theoretical framework for gene induction and experimental comparisons

Ligand-mediated gene induction by steroid receptors is a multistep process characterized by a dose-response curve for gene product that follows a first-order Hill equation. This behavior has classically been explained by steroid binding to receptor being the rate-limiting step. However, this predicts a constant potency of gene induction (EC₅₀) for a given receptor-steroid complex, which is challenged by the findings that various cofactors/reagents can alter this parameter in a gene-specific manner. These properties put strong constraints on the mechanisms of gene induction and raise two questions: How can a first-order Hill dose-response curve (FHDC) arise from a multistep reaction sequence, and how do cofactors modify potency? Here we introduce a theoretical framework in which a sequence of steps yields an FHDC for the final product as a function of the initial agonist concentration. An exact determination of all constants is not required to describe the final FHDC. The theory predicts mechanisms for cofactor/reagent effects on gene-induction potency and maximal activity and it assigns a relative order to cofactors in the sequence of steps. The theory is supported by several observations from glucocorticoid receptor-mediated gene induction. It identifies the mechanism and matches the measured dose-response curves for different concentrations of the combination of cofactor Ubc9 and receptor. It also predicts that an FHDC cannot involve the DNA binding of preformed receptor dimers, which is validated experimentally. The theory is general and can be applied to any biochemical reaction that shows an FHDC.