How THC works: Explaining ligand affinity for, and partial agonism of, cannabinoid receptor 1

Summary

Interaction with cannabinoid receptor 1 (CB1) partially determines the bioactivity of the phytocannabinoids. Consequently, there has also been significant effort directed toward preparing synthetic cannabinoids with either enhanced agonistic or antagonistic activity against this receptor. The design process of these molecules, and the identification of off-target effects at this receptor for molecules designed to target other proteins, would be aided by a reliable computational tool that can accurately predict binding. Furthermore, although the mechanism of CB1 agonism is understood, the conformational behavior that underlies the molecular mechanism of partial agonism is unclear. In this report, we provide a correction for calculating a ligand’s affinity to the orthosteric site of CB1 to account for their partition into membranes, use this to register the predicted affinity (high and low) of cannabinoids, and discuss how a mechanism for THC partial agonism arises natively from the model consistent with experimental data.

Graphical abstract

Highlights

• •Cannabinoid receptor 1 ligands enter the orthosteric pocket from the membrane
• •Induced fit docking scores corrected for hydrophobicity correlate to experiment
• •THC is a partial agonist of CB1 because it can occupy two different binding modes
• •Longer THC homologs pressure the toggle switch residues to increase their agonism

Biological sciences; Biophysics; Natural sciences; Pharmacoinformatics

Introduction

Phytocannabinoids, alkyl resorcinol-functionalized diterpenes produced most notably by Cannabis species, are thought to act primarily through agonism and antagonism of human G-protein-coupled receptors (GPCRs).¹ Δ⁹-Tetrahydrocannabinol (THC) is a well-established partial agonist of cannabinoid receptor 1 (CB₁) where it occupies the orthosteric site —the extracellular-facing well that is formed by the seven transmembrane helices (TMs, labeled TMI- TMVII)— that acts as the primary binding site for endogenous ligands. Most drugs that target GPCRs act at their orthosteric sites. Full agonists sitting in the orthosteric site open the G-protein binding domain on the cytosolic side of the protein, while antagonists prevent G-protein binding by inducing a conformational change that closes the site. Partial agonists induce intermediate activity. Reverse agonists can help recruit non-canonical G-proteins or act through the alternative β-arrestin pathway.² Since the initial discovery of THC,^3,4 numerous modifications and analogs of both the core ring system and the side chains (Figure 1A) have been synthesized to define the structure–activity relationship of THC with both CB₁ and CB₂.⁵ According to Bow et al., the length of the alkyl chain is the key parameter for determining CB₁ receptor activity; a minimum of three carbons is necessary to bind the receptor with agonist activity (Figure 1B).⁶

Figure 1.

Structural overview of THC and its ring system

The various side chain lengths discussed in the article are highlighted.

In 2019, Citti et al. reported a pair of phytocannabinoids: tetrahydrocannabiphorol (THCP) with a seven-carbon alkyl chain⁷ and tetrahydrocannabutol (THCB) with a four-carbon alkyl chain.⁸ Both had higher claimed in vitro binding affinity (K_i = 1.2 and 15 nM, respectively) than that reported for the intermediate five-carbon THC (K_i = 40 nM).^6,8 Citti proposed that this differential activity arises because the orthosteric binding site of CB₁ has three hydrophobic pockets⁹: the main hydrophobic pocket (M-pocket) which houses the ring system of THC homologs; the long hydrophobic pocket (L-pocket) formed by TMs III, V, and VI, which can accommodate the long heptyl chain of THCP and the pentyl chain of THC; and the hydrophobic sub-pocket (S-pocket) formed by F170, F200, L387, M363, L359, and C386 that lies toward the toggle switch residues needed to activate the receptor. This last is located at the intersection between the M-pocket and the L-pocket (and Video S1). As they are too short to benefit from the hydrophobic L-pocket, the propyl and butyl chains of THCV and THCB instead sit in the S-pocket. Citti argues that this is the reason for THCB’s higher affinity for CB₁ than the longer THC.^7,8

However, these findings contradict the literature: First, THC analogues with alkyl chains shorter than five carbons —or longer than eight carbons— have decreased binding affinity compared to those with lengths in that range with affinity peaking at eight carbons, as noted.⁶ However, they report that four-carbon THCB (K_i = 15 nM) has higher binding affinity than five-carbon THC (K_i = 40 nM). Second, the binding affinity of THCP and THCB was compared to the THC and THCV affinity values reported by Bow and Rimoldi which are the least generous available.⁶ Several binding affinities have been reported for THC (K_i = 40.7 ± 1.7,⁶ 35.64 ± 12.4,¹⁰ 25.1 ± 5.54,¹¹ 5.05¹² and 2.9 ± 0.3¹³ nM) and THCV (K_i = 75.4,⁶ 46.6¹⁴ and 22 ± 5¹⁵ nM). Experimental affinity data inherently contains noise, especially when comparing results from different laboratories due to experimental, specific protocol, and even reagent differences.¹⁶ There is a large variation in the experimental data available in the literature which could arise from different testing conditions and protocols and great caution must be taken in overreliance and overinterpretation of small differences that arise from any sort of concentration-dependent non-thermodynamic technique. This underlies the strong argument to be made that Ki values should only be reported as -logK_i as small differences, claimed to be meaningful, often are not.¹⁷ Access to these minor cannabinoids, however, previously restricted due to a combination of synthetic complexity and a low abundance in the plant, is likely to be continually made easier allowing for more reproductions of these data as controls during routine experimentation; for example, Magolan et al. recently disclosed a flexible modular synthesis through resorcinol functionalization that will accelerate diversification.¹⁸

As an aside, it is also important to note the distinction between various pharmacological concepts such as “affinity”, “activity”, “efficacy” and “potency”. These are often interchangeably used in the cannabis literature, and this leads to confusion and a tendency to attempt to equate incomparable experiments— contributing to the greater than an order of magnitude difference in reported THC@CB1 affinities (the extreme -logK_i are 7.4 and 8.6). Affinity refers to the strength of binding between a ligand and its receptor, typically measured by dissociation constant (Ki) values, although more accurately measured using a biophysical technique such as isothermal titration calorimetry which can provide ΔG of binding. Activity encompasses the ability of a ligand to elicit a biological response upon binding to its target receptor. Efficacy specifically relates to the magnitude of the downstream response generated by a ligand-receptor interaction, while Potency indicates the concentration of a drug required to produce a specific effect (generally the amount required for a given form of administration, e.g., oral potency will differ from intravenous or cerebral spinal potency). At the molecular interaction level only affinity has any meaning. The other terms (with the possible exception of activity should it be defined entirely in terms of a biochemical response) refer to systems-based responses that cannot be measured in a cell-based or, especially, cell-free assay.

For CB1, agonist activity is strongly correlated with the ability of a ligand occupying the orthosteric pocket to force open the “toggle switch” defined by W356 and F200; the movement of this switch, pushing TM3 and TM6 apart, correlates the conformational change on the cytoplasmic side of the protein allowing for G-protein interaction. In contrast, an antagonist simply occupies the pocket, preventing any agonist from entering that can trigger the switch.¹ Both agonists and antagonists can have high affinity of course. It is important to note that although activation of the toggle switch does correlate with the activity of a ligand, the directionality of causation is not completely clear.

The community understands the mechanism of action of agonists, but it is less clear whether there is a consensus mechanism of action for partial agonists. What makes them partial agonists? Lacking any crystallographic data of the receptor with any bound phytocannabinoid, this question remains outstanding. Furthermore, it highlights that we have an imprecise understanding of the experimental binding affinity, even for these well studied major cannabinoids, with reasonable estimates of the K_i varying by over an order of magnitude. These values serve as proxies for ligand-receptor interactions and guide our efforts to understand the structural determinants of binding affinity. By elucidating these distinctions, we wished to improve our ability to determine binding affinity for use in screening of new compounds and correct for factors that may not be normally accounted for in methods such as docking. Generally, this is done using an all-atomic molecular modeling study, but this provided inconsistent results: affinity for the receptor was not sufficient, in and of itself, to describe the observed Ki. This, however, can partially be explained by the different mode of entry of ligands into CB₁ compared to many GPCRs: it enters from the lipid membrane, not the solvent. This is a factor not considered by methods such as docking, which only considers binding to the receptor and assumes the ligand is solvated in water. With this information, and using a library of 21 THC homologues with experimental data (Figure 2), we propose an empirical correction to predict the affinity of a ligand for CB₁; a conceptual model to determine whether a ligand is likely to be agonist, antagonist, or partial agonist; and a mechanism by which partial agonists function as such. During the preparation of this article, Shukla et al. published on the mechanism of action of THC as a partial agonist using complementary techniques to our own, and in close agreement with our proposed mechanism, providing further confidence in the reliability of our hypothesis.¹⁹ Likewise, Gavryushov et al. recently published a thorough examination of TM movement in the CB1 in response to ligand binding that remains highly consistent with our understanding of GPCR activation and G-protein binding to receptors.²⁰ Finally, Gloriam et al. recently reported, as a preprint at the time of submission of this article, the cryo-EM structure of HU-210 bound to CB1²¹; this structure is very consistent with the predicted conformation for this ligand discussed in the article below.

Figure 2.

Structures of the THC analogues with known experimental binding affinities used in this study

Those in red are partial agonists, in purple weak agonists, in blue potent agonists, in brown antagonists.

Methods

Rigid-receptor docking (RRD) and induced fit docking (IFD) using the Glide module of the Schrödinger suite were conducted to study the binding of THC analogues to CB1, followed by MM-GBSA calculations using Prime MM-GBSA to estimate binding free energies. Molecular dynamics (MD) simulations of ligand-bound CB1 complexes were performed using AMBER22 to further investigate protein-ligand interactions and complex stability. The 3D coordinates of CB1 receptor complexes (PDB ID: 6N4B)²² were obtained from the Protein DataBank, prepared by using the protein preparation module in Schrödinger to add missing atoms, correct bond orders, and minimize the structure. The protonation state of the system was set to pH 7.4. The missing ICL3 loop was built using the linker design module in Schrödinger and refined. The structure was then subjected to a short 10 ns MD simulation for receptor relaxation and refinement of the loop. Ligands were prepared using Schrödinger software, energy minimized with the OPLS3e²³ force field and prepared using the LigPrep module. As with all structures in this article, these coordinates are available as supplemental information in their native, computer-readable file formats from the Borealis Dataverse (see note at the end of the article) to aid with their use by others in the future.

Ligand docking studies were conducted using the Glide module with a grid-based docking protocol, generating an active site using the Receptor Grid Generation module. The IFD extended sampling protocol was adopted to account for flexibility in both ligand and receptor, followed by Glide docking calculations with default parameters. Prime MM-GBSA was utilized to estimate ligand binding energies and strain energies of complexes, while MD simulations were performed using AMBER22 to observe ligand behavior over time. These computational methods provided comprehensive insights into the binding interactions and dynamics of THC analogues with CB1 receptor, shedding light on ligand-receptor interactions and complex stability. More information on how proteins and ligands were prepared, and the detailed parameters of the docking, MD, and MM-GBSA protocols are available in the STAR Methods section below.

Results and discussion

Docking or MM-GBSA scores only poorly predict experimental Ki values for CB1

To predict the binding affinity between ligands and receptors as well as to characterize the different binding modes, an in silico study was conducted on a total of 21 THC analogues with experimentally measured binding affinity toward CB₁, including the antagonist THCV,⁹ weak agonists THCA,²⁴ partial agonists THCB and THC,⁸ and agonists THCP,⁷ AM11542,²⁵ AM841,²⁵ AM12033,²⁶ AM4030,²⁷ HU-210,²⁸ ajulemic acid (AJA),²⁹ and Nabilone,³⁰ which demonstrate a range of potencies, activities, and selectivities (Figure 2).

We investigated several parameters to improve correlation between experimental binding affinity and in silico docking results. We want to highlight that this is a hard problem: Correlation of computational prediction to experiment when the experimental data were all collected in parallel using a single methodology by a single user is still challenging; however, this rich dataset does not exist for the CB1 receptor. Instead, we need to compare data collected by multiple research groups using similar (but not identical workflows) with various ligands. This will introduce variance as experimental Ki values are highly dependent on protein expression levels and the precise conditions of the data collection.^31,32 However, although this increases the difficulty in generating the model, it also makes any successful model far more robust and inherently more useful. To tackle this challenge, we first examined RRD with scaled van der Waals radii of non-polar atoms (1.0, 0.8, and 0.6) to represent some of the flexibility present within the receptor, an approach well precedented to provide good correlation to experiment.³³ Reduced van der Waals radii are crucial for achieving accurate results in some cases where some movement is required from the protein to adopt a binding conformation that can sterically accommodate ligands. Glide employs reduced atomic van der Waals radii to mimic minor protein readjustments, a critical aspect in the docking protocol that allows for a degree of flexibility with no increase to computational cost. This increased flexibility in the rigid-receptor approximation enhances ligand binding predictions; however, correct ligand docking is still not be achieved.³⁴ It generally works best when the initial protein structure best reflects the binding mode of the specific class of ligands, a reasonable expectation seeing the superficial similarity of the ligand library. The docking was followed by further analysis to better determine the free energy of the complex (and consequently the binding energy) using Prime/MM–GBSA calculations.³⁵ These analyses began with the lowest energy docked conformer in each case, once this pose was visually confirmed to be a reasonable conformer. The MM-GBSA model is a valuable tool for predicting the binding energies between ligands and receptors and is frequently used to evaluate protein ligand interactions, often with good success. However, it simplifies force fields that approximate molecular interactions, often neglecting important electronic effects and quantum mechanical contributions.³⁶ One of the limitations of MM-GBSA is its neglect of certain physics-based corrections, such as entropic effects, which are crucial for accurately predicting binding affinities. To approximate solvent effects, continuum solvent models like the implicit solvent model are commonly used. Although computationally efficient, these models may not fully capture the intricate interactions between the solute and solvent molecules.³⁷ Additionally, MM-GBSA may struggle to accurately capture complex interactions at the ligand-solvent interface, including hydrogen bonding, hydrophobic interactions, and solvent rearrangement effects. The implicit solvent model used in MM-GBSA assumes a uniform dielectric environment, which may not accurately represent the heterogeneous nature of the solvent environment surrounding the ligand.³⁸ To enhance accuracy, researchers integrate MM-GBSA with techniques such as explicit solvent models³⁸ and free-energy perturbation or thermodynamic integration. These techniques can account for entropic contributions and provide more accurate predictions of binding free energy.^39,40 The experimental K_i values, rigid docking scores (RRD) and Prime/MM-GBSA predicted binding free energies are listed in Table 1.

Table 1.

RRD scores, IFD scores, LogP, and predicted binding-free energies (kcal/mol) obtained by Prime/MM–GBSA and Md/MMBGSA of the CB₁ ligands

Ligand	Ki (nM)a	rw scaling factor						IFD docking score (kcal/mol)	LogP	MD/MM-GBSA ΔGbind (kcal/mol)
		Rigid Docking Score (kcal/mol)			Prime/MM-GBSA ΔGbind (kcal/mol)
		1	0.8	0.6	1	0.8	0.6
THCV (1)	2215	−9.12	−8.63	−7.99	−62.09	−54.83	−51.64	−10.81	4.91	−39.09
THCB (2)	158	−9.92	−8.99	−8.24	−62.78	−56.16	−54.25	−10.98	5.3	−43.71
THC (3)	2.913,41	−10.13	−9.07	−8.52	−61.93	−63.9	−55.76	−11.51	5.66	−44.92
THCP (4)	1.27	−5.07	−8.65	−8.02	−57.09	−55.65	−67.06	−11.81	6.44	−47.71
AM11542 (5)	0.1125	−8.51	−8.7	−8.05	−55.01	−68.11	−67.9	−12.65	7.58	−57.48
AM841 (6)	1.1426	−3.03	−11.36	−8.89	−47.7	−77.74	−73.36	−11.73	5.98	−65.25
AM12033 (7)	0.5126	−9.34	−10.03	−9.47	−70.63	−70.08	−73.55	−13.46	4.3	−61.36
AM4030 (8)	0.727,42	−5.44	−8.68	−9.07	−49.09	−64.51	−62.58	−12.28	5.34	−58.92
HU-210	0.7343	−8.68	−9.425	−8.25	−81.01	−68.02	−76.49	−12.18	5.83	−63.78
Nabilone (10)	2.1944	−9.75	−8.53	−7.78	−70.71	−69.33	−68	−11.91	5.5	−53.71
C-Nabilone (11)	1.8244	−5.45	−8.97	−7.51	−64.13	−58.11	−37.19	−11.6	6.72	−63.49
AJA (12)	32.245	---b	−9.45	−7.61	–	−55.43	−43.35	−10.62	5.83	−43.94
THCA (13)	23.5110	–	−5.98	−5.07	–	−34.99	−34.16	−10.89	5.59	−37.53
JWH-051 (14)	1.246	−9.25	−8.61	−6.92	−68.3	−71.1	−71.67	−12.1	6.56	−63.83
C5-AM11542 (15)	10.847	−9.88	−9.59	−7.85	−61.45	−65.45	−66.44	−10.88	5.9	−49.51
Δ8-THCV-C2 (16)	1448	−8.87	−9.27	−7.9	−62.07	−59.49	−61.29	−10.5	5.99	−40.22
Δ8-THCB-C2 (17)	10.948	−8.48	−8.79	−8.15	−66.37	−55.06	−65.55	−10.74	5.59	−43.87
Δ8-THC-C2 (18)	3.948	−8.51	−8.83	−7.8	−63.39	−64.84	−50.54	−11.27	5.79	−52.35
AJA-Aldehyde (19)	2.2444	−7.39	−9.27	−8.03	−64.5	−68.4	−64.81	−12.03	5.70	−54.56
CP55940 (20)	0.5843	−9.45	−8.71	−7.31	−67.49	−58.55	−74.27	−12.35	5.10	−60.67
Win55212-2 (21)	1.949	–	–	−6.25	–	–	−49.21	−12.35	4.15	−54.35

^aFor ligands where multiple K_i values have been reported in the literature, the lowest reported value was selected; with the differences in reported values ranging to an order of magnitude and dependent on the tool used to measure the value, there is error built into our model. The lone exception is for HU-210, where the employed reported value of 0.73 nM is higher than the lowest value, 0.25 nM. This provides better correlation with our model, suggesting that the higher value may prove more correct should the value be redetermined by a third measurement.

^bindicates that the ligand does not dock to the orthosteric binding site of CB₁.

There is only a weak correlation between the experimental values (log K_i(nM)) and the RRD score (kcal/mol; Figures 3A and S1). The Pearson correlation coefficient (R²) is 0.081, 0.065, and 0.110 for r_w scaling factors 1.0. 0.8 and 0.6, respectively. This is an extremely poor correlation. An MM-GBSA refinement does little to improve the correlations, and although it does become statistically significant with r_w scaling factors of 0.8 or 0.6, this remains a poor tool for predicting binding affinity (Figures 3B and S1). This suggests that there might be more adjustments occurring in the receptor depending on very fine details of the ligand than one would necessarily expect based on their similarity by inspection. This both implies that induced docking might prove more useful, and that mechanism might be dependent on minor adjustments to the binding pocket, not a surprise considering the dynamic nature of GPCR orthosteric pockets. Rigid docking is not expected to provide an accurate model alone.

Figure 3.

Correlation analyses between experimental values and computational models

The analyses were conducted for (A) RRD, (B) Prime/MM-GBSA, (C) IFD scores and (D) IFD scores adjusted for lipophilicity. AM11542 and AM12033, the two compounds that are the greatest outliers by IFD docking, are shown in green and purple, respectively.

(E) The reaction path of ligand binding to CB₁ that forms the basis for the need to correct for lipophilicity; the experimentally observed binding affinity (ΔG_Obs) is the combination of two steps, the ligand diffusing into the membrane (ΔG_Mem) and ligand binding CB₁ (ΔG_Bind). Computationally calculated affinities (ΔG_Calc) do not account for ΔG_Mem and assume the ligand enters from bulk solvent.

(F) Qualitative reaction energy diagram showing binding of a ligand to GPCR via the membrane or from solution. ΔG_mem is the energy of the ligand diffusing into the membrane. ΔG_Bind is the binding energy of the ligand from the membrane to the receptor. ΔG_Obs is the binding energy of the ligand directly from the solvent and ΔG^‡_Bind is the energy barrier for the ligand binding from solution.

IFD is far more computationally expensive than RRD, but it allows for considerable flexibility in the binding site residues which works well for systems with moderate differences in the binding mode of various ligands.⁵⁰ This can be important if the initial pocket in a given conformation is too restrictive or permissive to accommodate a ligand (meaning the RRD will be artificially poor), and both the pocket and ligand must mutually adapt to each other when forming a complex.⁵¹ However, IFD can introduce additional errors in measurement if the pocket is too flexible, and can be less useful for prediction than RRD if the ligand classes are all similar to one another. We have used extended sampling which involves a protocol that automates the process of softening potential and trimming side chains in docking studies. This process aims to enhance sampling efficiency and explore a broader conformational space of ligands within the binding site. IFD generally shows better results in reproducing the native conformations of complexes,⁵² and this was used with all 21 ligands (Figure 4C).

Figure 4.

Testing of the binding model against additional binding data not used in the model’s development

(A) Structures of cannabinoids used in the evaluation of the utility of the model.

(B) Plot of IFD scores of this cannabinoid test set against their measured logK_i. Both the uncorrected scores (orange) and lipophilic corrected scores (blue) datasets are provided. Trend lines shown are the same equations as used in Figures 3C and 3D ($K_i=\left(X+13.166\right)/1.1755)$.

(C) IFD scores, LogP, corrected docking score and predicted Ki of the CB₁ ligand test set.

Orthosteric ligands of CB1 enter via the lipid membrane; consequently, it is the concentration in the membrane, not the bulk concentration, that determines the available ligand for binding

Even by inspection, these results seem to reflect what we know from experimental science: increasing the number of side chain carbon atoms in the series from THCV to THCP leads to improved docking scores (Figure S2). Overall, the correlation between the experimental values (log K_i(nM)) and IFD (kcal/mol) has dramatically improved compared to the RRD. The Pearson correlation coefficient (R²) is 0.810 with a ρ-value of <1 x 10⁻⁵ (Figure 3C). However, there are several ligands whose behavior is not consistent, such as AM12033 and AM11542. This could be simply that no model is perfect and that we should be satisfied with a good correlation, or it could be that free energy of binding alone does not model the system correctly.

Let us consider the assumptions of the system. Efficacy depends on several factors beyond simply the affinity of a drug for its target, including the ability of the drug to enter the cell, the stability of the drug over the lifetime of the experiment, and whether it is sequestered through some competing biochemical mechanism. All processes will affect the localized concentration of the drug at the receptor. Generally, for drugs with a similar scaffold, many of these features would be expected to be largely equivalent. Furthermore, most GPCRs —indeed, most membrane proteins— interact with their ligand in the bulk extracellular fluid, so many of these mechanisms are not relevant. However, Class A GPCRs can have their orthosteric site opening into the lipid bilayer, and CB₁ is one such protein.¹ Consequently, the relevant concentration is not the concentration of the drug in solution, but rather the concentration of the drug in the lipid bilayer—these are not the same. The drugs first diffuse into the membrane and only then do they bind to the receptor (Figure 3E). The overall observed experimental binding affinity, ΔG_Obs, is a combination of ΔG_Mem and ΔG_Bind. Consider two drugs with the same binding affinity for a type A GPCR like CB₁ that differ only in their water solubility: hydrophobic A and hydrophilic B. For the same bulk concentration, A would be expected to partition into the lipid bilayer to a greater degree than B. This would give A a higher localized concentration to bind with the GPCR. Cannabinoids enter the cannabinoid receptors via the lipid bilayer.^53,54,55 Recently, Hurst et al. demonstrated using MD that ligands access the binding pockets of other class A GPCRs via the lipid bilayer.⁵⁶ This is consistent with our modeling where during all MD simulations, the orthosteric site’s opening never left the lipid bilayer.

This gives rise to a unique challenge when evaluating the binding affinity ligands with methods such as docking or MM-GBSA, as these methods assume that the ligand is in the bulk solvent. This gives rise to error when calculating desolvation effects as the bulk solvent is significantly more polar than the membrane and do not accurately reflect the ligand binding pathway (Figure 3E). The magnitude of the error is expected to be greater with more lipophilic ligands and is proportional to how likely the ligand is to enter the membrane. The barrier for a hydrophobic ligand to enter the membrane, and subsequently the receptor is likely to be considerably lower (Figure 3F) and more favorable than the ligand entering from solution (ΔG^‡_Bind). Methods which assume that the hydrophobic ligands are resident in solvent place it in an unfavorable environment which results in greater energy difference between the protein-bound and water-solubilized states (ΔG_Bind vs. ΔG_Obs), potentially overestimating their binding affinities, as methods like MM-GBSA calculate binding energy as the difference in energy between the states. They do not account for ligands entering the membrane prior to binding, ΔG_mem, which places them in a more favorable environment resulting in the difference between ΔG_Obs (overall binding free energy) and ΔG_Bind (binding free energy of ligand from the membrane, Figure 3F). ΔG_mem is related to how favorable the partition the ligand into the membrane is and is directly related to lipophilicity. Of course, the difference cannot be distinguished experimentally as only the overall binding can be measured but computationally the failure to account for ΔG_mem results in incorrect calculation of binding affinities. This can be addressed via a lipophilicity correction based on the log_p of the ligand, the partition coefficient between 1-octanol and water.^57,58,59 The prediction of this parameter is a key tool in modern drug design.⁶⁰ We calculated the log_P for all 21 ligands using QikProp (Table 1).⁶¹ We then employed the imperialist competitive algorithm, as implemented in MATLAB,⁶² to generate a series of best fit equations to the dataset with different exponential forms, constants, and relationships between the binding term, derived from the IFD binding, and the hydrophobicity partition term, derived from logP.⁶³ The best fit equation improved the Pearson correlation coefficient square (R²) from 0.81 to 0.92 (Figure 3D), and correctly shifted the “outlier” ligands toward the trend; partitionability into the lipid bilayer explains the discrepancy between AM12033 and AM11542 binding affinity and efficacy. The equation of our fit is as follows:

$${\text{Optimized}\text{Fit}:K}_i=\frac{\left(X+13.166\right)}{1.1755}$$

where K_i is measured in nM and $X=IFDScore-0.03{\left(\text{logP}\right)}^2$. The values of the constants are, of course, empirically derived. A similar solution was recently proposed, in a more general manner, by Morita, Shigeta, and Harada to address a similar challenge.⁶⁴ We see no reason why this same methodology could not be applied to any other system where ligands need to partition into compartments, although permeability functions might prove a more useful parameter if the ligand simply needs to passively pass through a bilayer rather than act from the bilayer as in this case. An enzymatic stability term could similarly be employed for ligands that enter a cell through the lysosome and must survive processing to engage with their target, although this is admittedly a bit more challenging to estimate without enzyme kinetic data for each of the ligands. For a further discussion of this point, please see the supplemental information.

The resulting model can be used to accurately predict the affinity of other ligands for the CB1 receptor

We then looked at how well the model worked to predict the binding affinities of different analogues that were not included in the dataset used to determine the mathematical relationship. We first tested nine other synthetic cannabinoids which were more structurally diverse and not part of the original set to see if the correction improved correlation with experimental data (Figures 4A and 4C). These spanned a range of K_i values from 0.20 to 80 nM. While induced fit docking scores showed good initial correlation (R² = 0.87), this was improved upon inclusion of the lipophilic correction (R² = 0.95) again indicating that lipophilicity of the molecules plays an important role (Figure 4B). Using Equation 1 the docking scores of the compounds, the K_i values of the compounds were calculated. These agreed well with the reported experimental values (Figure 4C). It is important to note that this test dataset is highly structurally diverse, the model is appropriate for ligands of CB1, not just THC-like derivatives, many of these molecules lack the resorcinol-terpene core all together.

We then compared the binding of Δ⁸-THC, whose binding affinity for CB₁ has been variously reported as 44 nM⁶ or 47 nM⁶⁴ with binding predicted by our model. Δ⁸-THC differs from THC only by the location of the olefin in Ring C, meaning we can expect similar lipophilicity and likely a similar binding mode; under this understanding the values do seem rather high compared to that of THC (2.9 nM). Docking the ligand using IFD provided a reasonable conformation, and a calculation of the lipophilicity and its use in our equation estimates a K_i of 11.02 nM (Figures 5C and 5D). This is lower than THC, and while within range of values reported in the literature, is on the lower end. This is important as one of the reports for Δ⁸-THC also estimated the binding affinity of Δ⁹-THC to be 40 nM,⁶ which is an outlier compared to other measurements (see above). Based on our model, we propose that the binding affinity of Δ⁸-THC has been significantly underestimated in reports to date, and its value might benefit from re-measurement.

Figure 5.

The current Structure Activity Relationship understanding of the cannabinoid core

(A) common chemical modifications on THC skeleton and (B) Proposed pharmacophore for classical cannabinoids interacting with CB1 receptors.

(C) structures of Δ⁸-THC, THCN and THCU.

(D) binding poses of THC (beige) and THCN (purple) in complex with CB1. In all figures, oxygen is in red and nitrogen is in blue. H-bonds are represented by yellow dotted lines and π-π interactions by blue dotted lines. Key residues related to the ligands are highlighted in the same color as their present ligand.

The establishment of a standardized dataset of binding data enabled the development of a computational molecular docking model capable of accurately categorizing binding affinity. This model effectively distinguished critical structural characteristics of THC derivatives that either enhance or reduce binding affinity. Using our model and our understanding of the structural features responsible for CB₁ binding (Figure S2), we prophesize two related molecules.

THC has been the subject of many structure activity relationship studies (Figure 5A). Gómez-Jeria et al. developed a pharmacophore model for classical cannabinoid-CB₁ interactions (Figures 5A and 5B).⁶⁵ The C1 phenol group is required for good selectivity for CB₁ over CB₂, and we have already discussed the importance of the alkyl chain. Binding affinity can also be enhanced by hydroxylation of the C11 methyl group as can be seen in the AM-series (Figure 5A).⁶⁶ Using this information, and aiming for synthetic simplicity, we propose two unknown compounds, both simple THC homologues — THCN with 9 methyl groups and THCU with 11 methyl groups. We conducted the IFD and calculated the lipophilicity and then predicted the binding affinity based on our model (Figure 5C). The alkyl side chain of THCN extends perfectly into S-pocket while THCU is too long and does not fit into the orthosteric site; it will not be able to fit in the receptor, and we expect it to be largely inactive (Figure 5D). THCN exhibited a docking score of −12 kcal/mol, translating to a predicted binding affinity of 0.84 nM when considering logP. This forecast is unsurprising, given the maintenance of toggle switch movement in THCU, potentially contributing to its superior predicted binding affinity compared to THC. If this computational model is predictive, it would make THCN the best binding phytocannabinoid-like molecule. The synthesis of these prophesized compounds is currently underway for their evaluation, but we wish to register the prediction in the literature in advance.

It is important to know which one of the reported binding affinities for THC and THCV correlates best with predicted values. We calculated the correlation of experimental binding affinity and IFD score for all ligands except THCV and THC (Figure S3). The Pearson correlation coefficient (R²) was 0.797 or 0.918 for IFD (kcal/mol) and IFD scores optimized with lipophilicity respectively. A calculation of the IFD score and the lipophilicity their processing through our equation estimates a K_i for THCV and THC of 26.9 and 4.1 nM, respectively, which is near the expected values.

Although determining a model for predicting binding affinity of designer cannabinoids is critical to our current research program, affinity, as can be clearly seen, does not define the functional role of the ligand. Tight binders and weak binders can be either antagonists, partial-agonists, reverse agonists, or full agonists. The activity of a ligand arises from the specific of how the ligand interacts with the receptor.⁹ We have not identified a clear theoretical literature model that differentiates between these roles. Consequently, we more closely investigated the binding mode of the homologous series of THCV, THCB, THC, and THCP using IFD as differential receptor response to the ligands likely explains why the first is an antagonist, the middle two partial agonists, and the latter a full agonist (Figure S3). Highly potent agonist AM11542 was included as a control.

THC is a partial agonist because it can occupy both the S and the L pockets and vacillate between them

THCV, THCB, THC, and THCP all adopt similar conformations in the orthosteric ligand-binding site. Their ring systems sit in the M-pocket in nearly superimposable geometries: they only differ in that the alkyl side chains of THCB, THC and THCP protrude into the smaller S-pocket toward the receptor-activating toggle switch (formed by F200 and W356), which does not occur for THCV, which instead extends into the L-pocket (Figures 6A and S3). The phenolic C1-OH of all four cannabinoids forms a hydrogen bond with S173; in the case of THCV and THCB, it forms an additional H-bond with H178. The ring systems, excepting that of THCV, participate in π-π interactions with the receptor’s F170, which sits at the intersection of the three pockets. Hydrophobic interactions help retain the ligands affinity to the rest of the surface, and as expected, these interactions increase in strength as the surface area increases due to a lengthening alkyl chain with the IFD score rising from −10.81 to −11.81 moving through the series from THCV to THCP (Figure 6C).

Figure 6.

Visualization of the calculated binding of CB1 partial agonists and antagonists with the receptor

(A) binding poses of THCV (Cyan), THCB (dark green), THC (orange) and THCP (purple) in complex with CB1 showing the available cavity in mesh (PDB ID: 6N4B).

(B) Alternative view of the same binding poses of THCV, THCB, THC in complex with CB1 with the mesh excluded for clarity.

(C) superimposition of THC@CB1 and TNB@CB1 (gray) ligand-binding pockets; (D) binding poses of THCP and THC in complex with CB1. The oxygen atoms are in red, nitrogen in blue and sulfur in yellow, H-bonds in yellow dotted lines, π-π interactions in blue dotter lines and hydrophobic pocket is bordered in dash dark gray mesh. Key residues related to ligands have the same colors.

(E) IFD scores of the THC homolog ligands when occupying either the S or L-pockets, and the energy difference between the two states. ∗Δ(IFDscore) = IFDscore_(S-pocket)−IFDscore_(L-pocket).

Interested in mechanism, we focused in on the effects that cannabinoid binding has on the dynamics of the toggle switch formed by F200 and W356, respectively located on transmembrane α-helix 3 (TM3) and TM6. When an alkyl chain pushes between them, it forces open the two helices like chopsticks revealing the G-protein binding site on the cytoplasmic face, allowing for binding and activating the receptor.^67,68 Their different positions are best described by comparing their form in the presence of THC and the highly potent inverse agonist Taranabant (TNB, Figure 6C; PDB ID: 5U09).⁶⁹ TNB@CB₁ is akin to the empty inactivated receptor, but reduces its flexibility (hence inverse agonism) locking the two aromatic residues that make up the switch parallel to one another. This holds the transmembrane helices together. The ligand sits in the M-pocket, extending its side chain down the L-pocket with high affinity to prevent other ligands from binding. THC, on the other hand, extending its tail into the S-pocket pushes the residues open activating the receptor.

THC, along with its shorter homologues THCV and THCB, all have similar effects on the toggle switch with the key residues adopting the same conformation in the activated form (Figures 6B and 6C). THCP extends deeper into this pocket, forcing the residues even further apart, further opening up the G-protein binding site, facilitating activity, and helping to explain its full agonist role (Figure 6D). However, this does not explain why the shorter analogues are only partial agonists or why THCV is an antagonist, as they interact the same way. The true story is more complicated.

We then turned to the very potent AM-series analogues. Consistent with the literature and published crystal structures,¹ our model places the C ring system of all ligands into the M-pocket. Most of them extend their alkyl chain into the S-pocket, but that of C5-AM11542-folds back over itself to extend into the L-pocket (Figure S4A). They are all, however, highly effective at forcing open the toggle switch, with the distance between F200 and W356 starting higher than for THC, and increasing in the order of C5-AM11452, AM4030, AM11542, AM12033, and AM841 (Figure S4A). AM11542, C5-AM11542, AM841, and AM12033 each have one π-π interaction with F170. AM841, a covalent inhibitor in its final form, has an extra H-bond with S173 and π-π interaction with F268 when it sits non-covalently in the pocket. The phenolic hydroxyl at C1 of AM12033 forms an H-bond with H178 and the aliphatic OH group at C11 forms two H-bonds with D176 and S173. AM4030 forms an extra π-π with F268 and the OH of the 6β-((E)-3-hydroxyprop-1-enyl) group form H-bond with F268.

Other agonists studied, like HU-210, Nabilone, JWH-051, Δ⁸-THCV-C2, Δ⁸-THCB-C2, and Δ⁸-THC-C2 behave very similarly (Figure S4B). In all cases the S-pocket-occupying side chain forces open the toggle switch. Exceptions are THCA and AJA, which adopt a different conformation in the orthosteric site. The carboxyl group of THCA forms two H-bonds, one with S383, the other with H178, which induces a repositioning of the ring system, and consequently the alkyl chain remains in the atrium between the S- and L-pockets entering neither (Figure S4C). Unusually, the ring system of AJA rotates 180° compared to all other ligands. The carboxyl and phenolic OH- groups form strong H-bonds with K192 and S173, respectively locking this unusual conformation (Figure S4C, found for the lowest 10 energy docking poses); however, this may be an outlier resulting from docking returning an incorrect pose and experiments would be required to determine if this pose is truly how it binds. All poses of C-nabilone show far different binding, with the ring sitting at the intersection of the S- and L-pockets and the alkyl chains sticking up into the M-pocket (Figure S4D). The third lowest energy pose of AJA-Aldehyde is identical to the activation state, and its alkyl chain extends to the S-pocket. Its docking score is also consistent with the equation, and it marginally improves the R-Squared value when added to the training set (≈0.03, Figure S4D).

These lowest energy–docked conformers, however, fail to capture the complexity of the dynamic binding of the phytocannabinoids. THC is a CB₁ partial agonist, meaning that upon binding it does not completely induce the conformational change associated with agonists. There are multiple mechanisms by which this could occur. One would be that in the docked conformation, THC simply does not induce enough pressure on the toggle switch to open the G-protein site. This is not supported by our model, which predicts that it forces a similar conformation onto the protein as full agonists like THCP does. Alternatively, THC might drift away from the core of the orthosteric site and occupy a position higher in the cavity as CBD is predicted to do in the presence of THC. A third possibility is that the alkyl chain can flip from the S-pocket to the L-pocket. Shao et al. computationally docked THC to a relaxed receptor derived from the antagonist TNB-bound structure (PDB: 5TGZ).⁶⁹ They predicted that the alkyl side chain of THC extends just toward toggle residue W356 and would likely activate it as an agonist. Similarly, when Hua et al. docked THC to the full-agonist bound structure (PDB: 5XRA),²⁵ they predicted that THC would behave similarly to AM11542 and that its alkyl side chain of THC extend toward F200 and W356. However, in the docking study accompanying their Cryo-EM structure of CB₁, Kumar et al.²² proposed that THC’s alkyl chain is more flexible and potentially able occupy either the L or S-pockets. This has been further supported by Dutta et al. who, like us, proposed that this “switch hitting” behavior explains the partial agonism of THC.¹⁹ Evidence appears to support that THCV and THCB protrude into the S-pocket toward the toggle switch,^7,8,9 while THCP behaves similarly to THC and occupies the L-pocket.⁷

As this might help mechanistically explain partial agonism, we analyzed the behavior of the alkyl chains of THCV, THCB, THC, THCP and AM11542 in the orthosteric site. We employed IFD and MM-GBSA refinements of conformations of these ligands occupying both the S- and L-pockets and calculated the difference in preference for the two pockets (ΔIFDscore_S/L, Figure 7). Among these ligands only THCV has a positive ΔIFDscore_S/L, meaning that it prefers to occupy the non-triggering L-pocket. This explains why it is an antagonist. However, the side chain is very short and does not extend far into either pocket: even when it does insert into the S-pocket, it does not disrupt the toggle switch residues (Figure 7A). THCV forms similar hydrophobic interactions in both conformations, interacting with S383, C382, F379, I362, L359 and F170. For the slightly longer THCB and THC, the ΔIFDscore_S/L are −0.18 and −0.07, respectively. This is essentially 0, meaning that in both cases we would predict that the ligand fluctuates rapidly between occupying the two pockets. Unlike for THCV, the toggle switch residues do significantly change orientation depending on the location of the alkyl chain (Figure 7B). This arises because although both ligands form the same core interactions at the M-pocket with C382, F379, I362, and F170 (and, for THC, with M363, S383, and L359) regardless of the orientation; they differ in their additional interactions when the alkyl chain enters one or the other pocket (Figure 7C). However, for THCP (Figure 7D) and AM11542, the ΔIFDscore_S/L is high as their alkyl chains are effectively unable to occupy the L-pocket if the ring system is in any reasonable position within the M-pocket.

Figure 7.

Visualization of the calculated binding of CB1 agonists with the receptor

Superimposed docking poses of ligands (A) THCV in the L-pocket (cyan) and S-pocket (blue), (B) THCB in the L-pocket (dark green) and S-pocket (light green), (C) THC in the L-pocket (yellow) and S-pocket (orange), (D) THCP in the L-pocket (purple) and S-pocket (rose-pink). Ribbons are shown in light blue color and residues are colored as same as their related ligands. (E) Distances between TM6 and TM5 from TM1. Used as a surrogate measurement for how open the G-protein binding site is; the greater the value, the more open the G-protein binding site.

This means they are locked into a conformation that forces open the toggle switch. They cannot move their alkyl chain into the non-activating L-pocket. Consequently, when bound, they must activate the toggle switch, explaining why they are full agonists. While we were working on this project, Dutta et al. employed MD simulations to show that THC’s alkyl side chain plays a crucial role in determining its partial agonism.¹⁹ Their research revealed that this side chain is essential for stabilizing the ligand in both agonist and antagonist-like conformations within the receptor binding pocket.¹⁹ Like us, they also showed that it can also fluctuate between the two pockets.

Agonism or antagonism can be predicted based on the induced motions of the TMs induced by the introduction of an orthosteric ligand

We conducted MD simulations for a diverse set of 21 ligands, embedding the CB1 receptor within a phosphatidylcholine (POPC) membrane and solvated with water and NaCl ions to achieve a physiological concentration of 0.15 M. Extending over a 200 ns simulation period, our analysis employed MM–GBSA calculations to estimate binding free energies within the orthosteric site. Notably, our findings revealed a strong correlation (R² = 0.66, Figure S5A) between calculated MM-GBSA values and experimentally determined Ki values, affirming the reliability of our computational approach for predicting ligand binding affinities. However, the addition of the hydrophobicity partition term to the training set did not significantly enhance the Pearson coefficient (0.03), suggesting its limited influence on binding free energy predictions in this context (Figure S5B). MD simulations of THCV, THCB, THC, and THCP and AM11542 in the L- or S-pocket were performed to investigate their effects on CB₁ activation via their interaction with toggle residues and conformational changes in the CB₁ transmembrane helices (RMSD plots are provided as Figure S6). CB₁ activation is characterized by the outward movement of TM5, TM6 and TM7 after the ligand interacts with toggle residues F200 and W356, which opens the G-protein binding pocket. This provides better correlation between MM-GBSA and Ki value (R² = 0.94, Figure S5C) showing the importance of the alkyl chain toward right pocket. GPCR activation and conformational change can take a long time but occurred rather quickly in our simulations with changes observable within the first 200 ns of simulations. MD simulations were also extended up to 1500 ns; however, this only resulted in the eventual movement of ligands out of the long hydrophobic pocket and once ligands (agonists or partial agonists) were no longer interacting with the toggle residues the receptor quickly converted to the inactive conformation, thus the analysis focused on the time frame were ligands remained within the pockets and interacting with the toggle residues to compare differences in receptor activation in these states.

In the case of AM11542, an agonist, clear activation and helix movement is observed when compared to the inactive receptor (Figure 8A). For THCV, very little movement is observed in the helices (Figure 8B). This agrees with the experimental observations that it is an antagonist as receptor activation is not observed. In the cases of THCB, THC, and THCP, some helical movement is observed and a partial opening of the G-protein binding site (Figure 8C, D, and E). The most notable change was observed in THCP which showed the largest movement of TM5 and TM6, though changes were not as pronounced as in AM11542, as THCP had begun migrating out of the binding pocket. In all cases besides THCV, the ligands bound with the side chain in the L-pocket exhibited greater movement in the helices than those in the S-pocket. This partial opening of the G-protein binding site could be the reason that some ligands act as partial agonists or antagonists. It could open just enough for the G-protein to be able to bind; however, as it is not fully open, G-protein binding affinity is decreased and overall, a lower response is observed.

Figure 8.

Superimposed structures of CB1 post MD simulation showing helix movement and receptor activation

(A) AM11542, (B) THCV, (C) THB, (D) THC, and (E) THCP. Superimposed structures of CB1 post MD simulation showing positions of toggle switches F200 and W356 (F) AM11542, (G) THCV, (H) THCB, (I) THC, and (J) THCP. For both sets of images, the receptor with no ligand is represented in green, the receptor/ligand with the ligand originating in the L-pocket are in blue, and the receptor/ligand with the ligand originating in the S-pocket are in orange.

An examination of the distances between the helices, specifically TM5 and TM6, shows an interesting trend (Figure 7E). These helices move the most during receptor activation to open the G-protein binding site. AM11542, a strong agonist, showed the greatest movement of the helices consistent with full activation. In nearly all cases, the ligand with the alkyl chain in the L-pocket resulted in greater receptor activation than when placed in the S-pocket. The exception being THCV; however, both L and S conformations showed minimal movement, and both conformations are consistent with an antagonist.

Taking a closer look at the toggle switches following MD simulations, the reason for the partial loop movement can be observed. The alkyl chain of AM11542 extends deep into the CB₁ pocket, hitting both F200 and W356 of the toggle switch—significant movement is observed for both residues (Figure 8F). In the case of THCV, little movement is observed in the toggle residues, with a slight shift in F200 but not enough to trigger activation (Figure 8G). THCB sits deeper in the pocket and as a result, in addition to this slight shift in F200, W356 also experience a slight shift downward (Figure 8H). THC interacts effectively with F200, and a significant rotation is observed (Figure 8I). Lastly, THCP sits significantly deeper in the pocket and can interact with both toggle residues in a manner like AM11542 (Figure 8J). In all cases, the ligands in the L-pocket resulted in a more significant movement of toggle residues compared to those in the S-pocket.

This indicates that the ability of the ligands to interact with these toggle residues is key to receptor activation and that smaller ligands with shorter chains fail to induce the structural changes required for full activation. Instead, what occurs is a partial activation, characterized by partial movement of TM5, TM6, and TM7, which correlates to the degree of how well the ligands can interact with either F200, W256, or both. This explains why some ligands such as THC behave as partial agonists, despite their high binding affinities and provides insight into the mechanism of partial agonists. This also highlights the importance of looking beyond the binding affinity when designing new ligands for receptors. The method through which they enter the binding pocket, in this case through the lipid membrane, is a key factor, along with the exact binding mode and residues that ligand interacts with. Depending on the active site residues that are interacted with, vastly different biological effects can be observed.

Conclusions

The hydrophobicity of the ligands was found to be essential for modeling and predicting binding affinity as the ligands enter CB₁ through the membrane. We developed a model for predicting binding affinity and activity of cannabinoids which can be used for further drug design efforts in the design of new cannabinoid-based ligands. We also determined that the binding pocket, which the alkyl chain of cannabinoids occupy in the orthosteric site, has a significant impact on their ability to activate the receptor and whether the ligands will act as agonists or antagonists. The ligands have to be able to interact with the toggle residues P200 and W356. How well they interact with the toggle residues also determines the degree of structural change in the receptor. Full agonists induct a larger conformation change in the toggle residues and subsequently TM helices 5, 6, and 7, move outward to open the G-protein binding site. Partial agonists and antagonists were found to adopt an intermediate structure, where the binding site was neither fully open nor fully closed, which could be the cause of reduced activity, despite high binding affinity of ligands. This explanation is likely extendable to other GPCRs with partial agonist activity and a toggle switch. Combined, this gives a more thorough understanding of how ligands interact with CB₁ and receptor activation, which in turn can be used to design and evaluate new cannabinoids.

Limitations of the study

The study provides an in-silico model and explanation for the behavior of ligands at CB1 based on the data available at the time of revision (March, 2025). As more precise data are obtained, the model may be further refined. The model also provides a method for incorporating a correction factor based on membrane-sequestration of ligands for receptors that bind to ligands that must be in the membrane. This correction factor may cease to be needed in the future as computational methods improve to allow for better estimations of entropies of ligand binding and desolvation. This, however, remains a computationally challenging problem and will likely continue to require this kind of adaptation for the foreseeable future.

Resource availability

Lead contact

Further information and requests for resources and reagents should be directed to, and will be fulfilled by, the Lead Contact: John Frederick Trant, jtrant@uwindsor.ca.

Materials availability

No new materials were created for this study.

Data and code availability

• •Data: All input and output files for the computational analyses that are performed in the article, including all docked structures, all apo-protein models, all analyzed cluster representatives from the MD simulations, and all optimized structures of the ligands and proteins, have been deposited at the Borealis Dataverse, available as a single annotated.zip file, and are publicly available as of the date of publication at: https://doi.org/10.5683/SP3/3KJKR8.
• •Code: This paper does not report original code.
• •Other items: Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Acknowledgments

The authors would like to thank the University of Windsor Faculty of Science Research Chair (to J.F.T.) and the Natural Sciences and Engineering Research Council of Canada (2018-06338 to J.F.T.) for providing funding. All authors wish to recognize that this work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca) and Compute/Calculation Canada, now the Digital Research Alliance of Canada (https://alliancecan.ca/en, qkh-310 to J.F.T.). The other authors wish to recognize A.M. and Dania Mousa for preparing the table of contents graphic.

Author contributions

Conceptualization, J.F.T. and F.S.-R.; funding acquisition J.F.T.; investigation, D.M., F.S.-R., A.M.; methodology, all authors; visualization, D.M. and F.S.-R.; project administration, J.F.T.; graphical abstract, A.M.; supervision, J.F.T.; writing – original draft, F.S.-R. and D.M.; writing – review and editing, all authors.

Declaration of interests

J.F.T., D.M., and F.S.-R. are all associated with Binary Star Research Services (BSRM). This generates an apparent conflict of interest. BSRM has no commercial interests in the subject of this manuscript and holds no intellectual property related to this manuscript. The interests of BSRM had no input into the methodology, research goals, or conclusions of this manuscript, and the company does not benefit from the publication of this manuscript nor did any of the authors receive any benefit from BSRM from its preparation or publication. BSRM provided no funding for this project.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
All computational geometries and co-ordinates	This paper, Borealis Dataverse	Borealis, Trant Team Dataverse: http://doi.org/10.5683/SP3/3KJKR8.
Software and algorithms
Schrodinger Maestro Suite (2024)	Schrodinger	Glide Release 2024-4
AMBER22	[ref.,70 Case et al.]	AMBER22
CHARMM	Jo et al.71 and Wu et al.72	CHARMM-GUI
ChemDraw Professional 21.0	Perkin Elmer (deprecated)	21.0.0.28

Method details

General methods

Docking simulations (both rigid and induced fit) were performed, to study the binding of ligands THC- analogues to the cannabinoid receptor 1 (CB1). Docking was performed using the Glide module of the Schrödinger suite.^34,73 This was followed by MM-GBSA calculations to calculate the binding free energy of each protein-ligand complexes which was done using Prime MM-GBSA, also part of the Schrödinger suite.^74,75 Molecular dynamics of the ligands bound to CB₁ were performed using AMBER22 to further study protein-ligand interactions and complex stability.⁷⁰

Protein preparation

The 3D coordinates of the receptors’ complexes for CB₁ (PDB ID: 6N4B)²² were retrieved from the Protein Data Bank; all the crystal waters were removed which had no immediate the interaction between the protein and ligand. The structures were prepared with the Protein Preparation Wizard workflow as follows: adding hydrogen, assigning partial charges using the OPLS3e force field, and assigning pH-appropriate protonation states. Minimization of the structure was considered complete after the root mean square deviation (RMSD) for all heavy atoms exceeded 0.3 Å. The protonation state of the system was set to pH 7.4. The missing ICL3 loop was built using the linker design module in Schrödinger and refined. The structure was then subjected to a short 10 ns MD simulation for receptor relaxation and refinement of the loop.

Ligand preparation

The studied ligands are listed in Table S1. The 3D molecular structures of all compounds were built with the Schrödinger software. The energy minimization was performed using the OPLS3e force field.⁷⁶ Then, all the compounds were prepared using the Ligprep module.⁷⁷

Rigid receptor docking studies

Ligand docking was performed using the GLIDE module⁷³ following grid-based docking protocol. The active site was generated by using the grid generation module ‘Receptor Grid Generation’ by keeping van der Waals radius (r_w) scaling factor 1.0, 0.8 and 0.6 and partial charge cutoff at 0.25 and remaining parameters set as their defaults. Ligands were docked against the predicted active site of the modeled receptor using the Glide XP docking protocol.⁷⁸ The r_w scaling factor for ligand was set to 0.8 in the receptor grid generation. The ligand in the active site was used as the centroid to generate the grid files for the following docking process. The default grid size was adopted from the Glide program. No constraints were applied for all the docking studies. For each compound, a maximum of 10 poses were saved after the docking process.

Induced-fit docking study

To address the flexibility of both ligand and receptor in our docking study, we employed the IFD extended sampling protocol.⁷⁹ Initially docking was performed to the rigid protein using the softened potential docking in the Glide program.⁷⁸ The top 10 poses of each ligand, ranked based on the docking results, were then used to explore protein plasticity using the Prime program in the Schrödinger suite.⁷⁴ Residues within 5 Å of any of the 10 ligand poses underwent a conformational search and energy minimization process, while residues outside this zone remained fixed. This approach ensured comprehensive consideration of protein flexibility. During the subsequent redocking stage, Glide docking parameters were set to the default hard-potential function, and Glide XP (extra precision) was employed for all docking calculations. The binding affinity of each complex was reported using the Glide Score.

Binding-free energy calculation using the Prime/MM-GBSA approach

Prime MM-GBSA³⁵ (Molecular Mechanics–Generalized Born Model and Solvent Accessibility) was used to estimate the ligand binding energies and ligand strain energies of complexes using the OPLS3e force field, VSGB solvent model, and rotamer search algorithms. The Prime MM-GBSA simulation was carried out using the best predicted binding mode of the ligand to calculate the total free energy of binding. The flexible residues distance from ligands was set at 8.0 Å.

The changes of free energy upon binding were calculated by using the following equations:

$$\Delta {\mathrm{G}}_{\text{bind}}={\mathrm{G}}_{\text{complex}}–({\mathrm{G}}_{\text{protein}}+{\mathrm{G}}_{\text{ligand}})$$

Where ΔG_bind is the ligand binding energy, G_complex is the energy of the complex, G_protein is the energy of the receptor without the ligand, and G_ligand is the energy of the unbound ligand.

Molecular dynamics simulations

Receptor-ligand poses obtained from docking were embedded in a phosphatidylcholine (POPC) bilayer using CHARMM-GUI.^71,72 A salt concentration of 0.15 M NaCl was used, and the system solvated using TIP3P water. Ligands used were parameterized using GAFF with charges derived in antechamber using AM1-BCC. MD simulations were performed using AMBER22 using the ff14SB forcefield for proteins, TIP3P water model and lipid14 forcefield for the bilayer. The system was gradually minimized over three minimisation steps each using 5000 steps steepest descent and 5,000 steps conjugate gradient with decreasing restraints of 10, 3 and 0 kcal/mol/Ų. The system was slowly heated to from 0 to 100 K then from 100 K to 300 K using the Langevin thermostat over 100 ps, followed by 50 ns equilibration and 200 ns production for a total of 200 ns. The NPT ensemble was used with periodic boundary conditions and a 2fs time step, 10 Šcut-off, and with SHAKE constrains on hydrogen atoms. Trajectories were analyzed using cpptraj and the last 50 ns of production were clustered to obtain representative structures for further analysis. MD simulations were also extended to 1500 ns to investigate further changes. It was found that the ligands began moving out of the pockets and once the ligands no longer interacted with the toggle residues the receptors of active compounds then became inactive.

Discussion on the implementation of the correction factor to the calculated binding energy to improve correlation to the experimental dissociation constants

As discussed in the article, we have introduced a correction factor to the computationally calculated binding affinity so as to improve the correlation between this calculated value and the experimentally observed Ki values. The observed binding energy is the result of partition of the molecule from solvent into the membrane.

The need for, and the validity of including, an empirical correction factor is worthy of discussion as it is not immediately obvious. As one reviewer rightly noted, the system describes a thermodynamic loop:

$$\Delta {\mathrm{G}}_{\text{obs}}=\Delta {\mathrm{G}}_{\text{Mem}}+\Delta {\mathrm{G}}_{\text{Bind}}=({\mathrm{G}}_{\text{Mem}}-{\mathrm{G}}_{\text{Bulk}})+({\mathrm{G}}_{\mathrm{R}}-{\mathrm{G}}_{\text{mem}})$$ (Equation 1)

Where G_Mem, G_Bulk, and G_R are the free energies of the entire system with the ligand in the bulk solution, in the membrane, and in the receptor, respectively. As G_mem disappears as one solves the equation, the equation of course simplifies to:

$$\Delta {\mathrm{G}}_{\text{obs}}={\mathrm{G}}_{\mathrm{R}}-{\mathrm{G}}_{\text{Bulk}}=\Delta {\mathrm{G}}_{\text{Calc}}$$ (Equation 2)

Consequently:

$$\Delta {\mathrm{G}}_{\text{obs}}=\Delta {\mathrm{G}}_{\text{Mem}}+\Delta {\mathrm{G}}_{\text{Bind}}=({\mathrm{G}}_{\text{Mem}}-{\mathrm{G}}_{\text{Bulk}})+({\mathrm{G}}_{\mathrm{R}}-{\mathrm{G}}_{\text{mem}})=\Delta {\mathrm{G}}_{\text{Calc}}$$ (Equation 3)

This is also the expected conclusion; thermodynamics is path independent and the paths for the two processes are identical, so the thermodynamics must be identical. This seems to imply that no correction is needed and WOULD be true if we were comparing directly measured energy values.

That is not the case. There are a few assumptions built into this model.

The first assumption is that computational ΔG values represent energies that are accurately measured (a stretch for any computational method). This is not necessarily true. The entropic term is often poorly estimated using computationally light, such as induced fit docking or MM-GBSA, calculations. Both docking and MMGBSA algorithms implicitly assume that the ligand comes from solvent (water); these solvation terms are often incorrectly calculated even for ideal cases, but in this case the error is greater as the ligand is in a hydrophobic environment (membrane) prior to entering the receptor—not water. In the case of Glide, there are desolvation penalties for example which would not apply to a ligand that is already inside a membrane. Consequently, like others, we do not attempt to correct the values for the solvent: these scores can use hexanes as the solvent, which would represent the membrane better than water, but the problem is that we do not know what percentage of the molecules are in hexanes (the membrane) and which percentage are present in the bulk water. This means that we need to apply a molar correction to these calculations to calculate the binding affinities.

This matters little if all the molecules under consideration have similar behaviour as these features would all cancel out; however that is not the case for this system—some ligands are highly hydrophobic, some are more hydrophilic. Second, these calculations, when used to compare two molecules, assume the same ratio of ligand and receptor are present for each substrate as all of these calculations are molar free energies. We shall see that this is also perhaps not a completely valid assumption.

Let us now consider the factors that generate an experimental Ki. These dissociation constants in the literature are generally obtained either through radioligand displacement assays (using ^3HHU-243) or calcium flux assays. In both cases one establishes an equilibrium concentration of the ligand to provide the displacement calculation. HU-243 is a highly potent binder with an affinity for CB₁ estimated at 0.041 nM.⁸⁰ This is a stronger binder than any of the molecules used in the dataset. Consequently, the concentration of the other ligands needs to be in significant excess to lead to any meaningful displacement. Due to the vagaries of the CB1 receptor, the concentration that matters for this displacement is the concentration of the ligand in the membrane. The total concentration of the ligand present in solution, although proportional to the membrane concentration (for a given logP), is not the important value (the concentration in the membrane is); but it is this bulk concentration that is both measured and referenced in the Ki value. There are numerous factors that can influence the accuracy of a measured dissociation constant, and these are far more complex for a membrane protein as the concentration of them protein and the bound radioligand can distort numbers precisely for this same reason of partition of the free radioligand between membrane and solution affecting the likelihood of rebinding as is discussed by Hulme and Trevethick.⁸¹ To demonstrate how this can lead to complications, let us consider two hypothetical CB1 ligands, A and B.

Assume that both A & B have the same calculated binding affinity to the receptor through the computational model. This implies that the sum of interactions between the molecules and the receptor along with the sum of energies of desolvation (using whichever solvation model is deployed) are equal. The estimate of desolvation might be quite poor. Now, consider that in this case compound A is quite hydrophilic, while compound B is quite hydrophobic. Compound A will remain largely in bulk solvent, while compound B will largely enter the membrane. This changes the localized concentration of A & B available to interact with the receptor. Calculation wise, we do not discriminate, but experimentally, we would expect more compound B to be found bound to the receptor. Remember that both A and B are in large relative excess to the amount of receptor and HU-243 present. Complete displacement of HU-243 by either the A or B in the membrane is not likely to meaningfully deplete the concentration of either A or B in the membrane (as so little is needed compared to the amount present). The simple computational method considers only a single molecule of A or B, but the experimental value is derived from the ensemble effect of all of the molecules present. The experimental ΔG values, as measured in the form of Ki, are mol fractions. So we could reconsider Equation 3:

$$\Delta {\mathrm{G}}_{\text{obs}}=\Delta {\mathrm{G}}_{\text{Mem}}+\Delta {\mathrm{G}}_{\text{Bind}}=({\mathrm{G}}_{\text{Mem}}-{\mathrm{G}}_{\text{Bulk}})+({\mathrm{G}}_{\mathrm{R}}-{\mathrm{G}}_{\text{mem}})=\Delta {\mathrm{G}}_{\text{Calc}}$$

If both A and B have the same ΔG_Calc, (ΔG_CalcA and ΔG_CalcB), then:

$$\mathrm{n}\Delta {\mathrm{G}}_{\text{MemA}}+\mathrm{n}\Delta {\mathrm{G}}_{\text{BindA}}=\mathrm{n}\Delta {\mathrm{G}}_{\text{MemB}}+\mathrm{n}\Delta {\mathrm{G}}_{\text{BindB}}$$ (Equation 4)

Where n represents an arbitrary number of molecules; equal for both cases as the calculation demands.

However, the observed binding is a function of the concentration of the ligand in the membrane. This is dependent on the hydrophobicity of the molecule. And only a percentage of the ligand will be present in the membrane at any one time. And if the hydrophobicity of the molecules are not the same, we do run into an issue. Let us define χA as the mol fraction of A present in the membrane, and χB as the mol fraction of B in the membrane. We have already stated that:

χB > χA (Relationship 1)

But this then raises a problem, as the observed binding energy will now deviate from the calculated energy, as:

χA ΔG_MemA + ΔG_BindA ≠ χB ΔG_MemB + ΔG_BindB (Relationship 2)

Must follow should Equation 4 and Relationship 1 both be true. This would lead to a deviation of the observed value from the calculated value. Essentially, molecules with higher partition to the membrane than the average in the dataset have higher experimental affinity than predicted by the computational model, and molecules with poorer partition to the membrane than the average of the dataset have lower experimental affinity than that predicted by the computational calculation.

Again, in an ideal situation, this would not occur as A) the calculation would account perfectly for the entropic effects of desolvation, and B) the measured Kis would be true thermodynamic values rather than dependent on relative concentrations, but this is not the case.

A possible solution to this challenge would be provided by a more accurate computational calculation, like the alchemical free energy perturbation approach which does provide a far more accurate measurement of entropy; however, this is not possible in this case as it assumes that the ligands are interacting with the receptor from bulk solvent and that concentrations are equal. Alternatively, were we able to experimentally determine the ratio of the ligand present in the membrane and in the bulk solvent for each ligand, these corrected concentrations could be deployed to correct the Ki values. However, this is a complicated measurement to make. It should be considered that this “fudge factor” is a currently needed correction due to the limitations of the computational models at the present moment, but hopefully can be eliminated in the future as accuracy improves. These are not uncommon, even for the simplest systems, let alone protein-ligand binding;⁸² and a similar method correcting for hydrophobicity was proposed by Harada recently as a general solution.⁶⁴ We also note that the relationship we identify is only valid when one employs the same computational methods and force fields used in the current report. As those continue to improve, the value of the factor will need to be adjusted, and hopefully the term gets smaller, until it can be eliminated all together.

Published: May 21, 2025