General quantitative treatment for the binding of divalent antibodies to antigens immobilized on a solid phase

A general expression for the binding isotherm of divalent antibodies to antigens bound to solid lattices with excluded volume effects is derived by using a statistical mechanical approach. The method is based on matrix generation of the partition function for the system, from which the degree of saturation of the antigen lattice may be computed directly. The saturation function has a simple form that under appropriate conditions reduces to forms derived previously for simpler cases (such as monovalent binding with and without excluded volume effects). Solution by numerical techniques of a simple secular equation for each concentration of antibody allows computation of the saturation function. Thus, the binding expression derived is easily fit to any set of binding data obtained and results in the determination of such parameters as intrinsic affinity constants, length of excluded space (and hence molecular size), and number of sites. It predicts that under conditions wherein divalent binding is favored over univalent binding, biphasic adsorption isotherms will be obtained.