Mathematical theory of complex ligand-binding systems applied to free triiodothyronine immunoassays

A theoretical basis for direct immunoassays of free hormones in serum is presented. The multiple-ligand/multiple-site binding theory employed makes it possible to predict the distribution of hormones among exogenous and endogenous binding proteins in the assay mixture. The model allows simulation of assay systems involving any number of ligands and binding sites. The simulation of an assay of free triiodothyronine illustrates the way in which assay parameters such as antibody concentration, antibody affinity, serum dilution, and labeled hormone interactions with serum binding proteins affect the validity of free hormone assays. The simultaneous equations describing these complex binding systems at equilibrium were solved on a personal computer, with the use of commercial mathematics software. This general method for solving and modelling free hormone assay systems provides a tool for predicting the behavior of free-hormone assays.