Effects of the Mechanism of Receptor-Mediated Gene Expression on the Shape of the Dose-Response Curve

A mathematical model of receptor-mediated gene expression that includes receptor binding of natural and xenobiotic ligands, protein synthesis and degradation, and metabolism of the xenobiotic ligand was created to identify the determinants of the shape of the dose-response profile. Values of the model's parameters were varied to reflect alternative mechanisms of expression of the protein. These assumptions had dramatic effects on the computed response to a bolus dose of the xenobiotic ligand. If all processes in the model exhibit hyperbolic kinetics, the dose-response curves can appear sigmoidal but actually be linear with a positive slope at low doses. The slope of the curve only approached zero at low dose, indicative of a threshold for response, if binding of the xenobiotic ligand to the receptor exhibited positive cooperativity (ligand binding at one site increases the affinity for ligand at another binding site on the receptor). Positive cooperativity in the rate-limiting step of protein synthesis produced dose-response curves which were "U-shaped" at low doses, also indicative of a threshold. Positive cooperativity in the metabolism of the xenobiotic ligand produced dose-response curves that increased more rapidly than linearly with increasing dose. The model illustrates the fact that response cannot be predicted from qualitative mechanistic arguments alone; any assessment of risk to health from xenobiotic chemicals must be based on a detailed quantitative examination of the kinetic behavior of each chemical species individually.