Selectivity of Agonists for the Active State of M₁ to M₄ Muscarinic Receptor Subtypes

Abstract

We measured the intrinsic relative activity (RA_i) of muscarinic agonists to detect possible selectivity for receptor subtypes and signaling pathways. RA_i is a relative measure of the microscopic affinity constant of an agonist for the active state of a GPCR expressed relative to that of a standard agonist. First, we estimated RA_i values for a panel of agonists acting at the M₄ muscarinic receptor coupled to three distinct G-protein pathways: G_i inhibition of cAMP accumulation, G_s stimulation of cAMP accumulation, and Gα₁₅ stimulation of phosphoinositide hydrolysis. Our results show similar RA_i values for each agonist, suggesting that the same active state of the M₄ receptor triggers the activation of the three G proteins. We also estimated RA_i values for agonists across M₁ to M₄ muscarinic subtypes stably transfected in Chinese hamster ovary cells. Our results show selectivity of McN-A-343 [4-I-[3-chlorophenyl]carbamoyloxy)-2-butynyltrimethylammnonium chloride] for the M₁ and M₄ subtypes and selectivity of pilocarpine for the M₁ and M₃ subtypes. The other agonists tested lacked marked selectivity among M₁ to M₄ receptors. Finally, we estimated RA_i values from published literature on M₁, M₂, and M₃ muscarinic responses and obtained results consistent with our own studies. Our results show that the RA_i estimate is a useful receptor-dependent measure of agonist activity.

Novel agonists for G protein coupled receptors (GPCRs) are often identified in high-throughput screens based on receptor coupling to alternative G proteins that mobilize Ca²⁺ (e.g., Gα₁₅) (for review, see Milligan and Kostenis, 2006). In such a screen, the profile of an agonist may differ from how it behaves when the receptor is coupled to its native G protein (e.g., G_i). Furthermore, the E_max and EC₅₀ values for triggering a response may vary, depending on the signaling pathway and response being measured. If the E_max values of a group of agonists differ within an assay, it is impossible to compare agonist activity accurately using potency ratios.

To understand how drug-receptor interactions influence the output of a functional assay, it is useful to consider different hierarchical levels of analysis of drug action (Fig. 1). On the surface (Fig. 1a), the behavior of an agonist in an assay can be characterized by its EC₅₀ and E_max values, which depend not only on the receptor but on other elements in the signaling pathway as described. At a deeper level of analysis (Fig. 1b), one can examine the relationship between the agonist concentration and the activation state of a population of receptors. For instance, at a ligand-gated ion channel, this activation function represents the whole-cell current or ensemble average. At a GPCR, the corresponding function is known as the stimulus (Furchgott, 1966). The maximal stimulus is equivalent to observed intrinsic efficacy (ε), and the concentration of agonist eliciting a half-maximal stimulus is equivalent to the observed dissociation constant (K_obs). Observed affinity (1/K_obs) and intrinsic efficacy are more invariant than EC₅₀ and E_max, yet nonetheless, these parameter are dependent on the G protein, the concentration of GTP, and other elements that physically interact with the receptor (Ehlert, 2000). It is possible to deduce the stimulus through the analysis of a downstream response using Furchgott's method of partial receptor inactivation (Furchgott, 1966). At an even deeper level of analysis (Fig. 1c), one can consider the microscopic affinity constants of the agonist for the ground and active states of the receptor (Colquhoun, 1998). These parameters are the ultimate determinants of agonist activity in different assays. It is possible to estimate these parameters at ligand-gated ion channels, in some instances, through single channel analysis (Colquhoun, 1998). At a GPCR, it is impossible to estimate microscopic constants from the concentration-response curve; however, it is possible to calculate a relative estimate of the microscopic affinity constant of an agonist for the active state of the receptor. Analysis of the results of a recent modeling study shows that the product of observed affinity (1/K_obs) and intrinsic efficacy (ε) of an agonist expressed relative to that of a standard agonist [ε′(1/K_obs′)] is also equivalent to the corresponding ratio of microscopic affinity constants for the active state of the receptor (K_b/K_b′) (Ehlert 2008). This ratio is termed, intrinsic relative activity (RA_i).

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Fig. 1.

Hierarchical levels of analysis of agonist action. The figure summarizes how agonist activity can be estimated at different, internally consistent levels of analysis. At the most superficial level (a, Level 1), agonist activity is estimated from the EC₅₀ and E_max values of the measured response. These parameters depend on how the agonist interacts with the receptor as well as various elements in the signaling pathway. The second level of analysis (b) refers to the relationship between the agonist concentration and the proportion of the receptor population in the active state (i.e., stimulus). For a GPCR, this relationship depends on the agonist-receptor interaction as well as the concentration of GTP and proteins that physically interact with the receptor (e.g., G proteins). At the ultimate level of analysis (c, Level 3), activity is governed by the affinity of the agonist for ground and active states of the receptor. The goal of pharmacological analysis is to estimate these purely agonist-receptor-dependent parameters from more superficial measurements, such as the stimulus and response to an agonist.

In prior work, we showed how to estimate RA_i from the concentration-response curves of the two agonists (Griffin et al., 2007). Thus, although observed affinity and efficacy are complex functions of microscopic constants, their product yields a simple constant proportional to the microscopic affinity constant of the agonist for the active state of the receptor.

Having a relative measure of the affinity of the agonist for the active state of a GPCR enables one to address several questions. For example, if different active states are involved in coupling to different G proteins, the estimate of the agonist RA_i value should change depending upon the signaling pathway. In addition, if the agonist exhibits selectivity for different receptor subtypes, its RA_i value should reflect this selectivity. Moreover, because all that is required for estimation of RA_i is the agonist concentration-response curve, it should be possible to address these questions from previously published data. In the present report, we have tested these postulates in connection with the subtypes of the muscarinic receptor. Using a panel of agonists, we found little difference in agonist activity for triggering responses through the M₄ receptor coupled to G_i, G_s, or Gα₁₅. Upon investigating agonist activity at muscarinic subtypes using RA_i analysis, we confirmed the selectivity of McN-A-343 for M₁ and M₄ receptors and also identified pilocarpine as an M₁- and M₃-selective agonist. Analysis of data from the literature also yielded a similar picture. Our results show that the RA_i parameter is a simple and useful estimate for comparing agonist activity across assays.

Materials and Methods

Cell Culture. Chinese hamster ovary (CHO) cells stably expressing the human muscarinic M₁ and M₄ receptors were obtained from Acadia Pharmaceuticals (San Diego, CA). The expression levels of muscarinic receptors in these cells were approximately 0.1 pmol (CHO M₄), 0.2 pmol/mg protein (CHO M₂), 1.2 pmol/mg protein (CHO M₃), and 1.3 pmol/mg protein (CHO M₁). HEK-293T cells stably expressing Gα₁₅ were provided by Dr. Olivier Civelli (University of California, Irvine, CA). CHO M₁ cells were cultured in F-12K. CHO M₄ and Gα₁₅ HEK-293T cells were cultured in Dulbecco's modified Eagle's medium with high glucose plus l-glutamine. All media were supplemented with 10% fetal calf serum, penicillin-streptomycin (100 units/ml), and G418 (0.4 mg/ml), and cells were cultured at 37°C with 5% CO₂. HEK-293T Gα₁₅ cells were also supplemented with puromycin (0.625 μg/ml). A plasmid containing the human M₄ receptor was obtained from the cDNA Resource Center (Missouri University of Science and Technology, Rolla, MO). An empty pcDNA3.1 vector was obtained from Invitrogen (Carlsbad, CA). HEK-293T Gα₁₅ cells were transfected with 10 μg of the human M₄ vector HEK Gα₁₅ M₄ or the empty plasmid HEK Gα₁₅ null using Lipofectamine (5:1 Lipofectamine/DNA ratio) for 48 h before experimentation.

cAMP Accumulation. The effects of muscarinic agonists on forskolin-stimulated cAMP accumulation were measured in CHO M₂ and M₄ cells using a modification of the [³H]adenine-prelabeling method as described by Griffin et al. (2007). Pertussis toxin treatment was accomplished by first incubating the cells with the toxin for 16 h before the assay.

Phosphoinositide Hydrolysis. Muscarinic agonist-mediated stimulation of phosphoinositide hydrolysis was measured in adherent CHO cells and suspensions of HEK Gα₁₅ cells using a modification of the [³H]inositol-prelabeling method of Berridge et al. (1982) and the extraction method of Kendall and Hill (1990). A detailed description of the method used for cell suspension experiments is described in Griffin et al. (2007). Confluent CHO M₁ cell monolayers cultured in 24-well plates or 100-mm Petri dishes were washed in KRB before overnight incubation with [³H]inositol (2 μCi/well). On the morning of the experiment, the 24-well plates were washed twice with KRB. After 15-min incubation with KRB (270 μl) containing LiCl (10 mM), agonists (30 μl) were added for a subsequent 30-min incubation at 37°C in 5% CO₂. The reaction was stopped with 5% perchloric acid (200 μl), and the samples were placed on ice. [³H]Inositol phosphates were isolated as described previously (Ehlert et al., 1996).

Analysis of Agonist Concentration Response Curves. E_max, EC₅₀, and Hill slope were estimated from agonist concentration-response curves by nonlinear regression analysis using Prism (GraphPad Software, Inc., San Diego, CA) as described previously (Griffin et al., 2007).

Estimation of RA_i. The RA_i of test agonist B is defined as the product of its observed intrinsic efficacy (ε) and reciprocal of its K_obs divided by that of standard agonist A as described above in eq. 1. To avoid confusion, we have rewritten eq. 1 below with subscripts to observed intrinsic efficacy (ε) and observed affinity (K) to denote the parameters of the standard and test agonists.

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The derivation of the RA_i value and its estimation using either a null method or the operational model have been described in detail previously (Griffin et al., 2007), and step-by-step instructions for estimating RA_i using Prism or a spreadsheet have also been described previously (Ehlert, 2008). A brief summary of the essential steps is given below. Because the RA_i value is a relative measure of agonist activity, we always ran the standard agonist carbachol in each experiment.

Null Method. Pairs of equiactive log agonist concentrations were estimated for the standard (LOGA) and test (LOGB) agonists as described previously (Ehlert, 2008). The following equation was fitted to these data using nonlinear regression analysis.

(3)

In this equation, LOGRA denotes the logarithm of the RA_i value, LOGKA denotes the logarithm of the observed dissociation constant of the standard agonist, and LOGP denotes the logarithm of the ratio of observed dissociation constants of the test agonist divided by that of the standard agonist (Log K_B/K_A). LOGKA was set to an arbitrarily high constant value of -1, and regression analysis yielded the best estimates of LOGRA and LOGP. It is possible to estimate the logarithm of K_B from the estimate of LOGP and LOGKA, even though the latter is set as an arbitrarily high constant.

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Operational Method. For decreasing agonist concentration-response curves, like agonist-mediated inhibition of cAMP accumulation, the concentration-response curves of the standard agonist (A) and the various test agonists (B) were fitted simultaneously to eqs. 5 and 6, respectively, by nonlinear regression analysis.

(5)

(6)

In these equations, P denotes cAMP accumulation in the absence of agonist, N denotes the transducer slope factor in the operational model, LOGR denotes the ratio of the τ value of A divided by its observed dissociation constant (τ_A/K_A), LOGKB denotes the logarithm of the observed dissociation constant of the test agonist (K_B), and LOGRA denotes the logarithm of RA_i, which is also a function of parameters in the operational model (Griffin et al., 2007).

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Global nonlinear regression analysis is done sharing the estimates of N, M, P, and LOGR among the curves, and unique estimates of LOGRA and LOGKB are obtained for each test agonist. If the standard agonist is a full agonist, the parameter LOGKA is set as a constant at an arbitrarily high value during regression analysis (e.g., -1).

For increasing agonist concentration-response curves, such as agonist-mediated simulation of phosphoinositide hydrolysis, the concentration-response curve of the standard agonist and the various test agonists were fitted simultaneously to eqs. 8 and 9, respectively, by nonlinear regression analysis.

(8)

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Global nonlinear regression analysis is done as described above for decreasing concentration-response curves, with the exception that the regression equations lack the parameter P.

Operational Method for HEK Gα₁₅ M₄ Cells. As described below, HEK Gα₁₅ M₄ cells express low levels of an endogenous M₃ receptor in addition to the transiently transfected M₄ receptor, indicating that the muscarinic phosphoinositide response in these cells is caused by activation of both M₃ and M₄ muscarinic receptors. To estimate the RA_i value corresponding to the M₄ component, we analyzed the agonist concentration-response curves in HEK Gα₁₅ M₄ and HEK Gα₁₅ null cells simultaneously according to the following two equations, respectively,

(10)

(11)

in which S₃₊₄ denotes a parameter proportional to the combined stimulus elicited by activation of both M₃ and M₄ receptors in HEK Gα₁₅ M₄ cells,

(12)

and S₃ denotes a parameter proportional to the stimulus elicited by activation of the M₃ receptor in HEK Gα₁₅ null cells.

(13)

The derivation of eqs. 10, 11, 12, 13 is given under Appendix. Regression analysis was done sharing the estimates of N, M, τ₃, and LOGK3 between the curves and obtaining unique estimates of τ₄ and LOGK4 for the data measured in HEK Gα₁₅ M₄ cells. With regard to full agonists in HEK Gα₁₅ M₄ cells, the estimates of K₄ and τ₄ are unreliable. Sometimes, it was necessary to set K₄ as a constant at an arbitrarily high value to obtain a fit. Regardless, the ratio of τ₄/K₄ can be estimated accurately. Knowing the ratio of τ/K for the test agonist and standard agonist for a given response (i.e., M₃ or M₄), it is possible to estimate the corresponding RA_i values using eq. 7 above.

Estimation of RA_i from Published Studies. In most instances (11 of 19), we calculated RA_i values from published concentration-response curves. To make this calculation, we carefully estimated the response values and agonist concentrations from published figures of agonist concentration-response curves. We then calculated the RA_i values from these estimated concentration-response data using the operational method described above. In the remainder of the cases (8 of 19), only the EC₅₀ and E_max values of the agonist were available from the literature. In these cases, we used the simple calculation for the estimation of RA_i as described previously (Ehlert et al., 1999; Griffin et al., 2007),

(14)

in which the subscripts refer to the parameters of the standard (A) and test (B) agonists. This calculation is completely valid if the Hill slopes of the agonist concentration-response curves are equal to one or if the E_max values of the agonists are the same, in which case the RA_i is equivalent to the potency ratio regardless of the Hill slopes. In six of the studies where the simple calculation (i.e., eq. 14) was used, the data were from studies on second messenger responses in cell lines transfected with subtypes of the muscarinic receptor. We have found that agonists typically exhibit Hill slopes close to one in these types of experiments, suggesting that the simple calculation was valid in these instances. In the remaining two cases, R-aceclidine in the rabbit vas deferens (Eltze et al., 1993) and McN-A-343 in guinea pig right atrium (Lambrecht et al., 1993), the E_max values of the agonists were 86 and 59% of the standard agonist, respectively. We expect the simple calculation of RA_i to be valid in the case of R-aceclidine because its E_max is close to 100%. If the Hill slope of McN-A-343 differs from that of carbachol in the right atrium substantially, the simple estimate of RA_i could be in error by 2- to 3-fold (see Ehlert et al., 1999).

Drug and Chemicals. Drugs and chemicals were obtained from the following sources: [³H]adenine and [³H]inositol (PerkinElmer Life and Analytical Sciences, Waltham, MA); F-12K, Dulbecco's modified Eagle's medium, trypsin-EDTA, and Lipofectamine (Invitrogen, Carlsbad, CA); G418 (Invivogen, San Diego, CA); arecoline, carbachol, McN-A-343, and oxotremorine-M (oxo-M), pilocarpine (Sigma-Aldrich, St. Louis, MO). The enantiomers of aceclidine were synthesized and resolved as described by Ringdahl et al. (1979).

Results

Analysis of Agonist Activity at the M₄ Muscarinic Receptor Signaling through Different G Proteins. To investigate how the activity of specific agonists may be modified by the G protein through which the M₄ receptor signals, we tested a panel of muscarinic agonists for their ability to elicit responses through M₄ receptor coupling to G_i, G_s, and Gα₁₅. The panel of compounds included agonists with varying structure, efficacy, and potency. The standard compound to which the RA_i values of the other agonists were normalized was carbachol, selected because of its similar structure to the endogenous neurotransmitter, acetylcholine. Oxo-M was selected as an example of a highly efficacious muscarinic agonist (Fisher and Bartus, 1985). McN-A-343 was investigated as an example of a subtype-selective agonist. This compound was originally described as a sympathetic ganglionic stimulant (Roszkowski, 1961) and has been shown more recently to exhibit selectivity for M₁ and M₄ receptors (Lazareno and Birdsall, 1993). The enantiomers of aceclidine (Ringdahl et al., 1982) were selected as rigid analogs of acetylcholine. The racemate has been used as a treatment for glaucoma (Fechner et al., 1975). The partial agonist, pilocarpine, and arecoline, the natural alkaloid from betel nuts, also were tested.

M₄ Receptor-Mediated Inhibition of cAMP Accumulation. Agonist activity for signaling through the M₄ receptor coupled to G_i was tested in CHO M₄ cells by measuring inhibition of forskolin (10 μM)-stimulated cAMP accumulation (Fig. 2, a and b). Carbachol, S-aceclidine, and McN-A-343 all produced concentration-response curves with similar potency and maximal effect. Oxo-M was slightly more potent than carbachol but shared a similar maximal response, whereas arecoline had a similar potency as carbachol but a slightly decreased E_max. R-Aceclidine had a response both lower in potency and maximal effect compared with carbachol. Pilocarpine exhibited an EC₅₀ at least two log units less potent than carbachol but displayed an increased maximal effect, although pilocarpine was not tested at higher concentrations. It is possible that pilocarpine causes a nonmuscarinic receptor-mediated inhibition of cAMP accumulation at high concentrations as has been previously seen with other agonists [e.g., R-acelidine in CHO cells (Griffin et al., 2007)]. The E_max, EC₅₀, and Hill slope of each agonist are summarized in Table 1.

Fig. 2.

Muscarinic agonist-mediated inhibition of forskolin (10 μM) stimulated cAMP accumulation in CHO M₄ cells. Concentration-response curves for carbachol, McN-A-343, S-aceclidine, and R-aceclidine (a) and carbachol, oxo-M, arecoline, and pilocarpine (b) are shown. The data represent the means ± S.E.M. of 4 to 10 experiments, each done in triplicate. The data are expressed relative to the level of stimulation caused by 10 μM forskolin alone.

TABLE 1.

Agonist activity for inhibiting forskolin stimulated cAMP accumulation in CHO M₄ cells The data are from Fig. 2, a and b. The data represent the mean estimates ± S.E.M. The values in parentheses to the right of some of the estimates are the Log mean ± S.E.M.

Agonist	Emaxa	EC50	Hill Slope	RAi
				Null	Operational
	%	μM
Oxotremorine-M	82 ± 2.4	0.030 (–7.52 ± 0.07)	0.84 ± 0.10	5.79 (0.76 ± 0.07)	6.61 (0.82 ± 0.07)
Carbachol	88 ± 2.1	0.23 (–6.63 ± 0.05)	0.76 ± 0.06	1.0 (0.0)	1.0 (0.0)
McN-A-343	80 ± 6.6	0.56 (–6.25 ± 0.17)	0.65 ± 0.13	0.49 (–0.31 ± 0.12)	0.63 (–0.20 ± 0.12)
S-Aceclidine	87 ± 5.5	0.37 (–6.43 ± 0.14)	0.60 ± 0.09	0.98 (–0.0074 ± 0.20)	1.00 (0.0044 ± 0.10)
R-Aceclidine	71 ± 9.1	5.74 (–5.24 ± 0.26)	0.61 ± 0.15	0.071 (–1.50 ± 0.09)	0.040 (–1.36 ± 0.04)
Arecoline	65 ± 3.7	0.13 (–6.88 ± 0.09)	1.10 ± 0.07	0.68 (–0.17 ± 0.10)	0.73 (–0.14 ± 0.15)
Pilocarpine	83 ± 5.8	9.75 (–5.01 ± 0.12)	0.88 ± 0.10	0.013 (–1.89 ± 0.13)	0.013 (–1.87 ± 0.15)

^aDenotes the maximal inhibition of forskolin-stimulated cAMP accumulation

M₄ Receptor-Mediated Stimulation of cAMP Accumulation. It has been shown that the cAMP response to muscarinic agonists in CHO M₂ and M₄ cells is biphasic. Low concentrations of agonist mediate inhibition of cAMP accumulation, whereas stimulation of cAMP accumulation occurs at higher concentrations of agonist (Mistry et al., 2005). The more potent inhibition of cAMP accumulation is prevented by pretreatment with pertussis toxin, which unmasks the G_s-dependent stimulation of cAMP accumulation. The role of G_s has been confirmed in small interference RNA studies (Michal et al., 2007). We investigated the ability of muscarinic agonists to enhance the cAMP accumulation elicited by a low concentration of forskolin (0.1 μM) in CHO M₄ cells treated with pertussis toxin (see Figs. 3, a and b, and Table 2). Oxo-M stimulated an increase in cAMP accumulation with a maximal effect and potency significantly higher than those of carbachol, whereas the E_max and potency of S-aceclidine were lower than those of carbachol. Both McN-A-343 and R-aceclidine failed to produce substantial concentration-dependent increases in cAMP accumulation. The potency of carbachol for inhibiting cAMP accumulation is more than 1.3 log units higher than that for stimulating cAMP accumulation in pertussis toxin-treated cells, illustrating the low sensitivity of the CHO M₄ G_s assay. This reduced sensitivity can account for the inability of the partial agonists to trigger a response in this assay, rather than inferring a selectivity based on the agonist-receptor-G protein interaction.

Fig. 3.

Muscarinic agonist-mediated stimulation of cAMP accumulation in CHO M₄ cells treated with pertussis toxin. Concentration-response curves for carbachol, oxo-M, and S-aceclidine (a) and McN-A-343 and R-aceclidine (b) are shown. The data represent the means ± S.E.M. of four experiments, each performed in triplicate. The data are expressed as a percentage above the level of stimulation caused by 0.1 μM forskolin.

TABLE 2.

Agonist activity for stimulation of cAMP accumulation in CHO M₄ cells previously treated with pertussis toxin The data are from Fig. 3a. The data represent the mean estimates ± S.E.M. The values in parentheses beneath some of the estimates are the Log mean ± S.E.M.

Agonist	Emaxa	EC50	Hill Slope	RAi
				Null	Operational
	%	μM
Oxotremorine-M	106 ± 3.8	0.54 (–6.27 ± 0.06)	1.25 ± 0.21	11.80 (1.07 ± 0.04)	10.67 (1.03 ± 0.10)
Carbachol	78 ± 3.2	5.3 (–5.28 ± 0.07)	1.26 ± 0.24	1.0 (0.0)	1.0 (0.0)
S-Aceclidine	53 ± 5.7	11.8 (–4.93 ± 0.23)	1b	0.39 (–0.41 ± 0.37)	0.45 (–0.35 ± 0.14)

^aDenotes the maximal stimulation of cAMP accumulation expressed as a percentage of basal cAMP accumulation, which is the amount of accumulation in the presence of forskolin (0.1 μM)

^bHill slope constrained to 1

M₄ Receptor-Mediated Phosphoinositide Hydrolysis via Gα₁₅. Offermanns et al. (2001) have described how Gα₁₅ can couple a wide variety G protein-coupled receptors to phospholipase C-ß. As a consequence, we investigated the ability of muscarinic agonists to stimulate the production of inositol phosphates in HEK Gα₁₅ cells transiently transfected with the M₄ receptor (HEK Gα₁₅ M₄ cells). Figure 4a shows the concentration-response curves of the five agonists tested in the HEK Gα₁₅ M₄ cells. Carbachol and S-aceclidine displayed full agonism with similar potency and E_max. Oxo-M also behaved as a full agonist but showed increased potency with its concentration-response curve located over one log unit to the left of carbachol. McN-A-343 was as potent as carbachol at stimulating phosphoinositide hydrolysis but had a decreased E_max, whereas R-aceclidine exhibited both lower potency and E_max. Table 3 lists the E_max, EC₅₀, and Hill slope values of agonists for these responses.

Fig. 4.

Muscarinic agonist-mediated phosphoinositide hydrolysis in HEK Gα₁₅ cells. Agonist-mediated phosphoinositide hydrolysis was measured in HEK Gα₁₅ M₄ cells (a) and HEK Gα₁₅ cells (b). The data represent the mean values ± S.E.M. of four experiments, each done in triplicate. The data are expressed relative to the E_max for carbachol.

TABLE 3.

Agonist activity for stimulating phosphoinositide hydrolysis in HEK Gα₁₅ M₄ cells The data are from Fig. 4. The data represent the mean estimates ± S.E.M. The values in parentheses to the right of some of the estimates are the Log mean ± S.E.M.

Agonist	Emaxa	EC50	Hill Slope	RAi
				Null	Operationalb
	%	μM
Oxotremorine-M	97 ± 1.1	0.078 (–7.11 ± 0.04)	0.82 ± 0.06	8.01 (0.90 ± 0.04)	10.67 (1.028 ± 0.12)
Carbachol	97 ± 0.9	0.90 (–6.05 ± 0.03)	0.82 ± 0.03	1.0 (0.0)	1.0 (0.0)
McN-A-343	70 ± 1.4	1.1 (–5.98 ± 0.06)	0.87 ± 0.08	0.65 (–0.19 ± 0.07)	0.44 (–0.36 ± 0.05)
S-Aceclidine	91 ± 1.7	0.62 (–6.21 ± 0.05)	0.82 ± 0.07	1.42 (0.15 ± 0.06)	1.24 (0.09 ± 0.06)
R-Aceclidine	61 ± 1.9	2.7 (–5.56 ± 0.08)	0.92 ± 0.13	0.22 (–0.65 ± 0.04)	0.13 (–0.87 ± 0.08

^aDenotes the maximum stimulation of phosphoinositide hydrolysis by carbachol

^bThe operational RA_i values for oxotremorine-M and carbachol were estimated using eqs. 10, 11, 12, 13, whereas those for McN-A-343, S-aceclidine, and R-aceclidine were estimated using eqs. 8 and 9. In each analysis the concentration-response curve of carbachol was analyzed simultaneously as the standard

In a prior study, we showed that an endogenous M₃ muscarinic receptor elicits a weak phosphoinositide response in the HEK Gα₁₅ cell (Griffin et al., 2007). Therefore, muscarinic responses measured in HEK Gα₁₅ cells transiently transfected with the M₄ receptor should represent the sum of M₃ and M₄ responses. To quantify the magnitude of the M₃ component, we measured agonist-stimulated phosphoinositide hydrolysis in HEK Gα₁₅ cells transfected with an empty pcDNA3.1 vector (HEK Gα₁₅ null, see Fig. 4b). In general, the activities of all of the agonists were much less in these cells. Oxo-M produced a maximal response similar to that of carbachol but exhibited 10-fold greater potency. S-Aceclidine exhibited similar potency to carbachol but had a lower E_max value. Neither McN-A-343 nor R-aceclidine produced measurable concentration-dependent agonism in the HEK Gα₁₅ null cells. Control experiments with HEK Gα₁₅ M₄ cells treated with pertussis toxin show a lack of contribution of G_i/o signaling to the phosphoinositide hydrolysis measured upon stimulation by the muscarinic agonists (data not shown).

Estimation of Agonist RA_i Values for M₄ Responses Elicited through G_i, G_s, and Gα₁₅. The RA_i values of agonists for eliciting responses through G_i (Fig. 2), G_s (Fig. 3), and Gα₁₅ (Fig. 4) were estimated using both the operational and null methods as described under Materials and Methods. An additional analysis was done using the operational model for those agonists that elicited a significant response in both the HEK Gα₁₅ M₄ and HEK Gα₁₅ null cells (carbachol and oxo-M). The concentration-response curves from both cell lines were analyzed simultaneously, sharing the estimates of the M₃ parameters between both curves and using only the HEK Gα₁₅ M₄ cells for estimation of the M₄ parameters. In this manner, the M₄ component of the phosphoinositide response in HEK Gα₁₅ M₄ cells was determined. Further details of the calculations are given under Materials and Methods. This analysis enabled us to estimate two RA_i values for an agonist: one for the M₃ response and one for the M₄ response. This careful analysis ultimately showed that the estimate of RA_i value for the M₄ component in the HEK Gα₁₅ M₄ cells was practically the same as that estimated assuming that the entire response was elicited by the M₄ receptor. Presumably, the endogenous M₃ response was too insensitive to influence the M₄ response significantly.

A summary of the RA_i estimates is shown in Fig. 5, and the corresponding RA_i values are also listed in Tables 1, 2, 3. Oxo-M exhibited the highest RA_i values, whereas carbachol, S-aceclidine, and McN-A-343 all exhibited values similar to each other but somewhat lower than those of oxo-M. R-Aceclidine exhibited the lowest RA_i values. None of the agonists exhibited a marked difference in activity for eliciting M₄ responses through the three different G proteins. No RA_i value was calculated for McN-A-343 and R-aceclidine in the CHO M₄ G_s assay because of the immeasurable response to these agonists.

Fig. 5.

Comparison of the RA_i values of muscarinic agonists for eliciting different responses through the M₄ receptor via different G proteins. The estimates are from Tables 1, 2, 3.

Comparison of Agonist Activity across M₁ to M₄ Muscarinic Receptors. We used our RA_i estimates to compare the activity of agonists across the M₁ to M₄ subtypes of the muscarinic receptor. For this analysis, we used data generated from our laboratory in which the test and standard agonists were assayed in the same experiment to minimize variation between experiments. Most of the RA_i estimates for the M₂ receptor were taken from Griffin et al. (2007) in which M₂ receptor-mediated inhibition of forskolin-stimulated cAMP accumulation was measured. We ran additional experiments with arecoline and pilocarpine, and the combined results are given in Table 5. The data for the M₃ receptor are from Ehlert et al. (1999). Additional data on the M₁ receptor were obtained and are described below to give a complete picture of activity across the M₁ to M₄ subtypes.

TABLE 5.

Agonist activity for inhibiting forskolin-stimulated cAMP accumulation in CHO M₂ cells The data represent the mean estimates ± S.E.M. The values in parentheses to the right of some estimates are the Log mean ± S.E.M. NC denotes not calculated because the E_max for the test agonist was the same as the standard carbachol; therefore, RA_i values were calculated as the potency ratio.

Agonist	Emaxa	EC50	Hill Slope	RAi
				Null	Operational
	%	μM
Oxotremorine-Mb	73 ± 2.3	0.047 (–7.32 ± 0.07)	1.02 ± 0.06	NC	4.7 (0.67 ± 0.03)
Carbacholb	73 ± 2.3	0.22 (–6.65 ± 0.07)	0.90 ± 0.08	1.0 (0.0)	1.0 (0.0)
McN-A-343b	32 ± 5.1	38 (–4.42 ± 0.13)	1.17 ± 0.28	0.0022 (–2.66 ± 0.23)	0.0024 (–2.62 ± 0.12)
S-Aceclidineb	73 ± 2.3	0.41 (–6.39 ± 0.10)	0.89 ± 0.07	NC	0.55 (–0.26 ± 0.06)
R-Aceclidineb	73 ± 2.3	2.6 (–5.59 ± 0.08)	0.83 ± 0.08	NC	0.087 (–1.06 ± 0.04)
Arecoline	45 ± 1.9	0.83 (–6.08 ± 0.07)	1.20 ± 0.16	0.43 (–0.36 ± 0.05)	0.35 (–0.45 ± 0.08)
Pilocarpine	40 ± 1.4	17 (–4.76 ± 0.06)	1.11 ± 0.16	0.014 (–1.86 ± 0.03)	0.015 (–1.85 ± 0.07)

^aDenotes the maximal inhibition of forskolin-stimulated cAMP accumulation

^bData are from Griffin et al., 2007

Our data on agonist-mediated stimulation of phosphoinositide hydrolysis in CHO M₁ cells are shown in Fig. 6, a and b. Most of the agonists exhibited a similar maximal response, with the exception of the enantiomers of aceclidine whose E_max values were moderately lower. In addition, most of the agonists exhibited similar potency with the striking exception of oxo-M, which exhibited approximately 10-fold greater potency than carbachol. The potency of pilocarpine was approximately one-fourth that of carbachol. These data are summarized in Table 4.

Fig. 6.

Muscarinic agonist-mediated phosphoinositide hydrolysis in M₁ CHO cells. Agonist-mediated phosphoinositide hydrolysis was measured in CHO cells stably transfected with the human M₁ receptor. Concentration-response curves are shown for carbachol, McN-A-343, S-aceclidine, and R-aceclidine (a) and carbachol, oxo-M, arecoline, and pilocarpine (b). Mean values ± S.E.M. of three experiments are shown with each done in triplicate. The data are expressed relative to the E_max for carbachol.

TABLE 4.

Agonist activity for stimulating phosphoinositide hydrolysis in CHO M₁ cells The data are from Fig. 6, a and b. The data represent the mean estimates ± S.E.M. The values in parentheses to the right of some of the estimates are the Log mean ± S.E.M.

Agonist	Emaxa	EC50	Hill Slope	RAi
				Null	Operational
	%	μM
Oxotremorine-M	100 ± 2.3	0.041 (–7.39 ± 0.05)	1.16 ± 0.13	32 (1.51 ± 0.28)	30 (1.48 ± 0.04)
Carbachol	98 ± 1.1	1.4 (–5.86 ± 0.02)	1.29 ± 0.07	1.0 (0.0)	1.0 (0.0)
McN-A-343	77 ± 1.7	1.9 (–5.72 ± 0.04)	1.09 ± 0.09	0.69 (–0.16 ± 0.06)	0.64 (–0.20 ± 0.07)
S-Aceclidine	102 ± 1.5	3.8 (–5.42 ± 0.03)	1.29 ± 0.07	0.72 (–0.14 ± 0.11)	0.66 (–0.18 ± 0.04)
R-Aceclidine	61 ± 0.46	3.1 (–5.51 ± 0.01)	1.25 ± 0.03	0.31 (–0.51 ± 0.11)	0.22 (–0.66 ± 0.04)
Arecoline	118 ± 2.9	1.7 (–5.77 ± 0.05)	0.93 ± 0.08	1.51 (0.18 ± 0.04)	1.22 (0.09 ± 0.04)
Pilocarpine	119 ± 3.1	5.7 (–5.24 ± 0.05)	0.81 ± 0.06	0.48 (–0.32 ± 0.06)	0.49 (–0.31 ± 0.04)

^aDenotes the maximal stimulation of phosphoinositide hydrolysis by carbachol

Agonist RA_i Values at M₁ to M₄ Muscarinic Receptors. A summary of the RA_i estimates for agonists across M₁ to M₄ muscarinic receptors is shown in Fig. 7. All values were estimated using the operational method. For this analysis, RA_i values were estimated from phosphoinositide assays in CHO M₁ and CHO M₃ cells and from cAMP assays on CHO M₂ and CHO M₄ cells in which the inhibition of cAMP accumulation elicited by forskolin was measured. Oxo-M displayed increased agonist activity relative to carbachol across the M₁ to M₄ muscarinic subtypes, with an especially high RA_i value of 30 at the M₁ receptor and values of 4.0 to 6.6 at the other subtypes. S-Aceclidine, arecoline, and R-aceclidine exhibited approximately uniform activity at the M₁ to M₄ subtypes. The former two compounds had activity similar to carbachol, whereas R-aceclidine exhibited approximately one-tenth the activity of carbachol. The most selective compounds were McN-A-343 and pilocarpine. McN-A-343 exhibited high selectivity for the M₁ and M₄ subtypes and much lower activity at the M₂ (0.0020) and M₃ (0.019) subtypes. The RA_i values of McN-A-343 at the M₁ and M₄ subtypes were comparable with those of carbachol. Pilocarpine exhibited activity less than carbachol but showed selectivity between the muscarinic subtypes; its RA_i values for the M₁ (0.49) and M₃ (0.15) subtypes were much higher than those for the M₂ (0.015) and M₄ (0.013) receptors. One way analysis of variance showed no significant differences among the log RA_i values of S-aceclidine (F_3,12 = 1.16; P = 0.37) and R-aceclidine (F_3,12 = 2.40; P = 0.12) across the M₁ to M₄ receptor subtypes. In contrast, oxo-M (F_3,12 = 43.29; P = 1.03 × 10^-6), McN-A-343 (F_3,12 = 105.9; P = 8.6 × 10^-10), pilocarpine (F_3,10 = 18.30; P = 2.2 × 10^-4), and arecoline (F_3,10 = 4.76 P = 0.0260) exhibited significant differences in their log RA_i values across receptor subtypes. Post hoc comparisons using T tests with the Bonferroni adjustment showed that oxo-M exhibited selectivity for M₁ receptors relative to M₂ to M₄ (P < 0.001), McN-A-343 exhibited selectivity for M₁ and M₄ relative to M₂ and M₃ (P < 0.001), and pilocarpine exhibited selectivity for M₁ and M₃ relative to M₂ and M₄ (P < 0.01). Post hoc comparisons failed to identify significant differences among the log RA_i values of arecoline at the M₁ to M₄ subtypes.

Fig. 7.

Comparison of the RA_i values of agonists for eliciting responses in CHO cells transfected with M₁ to M₄ muscarinic receptors. The estimates are from Tables 1, 4, and 5 and Ehlert et al. (1999).

Estimation of RA_i Values from Published Data. Because the estimation of RA_i only requires the agonist concentration-response curve, it should be possible to estimate RA_i values from previously published data for a variety of responses and determine how invariant the estimate is for a given agonist at a given receptor subtype. To investigate this issue, we calculated the RA_i values of selected agonists for eliciting responses through M₁, M₂, and M₃ muscarinic receptors. Five published studies were used to compare agonist activity at the M₁ receptor in addition to our own just described. Agonist-stimulated phosphoinositide hydrolysis was analyzed from studies by Richards and van Giersbergen (1995) (CHO M₁), Schwarz et al. (1993) (CHO M₁), and Mei et al. (1991) (B82 fibroblasts transfected with the M₁ receptor); agonist-stimulated GTPase activity in CHO M₁ cells (Lazareno and Birdsall, 1993) was also analyzed. We also examined the data of Eltze et al. (1993) on M₁ receptor-mediated inhibition of electrically stimulated contraction in rabbit vas deferens. However, there is some question that this response may be mediated by the M₄ receptor as described under Discussion. Four studies on cell lines, three on myocardial homogenates, and two on the isolated left atrium were selected for comparison of M₂ RA_i values. The studies on cell lines included experiments on the inhibition of cAMP accumulation in CHO M₂ cells by Griffin et al. (2007), Mistry et al. (2005), McKinney et al. (1991), and Wang and El-Fakahany (1993). The studies on inhibition of adenylate cyclase activity in myocardial homogenates included those of Ehlert (1985), Keen and Nahorski (1988), and Ehlert et al. (1996). The studies on the isolated, guinea pig left atrium were from Christopoulos and Mitchelson (1997) and Lambrecht et al. (1993). RA_i values for the M₃ receptor were estimated from studies measuring contraction in the guinea pig ileum and phosphoinositide hydrolysis in cells and tissues. The data on phosphoinositide hydrolysis were from Ek and Nahorski (1988) (parotid gland and ileum), Matsumoto et al. (1994) (ciliary muscle), and Ehlert et al. (1999) (CHO M₃ cells). The data on the contractility of the ileum was from Ringdahl et al. (1982), Hanin et al. (1966), and Ehlert et al. (1999). RA_i values were calculated as described under Materials and Methods and plotted as scatter plots for comparison in Fig. 8. We have indicated those values that were calculated from the rabbit vas deferens with an asterisk because this tentative M₁ response may actually be an M₄ response. If the E_max of the standard and reference agonist were the same, the RA_i would be estimated as the potency ratio (see Griffin et al., 2007).

Fig. 8.

Comparison of the RA_i values of agonists for eliciting different responses in assays for M₁, M₂, and M₃ muscarinic receptors. The estimates were calculated from the published concentration-response curves of Lazareno et al. (1993), Eltze et al. (1993), Mei et al. (1991), Richards and van Giersbergen (1995), Schwarz et al. (1993), Griffin et al. (2007), Ehlert (1985), McKinney et al. (1991), Ehlert et al. (1996), Keen and Nahorski (1998), Christopoulos and Mitchelson (1997), Ehlert et al. (1999), Matsumoto et al. (1994), Ek and Nahorski (1998), Hanin et al. (1966) and Ringdahl et al. (1982), Wang and El-Fakahany (1993), and Lambrecht et al. (1993). Asterisks are used to indicate the RA_i values estimated from the study of Eltze et al. (1993) on the rabbit vas deferens because there is a question whether this response is M₁ (as indicated in the figure) or M₄.

The greatest variation in RA_i values was noted at the M₂ receptor (standard deviation of Log RA_i = 0.45; 2.8-fold), the least variation at the M₃ receptor (standard deviation of Log RA_i = 0.14; 1.4-fold), and intermediate variation at the M₁ receptor (standard deviation of Log RA_i = 0.39; 2.5-fold). One-way analysis of variance revealed no significant differences in the Log RA_i values of oxotremorine (F_2,6 = 2.31; P = 0.18), S-aceclidine (F_2,5 = 3.77; P = 0.10), R-aceclidine (F_2,5 = 1.93; P = 0.24), and arecoline (F_2,11 = 1.26; P = 0.32) at the M₁ to M₃ subtypes. In contrast, oxo-M (F_2,11 = 5.78; P = 0.017), McN-A-343 (F_2,10 = 43.69; P = 1.14 × 10^-5), and pilocarpine (F_2,9 = 9.81; P = 0.005) exhibited significant differences at the M₁ to M₃ subtypes. Oxo-M had geometric mean RA_i values of 15.5, 8.6, and 3.0 at the M₁, M₂, and M₃ subtypes, respectively, suggesting increased activity at the M₁ and M₂ receptors relative to M₃. McN-A-343 exhibited the greatest variation in RA_i values across subtypes (172-fold) with a geometric mean of 0.70 at the M₁ receptor and lower values of 0.0041 and 0.023 at M₂ and M₃ receptors, respectively. The corresponding RA_i values for pilocarpine at the M₁ to M₃ subtypes are 0.63, 0.012, and 0.19, suggesting selectivity primarily for M₁ and M₃ receptors over M₂.

Assessment of RA_i values for an agonist within the same receptor type highlights differences between studies. RA_i values for R-aceclidine at the M₁ receptor vary from 0.017 in the rabbit vas deferens of Eltze et al. (1993) to 0.22 in CHO M₁ cell data from this study. The variation in RA_i estimates at the M₁ receptor is also seen for oxotremorine, with RA_i values ranging from 3.2 at the M₁ receptor in murine fibroblasts by Mei et al. (1991) to 50 calculated from GTPase activity in CHO M₁ cells by Lazareno et al. (1993). As shown in Fig. 8, the RA_i value (6.1) for pilocarpine from Lazareno et al. (1993) was also much higher than that estimated for pilocarpine in four other studies analyzed (0.49, 0.33, 0.35, and 0.28), in which phosphoinositide hydrolysis was measured in either CHO M₁ or B82 M₁ cells. Oxo-M, McN-A-343, S-aceclidine, and arecoline show less variation in RA_i values between the M₁ studies evaluated.

The RA_i values for oxo-M at the M₂ receptor vary from 2.7 (Ehlert et al., 1996) to 30 (Ehlert 1985). These studies both investigated cardiac adenylate cyclase activity but in different species (rat and rabbit, respectively). The RA_i values for McN-A-343, oxo-M, arecoline, R-aceclidine, and pilocarpine also show greater than a log unit range across M₂ studies. S-Aceclidine has the least difference in RA_i estimates of all compounds illustrated in Fig. 8, with a standard deviation of log RA_i values of 0.21. As described above, the variance in agonist RA_i values is substantially decreased when surveying M₃-based assays.

Discussion

The RA_i value is a relative measure of the microscopic affinity constant of an agonist for the active state of the receptor. Therefore, if different active states are involved in the coupling of a GPCR to different G proteins, different RA_i values might be expected. A panel of muscarinic agonists, carbachol, oxo-M, McN-A-343, S-aceclidine, and R-aceclidine, were assessed for possible selectivity for different active states of the M₄ receptor coupling to G_i, G_s, or Gα₁₅. Our data with the M₄ receptor provide no evidence for different active states of the M₄ receptor. This result may suggest that measurement of M₄ activation via Gα₁₅ is an appropriate substitute for estimating agonist activity at the M₄ receptor signaling through G_i, but it is conceivable that other novel agonists may preferentially direct signaling at the M₄ receptor through one G protein more than another. For example, at the M₂ receptor, it has been shown that McN-A-343 has 10-fold greater activity when activating M₂ receptor signaling via Gα₁₅ versus G_i (Griffin et al., 2007). Therefore, before implementation of a cellular screen based on alternative G protein signaling, it would seem prudent to use RA_i in conjunction with as many well characterized agonists as possible to evaluate potential differences in signaling caused by alternative G protein coupling. Agonist concentrations required to increase cAMP via M₄ signaling through G_s were much higher than those required to inhibit forskolin-stimulated cAMP via M₄ signaling through G_i, suggesting a possible physiological irrelevance of the M₄ activation via G_s. Nonetheless, this pathway does provide an additional example of the use of RA_i in alternative screening paradigms.

Because the RA_i value is a relative measure of the microscopic affinity constant of an agonist for the active state of the receptor, its use represents an improvement in prior characterizations of the M₁ to M₄ subtypes requiring the two parameters, EC₅₀ and E_max. RA_i also presents an advantage over the use of potency ratios because RA_i can be calculated in assays in which the agonists elicit different maximal responses. A rank order of agonist activity, based on selectivity for the active state, is given in Table 6. Our data on CHO M₁ cells generally agrees with published data. Two moderate differences are with regard to arecoline and pilocarpine, which gave a higher level of maximal stimulation (118 and 119%, respectively) than previously shown in studies on the phosphoinositide response in CHO M₁ cells by Schwarz et al. (1993) (87 and 66%, respectively) and Richards and van Giersbergen (1995) (85 and 76%, respectively).

TABLE 6.

Rank order of agonist activity based upon RA_i values calculated via the operational method Data were taken from Tables 1, 4, and 5 and Fig. 7.

Receptor	RAi Rank Order
M1	Oxo-M > >arecoline = carbachol > S-aceclidine = McN-A-343 > pilocarpine > R-aceclidine
M2	Oxo-M > carbachol > S-aceclidine > arecoline > R-aceclidine > pilocarpine > McN-A-343
M3	Oxo-M > carbachol = arecoline > S-aceclidine > pilocarpine > R-aceclidine = McN-A-343
M4	Oxo-M > carbachol = S-aceclidine > arecoline > McN-A-343 > R-aceclidine = pilocarpine

In this study, McN-A-343 displayed increased RA_i values at the M₁ and M₄ receptors compared with M₂ and M₃. This pattern correlates with previous data indicating selectivity of McN-A-343 for both M₁ and M₄ muscarinic receptors (Lazareno et al., 1993). Roszkowski (1961) first described the press- or effect of McN-A-343 in cats and suggested that this response was mediated by activation of a neuronal muscarinic receptor (M₁) in sympathetic ganglia triggering catecholamine release. In the rabbit vas deferens, McN-A-343 inhibits the contractile response to electrical field stimulation, and this response is blocked potently by the M₁-selective antagonist pirenzepine (Eltze, 1988). It is conceivable that this response is mediated by the M₄ receptor because pirenzepine exhibits moderately high affinity for the M₄ receptor (pK_D = 7.23) in addition to its high affinity for the M₁ receptor (pK_D = 7.77) (Ehlert et al., 1997). In cell lines, McN-A-343 exhibits greater potency and maximal effect at stimulating GTPase activity in CHO M₄ cells, compared with that observed in CHO M₁ cells, but exhibits much lower activity at the M₂ and M₃ subtypes (Lazareno et al., 1993).

Pilocarpine exhibited RA_i values of 0.49, 0.015, 0.21, and 0.01 across M₁ to M₄ receptors, respectively, indicating selectivity for M₁ and M₃ receptors compared with M₂ and M₄. Pilocarpine has previously been shown to exhibit selectivity for the M₁ receptor based on its activation of GTPase activity in CHO M₁ cells (Lazareno and Birdsall, 1993). More recently, Fox et al. (2001) showed that the salivating effect of pilocarpine is due to its selective stimulation of M₁ and M₃ receptors present on salivary glands, and Gautam et al. (2004) described how the salivary effect of pilocarpine is prevented in M₁/M₃ receptor double-knockout mice. These data and those of Hammer et al. (1980) and Buckley and Burnsock (1986), showing high-affinity binding sites for pirenzepine in the rat submaxillary gland, are consistent with the expression of both M₁ and M₃ receptors in this tissue. Our demonstration of the M₁ and M₃ selectivity of pilocarpine may explain its utility in Sjogren's syndrome for the treatment of dry mouth. Selectivity of pilocarpine has also been investigated centrally; Bymaster et al. (2003) showed that seizures were induced in mice by pilocarpine activation of the M₁ receptor.

The final section of this report compared RA_i values for selected agonists in 19 previously published studies dating from Hanin et al. (1966) to Griffin et al. (2007). If two assays are based upon the same receptor but provide significantly different RA_i values for a compound, it may indicate a difference in the active state of the G protein-receptor complex between the two assays or simply variability. It should be noted that, in evaluating historical data, there is no knowledge of whether the control agonist was tested within the same experiment as the test agonist and, hence, whether control for possible interassay variability was adequate. There is a distinct lack of variation in the estimates of RA_i by different investigators for agonist activity at the M₃ receptor (Fig. 7). With the exception of the RA_i of arecoline in the ciliary muscle of the rabbit (Matsumoto et al., 1994), all agonists presented very similar RA_i values across the different studies, which investigated phosphoinositide hydrolysis in cell lines, glands, and smooth muscle and contraction in the guinea pig ileum (Hanin et al., 1966; Ringdahl et al., 1979; Ek and Nahorski, 1988; Ehlert et al., 1996, 1999). Variability in agonist activity across assays was evident in the M₁ and M₂ sets of data. At the M₁ receptor, pilocarpine showed greater than a 20-fold difference between the high value from Lazareno et al. (1993) and the low value from Schwarz et al. (1993). These studies both used CHO M₁ cells; however, Lazareno et al. (1993) measured GTPase activity, whereas Schwarz et al. (1993) measured phosphoinositide hydrolysis. The high RA_i value of pilocarpine in the GTPase assay might be attributed to a particularly low potency response of carbachol, the standard to which other agonists were compared. RA_i values for all other agonists, with the exception of oxo-M, tested in the study of Lazareno et al. (1993) are higher than those calculated from other M₁-based studies, suggesting unusually low activity for carbachol. The pattern of selectivity that we observed in our studies (Fig. 6) is generally consistent with data from the literature on the M₁ to M₃ subtypes (Fig. 7). That is, both sets of data show that oxotremorine, S-aceclidine, R-aceclidine, and arecoline lack selectivity, whereas McN-A-343 exhibits selectivity for M₁ relative to M₂ and M₃, pilocarpine exhibits selectivity for M₁ and M₃ relative to M₂, and oxo-M exhibits selectivity for the M₁ relative to M₃. The data from the literature, however, do not support an M₁ selectivity of oxo-M relative to M₂, perhaps because of variation in RA_i estimates at the M₂ receptor. The RA_i value calculated for R-aceclidine in the M₁ rabbit vas deferens assay (Eltze et al., 1993) is more than 10-fold lower than that calculated here in the CHO M₁ cells. R-Aceclidine is a good substrate for acetylcholinesterase (Pyttel and Robinson, 1973). Therefore, its activity may be reduced in the isolated tissue because of cholinesterases but not in CHO M₁ cells, which lack these enzymes.

The potency and ability of an agonist to turn on a GPCR depends on its microscopic affinity constants for ground and active states of the receptor (Colquhoun, 1998; Kenakin, 2007; Ehlert, 2008). It is currently impossible to determine each microscopic affinity constant from the kinds of data we have analyzed; nonetheless, RA_i does provide a relative estimate of the microscopic affinity constant of the active state of the receptor. This parameter is completely dependent on the properties of the agonist and the receptor and is completely independent of G proteins and other elements in the signaling cascade. If there are multiple active conformations of the receptor available to the agonist, as well as multiple G proteins or effectors, the RA_i estimate represents a weighted average, depending on the receptor conformations selected by the ligand and attendant effectors (e.g., G proteins). Although it may seem that the G protein has an influence on the estimate of RA_i, G proteins actually provide a window for detecting different active conformations of the receptor. With defined experimental systems, it should be possible to estimate RA_i for specific GPCR-G protein pairs, similar to our results shown in Fig. 4, making RA_i analysis a powerful tool for quantifying ligand-directed signaling.

Appendix

This appendix describes the derivation of eqs. 10, 11, 12, 13, which were used for the analysis of the concentration-response curves in HEK Gα₁₅ M₄ and HEK Gα₁₅ null cells. These equations are based on the operational model (Black and Leff, 1983), which describes the agonist concentration-response curve as a logistic function of the stimulus (s).

(15)

In this equation, N denotes the transducer slope factor, M denotes the maximal response of the system, and K_E denotes a constant related to the sensitivity of the stimulus-response function. Equation 15 can be rearranged into the following form.

(16)

Substituting in a parameter (S) for s/K_E yields eqs. 10 and 11 under Materials and Methods. The stimulus is defined according to Furchgott (1966).

(17)

In this equation, X denotes the concentration of agonist, ε denotes the observed intrinsic efficacy of the agonist-receptor complex, R_T denotes the total receptor concentration, and K denotes the observed dissociation constant of the agonist-receptor complex. Dividing both sides of eq. 17 by K_E yields

(18)

in which

(19)

Equations 18 and 19 provide the basis for eqs. 12 and 13 under Materials and Methods.