Computer Calculation of Multiple Binding Equilibrium Isotherms: Application to the Binding of Bivalent Ligands to Antibodies Interacting with Cell Surface Fc-receptors

A method to calculate multiple binding equilibria by looking for a set of complexes satisfying the conservation principle among sets of concentrations of ligands, receptors satisfying the mass action equations is described. The method replaces complex analytical derivations of equations representing the interactions by the minimization of a single function. The method was implemented for use on microcomputers and applied to the calculation of the binding isotherms of the interactions between a bivalent ligand, a bivalent antibody and the cell surface Fc-receptor. The binding parameters were adjusted to experimental data obtained with P388D1 cells, a monoclonal antibody against DTPA-indium complexes and monovalent and bivalent DTPA-indium haptens. The binding of the antibody and of the haptens to P388D1 cells, as a function of antibody or hapten concentration, was satisfactorily represented using a model in which the antibody molecules bind co-operatively to the Fc-receptor in the presence of cross-linking bivalent hapten. The method can thus be used as a general tool for the numeric calculation of complex equilibrium involving simultaneous interactions of multiple receptors and ligands.