Application of the law of mass action to design and performance of receptor assays for 1,25(OH)₂ vitamin D

Abstract

The binding of 1,25(OH)₂ vitamin D₃ to its chick duodenal cytosol receptor protein has been analysed on a law of mass action model. Within the limits of experimental error there is such good agreement, when only one binding site is considered, that it is possible to fit the standard assay curve for practical use. Simple pocket-calculator methods are given for this. The equilibrium constant for the reaction, under the conditions used (pH 7.4, 25°C), was 2.1 ± 10¹⁰ 1 ± mol⁻¹. A kinetic analysis under the same conditions yielded forward and backward reaction rate constants of 6.5 ± 10⁶ mol⁻¹ ± s^−l ± 1² and 3.1 ± 10⁻⁴ s^−l ± 1, respectively. The kinetic curve also very closely fitted to the experimental data on the basis of the model. The theory for use of the mass action model to optimize the binding-site concentration to give a minimum absolute error for any measured ligand concentration is presented. The use of the model in assay design, standard curve fitting, quality control and problem solving are discussed.

Key Words:

• Assay
• law of mass action
• 1,25(OH)₂ vitamin D