Cooperativity manifest in the binding properties of purified cardiac muscarinic receptors.

Muscarinic receptors were solubilized from porcine atria in digitonin-cholate and were purified by chromatography on DEAE-Sepharose and 3-(2′-aminobenzhydryloxy)tropane-Sepharose. The product identified on Western blots migrated with an apparent molecular mass of 60-75 kDa, with additional bands indicative of homotrimers (190 kDa) and homotetramers (240 kDa). Receptor eluted from the affinity column was accompanied by a mixture of guanyl nucleotide-binding proteins (G-proteins) identified on Western blots as Gi1/2, Go, Gq/11, and Gs (preparation M2G); the G-proteins were largely removed by further processing on hydroxyapatite (preparation M2). Solubilized purified receptors bound muscarinic ligands in an apparently cooperative manner. In studies at equilibrium, the antagonists [3H]AF-DX 384, N-[3H]methylscopolamine (NMS), and quinuclidinylbenzilate (QNB) revealed Hill coefficients between about 0.8 and 1.2. Also, the apparent capacity for [3H]QNB exceeded that for [3H]AF-DX 384 and [3H]NMS by about 1.5-fold in M2 and by 2-fold in M2G. Binding to M2G at high concentrations of [3H]QNB was fully inhibited by unlabeled NMS, which therefore affected sites not labeled at similar concentrations of [3H]NMS. Oxotremorine-M displayed a biphasic inhibitory effect on the binding of [3H]AF-DX 384 in M2 and M2G, suggesting that multiple states of affinity are intrinsic to the receptor; 5′-guanylylimidodiphosphate was without appreciable effect in M2 but resulted in a bell-shaped binding profile for the agonist in M2G. All of the data can be described in terms of cooperative interactions within a receptor that is at least tetravalent and presumably an oligomer. In the context of the model, copurifying G-proteins and guanyl nucleotides serve to regulate the degree of cooperativity between successive equivalents of muscarinic ligands.

G-protein-mediated signaling is widely held to occur via a transient complex between the G-protein and the receptor; similarly, a mixture of uncoupled and G-protein-coupled receptors generally is assumed to account for heterogeneity seen in the binding of agonists (Gilman, 1987;Birnbaumer et al., 1990;Conklin and Bourne, 1993). The binding patterns are analyzed almost universally in terms of distinct, noninteracting, and noninterconverting sites (e.g. Munson and Rodbard (1980)), but that approach embodies a mechanistic paradox: in particular, the receptors appear to interconvert between the different states. Guanyl nucleotides act via the G-protein to effect an interconversion from higher to lower affinity for the agonist; there is a similar effect of sodium in some systems, whereas an interconversion from lower to higher affinity is promoted by magnesium (Birnbaumer et al., 1990). Also, the relative number of receptors ostensibly in one state or another differs among different agonists (e.g. Kent et al. (1980), Wong et al. (1986), ).
Variants of the "mobile receptor" or "ternary complex" model  accommodate the apparent interconversion and complement biochemical evidence that a complex between receptors and G-proteins is stabilized by agonists and destabilized by guanyl nucleotides (Gilman, 1987;Birnbaumer et al., 1990). In such schemes, the allosteric interactions between agonists and guanyl nucleotides are described explicitly in terms of ligand-regulated equilibria between free receptors (R) and free G-proteins (G), or subunits thereof, on the one hand and one or more complexes on the other (e.g. De , Onaran et al. (1993), Samama et al. (1993)). Agonists bind with higher affinity to RG than to R, and therefore promote coupling, whereas antagonists are indifferent or exhibit the opposite preference; guanyl nucleotides bind with higher affinity to G than to RG and therefore promote uncoupling. Schemes based on the mobile receptor hypothesis have been used to describe the binding properties of several receptors (e.g. Wreggett and De Lean (1984), Ehlert (1985), Neubig et al. (1988), Leung et al. (1990)), but a model that is fully consistent with the data has proved to be elusive (Lee et al., 1986;Wong et al., 1986;Wreggett, 1987;Ehlert and Rathbun, 1990).
In the absence of a viable mechanistic scheme, there is no conceptual basis for interpreting the consequences of disease, mutagenesis, or other perturbation that affects the binding of agonists. Since the multiple states of affinity and their sensitivity to guanyl nucleotides are a measure of efficacy and intrinsic activity (e.g. Kent et al. (1980), Ehlert (1985)), an inability to account for the binding properties implies uncertainty over the process whereby a receptor elicits a response. Recent studies in our laboratory have focussed on an alternative to the notion of a ligand-regulated distribution of receptors between free and G-protein-coupled states. Several lines of evidence suggest that the binding properties of membrane-bound receptors and their attendant G-proteins are a manifestation of cooperative effects between successive equivalents of the ligand bound at interacting sites; moreover, the reciprocal allosteric interactions between agonists and guanyl nucleotides emerge as changes effected by one ligand in the degree of cooperativity associated with the other (Chidiac and Wells, 1992;. If a multivalent receptor retains its structural integrity over time in a system at equilibrium, multiple states of affinity can rinsed in ice-cold PBS. 2 The rinsed tissue was minced in a Waring blender (20 s at full power) in 2.5 volumes (by original weight of tissue) of ice-cold buffer A, and the mixture was homogenized on ice with three bursts of a Polytron (20 s at setting 7, 20-s intervals). The homogenate then was centrifuged for 15 min at 4°C and 1000 ϫ g; this step was repeated once following resuspension of the pellet in 1 volume of buffer A in the Waring blender. The pooled supernatant was poured through eight layers of cheesecloth and centrifuged for 40 min at 4°C and 100,000 ϫ g (Beckman, 45Ti). The pellet then was resuspended in a few milliliters of buffer A, briefly homogenized (Polytron, 10 s, setting 7), and diluted with the same buffer to obtain a convenient volume for the next step (0.2-0.6 ml/g of original weight). The diluted homogenate (about 20 ml/tube) was centrifuged for 60 min at 2°C and 100,000 ϫ g (Beckman, SW28) through a stepwise gradient of 13% (w/v) sucrose (6 ml) and 28% (w/v) sucrose (7 ml) in buffer A. Material at the sucrose interface was recovered with a Pasteur pipette, diluted at least 3-fold with buffer A, and centrifuged for 40 min at 4°C and 100,000 ϫ g (Beckman, 45Ti). The final pellet was resuspended in a few milliliters of buffer A, briefly homogenized (Polytron, 10 s, setting 7), and diluted to about 0.05 ml/g of original weight. Sarcolemmal membranes obtained from this step usually were stored overnight at 2°C in a polypropylene tube.
To solubilize the sarcolemmal membranes, the suspension described above was diluted with buffer A to obtain a protein concentration of 5.5 mg/ml. Nine volumes of the diluted suspension then were mixed with 1 volume of a stock solution containing 4% digitonin (Wako) and 0.8% sodium cholate in buffer A. After gentle mixing by vertical rotation (30 rpm) for 10 min at room temperature, the membranes were collected by centrifugation for 40 min at 4°C and either 100,000 ϫ g (Beckman, 45Ti) or 150,000 ϫ g (Beckman, 70Ti). The pellet was resuspended in a few milliliters of buffer A, gently homogenized (Polytron, about 10 s, setting 4), and diluted with buffer A to 39% of the original volume. This preparation contained about 10 mg of protein/ml, assuming a 30% loss of protein from the first step . Four volumes of the suspension were mixed with 1 volume of the buffered detergent stock, and the preparation was rotated for 10 min as described above. An equal volume of ice-cold buffer A then was added, the mixture was centrifuged as described above, and the supernatant was stored at 2°C in a polypropylene tube. The material from this step was the crude solubilized preparation used in all subsequent procedures.
Purification of M 2 Muscarinic Receptors-All steps of the purification were performed at 4°C unless indicated otherwise. The solubilized atrial membranes were applied at a rate of about 0.5 ml/min to a column of Fast-Flow DEAE-Sepharose (20 ml, 3.5 cm in diameter) previously equilibrated in buffer A containing 0.1% digitonin (Wako) and 0.02% sodium cholate. The sample was washed into the column with a further 20 ml of the equilibrating buffer. Elution was carried out at a rate of about 1 ml/min with 80 ml of buffer B containing 50 mM NaCl followed by 80 ml of buffer B containing 250 mM NaCl; the last 60 ml of eluate was retained as the fraction containing the receptor. That fraction was concentrated about 30-fold (Amicon, Centriprep-30), diluted with buffer B such that the concentration of NaCl was reduced to 20 mM, and then used to suspend 3 ml of ABT-Sepharose previously equilibrated in buffer C. It was found that [ 3 H]NMS binding activity was cleared from the solution if the sample was diluted about 10-fold prior to its application to the affinity resin. The suspension was mixed gently by vertical rotation (30 rpm) in a polypropylene tube for 12-16 h at 4°C and then packed into an Econo-Column at a rate of 1 ml/min. Nonretained material was eluted with 1 bed volume of buffer C, and the column was washed with 20 bed volumes of buffer B containing 0.2 M NaCl. The column then was transferred to room temperature and washed with 4 bed volumes of buffer C prepared without Na 2 EDTA. The receptor was recovered from the column at room temperature with this same buffer supplemented with 0.3 M carbachol. One bed volume of the agonist-1 The abbreviations used are: GMP-PNP, 5Ј-guanylylimidodiphosphate; ABT, 3-(2Ј-aminobenzhydryloxy)tropane; NMS, N-methylscopolamine; PMSF, phenylmethylsulfonyl fluoride; QNB, l-quinuclidinyl benzilate; PBS, phosphate-buffered saline.
2 All solutions described here and in the text were titrated to the desired pH at room temperature. The constituents of the various buffer solutions were as follows: PBS, 20 mM KH 2 PO 4 , 150 mM NaCl, pH 7.4 with KOH; PBSTM, PBS containing 5% non-fat dried milk and 0.05% Tween 20; buffer A, 20 mM imidazole, 1 mM Na 2 EDTA, 0.1 mM PMSF, 0.02% (w/v) sodium azide, 1 mM benzamidine, 2 g/ml pepstatin A, 0.2 g/ml leupeptin, 200 g/ml bacitracin, pH 7.6 with HCl; buffer B, 20 mM KH 2 PO 4 , 1 mM Na 2 EDTA, 0.1 mM PMSF, 2.5% detergent stock, pH 7.4 with KOH; buffer C, buffer B supplemented with 20 mM NaCl; buffer D, 20 mM HEPES, 20 mM NaCl, 5 mM MgSO 4 , 1 mM Na 2 EDTA, pH 7.6 with NaOH. Buffers A and D were obtained by dilution of a stock solution prepared at the desired pH and at 10-fold the final concentration.
containing buffer was passed into the column, which then was left to incubate for 30 min; 4 more bed volumes were used for elution, and the eluate was collected as the fraction containing the receptor.
The material recovered from the affinity column was divided in two, and each half was processed at room temperature according to one of two chromatographic methods. Originally introduced to remove carbachol, each method subsequently was found to yield a distinct preparation of the receptor (see below). The material was processed by handheld disposable plastic syringes, and the two procedures were carried out in parallel. In the first procedure, the receptor-containing sample was supplemented with 1 mM EDTA from a solution previously adjusted to pH 7.0 with NaOH. That sample then was concentrated to less than 0.2 ml (Amicon, Centricon-10), adjusted to a volume of 0.2 ml with buffer C, and applied to an Econo-Pac P6 cartridge (5 ml, size-exclusion column) previously equilibrated with buffer C. Elution was carried out with buffer C at a rate of about 4 ml/min. The receptor was collected in 1.7-4.0 ml of eluate, and that fraction is designated here as preparation M2G. In the second procedure, the material eluted from the affinity column was applied to an Econo-Pac HPT cartridge (1 ml, ceramic hydroxyapatite column) at a rate of about 0.5 ml/min. The resin was washed first with 3 ml of EDTA-free buffer C and then with 15 ml of a phosphate buffer (0.12 M KH 2 PO 4 ) containing 0.1% digitonin (Wako), 0.02% sodium cholate, and 0.1 mM PMSF. The receptor then was eluted with 6 ml of the same buffer prepared with 0.5 M KH 2 PO 4 . The phosphate buffers were prepared from stock solutions of phosphate (1 M KH 2 PO 4 , adjusted to pH 7.6 with KOH) and detergent (4% digitonin (Wako), 0.8% sodium cholate). The first bed volume of eluate was discarded. The remainder was concentrated and then processed on an Econo-Pac P6 cartridge as described above in order to transfer the receptor into buffer C. That fraction of the eluate containing the purified receptor is designated here as preparation M2. Both preparations were stored in polypropylene tubes at 2°C.
The two preparations differed in their complement of G-proteins, which were largely absent from M2 but copurified with the receptor in M2G. All of the procedures described above, from initial homogenization of the tissue to the elution of nonretained material from ABT-Sepharose, were carried out in magnesium-free buffers containing EDTA. Such conditions promote the removal of endogenous guanyl nucleotides (e.g. Chidiac and Wells (1992)), and GDP therefore is expected to be absent from the G-proteins in M2G.

SDS-Polyacrylamide Gel Electrophoresis and Western
Blotting-Electrophoresis through SDS-polyacrylamide gels was performed according to the method of Laemmli (1970). Proteins resolved in the gel either were visualized by silver or Coomassie staining or else were transferred to a supported nitrocellulose membrane (Schleicher and Schuell) over about 1 h at 5 mA/cm 2 in a semi-dry blotting apparatus equipped with a plate cooling coil (Biometra, Maidstone, United Kingdom) (Towbin et al., 1979). All subsequent steps were performed at room temperature. Nonspecific protein-binding sites on the nitrocellulose were blocked by incubation for 30 min with PBSTM. Primary antibodies were diluted in PBSTM to obtain the concentrations indicated in the legends to the figures, and the solution was incubated with the blots for 3 h. The blots were washed with PBSTM, incubated for 45 min with a horseradish peroxidase-conjugated secondary antibody (1:1000 or 1:3000 dilution in PBSTM), and washed twice with PBS containing 0.2% Tween 20 and once with PBS alone. The activity of bound horseradish peroxidase was visualized by means of enhanced chemiluminescence and recorded on x-ray film, which was exposed for a range of times to obtain an optimal result. The data then were quantitated by computer-assisted densitometry on an image analyzer (MCID, Imaging Research Inc., St. Catherines, Canada) with a resolution of 256 gray levels per image point.
To probe sequentially for different antigens, IgGs were removed from previously treated nitrocellulose by means of a stripping buffer (125 mM Tris, 2% SDS, 0.1 M ␤-mercaptoethanol, adjusted to pH 6.8 with HCl). The buffer was applied twice for 20 min at 70°C (Kaufmann et al., 1987), and the membrane then was rinsed thoroughly at room temperature in PBS containing 0.2% Tween 20.
All samples containing detergent were prepared for electrophoresis by extraction with chloroform and methanol. After separation of the phases by the addition of water, the insoluble material was sedimented in a microcentrifuge, air-dried, and sonicated into SDS-polyacrylamide gel electrophoresis loading buffer containing ␤-mercaptoethanol or dithiothreitol at 0.1 M. The samples then were boiled for 5 min prior to application on the gel. In one experiment, the samples were left at room temperature for 20 min rather than boiled. The extraction procedure served both to concentrate the material and to remove constituents, such as salt and detergent, which impaired the performance of the gels.
In some cases, the samples were concentrated at 2°C on ultrafiltration membranes (Amicon, Microcon-10) before the extraction.
Binding to Purified Receptors-Aliquots of the receptor-containing solution (2-5 l) were diluted to 50 l by the addition of buffer D containing 0.1% digitonin (Wako), 0.02% sodium cholate, 0.1 mM PMSF, and various ligands as required. The samples were incubated at 30°C in polypropylene microcentrifuge tubes, and the total contents of the tube then were transferred to the top of a bed of Sephadex G-50 fine (0.3 ϫ 6.5 cm) packed in polypropylene columns (Disposaflex, Kontes Glass Co.) pre-equilibrated at room temperature with buffer D containing 0.025% digitonin (Sigma). For those steps up to and including application of the sample to the resin, all plastic making contact with the receptor was silanized by pretreatment with trimethylchlorosilane vapor. Elution was carried out at room temperature with buffer D containing 0.025% digitonin (Sigma). All of the eluant up to and including the void volume (1.45 ml) was collected in a plastic counting vial and mixed with a commercial scintillant (3 ml of ACS, Amersham or 4 ml of Ready-Safe, Beckman). The conditions of elution were optimized to provide virtually complete separation of free and bound radioligand with no loss of the latter through dissociation from the receptor. Assays were performed in duplicate, and the radioactivity in each sample was measured twice for 5 min at an efficiency of about 23% (ACS) or 33% (Ready-Safe). The four values then were averaged to obtain the mean (ϮS.E.) for use in subsequent calculations; standard errors typically were about 2% of the mean. To estimate the binding capacity of samples collected at different stages of purification, the specific binding of [ 3 H]NMS was measured at a concentration of 300 nM. Nonspecific binding was taken throughout as total binding in the presence of 0.1-1 mM unlabeled NMS.
Analysis of Data-All data were analyzed with total binding taken as the dependent variable (picomolar). Any subsequent manipulations were for the purpose of presentation only and did not alter the relationship between the data and the fitted curve. Nonspecific binding increased linearly with the concentration of unbound radioligand for each of the three compounds used in the investigation. Data acquired at graded concentrations of the radioligand were described empirically in terms of the Hill equation to obtain estimates of the Hill coefficient (n H ) and the concentration required for half-maximal specific binding (EC 50 ). The solution included an implicit correction for depletion of the free radioligand (i.e. Equations 203-205 in ).
Cooperativity was modeled according to Scheme I, in which a radiolabeled probe (P) and an unlabeled ligand (A) compete for sites on a tetravalent receptor (R) that presumably is an oligomer (tetramer). Bivalent (dimer) and trivalent (trimer) receptors can be described by truncated forms of R. It is assumed that the oligomeric integrity of R is retained under the conditions of the binding assays; the model can accommodate processes in which dissociated monomers regroup without exchanging partners, but there can be no exchange of individual subunits within the system. Asymmetry cannot be detected with the present data, and all sites of the vacant oligomer were assumed to bind P or A with the microscopic dissociation constant K P or K A (e.g. K P ϭ [P][R]/[PR]). 3 The parameters p j and a j represent the cooperativity factors for binding of the jth equivalent of P or A to form RP j or A j R, respectively (j Ն 2) (e.g. [RP jϪ1 ][P]/[RP j ] ϭ ⌸ iϭ2, j p i K P ); the parameters c j , cЈ j , and cЉ j represent cooperativity factors in the formation of mixed complexes, as shown in Scheme I.
The model was fitted to the data by means of Equation 1, in which B obsd represents total binding of the radioligand; [P] b represents specific binding at a total concentration [P] t , and NS is the fraction of unbound radioligand that appears as nonspecific binding.
The value of [P] b was calculated according to Equation 2a, 2b, or 2c for the bivalent, trivalent, or tetravalent forms of R, respectively. The concentration of each complex was obtained as described below. Coefficients greater than 1 reflect the degree of occupancy by P, since R is defined as multivalent, and the multiple forms of liganded receptor at each level of occupancy. Stoichiometrically equivalent species are functionally indistinguishable with the present data, and the microscopic 3 Microscopic or intrinsic dissociation constants (K i ) and macroscopic dissociation constants (K i Ј) are related according to the expression where i is the ith equivalent of ligand, and n is the total number of interacting sites (e.g. Wyman and Gill (1990) and ). If the values of K i for binding of the radioligand to a tetrameric receptor are K P , p 2 K P , p 2 p 3 K P , and p 2 p 3 p 4 K P , the corresponding values of K i Ј are ( 1 ⁄4)K P , ( 2 ⁄3)p 2 K P , ( 3 ⁄2)p 2 p 3 K P , and 4p 2 p 3 p 4 K P .
dissociation constant therefore was taken as the same for all vacant sites on partially liganded R (e.g. where O represents a vacant site on tetravalent R). The triliganded species A 2 RP 1 and A 1 RP 2 also were taken as identical (i.e. c 3 ϭ cЈ 3 ), as were the tetraliganded species A 3 RP 1 , A 2 RP 2 , and A 1 RP 3 (c 4 ϭ cЈ 4 ϵ cЉ 4 ). They are not necessarily indistinguishable in binding studies, but the additional parameters were found to be without effect on the sum of squares.
The values of individual terms in Equations 2a-2c were calculated from the equilibrium dissociation constants and the free concentrations of the reactants. The latter were obtained by solving a set of implicit equations derived from the equations of state for each ligand and the receptor. Solutions were obtained according to the Newton-Raphson procedure, but successful convergence often required initial estimates that were close to the desired roots. Values near or equal to the answer were computed in an iterative procedure that involved successive estimates of the free concentration of R on the one hand and of P and A on the other. The total concentrations of both ligands were taken as equal to the free concentrations and substituted in the equation of state for the receptor to obtain the value of ; the latter then was used to obtained revised estimates of the former (e.g.
, and the cycle was repeated until convergence occurred. Further details regarding the formulation of cooperative models have been described elsewhere .
All parameters were estimated by nonlinear regression, and values at successive iterations of the fitting procedure were adjusted according to the algorithm of Marquardt (1963). The squared residual for each measurement was weighted by the reciprocal of the estimated variance. Most analyses involved multiple sets of data, and the assignment of shared parameters is described where appropriate. Other details related to the statistical procedures have been described previously (Wong et al., 1986;Chidiac and Wells, 1992;.

Purification and Characterization of the Porcine Atrial M 2
Muscarinic Receptor-The purification was monitored by means of samples collected at each stage of the 2-day procedure and tested subsequently for immunoreactivity and the specific binding of [ 3 H]NMS. Results from the screening of a Western blot are shown in Fig. 1, where various fractions from a single purification are compared for their reactivity with antibodies specific either for various G-protein subunits or for the M 2 muscarinic receptor. Similar results were obtained with fractions from several other runs. As described previously , the lower concentration of detergent used in the first stage of solubilization caused a selective removal of nonreceptor material, including a substantial fraction of the total G-protein (Fig. 1, lane 1). At the levels of total protein applied to the gel, the antibody 31-1D1 revealed little or no receptor in the product obtained at either stage of solubilization ( Fig. 1, lanes 1 and 2); nonetheless, specific binding detected by 300 nM [ 3 H]NMS was 20-fold greater after the second stage than after the first.
Fractions obtained at almost every stage of the subsequent purification yielded a positive signal with each of the G-protein-specific antibodies used for screening, although the relative amounts of each subunit or subtype differed from fraction to fraction. G-protein subunits were retained on the anionexchange column and were eluted with the receptor (Fig. 1, lane 5). Most of the immunoreactivity was removed during subsequent processing on ABT-Sepharose, when G-protein subunits either were not retained (Fig. 1, lane 6) or tended to come off during the washing procedure ( Fig. 1, lanes 7 and 8). Elution of the affinity column with the low salt buffer at room temperature removed a small amount of M 2 receptor, which ran on the gel only as a large aggregate ( The M 2 muscarinic receptor was recovered from the affinity column by elution with carbachol (preparation M2G). Western blots treated with the receptor-specific antibody 31-1D1 revealed a diffuse band of material with the mobility expected of a globular protein with a molecular mass of 60 -75 kDa (Fig.  1A, lane 9); the receptor was accompanied by ␤-subunits and by the ␣-subunits of G q/11 , G s , G i , and G o (Fig. 1, A-D, lane 9). The degree of purification is indicated by the relative intensities of bands arising from antibodies to the receptor on the one hand and to the ␣and ␤-subunits on the other: in contrast to the strong signals obtained with G-protein-specific probes, the receptor was undetectable or nearly so in crude solubilized membranes (Fig. 1A, lane 2) and at each stage of the purification up to and including the high salt wash from the affinity column (Fig. 1A, lane 7). Bands identified by different G-protein-specific antibodies differed in their relative intensity between the eluate from the affinity column ( Fig. 1, A-D, lane 9) and that from the anion-exchange column (Fig. 1, A-D, lane 5). The different subunits thus appear to differ in their tendency to copurify with the receptor. Further processing of the affinitypurified receptor on hydroxyapatite yielded a product in which the relative amount of each measured G-protein was markedly reduced (preparation M2) (Fig. 1, A-D, lanes 10 -12). Smaller, epitope-containing bands were not detected in M2 or M2G, indicating that both preparations were free of major proteolytic activity.
The intensities of the immunoreactive bands identified on Western blots were quantified by densitometry, and the results are summarized in Fig. 1E. Preparation M2 (Fig. 1, A-D, lane 12) contained less than 6% of the ␣-subunits and less than 7% of the ␤-subunits found in preparation M2G (Fig. 1, A-D, lane  9). The residual ␣-subunits in M2 were mostly ␣ o (Fig. 1D); there was a lesser amount of ␣ i (Fig. 1C), whereas ␣ q/11 (Fig.  1A) and ␣ s (Fig. 1B) were undetectable. The amount of ␣ s in M2G (Fig. 1B, lane 9) was only 8% of that found in the fraction eluted from the anion-exchange column (Fig. 1B, lane 5). This value is substantially less than the mean of 37% estimated for the other ␣-subunits. G-proteins identified in M2G presumably copurified as a complex with the receptor, at least in the case of G i and G o ; since the ratio of total G-protein to receptor was SCHEME I. about 20-fold less in M2 than in M2G, the ratio in M2 is likely to be negligible.
The mean specific binding of [ 3 H]NMS in five different preparations of solubilized atrial membranes was 8 Ϯ 2 pmol/mg of protein at a radioligand concentration of 300 nM. Receptor eluted by carbachol from the affinity column and processed further to obtain the preparations M2G and M2 represented 30 -40% of the sites originally present in the solubilized mem-FIG. 1. Identification of M 2 muscarinic receptors and various subunits of G-proteins in purified fractions from porcine atrial tissue. Freshly prepared samples purified from solubilized sarcolemmal membranes were concentrated, run on SDS-polyacrylamide gel electrophoresis, and then blotted onto a nitrocellulose membrane as described under "Experimental Procedures." The data are from a single Western blot which was screened successively with antibodies either individually or in combination. Specific bands were detected by enhanced chemiluminescence following incubation with anti-IgG congugated to horseradish peroxidase, and the signal was recorded onto x-ray film by exposure for various times. The contents of each lane were as follows (A-D); further details are described under "Experimental Procedures": lane 1, first stage of solubilization; lane 2, second stage of solubilization; lane 3, pass-through from DEAE-Sepharose; lane 4, low salt wash from DEAE-Sepharose; lane 5, high salt elution from DEAE-Sepharose after concentration; lane 6, pass-through from ABT-Sepharose; lane 7, high salt wash from ABT-Sepharose; lane 8, low salt wash from ABT-Sepharose; lane 9, carbachol-elution from ABT-Sepharose after concentration and filtration on Econo-Pac P6 (preparation M2G); lane 10, pass-through from hydroxyapatite; lane 11, low salt wash from hydroxyapatite; lane 12, high salt elution from hydroxyapatite after concentration and filtration on Econo-Pac P6 (preparation M2). All of the lanes contained the same amount of protein, which corresponds in lanes 9 and 12 to approximately 50 ng of muscarinic receptor as measured with 300 nM [ 3 H]NMS. A, M 2 muscarinic receptor (31-1D1 at 1:1000) and ␣-G q/11 (QL at 1:3000) were detected by exposure of the film to ECL for 20 s. The open arrow marks the position of the receptor, and the black arrow marks the position of ␣ q/11 . B, ␣-G s and common ␤-subunits (both RM/1 and SW/1 at 1:6000) were detected by exposure of the film to ECL for 12 min. A lengthy exposure was required to reveal the small amounts of ␣ s in M2G and of ␤-subunits in M2. The striped arrow marks the position of ␣ s , and the gray arrow marks the position of ␤-subunits. C, ␣-G i (AS/7 at 1:3000) was detected by exposure of the film to ECL for 3 min. D, ␣-G o (GC/2 at 1:10,000) was detected by exposure of the film to ECL for 40 s. E, relative densities of G-protein subunits in preparation M2 (solid bars) and preparation M2G (hatched bars). The data were quantified by densitometry of the bands in lane 9 (M2G) and lane 12 (M2) following exposure of the blot for 40 s (A, D) or 3 min (C). Each value was divided by that obtained for the M 2 receptor in the same lane, and the normalized values are shown relative to the corresponding values in M2G. Densities corresponding to the ␤-subunit were measured using a much shorter exposure than that shown in the figure in order to avoid saturation of the film. branes; accordingly, the purified material is likely to be representative of the total population of muscarinic receptors in porcine atria. The apparent capacity of M2G and M2 for [ 3 H]NMS was 8 -12 pmol/ml in a volume of about 2 ml for each preparation. Both M2G and M2 were prepared in parallel from about 200 g of original tissue, and the combined yield was 3-5 g of M 2 muscarinic receptor. The level of purity was 4 -10% based on estimates of total recovered protein, an assumed stoichiometry of 1 eq of [ 3 H]NMS/molecule of receptor, and a theoretical specific activity of 19 nmol/mg for a pure protein with a molecular mass of 51,670 daltons (Kubo et al., 1986). This is consistent with the patterns obtained on silver-stained polyacrylamide gels, where M2G and M2 both yielded a major diffuse band corresponding to 60 -75 kDa and several minor bands spaced over the length of the gel; the latter were more prominent in M2G than in M2. Calculations based on the apparent capacity for [ 3 H]NMS may underestimate the actual yield 2-fold or more. As described below, estimates of maximal specific binding in each preparation differed among three different radiolabeled antagonists.
The pattern of immunoreactivity shown by the receptorspecific antibody in Fig. 1A was characteristic of preparations examined shortly after purification. Additional bands corresponding to discrete multiples of the monomeric receptor were found in purified material that had been stored for a period of weeks at 2°C. The larger forms exhibited the mobility of trimeric and tetrameric homooligomers (Fig. 2), and they were observed regardless of whether the sample in the loading buffer was boiled or kept at room temperature for up to 20 min prior to electrophoresis. Similar results have been reported previously by Leutje et al. (1987), who also found a time-dependent appearance of apparent oligomers identified by 31-1D1 on Western blots of purified porcine M 2 receptor.
Binding of Antagonists to purified M 2 Muscarinic Receptors in Solution-Muscarinic receptors in preparation M2 routinely yielded Hill coefficients greater than 1 for the specific binding of [ 3 H]AF-DX 384; values tended to be lower and more variable for [ 3 H]NMS, although the mean also exceeded 1 (Table I). Hill coefficients that exceed 1 raise the possibility of cooperative effects among interacting sites. Similar behavior also can arise with independent sites, either from a failure to achieve equilibrium or from the mutual depletion of receptor and radioligand , but neither possibility can account for the present results. Preliminary experiments at nanomolar concentrations of either radioligand indicated that binding became independent of time within 1 min of mixing and remained stable for at least 90 min thereafter. Depletion of the free radioligand was appreciable under some conditions, but the effect was accounted for in analyses with the Hill equation.
Cooperativity was assessed in terms of Scheme I in order to probe the nature of the effect and the minimum number of interacting sites. The results of the analyses are illustrated in Fig. 3, and the parametric values are listed in Table I. Data acquired with [ 3 H]AF-DX 384 can be described in terms of a dimeric receptor in which the first equivalent of the radioligand is positively cooperative with respect to the second (i.e. Ϫlog p 2 Ͼ 0) (Fig. 3A). Data acquired with [ 3 H]NMS require a receptor that is at least trimeric (Fig. 3B), since the sum of squares is 13.5% lower than that for a dimer. The first equivalent of radioligand is negatively cooperative with respect to the second (i.e. Ϫlog p 2 Ͻ 0), and the second equivalent is positively cooperative with respect to the third (i.e. Ϫlog p 3 Ͼ 0).
As illustrated in Fig. 3 Fig. 4 were obtained with material from the same lot of each radioligand. It follows that the differences in maximal observed binding cannot be attributed to an error in the specific radioactivity of one or another antagonist.
Neither a dimeric nor a trimeric receptor is sufficient for Scheme I to describe the behavior of all three ligands in both preparations, but excellent agreement was obtained with a tetramer. The fitted curves are shown in Fig. 4, and the parametric values are listed in Table II. The need for a tetravalent receptor derives in part from the multiple states of affinity apparent in the binding of [ 3 H]AF-DX 384 and [ 3 H]NMS (e.g. n H 1), which imply at least two interacting sites in terms of cooperativity, and in part from the relative apparent capacities for [ 3 H]QNB and either [ 3 H]AF-DX 384 or [ 3 H]NMS in preparations M2 (i.e. 1.5:1) and M2G (i.e. 2:1). Since the oligomeric composition of the receptor is assumed to be the same throughout, the pooled data cannot be described with fewer than four interacting sites.
In the context of Scheme I, the differences between M2 and M2G can be attributed entirely to differences in the degree of cooperativity between successive equivalents of the radioligand. Estimates of K P were similar or the same in both preparations, and the weighted sum of squares was not increased significantly with a single value for each antagonist (Table II).
The comparatively higher binding of [ 3 H]QNB in M2G emerges as a manifestation of reduced negative cooperativity between the last two equivalents of the radioligand. The macroscopic dissociation constants for the second and third equivalents of [ 3 H]QNB differ by 3-fold or less between the two preparations; in contrast, the corresponding value for the fourth equivalent is 27-fold higher in M2 than in M2G owing to a 35-fold difference in the value of p 4 . 4 The receptor in M2G therefore is saturated

H]AF-DX 384 (Equation 2a) and a trimeric receptor for [ 3 H]NMS (Equation 2b
). Single values of K P and p j were common to all of the data, and the fitted estimates are listed in the table; values of [R] t and NS were assigned separately to the data from each experiment, and the values listed for [R] t represent the means (ϮS.E.). There is a significant increase in the weighted sum of squares if binding is assumed to be noncooperative (i.e. Ϫlog p j ϭ 0) for [ 3 H]AF-DX 384 (p 2 , p Ͻ 0.00001) or for [ 3 H]NMS at either level of occupancy (p 2 , p ϭ 0.011; p 3 , p ϭ 0.0003). The data and the fitted curves from Equation 1 are illustrated in Fig. 3.

Hill equation
Equation 1 ϪLog EC Table  I. Values plotted on the ordinate represent specific binding, calculated as total binding (B obsd ) less the fitted estimate of nonspecific binding at the same concentration of unbound radioligand. Individual estimates of B obsd were normalized to the mean values of [R] t and NS according to the expression BЈ obsd ϭ B obsd [f(x i , a)/f(x i , a)], as described previously (i.e. Equation 5 in Chidiac and Wells (1992)). Each experiment included measurements with both radioligands, and the different symbols denote data from different experiments.

FIG. 4. Binding of radiolabeled antagonists to purified muscarinic receptors in M2 and M2G. Total binding was measured following equilibration of the receptor in preparation M2 (A) or in preparation M2G (B) with [ 3 H]AF-DX 384 (E), [ 3 H]NMS (छ), or [ 3 H]QNB (Ⅺ) at the concentrations shown on the abscissa.
All of the data were acquired in the same experiment, which included parallel assays containing 1 mM unlabeled NMS and shown in each panel as the base line. The lines represent the best fit of Equation 1 to all of the data taken together; the value of [P] b was calculated by assuming a tetrameric receptor (Equation 2c), and the fitted estimates of the parameters are listed in Table  II. Values plotted on the ordinate represent specific binding, calculated as total binding (B obsd ) less the fitted estimate of nonspecific binding at the same concentration of unbound radioligand.

at concentrations of [ 3 H]QNB that occupy only about threequarters of the sites in M2. Similarly, a high degree of negative cooperativity can account for the comparatively low level of maximal binding observed with [ 3 H]NMS and [ 3 H]AF-DX 384
in both preparations: that is, the values of p 3 and p 4 are sufficiently large to exclude the third and fourth equivalents of either radioligand at the concentrations used. 4 The notion that apparently unreactive sites reflect cooperativity is consistent with the inhibitory effect of unlabeled NMS on the binding of [ 3 H]QNB. The data illustrated in Fig. 5B were obtained in M2G at two concentrations of the radioligand, 7.8 and 21 nM. The corresponding levels of occupancy in the absence of unlabeled NMS were 66 and 81%, respectively; [ 3 H]QNB therefore occupied 26 -55% more sites than were labeled by tritiated NMS at 0.56 M, the highest concentration used (Fig. 5A). Unlabeled NMS nevertheless achieved 95% inhibition at concentrations of only 0.48 and 1.4 M, respectively (Fig. 5B). Comparatively low concentrations of unlabeled NMS therefore inhibited the binding of [ 3 H]QNB to more sites than were occupied by labeled NMS at similar or higher concentrations.
A good description of the data can be obtained in terms of Scheme I, as illustrated by the solid lines shown in Fig. 5. In assays with unlabeled NMS and [ 3 H]QNB, the noncompetitive effect of NMS reflects the formation of a biliganded species (i.e. NMS⅐R⅐[ 3 H]QNB) with low affinity for additional equivalents of either antagonist (Ϫlog c 3 Ͻ Ϫ2, Ϫlog c 4 Ͻ 0). To confirm the noncompetitive nature of the effect shown in Fig. 5B, the data acquired at graded concentrations of [ 3 H]QNB and unlabeled NMS also were analyzed by assuming that both ligands compete for a heterogeneous population of mutually independent sites. The binding profile inferred for NMS alone diverges from that measured independently with radiolabeled NMS, as shown by the dashed line in Fig. 5A; moreover, the inferred concentration for half-maximal binding exceeds the measured concentration by 2-3-fold. Noncompetitive effects therefore ac-count at least in part for the inhibitory effect of NMS, and a similar pattern has been observed in the binding of AF-DX 384. Fig. 6, and similar results were obtained with [ 3 H]NMS; the line represents the best fit of Scheme I to pooled data from several experiments. The receptor was assumed to be tetrameric, in accord with the interpretation afforded the binding of antagonists (e.g. Figs. 4 and 5) and the results described below. An analysis of the same data assuming two classes of independent sites yielded a sum of squares that was 52% higher than that obtained with Scheme I; the fit was not better with three or more classes of sites.

Binding of Oxotremorine-M to Purified M 2 Muscarinic Receptors in Solution-Binding of the agonist oxotremorine-M was manifestly biphasic in preparation M2 when measured at halfsaturating concentrations of [ 3 H]AF-DX 384 or [ 3 H]NMS. Multiple states of affinity therefore can occur in preparations with little or no detectable G-protein. The inhibition of [ 3 H]AF-DX 384 is illustrated in
The binding of oxotremorine-M in M2G is illustrated in Fig.  7, where the data were obtained at concentrations of [ 3 H]AF-DX 384 in excess of its EC 50 . In the absence of guanyl nucleotide, the agonist described a strictly inhibitory pattern similar to that illustrated for preparation M2 in Fig. 6. In contrast, the pattern obtained at a saturating concentration of GMP-PNP was bell-shaped at intermediate concentrations of oxotremorine-M. An agonist-dependent increase in the specific binding of [ 3 H]AF-DX 384 is inconsistent with any scheme based on mutually independent sites in a system at equilibrium; rather, the data point to cooperative effects between multiple equivalents of agonist and radioligand bound concurrently at interacting sites. The effect of GMP-PNP suggests that G-proteins in M2G interacted with the receptor and retained the functionality that is characteristic of native membranes and reconstituted preparations.
In terms of Scheme I, an agonist-dependent increase in binding can occur only at concentrations of the radioligand that are half-saturating or less with respect to all sites. Since the concentration of [ 3 H]AF-DX 384 was 36 -100 nM in the experiments represented in Fig. 7, approximately 53-77% of the observable sites were labeled in the absence of agonist. It follows that an equal or greater number of coupled sites must values for the third and fourth equivalents of [ 3 H]AF-DX 384 and [ 3 H]NMS exceed the highest concentration of the radioligand used in the experiment (i.e. Ϫlog (( 3 ⁄2)p 2 p 3 K P ) Ͻ 6 and Ϫlog (4p 2 p 3 p 4 K P ) Ͻ 6). Individual parametric values are listed in Table II.  (Equation 2c). Single values of K P were common to all data acquired with the same radioligand in both preparations, whereas single values of p j were common to data acquired with the same radioligand in the same preparation. Single values of [R] t were common to the data acquired with all three radioligands in the same preparation, and the fitted estimates of binding capacity are 428 Ϯ 13 pM for M2 and 578 Ϯ 12 pM for M2G (i.e. 4[R] t ). The data and the fitted curves are illustrated in Fig. 4.

Radioligand
ϪLog remain unlabeled by the radioligand at the concentrations used, in accord with the suggestion that negative cooperativity accounts for the 2-fold difference in maximal observable binding between [ 3 H]QNB and [ 3 H]AF-DX 384. A tetrameric receptor yields good agreement between Scheme I and the data, as illustrated by the fitted curves in Fig. 7. There was no appreciable effect of GMP-PNP on the affinity of the agonist for the vacant receptor, and all data therefore were assigned a single value of K A . As indicated by the fitted parametric values derived from the analysis (Fig. 7, legend), the nucleotide acts primarily by affecting the degree of cooperativity between the agonist and the radioligand (i.e. c j ).

A Mechanistic Model of the M 2 Muscarinic Receptor as a Cooperative, Multivalent
Oligomer-M 2 receptors purified from porcine atria exhibited functional heterogeneity and mutual dependence in two solubilized preparations: one containing a mixture of G proteins (M2G) and one in which G proteins were almost undetectable (M2). The apparent capacity for [ 3 H]QNB exceeded that for [ 3 H]AF-DX 384 or [ 3 H]NMS, but unlabeled NMS was inhibitory at all of the sites recognized by [ 3 H]QNB. Also, Hill coefficients defined by graded concentrations of the radioligand were consistently greater than 1 for [ 3 H]AF-DX 384 in both preparations and tended to exceed 1 for [ 3 H]NMS in M2. Finally, oxotremorine-M revealed a bell-shaped pattern in its dose-dependent effect on the binding of [ 3 H]AF-DX 384 in M2G at saturating concentrations of GMP-PNP. G-proteinlinked receptors generally are assumed to be mutually independent, and heterogeneity of binding typically is attributed to differences induced by the G-protein. If multiple states of affinity share a common origin in membranes and purified preparations, the present data argue for a reappraisal of the mechanism that governs muscarinic binding and its regulation by guanyl nucleotides.
All of the data can be accounted for by cooperative effects within a receptor that is at least tetravalent (i.e. Scheme I). A 4-fold stoichiometry or multiple thereof is consistent with the ratios of about 1.5:1 and 2:1 obtained in M2 and M2G, respectively, for the maximal observed binding of [ 3 H]QNB and [ 3 H]AF-DX 384. Heterogeneity implied by Hill coefficients greater than 1 is interpreted as positive cooperativity between two or more equivalents of the same ligand. Sites labeled by [ 3 H]QNB but not by [ 3 H]AF-DX 384 or [ 3 H]NMS emerge as a consequence of pronounced negative cooperativity in the binding of the latter; similarly, differences in negative cooperativity can account for relative differences in the apparent capacities of M2 and M2G for different probes. Multiphasic effects of oxotremorine-M on the binding of [ 3 H]AF-DX 384 are the net result of cooperativity between the two ligands and between successive equivalents of the agonist alone; bell-shaped effects and strictly inhibitory behavior differ only in the degree of cooperativity between agonist and radioligand. The complete inhibition of [ 3 H]QNB by unlabeled NMS and the bell-shaped effect of oxotremorine-M on [ 3 H]AF-DX 384 both were observed with the radioligand at high levels of occupancy relative to apparent capacity, thereby confirming the existence of functionally linked sites not labeled at practicable concentrations of [ 3 H]NMS or [ 3 H]AF-DX 384.
Ligand-dependent differences in binding capacity have been reported previously for G-protein-linked receptors in native membranes. The dopamine antagonist [ 3 H]nemonapride has been found to label 1.5-2-fold more D 2 receptors than were labeled by [ 3 H]spiperone in membranes from Sf9 cells, mammalian cell lines, and mammalian brain (Seeman et al., 1992;Ng et al., 1994b    ). Single values of K 1j ([ 3 H]QNB), K 2j (NMS), and F j (j ϭ 1, . . . n) were common to all of the data, and values of [R] t and NS were common to data from the same experiment. The fit was marginally better with two classes of sites rather than one (p ϭ 0.067), and the parametric estimates are as follows: Ϫlog K 11 ϭ 8.84 Ϯ 0.07, Ϫlog K 12 ϭ 7.57 Ϯ 0.56, Ϫlog K 21 ϭ 8.29 Ϯ 0.11, Ϫlog K 22 ϭ 6.84 Ϯ 0.80, F 2 ϭ 0.20 Ϯ 0.09. The line was calculated from the values of K 1j and F j . and Mayer, 1991). The differences were attributed to the comparatively high lipophilicity of QNB or to a heterogeneous population of receptors differentiated only by [ 3 H]AF-DX 384. Since the affinity of [ 3 H]AF-DX 384 differs by less than 10-fold among four of the five subtypes of muscarinic receptor (e.g. Dorje et al. (1991)), it seems unlikely that a subpopulation of one subtype or another could be overlooked. Differences related to the lipophilic nature of QNB imply a subpopulation of receptors that are less accessible to the more hydrophilic ligand. Unless access is denied absolutely, however, all ligands are expected to yield the same capacity in a system at equilibrium.
The present results recall earlier suggestions of cooperativity in the binding of ligands to ␤-adrenergic and muscarinic receptors in native membranes (Limbird et al., 1975;Mattera et al., 1985;Boyer et al., 1986). Since there appears to be one binding site per polypeptide chain (e.g. Dixon et al. (1988)), cooperativity is indicative of an oligomeric array comprising multiple equivalents of the M 2 protein. Oligomers of muscarinic receptors also have been inferred from binding studies on native and affinity-alkylated membranes from rat brainstem, where M 2 receptors have been suggested to occur in functionally asymmetric pairs (Potter et al., 1991). Furthermore, complementary chimeras of ␣ 2 -adrenergic and M 3 muscarinic receptors (e.g. ␣ 2 /m3 and m3/␣ 2 ) in membranes from COS-7 cells were found to bind adrenergic or muscarinic antagonists only when the two recombinant proteins were coexpressed (Maggio et al., 1993). Kinetic studies on the binding of [ 3 H]oxotremorine-M to recombinant m2 receptors expressed in CHO cells have been interpreted in terms of an agonist-regulated interconversion between monomers and asymmetric dimers (Hirschberg and Schimerlik, 1994).
It is implicit in analyses with Scheme I that the receptors were exclusively tetrameric. This arrangement may be unjustified, at least in principle, for material that is potentially heterogeneous despite a comparatively high degree of purity. Denaturation or differences in post-translational processing may affect function while having little or no effect on electrophoretic mobility. Also, differences in the apparent capacity for [ 3 H]NMS and [ 3 H]AF-DX 384 and in the occurrence of oligomers on Western blots tended to emerge over time. It follows that the purified material used in this study may contain oligomers of different size, and the prevalence of one or another form may depend on the age of the preparation. Cooperativity nevertheless is required by the data, and a tetrameric receptor emerges as the simplest acceptable arrangement. Since the model accounts for all of the results, any other structural forms apparently can be accommodated within that framework; tetramers may have predominated, or a mixture of forms may . Single values of K P and p j were common to all of the data, and single values of K A , a j , and c j were common to data acquired at graded concentrations of the agonist. The fitted parametric values are as follows: Ϫlog K A ϭ 6.24 Ϯ 0.22, Ϫlog K P ϭ 7.13 Ϯ 0.03, Ϫlog a 2 ϭ Ϫ2.72 Ϯ 0.24, Ϫlog a 3 ϭ 0.32 Ϯ 0.30, Ϫlog p 2 ϭ 0.29 Ϯ 0.10, and Ϫlog c 2 ϭ Ϫ2.17 Ϯ 0.06. The values of Ϫlog p 3 and Ϫlog p 4 were fixed at Ϫ4 and 0, respectively, in accord with the failure of [ 3 H]AF-DX 384 to label more than about 67% of the sites labeled by [ 3 H]QNB or more than 50% of the presumed total capacity (e.g. Fig. 4). The quantities Ϫlog a 4 and Ϫlog c 4 were defined only by upper bounds, and Ϫlog c 3 was defined only by a lower bound. They otherwise were without effect on the sum of squares or the values of other parameters, except for a negative correlation between c 2 and c 3 . The values therefore were fixed appropriately to obtain the fit illus- . The latter did not include GMP-PNP, which was found in separate experiments to be without discernible effect on the binding of the radioligand alone. The receptor was assumed to be tetrameric, and the value of [P] b in Equation 1 was computed according to Equation 2c. Single values of K P and p j were common to all of the data. A single value of K A was common to all data acquired at graded concentrations of the agonist; values of a j and c j were common to those data acquired either with or without GMP-PNP. The fitted parametric values are as follows (ϮGMP-PNP): Ϫlog K A ϭ 6.46 Ϯ 0.62 (Ϯ), Ϫlog K P ϭ 7.15 Ϯ 0.04 (Ϯ), Ϫlog a 2 ϭ Ϫ0.86 Ϯ 0.97 (Ϫ) and Ϫ1.39 Ϯ 0.71 (ϩ), Ϫlog a 3 ϭ Ϫ0.26 Ϯ 0.56 (Ϫ) and 0.29 Ϯ 0.53 (ϩ), Ϫlog p 2 ϭ Ϫ0.09 Ϯ 0.12 (Ϯ), Ϫlog c 2 ϭ 1.45 Ϯ 0.83 (Ϫ) and 0.22 Ϯ 0.94 (ϩ), Ϫlog c 3 ϭ Ϫ0.45 Ϯ 0.09 (Ϫ), and 0.98 Ϯ 0.45 (ϩ). The parameters a j , p j , and c j tend to be correlated, and most are not well defined by the present data. There was a significant increase in the sum of squares if GMP-PNP was assumed to be without effect on the value of c 3 (p ϭ 0.00089), and a smaller increase occurred in the case of c 2 (p ϭ 0.025); there was no appreciable change in case of a 2 or a 3 (p Ͼ 0.07). The values of Ϫlog p 3 and Ϫlog p 4 were fixed at Ϫ4 and 0, respectively. The values of Ϫlog a 4 and Ϫlog c 4 were fixed at Ϫ4, which is below the value at which either parameter affects the sum of squares or the values of other parameters. Values of [R] t and NS were common to data acquired within the same experiment; the means for the data shown in the figure are 128 Ϯ 41 pM and 0.00030 Ϯ 0.00010, respectively. The mean concentration of [ 3 H]AF-DX 384 was 58.7 nM. Further details are described in the legend to Fig. 6. have been indistinguishable from tetramers alone. Alternatively, time-dependent changes in relative apparent capacity may have arisen from changes in the cooperative properties of an otherwise stable tetramer.
In contrast to the oligomeric form predicted by cooperative effects, G-protein-linked receptors typically appear as monomers upon examination of their hydrodynamic properties. In some studies, however, the monomeric form has been accompanied by larger species that suggest the existence of oligomers. Molecular weights inferred from radiation inactivation point to dimers of ␣ 1 -and ␤ 2 -adrenergic receptors (Venter and Fraser, 1983). Also, glucagon receptors cross-linked with radiolabeled agonist appeared to migrate as dimers during ultracentrifugation on sucrose density gradients (Herberg et al., 1984). What appear to be dimers of metabotropic glutamate receptors (Pickering et al., 1993), c-myc-5-HT 1B receptors, c-myc-D 1 dopamine receptors, and D 2L dopamine receptors (Ng et al., 1994a(Ng et al., , 1994b have been identified on Western blots following electrophoresis of solubilized Sf9 membranes on SDS-polyacrylamide gels. Muscarinic receptors tagged with a labeled antagonist have exhibited the electrophoretic mobility expected of dimers (Avissar et al., 1983) or of dimers and larger aggregates (Dadi and Morris, 1984). Similarly, immunoreactive bands corresponding to dimers and larger oligomers have been found with M 2 muscarinic receptors purified from Sf9 membranes (Parker et al., 1991) and, in the present study, from porcine atria (Fig. 2).
Multimeric forms identified by their molecular size may be artifacts unrelated to those inferred from the binding studies. Oligomers found after electrophoresis in discontinuous buffers probably are stabilized by intermolecular disulfide bonds; while the samples typically are pretreated with a reducing agent, the receptor and the reagent can separate during the initial moments of migration (Dadi and Morris, 1984). Such cross-links may be of no biological relevance, but the nature of the products suggests a process that is specific nonetheless. Disulfide bonds arising from random interactions among receptors and other proteins might be expected to yield large aggregates of indeterminate molecular size, particularly with the mixtures of components obtained from native membranes. In contrast, the observed oligomers are typically of defined size and appear to comprise multiples of a single gene product. This pattern suggests that intermolecular cross-linking occurs subsequent to the formation of specific complexes in the highly concentrated environment of the stacking gel. If the process is specific, oligomers that survive or reassemble during electrophoresis may have some interactions in common with those that mediate the cooperative effects. It seems unlikely, however, that the patterns observed on polyacrylamide gels approximate the state of the system in the binding assays.
Nature and Role of the Interaction with the G-protein-In schemes based on the mobile receptor model, agonists increase the affinity of receptors (R) for G-proteins (G) and thereby increase coupling; similarly, G-proteins increase the affinity of receptors for agonists and thereby bring about the multiple states visible in the binding profiles (e.g. De ). It is implicit that RG dissociates spontaneously and rapidly on the time scale of a binding assay, and appreciable levels of the complex are not expected to occur in solution; whatever the rate of dissociation, the association of R and G is likely to be negligible when the reactants are diluted at least 1000-fold from their local concentrations in the native membrane. Solubilized receptors thus are not expected to exhibit those properties that derive from an association with the G-protein unless the complex is more stable, and less transient, than envisaged in the mobile receptor model and similar schemes.
The total amount of G i , G o , and G q/11 in M2 was only about 6% of that in M2G, yet both preparations displayed multiple affinities for antagonists and for the agonist oxotremorine-M. Similar results have been described previously, in that purified muscarinic receptors apparently devoid of G protein have revealed multiphasic binding of agonists in preparations from brain  and heart Ikegaya et al., 1990). Multiple classes of sites therefore appear to exist independently of G-proteins, particularly in preparation M2 but also in M2G. It follows that G-proteins in the latter preparation act by modulating properties that are intrinsic to the receptor. Scheme I can account in full for the properties of M2G, including the bell-shaped effect of oxotremorine-M in the presence of GMP-PNP; the differences between M2 and M2G emerge as nucleotide-or G-protein-related changes in the degree of cooperativity between successive equivalents of ligand. In contrast, the properties of M2G are difficult to rationalize in terms of ligand-regulated equilibria involving uncoupled and G-coupled receptors. The assays were performed in solution at subnanomolar concentrations of the labeled sites. As described above, it is expected that such a system would be shifted predominantly to the uncoupled state under those conditions. Also, the strictly inhibitory effect of oxotremorine-M in M2 is strikingly different from the bell-shaped profile induced by GMP-PNP in M2G. If coupling were precluded by the nucleotide, receptors devoid of G-protein ought to be indistinguishable from receptors plus G-protein at saturating concentrations of the nucleotide. The observed difference suggests that, in preparation M2G, receptors and G-proteins remained coupled in the presence of GMP-PNP.
G-proteins that copurify with M 2 receptors, and the nature of their participation in allosteric effects, suggest that the RG complex is more stable than implied by exchange-based models for binding and transduction. That stability differs from the general observation, first demonstrated for the ␤-adrenergic receptor (Limbird et al., 1980), that the RG complex survives solubilization only if the membranes are preincubated with agonist. A ligand-stabilized complex also is suggested by the observation that muscarinic agonists increase the amount of G i␣ and G o␣ immunoprecipitated by antibodies specific for the M 2 muscarinic receptor (Matesic et al., 1989;Offermanns et al., 1994). The requirement for an agonist is not universal, however, as illustrated by the binding properties of nucleotide-sensitive receptors labeled by [ 3 H]histamine in solubilized preparations from rat cortex (Wells and Cybulsky, 1990). Also, it has been shown previously that guanyl nucleotides do not necessarily promote the dissociation of G-proteins from M 2 muscarinic receptors (Matesic et al., 1989;Poyner et al., 1989).
It remains unclear which of the G-proteins in preparation M2G accounts for the sensitivity to GMP-PNP or for the differences between M2G and M2. Both G i and G o have been shown to interact with purified M 2 muscarinic receptors in an agonistand nucleotide-sensitive manner (Ikegaya et al., 1990;Parker et al., 1991). G s is believed not to associate with M 2 receptors , but the amount is comparatively small and may represent coelution of a nonspecific nature. The amount of copurifying G q/11 is comparatively larger, but its occurrence also may be an artifact. G q/11 is believed to mediate the regulation of phospholipase C (Blank et al., 1991), and M 2 receptors generally have been found not to affect the hydrolysis of phosphoinositides unless expressed at high density ; moreover, M 2 receptors have been shown to activate G i but not G q/11 in recombinant systems (Offermanns et al., 1994). The multiple subtypes of G-protein found in preparation M2G recall the observation that cardiac muscarinic re-ceptors can be immunoprecipitated with roughly equal amounts of G o and G i . The stoichiometry of the components in M2G remains unresolved, but at least two explanations for the observed heterogeneity come to mind: a single equivalent of one or the other G-protein may associate with each equivalent of receptor, or the G-proteins themselves may form a heterooligomeric array. The latter possibility could account for the presence of G q/11 , which may couple with the receptor via G i or G o , and it suggests a vehicle for the participation of G o in M 2 -initiated signaling.
The suggestion of an oligomeric array is consistent with hydrodynamic evidence that G-proteins occur as multimeric complexes comparable in size with cross-linked tubulin (Coulter and Rodbell, 1992;Jahangeer and Rodbell, 1993). A functional role for such an arrangement is suggested by evidence that cooperativity accounts for the agonist-sensitive, multiple states of affinity recognized by guanyl nucleotides at G-proteins linked to cardiac muscarinic receptors (Chidiac and Wells, 1992). Furthermore, there is a striking similarity between the effect of GMP-PNP on the binding of oxotremorine-M to M 2 receptors (Fig. 7) and the effect of carbachol on the binding of GDP to receptor-linked G-proteins (Fig. 4 in Chidiac and Wells (1992)). The reciprocal nature of these effects suggests a mechanism in which the functional unit of transduction is a heterooligomer comprising multiple equivalents of receptor and G-protein. In such a scheme, the allosteric interactions between agonists and guanyl nucleotides derive from the effects of one ligand on the degree of cooperativity in binding of the other.
Earlier objections to the notion of a transient RG complex arose in large part from the failure of such exchange-based schemes to describe the binding properties of G-protein-linked receptors (Lee et al., 1986;Chidiac and Wells, 1992;Graeser and Neubig, 1993). If binding is governed by cooperativity, however, the notion of exchange re-emerges in a different light: the RG heterooligomer may coexist in exchange with oligomers of receptors on the one hand and of G-proteins on the other, or it may retain its oligomeric integrity throughout the signaling process (Chidiac and Wells, 1992). The latter possibility is favored by the stability, at least in some circumstances, of the RG complex upon solubilization and during purification.