## Equations Derived From Drugreceptor 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 relate the drug, the receptor, and the response at the molecular level. Affinity is the measure of the net molecular 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 intrinsic 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 agonist. 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 presented. Unfortunately, the terms potency and efficacy are frequently used in a loose and misleading manner.

The mathematical relationship of response to efficacy and affinity is the following:

Ea F

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 dissociation constant (KA) plus the concentration of the agonist. Ka is the reciprocal of the affinity constant and, under equilibrium conditions,

[R] is the concentration of free receptors and [RA] is the concentration of receptors bound to agonist. Although the details are beyond the scope of this textbook, 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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