## B

FIGURE 7.10 Operational model fit of the allosteric effects of gallamine on electrically evoked contractions of guinea pig left atrium. (a) Dose-response curves obtained in the absence (filled circles) and presence of gallamine 10 mM (open circles), 30 mM (filled triangles), 100 mM (open triangles), 300 mM (filled squares), and 500 mM (open squares). Data fit to operational model (Equation 7.4) with KA = 30 nM, Emax = 200, t = 1. Data fit for gallamine KB = 1 mM and a = 0.0075. (b) Ratio of observed EC50 values (EC050 for curve in presence of gallamine/EC50 control curve) as a function of concentrations of gallamine. Data fit to rectangular hyperbola of max = 134 (1/maximum = a = 0.0075). Data redrawn from [30].

FIGURE 7.10 Operational model fit of the allosteric effects of gallamine on electrically evoked contractions of guinea pig left atrium. (a) Dose-response curves obtained in the absence (filled circles) and presence of gallamine 10 mM (open circles), 30 mM (filled triangles), 100 mM (open triangles), 300 mM (filled squares), and 500 mM (open squares). Data fit to operational model (Equation 7.4) with KA = 30 nM, Emax = 200, t = 1. Data fit for gallamine KB = 1 mM and a = 0.0075. (b) Ratio of observed EC50 values (EC050 for curve in presence of gallamine/EC50 control curve) as a function of concentrations of gallamine. Data fit to rectangular hyperbola of max = 134 (1/maximum = a = 0.0075). Data redrawn from [30].

However, the testing of a wide range of concentrations of an allosteric antagonist would show the saturation of the allosteric binding site as revealed by an approach to a maximal value for the antagonism. The Schild equation for an allosteric antagonist is given by (see Section 7.8.3)

Expected Schild regressions for allosteric antagonists with a range of a values are shown in Figure 7.11. It can be seen that the magnitude of a is inversely proportional to the

FIGURE 7.11 Schild regressions for allosteric antagonists of differing values of a. Dotted line shows the expected Schild regression for a simple competitive antagonist. With allosteric antagonists of lower values for a, the regression reaches a plateau at higher antagonist concentrations (i.e., curvature occurs at higher antagonist concentrations).

FIGURE 7.11 Schild regressions for allosteric antagonists of differing values of a. Dotted line shows the expected Schild regression for a simple competitive antagonist. With allosteric antagonists of lower values for a, the regression reaches a plateau at higher antagonist concentrations (i.e., curvature occurs at higher antagonist concentrations).

ability of the allosteric antagonist to appear as a simple competitive antagonist (i.e., the lower the value of a the more the antagonist will appear to be competitive). This is discussed further in Section 10.3.1, and an example of this type of analysis is given in Section 12.2.9.

The foregoing discussion has been restricted to allosteric ligands that reduce the affinity of the receptor for the agonist (i.e., allosteric antagonists or modulators). Since allosteric change is the result of a conformational change in the receptor, there is no a priori reason for allosterism to produce only a reduced agonist affinity, and in fact such changes can lead to increases in the affinity of the receptor for the agonist (note the stimulation of the binding of [3H]-atropine by alcuronium in Figure 4.12).

7.4.2 Insurmountable Allosteric Antagonism (£ = 0)

Another possible allosteric effect is to render the receptor insensitive to agonist stimulation (i.e., remove the capacity for agonist response). This may or may not be accompanied by a change in the affinity of the receptor for the agonist. This can be simulated by setting X = 0 in Equation 7.3 to yield

Response =

It can be seen that when there is no effect on the affinity of the receptor for the agonist (a = 1) Equation 7.6 is identical to the describing orthosteric noncompetitive antagonism derived by Gaddum and colleagues [31] (see Equation 6.10). However, while the equation is identical and the pattern of concentration-response curves is the same as that for an orthosteric antagonist it should be noted that the molecular mechanism is completely different. Whereas the system described by Gaddum et al. consists of a slow offset antagonist occluding the agonist binding site, the system described by Equation 7.6 consists of the modulator binding to its own site on the receptor separate from that of the agonist. This ambiguity underscores the failure of observing patterns of concentration-response curves to determine molecular mechanism of action and how different experimental approaches to discerning allosteric versus orthosteric mechanisms are required (vide infra).

Equation 7.6 defines the allosteric noncompetitive antagonism of receptor function and predicts insurmountable effects on agonist maximal response (i.e., as [A] ! 1) the expression for maximal response is

It can be seen that just as in the case of orthosteric noncompetitive antagonism for high-efficacy agonists or in systems of high receptor density and/or very efficient receptor coupling (high t values, basically systems where there is a receptor reserve for the agonist) the maximal response may not be depressed until relatively high concentrations of antagonist are present. Under these circumstances, there may be dextral displacement with no diminution of maximal response until fairly considerable receptor antagonism is achieved (e.g., see Figure 6.16b). The difference between the orthosteric system described in Chapter 6 and the allosteric system described here is that there can be an independent effect on receptor affinity. No such effect is possible in an othosteric system. Figure 7.12 shows concomitant effects on receptor affinity for the agonist in allosteric noncompetitive systems. Figure 7.12a shows the effects of an allosteric modulator that prevents agonist receptor activation and also decreases the affinity of the receptor for the agonist by a factor of 20 (a = 0.05). It can be seen from this figure that the EC50 agonist concentrations shift to the right as the maximal response to the agonist is depressed. In contrast, Figure 7.12b shows the effects of a modulator that prevents agonist activation of the receptor but also increases the affinity of the receptor for the agonist (a = 50). Here it can be seen that as the maximal response to the agonist is depressed by the modulator the sensitivity of the receptor to the agonist actually increases. It should be noted that a shift to the left of EC50 values should not automatically be expected when an allosteric modulator increases the affinity of the receptor for the agonist. This is because if there is a large receptor reserve in the system the EC50 will naturally shift to the right with noncompetitive blockade. Therefore, what is observed is an average of this effect shifting curves to the right and the increased affinity shifting curves to the left. The example shown in Figure 7.12b was deliberately modeled in a system with little to no receptor reserve to illustrate the effect of allosterism on the EC50 values. Figure 7.13a shows the effect of the allosteric modulator Sch-C on the responses of the CCR5 chemokine receptor to the chemokine RANTES, and Figure 7.13b shows the effect of the allosteric modulator UK 427,857.

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