Comparison of Curve Fitting Models for Ligand Binding Assays

In the case of ligand binding assays the relationship between instrumental response and analyte concentration is non-linear, usually either hyperbolic or sigmoidal. As it is not possible to calibrate an assay at all the levels to be measured a suitable method of constructing a concentration-response relationship (the standard curve), based on a limited number of carefully spaced standards is required. The method should be robust and operator independent. The two main approaches that have been used involve empirical and mechanistic (theoretical) models. Empirical models utilise any mathematical function(s) that appears to have the characteristics of the experimentally derived assay data. Empirical models require no understanding of the principles of the assay. Mechanistic models make assumptions about the physico-chemical processes involved in the assay procedure. In practice either single function or spline models are used. The curve fitting solution may be explicit (in the case of spline interpolation), or by least-squares curve fitting regression methods, including polynomial and logistic equations, the latter involving many iterations. Examples of good curve fitting selection are presented and contrasted with inappropriate models in a number of common assay formats.