Homogeneous and Heterogeneous Binding

At low r values, that is, when ligand concentrations are low, only the binding sites with the highest K s will start to fill with ligand. Hence the slope of the plot at these values is steep. As ligand concentration 

Since we have already derived the relationship, r = n K C — C Ka r, terms can be arranged to yield 

and r/(n — r) axis intercept of log If a population of naturally raised antihapten antibodies is subjected to this analysis, the plot will actually have a slope considerably less than 1. This slope is called the heterogeneity index and modifies the equation  

This relationship is truly valid only for a Gaussian type of distribution of binding constants around the mean Ka for the population, and no conclusions can be drawn from the heterogeneity index about the number of antibodies present when the index is less than 1.0. Because of the imprecision of the measurement, even when the index is 1.0 or close to that figure, more than one antibody may be present (Pincus et aL, 1968). 

The binding equilibrium between antibody binding site and ligand is composed of two rate reactions a forward reaction, whose velocity, Vi, is 

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