1. Introduction

2. Materials and Methods

3. Results

3.1. Crystal Selection and Homology Modelling

After the appropriate structures were selected (Figure 1) homology models were generated (Figure 2). Figure 4 illustrates the structural alignment of p-CBRs, highlighting their similarities and differences. The superimposition of CB₁ (purple) and CB₂ (pink) models allows for a visual comparison of their three-dimensional (3D) structures. This comparison can elucidate variations in their conformations that may relate to their distinct physiological roles, ligand specificities, and signalling mechanisms. Differences in structure between CB₁ and CB₂ are key to understanding their unique interactions with various ligands, which ultimately influences their differing functions in the body. For the p-CB₁ receptor, the intracellular region spans residues 214-409, while the segment embedded within the membrane encompasses residues 12-213 and 410-498. Similarly, the p-CB₂ receptor intracellular region extends from residues 222-381, with its membrane-bound segment comprising residues 20-221 and 382-472 (Figure A2). The Ramachandran statistics in Table 1 indicate that for CB₁ 94.2 % of amino acid residues in the favoured regions, thereby suggesting a reliable model consistent with known protein structural conformations Similarly, Table 1 shows the CB₂ receptor model, with 94.4 % of residues occupying energetically favourable regions, signifying a well-structured protein model. Additionally, a small percentage of residues are in the additional allowed regions, 5.5 % for CB₁ and 5.4 % for CB₂, while an even smaller fraction, 0.2 % for both receptors, are in generously allowed regions. Notably, there are no residues in disallowed regions for either receptor, which further underscores the structural integrity of the models. The distribution of residues within these plots (Figure A3) provides a qualitative measure of the overall quality of the protein homology models. It is a critical step in validating structural predictions for functional analyses.

Table 1. Ramachandran plot statistics for homology models of pseudo CB₁ and CB₂ receptors.

Table 1. Ramachandran plot statistics for homology models of pseudo CB₁ and CB₂ receptors.

Plot Statistics	Endocannabinoid Receptor 1		Endocannabinoid Receptor 2
Residues in most favoured regions	409	94.2 %	385	94.4 %
Residues in additional allowed regions	24	5.5 %	22	5.4 %
Residues in generously allowed regions	1	0.2 %	1	0.2 %
Residues in disallowed regions	0	0.0 %	0	0.0 %
Number of residues present in the structure	478	-	449	-

3.4. Energy Properties

The simulation quality analysis for both CB₁ and CB₂ systems (Tables 2.1. and 2.2.) over a 250 ns period demonstrates a slope energy of zero for all systems showing successful equilibration, with consistent temperatures at ~298 K. For CB₁, the degrees of freedom peak with Taranabant and NADA, while CB₂ displays higher degrees of freedom when interacting with NADA and E3R suggesting a more flexible simulation environment. This implies that the receptor can adopt a variety of conformations which is essential to the receptor's ability to bind to a diverse range of ligands or for the activation of different signalling pathways. When examining the energy properties of CB₁-complexes, the average total energy and potential energy displayed a trend where NADA displayed the lowest energies, suggesting the most stable interaction, aligning with the natural affinity of endocannabinoids for CBRs. The CB₁ apo state showed the highest total energy, which is normal as the unbound state of the receptor may not be the most energetically favourable configuration as ligand binding stabilises the conformation of GPCRs. Pressure variations are observed across all simulations which is normal and expected, as the system is dynamic and subject to fluctuations. These variations reflect the constantly changing interactions among molecules in the system and can indicate the level of system compactness or density . This is important as it helps ensure that the simulated environment behaves in a physically realistic way, which is crucial for the accuracy of the simulation's predictions about molecular behaviour and interactions. Volumetric analysis shows the largest systems with Taranabant for CB₁ and NADA for CB₂, corresponding to expanded receptor-ligand complexes. Each system is equilibrated, thereby confirming the stability of these dynamic molecular systems. The slope energy stability over time, remained at or near zero for all simulations which showed that the receptor maintains a stable conformation across various ligands with minor variations in energy, potentially reflecting different binding affinities and interactions within the binding pocket.

Table 2.1. Simulation Quality Analysis Energy Properties for CB1 Systems.

Table 2.1. Simulation Quality Analysis Energy Properties for CB1 Systems.

Statistical Parameters	Apo	NADA	FUB-MDMB	Taranabant	CBD
Simulation Period (ns)	250.00	250.00	250.00	250.00	250.00
Degrees of Freedom	141853	161211	153736	164349	146648
Number of Atoms	65690	74517	71224	76178	68022
Average Total Energy (kcal/mol)	–116151.80	–125664.51	–124343.60	–123603.39	–121447.47
Average Potential Energy (kcal/mol)	–158158.88	–173394.12	–169867.49	–172266.69	–164876.64
Temperature (K)	298.04	297.97	298.02	298.00	298.05
Pressure (bar)	0.87	1.47	1.25	1.29	1.30
Volume (Å3)	638265.35	723028.60	692012.22	739565.77	661813.67
Slope (ps-1)	-0.001	0.000	0.000	-0.001	0.000

Table 2.2. Simulation Quality Analysis Energy Properties for CB₂ Systems.

Table 2.2. Simulation Quality Analysis Energy Properties for CB₂ Systems.

Statistical Parameters	Apo	NADA	E3R	AM630	CBD
Simulation Period (ns)	250.00	250.00	250.00	250.00	250.00
Degrees of Freedom	150195	154383	153622	140182	144228
Number of Atoms	69961	71701	71400	65151	66969
Average Total Energy (kcal/mol)	–128263.10	–126944.28	–127483.56	–118506.84	–119839.14
Average Potential Energy (kcal/mol)	–172746.90	–172660.86	–172976.50	–160023.83	–162550.75
Temperature (K)	298.08	298.03	298.04	298.07	298.05
Pressure (bar)	1.36	0.70	0.75	1.30	0.86
Volume (Å3)	682471.69	698028.68	695374.07	634755.01	651847.95
Slope (ps-1)	0.000	0.000	0.000	-0.001	-0.001

3.5. Protein Backbone C_α RMSD

The C_α RMSD data for CB₁, as represented in Graph A (Figure 6.1) along with their corresponding PCA plots A – E (Figure 6.2). The endogenous ligand NADA showed a highly stable C_α RMSD, consistently under between a range of 2 Å, aligning with the tight clustering seen in PCA plot B which is line with the ECSs natural affinity for NADA. FUB-MDMB and Taranabant also showed stability from 30 ns into the simulation, however they both displayed an increase in dynamics, shown by a broader spread in their respective PCA plots (C and D), indicating a change in dynamics when bound yet still is still a stable conformation. In contrast, CBD causes a unique conformational change (Figure 6.1A) where CBD exhibits a different C_α RMSD pattern, indicative of an alternative binding mode such as a modulator. CB₂ receptor dynamics shown in Graph B (Figure 6.1) and PCA plots F – J (Figure 6.2) indicate a varied response to ligand interactions. The C_α RMSD for the CB₂ apo form shows natural flexibility, which increases when bound to NADA. These significant C_α RMSD peaks, imply that NADA might induce a range of conformations within CB₂, which is supported by the scattered PCA plot G. The agonist and inverse agonist exhibit C_α RMSD variability, thereby suggesting diverse conformational shifts. CBDs moderate C_α RMSD values display partially agonistic effect on CB₂ receptor conformation. The larger spread in the PCA plots for CB₂ compared to CB₁, correlates with the higher C_α RMSD values observed for CB₂, suggesting that CB₂ may undergo more pronounced conformational changes upon ligand binding. Additionally, both proteins display more dynamism after ~50 ns.

Finally, the scree plots (Figure 6.3) offer a comparative analysis of the PCs that describe the variance in the C_α RMSD of for p-CBRs. For CB₁, PC1 captures a sizeable portion of the variance (46.63 %), suggesting a dominant conformational change. The sharp decline to PC2 and gradual descent thereafter indicates that most of the dynamic behaviour is concentrated in the first two PCs. In contrast, the CB₂ protein exhibits a more even distribution of variance across the PCs, with a less pronounced drop between PC1 (39.38 %) and PC2 (26.95 %), which could imply a more complex ensemble of conformational states or a more evenly distributed set of movements. The differences in the variance distribution between CB₁ and CB₂ suggest distinct conformational flexibility and their different mechanisms of action in response to ligand binding.

Figure 6.1. Stability of ligand-receptor complexes over time C_α RMSD. (A) CB₁ and (B) CB₂ receptor dynamics represented by C_α RMSD measurements in Å over a 250 ns simulation. Each plot tracks the stability of CBRs in their apo form and in complex with various ligands: NADA, an agonist (FUB-MDMB for CB₁ and E3R for CB₂), an inverse agonist (Taranabant for CB₁ and AM630 for CB₂), and CBD. Higher C_α RMSD values indicate greater deviation from the initial structure, reflecting changes in conformational stability.

Figure 6.1. Stability of ligand-receptor complexes over time C_α RMSD. (A) CB₁ and (B) CB₂ receptor dynamics represented by C_α RMSD measurements in Å over a 250 ns simulation. Each plot tracks the stability of CBRs in their apo form and in complex with various ligands: NADA, an agonist (FUB-MDMB for CB₁ and E3R for CB₂), an inverse agonist (Taranabant for CB₁ and AM630 for CB₂), and CBD. Higher C_α RMSD values indicate greater deviation from the initial structure, reflecting changes in conformational stability.

Figure 6.2. PCA of CB₁ and CB₂ C_α RMSD receptor dynamics. PCA scatter plots (A – E) depict the C_α RMSD of various ligand-bound CB₁ systems in comparison to its apo state, while plots (F – J) similarly illustrate the CB₂ receptor dynamics. The spread of data points reflects the conformational diversity sampled during the simulations, with denser clusters indicating more frequently adopted conformations.

Figure 6.2. PCA of CB₁ and CB₂ C_α RMSD receptor dynamics. PCA scatter plots (A – E) depict the C_α RMSD of various ligand-bound CB₁ systems in comparison to its apo state, while plots (F – J) similarly illustrate the CB₂ receptor dynamics. The spread of data points reflects the conformational diversity sampled during the simulations, with denser clusters indicating more frequently adopted conformations.

Figure 6.3. Scree plots for CB₁ and CB₂ protein C_α RMSD variance. (A) depicts the variance explained by the principal components for the CB₁ protein, while (B) shows the same for CB₂.

Figure 6.3. Scree plots for CB₁ and CB₂ protein C_α RMSD variance. (A) depicts the variance explained by the principal components for the CB₁ protein, while (B) shows the same for CB₂.

3.6. Protein Backbone C_α RMSF

The C_α RMSF graph A for CB₁ (Figure 7.1) shows a well-conserved dynamic profile across all residues when in the apo state and when interacting with ligands. NADA has a compact C_α RMSF which indicates a stable receptor-ligand interaction. FUB-MDMB and Taranabant have C_α RMSF peaks in the membrane bound regions that differ when compared to the apo. Therefore, causing subtle conformational changes within the receptor in membrane bound regions. CBD shows a unique C_α RMSF profile to its counterparts especially in the membrane bound region such as between residues, Ile192 – Tyr204 and more residues showing distinct structural changes. Its PCA plot E also suggests a unique binding conformation, highlighting the allosteric or modulatory nature of CBD. CBDs effect on CB₂ presents an C_α RMSF profile with moderate fluctuations, aligning with its potential partial agonistic effect. However, CBD shows to be more dynamic than a full agonist as substantiated by PCA plot J (Figure 7.2). CB₂ displays a broader range of conformational adaptability as evidenced by higher C_α RMSF values and the scattered distribution within its PCA plots, especially in the presence of synthetic ligands. This comparative analysis emphasises the differential conformational responses of CB₁ and CB₂ to various ligands and emphasises the importance of considering receptor flexibility in the development of cannabinoid-based therapeutics. These findings suggest that while CB₁ may have a more rigid binding pocket, conferring specificity, CB₂ flexible nature could allow for broader ligand accommodation, which might be significant for its role in immune modulation. The scree plots provided in figure 7.3 offer a detailed view of the dynamical properties of p-CBRs by analysing the C_α RMSF across PCs derived from a PCA (Figure 7.2). For CB₁, PC1 accounts for a substantial 82.51 % of the total variance, indicating that a single collective motion characterises the flexibility and dynamic behaviour of the protein within the simulation period. This main fluctuation captured by PC1, may be associated with the protein's functional conformational changes or with its interactions with surrounding molecules. The steep drop to 8.05% variance explained by PC2 and even lower for subsequent PCs whereby fluctuations in the context of the protein's dynamics are minimal yet still affect signalling. Similarly, CB₂ protein exhibits a more pronounced dominance in its first principal component (PC1 at 91.42 %), suggesting an even more constrained set of motions across residues, indicative of a more rigid or stable structure. Comparatively, CB₂ displays less diversity in its motion patterns than CB₁, as evidenced by the higher proportion of variance explained by its PC1. This could reflect differences in their respective ECS roles, ligand-binding affinities, and stability. The minimal contributions of higher-order PCs (PC2 through PC5) for both proteins suggest that these additional fluctuations play a lesser role in defining the proteins' overall dynamics yet still influences cellular signalling.

Figure 7.1. Residue flexibility of ligand-receptor complexes. (A) CB₁ and (B) CB₂ C_α RMSF in Å across all residues. These plots illustrate the flexibility of each residue in the apo form and when bound to various ligands: NADA, an agonist (FUB-MDMB for CB₁ and E3R for CB₂), an inverse agonist (Taranabant for CB₁ and AM630 for CB₂), and CBD. The area between the grey lines shows the intracellular regions, while the rest represent membrane-bound regions. Higher C_α RMSF values indicate greater flexibility and potential dynamic regions within the protein structure.

Figure 7.1. Residue flexibility of ligand-receptor complexes. (A) CB₁ and (B) CB₂ C_α RMSF in Å across all residues. These plots illustrate the flexibility of each residue in the apo form and when bound to various ligands: NADA, an agonist (FUB-MDMB for CB₁ and E3R for CB₂), an inverse agonist (Taranabant for CB₁ and AM630 for CB₂), and CBD. The area between the grey lines shows the intracellular regions, while the rest represent membrane-bound regions. Higher C_α RMSF values indicate greater flexibility and potential dynamic regions within the protein structure.

Figure 7.2. PCA of CB₁ and CB₂ C_α RMSF receptor dynamics. Scatter plots from (A – E) represent the C_α RMSF of the CB₁ receptor in its apo form and complexed with various ligands, while plots (F – J) mirror this for CB₂. The scatter of points across the PCA plots reveals the diversity of conformational states examined in the simulations, with areas of higher density indicating a greater frequency of certain conformations by the receptors. These plots provide insights into the flexibility and dynamic behaviour of each receptor-ligand complex.

Figure 7.2. PCA of CB₁ and CB₂ C_α RMSF receptor dynamics. Scatter plots from (A – E) represent the C_α RMSF of the CB₁ receptor in its apo form and complexed with various ligands, while plots (F – J) mirror this for CB₂. The scatter of points across the PCA plots reveals the diversity of conformational states examined in the simulations, with areas of higher density indicating a greater frequency of certain conformations by the receptors. These plots provide insights into the flexibility and dynamic behaviour of each receptor-ligand complex.

Figure 7.3. Scree plots for PCA of Cα RMSF in CB1 and CB2 proteins. (A) Presents the scree plot for CB1, and (B) for CB2. The plots illustrate the proportion of total variance in atomic fluctuations captured by each PC, indicating the relative significance of these components to the overall movement observed in the proteins.

Figure 7.3. Scree plots for PCA of Cα RMSF in CB1 and CB2 proteins. (A) Presents the scree plot for CB1, and (B) for CB2. The plots illustrate the proportion of total variance in atomic fluctuations captured by each PC, indicating the relative significance of these components to the overall movement observed in the proteins.

3.7. Protein Backbone Cα Radius of Gyration

The RoG of CB₁ (Figure 8.1 A) remains consistent in the apo form, suggesting a stable and well-folded state. Upon binding with Taranabant, the receptor has a lower level of compactness, as indicated by the RoG values while CBD increase the compactness, implying that these ligands significantly perturb the overall folding and stability of the receptor when compared to the apo. Interestingly, towards 200 ns CBDs interaction with CB₁ shows a minor increase in RoG variability, suggesting subtle differences in the receptor’s compactness and perhaps slight changes in the folding dynamics, which is reflected in PCA plot E (Figure 8.2) with a slightly more dispersed cluster. The RoG plot for CB₂ exhibits greater variability, particularly in response to ligand interactions, signifying a more dynamic structural behaviour. The receptor in its apo state already shows a higher degree of fluctuation, indicating intrinsic flexibility. Upon binding with ligands such as NADA and E3R, spikes in RoG values are observed, indicative of transient expansions in the receptor's structure, which represent regions undergoing conformational changes. The inverse agonist AM630 also causes significant fluctuations in RoG, further emphasising the dynamic nature of CB₂ and its diverse ligand-induced states. These variations in protein compactness and folding dynamics are crucial for understanding the allosteric effects of ligand binding and the resulting functional outcomes.

The PCA of the RoG for p-CBRs (Figure 8.3) provides insightful data on the intrinsic flexibility and the dynamic nature of these proteins. The relatively even distribution of variance explained across the initial five PCs for both CB₁ and CB₂ suggests a complex interplay of gyrations within their structures. Specifically, CB₁ demonstrates a relatively uniform decline in variance explained, with PC1 accounting for 23.9 %, and a gradual decrease to 16.3 % by PC5. This uniformity in variance distribution could indicate that no single conformational change dominates the dynamic behaviour of CB₁, implying a more distributed and nuanced gyration pattern that may facilitate its interaction with various ligands. Similarly, CB₂ RoG variance follows a close pattern with PC1 explaining 23.7 % of the variance, only marginally less than that of CB₁, and PC5 accounting for 17.1 %. This suggests that CB₂ also does not rely on predominant conformational changes, but rather a combination of motions contributing to its dynamic profile. The slightly higher variance captured by the first PC in both receptors might reflect the overall size and conformational changes, which are critical for understanding how these receptors adapt and respond to different ligands. The subsequent PCs capturing a substantial portion of variance indicate multiple, significant conformational fluctuations rather than a single, dominant motion, which is typical for flexible proteins that interact with diverse molecules.

Figure 8.1. C_α Protein compactness analysis over time. (A) CB₁ and (B) CB₂ receptors structural compactness, indicated by the radius of gyration in measured in Å over a simulation period of 250 ns. The graphs compare the RoG of the apo CBRs to their complexes with NADA, agonists (FUB-MDMB for CB₁ and E3R for CB₂), inverse agonists (Taranabant for CB₁ and AM630 for CB₂), and CBD. .

Figure 8.1. C_α Protein compactness analysis over time. (A) CB₁ and (B) CB₂ receptors structural compactness, indicated by the radius of gyration in measured in Å over a simulation period of 250 ns. The graphs compare the RoG of the apo CBRs to their complexes with NADA, agonists (FUB-MDMB for CB₁ and E3R for CB₂), inverse agonists (Taranabant for CB₁ and AM630 for CB₂), and CBD. .

Figure 8.2. PCA of CB₁ and CB₂ radius of gyration. The PCA scatter plots from (A – E) correspond to the CB₁ receptor in its apo state and complexed with various ligands: NADA, FUB-MDMB, Taranabant, and CBD. Similarly, plots from (F – J) represent the CB₂ receptor in its apo state and in complex with NADA, E3R, AM630, and CBD. These plots assess the overall compactness of the protein-ligand complexes over the course of simulations, with the RoG serving as an indicator of the protein's structural integrity and folding dynamics.

Figure 8.2. PCA of CB₁ and CB₂ radius of gyration. The PCA scatter plots from (A – E) correspond to the CB₁ receptor in its apo state and complexed with various ligands: NADA, FUB-MDMB, Taranabant, and CBD. Similarly, plots from (F – J) represent the CB₂ receptor in its apo state and in complex with NADA, E3R, AM630, and CBD. These plots assess the overall compactness of the protein-ligand complexes over the course of simulations, with the RoG serving as an indicator of the protein's structural integrity and folding dynamics.

Figure 8.3. Comparative PCA of CB₁ and CB₂ radius of gyration. (A) The scree plot for the CB₁ receptor's RoG across the first five PCs. (B) The scree plot for the CB₂ receptor's RG across the first five PCs. Each plot illustrates the percentage of total variance explained by the corresponding PC, highlighting the distribution of conformational flexibility within the protein structure.

Figure 8.3. Comparative PCA of CB₁ and CB₂ radius of gyration. (A) The scree plot for the CB₁ receptor's RoG across the first five PCs. (B) The scree plot for the CB₂ receptor's RG across the first five PCs. Each plot illustrates the percentage of total variance explained by the corresponding PC, highlighting the distribution of conformational flexibility within the protein structure.

3.8. Simulation Trajectory Snapshots

The series of structural snapshots presented in Figure 9.1 shows a vibrant depiction of the dynamic nature of CB₁ and CB₂ receptors in the context of their membrane-bound regions over a 250 ns MD simulation. The colour gradient from blue to red effectively illustrates the temporal progression of the simulation, where the blue structures represent the starting conformations, and the red structures signify the conformations at the end of the 250 ns simulation period. For CB₁ in its apo state, the snapshots indicate a high degree of structural conservation with minor deviations from the initial conformation, suggesting a relatively stable receptor in the absence of a ligand. When bound to NADA, CB₁ exhibits subtle conformational adaptations, demonstrating the natural ligand's compatibility with the receptors active site. The structural changes are more pronounced with synthetic ligands such as FUB-MDMB and Taranabant, where the snapshots reveal greater shifts, especially in the transmembrane domains. CBDs interaction with CB₁ has deviations in its structure, thereby showing the structural changes over time influencing the structures signalling properties. In comparison, CB₂ apo snapshots also show a more dynamic conformational baseline, yet the presence of NADA has more noticeable shifts throughout the simulation, indicating a dynamic interplay between the receptor and its endogenous ligand. Synthetic agonists like E3R and the inverse agonist AM630 produce significant conformational changes in CB₂ suggesting a more flexible receptor that can accommodate various ligand-induced states. CBD's interaction with both receptors results in unique changes in CB₁, implying its modulatory role while CBD acts as a partial agonist in CB₂.

The ligand conformational snapshots over 250 ns in Figure 9.2 provide an intricate depiction of how various ligands occupy the binding sites of both p-CBRs, highlighting the dynamic nature of their interactions and the conformational flexibility within the protein environment. In A and C (Figure 9.3), NADA, and the synthetic agonist FUB-MDMB express a range of orientations within the CB₁ binding site, with NADA showing a more focused array of two main conformations. One conformation is predominant at the start of the simulation, whereas the second stabilises later, indicating a precise fit within its endogenous receptor. FUB-MDMB also follows a similar pattern but shows more alternative binding modes suggesting a more adaptable interaction space. Taranabant, shows an even more diverse conformational spread, potentially reflecting its ability to induce various inactive receptor states, each with distinct structural configurations. NADAs interactions with CB₂ show more flexibility compared to CB₁, with NADA showing more conformational range. This might relate to CB₂ role in modulating immune functions, requiring adaptability to a broader spectrum of endogenous ligand shapes. The synthetic agonist E3R shows one main conformation and the inverse agonist AM630 exhibits an extensive range of conformations, indicative of its capacity to explore and stabilise various inactive receptor conformations, which may correspond to different signalling outcomes or binding affinities with other ligands. The visual representation of CBD within the CB₁ binding site reveals a significant conformational range, as denoted by the spread from the initial blue conformations to the final red conformations. The spectrum of conformations suggests that CBD interacts with the CB₁ receptor in a versatile manner, potentially influencing various signalling pathways by inducing multiple receptor states. This aligns with CBDs known pharmacological profile as a compound with multiple mechanisms of action, including its role as a negative allosteric modulator that can alter receptor responsiveness. Similar to its interaction with CB₁, CBD exhibits a variety of conformations within the CB₂ binding site. However, the spread of conformations for CB₂ appears to be slightly more constrained compared to CB₁, which may reflect the distinct roles these receptors play in physiological processes. The dynamic interaction of CBD with CB₂ might contribute to its therapeutic effects related to the immune system and inflammation, as CB₂ is predominantly expressed in immune cells.

Figure 9.1. Membrane-bound conformational snapshots over 250 ns. These figures highlight a series of secondary structural snapshots of CB₁ and CB₂, capturing the conformational changes between the membrane bound region. This illustrates the dynamic behaviour of the receptors in their apo state and when bound to various ligands: (A – E) NADA, FUB-MDMB, Taranabant, and CBD for CB₁, and (F – J) NADA, E3R, AM630, and CBD for CB₂. These snapshots highlight the flexibility and the varying degrees of conformational states that each receptor-ligand complex can adopt over 250 ns.

Figure 9.1. Membrane-bound conformational snapshots over 250 ns. These figures highlight a series of secondary structural snapshots of CB₁ and CB₂, capturing the conformational changes between the membrane bound region. This illustrates the dynamic behaviour of the receptors in their apo state and when bound to various ligands: (A – E) NADA, FUB-MDMB, Taranabant, and CBD for CB₁, and (F – J) NADA, E3R, AM630, and CBD for CB₂. These snapshots highlight the flexibility and the varying degrees of conformational states that each receptor-ligand complex can adopt over 250 ns.

Figure 9.2. Ligand conformational snapshots over 250 ns. This figure presents overlaid conformations of ligands within the binding sites of CB₁ and CB₂. The snapshots depict the flexibility and range of orientations for NADA, FUB-MDMB, Taranabant, and CBD when bound to CB₁ (A – D) and NADA, E3R, AM630, and CBD when bound to CB₂ (E – H). These visualisations emphasise the dynamic nature of ligand-receptor interactions and the conformations they exhibit within the protein environment.

Figure 9.2. Ligand conformational snapshots over 250 ns. This figure presents overlaid conformations of ligands within the binding sites of CB₁ and CB₂. The snapshots depict the flexibility and range of orientations for NADA, FUB-MDMB, Taranabant, and CBD when bound to CB₁ (A – D) and NADA, E3R, AM630, and CBD when bound to CB₂ (E – H). These visualisations emphasise the dynamic nature of ligand-receptor interactions and the conformations they exhibit within the protein environment.

3.9. Ligand RMSD and Simulation Protein-Ligand Interactions

Figure 10 showcases the ligand RMSD trajectories for both CB₁ and CB₂ receptors over a simulation period of 250 ns, providing a quantitative depiction of the stability and conformational changes of various ligands while bound to CBRs. The lig-RMSD trajectory (Figure 10) NADA bound to CB₁ demonstrates a stable interaction towards the end of the simulation with all ligands reaching stability at ~185 ns in the simulation. FUB-MDMB, exhibits a slightly higher lig-RMSD, indicating a more flexible interaction compared to NADA but still within a range suggestive of consistent binding. Taranabant, shows increased fluctuations at first then stabilises, reflecting its potential to induce diverse conformations in the receptor, which may correlate with its inverse agonistic activity. CBDs trajectory is characterised by a moderate level of fluctuation, consistent with its role as a modulator, potentially affecting the receptor conformation and thereby its signalling pathways. CB₂ lig-RMSD for NADA with CB₂ shows more pronounced fluctuations compared to CB₁, hinting at a more flexible interaction or multiple binding conformations within this receptor. E3R, another synthetic agonist, presents a lig-RMSD profile with significant variation, suggestive of a dynamic binding that may promote a range of receptor states. AM630, as an inverse agonist, displays a highly variable lig-RMSD, indicative of its ability to stabilise CB₂ in multiple conformations, potentially inactive ones. CBD with CB₂ exhibits a similar pattern to that observed with CB₁, with fluctuations that are indicative of its modulatory influence on the receptor dynamics. The overall lower lig-RMSD values for CB₁ across all ligands imply a tighter and more consistent binding pocket, which may influence the receptor's signalling specificity. The greater variability in lig-RMSD for CB₂ suggests a more adaptable ligand-binding environment, which could allow for a wider range of physiological responses. The differences in lig-RMSD profiles for synthetic agonists and inverse agonists when compared to NADA underscore the potential for these compounds to elicit varied therapeutic effects.

Figure 10. Ligand-RMSD trajectories relative to protein. (A) illustrates the RMSD of each ligand when bound to the CB₁ receptor, and (B) displays the same for the CB₂ receptor, over a simulation time of 250 ns. Each trace represents the RMSD of ligand atomic positions relative to their initial frame, providing a measure of the ligands stability and conformational changes while bound to the receptor. The ligands include NADA, an agonist (FUB-MDMB for CB1 and E3R for CB2), an inverse agonist (Taranabant for CB₁ and AM630 for CB₂), and CBD. Stable RMSD values suggest a consistent interaction with the receptor, while fluctuations indicate dynamic binding and conformational adaptability.

Figure 10. Ligand-RMSD trajectories relative to protein. (A) illustrates the RMSD of each ligand when bound to the CB₁ receptor, and (B) displays the same for the CB₂ receptor, over a simulation time of 250 ns. Each trace represents the RMSD of ligand atomic positions relative to their initial frame, providing a measure of the ligands stability and conformational changes while bound to the receptor. The ligands include NADA, an agonist (FUB-MDMB for CB1 and E3R for CB2), an inverse agonist (Taranabant for CB₁ and AM630 for CB₂), and CBD. Stable RMSD values suggest a consistent interaction with the receptor, while fluctuations indicate dynamic binding and conformational adaptability.

The images (Figure 11) depict molecular structures of ligand atom contacts in complex with p-CBRs for more than 30.0% of the time during molecular dynamic simulations. Each ligand shows a distinct chemical structure with various functional groups that influence their interaction with the protein residues. NADA in both CB₁ and CB₂ complexes, NADA has a dopamine moiety that can be identified by its catechol structure and a long unsaturated fatty acid tail, which is a characteristic feature of endocannabinoids. NADA complexed with CB₁ has several key interactions such as the longest interaction between Ile179 and the NH group for 59% of the simulation while the O group attracted Met15 for 48 % of the simulation suggesting a stable hydrogen bond, potentially critical for signal transduction. The NH group of CB₂ complexed with NADA was in contact with Thr113 for 94 % of the simulation while a notable water was present at the OH group along with Ser415 (Fig 12). The other OH group was in contact with Ser179 for 75 % of the simulation showing a network of hydrogen bonds that might stabilise specific receptor conformations conducive to signalling.

FUB-MDMB shown in the CB₁ complex, is a synthetic compound with a distinct indazole core with potentially high binding affinity due to its rigid structure. Alternatively, CB₂ receptor agonist has two distinct π-π stacking bonds with its aromatic ring with residues Phe86 and Phe182 for 88 % and 66 % for the simulation, respectively. This stacking could be pivotal for stabilising the receptor in an active conformation, enhancing signal transduction. For the inverse agonists, Taranabant and CB₁ has a more complex structure with multiple rings, which may contribute to its activity as an inverse agonist, potentially blocking the receptors active site and preventing activation with three main contacts influencing its binding such as π-π stacking with Phe20 while the N group attracted Phe82 and Ser460 attracted the NH group. For CB₂, AM630 has a biphenyl structure linked to a heterocyclic moiety with a key π-π stacking interaction with Phe86 follows a similar pattern as CB₁, with π-π stacking interactions suggesting a potential lock on the receptor's conformation, which may reduce its ability to signal. Present in both CB₁ and CB₂ complexes, CBD is a well-known cannabinoid with a resorcinol core and a pentyl chain. Notably, water molecules in both complexes mediate interactions with the OH groups; in CB₁, they facilitate hydrogen bonding between OH and Met15, as well as OH and Ile179. In the CB₂ complex, water is attached to both the OH group and Ser460. For CB₁, the water-mediated hydrogen bonds suggest a dynamic modulation of receptor conformation. This water bridge could be essential for CBDs ability to modulate receptor activity subtly, rather than inducing a rigid active or inactive state. Such modulation could lead to nuanced signalling outcomes, which aligns with the known diverse physiological effects of CBD.

Figure 11. Post-MD simulation ligand-contact summary. This figure compiles a visual representation of sustained ligand-protein interactions within the binding sites of CB₁ and CB₂ receptors throughout molecular dynamic simulations. (A – D) illustrate the contact profiles for the following ligands with CB₁ with (E – H) depicting the ligand interactions with CB₂: These images capture the intricate contact dynamics and diverse orientation landscapes that ligands adopt within the protein environment, emphasising the variable and complex nature of ligand-receptor interplay.

Figure 11. Post-MD simulation ligand-contact summary. This figure compiles a visual representation of sustained ligand-protein interactions within the binding sites of CB₁ and CB₂ receptors throughout molecular dynamic simulations. (A – D) illustrate the contact profiles for the following ligands with CB₁ with (E – H) depicting the ligand interactions with CB₂: These images capture the intricate contact dynamics and diverse orientation landscapes that ligands adopt within the protein environment, emphasising the variable and complex nature of ligand-receptor interplay.

3.10. Water Analysis

The distance of the water molecule 9906 (Figure 12) demonstrates a notable stabilisation in its role as a bridge between the OH group of NADA and the Ser415 residue of CB₂. Initially, the distance between the interacting entities fluctuates, as indicated by the variable peaks early in the simulation. However, at ~ 45,000 ps into the simulation, we observe a significant change whereby the distance distinctly stabilises, hovering around a much lower value, indicative of a stable interaction being established. This stabilisation suggests that water 9906 has found an energetically favourable position where it can effectively mediate an H bond between the ligand and the receptor. The persistent short distance after 40,000 ps indicates that the water molecule maintains this bridge consistently for the remainder of the simulation. The implications of such a stable water bridge in the context of a lipid bilayer are interesting as the bilayer's hydrophobic environment typically restricts polar interactions to the periphery of the membrane, yet water 9906's persistent interaction deep within the membrane interface suggests a significant structural feature. This water bridge may play a crucial role in maintaining the conformational stability of the ligand-receptor complex, enabling correct signalling function such as a modulator. The provided plot (Figure 12) captures the intricate fluctuations between water molecule 11077 and residue Ile179 within the CB₁ receptor, complexed with CBD, over 250 nanoseconds. This variability in proximity suggests a non-static interaction, which is significant within the typically hydrophobic environment of the lipid bilayer. The water molecules (11077) recurring proximity to Ile179 suggests its potential influence on the receptor conformation and, consequently, on signal transduction mechanisms. Despite the variability, the intermittent closeness to Ile179 implies episodic bridging interactions that may be integral to the modulation of CBDs influence on the CB₁ receptor. The presence of a water molecule in the hydrophobic environment of a lipid bilayer is noteworthy, as it suggests an energetically favourable interaction that overcomes the hydrophobic exclusion effect This can be indicative of a polar pocket or channel within the receptor that can accommodate water molecules, potentially impacting the receptor's conformation and function when interacting with CBD to enable it to act as a modulator much like CB₂ in complex with NADA.

Figure 12. Interaction dynamics of water molecules 9906 with CB₂-NADA Complex and Water 11077 with CB₁-CBD Complex. This graph depicts the fluctuating distance (Å) between water molecules over the course of a 250 picosecond molecular dynamics simulation. The water (9906) stabilisation observed after 45 picoseconds highlight the formation of a significant water bridge, integral to the interaction network within the binding pocket. Water 11077 shows the dynamic nature of water molecule interactions within the receptor's binding site, with distance variations suggesting transient stabilising events.

Figure 12. Interaction dynamics of water molecules 9906 with CB₂-NADA Complex and Water 11077 with CB₁-CBD Complex. This graph depicts the fluctuating distance (Å) between water molecules over the course of a 250 picosecond molecular dynamics simulation. The water (9906) stabilisation observed after 45 picoseconds highlight the formation of a significant water bridge, integral to the interaction network within the binding pocket. Water 11077 shows the dynamic nature of water molecule interactions within the receptor's binding site, with distance variations suggesting transient stabilising events.

4. Discussion

5. Conclusions

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