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Theory of ligand binding to heterogeneous receptor populations: Characterization of the free‐energy distribution function

We present a method for characterizing the free‐energy and affinity distributions of a heterogeneous population of molecules interacting with a homogeneous population of ligands, by driving expressions for the moments as functions of experimental binding curve characteristics, and then constructing the distribution as an expansion over a Gaussian basis set. Although the method provides the complete distribution in principle, in practice it is restricted by experimental noise, inaccuracies in data fitting, and the severity with which the distribution deviates from a Gaussian. Limitations imposed by experimental inaccuracies and the requirement of an appropriate analytic function for data fitting were evaluated by Monte Carlo simulations of binding experiments with various degrees of error in the data. Thus a distribution was assumed, binding curves with random errors were generated, and the technique was applied in order to determine the extent to which the characteristics of the assumed distribution could be recovered. Typical inaccuracies in the first two moments fell within experimental error, whereas inaccuracies in the third and fourth were generally larger than standard deviations in the data. The accuracy of these higher‐order moments was invarient for experimental errors ranging from 2 to 10% and may thus be limited, within this range, primarily by the curve fitting procedure. The other aspect of the problem, accurate inference of the distribution, is limited in part by inaccuracies in the moments but more importantly by the extent to which the distribution deviates from a Gaussian. The extensive statistical literature on the problem of inference enables the delineation of specific criteria for estimating the efficiency of construction, as well as for deciding whether certain features of the inferred distribution, such as bimodality, are artifacts of the procedure. In spite of the limitations of the method, the results indicate that the mean and standard deviation are obtainable with greater accuracy than by a Sipsian analysis. This difference is particularly important when the distribution is narrow and width detection is beyond the sensitivity of the Sips plot. The method should be more accurate than the latter as an assay for homogeneity as well as for characterizing the moments, though equally easy to apply.