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A chemical kinetics model is described for the regulation of gene expression by the progressive binding of regulatory molecules to specific binding sites on DNA. Chemical rate equations are formulated and solved for the accumulation of regulatory molecules on DNA, the change in the level of induced mRNA, and the change in the level of the encoded protein in the activated tissue. Some special cases are examined, including that of an activation threshold created by a requirement for the binding of a minimum number of regulatory molecules prior to gene activation. Experimental data for several hormone-activated genetic systems are analyzed in the frame of the proposed model, and kinetic parameters are predicted. The model accounts for a number of experimental characteristics of hormone-inducible genetic systems, including the existence of a lag in the time course of mRNA accumulation, the sigmoidal curve of induced mRNA kinetics, the effect of hormone on mRNA stabilization, and the induction parameters observed when hormone analogues are used. The model also provides an explanation for the phenotypes of genetic variants with altered inducibility as changes in the molecular kinetic parameters of gene activity.

The determination of receptor-igand dissociation constants from displacement data has been restricted until recently to the condition of receptor saturation, in which the concentration of receptor is negligible as compared to the displaced ligand and the displacing ligand used. This restriction has lately been removed since an accurate method has been developed for the determination of the dissociation constants for all experimental conditions for a system that includes a single type of binding site. In many cases, however, there are two types of receptor binding sites that exhibit different affinities toward the ligand. The present study provides an analytic solution for the problem of determination of the two dissociation constants as well as the proportion of the two receptor types. The formal derivation of the equations is described, along with analysis of a displacement simulation. The sensitivity of the method to the ratio between the two dissociation constants is also investigated.