Introduction

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The five subtypes of muscarinic acetylcholine receptors are members of the superfamily of G protein-coupled receptors. The binding site for acetylcholine and conventional agonists and antagonists on muscarinic receptors seems to be located within a pocket formed by the seven -helical transmembrane domains characteristic of all G protein-coupled receptors (Hulme et al., 1990; Wess, 1993). There is a high degree of conservation of amino acid sequence in the regions that are considered to bind agonists and antagonists. This may be a reason for the difficulty in developing agonists and antagonists that are highly subtype selective.

Another feature of muscarinic receptors is the presence of a second, allosteric, binding site (Lee and El-Fakahany, 1991; Lazareno and Birdsall, 1995; Tucek and Proska, 1995; Ellis, 1997; Christopoulos et al., 1998; Holzgrabe and Mohr, 1998). Several observations have suggested that muscarinic allosteric ligands bind to more extracellular and presumably less conserved regions of the receptor, which may allow for greater selectivities. All five muscarinic receptor subtypes are subject to allosteric modulation (Ellis et al., 1991), and a wide array of structurally very different allosteric agents has been demonstrated to modulate the binding of conventional ligands to the five subtypes. Interestingly, among the allosteric agents that exhibit a high degree (>10-fold) of allosteric subtype selectivity, all have the greatest affinity toward the M₂ subtype and the lowest affinity toward M₅ (Ellis and Seidenberg, 2000). With regard to the M₂ receptor, gallamine, alcuronium and a number of other allosteric ligands have been demonstrated to interact competitively with the probe obidoxime providing strong experimental evidence for a common allosteric site (Ellis and Seidenberg, 1992, 2000; Tränkle and Mohr, 1997).

Studies of chimeric and mutant receptors have begun to identify receptor domains and amino acids that may constitute the muscarinic allosteric site. Almost every mutagenic study published so far has focused on gallamine as the allosteric modulator (Lee et al., 1992; Ellis et al., 1993; Leppik et al., 1994; Matsui et al., 1995; Gnagey et al., 1999). Of these studies, three have taken advantage of the subtype selectivity of gallamine by investigating chimeric substitutions. In studies with M₂/M₅ chimeric receptors, the affinity of gallamine was exclusively enhanced, relative to M₅, when the chimeric receptor included the M₂ third extracellular loop (Ellis et al., 1993) due to an asparagine residue at M₂⁴¹⁹ (Gnagey et al., 1999). Substitutions that did not include this epitope were without effect. Nonetheless, insertion of this epitope in M₅ did not restore M₂ affinity completely. Chimeric studies including other muscarinic subtypes have demonstrated that gallamine also interacts with acidic residues in the region of the second outer loop of both the M₂ and the M₅ receptor (Leppik et al., 1994; Ellis, 1997; Gnagey et al., 1999).

Recently, the mutagenic studies were extended to other muscarinic allosteric ligands (Ellis and Seidenberg, 2000). In M₂/M₅ chimeric receptors, the affinity of alcuronium, another prototype allosteric modulator, was not dependent on the source of the third outer loop of the chimera, but was exclusively sensitive to the source of the second outer loop plus flanking transmembrane regions. As in the gallamine study above, this epitope, although clearly very important, did not confer the entire M₂ affinity. Finally, even though these different allosteric agents seemed to derive affinity from different receptor epitopes, they nevertheless were shown to compete for the obidoxime-sensitive site (Tränkle and Mohr, 1997; Ellis and Seidenberg, 2000).

Diallylcaracurine V, structurally closely related to alcuronium, has recently been identified as an allosteric agent with a similar high binding affinity for the M₂ subtype (Zlotos et al., 2000). The structural formulae of these two compounds look almost identical (Fig. 1), but their stereochemistry is considerably different (Zlotos, 2000). Using this tool, we aimed to find out whether the stereochemical difference, relative to alcuronium, is sufficient to translate into divergent epitope sensitivities. Two other caracurine V derivatives and two flexible alkane-bisammonium-type allosteric modulators were included in our studies.

View larger version (22K): [in this window] [in a new window]   Fig. 1.   Structures of the muscarinic allosteric ligands investigated in this study.

Interestingly, we found that the affinities of the caracurine V and alkane-bisammonium compounds were sensitive to common epitopes. Like alcuronium, they had higher affinity for receptors that possessed M₂ sequence in the second outer loop and flanking regions. However, their affinities were also dependent on an epitope in the seventh transmembrane domain. Using site-directed mutagenesis, we identified the essential epitope in TM7 as M₂⁴²³threonine. This epitope is also present in the M₄ receptor, as M₄⁴³⁶serine. We have found that these two epitopes completely account for the M₂/M₅ selectivity of the caracurine V and alkane-bisammonium compounds. The simultaneous insertion of both M₂ epitopes into the M₅ receptor fully attained M₂ affinity. Some of these data have been reported previously in abstract form (Buller et al., 2001).

	Experimental Procedures

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Materials. Atropine sulfate was obtained from Sigma Chemical Co. (St. Louis, MO). Alcuronium was obtained from Roche Laboratories (Nutley, NJ). The bisquaternary caracurine V derivatives were synthesized as described previously (Zlotos et al., 2000). W84 was synthesized by Dr. Joachim Pfeffer (Department of Pharmacology, University of Kiel, Kiel, Germany), according to the method of Wassermann (1970). Dimethyl-W84 was generously provided by Prof. Dr. Ulrike Holzgrabe (Tränkle et al., 1998). [³H]N-methylscopolamine chloride ([³H]NMS; 70-82 Ci/mmol) was obtained from PerkinElmer Life Sciences (Boston, MA).

Mutagenesis and Expression. The preparation of the chimeric receptors has been described previously (Ellis et al., 1993); schematic diagrams are shown in Figs. 2 and 3. The exact sequence compositions are as follows: CR3: hM₅ 1-162, hM₂ 156-300, hM₅ 336-532; CR4: hM₅ 1-445, hM₂ 391-421, hM₅ 477-532; CR5: hM₂ 1-155, hM₅ 163-532; and CR6: hM₂ 1-69, hM₅ 77-445, hM₂ 391-466. Site-directed mutagenesis was performed with the QuikChange kit (Stratagene, La Jolla, CA). Briefly, oligonucleotides containing the desired base changes were synthesized and allowed to anneal with pcD plasmids containing the appropriate muscarinic receptor DNA sequence. A high-fidelity polymerase then extended the synthetic oligonucleotides in a thermocycled reaction. The parental DNA was digested by a methylation-specific endonuclease before transformation of bacteria. Mutations were confirmed by sequencing. Plasmids containing the human M₂ or M₄ wild-type or mutated receptor genes were purified from bacterial cultures and transiently transfected into COS-7 cells by calcium phosphate precipitation. M₅ wild-type receptors were stably expressed in CHO cells. For binding assays, cells were harvested by scraping into 5 mM Na,K,P_i buffer, pH 7.4 (PB). After homogenization and centrifugation at 50,000g for 20 min, membranes were resuspended in 5 mM PB and stored as aliquots at 70°C.

View larger version (31K): [in this window] [in a new window]   Fig. 2.   Allosteric effect at M2 and M5 wild-type and the chimeric receptors CR3 and CR6. Schematic representation of the chimeric receptors CR3 and CR6 (top). A through D, concentration-effect curves for the allosteric delay of [3H]NMS dissociation for the compounds CARALL, Alcuronium, CARMETH, and W84. The receptors were prelabeled with [3H]NMS and the rate of dissociation of the labeled ligand was then determined in the absence or presence of the indicated allosteric modulator. Ordinate, ratio of the rate of [3H]NMS dissociation in the presence of each concentration of allosteric modulator (kobs) to the rate of dissociation of [3H]NMS alone (k0), expressed in percent. Abscissa, concentration of allosteric modulator. Experiments were conducted in 5 mM PB. The data presented are mean values ± S.E. of two to four separate experiments and the curves are the best fits to the model described under Experimental Procedures.

View larger version (27K): [in this window] [in a new window]   Fig. 3.   Allosteric effects of CARALL at overlapping chimeric receptors. Schematic representation of the chimeric receptors CR4 and CR5 (top), concentration-effect curves for the allosteric effect of CARALL at M2 and M5 wild-type and the chimeric receptors CR4 and CR5 (bottom). Experiments were conducted as in Fig. 2. Indicated are mean values ± S.E. of three to four separate experiments.

Dissociation Binding Assays. Binding assays were conducted in 5 mM PB, pH 7.4, at 23°C. Membranes were prelabeled with 1 nM [³H]NMS for 30 min. Measurement of [³H]NMS dissociation was then initiated by the addition of 3 µM atropine, with or without the indicated concentration of allosteric modulator. After the appropriate time interval, the incubation was terminated by filtration through S&S 32 glass fiber filters (Schleicher & Schuell, Keene, NH), followed by two rinses with 40 mM PB (0°C). Membrane-bound radioactivity was determined by liquid scintillation counting. Nonspecific binding was determined by the inclusion of 3 µM atropine during the labeling period.

	Results

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The structures of the muscarinic allosteric ligands investigated in this study are shown in Fig. 1. All of the investigated compounds exhibited much greater allosteric affinity toward the M₂ subtype than the M₅ subtype. The ratio of these affinities ranged from about 70-fold to more than 300-fold higher affinity for the M₂ subtype. Dissociation assays have been used extensively to ensure that only effects mediated by the allosteric binding site are being observed. The effect on ligand dissociation results from an interaction of the modulator with the ligand-occupied receptor and is thus indicative of an interaction with a recognition site distinct from the ligand binding site. The concentration-dependent effects of an allosteric ligand on [³H]NMS dissociation should be proportional to the occupancy of the allosteric site (Ellis, 1997) and thus reflect the affinity of the allosteric ligand at the NMS-occupied receptor (Lazareno and Birdsall, 1995). To investigate the structural basis of their subtype selectivity, the compounds have been evaluated at M₂/M₅ chimeric receptors in which segments of low-affinity M₅ receptor were systematically replaced with analogous segments of high-affinity M₂ receptor. Subsequently, site-directed mutagenesis was performed with the aim of attributing their selectivities to specific residues.

The rates of dissociation of [³H]NMS from wild-type, chimeric, and point-mutated receptors in the absence of allosteric modulator (k₀) are compiled in Table 1. The rates for the wild-type and chimeric receptors are in good agreement with previously reported data (Ellis et al., 1993; Gnagey et al., 1999). [³H]NMS dissociated much more rapidly from the M₂ subtype than from M₅. The M₂/M₅ chimeric receptor CR3 exhibited a dissociation rate even slower than M₅ (factor of 2), whereas NMS dissociated from CR6 as fast as it did from the M₂ subtype itself. The subsequently studied point mutations in wild-type and chimeric receptors produced small but noticeable changes in k₀ that did not exceed a factor of 3 (see Discussion).

M₂/M₅ Chimeric Receptors. In a first round, the affinity of the compounds toward the two M₂/M₅ chimeric receptors CR3 and CR6 was investigated. CR3 contains a segment of M₂ sequence that includes the extracellular half of TM4, the second outer loop, TM5, and a portion of the third intracellular loop. CR6 contains M₂ segments at the amino and carboxyl termini embedded in the M₅ receptor (schematic diagrams are given in Fig. 2; for exact sequence compositions of the chimeric receptors, see Experimental Procedures).

Point Mutations in TM7. There is in general a high degree of conservation in TM7, but there is a striking divergence at the position corresponding to the M₂⁴²³threonine residue; M₅ has a histidine residue at this position (Fig. 4). To investigate whether this threonine residue makes a crucial contribution to the M₂ selectivity over M₅, a single point mutation was introduced into the M₂ receptor, replacing threonine⁴²³ with histidine. This point mutation markedly reduced the affinity toward the caracurine V derivatives and the compounds W84 and dimethyl-W84 (Fig. 5A, representatively for CARALL; Table 2). Interestingly, the affinity of this point mutant was about the same as that of the chimera CR3.

View larger version (12K): [in this window] [in a new window]   Fig. 4.   Amino acid sequences of the human M2, M4, and M5 receptors in the beginning of TM7. The shaded residues lie in homologous positions. Sequences are from Bonner et al. (1988).

View larger version (13K): [in this window] [in a new window]   Fig. 5.   Effects of point mutations in TM7 on the allosteric effects of CARALL. Reciprocal mutations were made in the M2 and M5 receptors, and in the chimeras CR3 and CR6, at the position homologous to M2423, as indicated. Experiments were conducted and analyzed as in Fig. 2. Indicated are mean values ± S.E. of two to four separate experiments.

Analogous Point Mutations in M₄. At the position corresponding to M₂⁴²³threonine, the M₄ receptor has a serine residue (M₄⁴³⁶serine; Fig. 4). In view of the similarity of these amino acids, it was hypothesized that the M₄ serine would be correspondingly involved in the selectivity of M₄ over M₅. To test this, two point mutations in the M₄ receptor were created. In one, M₄⁴³⁶serine was replaced with the corresponding (M₂) threonine; in the other, M₄⁴³⁶serine was replaced with (M₅) histidine. The compounds CARPROG, CARMETH, and dimethyl-W84 were investigated at the M₄ wild-type and mutant receptors. For all compounds, the M₄ wild-type affinity was somewhat lower than that of M₂, but nevertheless considerably higher than that of M₅ (Fig. 6, A-C). As expected, replacement of M₄⁴³⁶serine with threonine did not produce any significant effect on affinity toward the above compounds (Table 2). However, analogously to M₂⁴²³ThrHis, the mutation M₄⁴³⁶SerHis resulted in a marked loss of affinity toward the test compounds. There seems to be a correlation between the extent of affinity loss seen with M₄⁴³⁶SerHis and M₂⁴²³ThrHis (Fig. 6, A-C). That is, CARMETH, which displayed the highest sensitivity toward M₂⁴²³threonine, correspondingly showed the greatest loss in affinity (87-fold) when replacing M₄ serine with histidine. On the other hand, dimethyl-W84 was the least sensitive to the presence of M₂⁴²³threonine among the compounds studied and also showed the smallest loss in affinity when M₄⁴³⁶serine was mutated to histidine (4-fold). Thus, the M₂ and M₄ subtypes seem to contain a common epitope for the interaction with these allosteric ligands. This epitope is missing in M₅ and thus makes a crucial contribution to the M₂/M₅ and the M₄/M₅ subtype selectivities.

View larger version (15K): [in this window] [in a new window]   Fig. 6.   Effects of mutation at M4436serine on the potencies of allosteric ligands. Concentration-effect curves for the allosteric effect of CARMETH, CARPROG, and dimethyl-W84 were carried out with M2, M4, and M5 wild-type receptors and the indicated mutant receptors. Experiments were performed and analyzed as in Fig. 2. Data shown are mean values ± S.E. of two to three separate experiments.

	Discussion

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Recent studies with M₂/M₅ chimeric receptors provided evidence that structurally different allosteric ligands may derive affinity from different receptor epitopes (Ellis and Seidenberg, 2000). We have investigated derivatives of the bisquaternary strychnos alkaloid caracurine V that are closely related to the prototype allosteric ligand alcuronium, in particular the N,N'-diallyl derivative CARALL (Fig. 1). However, the stereochemistry of alcuronium and CARALL is considerably different (Zlotos, 2000). Here, we show that a stereochemical difference is sufficient to translate into divergent epitope sensitivities. The two flexible alkane-bisammonium allosteric ligands W84 (Tränkle et al., 1996) and dimethyl-W84 that strongly contrast the rigid and highly fused ring system of the caracurine V skeleton (Zlotos et al., 2000) were included in our studies. All of these compounds were highly M₂/M₅ selective and thus ideally suited for evaluation at M₂/M₅ chimeric receptors to study the specific epitopes that confer their subtype selectivity. Dimethyl-W84 is of additional interest because it has been developed and is currently used as a novel radioligand to label the allosteric site on M₂ receptors (Tränkle et al., 1998; 1999). Because the allosteric site seems to contain several potential epitopes for allosteric agent binding, we wondered whether the flexible agents could compensate for the removal of a point of attachment by switching to another conformation that would permit interaction with another epitope. If this were so, we would not expect to observe a clear-cut epitope dependence for the flexible compounds.

The affinity of alcuronium has been reported to be exclusively enhanced toward the M₂/M₅ chimera that includes the second outer loop and flanking regions of M₂, CR3 (Ellis and Seidenberg, 2000). However, the affinities of CARALL and the other caracurine V derivatives were enhanced not only at CR3 but also at CR6, which includes the seventh transmembrane domain of M₂. Thus, alcuronium and the caracurine V compounds may derive affinity from a common epitope in CR3, but they do not seem to share all points of attachment at the allosteric binding site. On the other hand, the flexible alkane-bisammonium compounds seem to be sensitive to the same epitopes that influence the binding of the caracurine V derivatives. With varying respective ratios, both groups of compounds had significantly greater affinities toward both CR3 and CR6, compared with M₅.

Our subsequent studies at other chimeric receptors and point mutations in wild-type and chimeric receptors demonstrated that the enhanced affinity of CR6 is caused entirely by a single amino acid at the top of TM7 (i.e., M₂⁴²³threonine). This epitope was also found present at the corresponding position in the M₄ receptor, as M₄⁴³⁶serine. Thus, both the M₂ and M₄ subtypes seem to contain a common epitope for the interaction with these allosteric ligands; absent in M₅, this epitope makes a crucial contribution to their M₂/M₅ and M₄/M₅ subtype selectivities. In addition, the data support the idea that these allosteric ligands adopt a similar orientation at the different subtypes.

In the present study we have taken the ability of the allosteric test compounds to slow the dissociation of [³H]NMS as a measure of their allosteric effect. The great advantage of this approach is that it ensures that only allosteric effects are being observed. On the other hand, affinities for the free receptor cannot be extracted from these data. There are, however, some indications that suggest that there is a common binding mode for allosteric ligands at the free and NMS-liganded receptors (Ellis and Seidenberg, 2000; Schröter et al., 2000). Because [³H]NMS dissociated much more rapidly from the M₂ subtype than from M₅, one could argue that high-affinity binding of the allosteric ligand is associated with a fast dissociation and low-affinity binding with slow dissociation of [³H]NMS. However, the rate of dissociation of [³H]NMS from the M₂/M₅ mutant receptors was not found to correlate with the potency of the allosteric agents. For instance, whereas M₂ and CR3 HisThr were very similar in terms of affinity toward the compounds (see Table 2), the respective half-times for the dissociation of [³H]NMS are clearly different (Table 1). A similar dichotomy can be appreciated by comparing M₅ and CR6 ThrHis. Several reasons have been previously discussed why rate constants (k₀) are not expected to be consistently tied to particular receptor epitopes (Ellis et al., 1993; Ellis and Seidenberg, 2000). Nonetheless, a certain consistency was observed in the way the threonine/histidine point mutations affected the respective half-times of [³H]NMS dissociation. Replacement of threonine with histidine at M₂⁴²³ and at the corresponding position of CR6 slowed the dissociation of [³H]NMS (as did the replacement of M₄⁴³⁶serine with histidine). On the other hand, replacement of the corresponding histidine with threonine in M₅ and CR3 accelerated [³H]NMS dissociation (Table 1).

The M₂⁴²³threonine residue has previously been investigated in a different context. Liu et al. (1995) demonstrated that a series of M₂/M₅ chimeric receptors were expressed but were unable to bind muscarinic radioligands. The authors concluded that in the pharmacologically inactive receptors, a TM1 threonine residue (M₅³⁷Thr) faced a TM7 threonine residue (M₂⁴²³Thr) that interfered with proper helix-helix packing. This might seem to imply that our M₅⁴⁷⁸Thr mutant (and the mutant CR3 HisThr) would suffer from the same helix-helix packing problem and be unable to bind [³H]NMS. However, our studies found that both mutant receptors M₅⁴⁷⁸HisThr and CR3 HisThr were expressed and gave the expected degree of [³H]NMS binding. More detailed studies with M₅⁴⁷⁸HisThr revealed exactly the same NMS affinity as for the M₅ wild-type receptor (data not shown). Indeed, the M₂/M₃ chimeric receptor "m3N2" has the corresponding threonine residues in TM1 (from M₃) and in TM7 (from M₂), yet has been reported to bind [³H]NMS with high affinity (Wess et al., 1990). In addition, the M₄ wild-type receptor has a serine residue at the corresponding position in TM7 (M₄⁴³⁶serine) and a threonine residue in TM1 (M₄³⁹threonine). Thus, although it seems likely that the findings of Liu et al. (1995) do reflect interhelical interactions, the conflict may be unique to the particular receptor constructs that they studied.

Nearly every mutagenic study of the muscarinic allosteric binding site that has been published to date has focused on gallamine as the primary allosteric modulator (Lee et al., 1992; Ellis et al., 1993; Leppik et al., 1994; Matsui et al., 1995; Gnagey et al., 1999). Matsui et al. (1995) mutated conserved aromatic and polar residues in the extracellular loops and loop/transmembrane helix interfaces of the M₁ receptor. This study found that the M₁⁴⁰⁰tryptophan residue at the junction of o3/TM7 was important for the binding of gallamine and that mutation to alanine reduced gallamine's affinity by about 10-fold. This tryptophan is conserved in all five subtypes and is adjacent to the M₂⁴²³threonine and M₄⁴³⁶serine residues identified in the present study (Fig. 4).

With regard to gallamine's subtype selectivity, previous studies with M₂/M₅ chimeric receptors have shown that gallamine derives affinity for the M₂ subtype from a region within the o3-chimera CR4 (Ellis et al., 1993), to which, so far, no other allosteric ligand has been found to be sensitive. Subsequent studies attributed gallamine's CR4 interaction to an asparagine residue in the third extracellular loop (i.e., M₂⁴¹⁹asparagine) (Gnagey et al., 1999), which lies four residues away from M₂⁴²³threonine. Thus, within this region of the receptor, the presently investigated ligands and gallamine seem to derive affinity from receptor loci that are near each other but not identical.

On the other hand, the investigated ligands were found to have enhanced affinity toward the chimeric receptor CR3 that included the M₂ second extracellular loop (o2) plus surrounding regions. In a study by Leppik et al. (1994), the binding of gallamine was also shown to be sensitive to an epitope in o2. The authors identified a four-residue sequence in o2 of the M₂ receptor (EDGE), which when mutated to its M₁ counterpart resulted in a significantly reduced affinity toward gallamine. However, gallamine had been found to bind equally well to the M₅ receptor and to the chimeric receptor CR3, which includes M₂ sequence in this region (Ellis et al., 1993). This apparent discrepancy has been explained by experiments that indicate that both the M₅ and M₂ receptor contain the essential epitope in this region, whereas M₁ lacks it (Gnagey et al., 1999). Nonetheless, this also implies that the ligands investigated in the present study, which did display significantly greater affinity toward CR3 than toward M₅, presumably derive affinity from an epitope that involves residues other than those that affect gallamine's affinity in this region of the receptor. This situation may be similar to that described above for the o3/TM7 region of the receptor. We are currently investigating smaller chimeric inserts to attempt to identify the responsible epitope(s) within CR3.

The present study confirms the suggestion that muscarinic allosteric ligands interact with different receptor loci. However, despite this apparent complexity, two main regions of the receptor stand out from which allosteric agents seem to derive affinity: 1) the second outer loop and/or adjacent regions of TM4 and TM5; and 2) the junction between the third outer loop and TM7. At the position corresponding to M₂⁴²³threonine, the M₄ receptor was found to contain an analogous epitope for the interaction with these compounds (i.e., M₄⁴³⁶serine). These findings are furthermore consistent with the notion that muscarinic allosteric ligands bind to regions that are located more extracellularly, relative to the classical ligand binding site. In TM7, Wess et al. (1991) identified two conserved tyrosine residues that seemed to be critical for muscarinic agonist binding. Relative to M₂⁴²³threonine or M₄⁴³⁶serine, these tyrosine residues are located about one and two helical turns down toward the intracellular side of the receptor. Recent studies have indicated the presence of a second muscarinic allosteric site, based on the lack of competition between two classes of allosteric ligands (Lazareno et al., 2000). The structural details of this site have not yet been investigated, but in view of the lack of sensitivity of the compounds investigated in the present study to substitutions in the N-terminal half of the receptor (i.e., CR5), one may speculate that this second allosteric site may be located in the N-terminal part of the receptor.

In summary, we have investigated a number of highly subtype-selective allosteric compounds at M₂/M₅ mutant receptors. The stereochemical difference between alcuronium and CARALL was found to translate into divergent epitope sensitivies. On the other hand, the rigid caracurine V derivatives and the flexible alkane-bisammonium compounds seemed to interact with the same receptor epitopes. In fact, the flexible compounds exhibited a substantially inflexible behavior with regard to their affinities toward the recombinant receptors; the respective mutations led to clear and predictable affinity shifts, indicating that they do not compensate for the removal of a point of attachment by changing their conformations. For the different allosteric ligands investigated in this study, two epitopes (the o2 region and M₂⁴²³threonine at the top of TM7) are sufficient to account fully for their M₂ selectivity over M₅.