FIGURE 3.4 Errors in the estimation of ligand potency for displacement of radioactive CD4-gp120 complex (surrogate for HIV binding) as a function of the concentration of radioactive CD4 (expressed as a fraction of the equilibrium dissociation constant of the CD4 for its binding site). Gray lines indicate a 50% error in the concentration of gp120. It can be seen that very little error in the potency estimation of a displacing ligand is incurred at low concentrations of radioligand but that this error increases as the concentration of CD4 is increased.
maximal response for the entire system (i.e., a = 1 indicates that the agonist produces the maximal response, a = 0.5 indicates half the maximal response, and so on). An intrinsic activity of zero indicates no agonism. Within this framework, the equation for response is thus:
where KA is the equilibrium dissociation of the agonist-receptor complex. Note how in this scheme response is assumed to be a direct linear function of receptor occupancy multiplied by a constant. This latter requirement was seen to be a shortcoming of this approach since it was known that many nonlinear relationships between receptor occupancy and tissue response existed. This was rectified by Stephenson  , who revolutionized receptor theory by introducing the abstract concept of stimulus. This is the amount of activation given to the receptor upon agonist binding. Stimulus is processed by the tissue to yield response. The magnitude of the stimulus is a function (denoted f in Equation 3.7) of another abstract quantity, referred to as efficacy (denoted e in Equation 3.7). Stephenson also assumed that the tissue response was some function (not direct) of stimulus. Thus, tissue response was given by
It can be seen that efficacy in this model is both an agonist and a tissue-specific term. Furchgott  separated the tissue and agonist components of efficacy by defining a term intrinsic efficacy (denoted e), which is a strictly agonist-specific term (i.e., this term defines the quantum stimulus given to a single receptor by the agonist). The product of receptor number ([Rt]) and intrinsic efficacy is then considered to be the agonist- and tissue-dependent element of agonism:
Response = f
The function f is usually hyperbolic, which introduces the nonlinearity between receptor occupancy and response. A common experimentally observed relationship between receptor stimulus and response is a rectangular hyperbola (see Chapter 2). Thus, response can be thought of as a hyperbolic function of stimulus:
where b is a fitting factor representing the efficiency of coupling between stimulus and response. Substituting for stimulus from Equation 3.7 and rearranging, response in classical theory is given as
Response = f
The various components of classical theory relating receptor occupancy to tissue response are shown schematically in Figure 3.5. It will be seen that this formally is identical to the equation for response derived in the operational model (see material following), where t = [RJe/p.
It is worth exploring the effects of the various parameters on agonist response in terms of classical receptor theory. Figure 3.6 shows the effect of changing efficacy. It can be seen that increasing efficacy causes an increased maximal response with little shift to the left of the dose-response curves until the system maximal response is achieved. Once this occurs (i.e., the agonist is a full agonist in the system), increasing efficacy has no further effect on the maximal response but rather causes shifts to the left of the dose-response curves (Figure 3.6a). In contrast, changing KA the equilibrium dissociation constant of the agonist-receptor complex has no effect on maximal response but only shifts the curves along the concentration axis (Figure 3.6b).
Black and Leff  presented a model, termed the operational model, that avoids the inclusion of ad hoc terms for efficacy. This model is based on the experimental observation that the relationship between agonist concentration and tissue response is most often hyperbolic. This allows for response to be expressed in terms of
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