Understanding the high electronic quantum similarity of a series of ligands used as inhibitors of the SARS-CoV-2 virus by molecular mechanics and density functional theory approaches

System preparation

To conduct the docking analysis, the receptor structures discussed in open access References 9–14 for the docking experiment were extricated utilizing the following protocols through the crystal Structure of SARS-CoV-2 RNA-dependent RNA polymerase, using Protein Data Bank (6M71), see also Underlying data, which was adjusted utilizing the protein preparation wizard module of the openly available input file for Schrödinger suite 2017-1. The system preparation has been implemented followed these steps:

The influence of pH (acidity or alkalinity) on the SARS-CoV-2 virus, which causes COVID-19, is an interesting topic. However, it’s important to note that SARS-CoV-2 primarily infects and spreads among human cells, and the virus itself doesn’t exist independently in the environment for long periods. The pH level becomes more relevant when considering how the virus interacts with the human body.

Molecular docking

In our research group the calculation (docking results) were carried out through the freely available Schrödinger suite using the Glide,^19,20 Glide is the program of the Schrödinger suite and was used to obtain the docking results. This program was used with default parameters (that is, the number of poses written per ligand was set to 10,000, and the scaling factors of the vdW radii and the partial atomic charge cut-off were set to the default values 0.80 and 0.15, respectively) and Standard Precision (SP) model has been used for docking outcomes. One of the most important parameters about the docking analysis is the grid. The grid generation implementation has been benchmarked using the target protein of SARS-CoV-2 RNA-dependent RNA polymerase. All molecular Docking has been supported by a molecular dynamic of 30 ns.

Quantum similarity analysis

Molecular quantum similarity measure

An important feature associated with structural and electronic point of view is the Molecular Quantum Similarity Measure (MQSM). The MQSM of the systems A and B, known as Z_AB, is obtained using the Density Functions (DFs) using Eq. (1).

Studying the nature of the operator Ω(r₁, r₂) with electronic densities for A and B,^21–26 used in Equation 1, provides the information being compared between the two systems while simultaneously designating our measure of similarity. For instance, if the chosen operator is the Dirac delta function (an efficient approach for functions with high peak values, such as the electronic density), i.e., Ω(r₁, r₂) = δ(r₁ - r₂).^26–33 Another widely used alternative is the Coulomb operator, i.e., Ω(r₁, r₂) = |r‌₁ - r₂|‌‌^-1, resulting in a Coulombic MQSM.^34–36

Chemical reactivity outcomes

Previously, several investigations have shown the relationship between quantum similarity and chemical reactivity descriptors.^37–47 In addition, the quantum similarity and DFT uses the density function as an object of study of the similarity indexes; specifically, the Coulomb index can be related to electronic factors associated with chemical reactivity.

Using the Frontier Molecular Orbitals (FMO) and the energy gap, the global reactivity indices, such as chemical potential (μ),⁴⁸ hardness (ɳ),⁴⁹ and electrophilicity (ω),^48,49 will be calculated.

These chemical reactivity indices (Eqs. 2-4) give an idea about the stability of the systems. The chemical potential measures the inclination of electrons to leave the equilibrium system,⁴⁸ whereas chemical hardness measures the resistance of a chemical species to change its electronic configuration.³⁹

Electrophilicity index (ω) measure the stabilization energy of the system when it is saturated by electrons from the external environment and is mathematically defined as^48,49:

In this work, the local reactivity descriptors are the Fukui functions. Equations (5, 6) represents the response of the chemical potential of a system to changes in the external potential.

Where $\left(f^{+}\right(\overrightarrow{r}\left)\right)$ is for nucleophilic attack and $\left(f^{-}\right(\overrightarrow{r}\left)\right)$ for the electrophilic attack.^50–54

All the calculations were carried out using the method B3LYP. B3LYP is one of the most used Density-Functional Theory (DFT) approaches. It is capable of predicting molecular structures and other properties according to the experimental data⁵⁵ and the basis set 6-311G (d,p)⁵⁶ which is the result of adding a correction to the 6-311G(d) basis set leading to calculations of electronegativity, hardness, reactivity indices and frontier molecular orbitals with a similar quality to those obtained with much larger basis sets (such as Aug-cc-pVQZ and Aug-cc-pV5Z). This method/basis set has been used in combination with Gaussian 16 package⁵⁷ and GaussView, Version 6.1⁵⁸ a free, alternative software that carries out a similar function is ORCA 5.0.3.

Molecular analysis

One of the objectives of this project involves an analysis about molecular coupling of the compounds on the active site. For this reason, a study about the best conformations on the active site of the selected compounds was carried out. Please note that all files associated with the results are available in Underlying data.⁵⁹

Figure 1 shows the conformation with the highest RMSD, in this conformation Lopinavir has a π-π stacking interaction with residue LYS621 with a length of 1.56Å. On the other hand, with this same residue they have an H-bond with a length of 1.62Å and 1.72Å, respectively. Additionally, this compound has an H-bond with residues ARG553, ARG555 and ASP623 with lengths of 1.56Å, 1.64Å and 1.42Å, respectively.

Figure 1. Molecular docking results for the Lopinavir using Schrödinger suite 2017-1.

Figure 2 shows that the Ganciclovir compound has a H-Bond with the residue ARG553 with a length of 1.58Å and ASP452 with a length of 1.62Å. Also, this compound has two H-bonds with the residue ASP760 with lengths of 1.59Å and 1.63Å, respectively.

Figure 2. Molecular docking results for the Ganciclovir using Schrödinger suite 2017-1.

Figure 3 shows that the Insoine compound has a H-bond with the residue ASP760 with a length of 1.65Å, with the residue ARG553 have two H-bonds with lengths of 1.58Å and 1.61Å, respectively. Finally, it compounds have a H-bond with a length of 1.48Å.

Figure 3. Molecular docking results for the Insoine using Schrödinger suite 2017-1.

The Fosamprenavir compound has two a π–π stacking interactions with the residue ARG624 with a length of 1.62Å, another interaction with the residue ARG553 with a length of 1.82Å (see Figure 4). Also have a H-bond with a residue ARG553 with a length of 1.62Å, another H-bond with ARG624 with a length of 1.57Å and with the residue THR556 with a length of 1.61Å.

Figure 4. Molecular docking results for the Fosamprenavir using Schrödinger suite 2017-1.

Ritonavir has a -H bond with the residues LYS298 and LYS621 with a length of 1.26Å and 1.43Å (Figure 5). Also has a H-bond with the residue THR687 with a length 1.13 Å, respectively.

Figure 5. Molecular docking results for the Ritonavir using Schrödinger suite 2017-1.

Darunavir compound has a π–π stacking interactions with the residue ARG553 with a length of 1.41Å (as can be seen in Figure 6). Also have a H-bond with the residue CYS622 with a length 1.38Å, with the residue LYS621 with a length of 1.68Å and two H-bonds with lengths of 1.48Å and 1.38Å, respectively.

Figure 6. Molecular docking results for the Darunavir using Schrödinger suite 2017-1.

Figure 7 shows that the Tipranavir compound has a π–π stacking interactions with three H-bonds with the residue CYS622 with a length of 1.66Å, with a residue LYS621 with a length of 1.63Å and a π–π stacking interactions with length of 1.46Å.

Figure 7. Molecular docking results for the Tipranavir using Schrödinger suite 2017-1.

Ganciclovir compound has two π–π stacking interactions with the residue ARG553 with lengths of 1.52Å and 1.61Å (see Figure 8). On the other hand, it compounds have a H-bond with the residue CYS622 with a length of 1.58Å and two H-bonds with the residue ASP760 with lengths of 1.61Å and 1.71Å, respectively.

Figure 8. Molecular docking results for the Ganciclovir using Schrödinger suite 2017-1.

The Molecular docking results for Dolutegravir (see Figure 9) involves a π–π stacking interactions with lengths of 1.64Å and two H-bonds with the residues LYS551 and ARG553 with lengths of 1.57Å and 1.59Å, respectively.

Figure 9. Molecular docking results for the Dolutegravir using Schrödinger suite 2017-1.

Molecular quantum similarity

In the Table 1 we can see the structural similarity results for the molecular reaction set. This analysis was developed with the aim the find the common features along the reaction set. From structural point of view the Darunavir (Daru), Dexamethasona (Dexame), Dolutegravir (Dolu), Fosamprenavir (Fosam), Ganciclovir (Gan), Insoine (Inso), Lopinavir (Lop), Ritonavir (Rito) and Tipranavir (Tipra) were analysed, the highest overlap similarity is between the compounds Fosam and Daru (0.343) with a Euclidean distance of 6.946 (see Table 2); Lop vs Fosam (0.414) with a Euclidean distance of 6.694 and Inso vs Gan (0.510) with a Euclidean distance of 0.510. These low values obtained are related with steric effects between structures. Additionally, they do not have a skeleton in common and substitutes groups have hight differences.

Due to the low indices of structural similarity, the electronic similarity has been calculated (see Table 2). These values highest values for electronic similarity are Fosam vs Dexame (0.884) with a Euclidean distance of 36.295; Rito vs Dexame (0.896) with a Euclidean distance of 43.347 (see Table 4), Lop vs Fosam (0.915) with a Euclidean distance of 33.223; and Rito vs Lop (0.881) with a Euclidean distance of 41.726. Unlike the values of structural similarity, the values of electronic similarity are above of 0.5. These values are supported with the Euclidean distances. We think that the structures, despite being structurally different, are electronically very similar.

Reactivity analysis and Fukui function comparison

Since the electronic similarity indices (see Tables 3 and 4) are higher than the structural ones, this section deepens on the electronic effects associated with the highest values of electronic similarity. In the previous section we have studied which ligands have greater structural and electronic similarity. To continue this analysis, from the point of view of chemical reactivity, several ligand pairs have been selected from those with indices indicating greater electronic and structural similarity. Table 5 shows the global parameters chemical potential, chemical hardness, lobal S softness and global electrophilicity that have been calculated in order to compare the chemical reactivity of these ligands, analysing the values of this table it can be concluded that Insoine, Ganciclovir and Fosamprenavir have a set of parameters that are closer to each other. Since the analysis of the global parameters is limited, we will complete it with the comparison of some local descriptor functions. The electrophile and nucleophile Fukui functions (as a measure of reactivity) are then compared using the Frontier Molecular Orbital (FMO) approach. The electrophilic-nucleophilic character of the following functions also shows those molecular areas that are most likely to form charge-donating interactions (basically by charge delocalisation). These types of interactions are important and are difficult to determine using docking analysis.

Figures 10 and 11 show the Fukui $f^{-}\left(\overrightarrow{r}\right)$ and $f^{+}\left(\overrightarrow{r}\right)$ functions corresponding to the Insoine and Ganciclovir ligands. Figure 10 shows a strong similarity between the two functions, which may indicate that both ligands have a similar nucleophilic behaviour and/or that they have a similar tendency to donate electronic charge. On the other hand, Figure 11 shows significantly different descriptor functions so we would expect different electrophilic behaviour for these ligands and/or a very different tendency in relation to the possible charge-withdrawing interactions. The Fukui Functions maps were obtained using Highest Occupied Molecular Oribital (HOMO) maps and the Lowest Unoccupied Molecular Orbital (LUMO) maps).

Figure 10. Fukui function $f^{-}\left(\overrightarrow{r}\right)$ calculated under the Frontier Molecular Orbital (FMO) approximation $\left({\left|\mathbf{HOMO}\left(\overrightarrow{r}\right)\right|}^2\right)$ for the ligands Insoine (left) and Ganciclovir (right).

Isovalue: 0.002 in both cases. Figure created using Schrödinger suite 2017-1.

Figure 11. Fukui function $f^{+}\left(\overrightarrow{r}\right)$ calculated under the Frontier Molecular Orbital (FMO) approximation $\left({\left|\mathbf{LUMO}\left(\overrightarrow{r}\right)\right|}^2\right)$ for the ligands Insoine (left) and Ganciclovir (right).

Isovalue: 0.002 in both cases.

Figures 12 and 13 show the Fukui functions for the ligands Lopinavir and Fosamprenavir. In Figure 12 it can be seen that there is no similarity between the two functions, indicating that the ligands have different nucleophilic behaviour and/or show a different trend in electronic charge donation. On the other hand, Figure 13 shows descriptor functions with a certain resemblance so we would expect comparable electrophilic behaviour between these ligands although the similarity is moderate. Figure created using Schrödinger suite 2017-1.

Figure 12. Fukui function $f^{-}\left(\overrightarrow{r}\right)$ calculated under the Frontier Molecular Orbital (FMO) approximation $\left({\left|\mathbf{HOMO}\left(\overrightarrow{r}\right)\right|}^2\right)$ for the ligands Lopinavir (left) and Fosamprenavir (right).

Isovalue: 0.002 in both cases. Figure created using Schrödinger suite 2017-1.

Figure 13. Fukui function $f^{+}\left(\overrightarrow{r}\right)$ calculated under the Frontier Molecular Orbital (FMO) approximation $\left({\left|\mathbf{LUMO}\left(\overrightarrow{r}\right)\right|}^2\right)$ for the ligands Lopinavir (left) and Fosamprenavir (right).

Isovalue: 0.002 in both cases.

Figures 14 and 15 show the Fukui functions for the ligands Fosamprenavir and Darunavir. Figure 14 shows a strong similarity between the two functions, which may indicate that both ligands have a similar nucleophilic behaviour and/or that they have a similar tendency to donate electronic charge. On the other hand, Figure 15 shows very similar descriptor functions so we would expect comparable electrophilic behaviour between these ligands. Figure created using Schrödinger suite 2017-1.

Figure 14. Fukui function $f^{-}\left(\overrightarrow{r}\right)$ calculated under the Frontier Molecular Orbital (FMO) approximation $\left({\left|\mathbf{HOMO}\left(\overrightarrow{r}\right)\right|}^2\right)$ for the ligands Fosamprenavir (left) and Darunavir (right).

Isovalue: 0.002 in both cases. Figure created using Schrödinger suite 2017-1.

Figure 15. Fukui function $f^{+}\left(\overrightarrow{r}\right)$ calculated under the Frontier Molecular Orbital (FMO) approximation $\left({\left|\mathbf{LUMO}\left(\overrightarrow{r}\right)\right|}^2\right)$ for the ligands Fosamprenavir (left) and Darunavir (right).

Isovalue: 0.002 in both cases. Figure created using Schrödinger suite 2017-1.

Figures 16 and 17 show the Fukui functions for the ligands Fosamprenavir and Dexamethasone. In Figure 16 it can be seen that there is no similarity between the two functions, indicating that the ligands have different nucleophilic behaviour and/or show a different trend in electronic charge donation. On the other hand, Figure 17 shows descriptor functions with a certain resemblance so we would expect comparable electrophilic behaviour between these ligands although the similarity is moderate.

Figure 16. Fukui function $f^{-}\left(\overrightarrow{r}\right)$ calculated under the Frontier Molecular Orbital (FMO) approximation $\left({\left|\mathbf{HOMO}\left(\overrightarrow{r}\right)\right|}^2\right)$ for the ligands Fosamprenavir (left) and Dexamethasona (right).

Isovalue: 0.002 in both cases. Figure created using Schrödinger suite 2017-1.

Figure 17. Fukui function $f^{+}\left(\overrightarrow{r}\right)$ calculated under the Frontier Molecular Orbital (FMO) approximation $\left({\left|\mathbf{LUMO}\left(\overrightarrow{r}\right)\right|}^2\right)$ for the ligands Fosamprenavir (left) and Dexamethasona (right).

Isovalue: 0.002 in both cases. Figure created using Schrödinger suite 2017-1.

Figures 18 and 19 show the Fukui functions for the ligands Ritonavir and Dexamethasone. In Figure 18 it can be clearly seen that there is no similarity between the two functions, so we think that these ligands have different nucleophilic behaviour. On the other hand, Figure 19 shows descriptor functions with a certain resemblance, so we would expect comparable electrophilic behaviour between these ligands, although the resemblance is very limited.

Figure 18. Fukui function $f^{-}\left(\overrightarrow{r}\right)$ calculated under the Frontier Molecular Orbital (FMO) approximation $\left({\left|\mathbf{HOMO}\left(\overrightarrow{r}\right)\right|}^2\right)$ for the ligands Ritonavir (left) and Dexamethasona (right).

Isovalue: 0.002 in both cases. Figure created using Schrödinger suite 2017-1.

Figure 19. Fukui function $f^{+}\left(\overrightarrow{r}\right)$ calculated under the Frontier Molecular Orbital (FMO) approximation $\left({\left|\mathbf{LUMO}\left(\overrightarrow{r}\right)\right|}^2\right)$ for the ligands Ritonavir (left) and Dexamethasona (right).

Isovalue: 0.002 in both cases. Figure created using Schrödinger suite 2017-1.