A mathematical model was created to examine how xenobiotic ligands that bind to nuclear receptor proteins may affect transcriptional activation of hormone-regulated genes. The model included binding of the natural ligand (e.g. hormone) and xenobiotic ligands to the receptor, binding of the liganded receptor to receptor-specific DNA response sequences, binding of co-activator or co-repressor proteins (Rp) to the resulting complex, and the consequent transcriptional rate relative to that in the absence of the xenobiotic agent. The model predicted that the xenobiotic could act as a pure agonist, a pure antagonist, or a mixed agonist whose dose–response curve exhibits a local maximum. The response to the agent depends on the affinity of the liganded receptor–DNA complex for binding additional transcription factors (e.g. co-activator proteins). An inverted U-shaped dose–response occurred when basal levels of the natural ligand did not saturate receptor binding sites and the affinity for co-activator is weaker when the xenobiotic ligand is bound to the receptor than when the endogenous ligand is bound. The dose–response curve shape was not dependent on the affinity of the receptor for the xenobiotic agent; alteration of this value merely shifted the curve along the concentration axis. The amount of receptor, the density of DNA response sequences, and the affinity of the DNA-bound receptor for Rp determine the amplitude of the computed response with little overall change in curve shape. This model indicates that a non-monotonic dose–response is a plausible outcome for xenobiotic agents that activate nuclear receptors in the same manner as natural ligands
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