M₂ receptors were solubilized as oligomers and purified as monomers in the manner described previously (Redka et al., 2013; 2014). cMyc- and FLAG-tagged receptors were extracted from co-infected Sf9 cells in digitonin–cholate, and oligomers were detected by co-immunoprecipitation (Figure 1A). The solubilized preparation was applied to an affinity resin of immobilized aminobenztropane (ABT), and western blotting of the purified receptor with an anti-M₂ antibody indicated that 97% of the immunopositive material migrated as a monomer. Eighty-three percent migrated as a monomer when the sample was cross-linked with BS³ (Figure 1B and Figure 1—source data 1). The affinity of [³H]NMS for the purified monomer (Equation 3, log K = −8.01 ± 0.04, N = 5) and the purity of the sample were the same as reported previously (cf. Redka et al., 2013; 2014).

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Panel B–Monomeric status of the purified M₂ receptor after chemical cross-linking.

Panel C–Parametric values for the effect of gallamine on the rate of dissociation of [³H]QNB. Panel D–Parametric values for the effect of gallamine on the binding of [³H]NMS at equilibrium. Panels E–G–Parametric values for the effect of strychnine on the binding of [³H]NMS to oligomers and monomers.

https://doi.org/10.7554/eLife.11685.004

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Figure 1–figure supplement 1–Parametric values for the effect of strychnine on the binding of [³H]NMS and [³H]QNB to membrane-bound M₂ receptor.

https://doi.org/10.7554/eLife.11685.005

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Figure 1-figure supplement 2–Rate constants for the simulated binding of strychnine and [³H]NMS according to Figure 6.

https://doi.org/10.7554/eLife.11685.006

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Monomeric M₂ receptors retain the interaction between ligands at the allosteric and orthosteric sites. The allosteric modulator gallamine slowed the dissociation of [³H]QNB, and the time-course of the dissociation was mono-exponential under all conditions. The dose-dependence of the decrease in the rate constant was monophasic with a Hill coefficient of 1 (Figure 1C, Figure 1—source data 1). Gallamine therefore appears to slow the release of [³H]QNB from monomers via a single allosteric site. In contrast, two or more allosteric sites can be inferred from the bell-shaped behavior of receptors that are predominantly or wholly oligomeric (Shivnaraine et al., 2012) (Figure 1C, Figure 1—source data 1).

Monomers of the M₂ receptor equilibrated slowly with [³H]NMS and either gallamine or the allosteric modulator strychnine when the two ligands were added simultaneously, and incubation for 21 hr was required for the attainment of equilibrium at 30°C. The binding profile upon equilibration was monophasic downward in each case, and the data can be described by a single hyperbolic term (i.e., Equation 2, n = 1) (Figure 1D and E; Figure 1—source data 1). Gallamine and strychnine therefore appear to modulate the equilibrium binding of [³H]NMS to monomers via a single allosteric site.

The monophasic nature of effects observed at purified monomers differs from the triphasic effect of gallamine on the binding of [³H]NMS to M₂ receptors in other preparations, including membranes and detergent-solubilized extracts from Sf9 cells, CHO cells, and porcine atria (e.g., Figure 1D, broken line) (Shivnaraine et al., 2012). Those multiphasic curves and the Hill coefficients of the individual components, taken together, are indicative of at least four interacting allosteric sites, which in turn are suggestive of four interacting receptors within a tetramer or larger oligomer. Similarly, the bell-shaped pattern obtained for strychnine in atrial extracts (Figure 1E–G) and in membranes from CHO cells (Figure 1—figure supplement 1, Figure 1—source data 2) is indicative of at least two allosteric sites and also points to an oligomer.

Allosteric ligands bind in a vestibule to the orthosteric site (Kruse et al., 2013), forming a cap that impedes the binding and dissociation of the orthosteric ligand (Figure 6) (Shivnaraine et al., 2012). Interference by one ligand in the binding kinetics of another leads to binding patterns that depend upon the order of mixing in a system that has not attained equilibrium. Such kinetic effects were examined experimentally by varying the sequence in which strychnine and [³H]NMS were added to the receptor. In one protocol, the two ligands were added simultaneously and incubated with the receptor for 21 hr to obtain the pattern at equilibrium. In another, one ligand was pre-equilibrated with the receptor prior to the addition of the second, and the mixture was incubated for a further 3 hr to obtain the pattern at a time prior to equilibrium.

With receptors in atrial extracts, the effect of strychnine on the binding of [³H]NMS was bell-shaped under all conditions (Figure 1E–G, Figure 1—source data 1). With purified monomers, strychnine was strictly inhibitory except when the receptor was pre-equilibrated with [³H]NMS, when there was no effect (Figure 1E–G, Figure 1—source data 1). The patterns observed in experiments on monomers are consistent with the patterns observed in simulations performed according to Figure 6 (Figure 1—figure supplement 2, Figure 1—source data 3), which describes a mechanism for allosteric capping of the orthosteric site in a monomer.

Allosteric effects that produce multiphasic binding profiles such as those illustrated by the dashed lines in Figure 1C,D have been attributed to a combination of inter- and intramolecular interactions within oligomers (Shivnaraine et al., 2012). For more direct information on those interactions and related conformational changes, we developed a sensor based on FRET between FlAsH and mCherry. FlAsH was incorporated via the hairpin-forming sequence FLNCCPGCCMEP (FCM) (Hoffmann et al., 2010), which was inserted after Val¹⁶⁶ in the second extracellular loop (ECL2), and mCherry was fused to the amino terminus (i.e., mCh-M₂-FCM).

A fluorophore at the N-terminus of the M₂ receptor has been shown previously to have no discernible effect on various properties, including transport of the receptor to the plasma membrane, agonist-induced responses, and the binding of muscarinic ligands (Pisterzi et al., 2010). Localization at the plasma membrane also was not affected by the modifications described here, as visualized by fluorescence from either the fused fluorophore or bound FlAsH (Figure 2—figure supplement 1), nor was there any apparent change in the binding properties. The affinity of the receptor for [³H]NMS was essentially the same, as measured in preparations of membrane-bound and detergent-solubilized mCh-M₂-FCM from transfected CHO cells (Equation 3: membranes, log K = −9.52 ± 0.10, N = 3; extract, log K = −8.26 ± 0.22, N = 3). The modified receptor also retained the triphasic allosteric effect of gallamine on the binding of [³H]NMS, as measured in membranes from CHO cells expressing mCh-M₂-FCM (Figure 2—figure supplement 2).

Molecular models of the native M₂ receptor, mCh-M₂-FCM, and the FlAsH-bound sensor were rendered from the crystal structures of mCherry (2H5Q) (Shu et al., 2006) and the receptor in an active state (4MQS) (Kruse et al., 2013). A structure of the sensor showing the positions of FlAsH and mCherry is given in Figure 2A. Insertion of the FlAsH-reactive sequence in ECL2 created a rigid extended loop (Figure 2B) without perturbing the conformation of the loop in the region of the adjacent EDGE motif. There was no distortion of the extended loop upon the addition of FlAsH.

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Panel A–Time-resolved fluorescence and fluorescence anistoropy of eGFP and eGFP-tagged M₂ receptors.

Panel E–Levels of significance for ligand-dependent changes in the FRET efficiency of FlAsH-reacted mCh-M₂-FCM.

https://doi.org/10.7554/eLife.11685.010

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To examine the mobility of a fluorophore at the amino terminus, eGFP was fused to the wild-type M₂ receptor (eGFP-M₂) and to a truncated mutant lacking the first 13 amino acids (eGFP-truncM₂). This truncation shortened the link between the fluorophore and the first helical domain and was expected to increase the likelihood that the movement of eGFP would approximate that of the fusion protein as a whole. Each tagged receptor was expressed in CHO cells and extracted in digitonin–cholate, and the rotational correlation time (φ) of the fused fluorophore was estimated from the fluorescence anisotropy according to Equations 4–9. The full-length receptor was examined with and without ligands, and eGFP alone was taken as a control.

Both the fluorescence (Equation 6) and the anisotropy (Equation 9) decayed as a single exponential under all conditions, and the parametric values are listed in Figure 2—source data 1. The value of 18 ns obtained for the correlation time of free eGFP agrees favourably with that of about 20 ns reported previously (Devauges et al., 2012) and was sixfold longer than the fluorescence lifetime of 3 ns. In contrast, values of 30–55 ns were obtained for eGFP-truncM₂, eGFP-M₂, and the various liganded states of eGFP-M₂. Such values are at least 12–22-fold longer than the corresponding lifetimes of 2.5–2.6 ns, and the latter are much shorter than the 12-ns measuring window of the fluorescence decay. The rotational correlation times obtained for receptor-bound eGFP therefore are indistinguishable, and the movement of the fluorophore at the N-terminus of the receptor appears to be determined primarily by the tumbling of the whole protein, with or without ligands.

Excitation of bound FlAsH at 498 nm gave the observed emission spectrum and unmixed components shown for a typical cell in Figure 2C. Fluorescence from the acceptor accounted for most of the total signal at 610 nm, and the corresponding peak derived predominantly from FRET. Only 6% of the emission from the acceptor came from direct excitation, and it was accounted for during spectral unmixing. The apparent FRET efficiency of each cell was calculated from the normalized amplitudes of the unmixed spectra (Equations 10 and 12), and the efficiencies from all cells gave a distribution centered on 60% with a width of 18% at half-maximal amplitude (Figure 2D). Controls in which FlAsH was reacted with mCherry-tagged receptors lacking the FCM sequence gave a narrow distribution centered on 0.5% (Figure 2D), confirming the specificity of the reaction with FlAsH.

The emission spectrum and corresponding FRET efficiency between FlAsH and mCherry was measured for each cell before and after the addition of various ligands. The inverse agonist NMS caused a marked increase in the amplitude of the peak near 610 nm, as illustrated in Figure 3A. Smaller increases were obtained with the partial agonist pilocarpine, the allosteric modulator gallamine, and the combination of gallamine plus NMS. In contrast, the agonist carbachol caused a decrease. The differences in efficiency at individual cells were averaged over all cells to obtain the mean for each ligand (Figure 2E, Figure 2—source data 1), which varied from an increase of 20 percentage points with NMS to a decrease of 22 percentage points with carbachol. The partial agonist pilocarpine caused an increase of 7.3 percentage points. These changes indicate that the sensor can distinguish between agonists and an inverse agonist at the orthosteric site. Gallamine caused an increase of 5.0 percentage points and reduced the increase caused by NMS from 22 to 8.0 percentage points, indicating that the sensor detects the effect of the allosteric ligand on NMS.

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Panel D–Levels of significance for ligand-dependent changes in the FRET efficiency of FlAsH-reacted mCh-M₂-FCM and mCh-M₂(D103A)-FCM

https://doi.org/10.7554/eLife.11685.015

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A receptor bearing eGFP at the N-terminus and mCherry rather than FlAsH-FCM after Val¹⁶⁶ in ECL2 gave a comparatively narrow distribution of FRET efficiencies with a mean of about 10% and a width of about 4% (Figure 2—figure supplement 3A). The effects of NMS and gallamine on FRET were eliminated (Figure 2—figure supplement 3B), suggesting that the insertion of mCherry within ECL2 disrupts the vestibule to the orthosteric site. The distribution of FRET efficiencies was narrower than that obtained with FlAsH and mCherry in the sensor, where the greater width of 40% may arise from differences in the labelling efficiency of FlAsH among different cells.

The substitution of alanine for aspartic acid at position 103 of the M₂ receptor removes the counter-ion for positively charged ligands at the orthosteric site (Haga et al., 2012). That mutation has been shown previously to prevent the specific binding of [³H]NMS or [³H]QNB to M₂ receptors in HEK293 membranes at concentrations of the radioligand up to 10 nM (Heitz et al., 1999). The same mutation in the sensor prevented the specific binding of [³H]NMS at a concentration of 1 µM, as measured with mCh-M₂(D103A)-FCM extracted from transfected CHO cells in digitonin–cholate. It also eliminated the effect of NMS on FRET. There was essentially no change in the emission spectrum at 610 nm (Figure 3B), in contrast to the increase observed with FlAsH-treated mCh-M₂-FCM (Figure 3A); also, the NMS-dependent increase in the mean FRET efficiency was reduced from 21.6 ± 11.2 percentage points in mCh-M₂-FCM to 0.45 ± 0.55 percentage points in the mutant (Figure 3D, Figure 3—source data 1).

Sensitivity to NMS was recovered when the binding-deficient mutant was co-expressed with the wild-type M₂ receptor (Figure 3C and D), resulting in a ligand-dependent change in the mean FRET efficiency of 9.5 ± 1.8 percentage points (Figure 3D, Figure 3—source data 1). The recovery indicates that M₂ receptors occur at least partly as oligomers in which the conformation in the region of the allosteric site of one protomer is affected by a ligand at the orthosteric site of another.

In cells such as that represented in Figure 3C, co-existence of the wild-type receptor and FlAsH-reacted mCh-M₂(D103A)-FCM is inferred from the effect of NMS on FRET. To confirm the cellular co-localization of the two proteins, cells were co-transfected with the plasmids for mCh-M₂(D103A)-FCM and the wild-type receptor fused at the N-terminus to eGFP (eGFP-M₂). Those FlAsH-treated cells displaying three fluorophores, and therefore both proteins, were identified by their spectral properties, and those spectra were unmixed to obtain the individual contribution from each fluorophore (Figure 3—figure supplement 1). NMS increased the FRET efficiency between FlAsH and mCherry by 5.3 ± 0.1 percentage points (N = 26) rather than 9.5 percentage points, in a further indication that the conformational change detected by FRET in one protomer derives from the binding of the ligand to another.

The first two inflections of the triphasic binding profile exhibited by gallamine have been attributed to intermolecular modulation via allosteric sites on different protomers of an oligomer (Shivnaraine et al., 2012). In a direct test for such interactions, the three negatively charged residues of the EDGE motif in ECL2 were replaced by three positively charged residues (i.e., KRGK) to obtain a mutant in which the binding of a cationic ligand such as gallamine to the allosteric site is precluded by electrostatic repulsion (M₂-ECL2+ve). When the mutant was expressed in CHO cells and extracted in digitonin–cholate, the substitution was found to be without effect on the affinity of [³H]NMS for the orthosteric site (Equation 3, log K = −8.26 ± 0.10, N = 3). The triphasic pattern revealed by gallamine at the wild-type receptor was lost, however, and in its place was a single inflection of comparatively low affinity (log K = −3.46 ± 0.16) (Figure 3F).

FLAG-tagged receptors lacking the orthosteric site (FLAG-M₂(D103A)) then were co-expressed with hexahistidyl-tagged receptors lacking the allosteric site (His₆-M₂-ECL2+ve), and purified complexes containing at least one copy of each mutant were obtained by successive passage of detergent-solubilized material on an immuno-affinity column of immobilized anti-FLAG antibody (Santa Cruz Biotechnology) and a chelating resin of Ni²⁺-NTA (Figure 3E). Binding of [³H]NMS to the purified heteromer displayed a triphasic dependence on the concentration of gallamine (Figure 3F), and the apparent affinities calculated in terms of Equation 2 (Figure 3F, legend) were in good agreement with those reported for the wild-type receptor (Figure 1—source data 1) (Shivnaraine et al., 2012). The magnitude of the inhibitory effect corresponding to the allosteric sites of weakest affinity was much less than that observed with the wild-type receptor (cf. Figure 1D, broken line). It was diminished further when corrected by subtraction of the single inhibitory component observed with M₂-ECL2+ve (Figure 3F, broken line).

Allosteric effects were examined in molecular dynamics simulations at the atomic level, starting from the crystal structure of the monomeric M₂ receptor occupied by the agonist iperoxo (4MQS) (Kruse et al., 2013). The ligand and accessory proteins were removed, and conformations of the receptor were sampled from a canonical ensemble accessible within a period of 30 ns. Simulations were performed in the absence of membrane and detergent, and ligands were docked prior to initiating the calculation. Interactions between allosteric and orthosteric ligands (Figure 4—figure supplement 1) were found to be affected by the degree of electrostatic repulsion between their positive charges and the conformational changes induced in one site by a ligand at the other, which together determine the positional stability of each ligand in its respective site.

The effect of electrostatic repulsion was evaluated by two correlates (Table 1): the distance between the spatial centers of the cationic nitrogen atoms of the two ligands (e.g., strychnine and NMS, Figure 4A; gallamine and QNB, Figure 4B), and changes in the electrostatic potential of an allosteric ligand upon the addition of an orthosteric ligand. All four allosteric–orthosteric pairs showed a degree of electrostatic repulsion, but steric effects reduced the difference between strychnine and gallamine to less than would be predicted on the basis of charge alone (Table 1). Gallamine has three cationic groups and therefore experiences greater electrostatic repulsion overall, but each group is surrounded by sterically bulky and electron-rich ethyl groups that diminish the repulsive effect (Figure 5—figure supplement 1). Also, the smaller steric load born by the single cationic nitrogen atom of strychnine allows for positioning closer to the orthosteric site.

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A network of interactions serves as a conformational link between the allosteric and orthosteric sites. Three tyrosine residues form a hydrogen-bonded aromatic cap over the orthosteric site (i.e., Tyr¹⁰⁴, Tyr⁴⁰³, and Tyr⁴²⁶) (Kruse et al., 2013). Between the cap and the allosteric site is a tryptophan residue that interacts with the cationic nitrogen atom of the allosteric ligand (i.e., Trp⁴²²). Tyrosine 426 within the aromatic cap and Trp⁴²² are linked via the peptide backbone of helix 7 (Figure 5). In the absence of an orthosteric ligand, the orientation of Trp⁴²² is unfavorable for the interaction with a cationic allosteric ligand (Figure 5A).

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Figure 5—source data 1

Figure 5–figure supplement 2–Distance between the α-carbon atoms of Tyr¹⁷⁷ and Asn⁴¹⁹ in crystal structures of the M₂ receptor

https://doi.org/10.7554/eLife.11685.021

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Figure 5–figure supplement 3–Mean distances (Å) between the α-carbon atoms of Tyr¹⁷⁷ and Asn⁴¹⁹ in the M₂ receptor with different combinations of allosteric and orthosteric ligands

https://doi.org/10.7554/eLife.11685.022

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Binding of NMS or QNB at the orthosteric site reduces the mobility of the residues of the aromatic cap (e.g., Figure 5A and B) and orients Trp⁴²² to interact with the cationic group of an allosteric ligand. The effect is greater with QNB than with NMS owing to the additional phenyl ring of QNB. Binding of an allosteric ligand draws the aromatic cap outward, leading to destabilization of the orthosteric ligand and greater flexibility in the region of the orthosteric site (e.g., Figure 5A and C). The effect is greater with gallamine than with strychnine, owing to the greater size and charge of gallamine, and it is suggestive of a reduction in the affinity of the receptor for orthosteric ligands.

Gallamine and strychnine affect the conformation of the receptor through interactions between the cationic ammonium group of each allosteric ligand and the side-chains of Trp⁴²² and Tyr¹⁷⁷. Gallamine also affects the receptor through π-cation interactions with Tyr⁸⁰ and Tyr⁸³ and through electrostatic interactions with Glu¹⁷² of the EDGE motif. The overall conformational effect of these interactions was tracked by measuring the distance between the α-carbon atoms of Tyr¹⁷⁷ and Asn⁴¹⁹. That distance is a measure of the width of the vestibule (e.g., Figure 5—figure supplement 2), and it differs among crystal structures of the M₂ receptor in different liganded states (Figure 5—source data 1): namely, with QNB in the orthosteric site (3UON) (Haga et al., 2012), with iperoxo in the orthosteric site (4MQS), and with iperoxo in the orthosteric site and LY2119620 in the allosteric site (4MQT) (Kruse et al., 2013).

The width of the vestibule in simulations with NMS or QNB at the orthosteric site was distributed as shown in Figure 5—figure supplement 3. The allosteric site was vacant (e.g., O_R_NMS) or occupied by strychnine or gallamine (e.g., Str_R_NMS or Gal_R_NMS). The mean distances obtained for all nine liganded and unliganded states are listed in Figure 5—source data 2. When the allosteric site is vacant or occupied by strychnine, the vestibule is wider with QNB than with NMS at the orthosteric site. The greater width is due to the additional phenyl ring of QNB, which disrupts the positions of Tyr⁴⁰³, Trp⁴²², and Asn⁴¹⁹. The vestibule is narrowest with strychnine and NMS. Other combinations of ligands have little or no effect owing to the bulk of QNB, the charge on gallamine, or both.

Destabilisation of the aromatic cap plus the electrostatic repulsion that exists with all positively charged allosteric–orthosteric pairs seems likely to prevent the simultaneous binding of both ligands to a monomeric receptor. The least disruptive effects of one ligand on the binding of another occurred with NMS and strychnine owing, in part, to conformational flexibility afforded by one ligand at the site of the other. The most disruptive effects occurred with QNB and gallamine owing to interactions involving the second phenyl ring of the former and the additional cationic centers of the latter (Figure 4C and D).

Substitutions, insertions, and deletions of bases were performed by site-directed mutagenesis (Quick-Change, Agilent Technologies). PAGE-purified primers were obtained from Integrated DNA Technologies (IDT). Constructs were prepared in pcDNA3.1 for expression in CHO cells and in Bac-N-Blue (Life Technologies) for expression in Sf9 cells. The human M₂ muscarinic receptor was used throughout, and all sequences were confirmed by DNA sequencing (Centre for Applied Genomics, Hospital for Sick Children, Toronto).

TC-FlAsH was obtained as a kit from Molecular Probes (Invitrogen), and labeling was carried out under reduced light according to a procedure adapted from the manufacturer’s instructions (Hoffmann et al., 2010). Transfected CHO cells growing at 50–75% confluency were washed twice with PBS, and the medium was changed to Opti-MEM reduced serum medium (Life Technologies, Inc.). After further incubation of the cells for 1 hr at 37°C, the medium was removed and replaced by a freshly prepared labeling solution of FlAsH in reduced serum medium (2.5 μM, 1 mL per dish). The culture was incubated for 20 min at 37°C in 5% CO₂; the labeling solution then was removed, and the cells were washed twice in a buffer containing 500 µM BAL (Life Technologies, Inc.). During the second wash, the BAL buffer was left for 5 min at 37°C prior to its removal. Washed cells were prepared for imaging by the addition of DMEM (2 mL) supplemented with 50 mM HEPES at pH 7.40 (Gibco Life Technologies, Inc.).

N-[³H]Methylscopolamine ([³H]NMS, 87 Ci/mmol) and (−)-[³H]quinuclidinylbenzilate ([³H]QNB, 42 Ci/mmol) were purchased from PerkinElmer as a solution in ethanol, which was removed by evaporation prior to use. Strychnine, gallamine, carbachol, pilocarpine, and unlabeled NMS and QNB were purchased from Sigma-Aldrich. All other reagents were from the sources described previously (Shivnaraine et al., 2012).

Binding was measured at pH 7.40 in buffer C or buffer D (Dulbecco’s phosphate-buffered saline, Sigma-Aldrich D5652, supplemented with 1 mM CaCl₂ and 1 mM MgCl₂). In the case of detergent-solubilized preparations, buffer C was supplemented with digitonin (1%) and cholate (0.02%). The separation of free and bound radioligand was achieved by chromatography on Sephadex G-50 Fine in the case of detergent-solubilized receptor and by filtration on fiberglass filters or microcentrifugation in the case of membrane-bound receptor. Further details have been described previously (Shivnaraine et al., 2012).

The net dissociation of [³H]QNB over time was analyzed in terms of a single exponential according to Equation 1, in which k_obsd is the rate constant; B_obsd represents total binding of the radioligand at time t, and B_t=0 and B_t→∞ are the initial and asymptotic levels of binding, respectively.

Time-courses at one or more concentrations of gallamine were accompanied in the same experiment by a control lacking the allosteric ligand. The data from all traces were analyzed in concert with a single value of B_t→∞ and separate values of k_obsd and B_t=0. The constraint on B_t→∞ was without appreciable effect on the sum of squares (p>0.05). The value of k_obsd measured in the absence of gallamine was designated k₀ and used to normalize each value measured in the presence of gallamine (i.e., k_obsd/k₀).

Dose-dependent effects of an allosteric modulator (A) on the normalized rate of dissociation of the radioligand (k_obsd/k₀) or on the level of total binding at a specified time (B_obsd) were analyzed empirically in terms of Equation 2.

Estimates of binding at graded concentrations of [³H]NMS were analyzed in terms of Equation 3.

The parameter B_max represents the maximal specific binding of the radioligand (P), and B_obsd and B_sp represent total and specific binding, respectively, at the total concentration [P]_t; n_H is the Hill coefficient, and K is the concentration of unbound [³H]NMS that corresponds to half-maximal binding. NS is the fraction of unbound radioligand that appears as nonspecific binding. Fitted estimates of the Hill coefficient ranged from 0.93 to 1.03 and were indistinguishable from 1 (p>0.05).

Analyses in terms of Equations 1–3 typically were performed on data from replicate experiments, which were taken in concert to obtain single fitted values of parameters that are expected to be invariant (i.e., k_obsd, K, n_H). In figures that show the results of such analyses, data from individual experiments have been presented with reference to a single fitted curve. To obtain the values plotted on the y-axis, measured estimates of B_obsd or Y_obsd were adjusted according to the equation ${\displaystyle Y^{\mathrm{\prime }}=Y[f(x_i,\overline{\mathbf{\text{a}}},\mathbf{\text{b}})/f(x_i,\mathbf{\text{a}},\mathbf{\text{b}})]}$ (Park et al., 2002). The function f represents the fitted equation, and x_i represents the independent variable at point i. The vectors a and b represent fitted parameters that were estimated separately for each experiment (a) or as a single value common to all experiments (b); $\overline{a}$ is the corresponding vector in which parametric values that differed among different experiments have been replaced by the means. Individual values of $Y\text{'}$ at the same x_i were averaged to obtain the mean and standard error plotted in the figure. Details regarding the optimization of parameters and statistical procedures are described in Appendix 1.

The rotational flexibility of eGFP fused to the N-termini of the wild-type M₂ receptor (eGFP-M₂) and a truncated mutant (eGFP-truncM₂) was measured by time-resolved fluorescence anisotropy of single molecules in a locally constructed instrument. Each fusion protein was expressed in CHO cells and solubilized at a concentration of 3–10 nM in buffer C supplemented with detergent (0.8% digitonin, 0.04% sodium cholate). Aliquots of the extract were applied to a coverslip and excited at 480 nm with an excitation beam obtained by frequency-doubling the output of a femtosecond laser (Tsunami HP, Spectra Physics, Santa Clara, CA, USA).

The emission from a confocal volume 5 µm above the surface was passed through a Plan-Apochromat oil-immersion objective (100×, Carl Zeiss, Canada) and projected onto an avalanche photodiode (APD). The emission was divided by means of a polarization cube into two beams with orthogonal polarizations and collected on two different detectors (PDM-5CTC, MPD, Milano, Italy). Photon arrival times were recorded at 4 ps resolution using a multichannel counter (PicoHarp300, PicoQuant, Germany).

The fluorescence signals from the two detectors were fit globally in Matlab using custom-written software and a Levenberg-Marquardt algorithm with iterative re-convolution. Repetitive excitation and the color off-set (s) between measurements of the instrument response function (IRF) and the fluorescence were accounted for according to Equations 4 and 5, in which d_par and d_perp represent the parallel and perpendicular decays before convolution.

The fluorescence signal in each plane was summed to obtain the total fluorescence at time t (F(t)), and the lifetime was obtained according to Equation 6.

The parameter A in Equation 6 is the amplitude, and T is the repetition time of the laser (i.e., 12.5 ns); t is the time bin, and τ is the decay constant. Corrections for collecting the fluorescence emission in the parallel and perpendicular planes through a high numerical-aperture lens were performed according to Equations 7 and 8.

The correction factors k₁ and k₂ have values of 0.33 and 0.065, respectively. The correction factor G corrects for the difference in the sensitivity of detection between the two channels and was taken as 1.061, as determined from a solution of rhodamine 110 (10 nM). The rotational correlation time of eGFP (φ) was estimated from the loss of anisotropy (r) over time (t) according to Equation 9, in which r(0) is the amplitude of the decay.

Where r0 is the is the decay amplitude and ϕ is the rotational correlation time.

Confocal imaging of intact CHO cells was performed on a Zeiss microscope (model LSM710) using a Plan-Apochromat oil-immersion objective lens (63×, 1.4 NA). Samples were irradiated at 488 nm and a power of 0.37 μW. An area of 134.7 × 134.7 μm² was captured through a pinhole of 1 Airy unit, and each pixel in the image represented 0.26 μm² according to the Nyquist theorem. A stack of 30 images was acquired at 5 nm intervals from 495 nm to 640 nm, and the data were processed through custom-written software in Matlab to obtain the emission spectrum corrected for background.

Individual spectra were unmixed by linear regression according to Equation 10 (two colors) or 11 (three colors), in whichk_D, k_A, and k_B, are the scaling factors for the contributions from FlAsH, mCherry, and eGFP, respectively.

The constants Em_D and Em_A represent the reference spectra for the donor (FlAsH) and acceptor (mCherry), respectively; Em_B represents the reference spectrum for eGFP, which was used as a marker for receptor with an intact orthosteric site when co-expressed with a binding-defective mutant.

The unmixed values of k for the donor (k_D) and the acceptor (k_A) were used to calculate the apparent FRET efficiency (E_app) according to Equation 12 (Patowary et al., 2013; Raicu, 2007). In the case of k_A, the fitted value from Equation 10 or 11 was reduced by 6% to compensate for the direct excitation of mCherry at 498 nm.

The constants Q_D and Q_A represent the quantum yields, which were taken as 0.70 for the donor and 0.22 for the acceptor (Subach et al., 2009); W_D and W_A are the corresponding spectral integrals, and the ratio of the regions between 495 and 640 (W_D/W_A) was computed from the reference spectra to be 0.94.

Time-dependent binding of an orthosteric ligand (L) to a monomeric receptor (R) was simulated according to Figure 6, in which access to and egress from the orthosteric site is precluded by an allosteric ligand (A). The system is defined by four ordinary differential equations (Equation 13), which were solved numerically to obtain the amount of bound orthosteric ligand at different times (i.e., [RL] + [ARL]). It was assumed that neither ligand is depleted through binding to the receptor, and the free concentrations in Equation 13 were taken as equal to the total concentrations. The simulations were performed in Matlab 2012b, and the integrals were calculated using the ODE23s subroutine.

The rate constants in Equation 13 were computed from the affinity constants according to Equations 14–16, as described previously (Shivnaraine et al., 2012).

Values of the cooperativity factor α were partitioned between the rate constants for association and dissociation according to Equation 17. The value of j was 2 throughout.

Simulations were performed in the isothermal-isobaric (NPT) ensemble according to the Nosé-Poincaré-Andersen (NPA) equations of motion with a time-step of 2 fs. A cut-off of 10 Å was applied to non-bonding interactions. Equilibration was for 1 ns (300 K, harmonic restraints of 0.5 kcal mol^-1 Å^-2 applied to non-hydrogen atoms), and production continued for 30 ns (300 K, no restraints). Water molecules were wrapped, bond-lengths to lone-pairs, and hydrogen atoms were constrained. Systems were sampled, atomic coordinates saved, and snapshots taken every 2.5 ps. Images were rendered using either MOE or VMD.

To maximize the quantum yield of FlAsH, the tetracysteine motif was bracketed by the flanking sequences FLN and MEP (Martin et al., 2005) (i.e., FLNCCPGCCMEP, abbreviated FCM). The tripeptide FLN was added upstream of CCPGCC (forward primer, 5'-CTCTTCTGGCAGTTCATTGTATTCTTGAACTGTTGCCCAGGATG-3'), and MEP was added downstream of FLNCCPGCC (forward primer, 5'-TGCCCAGGATGTTGCATGGAGCCGGGGGTGAGAACTGTG-3') to obtain the construct designated mCh-M₂-FCM.

To compare FlAsH with a fluorescent protein, mCherry was inserted in place of the FCM sequence after Val¹⁶⁶ in ECL2 of the eGFP-tagged receptor.

Negatively charged residues in the EDGE sequence at positions 172–175 of ECL2 were replaced by positively charged residues (i.e., Lys¹⁷²Arg¹⁷³Gly¹⁷⁴Lys¹⁷⁵) (forward primer, 5'-CATTGTAGGGGTGAGAACTGTGAAGCGTGGGAAGTGCTACATTCAGTTTTTTTC-3') in a receptor bearing hexahistidine at the N-terminus (i.e., M₂-ECL2+ve). Aspartic acid at position 103 was replaced by alanine (forward primer, 5'-CTTTGGCTAGCCCTGGCCTATGTGGTCAGCAAT-3') in a receptor bearing the FLAG epitope at the N-terminus [i.e., M₂(D103A)] and in the FRET-based sensor [i.e., mCh-M₂(D103A)-FCM].

The cells were cultured at 27 °C in Sf-900 II SFM insect cell medium supplemented with 2% fetal bovine serum, 1% Fungizone, and 50 μg/mL gentamycin (all from Gibco Life Technologies, Inc.). When growing at a density of 2 × 10⁶ cells/mL, they were infected with one or both baculoviruses at a total multiplicity of infection of 5.

Cells for transient transfections were grown in 5% CO₂ at 37°C in Dulbecco’s Modified Eagle’s Medium (DMEM, Gibco Life Technologies, Inc.) supplemented with 10% fetal calf serum, 1% non-essential amino acids, 100 U/mL penicillin, and 100 μg/mL streptomycin (all from Gibco Life Technologies, Inc.). Transfections were performed on cells growing at 50–75% confluence. Cells intended for microscopy were grown in 35 mm dishes containing a No. 1.5 glass coverslip (Mattek), which served as a 14 mm microwell, and were transfected with 1 μg total DNA using 3 μL GeneExpresso Max transfection reagent (Excellgen). Cells otherwise were grown in T-175 tissue-culture flasks, transfected with 120 μg total DNA using 360 μL GeneExpresso Max reagent, harvested by scraping in phosphate-buffered saline (PBS, 20 mM KH₂PO₄, 150 mM NaCl, adjusted to pH 7.40 with NaOH), centrifuged for 10 min at 3,000 × g and 4 °C, and stored at −20 °C. In either case, two plasmids were transfected using equal amounts of DNA for each (i.e., 0.5 μg or 60 μg). Frozen cells were thawed on ice as required and processed as described in Materials and Methods. 

Briefly, fresh atria were washed twice with ice-cold PBS and homogenized in buffer B (20 mM imidazole, 1 mM EDTA, 0.1 mM PMSF, 0.02% NaN₃, adjusted to pH 7.60 with HCl) supplemented with benzamidine (1 mM), pepstatin A (20 µg/mL), leupeptin (0.2 µg/mL), and bacitracin (200 µg/mL). All constituents of PBS and buffer B were from Sigma-Aldrich. The resulting homogenate was fractionated by centrifugation on a sucrose density gradient (13–28%) to obtain the sarcolemmal fraction, which was collected by centrifugation, resuspended in buffer B, recovered by centrifugation, and stored at −70°C.

Samples were heated at 65°C for 5 min prior to loading on precast polyacrylamide gels from Bio-Rad (Ready Gel Tris-HCl, 10%). These conditions do not induce aggregation of the M₂ muscarinic receptor from Sf9 cells. Resolved proteins were transferred onto nitrocellulose membranes (Bio-Rad, 0.45 µm), treated for 2 hr with the primary antibody (anti-M₂ muscarinic acetylcholine receptor monoclonal antibody, Thermoscientific) at a dilution of 1:1000, and then for 1 hr with the horseradish peroxidase-conjugated secondary antibody at a dilution of 1:3000. Proteins were visualized by chemiluminescence (ECL, Hyperfilm MP, GE Healthcare). The images were digitized at a resolution of 300 dpi, and the intensities of the bands were estimated from the densitometric trace using ImageJ (Rasband, 1997). Further details have been described previously (Park et al., 2003).

All equations were fitted to the data according to the Levenberg-Marquardt procedure unless indicated otherwise (Marquardt, 1963). Equation 3 was solved numerically, as described previously (Wells, 1992); other equations were solved analytically. Equilibrium constants and potencies in Equations 2 and 3 were optimized on a logarithmic scale; rate constants and other parameters were optimized throughout on a linear scale. The effects of various constraints on the weighted sum of squares were assessed by means of the F-statistic. Weighting of the data and other statistical procedures were performed as described previously (Wells, 1992). In the case of parametric values derived from one set of data or from two or more sets in a global analysis, the errors were estimated from the diagonal elements of the covariance matrix (Equations 1–3) or by bootstrapping (Equations 6 and 9). Parametric values that are the means of independent estimates are presented together with the standard error unless stated otherwise. Further details of the analyses and statistical procedures have been described previously (Shivnaraine et al., 2012; Wells, 1992).

Unresolved residues at the C-terminus of mCherry and the N-terminus of the M₂ receptor (i.e., mCh-GGMDELYKLE and NNSTNSSNNSLALTSPY-M₂) were modeled using a LowModeMD conformational search conducted in MOE with the CHARMM27 force field. The resulting structures were joined, and the new system was subjected to steepest-descent minimization and refined by a short molecular dynamics simulation (5 ns) in a distance-dependent dielectric implicit model of solvation. A restraining distance of 55.7 Å was maintained between FlAsH and the center of the mCherry barrel, in accordance with the experimentally measured distance calculated from the FRET efficiency and the Förster radius. The intracellular region of the receptor between transmembrane domains 5 and 6 (i.e., residues 233–374), which also is unresolved in 4MQS, was determined by homology modeling in Modeller 9.13 and protonated in MOE using the CHARMM27 force field at pH 7.0. The fusion product is shown in Figure 2A.

Models of the receptor were based on crystal structures from which the G protein-mimetic nanobody (4MQS), the agonist iperoxo (M4QS), and the allosteric modulator LY2119620 (M4QT) were removed. Unresolved residues at the N- and C-termini were not included (i.e., residues 1–18 and 457–466). Part of the intracellular region between transmembrane domains 5 and 6 also is unresolved (residues 233–374); the loop therefore was shortened to RIKKDKKEPVANQDPVSTRKK, which was modeled using Modeller 9.13. Five models of the loop were generated, with the rest of the protein constrained to its crystallographic conformation, and the structure with the lowest molpdf score was selected for subsequent simulations. The receptor, including the optimized third intracellular loop, then was protonated in MOE using the CHARMM27 force field at pH 7.0.

All orthosteric and allosteric ligands were built in MOE and protonated using the CHARMM27 force field at pH 7.0. A set of conformers was generated by means of LowModeMD, and force-field partial charges were calculated for each conformer. Those conformations whose energy exceeded the minimum by 9.0 kcal/mol or more were discarded.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

We are grateful to the managers and staff of Quality Meat Packers Ltd. for generous supplies of porcine atria. We thank Dr. Stephane Angers of the Leslie Dan Faculty of Pharmacy for helpful discussions over the course of the investigation and Dr. Donald F. Weaver of the Krembil Research Institute, University Health Network, for providing the facilities used for molecular dynamics simulations.

1. Received: September 17, 2015
2. Accepted: April 30, 2016
3. Accepted Manuscript published: May 6, 2016 (version 1)
4. Version of Record published: June 9, 2016 (version 2)

© 2016, Shivnaraine et al.

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