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A mathematical theory of competitive labelled-ligand assays was developed with the intention of theoretically re-evaluating the optimal assay conditions and precision data of assay systems established by experiment. Our theory is based upon the assumptions of a simple bimolecular reaction mechanism, homogeneous reactants, as well as kinetically indistinguishable labelled and non-labelled ligands. The general case of two-step (non-equilibrium) assay was considered including the one-step (equilibrium) assay as a special case. The solution of the system of corresponding kinetic differential equations was used to mathematically construct standard curves. Furthermore, intraassay precision profiles and indices as well as detection limits were calculated considering solely the pipetting error, epsilon, as a source of experimental error. A procedure was outlined to mathematically determine the optimal incubation conditions for any assay system targeted to a given analyte concentration, P, at which the standard deviation of assay results is to be minimized. Estimates of both the content of binding sites and the equilibrium constant, K, of the specific binding agent are necessary, and these can be derived from Scatchard plots. For six RIA systems, of which three were one-step and three were two-step assays, experimental assay conditions and precision data were compared with theoretical predictions. Experimentally determined antibody binding site concentrations agreed fairly well with those independently evaluated by mathematical optimization. Mean precision indices, defined as constituting an average over the complete precision profile, were found to be within the theoretically predicted range, i.e. two- to threefold the pipetting error.(ABSTRACT TRUNCATED AT 250 WORDS)

clinical chemistry and laboratory medicine

Mathematical Modelling of Competitive Labelled-Ligand Assay Systems. Theoretical Re-Evaluation of Optimum Assay Conditions and Precision Data for Some Experimentally Established Radioimmunoassay Systems