Coupling of G Proteins to Reconstituted Monomers and Tetramers of the M2 Muscarinic Receptor*

Background: The allosteric interaction between agonists and guanylyl nucleotides reports on the interaction between G protein-coupled receptors and G proteins. Results: Such allostery differs in kind between reconstituted monomers and tetramers of the M2 muscarinic receptor. Conclusion: Monomers and tetramers mediate allostery via different mechanisms. Significance: Only tetramers resemble muscarinic receptors in myocardial membranes in the nature of their sensitivity to guanylyl nucleotides. G protein-coupled receptors can be reconstituted as monomers in nanodiscs and as tetramers in liposomes. When reconstituted with G proteins, both forms enable an allosteric interaction between agonists and guanylyl nucleotides. Both forms, therefore, are candidates for the complex that controls signaling at the level of the receptor. To identify the biologically relevant form, reconstituted monomers and tetramers of the purified M2 muscarinic receptor were compared with muscarinic receptors in sarcolemmal membranes for the effect of guanosine 5′-[β,γ-imido]triphosphate (GMP-PNP) on the inhibition of N-[3H]methylscopolamine by the agonist oxotremorine-M. With monomers, a stepwise increase in the concentration of GMP-PNP effected a lateral, rightward shift in the semilogarithmic binding profile (i.e. a progressive decrease in the apparent affinity of oxotremorine-M). With tetramers and receptors in sarcolemmal membranes, GMP-PNP effected a vertical, upward shift (i.e. an apparent redistribution of sites from a state of high affinity to one of low affinity with no change in affinity per se). The data were analyzed in terms of a mechanistic scheme based on a ligand-regulated equilibrium between uncoupled and G protein-coupled receptors (the “ternary complex model”). The model predicts a rightward shift in the presence of GMP-PNP and could not account for the effects at tetramers in vesicles or receptors in sarcolemmal membranes. Monomers present a special case of the model in which agonists and guanylyl nucleotides interact within a complex that is both constitutive and stable. The results favor oligomers of the M2 receptor over monomers as the biologically relevant state for coupling to G proteins.


The data were analyzed in terms of a mechanistic scheme based on a ligand-regulated equilibrium between uncoupled and G protein-coupled receptors (the "ternary complex model"). The model predicts a rightward shift in the presence of GMP-PNP and could not account for the effects at tetramers in vesicles or receptors in sarcolemmal membranes. Monomers present a special case of the model in which agonists and guanylyl nucleotides interact within a complex that is both constitutive and stable.
The results favor oligomers of the M 2 receptor over monomers as the biologically relevant state for coupling to G proteins.
Oligomers of G protein-coupled receptors have been inferred from their functionality in pharmacological assays and detected in biochemical and biophysical studies on various systems, from native membranes to preparations reconstituted from purified components (1)(2)(3)(4)(5)(6)(7)(8). Oligomers (9 -15) and monomers (16 -18) have been detected in live cells by means of receptors labeled with fluorescent or bioluminescent probes. Evidence for the existence of both species, therefore, is persuasive (8,19), but their prevalence and biological roles remain unclear, and their relevance to signaling in particular has become a vexed question.
Some insight into these issues is available, in principle, from a comparison of monomers and oligomers assembled with G proteins in phospholipid bilayers, but the results have been inconclusive. Purified monomers of some GPCRs 6 have been reconstituted either as monomers in nanodiscs of modified apolipoprotein A1 (20,21) or as oligomers in liposomes (4,6,7,22). Both preparations exhibit the expected specificities for their respective ligands; inconveniently, however, both preparations also exhibit an allosteric interaction between agonists and guanylyl nucleotides that is recognized as a hallmark of efficacy (6,7,21,23).
Agonists to GPCRs reveal a dispersion of affinities (i.e. n H Ͻ 1) that can be described as a sum of hyperbolic terms representing two or more classes of receptor. In the presence of G protein, guanylyl nucleotides, such as GDP, GTP, and non-hydrolyzable analogues such as GTP␥S and GMP-PNP, promote an apparent interconversion of sites from higher to lower affinity such that the binding curve steepens and shifts rightward. Both the breadth of the dispersion in the absence of the nucleotide and the magnitude of the shift are correlated with measures of efficacy at the level of a response (24 -26). It follows that the mechanism of the allosteric interaction between an agonist and a guanylyl nucleotide is in effect the mechanism of signaling at the level of the receptor.
A common view of G protein-mediated signaling holds that agonists promote the formation of a transient complex between a monomeric receptor (R) and a G protein. As articulated in the ternary complex model (27), the complex accounts for the sites of higher affinity seen in the binding of agonists, and uncoupled receptors account for the sites of lower affinity; guanylyl nucleotides are thought to promote uncoupling of the RG complex and thereby to convert all of the receptors to the state of low affinity. It is implicit that receptors and G proteins exchange randomly between the complexed state and a pool of protomers. The degree of complexation therefore depends upon the mutual affinity and local concentrations of the reactants, and heterogeneity is induced by the G protein in an otherwise homogeneous population of receptors.
Both the ␤ 2 -adrenergic receptor and the -opioid receptor have been reconstituted as monomers in nanodiscs (21,23). In the absence of G protein, sites labeled by a radiolabeled antagonist were of uniformly low affinity for agonists. The introduction of a G protein was accompanied by the appearance of highaffinity sites, and their number increased with the amount of added G protein until they accounted for essentially all of the labeled receptors. Upon the addition of GTP␥S at a concentration sufficient to saturate the G proteins, the sites of high affinity were converted to sites of low affinity that resembled receptors in the absence of G protein.
A different pattern emerged when monomers of the M 2 muscarinic receptor were reconstituted in phospholipid vesicles, where they assembled spontaneously and almost wholly as tetramers (6,7). The sites appeared heterogeneous to agonists in the absence of G protein, indicating that heterogeneity was intrinsic to the receptor in its tetrameric state; the breadth of the dispersion correlated with efficacy, confirming its relevance to signaling (7). Heterogeneity was retained at saturating concentrations of G protein, and GMP-PNP promoted an interconversion from higher to lower affinity for the agonist (6).
The nucleotide-sensitive, agonist-selective heterogeneity displayed by monomers and tetramers of GPCRs leaves both forms as candidates for the biologically relevant unit of signaling. To distinguish between these possibilities, we have examined the binding properties of M 2 muscarinic receptors recon-stituted as monomers in nanodiscs and as tetramers in liposomes. Effects in the reconstituted preparations were compared with those at muscarinic receptors in myocardial membranes, taken as an example of a GPCR in its natural environment. Of particular interest has been the binding of agonists at intermediate concentrations of GMP-PNP, which can yield information about the process whereby receptors interconvert from one state of affinity to another.
The data have been analyzed in terms of empirical models for the purpose of comparison and in terms of the ternary complex model (27) for insight into the nature of the interaction between agonist and guanylyl nucleotide. The results indicate that tetramers but not monomers of the M 2 receptor resemble muscarinic receptors in myocardial membranes, suggesting that GPCRs signal as oligomers. Only the properties of monomers can be approximated by the ternary complex model and only if the RG complex is essentially constitutive and stable. Holo-G proteins were purchased from Calbiochem as a mixture of functional heterotrimers (i.e. ␣ o ␤␥ and ␣ i1-3 ␤␥) purified from bovine brain and supplied in buffer A (50 mM HEPES, 1 mM DTT, 1 mM EDTA, 0.1% Lubrol-PX, pH 7.6) at a total concentration of 6 -10 M. G proteins were concentrated 6-fold (Amicon Ultra 3K) prior to reconstitution with the M 2 receptor in nanodiscs or vesicles.

Ligands, Antibodies, and Other Materials-N-[
Ex-Cell 420 insect medium was purchased from JRH Biosciences, Inc. Fetal bovine serum, Fungizone, and gentamycin were from Invitrogen. Complete Protease Inhibitor Cocktail tablets were from Roche Applied Science.
Sephadex G-50 (fine) and Fast-Flow DEAE-Sepharose were purchased from GE Healthcare. Polypropylene columns used in the binding assays were purchased from Kontes (Disposaflex, 0.8 ϫ 6.5 cm). Econo-Pacs and Econo-Columns were from Bio-Rad, and receptor was concentrated using Centricon and Centriprep concentrators (Amicon) purchased from Millipore. Total protein was estimated by means of bicinchoninic acid using the BCA protein assay kit and bovine serum albumin, taken as the standard, purchased from Pierce.
Antibodies used for Western blots were purchased from commercial sources as follows: anti-HA polyclonal antibody (rabbit) and anti-FLAG monoclonal antibody (rabbit), Sigma-Aldrich; anti-His monoclonal antibody (mouse), GE Healthcare; anti-M 2 muscarinic acetylcholine receptor monoclonal antibody (mouse), Thermo Scientific. The agarose-conjugated anti-FLAG antibody (mouse) used for immunoprecipitation was from Sigma-Aldrich.
Purified M 2 Muscarinic Receptor-Reconstitutions were performed with purified human M 2 muscarinic receptor bearing the HA (YPYDVPDYA) or FLAG (DYKDDDDA) epitope at the amino terminus and, when required, a hexahistidyl tag at the carboxyl terminus. Sf9 cells were cultured at 27°C in Ex-Cell 420 insect medium containing 2% fetal bovine serum, 1% Fungizone, and 0.01% gentamycin. Cells growing at a density of 2 ϫ 10 6 cells/ml were co-infected with the two baculoviruses at a total multiplicity of infection of 5 and harvested 48 h later. The membranes were solubilized in digitonin-cholate (0.86% digitonin, 0.17% cholate), and the receptor was purified via successive passage on DEAE-Sepharose, ABT-Sepharose, and hydroxyapatite. Receptor was recovered from the last column in buffer B (20 mM KH 2 PO 4 adjusted to pH 7.40 with KOH, 20 mM NaCl, 1 mM EDTA, 0.1 mM PMSF) containing 0.1% digitonin and 0.02% cholate. The eluate was divided into aliquots (30 l) that were stored at Ϫ75°C. Further details regarding growth of the cells and purification of the receptor have been described previously (2,6,28).
Reconstitution in Nanodiscs-Modified apolipoprotein MSP1E3D1 (membrane scaffold protein 1E3D1) tagged with hexahistidine at the amino terminus was expressed in E. coli BL21Gold cells (Stratagene) and purified in a buffer containing 10 mM Tris (pH 7.4), 0.1 M NaCl, and 0.01% NaN 3 (29). The concentration of MSP1E3D1 in the purified preparation was 50 M. To assemble receptor-containing nanodiscs, aliquots of MSP1E3D1 (250 l) and buffer C (20 mM HEPES, 160 mM NaCl, and 0.8 mM EDTA, adjusted to pH 8.0 with KOH) (210 l) were added to premixed samples of POPC (50 mM in 10 l of 100 mM cholate) and purified M 2 receptor (0.3 M in 30 l of buffer B). The concentrations after mixing were as follows: POPC, 1,000 M; MSP1E3D1, 25 M; M 2 receptor, 0.018 M.
The mixture was incubated for 10 min at 4°C, treated with BioBeads (SM2-adsorbent, Bio-Rad) (250 mg), and incubated for an additional 4 h at 4°C. The BioBeads were removed on a 0.22-m filter (Millex SLGP 033RS), and the nanodiscs were separated by fast protein liquid chromatography on a column of Superdex 200 (10/300 GL) (GE Healthcare) eluted with buffer C. A control lacking the receptor was prepared in the same manner.
Total protein was monitored routinely in a flow cell by measuring the absorbance at 280 nm. The eluate was collected in fractions of 1 ml except when the receptor was to be monitored by means of N-[ 3 H]methylscopolamine, when the volume of each fraction was 0.5 ml. The radioligand was present at the nearly saturating concentration of 33 nM, and nonspecific binding was taken as total binding in the presence of 1 mM unlabeled N-methylscopolamine. Most of the UV-absorbing material and essentially all of the receptor emerged in a single peak centered in each case at about 12 ml. The major peak was preceded in some cases by a smaller peak of aggregated MSP1E3D1, which emerged at the void volume and varied in size from preparation to preparation. The receptor-containing fractions were pooled and stored at Ϫ75°C.
The nominal ratio of receptors to nanodiscs was 1:690, based on the amounts added initially and assuming the incorporation of 2 eq of MSP1E3D1/nanodisc. One nanodisc is expected to take up 160 -240 molecules of POPC (29), but the amount of MSP1E3D1 was disproportionately higher in order to ensure the sequestration of all POPC and thereby to avoid the formation of larger lipid structures. The true ratio of receptors to nanodiscs, therefore, was less than the nominal value of 690.
To reconstitute the receptor with holo-G proteins, an aliquot of G proteins in buffer A (3 l) was added to receptor-containing nanodiscs (500 l) prepared in buffer C and supplemented with DTT (1 mM) and MgCl 2 (6 mM). The ratio of ␣-subunits to receptors was 80:1, and the final concentration of Lubrol-PX was 0.0006%. To measure the effect of Lubrol-PX alone, an aliquot of buffer A lacking G protein was concentrated 6-fold and mixed with the reconstituted receptor as described above.
Reconstitution in Phospholipid Vesicles-Reconstitutions were performed as described previously (7). Briefly, POPC (1 mg), POPS (1 mg), and cholesterol (0.06 mg) were dissolved in chloroform and dried uniformly under argon to a thin film. The lipids then were hydrated for 1 h at 40°C in 1 ml of buffer C, followed by three cycles of freezing in liquid nitrogen and thawing. When the receptor was to be reconstituted with G proteins, buffer C was supplemented throughout with DTT (1 mM) and MgCl 2 (6 mM). Vesicles were prepared by extrusion through a polycarbonate membrane with 50-nm pores (Nuclepore Track-Etch Membrane, Whatman) mounted on an Avanti Mini-Extruder.
The purified M 2 receptor (3-4 pmol) in buffer B (30 l) was mixed with carbachol (100 mM) in buffer C (5 l) and an aliquot of buffer C alone (12 l). The sample was kept for 10 min at 4°C, mixed with an aliquot of G proteins in buffer A (3 l, 80 ␣-subunits/receptor), and kept for an additional 5 min at 4°C. When G proteins were omitted, the aliquot of buffer C alone was 15 l, and the mixture was kept for 15 min at 4°C. The final concentration of carbachol, therefore, was 10 mM in a total volume of 50 l. The sample then was mixed with the preformed vesicles (150 l) and applied to a column of Sephadex G-50 (0.8 ϫ 5.0 cm) pre-equilibrated with buffer C (6). The column was washed with 600 l of buffer C, and receptor-containing vesicles were eluted with a further 500 l of the same buffer.
Preparation of Sarcolemmal Membranes-Sarcolemmal membranes were prepared from porcine atria obtained from Quality Meat Packers Ltd. Toronto (2). Briefly, atria were collected immediately after slaughter, taking care to avoid the sinus and atrioventricular nodes. The tissue was washed twice with ice-cold phosphate-buffered saline (20 mM KH 2 PO4 and 150 mM NaCl, adjusted to pH 7.40 with NaOH) and blended by means of a Polytron homogenizer in buffer D (20 mM imidazole, 1 mM EDTA, 0.1 mM PMSF, and 0.02% NaN 3 , adjusted to pH 7.60 with HCl) supplemented with benzamidine (1 mM), pepstatin A (20 g/ml), leupeptin (0.2 g/ml), and bacitracin (200 g/ml). The homogenate was centrifuged for 15 min at 4°C and 3,000 ϫ g, and the pellet was washed by suspension in buffer E (20 mM HEPES, 1 mM EDTA, and 200 g/ml bacitracin, adjusted to pH 8.0 with NaOH), centrifugation for 15 min at 4°C and 3,000 ϫ g, and resuspension in buffer E. The resulting homogenate was fractionated by centrifugation on a sucrose density gradient (13-28%) to obtain the sarcolemmal fraction, which was collected by centrifugation for 45 min at 4°C and 100,000 ϫ g. To ensure the removal of GDP, the pellet was washed three times by resuspension in buffer D by means of a Potter-Elvehjem tissue homogenizer and subsequent centrifugation for 45 min at 4°C and 100,000 ϫ g. The pellet from the last wash was suspended in buffer D supplemented with 10 mM MgCl 2 and assayed for binding at a saturating concentration of [ 3 H]quinuclidinyl benzilate. The mixture was divided into aliquots that were centrifuged for 10 min at 4°C and 18,000 ϫ g, and the pellets were stored at Ϫ75°C until required for binding assays.
Cross-linking-An aliquot of the receptor was supplemented with BS 3 in deionized water (20 mM) to yield a final reagent concentration of 2 mM. The mixture was incubated for 30 min at room temperature, and the reaction was terminated by the addition of Tris-HCl (1 M, pH 8.00) to a final concentration of 20 mM. After further incubation for 15 min at room temperature, the sample was placed on ice pending examination by electrophoresis and Western blotting. Samples lacking BS 3 but treated in a parallel and otherwise identical manner were prepared as controls.
Immunoprecipitation, Electrophoresis, and Western Blotting-To test for coimmunoprecipitation, aliquots of tagged receptor (250 l) were mixed with a 50% slurry of the agarose-conjugated anti-FLAG antibody (20 l) and shaken overnight at 4°C. Immunoadsorbed receptor was collected by centrifugation for 5 min at 4°C and 1,000 ϫ g, and the precipitated beads were washed four times by resuspension in 1 ml of buffer F (9.1 mM Na 2 HPO 4 , 1.7 mM NaH 2 PO 4 , and 150 mM NaCl, adjusted to pH 7.40 with NaOH) and subsequent centrifugation. Further details have been described previously (6,28).
Samples for electrophoresis were heated at 65°C for 5 min prior to loading on precast polyacrylamide gels from Bio-Rad (Ready Gel Tris-HCl, 10%). It has been shown previously that these conditions do not induce aggregation of the M 2 muscarinic receptor from Sf9 cells (28). Resolved proteins were transferred onto nitrocellulose membranes (Bio-Rad, 0.45 m) in a Mini Trans-Blot transfer cell (Bio-Rad). The membranes then were treated with the primary antibody for 2 h at a dilution of 1:1,000 and with the secondary antibody for 1 h at a dilution of 1:3,000. Proteins were visualized by chemiluminescence using reagents and film purchased from GE Healthcare (ECL TM , Hyperfilm MP). The images were digitized at a resolution of 300 dots/inch, and the intensities of the bands were estimated from the densitometric trace using ImageJ (30).
Binding Assays with Receptor in Solution and after Reconstitution-The radioligand and any unlabeled ligands were dissolved in buffer G (25 mM KH 2 PO 4 and 4 mM HEPES adjusted to pH 8.00 with KOH, 230 mM NaCl, 0.8 mM EDTA, 10 mM MgCl 2 , and 0.1 mM PMSF, adjusted to pH 7.40 with NaOH). For assays with purified receptor in solution, buffer G was supplemented with 0.1% digitonin and 0.02% cholate. An aliquot of the ligand-containing solution (49 l for receptor in solution and vesicles, 43 l for receptor in nanodiscs) was added to the receptor (4 l, solution and vesicles; 10 l, nanodiscs) contained in a polypropylene microcentrifuge tube, and the reaction mixture was incubated at 30°C for 45 min in the case of N-[ 3 H]methylscopolamine and for 2 h in the case of [ 3 H]quinuclidinyl benzilate. Bound radioligand then was separated by applying an aliquot (50 l) to a column of Sephadex G-50 fine (0.8 ϫ 6.5 cm) pre-equilibrated with buffer H (20 mM HEPES, 20 mM NaCl, 5 mM MgSO 4 , and 1 mM EDTA, adjusted to pH 7.40 with NaOH) supplemented with 0.017% digitonin. Assays were performed in duplicate. In studies at graded concentrations of N-[ 3 H]methylscopolamine, assays with and without GMP-PNP were performed in parallel; in studies at graded concentrations of oxotremorine-M, assays at 2-4 different concentrations of GMP-PNP were performed in parallel. Nonspecific binding was measured in the presence of unlabeled N-methylscopolamine (1 mM), which was premixed with the radioligand prior to the addition of the receptor.
Binding Assays with Receptor in Sarcolemmal Membranes-Samples of frozen membrane were thawed and resuspended in buffer G by means of a Potter-Elvehjem tissue homogenizer. The final concentration of protein was 2-5 g/ml. Aliquots of the homogenate (1 ml) then were added to a mixture of the radioligand and any unlabeled ligands dissolved at the required concentrations in buffer G (20 l). The mixture was incubated for 45 min at 30°C, and the reaction was terminated when the sample was passed through a fiberglass filter mounted on a Brandel cell harvester. Assays were performed in duplicate. In studies at graded concentrations of N-[ 3 H]methylscopolamine, assays with and without GMP-PNP were performed in parallel; in studies at graded concentrations of oxotremorine-M or carbachol, assays at 4 -6 different concentrations of GMP-PNP were performed in parallel. Nonspecific binding was measured in the presence of unlabeled atropine (3 M), which was premixed with the radioligand prior to the addition of the receptor. Other details have been described previously (31).
Analysis of Data-All data were analyzed with total binding taken as the dependent variable (B obsd ) and the total concentrations of all ligands taken as the independent variables. The free concentration of a ligand was calculated numerically from the total concentration as required. The values listed for total receptor ([R] t ), maximal specific binding (B max ), and the concentrations of ligands are the concentrations in the binding assays.
Data acquired at graded concentrations of N-[ 3 H]methylscopolamine were analyzed empirically according to the Hill equation, formulated as shown in Equation 1 (32).
The parameter B max represents maximal specific binding of the radioligand (P), and B sp represents specific binding at the total concentration [P] t . The parameter EC 50 represents the concentration of unbound radioligand that corresponds to half-maximal specific binding, and n H is the Hill coefficient. The parameter NS represents the fraction of unbound radioligand that appears as nonspecific binding, which was found to increase linearly with the concentration of unbound N-[ 3 H]methylscopolamine in all preparations. Data acquired at graded concentrations of N-[ 3 H]methylscopolamine also were analyzed as a sum of hyperbolic terms formulated as shown in Equation 2, where F j is the fraction of total sites (⌺ jϭ1 n F j ϭ1), and other parameters are as defined above.
For data acquired at a single concentration of N-[ 3 H]methylscopolamine and graded concentrations of oxotremorine-M or carbachol, the Hill equation was formulated as shown in Equation 3.
The variable [A] t is the total concentration of unlabeled ligand, and IC 50  .
The parameter IC 50(j) represents the total concentration of unlabeled ligand that corresponds to half-maximal inhibition at the fraction F j of labeled sites (⌺ j ϭ 1 n F j ϭ 1), and other parameters are as defined above.
Mechanistic analyses were performed in terms of Schemes 1-3, in which heterogeneity arises from a static mixture of independent and distinct sites (Scheme 1) or is induced by G proteins in an otherwise homogeneous population of receptors (Schemes 2 and 3). Estimates of total binding were fit by the equation, B obsd ϭ B sp ϩ NS([P] t Ϫ B sp ), in which the variables and parameters are as described above for Equation 1. The value of B sp was computed for each scheme as described below.
Scheme 1 depicts an intrinsically heterogeneous system in which the radioligand (P) and an unlabeled ligand (A) compete for distinct and mutually independent sites (R j , where j ϭ 1, 2, . . . n). Sites of type j bind P and A with equilibrium dissociation constants K Pj and K Aj , respectively, and constitute the fraction F j of all sites (i.e.
. Total specific binding of the probe was calculated according to Equation 5, where the values of [PR j ] were calculated from the equilibrium dissociation constants and the concentrations of the reactants. The free concentrations of receptor and both ligands were calculated numerically from the total concentrations, as described previously (32). Scheme 2 is a variant of the ternary complex model (27) in which two different G proteins (G j , j ϭ 1 or 2) compete for a single site on the receptor (R) to form the spontaneously dissociating complex RG 1 or RG 2 (32, 33). All G proteins ([G j ] t ) can SCHEME 1. Heterogeneity by virtue of distinct and mutually independent sites.

SCHEME 3. Heterogeneity induced by constitutive coupling of receptors and G proteins.
interact randomly with all receptors ([R] t ) within the relevant volume. The radioligand (P) and unlabeled ligands (A) bind to the receptor with equilibrium dissociation constants K P and K A , respectively, and a guanylyl nucleotide (N), such as GMP-PNP, binds to each G protein with the equilibrium dissociation constant K Nj . The corresponding affinities of A and P for RG j are K P.Gj and K A.Gj , respectively, and the affinities for the nucleotide-liganded complex (RG j N) are K P.GjN and K A.GjN . The equilibrium dissociation constant for the interaction between R and G j is K Gj , and that for the interaction between R and G j N is K Gj.N . If receptors and G proteins are confined to the membrane, the volume of the interaction will be much smaller than the total volume of the reaction mixture. The values of K G obtained from analyses in terms of the model are uncorrected for such differences and therefore are nominal.
Total specific binding of the radioligand in Scheme 2 is given by Equation 6, where the value of each term was calculated from the relevant equilibrium dissociation constants and the concentrations of the reactants. The free concentrations of receptor, G proteins, and all ligands were calculated numerically from the total concentrations, as described previously (32,33). Parameters entered explicitly into the fitting procedure were Other binding constants are implicit in the multiple loops of Scheme 2 (e.g. K A /K A.Gj ϭ K Gj /K Gj.A ), and the values were calculated as required.
Scheme 3 is a special case of Scheme 2 in which the interaction between receptor and G protein is shifted wholly to the coupled state under all conditions, thereby reducing the free concentration of the minor constituent in effect to zero. This can be achieved in practice by selecting arbitrary values of K G that are at least 3 orders of magnitude below the nominal concentration of receptor. The system as depicted in Scheme 3 has G proteins in the minority (i.e.
; accordingly, only the receptor-coupled states of G j are populated to an appreciable degree at thermodynamic equilib- , despite an exchange that proceeds via the uncoupled states (e.g. Most analyses involved multiple sets of data, and data from different experiments generally were assigned separate values of All parameters were estimated by nonlinear regression. Equilibrium constants were optimized throughout on a logarithmic scale. The data were weighted according to the measured estimate of the S.E. on each point. Arithmetic means are presented together with the S.E.; parametric values derived from a single analysis of one or more sets of data are presented together with the errors as estimated from the covariance matrix. Other details regarding the analyses and statistical procedures have been described previously (see Ref. 6 and references cited therein).

Reconstitution of Monomers and Tetramers of the M 2
Receptor-The oligomeric status of the M 2 receptor after solubilization, purification, and reconstitution in phospholipid vesicles was the same as described previously (6,7,28,34). HA-and FLAG-tagged receptors extracted from co-infected Sf9 cells in digitonin-cholate were mostly oligomers, as indicated by their mobility on polyacrylamide gels ( Fig. 1) and their high efficiency of coimmunoprecipitation (Fig. 2). Only 28% of the immunopositive material identified by the anti-receptor antibody migrated with the apparent molecular mass of a monomer. That fraction was reduced to 10% upon treatment with the bifunctional reagent BS 3 , and the balance migrated as a dimer or larger aggregates (Fig. 1A). Sixty-eight percent of the HAtagged receptor was recovered in the precipitate obtained with the immobilized anti-FLAG antibody (Fig. 2, lanes 1 and 2).
Purified receptor that had been reconstituted into vesicles of POPC, POPS, and cholesterol at an initial ratio of 1 protomer per 2 vesicles (7) also migrated predominantly as a monomer (92%, 58.2 Ϯ 0.8 kDa), but the monomeric band was virtually eliminated by treatment with BS 3 . The cross-linked receptor migrated as a mixture of tetramers (51%, 214 Ϯ 7 kDa) and larger aggregates (42%) that may comprise tetramers (Fig. 1D). Oligomers formed in the vesicles therefore appear to dissociate under the conditions of electrophoresis. The oligomeric nature of the reconstituted receptor was confirmed by the high efficiency of coimmunoprecipitation (i.e. 91%, Fig. 2, lanes 7 and 8).
Purified receptor that had been inserted into nanodiscs of POPC and MSP1E3D1 at an initial ratio of one receptor per 690 nanodiscs migrated predominantly as a monomer (88%, 57 Ϯ 2 kDa) (Fig. 1C), and the efficiency of coimmunoprecipitation remained low at 14% (Fig. 2, lanes 5 and 6). Treatment with BS 3 eliminated the monomeric band and gave a mixture of larger species, one with an apparent molecular mass of 148 Ϯ 3 kDa and a broader band that migrated little beyond the stacking gel (Ͼ250 kDa) and varied in breadth and mobility from preparation to preparation (Fig. 1C). These new bands suggest that BS 3 tethers the receptor to the nanodisc.
The belt protein MSP1E3D1 has 22 lysyl residues and a molecular mass of 32 kDa. Cross-linking of one M 2 receptor and the two equivalents of MSP1E3D1 that make up one nano-disc would yield a species with an apparent molecular mass of about 122 kDa, which is slightly larger than a dimer of the receptor alone. Also, nanodiscs applied to non-denaturing gels have been shown previously to migrate with an apparent molecular mass of 232 kDa when empty (35) and 232-699 kDa when loaded with a membrane protein (36,37). To test for such adducts, nanodiscs were reconstituted with and without receptor, and their electrophoretic mobility on SDS-gels was measured before and after cross-linking with BS 3 (Fig. 1F). Only MSP1E3D1 bore the hexahistidyl tag, which was detected by the anti-His antibody.
Reconstituted MSP1E3D1 migrated exclusively as a monomer (31.1 Ϯ 2.9 kDa) (Fig. 1F, lanes 1 and 3). Treatment with BS 3 eliminated the monomeric band and introduced two broad bands corresponding roughly to a dimer of the belt protein (67.8 Ϯ 3.1 kDa) and larger species (152 Ϯ 8, 344 Ϯ 18 kDa) (Fig.  1F, lanes 2 and 4). The proportions of the multimeric components varied from preparation to preparation, and some samples also gave bands of higher molecular weight that traveled little beyond the stacking gel. There was essentially no effect of the receptor, either with or without cross-linking (Fig. 1F, compare lanes 1 and 3 with lanes 2 and 4), in accord with the low ratio of receptors to nanodiscs.
Disappearance of the monomeric band and the concomitant formation of what appear to be dimers suggest that the twin belt proteins of nanodiscs are cross-linked quantitatively by BS 3 , and those adducts may be linked in turn to produce the larger species seen on the gels. The bands of higher molecular mass that are detected by the anti-receptor antibody therefore appear to arise from cross-linking of a receptor to its surrounding dimer of MSP1E3D1 (ϳ125 kDa) and cross-linking of receptor-containing nanodiscs to empty nanodiscs (Ͼ250 kDa). Although the effects of BS 3 are complex in such a mixture of receptors and nanodiscs, the low level of coimmunoprecipitation confirms that the receptor was reconstituted as a monomer.
Binding Properties of the M 2 Receptor in Nanodiscs-The purified receptor reconstituted in nanodiscs appeared homogeneous to the antagonist N-[ 3 H]methylscopolamine under all conditions. Hill coefficients were indistinguishable from 1 throughout (p Ն 0.06) (Equation 1), and one class of sites is sufficient to describe the data in terms of Equation 2 (p Ն 0.14) ( Fig. 3A and Fig. 4, A, C, and E). Reconstitution of the receptor increased the affinity of the radioligand 4.3-fold, from 10 nM in solution (i.e. log K P ϭ Ϫ8.01 Ϯ 0.03 in Ref. 7) to 2.5 nM in nanodiscs (Fig. 4A). The subsequent addition of G proteins in buffer A at an 80-fold molar excess over the receptor reduced the affinity to about 10 nM (Fig. 4C), as did an equal volume of buffer A alone (Fig. 4A). There was a small but significant decrease in the affinity of the G protein-containing preparation upon the further addition of GMP-PNP at a concentration of 0.1 mM (p ϭ 0.00018) (Figs. 3A and 4E). Although reported previously (38), such a change is unusual. Guanylyl nucleotides generally have been found to increase the affinity of GPCRs for inverse agonists (6, 33, 39 -41) or to be without effect (26,42).
The Hill coefficient for the inhibitory effect of the agonist oxotremorine-M on the binding of N-[ 3 H]methylscopolamine to the reconstituted receptor was indistinguishable from 1 . The balance migrated as a dimer (b) or larger oligomers (c and d), as described previously (7,34). Longer exposures indicated that the monomeric receptor migrated as a doublet, also as previously (6, 7), with the lower and fainter band having a relative molecular mass of ϳ47 kDa. The data in A and B are representative of several batches of receptor prepared over the course of the investigation. The data in C and D are representative of three independent reconstitutions performed with two different batches of purified receptor. F, gels were loaded with samples of hexahistidyl-tagged MSP1E3D1 and POPC reconstituted as nanodiscs with (lanes 1 and 2) or without (lanes 3 and 4) purified M 2 receptor. Samples crosslinked with BS 3 and untreated controls were prepared in parallel. Transferred MSP1E3D1 was detected with the anti-His antibody. The data in F are representative of three reconstitutions. IB, immunoblot.
(n H ϭ 1.20 Ϯ 0.17, p ϭ 0.32), and one class of sites is sufficient to describe the data in terms of Scheme 1 (p ϭ 0.68). Reconstitution increased the affinity of the agonist 7-fold, from 89 M in solution (i.e. log K A ϭ Ϫ4.05 Ϯ 0.02 in Ref. 7) to 13 M in nanodiscs (Fig. 4B). Upon the addition of G proteins in buffer A ([G] t /[R] t ϭ 80:1), the Hill coefficient decreased to 0.74 Ϯ 0.06 (p ϭ 0.00070). Two classes are required in terms of Scheme 1 (p ϭ 0.0012), and most of the sites were in the state of higher affinity (F 1 ϭ 0.71) (Fig. 4D). Preliminary assays indicated that smaller quantities of G protein gave proportionately fewer high-affinity sites, suggesting that the low-affinity sites were receptors in excess of G proteins.
As with N-[ 3 H]methylscopolamine, the binding of oxotremorine-M to M 2 receptor in nanodiscs was affected by buffer A alone, which reduced the affinity of the agonist from 13 M to 0.35 mM at most of the sites (F 2 ϭ 0.83) (Fig. 4B). G proteins in buffer A therefore increase the affinity of the receptor from 0.35 mM to 12 M (Fig. 4D), a value that coincidentally approximates the value in the absence of buffer A (open symbols in Fig. 4B). A minor fraction of sites appeared to be unaffected by buffer A alone (F 1 ϭ 0.17) (closed symbols in Fig. 4B).
The effect of G proteins on the binding of oxotremorine-M was largely reversed by GMP-PNP at the saturating concentration of 0.1 mM. Two classes of sites are required to describe the data in terms of Scheme 1 (p ϭ 0.00012), and the sites of low affinity accounted for 90% of the total (Fig. 4F). The high-affinity component was not detected by the Hill equation, which returned a Hill coefficient indistinguishable from 1 (n H ϭ 0.91 Ϯ 0.06, p ϭ 0.20). The binding profile obtained in the presence of GMP-PNP and G proteins (closed symbols in Fig.  4F) resembles that obtained with buffer A alone (dashed line in Fig. 4F), and all of the parameters describing the two sets of data could be shared without a significant increase in the sum of squares (p ϭ 0.60). Receptors in the presence of G proteins and GMP-PNP, therefore, are indistinguishable from receptors in the absence of G proteins.
The 4 -18-fold reduction brought about by buffer A in the apparent affinities of N-[ 3 H]methylscopolamine and oxotremorine-M can be attributed to Lubrol-PX, which was absent during purification of the receptor and its reconstitution into nanodiscs. Other constituents, such as DTT and MgCl 2 , were present at the same concentrations throughout. Also, muscarinic receptor extracted from sarcolemmal membranes has been shown to bind N-[ 3 H]methylscopolamine 23-fold more tightly in digitonin-cholate than in Lubrol-PX (43). The concentration of Lubrol-PX was only 0.00060% in the reconstituted preparation and only 0.00011% in the binding assay, which is below the critical micelle-forming concentration of 0.0047% (44), and there was no effect of Lubrol-PX on the size of the particles, as determined by FPLC (data not shown).
Effect of GMP-PNP on G Protein-coupled M 2 Receptors in Nanodiscs-Progressive increases in the concentration of GMP-PNP caused a nearly parallel, rightward shift in the binding profile of oxotremorine-M (Fig. 5A), with Hill coefficients near or indistinguishable from 1 throughout (n H ϭ 0.77 at 7.9 nM GMP-PNP (p ϭ 0.036); otherwise, 0.79 Յ n H Յ 0.91 (p Ն 0.13)). The minor contingent of high-affinity sites that co-existed with 0.1 mM GMP-PNP (Equation 5, F 1 ϭ 0.10; Fig. 4F) was not observed at lower concentrations of the nucleotide, nor did it appear to influence the outcome of subsequent analyses.
To examine the nature of the change effected by GMP-PNP, the data acquired at all concentrations of the nucleo-  1 and 2), purified (lanes 3 and 4), and reconstituted in nanodiscs (lanes 5 and 6) or in vesicles (lanes 7 and 8). Gels were loaded with an aliquot of the untreated sample containing 10 -20 fmol of the M 2 receptor (lanes 1, 3, 5, and 7) or with the immunoprecipitate obtained from a 10-fold larger volume of the same sample treated with the agarose-conjugated anti-FLAG antibody (lanes 2, 4, 6, and 8). The amount of receptor was determined from the binding of [ 3 H]QNB. The corresponding lanes in A and B were loaded with equal amounts of the same sample, and the gels were processed in parallel through electrophoresis and subsequent transfer to nitrocellulose. One membrane then was blotted with anti-HA antibody (A) to determine the efficiency of coimmunoprecipitation (i.e. HA-tagged receptors with anti-FLAG antibody); the other was blotted with anti-FLAG antibody (B) to determine the efficiency of immunoprecipitation (i.e. FLAG-tagged receptors with anti-FLAG antibody). To test for cross-reactivity, an aliquot of the immobilized antibody in buffer C was processed in the same manner as receptor-containing samples subjected to immunoprecipitation (lane 9). The total density of the signal in each lane was determined with ImageJ (30); for the lanes in A, it was adjusted by subtracting the density of a band that represented the heavy chain of the mouse anti-FLAG antibody and was detected nonspecifically by the rabbit anti-HA antibody (small arrows). The adjusted density measured for each precipitated sample in A  (lanes 2, 4, 6, and 8) then was divided by that measured for the corresponding control in the same panel (lanes 1, 3, 5, and 7). To obtain the efficiency of coimmunoprecipitation, the ratio of densities from A was corrected for the difference in the amount of total receptor as determined from the corresponding densities measured for the untreated and precipitated samples in B. Based on the densities in B, about 5-fold more FLAG-tagged receptors were present in the samples obtained by immunoprecipitation (lanes 2, 4, 6, and 8) than in the controls (lanes 1, 3, 5, and 7). The mean values obtained for the efficiency of coimmunoprecipitation are as follows: unprocessed extract, 68 Ϯ 18% (n ϭ 5); purified M 2 receptor in solution, 13 Ϯ 7% (n ϭ 3); purified M 2 receptor reconstituted in nanodiscs, 14 Ϯ 5% (n ϭ 3); purified M 2 receptor reconstituted in vesicles, 91 Ϯ 28% (n ϭ 3). IB, immunoblot; IP, immunoprecipitation. tide were combined and analyzed empirically as a sum of two hyperbolic terms (Equation 4, n ϭ 2). In the first of two constrained analyses, single values of log IC 50(j) were common to all of the data, and a separate value of F 2 was assigned to the data acquired at each concentration of GMP-PNP. In the second, one value of F 2 was common to all of the data, and separate values of log IC 50(j) were assigned to the data acquired at each concentration of GMP-PNP. The sum of squares from each analysis then was compared with that obtained with separate values of all parameters for the data at each concentration of GMP-PNP.
The constraint on IC 50(j) led to a significant increase of 18% in the sum of squares over that from the unconstrained fit (p ϭ 0.013), indicating that GMP-PNP affects the apparent affinity of oxotremorine-M for the sites of at least one class. In contrast, the constraint on F 2 was without appreciable effect on the sum of squares (p ϭ 0.59), nor was there any change when a single value of log IC 50(2) also was common to all of the data (p ϭ 0.14). The fitted curves from the latter analysis are illustrated in Fig.  5A, and the parametric values are listed in Table 1. GMP-PNP therefore acted selectively on the affinity of those receptors that interacted with G proteins.
Effect of GMP-PNP on G Protein-coupled M 2 Receptors in Vesicles-Tetramers of the receptor reconstituted with G proteins at a molar ratio of 80:1 bound N-[ 3 H]methylscopolamine with a Hill coefficient of 0.66 Ϯ 0.04. Two classes are required to describe the data in terms of Equation 2 (p ϭ 0.00003), and most of the sites were in the state of low affinity (log K P2 ϭ Ϫ7.70, F 2 ϭ 0.84) (Fig. 3B). There was no effect of GMP-PNP, as confirmed by the absence of an appreciable change in the sum of squares with single rather than separate values of all parameters, including [R] t , for data acquired with and without the nucleotide (p ϭ 0.33). The insensitivity to GMP-PNP suggests that the heterogeneity revealed by the radioligand was unrelated to G proteins, in accord with evidence that it arises from constitutive or induced asymmetry within the tetramer (7). . A 10-fold molar excess of G proteins, therefore, is sufficient to saturate the receptor, as reported previously for another vesicular preparation (6).
When the data acquired at different concentrations of GMP-PNP are assigned common values of log IC 50(j) and separate values of F 2 , the sum of squares is not appreciably greater than that obtained with separate values of all three parameters (p ϭ 0.073). The fitted curves are shown in Fig. 5B, and the parametric values are listed in Table 1. In contrast, when the data acquired at different concentrations of GMP-PNP are assigned separate values of log IC 50(j) and a common value of F 2 , the sum of squares is increased significantly over that from the unconstrained analysis (p ϭ 0.0022). GMP-PNP therefore acted selectively on the apparent distribution of sites between the two states.
Effect of GMP-PNP on Muscarinic Receptors in Sarcolemmal Membranes-Cardiac muscarinic receptors appeared homogeneous or nearly so to N-[ 3 H]methylscopolamine (Fig. 3C). The Hill coefficient revealed some heterogeneity, both in the absence and presence of GMP-PNP (n H Ͻ 1, p Ͻ 0.002), but the values are close to 1 nonetheless (n H ϭ 0.95 Ϯ 0.01 and 0.96 Ϯ 0.02, respectively). Similarly, two classes of sites are required with Equation 2 (p Յ 0.0011), but one class with an affinity of about 0.6 nM predominated irrespective of the nucleotide (Fig. 3C). GMP-PNP was essentially without effect on binding overall, as illustrated by the data and fitted curves in  The affinity of the radioligand was taken as the same for both classes of sites (i.e. K P1 ϭ K P2 ' K P ). The fitted parametric values are as follows: M 2 R (A and B, n ϭ 1), log K A ϭ Ϫ4.89 Ϯ 0.13, log K P ϭ Ϫ8.60 Ϯ 0.12; M 2 R plus buffer A (A and B, n ϭ 2), log K A1 ϭ Ϫ6.19 Ϯ 0.28, log K A2 ϭ Ϫ3.46 Ϯ 0.05, F 2 ϭ 0.83 Ϯ 0.02, log K P ϭ Ϫ8.01 Ϯ 0.03; M 2 R plus G proteins in buffer A (C and D, n ϭ 2), log K A1 ϭ Ϫ4.93 Ϯ 0.14, log K A2 ϭ Ϫ3.64 Ϯ 0.32, F 2 ϭ 0.29 Ϯ 0.12, log K P ϭ Ϫ8.04 Ϯ 0.05; M 2 R plus G proteins in buffer A plus GMP-PNP (E and F, n ϭ 2), log K A1 ϭ Ϫ6.09 Ϯ 0.42, log K A2 ϭ Ϫ3.40 Ϯ 0.05, F 2 ϭ 0.90 Ϯ 0.02, log K P ϭ Ϫ7.86 Ϯ 0.04. Three independent experiments were performed on each preparation, and each experiment was performed on a different reconstituted sample. For the purpose of comparison, the data for binding to M 2 R plus buffer A are shown in the top (A and B) and middle panels (C and D); similarly, the data for binding to M 2 R plus G proteins in buffer A are shown in the middle (C and D) and bottom panels (E and F). The fitted curve in D for binding to M 2 R plus buffer A without G proteins is reproduced as the dashed line in F.  A, B, and D) or three (C) classes of sites, as determined by the F-statistic, to all of the data taken together. The parameters were constrained as described under "Results" and in the legend to Table 1, and the fitted values are listed in Table 1

TABLE 1 Parametric values for the binding of oxotremorine-M and carbachol to muscarinic receptors in reconstituted preparations and sarcolemmal membranes
The data represented in each panel of Fig. 5 were analyzed in terms of Equation 4 to obtain the parametric values listed in the table. Single values of log IC 50(j) or F j were assigned as indicated to all of the data acquired at all concentrations of GMP-PNP ("All curves"); otherwise, a separate value of each parameter was assigned to all of the data acquired at each concentration of the nucleotide. The constraints were without significant effect on the sums of squares (p Ͼ 0.07), as described under "Results. separate values of log IC 50(1) and F 2 are illustrated in Fig. 5D, and the parametric values are listed in Table 1. A 4.7-fold variation in the value of IC 50(1) shows no obvious dependence upon the concentration of the nucleotide and may derive from a third class of sites that cannot be detected at the resolution of the present data. The alternative analysis in which data acquired at different concentrations of GMP-PNP are assigned separate values of log IC 50(j) and a single value of F 2 gave a significantly higher sum of squares (p ϭ 0.00009). GMP-PNP therefore acted selectively on the apparent distribution of sites revealed by oxotremorine-M and by carbachol.
Mechanistic Evaluation of the Sensitivity to GMP-PNP-The effects of GMP-PNP in each preparation were examined in terms of the explicit mechanistic proposal known as the ternary complex model (27). Two versions of the model were considered: a general case in which no restriction was placed on the affinity of the G protein for the receptor (Scheme 2) and the extreme case in which the values of K G and K G.N were set arbitrarily at 10 Ϫ15 M, approximating a stable RG complex (Scheme 3). Both schemes were applied with one class of G protein, as proposed originally (27), and with two classes (G 1 and G 2 ), the members of which compete for a single site on the receptor (33). The latter case of Scheme 2 is a specific example of ligandbiased signaling, in that the preference of the receptor for G 1 or G 2 will be determined by the relative affinity of the agonist for the free receptor on the one hand and each RG j complex on the other.
For each preparation, the data acquired at graded concentrations of agonist (Fig. 5) were combined with those acquired at graded concentrations of N-[ 3 H]methylscopolamine (Fig. 3). Preliminary analyses in terms of Scheme 2 indicated that the data placed only a lower bound on the affinity of N-[ 3 H]methylscopolamine for the RG complex (i.e. K P.G and K P.GN ), which therefore was fixed at 10 Ϫ5 M during successive iterations of the fitting procedure. It follows that the antagonist promotes uncoupling of the complex (i.e. K P Ͻ K P.G ). The same constraint was required in previous analyses with the ternary complex model (33), and it is consistent with reports that N-[ 3 H]-methylscopolamine is an inverse agonist (45). All other parameters were defined by a minimum in the sum of squares.
With monomers reconstituted in nanodiscs, the binding of oxotremorine-M can be described to at least a first approximation by Scheme 2 taken with one class of G protein. The fitted curves are illustrated in Fig. 6, and the parametric values are listed in Table 2. Although the correlation of neighboring residuals for all of the data is significant (p Ͻ 0.00001), there is no effect on the sum of squares (p ϭ 0.97) or the correlation of neighboring residuals when Scheme 2 is applied with two classes of G protein rather than one. The fit is therefore the best obtainable within the context of the model.
According to Scheme 2, the estimated affinity of R for G (log K G ϭ Ϫ11.40) is comparable with the measured concentration of receptors (log [R] t ϭ Ϫ10.89) and the inferred concentration of G proteins ([G] t /[R] t ϭ 1.00) ( Table 2). At those values, about 58% of R and G were coupled in the absence of ligands. Oxotremorine-M bound 43-fold more tightly to the RG complex than to free R (log K A ϭ Ϫ3.25, log K A.G ϭ Ϫ4.88) ( Table 2) and thereby increased coupling to 92% due to the reciprocal relationship between the effect of the G protein on the affinity of the agonist and vice versa (log K G ϭ Ϫ11.40, log K G.A ϭ Ϫ13.03).
GMP-PNP caused an 8.3-fold increase in the affinity of the receptor for the G protein (log K G ϭ Ϫ11.40, log K G.N ϭ Ϫ12.32) and therefore also promoted coupling. Such an outcome is at odds with the presumed effect of GMP-PNP in the ternary complex model (27,46) and with biochemical evidence that guanylyl nucleotides cause dissociation of the RG complex (47,48). Because the nucleotide and the agonist both favor the coupled state, the negative allosteric effect of the former on the latter cannot derive from a change in coupling; rather, the rightward shift in the binding profile of oxotremorine-M emerges from the model as a nucleotide-dependent reduction in the affinity of the agonist for the RG complex (log K A.G ϭ Ϫ4.88, log K A.GN ϭ Ϫ3.52).
In the case of Scheme 3, the arbitrary values assigned to K G and K G.N preclude a correlation that otherwise exists between  Table 2.
K G and K P.G , eliminating the need to constrain K P.G . Because there was almost no effect of GMP-PNP on the binding of N-[ 3 H]methylscopolamine (Fig. 6A), the fitted values of log K P.G and log K P.GN are virtually identical (i.e. log K P.G(N) Ϸ Ϫ7.88; Table 2). With the system driven fully to the coupled state under all conditions (i.e. log K G ϭ log K G.N ' Ϫ15), the heterogeneity recognized by oxotremorine-M emerges from the model as an excess of receptors over G proteins ([G] t /[R] t ϭ 0.87). The sites of high affinity correspond to the constitutive RG complex, and the rightward shift effected by GMP-PNP derives exclusively from the allosteric interaction between nucleotide and agonist within the complex.
Because most of the receptors and G proteins were precoupled in terms of Scheme 2 (i.e. 58%), the assumption of complete coupling in Scheme 3 had little effect on the fitted values of log K A , log K A.G , and log K A.GN (Table 2). Nevertheless, the restrictions in Scheme 3 increase the sum of squares by 6.9% over that obtained with Scheme 2 (p ϭ 0.00001). It therefore appears that the effect of the agonist on coupling detected by Scheme 2, although comparatively small, contributes a degree of heterogeneity that cannot be provided by what is, in effect, a sum of two hyperbolic terms in the case of Scheme 3. The sum of squares with Scheme 3 is not reduced significantly with two classes of G protein rather than one (p ϭ 0.11).
With tetramers reconstituted in vesicles, one class of G protein is insufficient for a description in terms of Scheme 2; the correlation of neighboring residuals is significant (p ϭ 0.00026), and the sum of squares is reduced by 25% upon the addition of a second class (p Ͻ 0.00001). The parametric values from both analyses are listed in Table 2. Hill coefficients for the binding of oxotremorine-M are markedly less than 1 at all concentrations of GMP-PNP (0.46 Յ n H Յ 0.71), and the dispersion cannot be accommodated by depletion of free G protein alone. Heterogeneity therefore emerges as an excess of receptors over G proteins, irrespective of whether the latter occur as one class Two classes of G protein give rise to a divergence in the effect of GMP-PNP. The nucleotide is seen to effect a surprising 3.3fold increase in the affinity of R for G 1 (log K G1 ϭ Ϫ12.13, log K G1.N ϭ Ϫ12.65) and a 126-fold increase in the affinity of oxotremorine-M for RG 1 (log K A.G1 ϭ Ϫ5.09, log K A.G1N ϭ Ϫ7.19); there is little change in the affinity of R for G 2 (log K G2 ϭ Ϫ12.99, log K G2.N ϭ Ϫ12.84) and a 60-fold decrease in the affinity of oxotremorine-M for RG 2 (log K A.G2 ϭ Ϫ5.58, log K A.G2N ϭ Ϫ3.80) ( Table 2). G 2 outnumbered G 1 by a ratio of 67:33, and the effects at G 2 predominated.
All values of K G in Scheme 2 are exceeded by the total concentrations of R and G, and about 87% of all G proteins supposedly were coupled to receptors in the absence of ligands. There accordingly is no increase in the sum of squares when the data are analyzed with Scheme 3 rather than Scheme 2 (p Ն 0.11), and GMP-PNP affected the binding of oxotremorine-M exclusively via an allosteric interaction within each RG j complex. As

TABLE 2 Parametric values from Schemes 2 and 3 for the binding properties of M 2 receptors reconstituted with G proteins in nanodiscs and vesicles
The data represented in Figs. 3 and 5 (panels A, nanodiscs; panels B, vesicles) were analyzed simultaneously in terms of Schemes 2 and 3 taken with one and two classes of G protein. Parameters were shared among the different sets of data in accord with mechanistic consistency. Single values of ͓G 1 ͔ t /͓R͔ t , ͓G 2 ͔ t /͓R͔ t , and each equilibrium dissociation constant (i.e. log K) were common to all of the relevant data; single values of ͓R͔ t and NS were common to data obtained in the same experiment without regard to the complement of oxotremorine-M or GMP-PNP. The parametric values from all analyses are listed in the table. The fitted curves obtained with Scheme 2 (one class of G proteins) for binding to receptors in nanodiscs are illustrated in Fig. 6. Oxo-M, oxotremorine-M. with Scheme 2, the cooperativity was positive in RG 1 and negative in RG 2 .

Reactants
With muscarinic receptors in sarcolemmal membranes, the Hill coefficient is markedly less than 1 for carbachol (0.55 Յ n H Յ 0.73) and for oxotremorine-M (0.43 Յ n H Յ 0.67) at all concentrations of GMP-PNP (p Ͻ 0.00001). When the data obtained with both agonists were analyzed together in terms of Scheme 2, the model proved to be inadequate irrespective of the number of classes of G protein. The correlation of neighboring residuals is highly significant with one class of G proteins (p Ͻ 0.00001), and it remains so upon the addition of a second (p Ͻ 0.00001) despite a reduction of 22% in the sum of squares (p Ͻ 0.00001). With each agonist, the deviations are evident in a plot of the residuals from either analysis (data not shown).
As with tetramers reconstituted in vesicles, the breadth of the dispersion in sarcolemmal membranes is interpreted by the model as an excess of receptors over G proteins (one class, . Scheme 3 gives a higher sum of squares than Scheme 2 with one class of G proteins (p Ͻ 0.00001) but not with two classes (p ϭ 0.36). The fitted parametric values from both schemes show a pattern similar to that obtained with reconstituted tetramers (data not shown), but their physical meaning is unclear due to lack of agreement between the model and the data.

Identification of the Functionally Relevant Reconstituted
State-Purified GPCRs have been reported to exhibit the characteristic interaction between agonists and guanylyl nucleotides after reconstitution in two different states: as monomers in nanodiscs, in the case of the ␤ 2 -adrenergic and -opioid receptors (21,23), and as tetramers in liposomes, in the case of the M 2 muscarinic receptor (6,7). Both preparations exhibit at least two classes of sites, as distinguished by agonists, and saturating concentrations of the nucleotide promote their apparent interconversion from higher to lower affinity. These similarities notwithstanding, the interaction appears to be of a different kind in each case. Whereas the heterogeneity revealed by monomers is induced by the G protein in an otherwise homogeneous population of sites (21), that revealed by tetramers is intrinsic to the receptor in its tetrameric state (7). G proteins in the latter case may have a modulatory effect, and they impart sensitivity to guanylyl nucleotides, but they are not required for heterogeneity per se.
Differences between monomers and tetramers in the origin of heterogeneity have implications for the nature of the process whereby receptors interconvert from one state of affinity to another, but assays performed only at saturating concentrations of a guanylyl nucleotide provide little insight into such details. Reconstituted monomers and tetramers of the M 2 muscarinic receptor therefore were compared for the effect of GMP-PNP on the binding of agonists at intermediate concentrations of the nucleotide.
The oligomeric status of the receptor in each preparation was confirmed by its electrophoretic mobility after cross-linking with BS 3 and its efficiency of coimmunoprecipitation. The purified receptor was largely monomeric. Reconstitution in lipo-somes yielded a preparation that was predominantly tetrameric or larger, as described previously (6,7). Reconstitution in nanodiscs yielded a preparation that was largely or wholly monomeric. The efficiency of coimmunoprecipitation was the same as that of purified monomers in solution (i.e. 13-14%) and markedly less than that of receptors in unprocessed extracts (68%) or reconstituted in liposomes (91%).
Cross-linking of receptors in nanodiscs led to the appearance of bands that were not observed with the receptor alone and probably included the belt protein. BS 3 was found to stabilize dimers and larger oligomers of MSP1E3D1 in receptor-free preparations, apparently by linking the two protomers that make up a nanodisc and by tethering one nanodisc to another. The electrophoretic mobility of such structures suggests that the novel bands observed with reconstituted receptors were cross-linked adducts of the receptor and two or more of the belt proteins that dimerize to form a nanodisc.
The monomeric status of GPCRs in nanodiscs has been confirmed previously for the ␤ 2 -adrenergic receptor, which was reconstituted at an initial ratio of 1 protomer per 50 nanodiscs (21), and for rhodopsin after reconstitution at a ratio of 1 protomer per 5 nanodiscs (49). Although dimers have been observed in the case of reconstituted rhodopsin, they required an initial ratio of two receptors per nanodisc (49,50). In contrast, the reconstitutions described here were carried out at an initial ratio of one M 2 receptor per 690 nanodiscs.
The binding of oxotremorine-M to M 2 receptors in each reconstituted preparation was analyzed empirically as a sum of hyperbolic terms (Equation 4), and the parametric values are compared in Fig. 7. Monomers reconstituted in nanodiscs revealed two classes of sites in the absence of guanylyl nucleotide. Those of higher affinity accounted for about 80% of total specific binding and were induced by G proteins, as reported previously for other GPCRs (21,23); those of lower affinity appeared to be receptors in excess of G proteins. Such an assignment is consistent with the observation that GMP-PNP acted selectively to reduce the inhibitory potency of oxotremorine-M at the high-affinity sites (IC 50(1) in Equation 4) without affecting that at the low-affinity sites (IC 50 (2) ) or the apparent distribution of receptors between the two states (F j ) (Fig. 7, A  and B). The persistence of uncoupled receptors despite a nominal, 80-fold molar excess of G proteins appears to result primarily from partitioning of the latter into otherwise empty nanodiscs, which greatly outnumbered those containing receptor. Also, some of the G proteins may aggregate and precipitate upon removal of the detergent, as observed in earlier studies on the ␤ 2 -adrenergic receptor and G s (21).
Tetramers reconstituted in phospholipid vesicles similarly revealed two classes of sites for oxotremorine-M in the absence of nucleotide, but the heterogeneity cannot be attributed to a shortage of G proteins. The amount used in the experiments described here was 8-fold greater than amounts that were sufficient to saturate M 2 receptors in previous studies on similar preparations (cf. Refs. 6 and 7). It follows that the heterogeneity revealed by reconstituted tetramers emerges from a defined complex of receptors and G proteins, in contrast to the G protein-limited mixture of coupled and uncoupled receptors that occurs with nanodiscs.
Such a difference in the origin of heterogeneity has mechanistic implications that are evident in the sensitivity of reconstituted monomers and tetramers to GMP-PNP. The effect in monomers was a lateral, rightward shift in the binding profile of oxotremorine-M with no change in the relative numbers of high-and low-affinity sites (Fig. 7, A and B); in contrast, the effect in tetramers was an upward shift or apparent interconversion of sites from high to low affinity with no change in affinity per se (Fig. 7, C and D). Monomers and tetramers of the M 2 receptor therefore appear to differ in the mechanism whereby the sites interconvert from one state to another upon the addition of GMP-PNP.
Only reconstituted tetramers resembled muscarinic receptors in porcine sarcolemmal membranes, where oxotremorine-M and carbachol recognized three and two classes of sites, respectively, and GMP-PNP favored the sites of low affinity over those of higher affinity with little or no change in affinity per se (Fig. 7, E-H). Essentially the same pattern has been observed previously with muscarinic receptors in rat myocardial membranes (51) and ␤-adrenergic receptors in frog erythrocyte membranes (25,27) when the concentration of a guanylyl nucleotide was increased in a stepwise manner.
The molar ratio of G proteins to receptors in the relevant compartment of porcine sarcolemmal membranes is unknown, but it seems likely to equal or exceed 1. An RG complex containing equimolar amounts of muscarinic receptor and G proteins has been purified from the same tissue (52). Also, the total number of G proteins in natural membranes has been found to exceed the number of receptors of any particular type by 20 -240-fold, although some of the G proteins may be sequestered in a receptor-free compartment (53,54).
Mechanistic Implications of the Data and Relevance of the Ternary Complex Model-The dispersion of affinities revealed by agonists at GPCRs often is rationalized qualitatively in terms of the ternary complex model (27), which embodies the notions of transient coupling and G protein-induced heterogeneity. Quantitative applications of the model have been rare, but agreement with the data typically has required mechanistic compromises. In particular, the effects of guanylyl nucleotides and differences among agonists in the shape and breadth of the dispersion have been attributed to nucleotide-and agonist-dependent changes in the ratio of total G proteins to total receptors (i.e. [G] t /[R] t ) (27,39,55). Such accommodations are inconsistent with the inherent premise that ligands to the receptor and the G protein act allosterically through the RG complex or by shifting the presumed equilibrium between uncoupled and coupled receptors. The discrepancies are confirmed when mechanistic consistency is enforced during the fitting procedure, and the model is unable to describe the data (33,56). Agreement with the model also has tended to require an excess of receptors over G proteins (26,33,57), which is a result of limits on the breadth of the dispersion that can be accommodated when G proteins equal or outnumber receptors (57). Problems with the model reside partly in its prediction that guanylyl nucleotides will cause a lateral, rightward shift in the semilogarithmic binding profile of an agonist. That general pattern is expected irrespective of the quantities of interacting receptors and G proteins or their mutual affinity, as illustrated by the simulations presented in Fig. 8. With either Scheme 2 (Fig. 8, A-C) or Scheme 3 (Fig. 8, D-F), increasing concentrations of the nucleotide (N) cause the binding curve to migrate between two positions, the limits of which are established by the affinity of the agonist for the RG complex on the one hand and the uncoupled receptor on the other (i.e. KЈ A.G Յ IC 50 Յ KЈ A ). 7 The proximity of the curve to those limits when [N] ϭ 0 and as [N] 3 ∞ depends upon the degree of constitutive coupling (i.e. [R] t /K G ) and the ability of the nucleotide to cause uncoupling (i.e. K N /K N.RA ).
Ligand-regulated coupling occurs only in the case of Scheme 2. When [G] t exceeds [R] t by a factor of about 4 or more (Fig.  8A), the binding curves for an agonist are monophasic throughout (i.e. n H Ϸ 1). A guanylyl nucleotide causes a shift to the right as the tendency of the agonist to promote coupling (i.e. K A.G Ͻ K A ) is overcome by the tendency of the nucleotide to promote uncoupling (i.e. K N Ͻ K N.R ). As the nucleotide becomes saturating, the curve asymptotically approaches the limit at which IC 50 ϭ KЈ A (Fig. 8A).
When [G] t equals [R] t (Fig. 8B), the curve in the absence of nucleotide reveals a heterogeneity that arises from the agonistdriven formation of the RG complex and concomitant decrease in the concentration of free G protein. Under such conditions, the latter becomes an implicit variable that is disregarded when the data are plotted on two-dimensional coordinates. That leads in turn to binding profiles that can diverge, within limits, from monophasic behavior (i.e. 0.67 Յ n H Յ 1.00) (57). As the concentration of the nucleotide is increased, the curve steepens and moves rightward toward the limit at which IC 50 ϭ KЈ A and n H ϭ 1 (Fig. 8B).
When [G] t is less than [R] t (Fig. 8C), the curve in the absence of nucleotide will appear at least biphasic and perhaps triphasic in terms of Equation 4; the sites of lowest affinity are receptors in excess of G proteins, and those of higher affinity are receptors that interact with G proteins to form the RG complex. An increase in the concentration of the nucleotide is accompanied by steepening of the binding curve in the region of high affinity and its movement to the right (Fig. 8C).
The overall pattern is similar with Scheme 3, with the difference that ligand-regulated coupling is precluded by the constrained values of K G and K G.N . The equilibrium between R and RG is shifted wholly to the coupled state under all conditions, and there is no change in the concentration of free G protein. Heterogeneity therefore appears only when [R] t exceeds [G] t (Fig. 8, D-F). The Hill coefficient is 1 for each binding curve (Fig. 8, D and E) or component thereof (Fig. 8F), and the distribution of receptors among different states of the RG complex is determined solely by the concentrations of the ligands.
Both schemes predict essentially the same effect with two classes of G protein, in that the curves are shifted to the right by the nucleotide. An agonist may differ in its affinity for RG 1 and 7 The parameters KЈ A and KЈ A.G represent the adjusted values of K A and K A.G that incorporate the competitive effect of the radioligand on the apparen affinity of the agonist (i.e. KЈ A ϭ K A (1 ϩ [P]/K P ), and KЈ A.G ϭ K A.G (1 ϩ [P]/K P.G )).
The values of K A , K A.G , and K A.GN were selected to yield inhibitory potencies (log IC 50 ) of Ϫ8.0 or Ϫ4.0 at the concentration of the probe used in the simulations (i.e. [P] ϭ K P ). The dashed lines in A-C depict the binding profile corresponding to log K A.G ϭ Ϫ8.301. Scheme 2 is configured such that the allosteric interaction between agonist and nucleotide occurs strictly via their opposing effects on coupling of the receptor and the G protein. In Scheme 3, the interaction occurs strictly within the RG complex, which remains intact under all conditions. The Hill coefficient is 1 for all curves in D and E, and for each inflection of the curves in F. RG 2 , however, and the binding curves therefore can be broader and more complex than those illustrated in Fig. 8.
Of the three preparations of M 2 receptor described here, only monomers in nanodiscs exhibited the rightward shift predicted by the model (Figs. 5A and 6B). The binding profiles are not especially shallow at any single concentration of GMP-PNP (n H ϭ 0.77-0.91), and Scheme 2 attributes the dispersion entirely to the agonist-driven decrease in free G protein that can occur with equimolar amounts of receptor and G protein and a comparatively high level of constitutive coupling (i.e. [R] t / [G] t ϭ 1, log K G ϭ Ϫ11.40, log K G.N ϭ Ϫ12.32) (Fig. 6 and Table 2).
Given the apparent agreement between Scheme 2 and the binding properties of monomers in nanodiscs, it is of interest to consider the parametric values for their biochemical implications. At an initial molar excess of 80 G proteins/receptor, a fitted value of 1 for [G] t /[R] t seems unlikely to be a coincidence; rather, it suggests that one G protein may associate with a receptor-containing nanodisc and remain there. With the exception of transducin, which is not palmitoylated and can survive in the absence of lipid or detergent (58), G proteins denied a hydrophobic berth tend to come out of solution due to myristoylation, palmitoylation, and farnesylation of their constituent subunits (58,59). The likelihood that G proteins do not exchange between nanodiscs is consistent with the low value obtained for [R] t /K G , which places 58% of the receptors and G proteins in the coupled state in the absence of ligands, and with values of K A , K A.G , and K A.GN that assign the effect between GMP-PNP and oxotremorine-M largely to interactions within the RG complex.
These considerations suggest that a mechanistically inappropriate model based on the notions of a transient complex and random collisions accounts for the data by finding a region of parameter space wherein it mimics a stable complex that interconverts spontaneously between two states. Agreement, therefore, is achieved by adopting parametric values that suppress ligand-regulated coupling, an ironic twist that negates a property typically ascribed to the model. It follows that GPCRs reconstituted as monomers in nanodiscs neither mimic the native state nor exchange G proteins through collision coupling. A preparation of monomers reconstituted in patterned arrays of phospholipid bilayers (60 -62), in which G proteins would be able to diffuse randomly and exchange at the level of single receptors, may offer a better model of transient interactions with different G proteins in succession.
The apparent interconversion of sites observed with tetramers reconstituted in liposomes and with receptors in sarcolemmal membranes (Fig. 5, B-D) cannot be described by Scheme 2 or Scheme 3. Attempts to enforce mechanistic consistency therefore prompt what is, in effect, evasive action on the part of the model. At least two classes of G protein are required for reconstituted tetramers, and at least three classes appear to be required for the myocardial preparation. In the case of the latter, the fit with two classes is not improved if the model is expanded to include a population of receptors sequestered in a compartment devoid of G protein. All scenarios require an unexpected excess of receptors over G proteins, a high degree of constitutive coupling, and an anomalous increase in the affinity of the receptor for one of the G proteins upon the addition of GMP-PNP. Such results are a consequence of the discrepancy between the nucleotide-dependent, upward shift in the binding profiles of agonists and the lateral shift predicted by the model.
If the requirement for mechanistic consistency is abandoned for receptors in liposomes and sarcolemmal membranes, Scheme 2 can account for the effects of GMP-PNP by reducing the ratio of G proteins to receptors (i.e. [G] t /[R] t ). Because there is a direct measure of [R] t but not of [G] t , the result is an inferred decrease in [G] t and a greater excess of receptors over G proteins; thus, the apparent interconversion of sites from higher to lower affinity is interpreted as a loss of G proteins. The same accommodation has been used previously to obtain agreement between the ternary complex model and the effect of guanylyl nucleotides at ␤-adrenergic (27) and cardiac muscarinic receptors (55). Guanylyl nucleotides are not known to cause the permanent inactivation of G proteins, however, and the effects of GMP-PNP are reversible (63,64). It follows that, with such an accommodation, the model loses its mechanistic relevance and becomes a device for parameterizing the data.
Reconstitution of the Functional Complex and the Mechanism of Signaling-An empirical comparison of the data from three preparations of muscarinic receptor indicates that the binding properties of receptors in myocardial membranes are replicated by tetramers reconstituted with G proteins in phospholipid vesicles but not by monomers reconstituted with G proteins in nanodiscs. In a previous comparison of monomers in solution and tetramers reconstituted without G proteins, only the latter exhibited an agonist-specific heterogeneity akin to that of receptors in native membranes (7). These observations suggest that the functional state of the M 2 receptor in vivo is an oligomer, very likely a tetramer. Although the oligomeric status of muscarinic receptors in heart cells has not been identified directly, a tetramer has been inferred from the binding properties of receptors in native and detergent-solubilized myocardial membranes (1,2,43). Also, a quantitative assessment of FRET efficiencies between fluorophore-tagged protomers has indicated that the M 2 receptor exists wholly or predominantly as a tetramer in CHO cells (13). Clusters of ␤-adrenergic receptors have been identified in cardiac myocytes by means of fluorescent antibodies and near-field scanning optical microscopy (9).
The inability of the ternary complex model to describe the binding properties of cardiac muscarinic receptors suggested early on that the observed heterogeneity is not induced by the G protein in an otherwise homogeneous population of monomers (33,56). In contrast, a mechanistically consistent description of the binding patterns is provided by models in which heterogeneity arises from induced and perhaps constitutive asymmetry among the protomers of an oligomeric array (1,6). Such models interpret the nucleotide-dependent upward shift in the binding profile of an agonist as a redistribution of oligomers between two states that differ in their cooperative properties and perhaps in their asymmetry (e.g. see Fig. 9 in Ref. 1).
Although the ternary complex model cannot account for the agonist-specific heterogeneity of GPCRs, several lines of evidence support the idea of a transient complex and ligand-reg-ulated coupling. For example, direct and indirect measures of the RG complex suggest that coupling can be increased by agonists (65)(66)(67) and decreased or prevented by antagonists (66,68). Also, the supposed distribution of receptors between uncoupled and coupled states appears to be shifted by mutations and environmental factors that favor the latter and increase constitutive activity (45, 65, 67, 69 -72). In NIH-3T3 cells, overexpression of G␣ q with M 1 , M 3 , and M 5 muscarinic receptors has been shown to increase constitutive activity and the potency of agonists (73). The ternary complex model and its critical assumption of a transient RG complex cannot account for agonist-specific heterogeneity. Such transience therefore can be ruled out in the context of the model. If heterogeneity derives from an oligomer, however, questions regarding the existence and biological role of transient coupling remain open.