Interactions between carbon nanotubes and external structures of SARS-CoV-2 using molecular docking and molecular dynamics

doi:10.21203/rs.3.rs-1578453/v1

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Interactions between carbon nanotubes and external structures of SARS-CoV-2 using molecular docking and molecular dynamics

https://doi.org/10.21203/rs.3.rs-1578453/v1

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Molecular modeling techniques are used to describe the process of interaction between nanotubes and the main structures of the Covid-19 virus: the envelope protein, the main protease, and the Spike glycoprotein. Molecular docking studies show that the ligands have interaction characteristics capable of adsorbing the structures. Molecular dynamics simulations provide information on the mean squared deviation of atomic positions between 0.5 and 3.0 Å. The Gibbs free energy model and solvent accessible surface area approaches are used. Through the results obtained through molecular dynamics simulations, it is noted that the zigzag nanotube prefers to interact with E-pro, M-pro, and S-gly, respectively. Molecular couplings and free energy showed that the S-gly active site residues strongly interact with zigzag, chiral, and armchair nanotubes, in this order. The interactions demonstrated in this manuscript may predict some promising candidates for virus antagonists, which may be confirmed through experimental approaches.

Sars – CoV-2

Carbon nanotube

Molecular docking

Molecular dynamics

DFT

In silico study

Antiviral effect

The emergence of the severe acute respiratory syndrome (SARS-CoV-2), which is a pleomorphic ribonucleic acid virus belonging to the coronavirus family), or Covid-19, originated in Wuhan, China, at the end of the year 2019. Its outbreak generated a global pandemic, [1,2] causing great concern to the population because of the high contamination rate and ability to spread the lethality [3,4]. Since their transmission is made through the air or physical contact, they also propagate at short range and / or longer distances, through aerosols, called airborne transmission [5]. So, preventive care against the spread of the virus such as the proper use of masks and use of gloves, besides disinfection of surfaces [6].

Therefore, the use of graphene and its derivatives, such as carbon nanotubes (CNT) appear as potential materials for effective control of the spread and rapid detection of the virus. One can effectively use these materials in antiviral coatings and surface development to prevent contagious and virulent virus contamination in fabrics such as personal protective equipment (PPE), face masks, and gloves [7]. It is important to mention that CNTs have excellent electrical conductivity due to their almost one-dimensional electronic structure. In SWNTs and MWNTs, electronic transport occurs ballistically (i.e. without scattering) along the lengths of nanotubes, allowing them to carry high currents essentially without heating [8-9]. CNTs also have an electrically conductive capacity and can, during an interaction with a solute, or a solvent, generate an electrical current [10,81,82]. So, it can be considered that a SAR-CoV 2 protein, when approaching very close to the CNT during the interaction, can produce an electrochemical potential, so that the virus, when receiving an electrical current through the chemical bond made in the approach at the instant that the CNT absorbs and emits light because of electronic jumps between layers of different energy levels. Until now, one has used CNTs for drug delivery nanosystems and against various viruses, such as the SARS-CoV-2 virus and viral proteins [11]. The in silico study of the therapeutic target compound present in a plant extract is an economical and rapid investigation tool through techniques, such as molecular docking (DOC) and molecular dynamics (MD) that allow estimating the affinity between molecules, such as protein-ligand and protein-protein and the side effects and cytotoxicity of the compounds studied. Thus, the study of computer simulation and ethnopharmacological knowledge combined with experimental tests can help in the discovery and performance of new virus inhibitors [12-13-14].

In the development of this research, the intermolecular interactions of CNT, treated as ligand, with the SARS-CoV-2 proteins, treated as receptors, are studied by DOC simulations using autodock tools and autodock vina [15, 16] and molecular dynamics with the biomolecular software package GROMACS-2018.1 [17] is used for the molecular dynamics simulations of the protein-ligand complex with the protein interactions approximated by the CHARMM36 force field and ligand parameters generated using CgenFF [18]. Besides Gibbs free energy calculations (GMMPBSA) [19] and van der Waals energy variation (VDW) [20]. Data were obtained in DOC regarding electrostatic potential, molecular coupling system, binding energy, binding types, and hydrophobicity, in addition to validating the change of binding positions in the active site of the receptors. Subsequently, deepening the studies, the MD was used, which allowed more complex calculations such as root-mean-square deviation (RMSD)[15], mean square fluctuation (RMSF)[16], the radius of gyration (Rg)[17], and surface area Solvent Accessible (SASA)[15], with an analysis of molecular interactions and possible structural mutations to analyze whether there are significant alterations or deformations in the sequence of receptors and whether these alterations may be related to the use of CNTs for applications in the production of materials and SAR-CoV inhibitor equipment 2.

2.1 Background about the receptors and ligand

The major protease (M-pro) or 3CL pro [18] (Fig 1a) catalyzes most maturation cleavage events after protein activation. Thus, M-pro is an essential enzyme for viral replication and is one of the best-characterized drug targets among coronaviruses [19, 20]. The crystal structure of this SARS-CoV-2 protein is highly similar to that of other coronaviruses [21]. The active site of the protein is in a cleft between a catalytic histidine/cysteine dyad. In M-pro, Cys 145 acts as a nucleophile during the first step of the His 41-assisted hydrolysis reaction, which acts as a basic catalyst [22]. The coronavirus E-pro glycoprotein protein is a small membrane protein found in the envelope of the virus [23]. Different coronavirus proteins share striking biochemical and functional similarities, but sequence conservation is limited [24]. From the different viral proteins identified, one of the most relevant is the spike glycoprotein, recognized as Spike protein (S-pro) or spike glycoprotein [25-26-27]. Primary virus entry is premeditated by ACE2 receptors forming complexes with S-pro, which then regulate invasive processes important for viral replication during cellular stress [28-29].

2.2 Importance of uses nanotubes

CNTs are cylindrical nanostructures [30] with unusual and interesting behaviors, which make them valuable new materials, especially for their applications in new technologies [31]. The modification of their surfaces (figure 1) through chemical or physical methods has been an object of interest for the development of science and technology of CNTs [32,33]. One has employed these materials in many applications, such as catalysis [34], gas sensors [35], nanoelectronics [36], field-effect transistors (FTE) devices [37], biosensors [38]. Among the different applications of CNTs, the surface adsorption of different molecules has been studied by a wide variety of scientists. CNTs can be doped by various heteroatoms, such as nitrogen, boron, silicon, and sulfur, to change their properties and reach new applications. Noticeably, CNTs have different adsorption behaviors [39-40] and this ability has been used in many applications, such as drug delivery [41-42], pollution removal (in nature or chemical reactions), and the design of new sensors [ 43-44]. Therefore, many surface-functionalized CNTs [45-46] have been employed widely in biomedicine [47], drug delivery [48], biomedical imaging, chemical detection [49], drug design [50], diagnosis of cancer [51–52], and tissue engineering [53]. Furthermore, CNTs have been employed in drug delivery systems because of their hollow structure (Figure 2), which allows them to encapsulate the drug and deliver it to target tissues [54,55,80].

The dimensions of the CNTs correspond to the following values, 3.98 Å in radius and 28.43 Å in length for the zigzag CNT, 4.00 Å in radius and 28.54 Å for the CNT armchair, and finally 4.04 Å in radius and 28.65Å in length for the chiral CNT. The CNTs had an average diameter of 12.04 Å and a length of 28.54 Å, with a percentage variation of 2.4% and 0.8% for radius and diameter, respectively.

Preparation of the targets and ligands

The crystal structures of M-pro, S-pro, and E-pro (PDB ID: 6M2N, 7BW4, and 7K3G) were retrieved from the Protein Data Bank (PDB) (https://www.rcsb.org) repository [56- 57-58]. The structures were prepared using GaussView 6 software [59-60-26] and further minimized using the energy refinement model-assisted construction (AMBER) ff14SB force field [61-62-55]. After minimizing the structures, they were submitted to a virtual sorting process by DOC and MD. The ligands were modeled using the Nanotube Modeler software (http://www.jcrystal.com/products/wincnt/), and all the ligand geometry optimization calculations were performed using the Gaussian 09W software [63]. Structure optimizations and adsorption energy calculations were performed using the Density Functional Theory (DFT) method [64,65], which presented reliable results, concerning computationally more expensive methods [66,67]. Optimizations of all structures were performed using the B3LYP method in combination with 6–31G base sets. These basic sets and methods were used because of our limited computational resources and because of the study of large systems. However, single point and solvent effect calculations were performed using the more appropriate DFT method, the 6–311G basis set, to obtain more reliable values. This method is one of the best DFT methods for studying intermolecular interactions. All simulations were performed based on the receptor + ligand model [68], where three receptor structures were selected (E-pro, M-pro, and S-gly) from the Protein Data Bank (PDB; (www.rcsb.org / pdb) [69] that were used, while the ligands were the 3 CNTs with different geometric shapes. The receptor structures were optimized using the Chimera 1.15.6 (CHM) software [70] to find the ideal conditions that satisfied the multiple pre-defined targets, additional complexity arises for tasks that involve experimentation or computational calculations [71]. We use CHM as a scalar realization of general-purpose function for multi-target optimization, where evaluations are the limiting factor and its performance has been well established using different algorithms The results show the CHM allows a wide class of optimization algorithms to find the ideal conditions, in this sense we use the AMBERFF14 force field SB [72]. Docking was performed using AutoDock Vina 4.2.6 (ADV) software [73]. In this calculation, ligands were flexible, while receptors were treated as a rigid structure. In these interactions, we consider the change in affinity energy (kcal/mol). However, for the three ligands investigated, 30 poses along the macrostructures were generated from the ADV genetic algorithm that assesses protein binding affinity energy using a scoring function as a basis.

2 Molecular docking (DOC)

After receptor minimization and ligand optimization processes, the three-dimensional structures of the proteins were added to the DOC platform as PDB formats. Molecular coupling was performed using the ADV and AutoDock Tools (ADT) software package (http://autodock.scripps.edu/) [74], the procedure was performed using a ligand in a flexible active site protocol, where the ligand could be flexible, with twisting within a grid box encompassing the ligand connection cavity of each receptor predicted by the algorithms [79]. After each run, ADV provided a set of snapping poses for the ligand with calculated binding affinities, where the fit pose with the best affinity was chosen to represent the set and subjected to post-snap analysis. Visualization and analysis of the ligand-receptor complex conformation were performed in the BIOVIA Discovery Studio (version 4.1) [16]. All torsion angles on the ligand were relaxed, allowing flexible anchoring to be performed, while the receptors remained rigid throughout the process. With polar hydrogens added to the protein, the model of partial charges of the joined Kollman atoms [15] was assigned to the ligand and the receptors. The Gridbox [21], which defines the Lennard-Jones potential with electrostatic factors and provides values for all receptor atoms, was used for the simulations and had the following dimensions: 80 Å × 60 Å × 48 Å for M-pro, 82 Å × 56 Å × 42 Å for S-gly and 40 Å × 30 Å × 20 Å for E-pro, for the x, y, and z directions respectively for the binding site of each of the macromolecules.

The empirical free energy function and the Lamarckian genetic algorithm (LGA) were used for anchoring simulations according to the recommended parameters [31, 60, 75]. Based on the results obtained in the DOC, 40 major conformations were selected through the software for each ligand-receptor system. For each molecular system, we chose a conformation with the lowest affinity energy (AE) and with chemically reasonable bonds, with adequate lengths for chemical bonds. In this step, we use the parameters of the active sites specified in the input file for the fit method, which is acceptable and capable of recovering the structure and interactions of a known complex [38]. Thus, this computational process involved the original position of the ligand in the first simulation of the complexes in an induced way, to evaluate if the positions and change parameters obtained by the different programs could recover the structure and interactions of a known complex and also its active site.

3.Molecular dynamics (MD)

After the DOC process, configurations were used as initial conformations in the MD process simulations, helping to understand the prediction of the position where the active site of macromolecules could be and the essential interactions to predict the stability of the complex-receptor ligand. For this, four octahedral boxes were created with a spacing of 10 Å between the solute and each octahedral face, with approximately 14,496 water molecules using the TIP3P model for the solvation of the systems [38, 48]. Next, Na+ and Cl- ions were added to neutralize the amino acid terminals to ensure the net neutral charge of the systems.

Periodic boundary conditions were performed using the Particle Mesh Ewald (PME) method [33, 48] to ensure that the solute (ligand-receptor) was immersed in the solvent not only during minimization but also in MD. The systems were kept fixed with positional constraints of 50 kcal/mol.Å2, with a cutoff of 10 Å to truncate the long-range interactions of VDW, with constant volume per NVT (canonical set - moles (N), volume (V), and temperature (T) conserved) [65], thus ensuring optimized periodic boundary conditions at 20,000 cycles, where 10,000 cycles were through the steepest descent algorithm [46] and 10,000 cycles through the conjugate gradient algorithm [54]. The system went through the heating step for 10 ns with an integration time of 2 fs using the SHAKE algorithm [27], restricting and fixing the bond lengths of the hydrogen atoms. To understand the dynamic behavior of all higher scoring complexes, MD simulation was employed using GROMACS 2021.1 software [1].

Molecular dynamics simulations selected and further analyzed the major results with the best affinity energy properties using GROMACS 2021.1 [1]. The energy minimization of the systems was performed using the steepest descent of 5,000 steps (maximum number of minimization steps to be performed) to remove the power-related contacts from VDW. Energy minimization was stopped when the maximum force was less than 1.0 kJ/mol. The system was further balanced for 50 ps in constant volume and temperature of 300 K. Molecular dynamics simulations were performed for 100 ns and for each protein-ligand complex, where the coordinates were saved at every 2 ps interval. VDW interactions were set at 1.6 nm. The Linear Constraint Solver (LINCS) algorithm [41] was applied to constrain covalent bonds, including heavy bonds of hydrogen atoms, during MD simulations. The MD results were used to calculate mean squared deviations (RMSD), mean squared fluctuation (RMSF), the radius of gyration (Rg), hydrogen bonds (HB), and SASA, respectively. Finally, the trajectories were saved for further analysis using Xmgrace.

4.Root-mean-square deviation (RMSD) and root-mean-square fluctuation (RMSF)

To perform the RMSD and RMSF calculations, the CPPTRAJ tool, included in the GROMACS package [1] was used. The information was extracted through the program module to create graphs of RMSD values as a function of time (100 ns). RMSD values show the deviations of the structures generated during the MD simulation concerning the initial structure, that is, the stability and equilibrium of the system over time, corresponding to the conformations of a certain set of points already obtained, providing a measure of the difference in the initial position of these same sets, therefore, the greater the value of RMSD, the greater the difference between the structures [23]. The RMSF calculation refers to the displacement of a certain atom or group of atoms to the reference structure, contributing to the understanding of the region of the ligand-receptor complex that is being fluctuated during the simulation, in this way the result is the calculation of the flexibility of each residue, thus getting a view of the extent to which ligand binding affects the flexibility of the protein [43, 55].

5.The radius of gyration and solvent-accessible surface area

Rg and SASA were calculated from the MD trajectories for the four systems to measure the interaction between protein-ligand complexes and solvents using the GROMACS software. [1]. The Rg measures the strength of the macromolecular system, through the root mean square of the distance between the axis of rotation and the center of mass obtained in the MD simulation, the parameter shows the changes over time in the protein structure, evaluating the compaction and system stability [61, 76]. The calculated surface area is the canonical SASA surface area and includes the total hydrophobic, hydrophilic and solvent-accessible surface area of the protein molecule, the extent to which amino acids interact with the solvent, and the protein core is proportional to the area surface exposed to solvent. Polar and non-polar surface areas are often defined using partial atomic charges taken from the molecular potential used. These partial charges differ significantly between force fields, the Rg and SASA module residue option of the GROMACS package.

6.Free energy

To automatically perform all the steps necessary to estimate the free binding energy of the complex, we used the MM/PBGBSA scripts (MM: Molecular Mechanics; PB: Poisson–Boltzmann; GB: Generalized Born; SA: Surface Area) [29,61, 66] included in GROMACS [1]. However, it is generally expected that no significant conformational changes will occur after connection, so snapshots of all three species can be taken from a single trajectory. The free binding energies of the complexes complexed with the most promising successful compounds were calculated using the MM-GBSA (Molecular Mechanics Poisson-Boltzmann Surface Area) method [18].

3.1 Molecular docking (DOC) analysis

The CNTs were considered flexible and the E-pro, M-pro, and S-pro receivers were treated as rigid bodies, thus the phase space was limited to the active site of the receptors, as shown in Figure 3. Here, the flexibility of the ligand can be addressed using a calculated set of ligand conformations or by allowing atom-atom overlap between the protein and the ligand.

The affinity energies (AEs) obtained for the interactions between these molecules demonstrated the formation of a favorable complex since the AEs presented relatively low values, as shown in table 1 with the AE values for all simulations. It is verified that the best results presented are for S-gly, the most external glycoprotein, and sequentially for the M-pro and E-pro proteins, which are more internal.

Table 1: AutoDock Vina simulations.

Protein	CNTs	Affinity Energy (kcal/mol)
E-pro	zigzag	-9.48
	armchair	-8.29
	chiral	-6.54
M-pro	zigzag	-9.98
	armchair	-9.06
	chiral	-7.14
S-gly	zigzag	-10.08
	armchair	-9.49
	chiral	-8.23

Figure 4 shows the interactions between the three types of CNTs and E-pro, chosen based on the final pose with the most favorable AE value among the 40 conformations obtained. One can note that there were four interactions of the alkyl type shown in pink.

Analyzing the four interactions of the DOC results, it is observed that the mode of interaction predicted by the DOC poses of the selected compounds in the visual inspection was like the poses of the crystallographic structures at the E-pro binding site. Figure 5 shows the interactions between the three types of CNTs and the M-pro.

An aspect observed in figure 5, where the M-pro interaction site has hydrophobic characteristics and this type of interaction is present in the analyzed compound. Thus, considering the distances of such connections, the DOC results revealed seven interactions for the CNT armchair, five for the zigzag, and seven for the chiral, interactions made at the protease site where there may be a greater occurrence of reaction. The DOC between the CNTs and the S-gly obtained the highest EA value according to table 1. The results showed that the π-alkyl bonds involving PRO225, TYR248, PHE250, PRO3663, ARG251, and VAL577 were maintained and were closed after the link with the CNTs because of VDW forces. Only in this interaction, π - σ bonds (PHE490) were observed, in purple in figure 6, being able to bind to the active pockets of the protein interface.

The CNTs had a certain degree of freedom of translation, vibration, and rotation, so the DOC process was positioned in the active site of the receptors. The bonds involve the electron-rich π system with another π system, anion, cation, or other molecules. Among all π interactions investigated in this study, π - σ bonds have the strongest binding strength due to the greater overlap of their s orbitals [77; 78]. The interactions could produce changes in the charge distribution of the ligand, which favored the appearance of electric dipoles at its ends. DOC research data suggest that ligands have intercalation potential to form a complex with all three receptors, because of interaction with the binding sites.

3.2 Molecular Dynamics (MD) and Root-Mean-Square Deviations (RMSD) analysis

The RMSD of the backbone atoms of the SARS-CoV-2 receptors were studied for the initial structures of the complexes to perform the conformational analysis and verify the stability of the complexes. The RMSD as a function of time shown in Figure 7 for the nine complexes performed accumulated at the beginning of the MD simulation; this behavior was expected, since, in general, the interaction of the inhibitor with the protein decreases the global flexibility of the MD. protein. On the other hand, a decrease in flexibility was observed in the substrate-binding region, which revealed the influence of inhibitor interactions, mainly in the simulation with residues in the binding pocket of the simulated macrostructures with the zigzag and armchair CNTs.

The MD simulations described allowing the atoms of the system to reach speeds compatible with thermal equilibrium. Electrostatic interaction plays an important role in the dynamic stability of the ligand-protein complex. Thus, variations in the RMSD of the structures are used to illustrate the fluctuation of conformation around the mean, being an important tool for studying the stability of proteins in MD simulation. The MD simulations were concluded when the values of the α carbon atoms of the main protein chains and RMSD of the ligand atoms, except for the hydrogen atoms, had their trajectories described during the calculated simulation time. In general, the CNTs were positioned during most of the time of the simulations in the active site of the receptors, presenting varied behavior when the RMSD values were compared. In the simulation with an E-pro, there were no significant changes in the initial positions of the CNTs in any of the receivers, but there was an upward trend with some deviations for the chiral CNT and some fluctuations in the armchair. Among these, the CNT zigzag obtained a better stability pattern and remained more stable with the S-gly protein. We can relate this behavior to a large amount of hydrogen and hydrophobic interactions that occurred between the ligand and the protease amino acids. In conformation with M-pro, all ligands remained unstable at the beginning of the simulation with an RMSD, ranging from 0.5 to 2A, but from 40 ns onwards the CNTs started to stabilize, the chiral nanotube obtained a significant increase in its trajectory. , the armchair remained between 1.0 and 1.5A and there was a drop in the initial distance of the zigzag nanotube, demonstrating greater stability from the initial structure. The CNTs+S-pro complexes showed stability at the beginning of the simulation and potential growth for the chiral and armchair CNTs, despite many variations, but remained stable in the final stages, resulting in an RMSD of 2.0 to 2.5 Ǻ during the simulation. We can observe that the ligands stabilize quickly and that they follow the global fluctuations that the protein undergoes. However, this fluctuation, as we will see when analyzing the turning radius, may be because of a rotation or “breathing” movement of the protein.

3.3 Root-mean-square fluctuation (RMSF)

The MD simulation was performed for 100 nanoseconds for each protein in order to understand the conformational changes that the protein undergoes after interacting with different ligands. The statistics obtained from the trajectory helped in the investigation of the RMSF as a function of time shown in Figure 8 for the nine complexes performed. During MD, RMSF fluctuations of binding site residues were analyzed to determine the outcome of ligands on the dynamics of the protein's active site residues. In the combined RMSF spectra for the simulated complexes, it appears that the values measure the average deviation of a particle over time from a reference position (typically the time average position of the particle). Thus, the RMSF analyzes the portions of the structure that are floating from its average structure. In analogy, we assume that stochastic fluctuations of macrostructures can facilitate the entry of CNTs into the active site deep within viral macrostructures.

In the graphic analysis of the behavior of the RMSF values, a pattern of behavior of the CNTs with the M-pro and S-gly was observed, clearly showing the dynamic movement that occurs in the regions of the catalytic site where there are more significant openings, thus demonstrating greater flexibility then the other macrostructure. During the simulations, with the E-pro the RMSF has greater instability and consequently less mobility and flexibility. MD simulation results for the complex and receivers are analyzed on the 100 ns timescale to understand dynamic behavior and stability.

3.4 The radius of gyration (Rg)

The turning radius gives us information about the evolution of the protein’s geometry, whether it turns or whether it is performing periodic contraction and expansion (breathing) movements. This turning or contraction movements occur when the turning radius regarding the axes intersects. Figure 9 shows the calculations of Rg as a function of time for the nine ligand/receptor complexes.

The bulkier the protein, the higher its Rg. In this case, it can be understood that when the protein is denaturing, its Rg increases. In these simulations, the complexes presented large domain movements with oscillations and rotations. However, these movements are not conclusive, as we are analyzing only 100 ns and a single simulation of each complex. Thus, we do not have enough temporal samples for analysis, so it appears that Rg was unstable for all ligand-receptor simulations, indicating that the binding of both ligands leads to the unpacking of these macrostructures and their possible denaturation.

3.5 Solvent-accessible surface area (SASA)

SASA was calculated for three complex systems in order to measure the interaction between protein-ligand complexes and solvents in the nine-time interactions (figure 10) using the GROMACS 2021.1 packages. Polar and non-polar surface areas are often defined by partial atomic charges taken from the molecular potential used. These partial atomic charges differ significantly between force fields. To avoid this dependence on the force field, we recalculate the surface areas accessible to the average polar and nonpolar solvents, summing the contributions not according to the partial charges of the atoms, but according to whether these atoms belong to hydrophobic or hydrophilic residues. Solvent-accessible surfaces of terminal amino acids are much larger and do not depend on force fields, indicating that they are largely exposed to solvent. The central residues that have the smallest mean square fluctuation are also the residues that have the smallest area exposed to the solvent, as they are in the most central part of the receptor structure and are therefore protected from the solvent. Free energy of the non-polar solvation of each atom in a molecule is proportional to the SASA. The term non-polar handles the rearrangement of solvent molecules around the solute and the contact interaction between the solute and the solvent molecules.

Modeled E-pro conformational changes over the simulation period were estimated using SASA calculations. The average SASA value calculated for E-pro during the 100 ns simulation was relatively stable, showing that there were no significant changes in its structure, but in the interaction with the CNT zigzag, there were significant variations in the period from 80 to 100 ns as seen in figure 10. Results confirmed that M-pro residues were well exposed and accessible to solvent. SASA presents the surface area of a biomolecule that is accessible to a solvent and the SASA range of interaction with CNT zigzag is between 10 and 40 ns, where the receptor surface becomes more accessible. It was soon observed that the SASA value was stable for the interaction with the chiral CNT. For the M-pro+ CNT armchair, the SASA becomes larger between 30 and 50 ns. We can analyze in all the graphs of figure 10(c), the complexes in this simulation remained more stable allowing little presence of variations, the increase of the SASA value showed a decrease in the amount of protein, which indicates that it shows a decrease in the surface area accessible to the solvent, which results in an increase in protein stability. From the graph shown in Figure 10(c), it can be seen that the SASA value of the structure formed by the CNTs with the S-gly is globally more stable when compared to the other interactions. Relative SASA can predict protein conformational changes after ligand binding. According to the results of SASA; it was observed that the binding of the macrostructures with the CNTs induced small conformational changes of the viral structures. Modeled conformational changes over the simulation period were estimated using SASA calculations. The results confirmed that the macrostructure residues were well exposed and accessible to the solvent.

3.6 Gibbs free energy analysis

The free binding energy and percentage relative standard deviations of single-system simulations above 100 ns were calculated assuming that the ligand-receptor complexes were moving separately, however, single-system simulations were still stable. From the total negative binding free energy, the ΔGBinding values indicated a higher occurrence of interactions. The interaction with the receptors is largely controlled by the adsorption that takes place on them, since the interaction occurs directly with the adsorbed ligand. Because of this adsorption, there is a change in the ΔG of the system, which decreases during the interaction process. The electrostatic interactions between the charged residues presented by the surface of the receptors with the CNTs have an important contribution to the negative ΔG. The dynamic behavior of the selected compounds is analyzed for low energy profiles using the g_MM/PBSA script, which uses the MM/PBSA method, which is used for post-processing of coupled structures along with the reliability of the bonding of the compound inside the pocket of flexible connection. The 100 ns simulation of the protein-ligand complexes together with the binding free energy of MM-PBSA suggests that the main molecules fit perfectly at the binding site and are structurally stable with a low energy profile. The MM-GBSA method was calculated from the free energy of the CNTs with the viral structures, and this was done using the surface area energy, solvation energy, and energy minimization of the ligand and receptor complexes. The analysis of VDW energy variation for this interaction aimed to investigate the structural properties of CNTs. Thus, VDW interactions play an important role in the properties of systems in which much stronger dipole-dipole interactions are present at potential energy in the solvent. Including bound terms such as angle and torsional energies as well as unbound terms such as VDW and electrostatic interactions. The second term is responsible for the dissolution of the different species. It is quantified by the sum of two energy terms, i.e. the polar and non-polar solvation energies using an implicit solvation model.

The values for apolar solvation in Table 2 show a marked increase as the interaction approaches the surface of SARS-CoV-2, indicating structural relaxation. Thus, we assume that simulation times of 100 ns were enough to sample balanced systems. The highest nonpolar solvation energy value is found for the interaction of CNTs with S-gly. The parameters for these models were optimized based on explicit solvent simulations and validated against the free energies of solvation. g_mmpbsa provides options for using three alternative non-polar models. The influence of model choice on binding energy was therefore examined. Non-polar values were calculated using these different non-polar models, with the parameters shown in Table 2.

Table 2. Power components for all simulations (Mean ± relative standard deviation %).

Complex	VDW (kJ/mol)	Electrostatic (kJ/mol)	Polar solvation (kJ/mol)	Apolar solvation (kJ/mol)	ΔGBinding (kJ/mol)
E-pro + Zig	-79.71 ± 1.31	-10.18 ± 0.68	40.93 ± 3.43	-13.31 ± 1.03	-93.24 ± 3.88
E-pro + Arm	-61.71 ± 1.81	-7.16 ± 0.71	37.04 ± 2.03	-15.31 ± 1.03	-76.24 ± 3.86
E-pro + Chi	-54.82 ± 1.91	-5.12 ± 0.79	25.23 ± 4.02	-15.31 ± 1.03	-64.22 ± 3.86
M-pro + Zig	-96.92 ± 1.79	-22.84 ± 0.70	43.10 ± 2.45	-11.08 ± 1.96	-99.09 ± 3.92
M-pro + Arm	-84.92 ± 1.45	-17.93 ± 0.64	67.56 ± 3.68	-9.08 ± 0.96	-87.57 ± 4.96
M-pro + Chi	-65.29 ± 5.69	-15.94 ± 3.10	60.93 ± 2.57	-10.06 ± 1.52	-62.73 ± 3.89
S-gly + Zig	-166.29 ± 4.68	-24.67 ± 3.92	71.30 ± 1.12	-10.06 ± 1.52	-112.73 ± 3.33
S-gly + Arm	-132.29 ± 9.58	-16.51 ± 2.94	63.28 ± 3.62	-10.06 ± 1.52	-94.38 ± 3.45
S-gly + Chi	-107.29 ± 2.57	-08.52 ± 1.19	44.37 ± 2.99	-10.06 ± 1.52	-80.49 ± 3.67

However, it can be observed that the electrostatic energy of the interaction of CNTs increased significantly as binding structures were tested over the surface of the virus, which may contribute to the interaction at these sites. The electrostatic attraction is considered a common characteristic of all systems. Among the simulations, the S-gly+ CNT zigzag showed a high value of VDW energy, using the simulation strategies. The potential energy of VDW varies mainly by two factors, specifically, surface area (molecule geometry) and electronic polarizability (molecular size), among the different energy calculated. We can relate this to the possibility of fitting in a more external area of the glycoprotein, besides the zigzag CNT having electrical properties. Large molecules are associated with greater polarizability. The more stable CNTs are more polarizable as there is a better distribution of charge to deform and interact. The results of the energetic analysis shown in the graph of figure 11 demonstrate the behavior of the ΔGBinding values for the three types of proteins. The ΔGBinding values obtained show that the contributions to the ligand coupling were the polar solvation, non-polar solvation, and VDW terms. These identified inhibitors do not represent any major changes in their free binding energies. Among the interactions, the ones with S-gly stand out, the values of ΔGBinding have a strong affinity value, demonstrating the effectiveness of the interaction with the residues of the glycoprotein. E-pro also shows affinity, the ligands do not significantly interact with the binding site residues and it also has a high instability, which translates into a high standard deviation value, the interaction with M-pro has an intermediate value, even though it demonstrates stability when compared to E-pro, this last receptor is not so suitable for interaction for the inhibition of SARS-CoV-2, but the interaction within the binding site persists throughout the simulation. The potential energy of VDW varies mainly by two factors, specifically, surface area (molecule geometry) and electronic polarizability (molecular size), between the different calculated energy types. Large molecules are generally associated with greater polarizability. Electrostatic potential energy is influenced by the polarity of the interacting molecules, which can be expressed by a dipole moment. The greater the difference in the electronegativity values of the bonded atoms, the greater the dipole moment.

The computer simulation of MD from the docking performed by the interaction between CNTs (ligands) and proteins (receptor) aimed to show the potential of CNTs as inhibitors of SAR-CoV 2. This purpose showed very relevant results of the interaction. It was found that all CNTs in their three different geometric shapes interacted with the three outer protein structures: E-pro, M-pro, and S-gly of SAR-CoV2. Then, according to the simulation results, the following descriptive analysis can be carried out. The results obtained through the RMSD show the global behavior of the complexes, thus allowing to monitor dynamically the variations that occur. It was soon verified that the S-gly + zigzag and E-pro + zigzag complexes presented smaller fluctuations and stabilized from 10 ns, time corresponding to the heating of the complex, as for the M-pro + zigzag complex, stabilization starts from of the 40 nos. However, the S-gly + chiral and M-pro + armchair complexes are the ones that suffered the most fluctuation, this may be due to a rotation movement of the protein. As for the RMSF results, which describe how the position of each atom of the protein structure varies its position, it was observed that the E-pro showed less flexibility and fluctuation in the interaction with the CNTs. However, S-gly and M-pro showed greater stability because of greater flexibility in interactions with CNTs.

Regarding the Rg results in the simulations, it was found that the complexes presented large oscillations and rotations in the time interval of 100 ns, a fact that may have occurred because the protein is denatured, thus producing an increase in Rg. The results obtained for the SASA confirmed that for the interaction CNT armchair + M-pro, the SASA becomes larger between 30 and 50 ns. We can analyze in all the graphs of Fig. 10(c), that the complexes in this simulation remained more stable, allowing brief presence of variations. Other interactions. It is important to mention that the relative SASA can predict the conformational changes of the protein after ligand binding. Regarding the structure of SAR CoV 2 proteins, their conformational versatility and stability were characterized by analyzing the RMSD, RMSF, and SASA of each protein receptor linked to different CNTs. And it was observed how the ligands interact with passaging time and how this interaction occurs since the CNTs could bind to the residues of the active site of the macromolecules. They demonstrated good interactions; in particular, the CNT zigzag linker. The zigzag CNT with the chemical structure optimized via DFT showed the best interaction with the SARS-CoV-2 structures through alkyl bonds, as revealed in the MD tests. These obtained a more stable posture in relation to the others. However, this is perceived through the results obtained for the energies of VDW and ΔG, a fact that establishes the strongest connection between ligand and receptor. Among the external proteins, the one that showed the best adsorption of carbon ligands, was S-gly, this optimal behavior may be related to the hydrophobic interactions and hydrogen bonds that occurred between the active site of the receptor and the hydroxyls present in the ligand, evidencing a more stable behavior of the ligand in this complex, with several twists in the structure around its primary structure and a greater tendency towards stability. It is of fundamental importance to mention that the S-gly protein is the most external of the SAR-CoV 2 and the main facilitator of the entry of the virus into the host cell for the virus replication process to occur, so this result is very good because the variants or strains arise when a virus undergoes a series of changes in the course of its replication process within the infected cell.

Comparing the results, it was observed that the chiral CNT was the ligand that obtained, according to the simulation, the lowest interaction with the three external proteins, being less attractive than the armchair CNT and the zigzag. And within this perspective, its lesser interaction occurred with the E-pro protein, a fact that is explained because it is the least external protein of the SAR-CoV 2. However, following the reasoning, it became clear that E-pro was the protein that had the least interaction with three ligands from the simulation because of the results obtained for the affinity energies VDW and ΔG. However, it can be concluded that the research by computer simulation analysis of MD reached its aim, precisely by showing that there was an interaction between the CNTs and the external proteins of the SAR-CoV 2. Showing an optimization for the CNT zigzag + S- gly and sequentially CNT armchair + S-gly and CNT chiral + S-gly. As demonstrated through this integrated approach, the computational prediction for inhibition of the main external structures of SARS-CoV-2 has resulted in some promising leads for further experimental validation. It is expected that the results and in silico predictions obtained in this study, including the potential clinical insights, can facilitate the discovery of inhibitor materials and, through them produce, PPEs, Sprays, and waterproofing solutions. In this way, the CNTs come to add to the fight against the new coronavirus pandemic.

Acknowledgments The authors would like to thank the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES). The authors are grateful for the support of the PROPESP/UFPA (PAPQ) and the National Council for Scientific and Technological Development (CNPq)

Funding - This study was financed in part by PROPESP/UFPA (PAPQ) and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001.

Conflicts of interest/Competing interests - The authors declare no conflict of interest.

Availability of data and material - All relevant data is provided in the manuscript.

Code availability - Software used is commercially available.

Authors' contributions J. C. M. Lobato: conceptualization, methodology, software, formal analysis, resources, writing; T. S. Arouche: conceptualization, methodology, software, formal analysis, resources, writing; T. A. Filho: formal analysis, writing, supervision; J. Del Nero: formal analysis, revision. A. M. J. C. Neto: formal analysis, writing, supervision, project administration. All authors have read and agreed to the published version of the manuscript.

Ethics approval - Not applicable.

Consent to participate - Not applicable.

Consent for publication - All authors agree to the publication of the manuscript.

Data availability - Manuscript data can be retrieved from: https://www.scidb.cn/anonymous/bVlWVk5i

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Interactions between carbon nanotubes and external structures of SARS-CoV-2 using molecular docking and molecular dynamics

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