Classical Approaches to the Study of Drug–Receptor Interactions 33 FIGURE 1.11 A model to show the influence of a ligand, L, on the equilibrium between the active and inactive forms of a constitutively active receptor, R. Note that if L, R, and LR are in equilibrium, and likewise L, R* and LR*, then the same must hold for LR and LR* (see Appendix 1.6B (Section 184.108.40.206) for further explanation). with what has been learned about how ion channels work, is that such receptors can isomerize spontaneously to and from an active form: R R* ( inactive) ( active) In principle, both forms could combine with agonist, or indeed with any ligand, L, with affinity, as illustrated in Figure 1.11. Suppose that L combines only with the inactive, R, form. Then the presence of L, by promoting the formation of LR at the expense of the other species, will reduce the proportion of receptors in the active, R*, state. L is said to be an inverse agonist or negative antagonist and to possess negative efficacy. If, in contrast, L combines with the R* form alone, it will act as a conventional or positive agonist of very high intrinsic efficacy. Exploring the scheme further, a partial agonist will bind to both R and R* but with some preferential affinity for one or the other of the two states. If the preference is for R, the ligand will be a partial inverse agonist, as its presence will reduce the number of receptors in the active state, though not to zero. As shown in Section 1.10 (see the solution to Problem 1.4), application of the law of mass action to the scheme of Figure 1.11 provides the following expression for the fraction of receptors in the active state (i.e., p R* + p LR*) at equilibrium: p active E L KL E 1+ * K [L] 0 = ⎛ [ ] + ⎞ ⎜ 1 ⎜ ⎟ 0 + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ (1.39) * Here, the equilibrium constant E0 is defined by pR*/pR, KL by [L]pR/pLR, and KL by [L]pR*/pLR*. Figure 1.12 plots this relationship for three hypothetical ligands that differ in their relative affinities for the active and the inactive states of the receptor. The term α has been used to express the ratio * of KL to KL. When α = 0.1, the ligand is an inverse agonist; whereas when α = 100, it is a conventional agonist. In the third example, with a ligand that shows no selectivity between the active and inactive forms of the receptor (α = 1), the proportion of active receptors remains unchanged as [L] (and therefore receptor occupancy) is increased. Such a ligand, however, will reduce the action of either a conventional or an inverse agonist, and so in effect is an antagonist. More precisely, it is a neutral competitive antagonist. If large L
34 Textbook of ReceptorPharmacology, Second Edition FIGURE 1.12 The relationship between the total fraction of receptors in the active state (pR* + pAR*) and ligand concentration ([L]) for a constitutively active receptor. The curve has been drawn according to Eq. * (1.39), using the following values: E0 = 0.2, KL = 200 nM, α = KL/ K = 0.1, 1, and 100, as shown. Note that L on this model some of the receptors (a fraction given by E0/(1 + E0) = 0.167) are active in the absence of ligand. numbers of competitive antagonists of the same pharmacological class (e.g., β-adrenoceptor blockers) are carefully tested on a tissue or cell line showing constitutive activity, some will be found to cause a small increase in basal activity. They are, in effect, weak conventional partial agonists. Others will reduce the basal activity and so may be inverse agonists with what could be a substantial degree of negative efficacy.* Few of the set can be expected to have exactly the same affinity for the active and inactive forms of the receptor and so be neutral antagonists. However, some compounds of this kind have been identified, and Figure 1.13 illustrates the effect of one on the response to both a conventional and an inverse agonist acting on 5HT 1A receptors expressed in a cell line. As with the experiments of Figure 1.13, constitutive activity is often investigated in cultured cell lines that do not normally express the receptor to be examined but have been made to do so by transfection with the gene coding for either the native receptor or a mutated variant of it. The number of receptors per cell (receptor density) may be much greater in these circumstances than in cells that express the receptors naturally. While overexpression of this kind has the great advantage that small degrees of constitutive activity can be detected and studied, it is worth noting that constitutive activity is often much less striking in situ than in transfected cells. Hence, the partial agonist action (conventional or inverse) of an antagonist may be much less marked, or even negligible, when studied in an intact tissue so that simple competitive antagonism is observed, as described in Section 1.5. Nevertheless, the evidence that some receptors have sufficient constitutive activity to influence cell function in vivo even in the absence of agonist makes it necessary to extend the simple models already considered for the activation of G-protein-coupled receptors. In principle, the receptor can now exist in no less than eight different conditions (R, R*, LR, LR*, RG, R*G, LRG, LR*G), which is best represented graphically as a cube with one of the conditions at each vertex (see Figure 1.14). The calculation of the proportions of activated and occupied receptors is straightforward, if lengthy (see the answer to Problem 1.5 in Section 1.10). Finding the proportion in the active form is more difficult if the supply of G-protein is limited but can be done using numerical methods. * The possibility that the depression in basal activity may have some other explanation (e.g., an inhibitory action on one or more of the events that follow receptor activation) should not be overlooked.