Specific allowance for antibody bivalence in the determination of dissociation constants by kinetic exclusion assay

Theory that takes rigorous account of antibody bivalence in the characterization of immunospecific reactions by kinetic exclusion assay is presented. In addition to reinforcing the basic correctness of quantitative expressions currently being used for the determination of dissociation constants (K_d) by this method, the current study highlights a requirement for conformity of the system with critical assumptions/approximations therein. Published results for the interaction between the extracellular domain of human insulin-like growth factor (hIGFR) and anti-hIGFR are used to illustrate aspects of the theoretical predictions for a system to which those assumptions/approximations may well apply; and those for a cadmium–ethylenediaminetetraacetic acid (Cd–EDTA) antibody interaction to emphasize the consequences of adopting the same analytical procedure in a situation where one of those assumptions does not apply. The major weakness of current protocols for the characterization of antigen–antibody interactions by kinetic exclusion assay is an absence of any check on the likely magnitude of the probability of antibody capture by the affinity beads—a parameter that needs to be 5% or lower for validity of the quantitative expression on which the analysis is based.