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# Equations Derived From Drug–Receptor Interactions

It is important not to confuse the term potency with affinity or the term intrinsic activity with efficacy.

EQUATIONS DERIVED FROM DRUG–RECEPTOR INTERACTIONS

It is important not to confuse the term potency with affinity or the term intrinsic activity with efficacy. The constants that relate an agonist A and its receptor R to the response may be represented as follows:

Affinity is k1/k2, and efficacy is represented by k3. Thus, affinity and efficacy represent kinetic constants that re-late the drug, the receptor, and the response at the mo-lecular level. Affinity is the measure of the net molecu-lar attraction between a drug (or neurotransmitter or hormone) and its receptor. Efficacy is a measure of the efficiency of the drug–receptor complex in initiating the signal transduction process. In contrast, potency and in-trinsic activity are simple measurements, respectively, of the relative positions of dose–response curves on their horizontal axes and of their relative maxima. Affinity is one of the determinants of potency; efficacy contributes both to potency and to the maximum effect of the ago-nist. Figure 2.4 shows that drug c has less efficacy (and less intrinsic activity) than either drug a or drug b. However, in contrast to intrinsic activity, no numerical value of efficacy can be calculated from the data pre-sented. Unfortunately, the terms potency and efficacy are frequently used in a loose and misleading manner.

The mathematical relationship of response to effi-cacy and affinity is the following:

This equation states that the ratio of the response (EA) to a given concentration of an agonist to the maximum response (Em) of the test system, such as an isolated strip of muscle, is a function (f) of efficacy (e) times the concentration of the agonist ([A]) divided by the disso-ciation constant (KA) plus the concentration of the ago-nist. KA is the reciprocal of the affinity constant and, un-der equilibrium conditions,

KA = [R][A] / [RA]

[R] is the concentration of free receptors and [RA] is the concentration of receptors bound to agonist. It should be noted that by the use of combinations of agonists and antagonists, dose–response curves, and mathematical relationships, it is possible to estimate the dissociation constants of agonists and antagonists for a given receptor and to estimate the relative efficacy of two agonists acting on the same receptor.

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