Design, synthesis, and structure–activity relationships of diindolylmethane derivatives as cannabinoid CB₂ receptor agonists

2.2.1 Radioligand binding studies and SARs

A total of 99 DIM derivatives and analogs were evaluated for their binding affinities at the human CB₂ receptor. The K_i value of the lead structure DIM (4) in our assay system was 0.690 µM, which is comparable to the reported value of 1.1 µM (see Table 1). SAR analysis revealed that many of the symmetrically substituted indole derivatives displayed higher affinity at the CB₂ receptor when compared to the unsymmetrically substituted ones. Substitutions on the methylene bridge of the DIM derivatives were in general not well tolerated, leading to only moderate potency compared to the unsubstituted analogs (all results are collected in Tables 1–4).

The effects of substituents at the 4,4′-position of the indole rings were studied. The following substituents were introduced: 4,4′-dimethyl (40: K_i  0.845 µM), 4,4′-dimethoxy (41: K_i 0.579 µM), 4,4′-difluoro (42: K_i 0.279 µM), 4,4′-dichloro (43: K_i 0.332 µM), 4,4′-dibromo (44: K_i  0.374 µM), 4,4′-dinitro (45: K_i > 5.0 µM), and 4,4′-dicyano (46: K_i 0.339 µM). Substituents in that position could slightly improve potency as compared to the unsubstituted DIM. 4,4′-Difluoro, 4,4′-dichloro, and 4,4′-dicyano substitution was best tolerated.

Next, substituents were introduced at the 5,5′-positions of DIM-yielding compounds 47–58. In general, compounds with 5,5′-substituents on the indole rings showed, in most cases, lower binding affinity compared to the 4,4′-substituted DIM derivatives. The 5,5′-dichloro-DIM (51: K_i 0.747 µM) exhibited the highest affinity among all derivatives of this series. Notably, it displayed only 73% maximum displacement of the radioligand in our assay system. 5,5′-Dimethyl-DIM (47: K_i 2.78 µM), 5,5′-dimethoxy-DIM (48: K_i 2.84 µM), 5,5′-difluoro-DIM (49: K_i 1.17 µM), 5,5′-dibromo-DIM (52: K_i 1.27 µM), 5,5′-ditrifluromethyl-DIM (50: K_i 1.98 µM), and 5,5′-dicarboxylic acid-DIM (57: K_i > 5.0 µM) showed moderate affinities, while 5,5′-diformyl-DIM (56: K_i 7.25 µM), 5,5′-dicyano-DIM (53: K_i > 5.0 µM) and 5,5′-dinitro-DIM (54: K_i > 5.0 µM) were only weakly potent or inactive at a concentration of 5 µM.

Substitution at the 6,6′-positions of DIM did not improve binding affinity (see compounds 59–63 in Table 1). Substituents such as 6,6′-dimethyl (59: K_i 0.524 µM), 6,6′-difluoro (61: K_i 0.985 µM), and 6,6′-dichloro (62: K_i 0.911 µM) were tolerated, showing similar affinity as lead compound 4. Bulkier substituents, namely 6,6′-dimethoxy (60: K_i 5 µM) and 6,6′-dibromo (63: K_i 3.44 µM) reduced the binding affinity. This is probably caused by limited space in the binding site of the CB₂ receptor. We next studied 7,7′-substituted DIM derivatives (see Table 1). 7,7′-Difluoro-DIM (64: K_i > 5 µM) and 7,7′-dimethoxy-DIM (65: K_i > 5 µM) derivatives were inactive at 5 µM, indicating that substitutions at the 7,7′-positions are detrimental.

Our next effort was aimed at introducing multiple halogen substituents (compounds 66–70). In general, this modification tended to reduce binding affinity irrespective of the positions of the halogen atoms. Chloro-substitution at the 4- and 6-positions (66: K_i 0.624 µM) was the best combination with equipotent binding affinity to lead compound 4. It was interesting to note that compound 69 was less potent when compared to its 4,4′-dichloro-DIM analog 43 and slightly more potent than its 6,6′-dichloro-DIM derivative (62). Other combinations, as indicated in Table 1 (compounds 67–70), reduced binding affinity. The 1,1′-dimethyl-DIM derivative 71 (K_i 3.39 µM) reduced binding affinity, confirming a role for NH in interacting with the CB₂ receptor. Substitution of the 2-position as in the 2,2′-dimethyl derivative 72 (K_i > 5 µM), or introduction of a nitrogen atom in the 7-position of the indole rings as in di-(7-azaindolyl)methane (73: K_i > 5 µM), led to a loss in CB₂ receptor binding affinity. These results indicated that substituents at the 4,4′- or 6,6′-positions were well tolerated, and in some cases, especially those substituted in the 4,4′-positions, could lead to an improvement in binding affinity compared to lead structure 4. Concentration-inhibition curves for selected compounds are shown in Figure 2.

In the next set of experiments, we investigated the effects of substitution of the 3,3′-methylene bridge (C-10) of lead structure 4 (Table 2). A large variety of (aryl)alkyl substituents was introduced. Methyl substitution (100: K_i 5.74 µM) reduced binding affinity, while ethyl (101: K_i  0.804 µM) resulted in an affinity comparable to that of the lead compound. A further increase in the carbon chain length to propyl (102: K_i > 5 µM) and butyl (103: K_i > 5 µM) abolished affinity for the CB₂ receptor. Introducing aryl substituents at the 3,3′-methylene bridge either reduced or abolished CB₂ receptor affinity. Selected examples included p-tolyl (104: K_i 2.55 µM), m-tolyl (105: K_i 1.79 µM), o-tolyl (106: K_i  4.55 µM), p-anisyl (109: K_i 2.41 µM), m-anisyl (110: K_i 2.07 µM) and o-anisyl derivatives (111: K_i 2.72 µM), (4-phenoxy)phenyl (113: K_i > 5 µM), and a 4-hydroxyphenyl (114: K_i 7.13 µM)-substituted derivatives. The combination of substituents on the indole rings and on the methylene bridge of DIM did not improve binding affinity (see compounds 121–134, Table 2). Interestingly, a DIM derivative with a quaternary center (135: K_i 0.674 µM) showed an equipotent binding affinity to DIM, although the maximal displacement of radioligand binding was limited to 53% (see Table 2 and Figure 2b). However, its methoxyl derivative (136: K_i > 5 µM) lost the affinity for the CB₂ receptor, indicating unfavorable interaction when a bulky substituent was present.

In summary, the substitution of the methylene bridge of DIM derivatives did not improve the compounds' binding affinity for the CB₂ receptor, but a few derivatives retained moderate affinity.

As a next step, we investigated a series of unsymmetrically substituted DIMs for their binding to the CB₂ receptor (see Table 3). Initially, only on one of both indole rings a substituent was introduced in the 4-position. The following rank order of potency was observed: 4-methyl-DIM (149: K_i 0.498 µM) > 4-F-DIM (150: K_i 0.758 µM) > 4-Br-DIM (151: K_i 0.944 µM). Thus, these compounds showed comparable binding affinity as the lead compound DIM. All of them were able to completely displace the radioligand in our experiments.

Next, mono-substitution at the 5-position of one of the indole rings was introduced. The following rank order of potency was observed: 5-Cl-DIM (154: K_i 1.21 µM) ≥ 5-methoxy-DIM (152: K_i 2.32 µM) ≥ 5-F-DIM (153: K_i3.78 µM). In general, mono-substitution at the 5-position appeared to be less advantageous than di-substitution on both indole rings in that position. We further investigated the behavior of unsymmetrical DIM derivatives with multiple substitutions, see compounds 157–170. As expected, substituents in the 4-position were found to yield the best unsymmetrical DIM derivatives. The following rank order of potency was observed: 4-Cl,4′-Br-DIM (157: K_i  0.237 µM) > 4-Cl,4′-CH₃-DIM (158: K_i 0.536 µM). Both derivatives were able to nearly completely displace the radioligand. Compounds that have a 5-methoxy or 5-benzyloxy substituent combined with other substituents showed only moderate affinities (see compounds 159–168). 5-OCH₃,4′-F-DIM (159: K_i 1.17 µM), and 5-OCH₃,5′-CH₃-DIM (164: K_i 1.20 µM) were among the most potent ligands in this series showing complete displacement of the radioligand. Introducing a polar hydroxyl group at position 5 of the indole ring (165: K_i 12.0 µM) reduced binding affinity. The N-methylated compound lost binding affinity (169: K_i > 5 µM), but introducing a methyl group at position 4′ of 170 restored affinity (170: K_i 0.716 µM).

We extended the SARs of DIM derivatives by preparing unsaturated (175–177) and saturated 2-oxyindole derivatives (178–180; Table 4). Among them, compound 176 showed moderate binding affinity, but the other compounds lost affinity.

The SARs of DIM derivatives at the CB₂ receptor is summarized in Figure 3. DIM derivatives represent a new class of CB₂ receptor ligands with K_i values reaching the submicromolar concentration range. In general, symmetrically substituted DIMs without substitutions on the methylene bridge showed similar or higher affinities as compared to the lead compound DIM. In particular, the presence of halogen at position 4 of both indole rings improved the binding affinity, while aryl substituents at the methylene bridge reduced it. At least one unsubstituted indole-NH appears to be required for CB₂ receptor binding.

Some of the DIM derivatives, even very potent ones, showed incomplete inhibition of [³H]CP55,940 binding, see, for example, 51, 56, 136 (Tables 1 and 2, Figure 2). This may indicate that the DIM derivatives do not bind to the same binding site as the radioligand, that is the orthosteric binding site, but act as allosteric agonists. Another explanation could be that they do bind—at least in part—to the orthosteric binding site, but to a conformation that differs from the conformation to which classical CBs are binding or which they are stabilizing.

2.2.2 Functional assays at CB₂ receptors

Next, we studied the functional activity of selected ligands. First, we performed cAMP accumulation assays as well as β-arrestin recruitment assays for DIM at the CB₂ receptor to confirm previous results.^[34] DIM behaved as a partial agonist in both cAMP and β-arrestin assays with EC₅₀ values of 0.334 µM (E_max 65% compared to 1 µM full agonist of CP55,940) and 0.562 µM (E_max 63% compared to 0.1 µM full agonist of CP55,940) (see Figures 4 and 5, Table 5). Thus, DIM behaved similarly as the partial agonist THC, which displayed E_max values of 59% (cAMP) and 32% (β-arrestin assay), respectively.

Table 5. The potency of diindolylmethane derivatives as agonists at the human CB₂ receptor

		Human CB2 receptor
		Radioligand binding assay	cAMP assay	β-Arrestin recruitment assay
		Ki ± SEM (µM)	EC50 ± SEM (µM)	EC50 ± SEM (µM)
		(or percent inhibition of [3H]CP55,940 at 5 µM)	(or percent receptor activation at 10 µM)	(or percent receptor activation at 10 µM)
Compound		[Maximal inhibition (%)]	[efficacy]a	[efficacy]b	ΔΔlog (Emax/EC50)c
1	THC	0.00595 ± 0.00027	0.00527 ± 0.00019	0.00142 ± 0.00003	0.8
		[100%]	[59%]	[32%]
2	CP55,940	0.000293 ± 0.00008	0.00320 ± 0.00068	0.00262 ± 0.00003	0
		[100%]	[100%]	[100%]
4 DIM		0.690 ± 0.159	0.334 ± 0.174	0.562 ± 0.195	0.3
		[98%]	[65%]	[63%]
42		0.279 ± 0.056	0.0551 ± 0.0189	0.290 ± 0.148	0.9
		[99%]	[80%]	[70%]
44		0.374 ± 0.074	0.509 ± 0.100	0.0450 ± 0.0189	−0.8
		[100%]	[85%]	[61%]
46		0.339 ± 0.061	0.0144 ± 0.0023	0.0149 ± 0.0021	0.2
		[99%]	[95%]	[67%]
149		0.498 ± 0.176	0.0652 ± 0.0112	1.08 ± 0.37	1.3
		[98%]	[89%]	[93%]
157		0.237 ± 0.006	0.237 ± 0.081	0.0385 ± 0.0125	−0.6
		[98%]	[87%]	[69%]
158		0.536 ± 0.058	0.281 ± 0.109	0.120 ± 0.045	0.2
		[96%]	[110%]	[51%]
170		0.716 ± 0.001	0.228 ± 0.030	0.0803 ± 0.0340	−0.3
		[99%]	[89%]	[70%]

• ^a Efficacy relative to the maximal effect of the standard agonist CP55,940 at 1 µM set at 100%.
• ^b Efficacy relative to the maximal effect of the standard agonist CP55,940 at 0.1 µM set at 100%.
• ^c Bias factor was calculated as described in experimental section. Negative numbers indicate β-arrestin-biased compounds; positive numbers indicate G protein-biased agonists. The bias factor is logarithmic: 1 corresponds to a 10-fold bias, and two corresponds to a 100-fold bias.

Results for compounds selected for cAMP accumulation studies are shown in Figure 4. Like DIM, all investigated DIM derivatives behaved as partial agonists at the CB₂ receptor, but their efficacy differed, some of the new compounds being more efficacious than DIM and significantly more efficacious than THC. Concentration-response curves were determined for compounds that showed more than 50% receptor activation at a concentration of 5 µM (see Figure 5). The results are collected in Table 5.

In the cAMP assay, the symmetrical substitution of DIM with 4,4′-difluoro-DIM (42: EC₅₀ 0.0551 µM) led to an increase in agonistic activity. The larger substituents in 4,4′-dibromo-DIM (44: EC₅₀ 0.509 µM) resulted in reduced activity at the CB₂ receptor. Surprisingly, the 4,4′-dicyano-DIM derivative 46 (EC₅₀ 0.0144 µM) showed low nanomolar potency; in fact, compound 46 is the most potent agonist identified in the present series showing full intrinsic activity at the CB₂ receptor. The mono-substituted 4-methyl DIM (149) displayed slightly lower activity at the CB₂ receptor with an EC₅₀ of 0.0652 µM. Reduced potency was found with unsymmetrically substituted DIM derivatives indicating that unsymmetrical substitution was not favorable for agonistic activity at the CB₂ receptor. Concentration-response curves for selected compounds are depicted in Figure 5.

We further evaluated these selected compounds in β-arrestin recruitment assays using an enzyme complementation assay. The standard agonist CP55,940 was used as a reference agonist. Like in the cAMP assays, our lead compound DIM (4) showed partial agonistic activity in the β-arrestin recruitment assays as well (EC₅₀ 0.562 µM, 63% maximal activation). Thus, DIM showed nearly identical EC₅₀ values in both the cAMP and the β-arrestin assays (Table 5). 4,4′-Difluoro-DIM (42: EC₅₀ 0.290 µM) exhibited an increase in agonistic activity compared to lead compound 4 (Figure 5). Surprisingly, introducing larger substituents like 4,4′-dibromo (44) 4,4′-dicyano (46), or 4-chloro,4′-bromo (157) increased the potency of the DIM derivatives in the β-arrestin assays dramatically yielding EC₅₀ values of 0.0450, 0.0149, and 0.0385 µM, respectively.

We calculated bias factors for the most potent agonists, comparing their effects in G_i-dependent cAMP assays with those determined in β-arrestin assays, as previously described.^{[40, 41]} CP55,940 was used as a reference compound (Table 5). A bias factor of 0 means no bias between two pathways, whereas a factor of 1 corresponds to a 10-fold preference, and a bias factor of two corresponds to a 100-fold preference for the G protein-dependent pathway. The partial agonist THC showed a slight preference for cAMP over β-arrestin signaling in our assay system (bias factor 0.8- or 6-fold preference for cAMP compared to β-arrestin signaling). This finding is well in agreement with published data.^{[42, 43]} DIM (4) displayed a two-fold preference (bias factor 0.3) for cAMP over β-arrestin signaling. Compound 42 (4,4′-difluoro-DIM) showed a seven-fold preference (bias factor 0.9) for inhibition of cAMP accumulation, while 4,4′-dibromo-DIM (44) had the opposite preference being biased toward the β-arrestin over the cAMP pathway (bias factor −0.8). 4,4′-Dicyano-DIM (46) was characterized as a virtually unbiased agonist (bias factor: 0.2). In fact, 46 was found to be the most potent non-biased CB₂ receptor agonist of the present series. The asymmetrical DIM-derivative 149 displayed the strongest bias towards cAMP over β-arrestin signaling, preferably activating G_i-dependent cAMP over β-arrestin signaling (bias factor: 1.3- or 19-fold preference). In contrast, unsymmetrically disubstituted DIM derivatives showed a preference for β-arrestin signaling over G_i-dependent cAMP signaling. This may result in functional antagonistic activity depending on the employed concentration since receptor internalization can be expected as a result of β-arrestin recruitment.

Next, we calculated the correlation of the results obtained in different experiments. The correlation between the potency of the DIM derivatives in cAMP and β-arrestin assays (Figure 6a) showed a low correlation. Some agonists are somewhat G_i protein-biased, which would result in longer-lasting activity because receptor internalization is less pronounced, while others are β-arrestin biased, which will lead to fast receptor internalization. Additionally, a comparison of functional and radioligand binding data revealed only a very low correlation (Figure 6b). This may be explained by the fact that DIM derivatives bind to a different binding site than the orthosteric agonist radioligand. Thus, DIM derivatives appear to act as allosteric CB₂ receptor agonists.

2.2.3 Selectivity studies

Radioligand binding studies at the CB₁ receptor subtype were performed and compared with results at the CB₂ receptor (see Tables 1–4). The results showed that many of the compounds were able to bind to the CB₁ receptor as well. Among them, 6,6′-di-Cl-DIM (62, CB₁: K_i 0.820 µM; CB₂: K_i 0.911 µM) was found to display comparable binding affinity at both CB₁ and CB₂ receptors. However, only a few compounds displayed CB₁ receptor selectivity. Selected examples include 58 (K_i 2.95 µM), 119 (K_i 0.983 µM), 122 (K_i 0.541 µM), 123 (K_i > 0.414 µM), and 136 (K_i > 2.84 µM). Among these, compound 122 might be further developed in the future to obtain potent, selective CB₁ receptor ligands. Importantly, the most potent CB₂ receptor ligands, including 4, 42, 44, 46, 149, 157, 158, and 170, were selective for the CB₂ versus the CB₁ receptor (Supporting Information: Table S2, Figure 7). In contrast to THC, which is nonselective (see Figure 7), potent, CB₂-selective agonists were discovered among the developed DIM derivatives. DIM (4) itself showed 8-fold selectivity for the CB₂ versus the CB₁ receptor. Compounds 42 (4,4′-di-F-DIM) and 46 (4,4′-di-CN-DIM) displayed the highest selectivity, being 36- and 30-fold selective for the CB₂ receptor, respectively. Unsymmetrically substituted DIMs such as 149, 157, 158, and 170 showed a slightly lower CB₂-selectivity index.

It is important to note that compound 70 (PSB-16671), a potent GPR84 allosteric agonist (EC₅₀ 0.043 µM) identified by our group, was shown to bind to both CB₁ (K_i 1.10 µM) and CB₂ receptors (K_i 2.64 µM) with comparable affinities. Mancini et al. recently reported that the ability of PSB-16671 to activate G proteins in mouse bone marrow-derived neutrophils was due to “off-target effects” and not mediated by GPR84.^[44] This result was further supported by the inability of a GPR84 antagonist to block the effects of PSB-16671 on mouse GPR84 in both transfected cells and in the RAW264.7 cell line. Based on our results that PSB-16671 is able to interact with both CB receptor subtypes, we suggest that the observed effects of PSB-16671 could be due to its interaction with CB receptors natively expressed in the employed cell lines.

In native, nontransfected CHO cells DIM and its derivatives did not show any inhibition of cAMP accumulation. This clearly shows that the observed effects of DIM and its derivatives observed in the present study are due to the activation of the recombinantly expressed CB receptors in CHO cells. SARs at CB₂ receptors and GPR84 are quite different, and both, CB₂-selective or GPR84-selective agonists could be developed. However, one has to carefully choose concentrations—if high concentrations are employed, selectivity may not be given anymore.

We further investigated several DIM derivatives in functional assays at CB₁ receptors employing cAMP accumulation as well as β-arrestin recruitment assays (Table 6, Figure 8, Supporting Information: Table S3). Interestingly, none of the compounds was active in cAMP assays at concentrations up to 10 µM, neither as agonist nor as antagonist versus the standard agonist CP55,940 (see Supporting Information: Table S3). However, they showed antagonistic activity in β-arrestin assays at micromolar concentrations (Table 6, Figure 8). This indicates once more that DIM derivatives can act as allosteric modulators, not only of CB₂ but also of CB₁ receptors. Depending on their substitution pattern, they can, in fact, act as biased CB₁ receptor antagonists.

4.1.1 General

All commercially available reagents were used as purchased (Acros, Alfa Aesar, Sigma-Aldrich, ABCR or TCI). Solvents were used without additional purification or drying except for dichloromethane, which was distilled over calcium hydride. Thin layer chromatography (TLC) using aluminum sheets with silica gel 60 F254 was employed to monitor the reactions (Merck). Column chromatography was performed with silica gel 0.060–0.200 mm, pore diameter ca. 6 nm. For microwave reactions, a CEM-Focused Microwave Synthesis type Discover apparatus was used. All synthesized compounds were finally dried in a vacuum at 8–12 Pa (0.08–0.12 mbar) using a sliding vane rotary vacuum pump (Vacuubrand GmbH). ¹H-, ¹³C NMR, and ¹³C_apt NMR data were collected on a Bruker Avance 500 MHz NMR spectrometer at 500 MHz (¹H), or 126 MHz (¹³C), respectively. If indicated, NMR data were collected on a Bruker Ascend 600 MHz NMR spectrometer at 600 MHz (¹H), or 151 MHz (¹³C), respectively. DMSO-d₆ was employed as a solvent at 303 K unless otherwise noted. Chemical shifts are reported in parts per million (ppm) relative to the deuterated solvent; that is, DMSO, δ ¹H: 2.49 ppm; ¹³C: 39.7 ppm. Coupling constants J are given in Hertz and spin multiplicities are given as s (singlet), d (doublet), t (triplet), q (quartet), sext. (sextet), m (multiplet), br (broad). Melting points were determined on a Büchi 530 melting point apparatus and are uncorrected. The purities of isolated products were determined by ESI-mass spectra obtained on an LCMS instrument (Applied Biosystems API 2000 LCMS/MS, HPLC Agilent 1100) using the following procedure: the compounds were dissolved at a concentration of 1.0 mg/ml in acetonitrile containing 2 mM ammonium acetate. Then, 10 μl of the sample were injected into an HPLC column (Macherey-Nagel Nucleodur® 3 µl C18, 50 × 2.00 mm). Elution was performed with a gradient of water/acetonitrile (containing 2 mM ammonium acetate) from 90:10 to 0:100 for 20 min at a flow rate of 300 μl/min, starting the gradient after 10 min. UV absorption was detected from 200 to 950 nm using a diode array detector. Purity of all compounds was determined at 254 nm. The purity of the compounds was generally ≥95%. Compounds 44–46, 50, 105, 106, 108, 110, 111, 113, 119, 124, 125, 135, 136, and 165 are new, and not previously reported in the literature.

The InChI codes of the investigated compounds, together with some biological activity data, are provided as Supporting Information.

4.1.2 General procedure for the synthesis of diindolylmethane derivatives

4.2.1 Radioligand binding assays at CB₁ and CB₂ receptors

Competition binding assays were performed using the nonselective CB receptor agonist radioligand [³H](−)-cis-3-[2-hydroxy-4-(1,1-dimethylheptyl)phenyl]-trans-4-(3-hydroxypropyl)cyclohexanol ([³H]CP55,940, final concentration 0.1 nM) as previously described.^{[38, 46, 47]} Membrane preparations of CHO cells stably expressing either human CB₁ or CB₂ receptor were used (CB₁: 30 μg of protein/well and CB₂: 16 µg of protein/well) for all of the radioligand binding experiments. Stock solutions of the DIM derivatives were prepared in DMSO. The mixture containing 15 μl of the test compound in DMSO, 60 μl of [³H]CP55,940 solution in assay buffer (50 mM TRIS, 3 mM MgCl₂, 0.1% bovine serum albumin [BSA], pH 7.4), 60 μl of membrane preparation and 465 μl of assay buffer was incubated for 2 h at room temperature (final DMSO conc. in the assay was 2.5%). Incubation was terminated by filtration through GF/C glass fiber filters (presoaked for 0.5 h in 0.3% aq. polyethyleneimine solution). Total binding was determined by adding DMSO without test compound, while nonspecific binding was determined in the presence of 10 μM of unlabeled CP55,940. The filter was then dried for 1.5 h at 50°C. Radioactivity on the filters was determined in a liquid scintillation counter (Top count NXT, Packard/Perkin-Elmer) after 10 h of preincubation with 50 µl of scintillation cocktail (Multiscint 25, Perkin-Elmer). Data were obtained in minimum of three independent experiments, performed in duplicates. For the calculation of K_i values, the Cheng-Prusoff equation and K_D values of 2.4 nM ([³H]CP55,940 at CB₁) and 0.7 nM ([³H]CP55,940 at CB₂) were used.^[48]

4.2.2 cAMP accumulation assays at human CB₁ and CB₂ receptor

The inhibition of adenylate cyclase activity was determined according to a described procedure in the literature using a competition binding assay for cAMP quantification in CHO cells stably expressing the CB₁ or the CB₂ receptor subtype, respectively.^{[21, 30]} Briefly, cells were seeded into a 24-well plate (200,000 cells/well) and incubated for 24 h. On the day of the assay, the medium was exchanged for Hank's buffered saline solution (HBSS, Gibco) and the cells were further incubated for another 2 h. About 20 µl of 40 µM Ro-20-1724 (4-(3-butoxy-4-methoxybenzyl)-2-imodazolidinone) as phosphodiesterase inhibitor was added into each of the wells. After 10 min incubation, 15 µl of test compound (diluted in HBSS) was added to the mixture and the cells were further incubated for another 5 min. The adenylate cyclase activator, forskolin (final concentration 10 µM), was added to the mixture, and incubation was continued for a further 15 min. The final DMSO concentration was 1.9%. The reaction was stopped by lysis of the cells with hot lysis buffer (100°C; 4 mM EDTA, 0.01% Triton X-100). The cAMP quantification was performed by mixing 50 μl of cell suspension, 30 μl of [³H]cAMP (3 nM in Tris buffer), and 40 μl of cAMP-binding protein (50 µg per well in Tris buffer). The mixture was incubated for 1 h on ice. Bound and free radioligand were separated through GF/B glass fiber filters, and the radioactivity was measured after 9 h of preincubation with a scintillation cocktail (LumaSafeplus, Perkin-Elmer). Data were obtained from three independent experiments, performed in duplicates.

4.2.3 β-Arrestin assays at human CB₁ and CB₂ receptor

β-Arrestin recruitment assays based on galactosidase enzyme complementation assay (DiscoverX) were performed according to previously published.^[38] Briefly, CHO β-arrestin2 cells stably transfected either human CB₁-prolink1 or human CB₂-prolink1 were seeded in the density of 30,000 cells/well (CB₁), or 20,000 cells/well (CB₂), and incubated for 24 h. On the day of the assay, about 10 µl of the test compound was added and the cells were further incubated for another 90 min. CP 55,940 (0.1 µM) was used as the standard agonist for maximal response. For antagonistic activity, the test compounds (5 µl) were added to the wells, and incubated for 60 min at 37°C, and then the agonist at its EC₈₀ was added (5 µl) and the mixture was incubated for another 90 min at 37°C. The galactosidase activity was measured by lysis of the cells according to the manufacturing protocol. The luminescence was measured with an LBMitras 940 plate reader (Berthold, Bad Wildbad). A minimum of three independent experiments was performed, each in duplicate.

4.2.4 Operational model to determine the bias factor of the agonists

The pathway bias was calculated as described by Winpenny et al.^{[41, 49]} and Pillaiyar et al.^[40] The E_max (max activation in %) and the EC₅₀ (in M) for each compound were used to obtain the transduction ratio (log (E_max/EC₅₀). The transduction ratio within a pathway (Δlog(E_max/EC₅₀)) was calculated by subtracting the transduction ratio of the agonist (log(E_max/EC₅₀) of the test compound) from the transduction ratio of the reference compound CP55,940 (log(E_max/EC₅₀) of CP55,940 regarding the same pathway. Ligand bias (or bias factor) between two pathways (ΔΔlog(E_max/EC₅₀)) was determined by calculating the difference between the transduction ratio (Δlog(E_max/EC₅₀)) of one pathway and the transduction ratio of the other pathway (Δlog(E_max/EC₅₀) cAMP – Δlog(E_max/EC₅₀) β-arrestin).