Probability analysis of the interaction of antibodies with multideterminant antigens in radioimmunoassay: application to the amino terminus of the beta chain of hemoglobin S.

A simple theory, based on probability, is developed for the analysis of the interaction of multideterminant antigens with multispecific antisera in radioimmunoassays. The theory is completely general except for the assumptions that the determinants be unique and bind antibodies independently of one another. The analysis shows that the shape of the curve of bound/free as a function of the antigen concentration is very sensitive to the multiplicity of determinants. The predictive ability of the theory is illustrated for the case of antibodies to subregions of the N-terminal third of the beta chain of sickle hemoglobin, studied using antisera fractionated on affinity chromatographic columns of synthetic peptides. The implications for obtaining quantitative binding data by radioimmunoassay for natural antigens, which almost universally have more than one antigenic determinant on the same molecule, are discussed.