Neutralization of the biological activity of cytokines and other protein effectors by antibody: theoretical formulation of antibody titration curves in relation to antibody affinity.

Patients treated with interferons, other cytokines, or various biologically active proteins may form neutralizing antibodies, which can adversely affect clinical outcome. It is therefore important to understand how antibodies neutralize such soluble protein antigens and how best to quantitate such antibodies. By applying the mass action law to antigen-antibody reactions, we previously developed a mathematical model applicable in two situations: first, for antibodies having low affinity for the antigen concerned (the Constant Proportion (CP) case), and, second, for antibodies having high affinity (the Fixed Amount (FA) case). The results allowed calculation of neutralization titers which were independent of the particular assay method used. Neutralization by antibodies of intermediate affinity, however, requires different mathematical treatment because the mode of neutralization does not fit the two cases mentioned above. In this paper, theoretical neutralization curves were derived, based on the same mathematical model, for antibodies of intermediate affinity. We show that the slope of the neutralization curve relating residual active antigen to the concentration of antibodies is determined by the antibody association constant and the molar concentration of the effector antigen. It is therefore possible to infer the magnitude of the association constant from the observed neutralization curve. We show that values obtained for the neutralization titer of antibodies of intermediate affinity by the use of the formula previously described for the Fixed Amount and Constant Proportion cases may deviate from the theoretically sound values; the magnitude of the deviation can be estimated by applying the formulas described herein. These relationships should apply generally to antibody neutralization reactions with all biologically active soluble protein effector molecules that have a single and nonrepetitive epitope.