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 (EC 50 ) 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.dose-response | Michaelis-Menten | gene expression | steroid receptors | glucocorticoids | pharmacology I n ligand-mediated gene induction, the amount of gene expressed depends on the amount of ligand present. Thus, the specific shape and properties of the dose-response curve of gene induction, which is of crucial importance for development, differentiation, and homeostasis in many biological systems, provide a quantitative means for probing the gene-induction process. In many cases, the dose-response curve in gene induction obeys a sigmoidal curve, but not all sigmoidal curves have the same shape. For example, a dose-response curve obeying a first-order Hill equation or function (Hill coefficient equal to 1) goes from 10 to 90% of maximum activity over an 81-fold change in ligand concentration, whereas only a 9-fold change is required in a secondorder Hill function, which thus has a different shape (Fig. S1). (A first-order Hill function is sometimes called a Michaelis-Menten function.) Depending upon the shape of the dose-response curve, the responsiveness of gene induction to the same variation in ligand concentration will differ greatly. In addition to the shape, the position or potency [i.e., concentration required for 50% of maximal response (EC 50 )] and maximum activity (A max ) of the dose-response curve are required to specify the amount of gene expressed for a given amount of ligand. Despite the vital...