Adaptation of the Müller method to allow quantitative characterization of the affinity and cross-reactivity of antibodies by competitive radioimmunoassay.

A quantitative expression is derived for the evaluation of antigen-antibody affinity constants from radioimmunoassays for the completely general situation in which antigen and antibody are both multivalent. The theoretical analysis is then extended to encompass quantitative characterization of the competitive inhibition observed in screening tests for cross-reactivity of antibody with structural analogs of the eliciting antigen. These procedures are illustrated with a radioimmunological study of the cross-reactivity of a desipramine-elicited monoclonal antibody with other tricyclic antidepressants. An unexpected finding to emerge from this immunochemical study is the demonstration that a single affinity constant suffices to describe the interaction of desipramine with a polyclonal antibody elicited by this univalent antigen.