Derivation of antibody distribution from experimental binding data

It can be demonstrated that antibody populations cannot be suitably described in terms of a Sips distribution. Use of the Stieltjes transform allows instead derivation, fromexperimentalbindingdata, of the most probable distributionof the association constants. From graphical interpolation of the experimentaldata four parameters can be obtained, which characterize a satisfactory bimodal distribution. By this procedure, analysis ofdata taken at different times of a humoral immune response, indicates that the relative abundance of the two sub-populations, rather than their mean association constant, is mainly affected by time or by variations of antigen dose. By use of the same procedure it is also possible to show that, at least as far as haptens are concerned, the slope of the 50% antigen-binding plot, often taken as a measure of the “avidity” ofantibodies, is instead a function of the relative weight of the two sub-populations and of the spread of each of them.