Classical Approaches to the Study of Drug–Receptor Interactions 37 FIGURE 1.15 Estimating the efficacy of a partial agonist by comparing its concentration–response curve with that for a full agonist (see text for further details). that the macroscopic dissociation equilibrium constant K eff is determined not only by the value of K A but also by E, which is directly related to efficacy. In the same vein, both the efficacy and the macroscopic affinity of an agonist acting through a G-protein-coupled receptor depend on tissue factors such as the relative and absolute quantities of G-protein and receptors, as well as on the microscopic equilibrium constants. With these reservations in mind, we will next consider three approaches that have been used in the past to measure the efficacy of a partial agonist acting on an intact tissue. Each will be analyzed in two ways with the details given in Appendix 1.4C (Section 18.104.22.168). The first is of historical interest only and is based on Stephenson’s original formulation, as expressed in Eq. (1.27) (Section 1.4.2) and with receptor occupancy given by the Hill–Langmuir equation in its simplest form, which we have already seen to be inadequate for agonists. The second analysis defines receptor occupancy as all the receptors that are occupied, active plus inactive. The first two of the three methods presuppose that the measurements are made with a tissue that has a large receptor reserve. It is also assumed that a full agonist is available that can evoke a maximal response when occupying only a small fraction of the receptors. Method 1. Concentration–response curves are constructed for the full agonist (A) and for the partial agonist [P], the efficacy of which is to be determined (Figure 1.15). Two concentrations are read off the curve for the full agonist. The first, [A] 1, causes a halfmaximal response. The second, [A] 2, elicits the same response as the maximum seen with the partial agonist. The efficacy of the partial agonist is given by the ratio of [A] 2 to [A] 1 (see Appendix 1.4C, part A). Method 2. Exactly the same measurements and assumptions are made as before (see again Figure 1.15). From the concentration–response curves for the full and partial agonists, the values of [A] and [P] that elicit the same response are read off for several levels of response. A plot of 1/[A] against 1/[P] is constructed and should yield a straight line from which the efficacy of the partial agonist could be obtained if the underlying assumptions are correct (see Appendix 1.4C, part B). Method 3. This method is more general than the other two in the sense that it is also applicable to full agonists, at least in principle. Suppose that we had some reliable means of determining the dissociation equilibrium constant for the combination of the agonist with its receptors. One procedure that has been used in the past is Furchgott’s irreversible antag-
38 Textbook of ReceptorPharmacology, Second Edition onist method, as described in Section 1.6.4. We can then apply the appropriate occupancy relationship to calculate the proportion of receptors occupied at the concentration of agonist that produces a half-maximal response. Because S is then unity, according to the convention introduced by Stephenson, the reciprocal of this occupancy gives the value of e (from Eq. (1.27)). This is the basis of Furchgott’s estimate of the efficacy of histamine acting on isolated guinea-pig ileum (see Figure 1.24 in Section 1.6.3.). Clearly, this method stands or falls by the validity of the procedures used to measure the dissociation equilibrium constant and to relate agonist concentration to occupancy. We shall see in Section 1.6.4 that Furchgott’s irreversible antagonist method provides an estimate, not, as was first thought, of the microscopic equilibrium constant, K A, but rather of the macroscopic equilibrium constant, K eff. Hence, receptor occupancies calculated from it using the Hill–Langmuir equation will be of total occupancy, active plus inactive. It follows that efficacies calculated in this way are to be regarded as defined by Eq. (1.40) and not Eq. (1.28), as formulated by Stephenson. Are the efficacy values obtained in these ways useful? They are certainly no substitute for measurements, if these can be made, of the microscopic equilibrium constants that govern the proportion of receptors in the occupied and active forms. Also, because e* is influenced by tissue factors (e.g., [G] T and [R] T, as well as E and K ARG for G-protein-coupled receptors), a particular value can result from several combinations of these variables; E, the isomerization equilibrium constant for the formation of active receptors, is not the only determinant. Hence, the value of e* (or of e) cannot be used as a reliable measure of E. Comparison of e* values for different agonists acting on a particular tissue is more informative because tissue-dependent factors such as [G] T and [R] T are the same. The ratio of e* for two agonists should then give an estimate of the inverse ratio of the total receptor occupancies required to elicit a certain response. However, the key question of how these occupied receptors are distributed between the active and inactive states remains unanswered in the absence of other kinds of evidence. Despite the great importance of Stephenson’s concept of efficacy, we have to conclude that numerical estimates of efficacy, as originally defined, and based on measuring the responses of intact tissues, are of little more than descriptive value. 1.4.9 APPENDICES TO SECTION 1.4 22.214.171.124 Appendix 1.4A: Definition of a Partial Agonist The term partial agonist has come to be used in two slightly different senses. The first, as in this account, is to refer to an agonist that in a particular tissue or organism, under specified conditions, cannot elicit as great an effect (even when applied in large amounts) as can a full agonist acting through the same receptors. The second, more restricted, usage adds the condition that the response is submaximal because not enough of the receptors occupied by the partial agonist convert to the active form. The distinction can be illustrated by considering the action of decamethonium on the nicotinic receptors of skeletal muscle. Like acetylcholine, decamethonium causes the ion channels intrinsic to these receptors to open, so that the electrical conductance of the endplate region of the muscle fibers rises. However, even at very high concentrations, decamethonium cannot match the conductance increase caused by acetylcholine. This is not because decamethonium is much less able to cause the receptors to isomerize to the active form; rather, the smaller maximal response is largely a consequence of the greater tendency of decamethonium to block the nicotinic receptor ion channel. Hence, decamethonium would not be regarded as a partial agonist in the second sense defined above. However, if compared with acetylcholine for its ability to contract a piece of skeletal muscle, then it would be found to produce a smaller maximum response and so would be described as a partial agonist in the first, more general, sense.