G Protein-Coupled Receptor Allosterism and Complexing

1. Cooperativity in Binding.

The first important development in allosteric theory came from experimental evidence indicating that more than one molecule of ligand was able to bind to certain enzymes or ion channels to effect a change in the properties of the protein, a phenomenon termed “cooperativity”. In fact, the well known Hill equation commonly used nowadays to empirically fit concentration-response data was originally derived to describe cooperative binding (Hill, 1910). Figure1 illustrates two classic examples of cooperative binding proteins, the enzyme hemoglobin and the GABA_A ion channel-receptor complex. Simple mass-action kinetics predict that the binding of a single molecule of ligand to a single binding site on a protein would yield a hyperbolic isotherm (when plotted on a linear scale) with a slope coefficient equal to unity. However, the binding of oxygen to hemoglobin (Fig. 1A) or GABA to the GABA_A receptor (Fig. 1B) are characterized by distinctly sigmoid curves when plotted on a linear scale, reflecting the multiple equivalents of ligand binding to the same protein complex. Studies such as these conducted on a variety of ion channel-linked receptors, thus, led to the conclusion that certain receptors can possess more than one binding site for ligands. This concept invoked another phenomenon that was also originally described in the field of enzymology, that is, the idea of allosteric (or allotopic) binding sites.

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Figure 1

Cooperative binding in enzymes and ion channel-linked receptors. A, the binding of oxygen to hemoglobin dimers (curve D, Hill slope = 1) and tetramers (curve T, Hill slope = 3.3). Concentrations of hemoglobin range from 40 nM (D) to 100 μM (T). Data taken from Ackers et al. (1992). B, conductance change at the crustacean neuromuscular junction produced by γ-aminobutyric acid (GABA). Redrawn from Colquhoun (1973) based on data of Takeuchi and Takeuchi (1969).

The term “allosteric” (from the Greek meaning “other site”) was first used by Monod and Jacob (1961) and subsequently defined by Monod et al. (1963) in a paper describing the ability of enzymes to have their biological activity modified, in either a positive or negative fashion, by the binding of ligands to sites that were topographically distinct from the substrate-binding site. Monod et al. (1963) defined these accessory binding sites as allosteric sites, in contrast to the substrate-binding (active) site, which was defined as the isosteric site. In their original paper, Monod et al. (1963) outlined three general classes of interactions between two ligands on the one enzyme molecule. Class I interactions represented classic competition, where the substrate and inhibitor competed for overlapping regions on the receptor. Class II interactions were deemed to encompass situations where an inhibitor could form an attachment with a region of the enzyme not recognized by the substrate while some of the inhibitor molecule could interact with the substrate-binding site in a competitive manner. An example of this type of “direct interaction” nowadays is the effect of the “captive agonist” salmeterol at the β₂-adrenoceptor, where the long alkyl side chain of the molecule forms a persistent attachment with the receptor that allows its salbutamol-like active moiety to interact with the classic agonist binding domain to yield a persistent response (seeColeman et al., 1996). The final type of interaction (class III) was termed “indirect” or “allosteric”. These interactions arise when the binding of a ligand to the allosteric site induces a conformational change in the protein and modulates the binding of the substrate to the isosteric site, and vice versa. The biological activity of the enzyme was subsequently assumed to arise from the modified properties of the substrate-binding site, and not through a direct effect of the allosteric modulator itself. Monod et al. (1963)referred to this conformational change in the enzyme as anallosteric transition, although that term has since come to encompass a slightly different concept (see below).

With regards to receptor proteins, the primary binding site recognized by the endogenous agonist or hormone is conceptually equivalent to an enzyme's isosteric site, and has been referred to as the orthosteric site (Proska and Tucek, 1994; Christopoulos, 2002). Any binding site on a receptor protein that is able to modulate the binding properties of the orthosteric site by mediating a conformational change in the receptor may be classed as an allosteric site. Hence, many of the cooperative interactions that had been reported for ion channel-linked receptors in the literature in the past, such as the binding of two acetylcholine molecules to a single nicotinic acetylcholine receptor (Galzi et al., 1991) or the binding of two GABA molecules to a GABA_A receptor (Sigel and Buhr, 1997), are also allosteric interactions because the binding of one equivalent of ligand actually alters the affinity of the subsequent binding of the next equivalent(s) of ligand.

2. Allosteric Transitions: Multistate Models of Receptor Action.

Before discussing allosteric mechanisms in greater detail, it is necessary to address some of the issues that have arisen in the past regarding the terminology applied to allosteric proteins (Table 1). The term “allosteric” has been used by a number of authors in different ways, and this has led to some confusion in the literature as to what it actually means (e.g., see Colquhoun, 1998). Nowadays, it seems that a distinction is necessary between the terms “allosteric interaction” and “allosteric transition”. For the purposes of this review, an allosteric interaction is defined as an interaction that occurs between two (or more) topographically distinct binding sites on the same receptor complex. The essential features of a simple allosteric interaction are as follows: (a) The binding sites are not overlapping, that is, there is no mutual exclusivity in binding. (b) The binding of one ligand to its site affects the binding of the second ligand at the other site and vice versa. Allosteric interactions are, thus, reciprocal in nature. (c) The effect of an allosteric modulator can be either negative or positive with respect to the binding and/or function of an orthosteric ligand.

Although Monod et al. (1963) initially defined the conformational change in protein structure associated with an allosteric interaction as an allosteric transition, they subsequently presented a more formalized model of allosteric proteins that gave rise to the second major development in allosteric theory, namely, an emphasis away from interactions occurring between sites to interactions occurring between conformational states (Monod et al., 1965). Allosteric proteins were then described by these authors as follows: (a) They are oligomeric in nature (i.e., composed of more than one subunit). (b) Each subunit possesses one (equivalent) binding site for ligand, thus, giving rise to cooperative interactions. (c) They can exist as an equilibrium mixture of two or more states in the absence of ligand, with the transition between states now being defined as the allosteric transition. (d) The transition between conformational states involves a conservation of molecular symmetry such that all subunits “flip” from one state to another in a concerted fashion. (e) Ligands that prefer binding to one state over another will “select” the preferred state and, thus, increase the proportion of proteins in that state. As a consequence, observed (macroscopic) ligand affinity will alter depending on the type and amount of conformational state that predominates.

It can be seen that this last definition of allosteric proteins is quite explicit. Its description of interactions between multiple subunits makes it immediately applicable to oligomeric proteins that display cooperative binding, e.g., ion channel-linked receptors. It should be noted that models dealing with receptor isomerization between different conformational states were published as early as the 1950s to describe the postulated mechanism of action of the nicotinic acetylcholine receptor (del Castillo and Katz, 1957; Katz and Thesleff, 1957), although the actual term allosteric was not coined until the subsequent work of Monod and colleagues (1963). An important property of receptor models that incorporate allosteric transitions between conformational states is the prediction of receptor activity in the absence of ligand as a consequence of the isomerization process, i.e., constitutive receptor activity (Karlin, 1967; Colquhoun, 1973; Thron, 1973; Leff, 1995). These models are now more commonly referred to as “two-state” or “multi-state” models and represent the simplest mechanism approximating certain known aspects of protein behavior. In essence, the two-state model of receptor action is a mechanism of conformational selection, whereby a ligand selectively binds to a pre-existing receptor conformation, thereby creating a bias toward that conformation. In terms of free energy, this mechanism is generally preferable to one of conformational induction, where the ligand actually creates the conformation through the binding process (Burgen, 1981; Kenakin, 1995a). It should be noted, however, that conformational selection and conformational induction most likely represent two extremes of a common mechanism used by proteins in changing the type and abundance of conformational state in the presence of ligand.

On the surface, the concept of receptor allosterism within the context of multiple conformational equilibria may seem somewhat removed from the concept of an interaction occurring between distinct binding sites on the one protein. For instance, multistate models allow allosterism to arise simply as a consequence of the transition between one orthosteric conformation to another, without necessarily postulating the existence of a second binding site in each conformational state. In contrast, the simple model of allosteric interaction between two sites does not explicitly consider the existence of multiple conformations of the protein on which the sites are situated. As will be discussed below, these two ideas are not mutually exclusive; rather they address different aspects of a protein's ability to undergo conformational changes. To avoid engendering further confusion, the remainder of this review will use the term “receptor isomerization” when describing the transition of receptors between multiple conformational states and “allosteric interaction” when describing a reciprocal interaction between multiple binding sites on the same protein.

3. Allosteric Interactions: Ternary Complex Models.

Ion channels and ion channel-linked receptors are known to exist as oligomers; that is, they are composed of multiple protein subunits, and with an increased complexity in macromolecular structure comes an increased probability of multiple ligand binding sites. Allosteric interactions at ion channel-linked receptors, therefore, have been well documented and studied for almost half a century now. In contrast, GPCRs have, until recently, been considered traditionally to exist as monomers, and relatively fewer allosteric interactions occurring at GPCRs have been identified relative to ion channel-linked receptors. Nevertheless, it is now apparent that orthosteric ligand binding at GPCRs can be subject to allosteric modulation by other ligands or other proteins.

The best known example of an allosteric modulator of ligand binding to GPCRs is the G protein itself, and, as with the original formulation of allosteric theory in relation to enzymes and ion channels, the development of the current allosteric models for GPCRs was also based on two major ideas. The first idea was the development of two-state theory for ion channels and ion channel-linked receptors, as described above (del Castillo and Katz, 1957; Katz and Thesleff, 1957; Karlin, 1967; Colquhoun, 1973; Thron, 1973; Leff, 1995). These models described how selective affinity of ligands for specific receptor states (in the case of either open or shut ion channels) could bias the system toward the favored state. The second major idea in the GPCR field was that receptors could translocate within membranes and associate with other membrane-bound proteins (Cuatrecasas, 1974). Thus, any mechanism ascribed to a GPCR would need to explicitly invoke the presence of at least two binding sites on the same receptor protein, one for the orthosteric ligand and one for the G protein. This tripartite coupling mechanism represents the simplest scheme for an allosteric interaction occurring between distinct sites (as opposed to states) on a single receptor protein.

In general, the interaction between agonist binding and G protein coupling is positively cooperative in nature (Ehlert, 1985). This is logical, given the mechanisms that are thought to underlie signaling via GPCRs (Gilman, 1987; Bourne, 1997; Hamm, 1998). Agonist binding to the orthosteric site results in an alteration of receptor conformation that displays a higher affinity toward the G protein, thus favoring coupling. However, the binding of GTP to its site on the G protein results in a change of G protein structure that is transmitted to the receptor's conformation as a negatively cooperative effect on agonist binding, thus promoting the uncoupling of the activated G protein from the receptor and allowing signaling to proceed. These negatively cooperative effects of GTP on agonist binding underlie the so-called “GTP shift” that has often been used as a biochemical measure of agonist efficacy (Kenakin, 1997c; Christopoulos and El-Fakahany, 1999).

Figure 2 summarizes the evolution of GPCR models from simple operational schemes to the contemporary ternary complex mechanisms. The original TCM, as described by De Lean et al. (1980) allowed a ligand-bound activated receptor to form a G protein complex resulting in activation. This is a simple example of a receptor isomerization mechanism, where the binding of ligand A promotes a conformation of receptor that either signals in its own right (e.g., ion-channels; Fig. 2A, left) or couples to and activates a G protein (Fig. 2A, right). The next level of progression toward present GPCR models also involved the incorporation of different receptor conformations into the GPCR scheme. This latter development owed much to the introduction of recombinant receptor systems into receptor pharmacology, because it allowed for the ability to control the stoichiometry between receptors and G proteins. With this capability came the discovery of constitutive GPCR activity due to the spontaneous coupling of receptors in active conformations to G proteins in the absence of ligands. For this to occur, the minimal receptor model for such a system is shown in Fig. 2B (left). In the figure, L is the isomerization constant defining the equilibrium between active (R*) and inactive (R) receptor states, K _a is the equilibrium association constant of the ligand-receptor complex and α is referred to as a “cooperativity factor”, i.e., it is a ratio of the affinity of the ligand for the active versus the inactive state of the receptor. Alternatively, it may be viewed as a measure of the ability of ligand-bound receptor to enrich the R* state. The use of cooperativity factors in closed equilibrium reaction schemes such as those shown in Fig. 2 serves to reduce the number of parameters required to describe a model while satisfying the principle of microscopic reversibility (Wyman and Allen, 1951; Weber, 1975; Wyman, 1975; Ehlert, 1985; Weiss et al., 1996a). This idea, also referred to as the concept of “free energy coupling” (Weber, 1972, 1975), states that the energy required to reach one species from another must be the same at equilibrium, irrespective of what path is chosen, hence, the use of the cooperativity factor α.

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Figure 2

The evolution of allosteric receptor models for GPCRs. The earliest models were based on the assumption that the law of mass action dictates the binding of ligand A to the receptor, R, according to the equilibrium association constant,K _a, and then subsequently resulted in a response. This operational approach was then impacted upon by a progression of mechanistic insights. A, the agonist bound receptor can isomerize to produce a different state that can signal on its own (left) or translocate within the membrane to interact with a G protein (right). B, the receptor, R, can spontaneously isomerize to an active state, R*, (left) or couple to a G protein, G, or allosteric ligand, B, (right) in the absence or presence of orthosteric ligand. Thermodynamic considerations dictate that the isomerization constant, L, and the equilibrium association constants, K _a,K _b, and K _g, are modified to an extent governed by the cooperativity factors, α, γ, or θ, when the same interactions take place on an occupied receptor. C, the ETC model of Samama et al. (1993) combines the two-state model with the ternary complex model but only allows for the active receptor state to interact with G protein. D, the CTC model (left) of Weiss et al. (1996a, 1996b, 1996c) allows the inactive R state to interact with G protein and the active state. This model is formally identical with the allosteric two-state model (right) of Hall (2000), which describes the interaction of an allosteric modulator and orthosteric ligand on a receptor that can adopt active and inactive conformations.

When developing the original TCM, De Lean et al. (1980) also considered the possibility of a closed (cyclic) system operating in equilibrium, that is, they speculated about the existence of precoupled RG complexes in the absence of bound ligand (Fig. 2B, right). However, direct evidence for this phenomenon was lacking at the time and had to be inferred from the analysis of complex radioligand binding isotherms. Nevertheless, the proposal of a requisite ternary complex mechanism to account for the known behavior of GPCRs paved the way for further explorations into the properties of such a model (Wregget and De Lean, 1984; Ehlert, 1985). Importantly, the symmetry of the model allowed it to be equally applicable to situations where more than one type of drug molecule could occupy the receptor at the same time (Stockton et al., 1983; Ehlert, 1988). Observations made initially on studies of the actions of a series of hexamethonium derivatives and the neuromuscular blocking agent gallamine on muscarinic acetylcholine receptors had already suggested that such a mechanism may be operative (Lüllman et al., 1969; Clark and Mitchelson, 1976; Stockton et al., 1983). Thus, the simultaneous binding of an orthosteric ligand, A, and an allosteric ligand, B, to the receptor would be governed by the respective equilibrium association constants, K _aand K _b, just like the binding of an orthosteric ligand and G protein would be governed by the constantsK _a andK _g (Fig. 2B, right). As before with the closed two-state model, the thermodynamic requirement of reversibility also adds cooperativity factors to the affinities between receptor, orthosteric ligand, and allosteric ligand (θ) or G protein (γ) in the full ternary complex model. Interestingly, this principle is common in most applications of allosteric theory and stems from the idea that, as described by Sir Francis Bacon in 1620 “it is certain that all bodies whatsoever have perception”; in terms of the ternary complex model for receptors, if a receptor species is bound to some other species in the system, then it cannot be considered identical with its unbound counterpart. For example, if the receptor is bound to ligand, its affinity for G protein is γK _g notK _g. If it is bound to another ligand, B, then its affinity for agonist is θK _a and notK _a. This form of the TCM was the first explicit model of allosteric interactions occurring between topographically distinct binding sites applied to a GPCR, and it is still a useful, minimal model with which to assess and quantify experimental data (vide infra). It should be noted, however, that the TCM as an allosteric model of receptor-G protein interactions, on one hand, and receptor-modulator interactions, on the other, can lead to different predictions with respect to the binding curve of the orthosteric ligand. This is because G protein accessibility to receptors within the plane of the membrane can often be limiting, leading to shallow and/or biphasic orthosteric ligand binding curves due to G protein depletion (see Ehlert, 1985). In contrast, allosteric modulator drugs, like orthosteric ligands, are invariably present in vast excess relative to the concentration of receptor, and ligand depletion is, thus, much less likely to occur; the simple TCM does not predict biphasic or shallow binding curves in the absence of ligand depletion (vide infra).

The subsequent conclusive demonstration of constitutive GPCR activity by Costa and Herz (1989) indicated that receptors could couple to and activate G proteins in the absence of ligand. This necessitated the modification of the original TCM described by De Lean et al. (1980), which did not have the capability of spontaneous formation of the R*G species, into the extended ternary complex model (ETC model; Samama et al., 1993), as is shown in Fig. 2C. From this scheme, it can be seen that the amount of active-state receptor available for subsequent coupling to G protein is given by the isomerization constant L. Therefore, increasing the relative stoichiometry of receptors versus G protein leads to an elevated abundance of R*G, the species responsible for agonist independent response (constitutive receptor activity). For example, for a system containing 1000 receptors and a value for L of 0.001, there will be one single R* species. However, if the receptor number were to be increased by a factor of 1000, then the number of receptors in the signaling R*G form would be 1000. By increasing the number of receptors present in the system, the number of spontaneously active receptors can be increased until a threshold is attained where the resulting response from the spontaneously formed R*G species can be observed. The ETC model was, thus, the first GPCR model to explicitly incorporate allosteric transitions between receptor states (e.g., governed by L and α) and allosteric interactions between multiple binding sites (e.g., governed by β and γ).

Although the ETC model went beyond the original ternary complex model to accommodate experimental findings, it is thermodynamically incomplete. Again, this is directly related to the principle of free energy coupling described above, and has culminated in the development of the more thermodynamically complete, albeit more complex, cubic ternary complex (CTC) model by Weiss et al. (1996a–c; Fig. 2D, left). Although the CTC model is formally more correct than the ETC model, this correctness comes at a price of carrying too many parameters to allow for useful estimation based on experimental observations. In turn, this can make the model less predictive. Therefore, in practical terms, it is worth considering whether the more complex CTC model is worth applying to experimental data instead of the ETC model. The critical issue is the need for the ARG complex, the nonsignaling ternary complex between ligand, receptor, and G protein.

There are two approaches that can be used to try to determine which model, ETC or CTC, has greater utility in the receptor pharmacology of GPCR systems. One is the biochemical evaluation of the evidence for the existence of the inactive ARG complex. To date, there is a paucity of such evidence but it is not clear whether this is because of the apparent rarity of this species in biological systems or because of the lack of tools for detecting this species. There are isolated cases where experimental data are consistent with the existence of a nonsignaling ternary complex species. One example involves the inverse agonist ICI-174,864 (N,N-diallyl-Tyr-Aib-Aib-Phe-Leu-OH) acting at the G_i/o-coupled δ-opioid receptor expressed in HEK 293 cells (Chiu et al., 1996). Whereas the opioid agonist DPDPE mediated an inhibition of forskolin-stimulated cAMP accumulation, ICI-174,864 caused a further stimulation of the cAMP response above the basal forskolin response, consistent with the inverse agonist properties previously ascribed to ICI-174,864 (Costa and Herz, 1989). However, pretreatment of the cells with pertussis toxin, which uncouples G_i/o-proteins from their receptors, resulted in an abolition of both the agonistic effects of DPDPE and the inverse agonist effects of ICI-174,864. Although the former finding is consistent with the expectation that agonists require active receptor-G protein complexes, the latter finding with ICI-174,864 is inconsistent with the notion that inverse agonists prefer uncoupled receptor-G protein complexes to promote a reduction in constitutive receptor activity. One explanation for the pertussis toxin sensitivity of the ICI-174,864 effect is the possibility that this particular inverse agonist attenuates constitutive receptor activity not by uncoupling receptor-G protein complexes, but rather by promoting a stable ARG complex that is unable to signal.

Another example of a possible nonsignaling ARG ternary complex involves the cannabinoid CB₁ receptor, where the inverse agonistN-(piperidino-1-yl)-5-(4-chlorophenyl)-1-(2,4-dichlorophenyl)-4-methyl-pyrazole-3-carboxamide decreased constitutive receptor activity (as measured by activation of mitogen-activated protein kinase) according to standard inverse agonist kinetics for the receptor but also, unexpectedly, blocked the pertussis toxin-sensitive activation of the same kinase by insulin (Fig.3A) and insulin-like growth factor 1 receptors (Bouaboula et al., 1997). The crossover inhibition was dependent on the presence of the CB₁ receptor and did not occur with the non-GPCR, fibroblast growth-factor receptor. Crossover inhibition was also observed when Mas-7 (a mastoparan analog) was used to directly activate G_i/o proteins and suggests that G protein “trapping” was operative through the interaction between SR141716A and CB₁ receptors to make G_i/o protein inaccessible to other receptor pathways. This suggests the existence of the nonsignaling ARG species in this receptor system.

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Figure 3

Biochemical evidence for a nonsignaling [ARG] ternary complex. A, interaction of the inverse agonist, SR141716A, with the cannabinoid CB₁ receptor abolishes G_i/o-dependent mitogen-activated protein kinase signaling mediated by the insulin receptor tyrosine kinase, possibly by sequestering G protein in an inactive ternary complex of inverse-agonist, CB₁ receptor, and G protein. Data taken from Bouaboula et al. (1997). B, dissociation kinetics of opioids in CHO cell membranes expressing the human μ-opioid receptor. Unlike the antagonist [³H]diprenorphine, the antagonist [³H]NalBzOH and the agonist [³H]DAMGO each displayed biphasic dissociation kinetics, indicative of two affinity states of the receptor. The biphasic binding was sensitive to guanine nucleotides, suggesting that both [³H]DAMGO and [³H]NalBzOH were coupling to G proteins, but only the former agent was able to initiate a response. Data taken from Brown and Pasternak (1998).

Similarly, in CHO cells stably transfected with μ-opioid receptors, there is biochemical evidence of a nonsignaling ligand/receptor/G protein complex. In this system the potent μ-opioid receptor antagonist naloxone benzoylhydrazone (NalBzOH) blocks agonist-mediated cyclic AMP responses. However, a 3-fold enhancement of affinity was observed for NalBzOH in equilibrium binding studies in the presence of the stable GTP analog Gpp(NH)p. This indicated a low level of negative efficacy for this ligand at this receptor and also that NalBzOH has a preferential affinity for the inactive state of the receptor. In apparent contrast to this, [³H]NalBzOH demonstrated biphasic kinetics indicative of two affinity states (Fig.3B), consistent with an association of at least one state with G protein (Brown and Pasternak, 1998). An association with G protein (with no concomitant signaling) was indicated by the elimination of the high affinity state by Gpp(NH)p. The lack of a similar effect by the μ-opioid antagonist diprenorphine and the production of this same effect with pertussis toxin treatment indicated that the high-affinity component was a ligand-specific receptor complex associated with G_i/o protein.

Most recently, a study by Chen et al. (2000a) provided strong evidence for the potential of a mammalian GPCR to inhibit signaling in a dominant-negative manner by sequestering G protein α-subunits in a nonsignaling ternary complex. Specifically, a point mutation in Phe303 in the sixth transmembrane domain of the α_1b-adrenoceptor resulted in a receptor that displayed enhanced agonist binding affinity relative to the wild type, but a loss in agonist-mediated signaling through the phosphoinositide (PI) pathway. Furthermore, the mutant receptor, but not the wild type, could be coimmunoprecipitated with Gα_q in the absence of agonist, indicating a tight coupling of mutant receptor to G protein, and overexpression of Gα_q-subunits resulted in a rescue of the dominant negative activity of the mutant with respect to PI signaling. Taken together, these findings are compatible with the ability of the mutant α_1b-receptor to selectively sequester Gα_q-subunits in a conformation that promotes high agonist binding affinity but not signaling.

A second potential method of determining which model best fits a given experimental system is to examine the predictions of the models and compare those with experimental findings. For example, both the ETC and CTC models predict that increasing the amount of G protein available to the receptor will increase the amount of R*G species and, subsequently, the amount of constitutive activity. The relationship between G protein and constitutive activity predicted by the ETC model is given by (Chen et al., 2000b) Equation 1As can be seen from the above equation, at theoretically infinite concentrations of G protein, the constitutive activity will reach the system maximal response. A different relationship is predicted by the CTC model. As described by Weiss et al. (1996a,b,c), the relationship between constitutive activity and receptor number, expressed as a fraction of the maximal system response, is given by Equation 2If receptor concentration is not limiting (i.e., as [R] → ∝), then the constitutive activity will reach an asymptotic value of Equation 3For a high-efficacy agonist, δα ≫ 1 and the expression reduces to Equation 4Due to the possibility of producing a nonsignaling RG species, the CTC model predicts that the constitutive activity produced by addition of G protein need not reach the system maximum.

It can be seen that the two models predict the same qualitative but differing quantitative responses. Unfortunately, although submaximal levels of constitutive activity have been observed with receptor transfection experiments in Xenopus laevis melanophores (Chen et al., 2000b), it is not possible to determine whether the G protein levels in these cells were limiting and, thus, prevented the production of system maximal response. Also, because cellular responses are amplified functions of [R*G], it is not possible to determine whether a full constitutive maximal response relates to a submaximal or fully maximal conversion of receptor species to R*G.

It is presently unclear which of these models better predicts and describes experimental findings with GPCRs. On the practical side, the ETC model has fewer parameters, is simpler to use, and is, therefore, parsimonious. The CTC model is heuristic and more encompassing but has a greater number of nonestimatable parameters. It could be that different systems are better suited for different models, i.e., there may be GPCR systems where the ARG is so unimportant as to be negligible, thereby, making the ETC model preferable, and other systems where the ARG species plays a role, thus, necessitating use of the CTC model.

Another application of the CTC model exploits the symmetry in the model with respect to the reciprocity of interaction between orthosteric and allosteric sites. If it is assumed that the ligand occupying the secondary site on the receptor is not a G protein, but rather an allosteric modulator drug, then the model can be recast to yield a mathematical description of drug-drug allosteric modulation between two binding sites on a receptor that exists in both active and inactive states (see Fig. 2D, right). The properties of this “allosteric two-state model” were recently explored by Hall (2000), who compared it to the CTC model for agonist-G protein interaction. Although the equations derived from the model are formally identical with those of the G protein-based CTC model, there are important differences between the two models with respect to the effects of the cooperativity factors on receptor activation (Hall, 2000). This is because the allosteric two-state model (Fig. 2D, right) quantifies response as the production of activated receptor species (R*, AR*, BR*, and AR*B), as would be the case for ion channel-linked receptors. In contrast, the CTC model quantifies response as the production of activated receptor-G protein species (i.e., R*G, AR*G). Thus, the θ parameter in the allosteric two-state model only modifies orthosteric ligand affinity; the equivalent parameter in the CTC model, γ, modifies the ability of agonist to interact with G and, thus, affects response production and efficacy. As with the CTC model versus the ETC model, the applicability of the two-state allosteric model will depend on the observations to which it is applied and the systems in which it is tested. The allosteric two-state model would be most suitable, for instance, at ion channel-linked receptors, where the production of stimulus is equivalent to production of response. One interesting prediction of the model is the property of coagonism, whereby an allosteric modulator can modify orthosteric ligand intrinsic efficacy without itself possessing any efficacy; this is embodied in the parameter, ι, in Fig. 2D. Coagonism is commonly observed for ligands acting at the NMDA receptor, for example (Corsi et al., 1996).

1. G Protein-Specific Receptor Conformations.

There are numerous lines of evidence to suggest that different agonists produce response through the formation of different receptor active states. The most compelling data are obtained from receptors that are pleiotropic with respect to the G proteins with which they interact because these different G proteins provide a means of differentiating signaling active states. From this standpoint, the pattern of activation of various stimulus-response pathways can be used to infer the existence of these states. This phenomenom is termed “stimulus trafficking”, whereby agonists differ in the ability to stimulate separate stimulus-response pathways through a single receptor (Kenakin, 1995a,1995b, 1997a).

It is known that different regions of the cytosolic loops of GPCRs activate different G proteins (Ikezu et al., 1992; Wade et al., 1999), and it would not be expected that different tertiary conformations of the receptor protein would expose these different regions in an identical manner. Therefore, if ligands produce different tertiary conformations, then these may be detected through the relative capabilities of the resulting species to activate different G proteins. This should not be confused with differential activation of pathways through strength of stimulus. If a receptor couples to one pathway with great efficiency and to another one poorly, a strong agonist with high efficacy may activate both pathways, whereas a weaker agonist would activate only the most efficiently coupled pathway; this is not stimulus trafficking. To conclude true differences in receptor active state, a reversal of potency for the pathways or differences in the maximal activation of the pathways by the agonists must be demonstrated. This has been shown for some receptors. For example, the human 5-HT_2C receptor is coupled to two separate response pathways in CHO cells, namely phospholipase A₂-mediated arachadonic acid release and phospholipase C-mediated inositol phosphate accumulation (IP accumulation). There is a striking reversal in the maximal responses of agonists in this system that cannot be accommodated by postulating the production of a single receptor active state. Thus, the agonist (±)-1-(2,5-dimethoxy-4-iodophenyl)-2-aminopropane produces a higher maximal stimulation than the 5-HT agonist quipazine for arachadonic acid release (Berg et al., 1998). Because efficacy is the sole receptor-related determinant of maximal response, these data indicate that (±)-1-(2,5-dimethoxy-4-iodophenyl)-2-aminopropane has a greater efficacy for IP accumulation than quipazine for arachadonic acid release. This relative efficacy for these agonists is reversed for IP accumulation where quipazine has the greater efficacy. Thus, a receptor-related parameter, namely efficacy, reverses with the two agonists for the same receptor. Similarly, there is a reversal of the relative potency of substance P analogs on neurokinin NK-1 receptors described where substance P is 2.1 times more potent than the analog [P₃ ^Emet(O₂)¹¹]SP for producing cyclic AMP through NK-1 receptor activation, but is 0.11 times less potent than the analog for producing phosphoinositol hydrolysis through activation of the same receptor (Sagan et al., 1999). Reversals of efficacy also have been reported for pituitary adenylate cyclase-activating polypeptide receptors (Spengler et al., 1993), dopamine receptors (Meller et al., 1992), andDrosophila tyramine receptors (Robb et al., 1994). In general, these data cannot accommodate a mechanism whereby all of the agonists involved produce an identical active receptor state.

Specially designed recombinant GPCR systems (termed “stimulus-biased” assay systems; Watson et al., 2000) also can be used to detect stimulus trafficking. These systems consist of surrogate host cells for receptor transfection with identical cellular backgrounds except for the enrichment of a single Gα-subunit. A study with human calcitonin receptor (type 2), a pleiotropic receptor that can interact with G_s, G_q, and G_i, (Horne et al., 1994), showed striking reversals in relative potencies of peptide calcitonin agonists. Specifically, after transfection of the receptors into wild-type HEK 293 cells and HEK cells stably transfected with enriched populations of Gα-subunits, differences in relative agonist potencies were observed. For example, the relative potency of porcine calcitonin and rat amylin changed by a factor of 18 (from 4.6 to 84) when compared in wild-type and Gα_s-enriched cells. This suggests that porcine calcitonin produces a conformation more conducive to using G_s than does amylin. In these studies, even the rank order of potency of the agonists changed in that the potency of rat calcitonin gene-related peptide (CGRP) was 0.3 times that of rat amylin in wild-type cells and three times greater than rat amylin in Gα_s-enriched host cells (Watson et al., 2000). Because the classification of receptors using agonist potency ratios and rank orders of potency is based on the tenet that the active state produced by the agonists is the same, deviations from this behavior suggest that the tenet is not valid in this system.

Another observation not consistent with the idea that agonists simply enrich the spontaneously formed receptor active state is the phenomenom of “protean agonism”. This behavior has been described in theoretical terms as the formation, by an agonist, of a receptor active state that is less efficacious than the spontaneously formed constitutive one (Kenakin, 1995c, 1997b). It was named for the Greek god Proteus who could change shape at will. The hallmark of protean agonists is the production of positive agonist response in nonconstitutively active systems and inverse agonism in constitutively active ones. Such a pattern of response can be used as presumptive evidence that the agonist produces a receptor active state that is different (i.e., of lower efficacy) than the spontaneously formed active state, i.e., ligand selective agonism. Under these circumstances, protean agonism can be considered a looking glass into receptor states.

There are theoretical conditions under which protean agonism could occur. For example, in the CTC, a ligand could promote the R* form of the receptor by having α > 1 but then produce a liganded form of the receptor active state of lower affinity than the unliganded form (γ < 1); the result would be a reversal of the positive to a negative agonism under conditions of constitutive activity. Importantly, there are also experimental examples of protean agonism. The β-adrenoceptor ligand dichloroisoproterenol has been shown to produce positive partial agonism in Sf9 cells transfected with β₂-adrenoceptors. When membranes were prepared from these same cells, the system demonstrated constitutive activity (due to removal of cellular GTP) and dichloroisoproterenol then became an inverse agonist. The same behavior was observed for the ligands labetolol and pindolol (Chidiac et al., 1994, 1996).

The kinetics of cyclic AMP formation have been used to detect agonist-selective receptor states. Thus, in the presence of limiting GTP concentrations, such kinetics indicate a differential rate of heterotrimer dissociation of G protein subunits with different β-adrenoceptor agonists (Krumins and Barber, 1997). Similarly, differences in the ability of β-adrenoceptor agonists to hydrolyze inosine versus guanosine triphosphate suggest the formation of ligand-specific receptor active states as well (Seifert et al., 1999).

Mutation studies also suggest that ligands stabilize different tertiary conformations of receptors. For example, mutations of dopamine D₂ receptors produce agonist-specific abolition of G protein activation (Wiens et al., 1998). Desensitization of receptors by some agonists also suggests differential receptor active state formation. Whereas it would be expected that the ability of agonists to induce desensitization would parallel their ability to produce response (i.e., intrinsic efficacy), studies on μ-opioid receptors have indicated a disproportionate desensitizing and receptor phosphorylating property of methadone and l-α-acetyl methadone, thereby, suggesting different receptor conformational changes with these ligands (Yu et al., 1997). Differential desensitization also has been demonstrated for methadone and buprenorphine on μ-opioid receptors (Blake et al., 1997).

Studies with purified β-adrenoceptor covalently labeled with cysteines with an environmentally sensitive fluorophore 4[(iodoacetoxy)ethylemethylamino]-7-nitro-2,1,3-benzoxadiazole allowed observation of changes in protein conformation with ligand binding (Gether et al., 1995). A statistical analysis of these data indicates serious deviation from a simple two-state model of receptor activation suggesting that different ligands produce uniquely different protein conformations (Onaran et al., 2000).

The major window of detection of allosteric effects historically has been receptor-mediated physiological response. Thus, ligands have been detected as allosteric modulators or enhancers on the basis of effects resulting in changes in tracer ligand affinity and/or tracer ligand-induced response. However, different receptor conformations are involved in receptor-mediated effects other than cellular signaling (Kenakin, 2002). Thus, conformations resulting in changes in receptor phosphorylation and/or receptor internalization also can be relevant to the therapeutic effect of allosteric ligands. For example, studies on receptor internalization suggest ligand-specific receptor conformations. Thus, the cholecystokinin receptor antagonist d-Tyr-Gly-[(Nle^28,31,d-Trp³⁰)cholecystokinin-26–32]-phenethyl ester is an antagonist on the receptor producing blockade of responses to cholecystokinin but produces profound acceleration of receptor internalization (Roettger et al., 1997). This indicates the formation of a unique conformation that does not signal to G proteins but is more amenable to receptor phosphorylation and subsequent internalization. Similarly, whereas enkephalins and morphine both stimulate δ- and μ-opioid receptors, enkephalins induce rapid receptor internalization while morphine does not (Keith et al., 1996).

2. Ligand-Specific Receptor Conformations.

Although the preceding discussion of specific receptor conformations focused on the receptor-G protein interaction, it is evident that the entire surface of a GPCR may be viewed as a potential binding site, and any ligand binding to either the orthosteric or allosteric site(s) on a GPCR has the potential to alter receptor conformation such that the affinity and/or intrinsic efficacy of a ligand binding to the other site(s) on the GPCR will also change. This scheme is also compatible with the potential for multiple ligand-specific receptor conformations to be engendered depending on the binding site and extent of conformational change induced in the receptor protein. Thus, ligands that would be classed as allosteric modulators with respect to their effects on the endogenous orthosteric agonist for the receptor of interest should be placed in the same realm as other modifiers of receptor properties, such as agonists, inverse agonists, and G proteins. At the molecular level, therefore, the classic TCM of allosteric interactions and its variants (Fig. 2) are all subsets of a more general, extended, model of receptor activity. To visualize such a model, one can begin with a general picture of a receptor protein that contains separate binding sites for an orthosteric ligand, an allosteric modulator, and a G protein. Thermodynamic considerations imply that the occupancy of any one of the binding sites on this receptor can alter its conformation such that the occupancy of any of the other sites on the protein is also altered. This cross-reciprocity can be quantified in terms of separate cooperativity factors for the interaction between orthosteric and allosteric sites, orthosteric and G protein sites, and allosteric and G protein sites. Because efficacy at GPCRs is invariably related to the ability of the receptor to interact with its cognate G protein(s), then efficacy at the molecular level can be impacted not only by the interaction between orthosteric ligand and G protein or orthosteric ligand and allosteric modulator (e.g., Section IIB), but also by the interaction of the allosteric modulator and the G protein. For instance, Fig. 5A shows the effects of the allosteric modulator alcuronium on PI hydrolysis in CHO cells transfected with the human M₁ muscarinic acetylcholine receptor (Jakubı́k et al., 1996). Even in the absence of the muscarinic agonist carbachol, alcuronium was able to elicit a significant stimulatory effect on PI hydrolysis that was insensitive to antagonism of the orthosteric site by the classical muscarinic antagonist quinuclidinyl benzilate. The effect of alcuronium on PI hydrolysis was absent in cells that did not express the M₁ muscarinic receptor. Thus, it can be concluded that alcuronium was promoting receptor-G protein coupling via an action at the allosteric site on M₁ receptors. In a similar manner, the allosteric modulator gallamine was also found to activate the M₁, M₂, and M₄ muscarinic receptors in the absence of any other ligand (Jakubı́k et al., 1996), although it inhibits the binding of the endogenous muscarinic agonist acetylcholine at the same receptors (Lazareno and Birdsall, 1995). This latter finding is a striking example of ligand-specific receptor conformations, whereby gallamine (and alcuronium) can promote conformations that are positively cooperative for G protein coupling but negatively cooperative for agonist binding.

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Figure 5

G protein-dependent effects of allosteric modulators. A, effects of the orthosteric agonist, carbachol (○), and allosteric modulator, alcuronium (■), on phosphoinositol production in CHO cells transfected with the human M₁ muscarinic acetylcholine receptor. Data taken from Jakubı́k et al. (1996). B, effect of the allosteric modulator, PD 81,723, on the binding of the orthosteric agonist [³H]CHA to adenosine A₁receptor-G protein complexes in CHO cells. Data taken fromKollias-Baker et al. (1997).

Allosteric ligand-mediated receptor-G protein interactions are not restricted to the muscarinic acetylcholine receptors. Figure 5B shows the effect of the allosteric modulator PD 81,723 on the saturation binding properties of the agonist [³H]N ⁶-cyclohexyladenosine ([³H]CHA) at the adenosine A₁ receptor. In the absence of modulator, the radiolabeled agonist could only recognize approximately one-ninth of the total receptor population, as defined by the binding of the radiolabeled antagonist, 8-[dipropyl-2,3-³H(N)]cyclopentyl-1,3-dipropylxanthine, [³H]CHA (Kollias-Baker et al., 1997). This finding indicated that the agonist [³H]CHA was selectively labeling only high-affinity receptor-G protein complexes, rather than the entire receptor pool. Interestingly, the addition of PD 81,723 resulted in a significant enhancement in the total density of binding sites recognized by [³H]CHA with no change in the agonist K _D value. This finding is inconsistent with a direct allosteric effect of the modulator on agonist affinity, but is in accord with a positive allosteric effect on receptor-G protein coupling. In essence, it seemed as if PD 81,723 was able to “create” more binding sites by promoting a greater proportion of high-affinity receptor-G protein states for the radiolabeled agonist (Fig. 5B). This finding is in agreement with previous studies using PD 81,723, which showed that this particular modulator could enhance agonist binding to adenosine A₁ receptors (Cohen et al., 1994), decrease antagonist binding at these receptors (Bruns and Fergus, 1990), and activate the receptors in its own right (Bruns and Fergus, 1990).

It is evident, therefore, that allosteric modulators of GPCRs may directly affect receptor function in the absence of orthosteric ligand and can, thus, be subdivided into the following categories (Lutz and Kenakin, 1999). (a) Allosteric enhancers: These ligands exert their effects by enhancing the affinity of the orthosteric ligand for its site on the receptor. (b) Allosteric agonists: These ligands exert their effects by promoting G protein coupling independent of any effects on orthosteric agonist binding. (c) Allosteric antagonists: These ligands can exert their effects by one or a combination of mechanisms; they can decrease the affinity of the receptor for its orthosteric agonist and/or decrease the affinity of the receptor for its G protein(s).

To be thermodynamically complete, any model of allosteric interactions between multiple ligands on the same GPCR must, thus, take into account the ability of the receptor to isomerize between multiple conformational states and to bind to G protein. At equilibrium, each conformational state is characterized by its own set of cooperativity factors. Even for the “simplest” case of two receptor conformations (R for inactive and R* for active) the resulting thermodynamic picture (Christopoulos et al., 1998) can become quite complicated; the model is shown in Fig. 6. Nevertheless, this quaternary complex model (QCM) of receptor allosterism reflects the fact that allosteric modulators of GPCRs possess a rich repertoire of behaviors that can extend beyond simple changes on orthosteric ligand binding affinities. In addition to the possible ternary complexes comprising the receptor, G protein, and either orthosteric or allosteric ligand, the model also allows for the quaternary complexes of orthosteric ligand, allosteric ligand, G protein, and receptor in both active (AR*BG) an inactive states (ARBG). Table3 defines the constants and cooperativity factors that describe the model, whereas Table4 lists the equations describing occupancy, potency, and response parameters of an orthosteric ligand based on the model. Table 5 shows the equations for K _App, response and EC₅₀ from the QCM under the special conditions of [B] = 0 or [G] = 0, where it can be seen that the model then becomes formally identical with the CTC model of Weiss et al. (1996a)or the allosteric two-state model of Hall (2000), respectively. Thus, both latter models are subsets of the quaternary complex model of allosterism at GPCRs.

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Figure 6

The quaternary complex model of allosteric interactions at GPCRs; a thermodynamically complete, extended model taking into account the concomitant binding of orthosteric ligand, A, allosteric ligand, B, and G protein, G, on a receptor that can exist in two conformational states (R and R). The model parameters are defined in Table 3.

Although a detailed examination of the properties of the QCM are beyond the scope of this review, one important aspect of the model is the ability to incorporate allosteric modulator effects on receptor-G protein coupling. For example, simulations based on the model (not shown) reveal that an increase in the cooperativity factor ε, which governs G protein binding to the receptor occupied by allosteric ligand, can result in an enhancement of maximal orthosteric ligand binding capacity (defined as total G protein-coupled receptors bound to [A]) with no effect on apparent orthosteric ligand affinity. This is exactly what has been observed experimentally with the effects of PD 81,723 on adenosine A₁ receptors (e.g., Fig. 5B) and cannot be accommodated within the other allosteric receptor models described above.

1. Equilibrium Binding Assays.

Radioligand binding assays often provide the most direct means for visualizing allosteric behavior. For example, Fig. 7A shows the effects of the negative allosteric modulator, oleamide, on the saturation binding properties of [³H] 5-HT at the 5-HT₇ receptor expressed in HeLa cells, whereas Fig. 7B shows the effect of the modulator gallamine on the saturation binding of [³H]N-methylscopolamine at the M₂ muscarinic receptor expressed in CHO cells. Although in each instance the modulator is able to shift the radioligand binding curves to the right, the allosteric nature of the interaction is revealed as progressively higher concentrations of antagonist fail to cause significant dextral displacements of the radioligand saturation curve. These observations are in direct contrast to what would be expected for a simple competitive interaction, where, theoretically, there would be no limit to the dextral displacement of the radioligand curve attainable in the presence of increasing antagonist concentrations. A common graphical method for assessing the relationship between radioligand saturation binding and antagonist concentration involves the determination of the affinity shift, that is, the ratio of radioligand affinity in the presence (K _App) to that obtained in the absence (K _A) of each concentration of antagonist. A plot of log (affinity shift − 1) versus log [antagonist] should yield a straight line with a slope of 1 for a competitive interaction, but a curvilinear plot for an allosteric interaction. Such curves are evident in Fig. 7, C and D, which shows the affinity shift plots for the interaction between oleamide and [³H]5-HT or gallamine and [³H]N-methylscopolamine, respectively.

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Figure 7

Allosteric modulation by oleamide (A and C) of the binding of [³H]5-HT in HeLa cell membranes transiently transfected with the 5-HT₇ receptor or gallamine (B and D) of the binding of [³H]NMS in cell membranes stably transfected with the human M₂ muscarinic acetylcholine receptor. A, radioligand saturation binding curves obtained in presence of the following concentrations of oleamide: 0 (○), 0.1 nM (▵), 10 nM (●), 30 nM (▴), 100 nM (▪), 300 nM (■), and 1 μM (⋄). B, effect of oleamide on the ratio of [³H]5-HTK _D values (“affinity-shift”) determined in the presence or absence of the modulator. The dashed line shows the predicted behavior of a competitive antagonist. Data taken from Hedlund et al. (1999). C, radioligand saturation binding curves obtained in presence of the following concentrations of gallamine: 0 (●), 1 μM (○), 3 μM (■), 10 μM (⋄), and 100 μM (▵). D, affinity-shift for the interaction between [³H]NMS and gallamine. Data taken from Christopoulos (2000b).

2. Inhibition Binding Assays.

Radioligand inhibition, or competition, binding assays are more commonly used for the routine screening of novel chemical entities than saturation binding assays, so it is quite likely that the first detection of an allosteric modulator may occur during this type of experiment. Of course, in the latter instance, the interaction cannot be called competitive; but for allosteric modulators with high degrees of negative cooperativity, the interaction may be mistaken as competitive if low degrees of radioligand occupancy are investigated. Because of this potential pitfall in interpreting inhibition binding experiments, it is useful to explore the meaning of the standard observed parameters in binding curves in terms of the simple allosteric model outlined above (section IIB). Thus, an inverse sigmoidal curve is predicted for an allosteric inhibition of a given amount of bound radioligand much like what is observed for a competitive antagonist. Considering only specifically bound radioligand, the signal (ρ_A) from a radioligand [A], in the presence of a given concentration of allosteric antagonist [B], is given by eq. 5. Whereas a competitive ligand will decrease the bound ligand down to nonspecific binding levels, the maximal inhibition produced by an allosteric antagonist will depend upon the magnitude of the cooperativity factor, α. The maximal scale of inhibition of specific radioligand binding is equal to Equation 7It can be seen from this expression that the maximum degree of antagonism of any given bound concentration of radioligand A is a function of α. This is because the inhibition of a radioligand by either an allosteric ligand or a competitive (i.e., orthosteric) ligand follows the receptor occupancy of a single concentration of radioligand as the saturation binding curve to that ligand is shifted to the right by the nonradioactive ligand. This is shown in Fig.8A, where the saturation curve to a radioligand is shifted to the right by a high concentration of allosteric ligand with α = 0.2. This results in a maximal shift to the right of 5-fold by the allosteric ligand. If receptor occupancy is viewed at a fixed radioligand concentration of approximately 1.5 × K _A then the inhibition curve shown in the right panel of Fig. 8A is observed. It can be seen that the strength of the allosteric blockade (magnitude of α), thus, determines the amount of maximal inhibition of the binding curve (see eq. 7.

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Figure 8

Inhibition of radioligand binding by allosteric antagonists. A, Saturation binding curve for a radioligand shifted to the right by a maximally effective concentration of allosteric antagonist with α = 0.2. The curve to the left of the panel shows the displacement of a defined concentration of radioligand by a range of concentrations of allosteric antagonist. Note how the displacement does not reduce the bound counts to nonspecific binding levels. B, same as A but for a more powerful allosteric antagonist (α = 0.01). In this case, the displacement counts are reduced to nonspecific binding levels. C, the increase in the IC₅₀ for antagonism (as a ratio of the K _B) as a function of the amount of radioligand in the assay (as a ratio ofK _A). A linear relationship is predicted for a competitive ligand. For allosteric ligands, hyperbolic curves are generated.

The expected behavior of allosteric antagonists in inhibition binding assays outlined in the preceding paragraph gives rise to two important considerations. The first is that a curve where the radioactivity is not inhibited completely to nonspecific binding levels may denote an allosteric, as opposed to a competitive, antagonism. Such an effect may reflect the inability of the antagonist to produce large enough shifts to the right of the saturation curve to bring the signal completely to nonspecific binding levels. For example, the small molecule antagonist of CCR3 chemokine receptors UCB35625 is a full antagonist of chemokine-induced chemotaxis but produces only a 15% maxmimal displacement of radioactive chemokine binding (Sabroe et al., 2000); this antagonist may be acting through an allosteric mechanism. The second consideration is that the maximal inhibition of specific radioligand binding attainable by an allosteric antagonist will depend on the concentration of radioligand. Thus, it can be seen that if a radioligand concentration was chosen to be 0.01 ×K _A, then the antagonist shown in Fig.8A would have taken the binding to near nonspecific binding levels. Also, if the negative cooperativity is high, for example α is less than 0.1, then the dependence of the maximal displacement window on α becomes moot because the shift produced by the allosteric antagonist would bring the binding down to nonspecific binding levels as well (see Fig. 8B). Hence, whereas a maximal displacement above nonspecific binding levels can denote allosteric antagonism, a complete displacement to nonspecific binding levels does not necessarily implicate competitive antagonism and preclude allosteric blockade.

Another potential method to detect allosteric, as opposed to competitive, antagonism in radioligand binding studies is to examine the relationship between the amount of radioligand present in the assay (denoted [A*]) and the amount of antagonist required to reduce the specific binding produced by that radioligand to 50% of B₀. For competitive antagonists, this can be calculated from the Gaddum (1936) equation for competitive antagonism. Thus, the receptor occupancy for a radioligand A* in the presence of a competitive antagonist [B] is given by Equation 8where K _A andK _B are the equilibrium dissociation constants of the radioligand and competitive antagonist, respectively. From this equation, the concentration of antagonist required to reduce a defined level of specific radioligand binding to 50% B₀ can be calculated as Equation 9According to this relationship, therefore, the concentration of antagonist (expressed as a multiple of theK _B) is linearly related to the concentration of radioligand present in the assay. This relationship, as defined for enzymes, is commonly referred to as the Cheng-Prusoff (1973) relationship. A corresponding relationship for allosteric ligands can be also be derived Equation 10where IC₅₀ denotes the concentration of allosteric antagonist producing 50% inhibition of specific radioligand binding. It can be seen from this equation that if the concentration of radioligand is low (i.e., if [A] ≪K _A), then the IC₅₀ will be approximately equal to theK _B (see also Ehlert, 1988). It can also be seen that this is not a linear relationship but rather a hyperbolic one. Thus, one way to potentially differentiate competitive and allosteric antagonism in radioligand binding assays is to compare the IC₅₀ for blockade as a function of radioligand concentration. Figure 8C shows such a relationship for a competitive antagonist (linear dotted line) and a series of allosteric antagonists with α values ranging from 0.1 to 0.003. It can be seen that the pronounced curvature of the relationship for the allosteric ligands differentiates them from the competitive ligand.

The variability of the extent and the direction of allosteric modulation of radioligand binding can be practically demonstrated by the effects of two different allosteric modulators of M₂ muscarinic acetylcholine receptors on the same radioligand in the same membrane preparation. Figure9A shows the interaction between the muscarinic receptor antagonist [³H]N-methylscopolamine and the allosteric modulator gallamine, which is characterized by negative cooperativity. It can be seen that the use of a sub-K _A concentration of radioligand (which is quite common for these types of screening assays) results in an apparently complete inhibition of specific radioligand binding. Increasing the concentration of the radioligand to 10 times itsK _A, however, unmasks the limited ability of the negative allosteric modulator to inhibit specific binding. In contrast, the interaction between the same radioligand and the modulator, alcuronium, at the same receptor, is characterized by a marked positive cooperativity, clearly deviating from the predictions of simple competition (Fig. 9B). Findings such as these highlight another important aspect of allosteric interactions, that is, they are unique for each and every pair of interacting ligands involved. A positive allosteric modulator of one particular orthosteric ligand is not necessarily a positive modulator of another orthosteric ligand. Table 6 demonstrates this with examples of the interaction between alcuronium and a variety of orthosteric ligands at the M₂ muscarinic acetylcholine receptor.

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Figure 9

Effect of the allosteric modulators gallamine and alcuronium on the binding of the orthosteric antagonist, [³H]N-methylscopolamine, at M₂muscarinic acetylcholine receptors in guinea pig atrial membranes. A, negative cooperativity between gallamine and two different concentrations of the radioligand: 0.1 nM (○; 0.5 ×K _A) and 2 nM (●; 10 ×K _A). B, positive cooperativity between alcuronium and 0.1 nM radioligand. Also shown on the figure are the best estimates based on fitting the data to the allosteric model (eq.5). Data taken from Christopoulos (2000a).

The preceding discussion suggests important practical considerations when screening for allosteric ligands. For instance, assays can generally use low concentrations of radioligand (<K _A) in the first instance, but these may then need to be supplemented with assays using a high radioligand concentration to demonstrate the limiting effects of cooperative interactions on the pattern of the resulting binding curve. Second, because the allosteric interaction is unique for each drug pair, it is logical that screening programs for allosteric ligands should include, at the very least, the endogenous hormone or neurotransmitter for the receptor of interest as part of the assay. Yet another important factor in radioligand binding experiments is the actual choice of radioligand. Agonist radioligands rely on the ability of the receptor to couple to G proteins and would be most useful in detecting allosteric modulators that are able to modify receptor-G protein coupling, whereas radiolabeled antagonists may not. In general, the design of radioligand binding assays to detect allosteric modulators should, where possible, use the endogenous orthosteric ligand for the receptor of interest as the radiolabel. If this is not possible, then the radioligand used may still detect an allosteric interaction, but the experimenter should remain aware that the magnitude and direction of that interaction can be quite different from the situation with the endogenous ligand probe.

Sometimes, radioligand binding assays may reveal unusual behavior that may not seem compatible with the simple allosteric TCM. Figure10A shows the interaction between methylisobutylamiloride (MIA) and [³H]spiperone at the dopamine D₂ receptor, which is characterized by a very steep inhibition curve (Hill slope ∼ 2), and Fig. 10B shows the interaction between PD 81,723 and the agonist [³H]CHA at the adenosine A₁ receptor, which is characterized by a bell-shaped curve. Although each of these interactions involves allosteric mechanisms, it has been suggested that MIA and PD 81,723 can interact with both orthosteric and allosteric sites at the D₂ and A₁ receptors, respectively (Bruns and Fergus, 1990; Hoare and Strange, 1996). This leads to an additional level of complexity in the observed binding profiles. Specifically, if a modulator is able to compete with the radioligand at the orthosteric site and modulate the radioligand's binding (and its own) through an additional allosteric mechanism, then the curves illustrated in Fig. 10, A and B, may be observed. The relevant model in this instance is shown in SchemeFS2, where the parameters are as defined previously except that subscript 1 refers to binding of ligand B to the orthosteric site, subscript 2 refers to binding of B to the allosteric site, and the cooperativity factor, β, denotes the allosteric interaction between the two molecules of B on the receptor. From this model, the following equation can be derived describing the fractional receptor occupancy by A at equilibrium. Equation 11where K _A,K _B1, andK _B2 denote equilibrium dissociation constants. eq. 11 was used to simulate the binding curves shown in Fig.10, C and D. In Fig. 10C, the interaction between the two molecules of B is positively cooperative (β > 1), whereas the interaction between B and A is negatively cooperative (α < 1). This yields a very steep inhibition curve (Hill slope of approximately 2), as was observed experimentally for the interaction between MIA and [³H]spiperone at the D₂receptor. In Fig. 10D, the interaction between A and B is positively cooperative (α > 1), whereas the interaction between the two molecules of B is neutrally cooperative (β = 1), yielding the observed bell-shaped curve.

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Figure 10

Mixed modes of allosteric/competitive interactions. A, inhibition of [³H]spiperone binding by MIA at dopamine D₂ receptors in membranes from Ltk59 cells. The dotted line corresponds to a curve fit based on the simple allosteric ternary complex model (eq. 5) or to a simple model of competitive interaction. The solid line denotes the fit of the data to a model allowing for the allosteric modulator to recognize both orthosteric and allosteric sites. Data taken from Hoare and Strange (1996). B, enhancement and inhibition of the binding of the agonist, [³H]N⁶-cyclohexyladenosine ([³H]CHA) by the modulator PD 81,723 at the A₁ adenosine receptor in rat brain membranes. Data taken from Bruns and Fergus (1990). C, simulations based on a model of concomitant orthosteric and allosteric binding by an allosteric modulator (eq. 11). The following parameters were used pK _A = 4.6, pK _B1 = pK _B2 = 4.7, α = 0.25, β = 27, and log[A] = −5. D, simulations based on the same model, but with the following parameters pK _A = 9, pK _B1 = pK _B2 = 5, α = 7, β = 1, and log[A] = −9.

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Figure FS2

3. Nonequilibrium (Kinetic) Studies.

The study of allosteric modulator effects on radioligand kinetic binding properties probably represents the most sensitive direct measurement of allosteric interactions at GPCRs. The rates of association and dissociation of a ligand from its binding site (be it orthosteric or allosteric) on a receptor are exponential processes. Importantly, the actual rate constants that govern the ligand association (k _on) and dissociation (k _off) can be determined experimentally from kinetic experiments that measure radioligand binding as a function of time, and are very sensitive indicators of the interaction of the ligand with a particular conformation of receptor. Hence, a change in receptor conformation induced by an allosteric agent would be expected to result in an alteration of orthosteric ligand association and/or dissociation characteristics. It is this alteration in orthosteric ligand kinetics that underlies the effects of allosteric modulators on orthosteric ligand affinity at equilibrium.

From the simple TCM, the association constant,K _a, can be re-defined according to its respective kinetic rate constants. That is,K _a =k _onA/k _offA, where k _onA equals the association rate constant and k _offA equals the dissociation rate constant of ligand A. In the simplest case (and, thus far, the most commonly observed experimental situation), the kinetics of the modulator are more rapid than those of the orthosteric ligand. Under these conditions, the rate of dissociation of an orthosteric ligand in the presence of an allosteric modulator may be derived as follows (Lazareno and Birdsall, 1995; Christopoulos, 2000b) Equation 12where Equation 13In these two equations, ρ_At denotes the receptor occupancy by [A] at time t, ρ_Adenotes the receptor occupancy by [A] at equilibrium,k _offobs denotes the experimentally observed dissociation rate constant for [A], andk _offAB denotes the dissociation rate constant for [A] from the ternary complex [ARB]. The remaining parameters are as defined previously. The association of an orthosteric ligand under similar conditions is derived as Equation 14where Equation 15The parameter, k _onobs, denotes the apparent association rate constant of orthosteric ligand in the presence of allosteric modulator. K _Appis defined in eq. 6.

Allosteric modulators may increase or decrease the association and/or dissociation characteristics of the orthosteric ligand at its binding site on the receptor. Positive allosteric modulation can, thus, be manifested through an overall enhancement of orthosteric ligand association rate and/or a reduction in dissociation rate. To date, however, an enhancement of orthosteric ligand association rate has not been conclusively demonstrated for any allosteric modulators of GPCRs, although a recent study by Molderings et al. (2000) has suggested that agmatine is able to enhance the association rate and retard the dissociation rate of [³H]clonidine at the α₂-adrenoceptor through an allosteric mechanism, thus, enhancing radioligand affinity at equilibrium. For negative allosteric modulators, their equilibrium effects on orthosteric ligand affinity can generally be mediated via slowing orthosteric ligand association and/or enhancing dissociation. Unfortunately, the former mechanism is experimentally difficult to distinguish from simple competitive inhibition because competition will also lead to an apparent reduction in the observed orthosteric ligand association rate. In contrast, dissociation kinetic experiments theoretically monitor only the disintegration characteristics of a preformed orthosteric ligand-receptor complex, and any changes in the observed dissociation rate are much more unambiguously attributed to allosteric effects. These latter types of experiments, therefore, represent the most common type of radioligand kinetic assay used to detect and quantify allosterism at GPCRs.

Figure 11A shows the effects of the allosteric modulator 5-(N-ethyl-N-isopropyl)-amiloride (EPA) on the dissociation of [³H]yohimbine from the human α_2A-adrenoceptor. It can be seen that increasing the concentration of EPA results in a progressive increase in the dissociation of the orthosteric radioligand as the occupancy of the allosteric site by EPA becomes greater. This effect explains the reduction in [³H]yohimbine affinity by EPA observed in equilibrium binding assays. In contrast, the allosteric modulator, PD 117,975 slows the dissociation rate of the agonist [³H]CHA from adenosine A₁receptors (Fig. 11B), thus, accounting for its positively cooperative effects on agonist radioligand affinity at equilibrium. An interesting situation can arise, however, with certain allosteric modulators. Figure 12 illustrates the effects of the modulator, tetra-W84, on the apparent association and dissociation rates of the orthosteric antagonist [³H]N-methylscopolamine from the cardiac M₂ muscarinic acetylcholine receptor. It can be seen that the concentration-effect curves for the ability of the modulator to slow both kinetic properties of the radioligand are very close together. The consequence of this dual effect is seen in the curve of the interaction between tetra-W84 and [³H]N-methylscopolamine determined separately in an equilibrium binding assay (open circles). Under equilibrium binding conditions, it seems that tetra-W84 has no effect on binding. In fact, this is an example of a neutrally cooperative interaction (α = 1). Its allosteric nature is quite convincingly revealed in the radioligand kinetic assays, whereas it can be missed in equilibrium binding assays. Finally, it should also be noted that allosteric modulation of orthosteric ligand equilibrium affinity may be brought about by changes in both association and dissociation rates of the orthosteric ligand in the same direction (e.g., slowing or enhancing), provided that the magnitude of the change is not uniform for both rate constants. For example, most negative allosteric modulators of muscarinic acetylcholine receptors are known to retard the dissociation rate of orthosteric radioligands while still reducing equilibrium binding affinity (Ellis, 1997). This can most easily be reconciled in a mechanism where orthosteric ligand association is also slowed by the modulator to a greater extent than dissociation.

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Figure 11

Effects of allosteric modulators on orthosteric ligand dissociation kinetics. A, enhancement of the dissociation rate of [³H]yohimbine from the human α_2Areceptor expressed in CHO cell membranes by the modulator EPA. Data taken from Leppik et al. (1998). B, slowing of the dissociation rate of [³H]CHA from the adenosine A₁ receptor in rat brain membranes by the modulator PD 117,975. Data taken from Bruns and Fergus (1990).

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Figure 12

Neutral cooperativity between [³H]N-methylscopolamine and the modulator, Tetra-W84 at the M₂ muscarinic acetylcholine receptor. Increasing concentrations of modulator are able to decrease the rate of radioligand association and dissociation, thus, revealing the allosteric nature of the interaction (solid symbols). However, because the kinetics of the radioligand are influenced over similar concentration ranges and to similar extents, equilibrium binding studies show minimal effects on levels of radioligand binding (open circles). Data taken from Kostenis and Mohr (1996).

The quite profound effects that allosteric modulators can exert on orthosteric ligand kinetics can also lead to pitfalls in data analysis and interpretation. The most insidious effect is seen in binding experiments that are ostensibly conducted under standard “equilibrium” conditions but are, in fact, not at equilibrium due to the marked effects of the modulator on orthosteric ligand association and dissociation. This is most commonly observed with positive and neutrally cooperative ligands because their kinetic effects on the approach of the system to equilibrium occur over most concentrations of modulator that are tested, thus, increasing the likelihood of equilibrium not being achieved over the time course of a typical experiment. The consequences of this kinetic artifact can be modeled using eq. 14 and are shown in Fig.13. Even after 64 h, a positive allosteric modulator that is able to completely inhibit the dissociation of an orthosteric ligand from the ARB complex (k _offAB = 0) yields a bell-shaped binding curve. The effects of high concentrations of the modulator on the kinetics of the orthosteric ligand are so marked that equilibrium has not been achieved in the presence of the high modulator concentrations. Only after 2048 h (approximately 85 days) is equilibrium achieved. Experimentally, the easiest way of circumventing this problem is to prelabel the receptors with orthosteric radioligand before exposure to the allosteric agent (see Lazareno and Birdsall, 1995; Christopoulos, 2000b). Alternatively, the use of nonequilibrium kinetic assays to directly quantify the interaction may be preferred (Lazareno and Birdsall, 1995). Parenthetically, this kinetic effect is reminiscent of the binding profile that has been seen in equilibrium binding assays in some receptor systems (e.g., Fig. 10B). Although that binding profile may be due to mixed allosteric/competitive modes of interaction, the investigator must first rule out any kinetic artifacts of the allosteric modulator on the approach of the orthosteric radioligand to equilibrium.

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Figure 13

Allosteric modulation under nonequilibrium conditions. Orthosteric radioligand binding was simulated for a positive allosteric modulator (α = 10) using eqs. 12 through 15 and the following parameters: pK _A = pK _B = 7,k _offA = 0.5 min⁻¹,k _offAB = 0 min⁻¹, and log[A] = −7. The curves represent the concentration-occupancy relationship for the interaction at the different times (hours) shown in the figure. It is evident that allosteric modulators may slow the kinetics of the system to such an extent that equilibrium is unachievable during the time course of the experiment, thus, yielding complex binding curves.

1. Schild Analysis.

Competitive antagonism follows a strict adherence to the model defined by Gaddum (1936, 1957) and quantified by Arunlakshana and Schild (1959). Thus, the effect of a competitive antagonist on the concetration-response curve to an agonist is strictly defined by the term 1 + [B]/K _B, where [B] is the concentration of antagonist and K _B the equilibrium dissociation constant of the receptor-antagonist complex. Under these circumstances, the dextral displacement produced (expressed as “CR”, which is the equiactive concentration ratio of agonist concentrations measured in the presence and absence of antagonist) is related to [B] and K _B by the Schild equation (Arunlakshana and Schild, 1959). Equation 16The slope and linearity of the Schild regression become very useful criteria for the definition of competitive antagonism. Deviations from linearity or from a line with slope of unity can occur as a result of a number of nonequilibrium situations including agonist uptake processes, receptor heterogeneity, and temporal disequilibrium (Kenakin, 1982). However, one notable deviation also can occur with allosteric antagonism. Specifically, an allosteric antagonist can produce a Schild regression, which, at some point along the concentration axis, deviates from linearity or has a slope of less than unity. This would occur because of the saturable nature of the antagonism (i.e., the magnitude of α). Thus, allosteric antagonists will shift the agonist concentration-response curve to the right according to a limit defined by (1 + [B]/K _B)/(1 + α[B]/K _B). These relationships become very apparent when plotted in the form of Schild regressions, with the maximal concentration-ratio attainable being determined by the cooperativity factor, α. Figure 14A shows the antagonism by gallamine of the negative inotropic effects of acetylcholine at M₂ muscarinic receptors in the guinea pig electrically stimulated left atrium. It can be seen that as the concentration of modulator is increased, the dextral displacement of the acetylcholine curves approaches a limit. The Schild regression of the same data are shown in Fig. 14B, where the deviation from a straight line is clearly evident. In fact, a linear regression through the data points yields an unsatisfactory fit with a slope factor of 0.65. The appropriate fit of the allosteric model to the data can be obtained with the following equation (Ehlert, 1988). Equation 17As shown in Fig. 14B, eq. 17 allows an estimate to be obtained of the cooperativity factor and the dissociation constant of the modulator for the allosteric site.

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Figure 14

Schild analysis of allosteric interactions. A, effects of acetylcholine (ACh) on the electrically evoked contractions of the guinea pig left atrium in the absence (▪) or presence of the allosteric modulator gallamine at the following concentrations: 10 μM (▴), 30 μM (▾), 100 μM (♦), 300 μM (■), and 500 μM (●). All experiments were conducted in the presence of the cholinesterase inhibitor, diisopropylfluorophosphate. B, Schild plot of the data shown in A. The solid line (slope = 1) denotes the behavior expected for a competitive antagonist, whereas the dashed line shows the best fit linear regression (and associated slope factor) through the points. The curve through the points and associated parameter estimates represent the fit of the allosteric model (eq. 17). Data taken from Christopoulos (2000a). C, agonist-dependence of functional allosterism. Schild regressions for gallamine as an antagonist of muscarinic agonist responses in rat trachea. Data taken from Kenakin and Boselli (1989).

Another prediction of the allosteric model directly related to the dependence of allosterism on the choice of orthosteric ligand (e.g., agonist) is the phenomenon of agonist-specific degrees of antagonism. This trait is also demonstrated by gallamine (Clark and Mitchelson, 1976; Kenakin and Boselli, 1989). Although gallamine produces dextral displacement of muscarinic agonist concentration-response curves in rat trachea, the resulting regressions are agonist-dependent (Fig. 14C), and some deviate from a slope of unity (Kenakin and Boselli, 1989). Agonist-dependent Schild regressions can also be obtained in systems with mixtures of receptors (Kenakin, 1982, 1992), but in those instances, the pattern is a set of parallel displaced Schild regressions with differing intercepts (pA₂values). In contrast, allosteric antagonism would show the pattern in Fig. 14C, namely, little change in intercept with deviations occurring at higher concentration ratios (as saturation of the allosteric sites occurs).

2. Additivity of Concentration Ratios.

As discussed previously, competitive antagonism defines a formal relationship between the concentration of the antagonist and its expected effects on agonist concentration-response curves, i.e., a parallel dextral displacement with no diminution of curve maxima, and a magnitude of curve shift defined by the Schild equation. The addition of a second antagonist to a mixture of agonist and antagonist would simply produce re-equilibration of the three molecules with their respective contributions to receptor activity being defined by the ratio of their concentration and equilibrium dissociation constants (i.e., [B₁]/K _B1 + [B₂]/K _B2 + [B₃]/K _B3… etc.). Thus, the measured effect of adding a second antagonist of known receptor potency into a system can be used to detect possible deviation from true competitivity by the two antagonists in terms of additive concentration ratios (Paton and Rang, 1965). Specifically, if two antagonists, B and C, were combined and tested against an agonist, then their combined concentration-ratio (CR_BC) would be given as follows for a competitive interaction. Equation 18where CR_B and CR_Cdenote the concentration ratios obtained for the agonist in the absence or presence of each respective antagonist alone. In contrast, if the antagonists were not mediating their inhibitory effects by a simple competitive mechanism through the orthosteric binding site, then CR_BC would be a multiplicative, rather than additive, function of CR_B and CR_C (Paton and Rang, 1965). For the specific case of the allosteric TCM, the actual expression for the interaction between an agonist, a competitive antagonist (B) and an allosteric modulator (C) is given as (Christopoulos and Mitchelson, 1994). Equation 19where α′ denotes the cooperativity factor for the interaction between the antagonist, B, and modulator, C. A direct consequence of the dependence of allosteric modulation on the ligand occupying the orthosteric site is that markedly greater-than-additive or less-than-additive combination concentration ratios may be observed, clearly deviating from the additivity predicted by simple competition. Figure 15A illustrates this with an example of the interaction between the muscarinic agonist carbachol, the orthosteric antagonist N-methylscopolamine, and the allosteric modulator alcuronium. The dashed line represents the expected shift of the carbachol curve in the presence of bothN-methylscopolamine and alcuronium if the interaction between all ligands was competitive. This predicted shift was calculated from the individual shifts produced by eitherN-methylscoplamine or alcuronium alone. However, the actual observed shift lies much farther to the right of the predicted shift, an example of supra-additive antagonism. This finding is consistent with the known ability of alcuronium to allosterically potentiate the binding of N-methylscopolamine, while simultaneously reducing the binding of carbachol, thus, enhancing the overall antagonism observed.

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Figure 15

Additivity of concentration-ratio analysis. A, M₂ muscarinic acetylcholine receptor-mediated effect of carbachol on the electrically evoked contractions of the guinea pig left atrium in the absence (●) or presence of the antagonist, 3 nMN-methylscopolamine, alone (■) or combined with the allosteric modulator, 10 μM alcuronium (⋄). The dashed line shows the expected location of the agonist curve in the presence of both antagonists if all ligands were interacting in a competitive manner at the orthosteric site, based on eq. 18. B, effect of carbachol in the absence (●) or presence (■) of the combination of the two allosteric modulators, 10 μM alcuronium and 10 μM heptane 1,7-bis-(dimethyl-3′-pthalimidopropyl) ammonium bromide. The dashed line shows the expected location of the agonist curve in the presence of both antagonists if the inhibitors were interacting in a competitive manner at a common allosteric site, based on eq. 20. Data taken fromLanzafame et al. (1997).

Concentration-ratio analysis is not only restricted to the combination of orthosteric antagonists with allosteric modulators. The combination of two allosteric modulators against an agonist can also be studied using this approach. This is particularly useful in demonstrating whether two different allosteric modulators interact with the same allosteric site on a GPCR. In this instance, the appropriate equation is (Lanzafame et al., 1997). Equation 20where B and C denote two different allosteric modulators, and α and β denote their respective cooperativity factors for interaction with the agonist. Figure 15B illustrates the interaction between carbachol and the two modulators, alcuronium and heptane 1,7-bis-(dimethyl-3′-pthalimidopropyl) ammonium bromide, at atrial muscarinic receptors. The excellent agreement between the observed carbachol curve in the presence of both modulators and the predicted curve based on eq. 20 is in accordance with both modulators interacting with the same allosteric site on the M₂muscarinic receptor.

3. Pharmacological Resultant Analysis.

Although the additivity-of-concentration-ratio approach described above is obviously useful in detecting allosterism, a potentially significant shortcoming of this procedure is the required tacit assumption that neither antagonist has a secondary property that modifies the system sensitivity. A powerful tool to measure the additive effects of antagonists that does not have this handicap is pharmacological “resultant analysis” (Black et al., 1986). This technique compares the effect of a “test” antagonist on the observed antagonism produced by a “reference” antagonist. The strength of this method lies in the fact that the test antagonist is added to the system from the very start of the experiment (even present for the control curve), and, thus, any secondary effects of this antagonist are negated by the fact that these effects are present for all measurements of sensitivity of the system to the reference antagonist and, thus, cancel. Several Schild regressions for the reference antagonist are obtained in the presence of different concentrations of the test antagonist and then the displacements of these Schild plots, along the reference antagonist concentration axis, are used to construct resultant plots. These have strictly defined properties for two competitive antagonists, therefore, deviations from these requirements may indicate allosterism in the actions of the test antagonist.

The response (E′) to an agonist in the combined presence of a test antagonist [C] and reference antagonist [B] is given by Equation 21where [A] refers to the concentration of agonist in the absence of reference antagonist, [A′] refers to the concentration of agonist in the presence of reference antagonist, [B′] refers to the concentration of reference antagonist in the presence of test antagonist ([C]), and K _A,K _B, andK _C refer to the respective equilibrium dissociation constants of the receptor and molecules A, B, and C. The response in the absence of reference antagonist (denoted as E) is given by eq. 21 with [C] = 0. Comparison of equiactive concentrations (E = E′) with the reference antagonist present and not present is given by Equation 22A ratio, r, can be defined for equiactive agonist doses in the absence of test antagonist by setting [C] = 0 in eq. 22. Comparing equal levels of antagonism (in essence measuring the dextral displacement of Schild regressions along the test antagonist axis at a constant level of antagonism) leads to the expression of equiactive (from the point of view of equal levels of antagonism) concentrations of the reference antagonist in the absence ([B]) and presence ([B′]) of test antagonist. Equation 23The logarithmic metameter of eq. 23 is Equation 24Thus, a plot of log (φ − 1) as a function of concentration of test antagonist should be linear and have a slope of unity with an intercept equal to the equilibrium dissociation constant of the test antagonist. This latter parameter can be measured independently; thus, there are three observable tests (slope, linearity, and intercept) for competitivity in this procedure, including one that can be independently verified, consistent with the known allosteric nature of gallamine's mechanism of action.

Although resultant analysis, as described above, is a powerful technique for detecting allosterism, it is unable to quantify the allosteric interaction because, in its original form, it is not formulated based on an allosteric model. However, the theoretical underpinnings of the procedure can readily be modified to incorporate an allosteric model (Christopoulos and Mitchelson, 1997), leading to the following variant of eq. 24. Equation 25Thus, the methodology behind pharmacological resultant analysis allows for both the detection of allosteric interactions between two antagonists in a functional tissue assay and for the derivation of quantitative parameters describing the interaction.

1. Multiple Allosteric Sites.

Not all of the data derived from studies on GPCR allosterism are compatible with the notion of a single extracellular allosteric site in addition to the orthosteric site. For instance, gallamine and tubocurarine exert biphasic effects on the dissociation of [³H]QNB at M₂ muscarinic receptors in low ionic strength media, first enhancing and then retarding radioligand dissociation depending on the concentration of modulator used (Ellis and Seidenberg, 1989; Ellis et al., 1991). These data are difficult to explain without postulating the existence of two separate allosteric sites that the modulators recognize with different affinities. Other examples include the green mamba venom “m1-toxin”, which forms an almost irreversibly bound cap across the extracellular regions of the M₁ muscarinic receptor by using multiple binding points (Max et al., 1993), and different attachment points have also been suggested for a series of hexamethonium derivatives (Bejeuhr et al., 1994) and unilaterally ring-substituted bispyridinium derivatives (Kostenis et al., 1996) on M₂ muscarinic receptors. Significantly, the anticholinesterase tetrahydroaminacridine (THA) consistently results in inhibition curves with slopes steeper than unity for various orthosteric radioligands at muscarinic receptors (Flynn and Mash, 1989; Potter et al., 1989; Kiefer-Day et al., 1991;Mohr and Tränkle, 1994). The simplest scheme to accommodate these results would involve THA recognizing both the orthosteric and allosteric sites but only exerting positive cooperativity with respect to its own binding. Alternatively, THA may recognize two modulatory sites, each interacting positively co-operative with one another and negatively cooperative with the orthosteric site.

Figure 20 shows the results from a series of radioligand dissociation kinetic experiments performed at the M₂ muscarinic receptor using a variety of allosteric modulators; the data are plotted in the form of Schild regressions. It can be seen that the weak modulator, obidoxime, was able to concentration-dependently inhibit the allosteric effects of gallamine, W84, alcuronium, and WDuo3 and that the estimates of obidoxime's affinity for the allosteric site were in general agreement in each case (Tränkle and Mohr, 1997). However, the interaction between obidoxime and the modulator, Duo3, is characterized by a significantly lower pA₂ value, strongly suggestive of interaction at a different allosteric site. Unfortunately, one of the limitations of using ligands such as obidoxime is that its low affinity for the allosteric site(s) limits the concentration ranges over which it can be tested. More recent studies have identified the indolocarbazole, KT5720, as a relatively high-affinity allosteric modulator of M₁muscarinic receptors that shares obidoxime's ability of exerting minimal effects on orthosteric ligand dissociation kinetics while maintaining the ability to bind to an allosteric site (Lazareno et al., 2000). This important property has been used in combination experiments monitoring the interaction between KT5720 and [³H]NMS in the absence or presence of acetylcholine and other allosteric modulators such as gallamine and brucine. Surprisingly, it was found that KT5720 could bind simultaneously to the receptor with gallamine or brucine and orthosteric ligands. The interaction between KT5720 and gallamine or brucine was neutrally cooperative, whereas it exerted positive cooperativity with [³H]NMS and acetylcholine. Thus, the presence of two distinct allosteric sites has been suggested for the M₁ receptor.

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Figure 20

Schild plots of the interaction between the allosteric modulator, obidoxime, and other modulators at the M₂ muscarinic acetylcholine receptor. Dose ratios (DR) were calculated as the concentration of indicated allosteric modulator producing half-maximal slowing of [³H]NMS dissociation from the receptor in the absence to that obtained in the presence of increasing concentrations of obidoxime. The interaction between obidoxime and Duo3 is not consistent with binding to a common allosteric site recognized by the other modulators. Data taken fromTränkle and Mohr (1997).

Recent data also suggest that more than one allosteric site exists on the α₁-adrenoceptor. For example, the allosteric modulator 5-(N,N-hexamethylene)-amiloride enhances [³H]prazosin dissociation at the human α₁-adrenoceptor, but the data cannot be fitted to the simple allosteric TCM (Leppik et al., 2000). However, an extension of the allosteric model to incorporate two binding sites for 5-(N,N-hexamethylene)-amiloride on the α₁-receptor can adequately accommodate the entire dataset.

Finally, it is possible that other highly conserved allosteric sites may be present on many GPCRs. Table 8lists the inhibition binding parameters for the novel thiadiazole compoundN-(2,3-diphenyl-1,1,4-thiadiazol-5-(2H)-yildene)methenamine at a range of class I GPCRs. This compound inhibits the binding of both agonists and antagonists with low micromolar potency at these receptors in a reversible manner that is independent of receptor-G protein coupling (Fawzi et al., 2001). This is in contrast to other general modulators of GPCRs such as suramin (see above) that lose their allosteric properties in the absence of G proteins. Furthermore, the inhibition of orthosteric binding byN-(2,3-diphenyl-1,1,4-thiadiazol-5-(2H)-yildene)methenamine is accompanied by a concentration-dependent reduction in radioligandB _max values, thus, suggesting a noncompetitive mode of binding. Overall, however, the presence of a distinct and conserved allosteric site for small molecules at a variety of class I GPCRs is still mostly speculative at the moment and remains to be further investigated.