B lymphocyte responses to the cross-linking of surface Ig (sIg) are known to be inhibited, when IgG is the cross-linking agent, by the concurrent binding of the Fc portion of the IgG to Fc gamma R. We present a mathematical framework for designing and analyzing experiments aimed at uncovering the inhibition mechanism(s). From our model, we calculate concentrations of receptors and ligands in the different cell surface states, at equilibrium or as a function of time. IgG can cross-link surface receptors in three ways, i.e., by bridging two sIg molecules without Fc binding, by bridging two sIg while binding as well to an Fc gamma R, and by binding to an Fc gamma R and only one sIg. We show how the concentrations or fractions of these distinct cross-linked states depend on experimentally manipulable variables, including the concentrations of intact IgG, bivalent and monovalent IgG fragments, and agents that block Fc binding. Then, using simple signal/response relationships, reflecting active and passive mechanisms of Fc-mediated inhibition, we simulate the results of a variety of experiments. In cases where published experimental results are available, we find that the qualitative predictions of our general model are consistent with the data and that comparisons of simulations with available data provide some quantitative information about the parameters governing the cell surface signaling events. In particular, comparison of model predictions with published experiments on the kinetics of IgG-induced inositol trisphosphate production indicate that sIg cross-links form more rapidly than sIg-Fc gamma R "co-cross-links." Further, IgG-sIg bonds stabilize Fc attachments, i.e., the dissociation of IgG from Fc gamma R is slowed significantly when the IgG is also cross-linked to sIg. Predictions of the model suggest other experiments and ways of presenting the data that will help to identify relationships between the molecular signaling events occurring on the cell surface and the various cellular responses.

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