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Receptor Agonist/Antagonist Models

Mathematical representations of drug interactions with receptors, detailing binding affinities and efficacy, crucial for understanding drug action.
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The statement of the theorem

Consider the binding equilibrium between a receptor RR, a ligand LL, and a drug DD. The fractional occupancy θ\theta of the receptor sites is defined by the generalized binding equation: \n\nθ=[L]+KA[D]KD+[L]+KA[D]\theta = \frac{[L] + K_{A} [D]}{K_{D} + [L] + K_{A} [D]} \n\nwhere [L][L] is the concentration of the natural ligand, [D][D] is the concentration of the drug, KDK_{D} is the dissociation constant for the natural ligand, and KAK_{A} is the apparent affinity constant for the drug, derived from the ratio of the binding rate constants KA=kon,D/koff,DK_{A} = k_{on, D} / k_{off, D}. For an antagonist, the binding term is modeled such that the drug binding does not induce a conformational change leading to signal activation.
Source: Wikipedia