The heterogeneity of antibodies with respect to equilibrium constants: Calculation by a new method using delta functions,and analysis of the results

A method of data analysis has been developed which approximates the probability density of association constants of the reaction of hapten with antibody by a minimum number of delta functions, and alternatively, by a large number of delta functions. The method has been computerized and found able to approximate any physically possible affinity distribution.We have calculated the delta function distributions which describe known distributions of association constants and analyzed experimental data,. From 2 to 4 delta funticons we3re required to describe the probability density of Sips distributions. Not more than three delta functions were needed to describe the probability density functions of each of three antibody populations obtained from pooled antisera. These delta function distributions were found in one case to fit the data significantly more accurately than a Sips distribution. In the other two cases the fit was about the same as the Sips distribution. Affinity heterogeneity analysis using a large number of delta functions gave roughly equivalent results in terms of closeness of fit to the data to the results using a minimum number of delta functions. It is shown that binding measurements do not contain sufficient information to prove homogeneity of antibody. An analysis of factors affecting the resolution of delta functions is given.