half to obtain near-saturation occupancy of the binding sites on the C. neoformans capsule. C. neoformans (in the solution) was then added to the macrophage monolayer (see Materials and Methods). The two sets of results represent experiments without and with (partial) blocking of complement (C3R) receptors. Error bars represent standard deviations.

FIG. 6.

Plots of efficacy of phagocytosis computed from the experimental data. We computed the efficacy using the formula r_T = −ln(1 − P_I/200)/120 and experimental data from the three sets of experiments presented in Fig. 4 and 5. The efficacy of phagocytosis is plotted as a function of the initial concentration, c₀, of antibody (A) and as a function of the fraction (A_P/L_P) of the antibody binding sites on the C. neoformans capsule occupied by IgG (B). A summary of experimental conditions in given in Table 4.

FIG. 7.

Comparison of the model simulations and experimental results presented in Fig. 4A. Panels A and B present the same data and simulations but using different scales. The same legend applies to both panels. Error bars represent standard deviations. Summaries of experimental conditions and simulation parameters are given in Tables 4 and 5.

FIG. 8.

Comparison of the model simulations and experimental results presented in Fig. 4B. Panels A and B present the same data and simulations but using different scales. The same legend applies to both panels. Error bars represent standard deviations. Summaries of experimental conditions and simulation parameters are given in Tables 4 and 5.

FIG. 9.

Comparison of the model simulations and experimental results presented in Fig. 5. Panels A and B present the same data and simulations but using different scales. The same legend applies to both panels. Error bars represent standard deviations. Summaries of experimental conditions and simulation parameters are given in Tables 4 and 5.