The receptor occupation theory of drug action equates drug effect to receptor occupancy. The intensity of drug effect is proportional to the number of receptors that are occupied by drug and the maximum effect occurs when all receptors are occupied by drug.

The relationship between drug effect and the concentration of free drug at the site of action (C) can be described at equilibrium by the following equation:

Effect =

Maximum effect • C

where the maximum effect is the intensity of the pharmacological effect that occurs when all of the receptors are occupied, and Kd, which equals k2/k1, is the equilibrium dissociation constant of the drug-receptor complex. The dissociation constant (Kd) is also a measure of the affinity of a drug for its receptor, analogous to the Michaelis-Menten constant (Km), which is a measure of the affinity of a substrate for its enzyme. The expression C/(Kd + C) in this equation represents the fraction of receptors that are occupied with drug. When C ^ Kd, the expression equals 1 (i.e., all of the receptors are occupied with drug), and Effect = Maximum effect.

The equation relating a drug's pharmacological effect to its concentration describes a hyperbolic function that is shown graphically in Figure 18.4A. As free drug concentration increases, the drug effect asymptotically approaches the maximum effect. When the free drug concentration on the x-axis is transformed to a logarithmic scale, the dose-effect curve becomes sigmoidal, with a central segment that is nearly log-linear (Figure 18.4B). Semilogarithmic dose-effect curves allow for a better assessment of the dose-effect relationship at low doses and of a wide range of doses on the same plot. The EC50 is the dose at which 50% of the maximum effect is produced or

FIGURE 18.4 Dose-effect curves plotted using a (A) linear or (B) logarithmic scale for drug dose/concentration on the x-axis. The function relating effect to dose/concentration is based on the receptor occupation theory, described in the text. The relationship is nonlinear and with each increment in dose/concentration there is a diminishing increment in effect. EC5 0 is the dose/concentration producing half of the maximum effect.

FIGURE 18.4 Dose-effect curves plotted using a (A) linear or (B) logarithmic scale for drug dose/concentration on the x-axis. The function relating effect to dose/concentration is based on the receptor occupation theory, described in the text. The relationship is nonlinear and with each increment in dose/concentration there is a diminishing increment in effect. EC5 0 is the dose/concentration producing half of the maximum effect.

the concentration of drug at which the drug is half-maximally effective. On a semilogarithmic plot, the EC50 is located at the midpoint, or inflection point, of the curve. When the relationship between receptor occupancy and effect is linear, the Kd = EC50. If there is amplification between receptor occupancy and effect, such as if the receptor has catalytic activity when the receptor ligand is bound, then the EC50 lies to the left of the KD.

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