The conceptual DFT approach (Domingo et al., 2016; Frau and Glossman-Mitnik, 2017; Frau and Glossman-Mitnik, 2018) was used to evaluate the global reactivity descriptors, such as chemical potential (μ), electronegativity (χ), hardness (η), softness (s), and electrophilicity index (ω), from the Frontier molecular orbitals energies, E_HOMO and E_LUMO, using the following equations: μ = (E_HOMO + E_LUMO) ⁄ 2; χ = −(E_HOMO + E_LUMO) ⁄ 2; η = E_LUMO−E_HOMO; s = 1 ⁄ η, ω = μ² ⁄ 2η. In addition, the local reactivity descriptors, such as the Fukui functions f ( r )   for electrophilic f − ( r ) and nucleophilic f + ( r ) attacks, and the dual descriptor f ( 2 ) ( r ) was calculated using the following equations: f k − = q k ( N ) − q k ( N − 1 ) ; f k + = q k ( N + 1 ) − q k ( N ) ; f k ( 2 ) = f k + − f k − , where q k are the electronic population of the kth atom of the molecule with N − 1 , N , and N + 1 electrons (Yang and Mortier, 1986; Morell et al., 2005). Hirshfeld population analysis was carried out by using the Multiwfn program (Lu and Chen, 2012). The Parr functions P ( r ) for electrophilic P − ( r ) and nucleophilic P + ( r ) attacks were performed using the equations: P k − = ρ k rc ; P k + = ρ k ra , where ρ k rc   and ρ k ra is the atom spin density (ASD) of the kth atom at the cation and the anion of the molecule, respectively (Chamorro et al., 2013; Domingo et al., 2013). The data of the optimized conformers of anandamide were obtained from the BP86 functional (Becke, 1988) and cc-pVTZ basis set (Dunning, 1989) in chloroform solvent, as previously reported (Rangel-Galván et al., 2022a). DFT calculations have been shown to be a reliable tool to analyze reactivity descriptors within the framework of conceptual DFT (De Proft et al., 2003; Vivas-Reyes et al., 2003; Vivas-Reyes et al., 2008). Calculations were carried out using the Gaussian16 program (Frisch et al., 2016).

Topological parameters, based on the QTAIM approach (Matta and Boyd, 2007; Hernández-Paredes et al., 2017; Bayat and Fattahi, 2019), were calculated, such as electronic density, ρ ( r ) , the Laplacian, ∇ 2 ρ ( r ) , the Lagrangian kinetic energy, G, the Hamiltonian kinetic energy, H, the potential energy density, V, the interaction energy, E _{H … Y} , the interatomic distance D _inter , and the delocalization indexes, DI, in order to characterize the hydrogen bonds and other intramolecular interactions in the anandamide conformers. The intramolecular hydrogen bond in the ethanolamide (EA) group was evaluated in the anandamide conformers with the closed ring. These topological properties were calculated using the equations: H ( r ) = G ( r ) − V ( r ) , and E H ⋯ Y = 1 2 V ( r ) . The QTAIM calculations were performed using the AIMAll (Version 17.11.14) program (Tood, 2017).

Molecular docking calculations were carried out for the Ca_v3.2 calcium channel and the conformers of anandamide. The rigid blind docking was performed using the AutoDockVina (version 1.1.2) program (Trott and Olson, 2010). AutoDockVina uses a genetic algorithm as a searching method and the binding free energy parameter (−ΔG) as the scoring function. The binding free energy is calculated through the equation: c = ∑ i < j f t i t j ( r i j ) , where each atom i is assigned an atom type t i , and f t i t j are a symmetric set of interaction functions occurring at the interatomic distance r i j . The sum can be seen as the addition of the intermolecular and intramolecular contributions of all the pairs of atoms interacting with each other. The optimization algorithm finds the global minimum c in terms of the free energy values obtained for each conformation (Trott and Olson, 2010). The grid dimension space was 90 Å × 110 Å × 110 Å, containing the entire receptor structure. The default exhaustiveness value of 8 and 80 were used with 10 resulting poses. The structures of anandamide conformers, used as ligands, were obtained from the optimized structures at the BP86/cc-pVTZ level of theory in chloroform solvent (Rangel-Galván et al., 2022a). The Ca_v3.2 structure, used as the receptor, was taken from the homology model previously reported (Rangel-Galván et al., 2022b). The ligand Gasteiger charges were calculated and hydrogen atoms were added with Autodock tools (Sanner, 1999). The interactions were visualized with PyMOL v2.0 (Schrödinger, 2017).

Six minimum energy structures for anandamide were selected for the conceptual DFT analysis: extended with closed EA ring (E_closed), extended with open EA ring (E_open), U-shape with closed EA ring (U_closed), U-shape with open EA ring (U_open), hairpin with closed EA ring (H_closed), and hairpin with open EA ring (H_open). Global reactivity descriptors for the six conformers of anandamide E_closed, E_open, U_closed, U_open, H_closed, and H_open, were evaluated: chemical potential (μ), electronegativity (χ), hardness (η), softness (s), and electrophilicity index (ω), according to conceptual DFT approach (Domingo et al., 2016; Frau and Glossman-Mitnik, 2017). Table 1 summarized the HOMO and LUMO energies and the global reactivity descriptors for the conformers of anandamide.

For the E_closed/E_open, U_closed/U_open, and H_closed/H_open shapes of anandamide, in Table 1 it is observed that there are no significant changes when anandamide changes the curvature of this structure. Some slight differences are found in hardness, softness, and the electrophilicity index. The hardness increases a 4.6/3.5 and 7.4/6.3% for U_closed/U_open and H_closed/H_open shapes, respectively, relative to the E_closed/E_open conformers. The softness suffers a decrement keeping the same proportion. Finally, a decrease of the electrophilicity index of 3.3/3.6 and 10.6/12.0% is observed for U_closed/U_open and H_closed/H_open shapes, respectively, with respect to the E_closed/E_open conformers. The effect of the ethanolamide (EA) open ring conformers in comparison with the corresponding closed shapes is seen in slight differences, an increase in chemical potential, and a decrease in electronegativity and electrophilicity index. For example, for the electrophilicity index, the decrease represents a 2, 2.3, and 3.5% for E_open, U_open, and H_open with respect to their corresponding closed shapes.

In addition to anandamide as a dual ligand for the T-type calcium channels and the cannabinoid receptors, the NMP compounds have been shown to be capable of binding both proteins (You et al., 2011; Gadotti et al., 2013; Bladen et al., 2015), which is relevant in the treatment of pain disorders.

Taking into account the conceptual DFT analysis previously executed for the NMP compounds, the global reactivity descriptor that changes the most when anandamide and NMP compounds are compared (NMP-7 and H_closed shape for representation), is the hardness of 51%, from 4.76 eV in the H_closed conformation of anandamide and 3.14 eV in the NMP-7 ligand (Rangel-Galván et al., 2022b). Anandamide has a higher resistance to changing electronic distribution compared to the NMP compounds (Rangel-Galván et al., 2022b). It is worth mentioning that significant changes in the hardness index have been observed when a ligand-receptor interaction process is modeled (Aliste, 2000). The electrophilicity index is another uneven descriptor; a higher value corresponds to the NMP compounds with respect to anandamide conformers with a difference of 37.6%. The electrophilicity index results are well correlated to the receptor affinity properties and biological activity (Parthasarathi et al., 2004).

Respect the local reactivity descriptors, Table 2 shows the condensed Fukui functions, f + ( r ) and f − ( r ) , the dual descriptor, f ( 2 ) ( r ) , and the Parr functions, P − ( r ) and P + ( r ) , the conformers of anandamide with a closed ring of ethanolamide (EA). For E_closed, U_closed, and H_closed shapes of anandamide, values of Fukui functions were found in the ranges f ⁺ = 0.007–0.071 and f ^– = 0.007–0.053 for E_closed, f ⁺ = 0.012–0.080 and f ⁻ = 0.008–0.057 for U_closed, and f ⁺ = 0.005–0.081 and f ^– = 0.009–0.052 for H_closed. In addition, for open ring the values were found in the ranges f ⁺ = 0.020–0.079 and f ^– = 0.022–0.059 for E_open, f ⁺ = 0.023–0.087 and f ^– = 0.017–0.064 for U_open, and f ⁺ = 0.022–0.089 and f ^– = 0.028–0.060 for H_open, as shown in Supplementary Table S1. The most relevant values are in the atom O22 of the hydroxyl group in the closed ring conformers, O21 of the carbonyl group in the open ring conformers in the ethanolamide (EA) group for nucleophilic attacks, and C12 in the middle alkyl region (Alkyl-M) for electrophilic attack for all the conformers. For the Parr functions, it is found a correspondence in the location of the highest values with the values found in the Fukui indices. Figure 1 presents the isosurfaces for Fukui functions with the major value for f ⁺ and f ^– for all shapes of anandamide. In Figure 1, it is observed that f ⁺ distributions are located on the hydroxyl oxygen O22 in closed conformers, and in the carbonyl oxygen O21 in open conformers, as shown in Supplementary Figure S1 in the SM section, also in the vinylic carbons on the Alkyl-M region for all conformers. While the f ^– distribution is located on the carbonyl carbon C2 in the closed conformers, it is also found on the vinylic carbons in the Alkyl-M region for all conformers. This finding is in accord with the experimental data which show that the double bonds region for anandamide is an essential factor for the T-type calcium channel blocking mechanism (Chemin et al., 2014).

The QTAIM analysis was focused to characterize the intramolecular hydrogen bond of the closed ring formed in the ethanolamide group in the conformers E_closed, U_closed, and H_closed of anandamide. This interaction of the hydrogen bond generates a ring structure of seven atoms in the EA group. The stability of the conformers with a closed ring of anandamide by the hydrogen bond formation effect is analyzed by means of interaction energy for each closed ring anandamide conformer from electronic density obtained from the BP86/cc-pVTZ level of theoretical calculations in chloroform. Table 3 and Supplementary Table S2 show the values of electronic density, ρ ( r ) , the Laplacian, ∇ 2 ρ ( r ) , the Lagrangian kinetic energy, G, the Hamiltonian kinetic energy, H, the potential energy density, V, the interaction energy, E _{H … Y} , the interatomic distance, D _inter , and the delocalization indexes, DI, of the main bond critical points (BCP) of the anandamide conformers. Atom labels correspond to Figure 2.

From the results, it is observed the non-covalent interaction corresponds to the hydrogen bond in the EA group in O21⋯H58-O22 with ρ(r) = 0.043 and ∇²ρ(r) = ∼ 0.096 a.u. for conformers E_closed, U_closed, and H_closed. These values are in agreement with those reported in the literature of 0.002–0.035 and 0.024–0.139 a.u., respectively (Popelier, 2000). On the other hand, the sign of H(r) parameter indicates, in the three closed conformers, that the accumulation of charge density on the hydrogen bond is a stabilizing bond (H(r) < 0) (Cremer and Kraka, 1984). In addition, the DI parameters have values in the range of 0.1106–0.1110 a.u. for the intramolecular hydrogen bond O21⋯H58−O22 in the three closed conformers, indicating that is an interaction <1.0 corresponding to a non-covalent interaction, while the DI for BCP between H58−O22 have values in the range of 0.5371–0.5402 a.u., indicating that this bond has a minor strength than a single bond (value close to 1.0 a.u.), due to the H58 is also contributing to the hydrogen bond formation with the atom O21. The interaction energy of the intramolecular hydrogen bond O21⋯H58−O22 corresponds to 12.33–12.46 kcal mol⁻¹ and it forms an RCP with ρ(r) = 0.0115–0.0116 a.u. for the three conformers, being slightly major the E _{H … Y} value in the conformer U_closed. It indicates that this hydrogen bond has a stabilizing effect larger than in the other conformers with the closed ring. The value of ρ(r) in the RCP of ethanolamide indicates that the ring formation stabilizes in the same order as the structures in the three conformers of the closed ring.

The non-covalent interactions H⋯H in the Alkyl-M region with a value of ρ(r) in the range of 0.011–0.020 a.u. generate the formation of four ring structures with ρ(r) in the RCP of 0.010–0.015 a.u. for the three closed conformers. The interaction energies between H⋯H are very small indicating weak interactions with values of DI of 0.03 a.u. approximately. Only in the conformer H_closed, is observed the non-covalent interaction C₆−H₃₇C₁₀ with values of ρ(r) in the BCP and RCP of 0.0135 and 0.0092 a.u., respectively, and a DI value of 0.045 a.u. In addition, the conformer H_closed forms an additional ring structure for the interactions between C₁₇H₄₅−O₂₄ and C₂₀H₅₃−O₂₄ with the value of ρ(r) = 0.0013 a.u. in the RCP. On the other hand, the DI values between atoms C5 = C6, C8 = C9, C11 = C12, and C14 = C15 in the Alkyl-M region are 1.77 a.u., corroborating the cis double bonds formation in the three closed conformers. Figure 2 and Supplementary Figure S2 show the molecular graphs of the anandamide conformers. The purple dots represent the bond critical points (BCP) and the green points represent the ring critical points (RCP).

Given the importance of mixed T-type/cannabinoid blockage in the pain diseases context, in this molecular docking analysis, and as a comparison, we consider the five proposed sites of the complex formed by the Ca_v3.2 channel and other dual blockers, the NMP compounds. The sites named S6DI, S6DII, S6DIII, S5DIV, and pore-blocking (Figure 3), are located in the transmembrane region, where aromatic and hydrophobic amino acids are prevalent (Rangel-Galván et al., 2022b). In this work, were analyzed the conformers E_closed, U_closed, and H_closed in interaction with the Ca_v3.2 calcium channel. In addition, the conformers E_open, U_open, and H_open were included to confirm our previous observations that the closed ring structures are more stable than their open counterparts (Rangel-Galván et al., 2022a) and probably more like to participate in the interaction with biological macromolecules, specifically with the Ca_v3.2 calcium channel. Figure 3 shows the anandamide conformers as ligands and the Ca_v3.2 channel as the receptor, showing the main interacting segments.

In the S5DIV site (Figure 4), the U_closed and U_open conformers place their polar head groups into the S4DIII segment, where the polar interactions are formed with the hydrogen N23−H⋯O of U_closed and the carbonyl oxygen of L806 (backbone), and the hydrogen O22−H⋯O of U_open and the carbonyl oxygen of R807 (both residues are located at 2.6 Å from the ligands). Also, is observed an unfavorable acceptor-acceptor interaction with O21 of U_closed and U_open conformers and the side chain carbonyl oxygen of D767 residue (Figure 4). The U_closed conformer forms an additional hydrogen bond, formed by hydrogen O22−H⋯O and the side chain carbonyl oxygen of acidic residue D767, however, this interaction does not contribute to the affinity of the ligand for the calcium channel with interaction energy of −9.2 kcal mol⁻¹ for both conformers. The non-polar portion of both conformers (U_closed and U_open) is placed in the S5DIV segment where the hydrophobic residues are located forming alkyl–alkyl interactions with the L815, L1151, L1154, and V1249 residues. In the X-ray structures of the TRPV5, TRPV2, and TRPV1 channels, which are close members of the T-type calcium channels, in complex with econazole (Hughes et al., 2018), resiniferatoxin (Zubcevic et al., 2018), and capsazepine (Gao et al., 2016), respectively, we observed ligand binding sites located in equivalent positions to that defined as the segment S5DIV in the Ca_v3.2.

As for the pore-blocking site, we identified a common hydrophobic region formed by the residues V1251, V1254, M948, F949, V945, L946, I331, and M330, where the non-polar tail (Alkyl-F) of the anandamide conformer U_open and the pentyl group of the NMP-181 compound established alkyl-alkyl interactions. In these molecular poses, the carbonyl oxygen of S900 and T568 residues in Ca_v3.2, form a hydrogen bond with the polar head (C2’−H⋯O) of the conformer U_open of anandamide and the amine group (C7−H⋯O) of the NMP-181, respectively. The conformer U_closed, in the pore-blocking site, is located very similar to the conformer U_open (Figure 5) but the EA group is oriented towards the segment P of the DI forming a polar interaction (C−H⋯O22) with O22 of anandamide and the carbon of G1206. In this context, it can be observed an equivalence of the interaction modes of the functional groups of anandamide and the NMP ligands (Rangel-Galván et al., 2022b) with the channel Ca_v3.2. Electrophysiological experimental registers show a blocking preference of the inactivation phase of the Ca_v3.2 channel by both anandamide (Chemin et al., 2001) and the NMP compounds (You et al., 2011; Gadotti et al., 2013; Bladen et al., 2015) was the MFV residues, located in the site S6-DIII, contribute to the inactivation phase of the Ca_v3 channels (Marksteiner et al., 2001). In the case of the Ca_v3.2, the corresponding residues are M948, F949, and V950 which are located in the pore-blocking site. Also, in a recent study, the Ca_v3.1/Z944 complex was solved by cryo-EM (Zhao et al., 2019), where common hydrophobic interacting residues stabilize the ligand binding pose, including the residue T921 (which is equivalent to T586 of the Ca_v3.2 located in the pore-blocking site). This ligand binding site was proposed also for the genistein/Ca_v3.3 complex using a combination of in vitro and in silico technics for the study (Rangel-Galván et al., 2021). Another recent study mapping the binding site of the Ca_v3.1 channel with a small cyclic peptide PnCs1 using docking and molecular dynamics showed a pocket located mainly in the pore region and including some fenestration (Depuydt et al., 2021). Based on the aforementioned experimental evidence, it is possible that the most probable pose for this type of ligand is located in the pore-blocking site.

In the pose S6DII, the E_closed and E_open anandamide conformers (Figure 6A) form a π-σ interaction with residue F161 while the Alkyl-F region forms an alkyl interaction with residues M330 and L333. The H_closed and H_open conformers form a π−σ interaction with the residues F316 and F1197 in the S6DI site (Figure 6B) and with the F943 in the S6DIII site (Figure 6C).

The energy values are summarized in Table 4. According to this analysis, the higher interaction energy in the Ca_v3.2/anandamide complex corresponds to the E_closed conformer in the S6DI site. Nevertheless, due to anandamide flexibility is more probable for anandamide to prefer folded conformers. Indeed, the X-ray data of anandamide interacting with its protein transporter (FABP5) show a hairpin shape conformer (Sanson et al., 2014) and according to MD simulations, anandamide prefers curved shapes in the pocket binding FAAH interaction (Palermo et al., 2013).

It is observed that there is a negligible difference in the values for the interaction energy related to the formation of a seven-atom ring in the EA group (open versus closed conformations). Only in the S6DI site, a preference for the closed ring conformers is obtained with a difference not greater than 0.7 kcal mol⁻¹. In addition, our results indicate that better interaction energy for the U-shape conformers (U_closed/U_open) with respect to the hairpin shape conformers (H_closed/H_open) is observed. Along these lines, the drug Z944 is placed in a U-shape form in the binding pocket of the T-type calcium channel (Zhao et al., 2019).