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The investigation of energy management and atomic interaction between coronavirus structure in the vicinity of aqueous environment of H2O molecules via molecular dynamics approach

The coronavirus pandemic is caused by intense acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Identifying the atomic structure of this virus can lead to the treatment of related diseases in medical cases. In the current computational study, the atomic evolution of the coronavirus in an aqueous environment using the Molecular Dynamics (MD) approach is explained. The virus behaviors by reporting the physical attributes such as total energy, temperature, potential energy, interaction energy, volume, entropy, and radius of gyration of the modeled virus are reported. The MD results indicated the atomic stability of the simulated virus significantly reduced after 25.33 ns. Furthermore, the volume of simulated virus changes from 182397 Å3 to 372589 Å3 after t = 30 ns. This result shows the atomic interaction between various atoms in coronavirus structure decreases in the vicinity of H2O molecules. Numerically, the interaction energy between virus and aqueous environment converges to −12387 eV and −251 eV values in the initial and final time steps of the MD study procedure, respectively.


Introduction
A group of related RNA viruses that cause illnesses in mammals and birds is named coronavirus [1,2]. They cause respiratory tract infections ranging from mild to lethal in birds and humans [3]. At first, coronavirus was identified in Wuhan, China [4]. As of 16 June 2021, more than 3.82 million confirmed deaths were attributed to coronavirus, making it one of the deadliest pandemics in the world [5]. Due to the significant spread of this disease, accurate knowledge of the behavior of coronavirus can be a very important factor in the treatment of this disease. The MD method is one of the most powerful tools to identify atomic structures in nanometric structures [6][7][8]. Ibrahim et al. [9] researched the dynamical behavior of H 2 O molecule structure around an HIV (3LPT protein) by the MD method. The MD simulation outcomes display that increasing the atom's temperatures causes an enhancement in the amplitude of atomic oscillation. This research group reported the atomic interactions between histone molecule and 3LPT protein in other work [10]. Jolfaei et al. [11] reported the thermal conductivity of Deoxyribonucleic acid molecules is essential for nanotechnology applications by using the MD approach.
Technically, the MD simulation approach uses Newton's equations of motion to computationally simulate the time evolution of a set of interacting atoms [12][13][14]. In previous reports, MD simulations were used successfully in the physical study of biomaterials compounds. So, the MD simulations can predict coronavirus behavior in various conditions. Karimipour et al. [15] describe the atomic behavior of this virus in contact with a different metallic matrix such as Al, steel, and Fe with the MD approach. Their outcomes show that virus interaction with steel matrix causes the highest removal of the virus from the surfaces. Malekahmadi et al. [16] studied the atomic stability of the coronavirus at various thermodynamic attributes such as pressure and temperature. The outcomes express that coronavirus stability has reciprocal relation with atomic pressure and temperature. In current computational work, MD simulations to calculate the atomic stability of coronavirus structure in an aqueous environment is used for the first time. For this purpose, the initial pressure and temperature of simulated structures are set to 1 bar and 300 K. The MD simulation in our case study runs for t = 30 ns, and physical parameters such as total energy, potential energy, temperature, interaction energy, volume, entropy, and radius of gyration are reported. Technically, Large Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package is used for molecular dynamics simulations done in our computational research [17][18][19]. The results can be used for more effective designing of COVID-19 treatment for clinical applications.

The MD simulation details
As reported before, MD approach to predict the physical stability of coronavirus in the aqueous environment is used. For this purpose, Nose-Hoover thermostat to equilibrate atomic structures at initial temperature and pressure for t = 10 ns is applied [20,21]. After the equilibrium process, simulated structures run for t = 20 ns to describe the atomic destruction process in a microcanonical ensemble [22]. In the destruction process, particles are allowed to interact, and particle evolution in phase space is reported using Newton's equation. The boundary condition is one of the important parameters to calculate valid results. Periodic boundary conditions were used in x, y, and z directions in this work [23]. The interatomic force field is another important parameter in MD simulations. DREIDING force-field is used as the main function to simulate virus structure in the MD box [24]. Furthermore, the TIP4P model is used for aqueous environment simulation [25]. The four-point TIP4P rigid water model extends the traditional three-point TIP3P model by adding an additional site where the charge associated with the oxygen atom is placed. In described models, non-bond interaction between various particles presented by Lennard-Jones (LJ) and Columbic formalisms [26,27]. The LJ potential is a mathematically simple equation that describes the interaction between a pair of particles. This interatomic function defined as below [26]: where r constant is the distance at which the potential get 0, e constant is the depth of the potential well; r ij is the distance between the I and j particles. Numerically, the e and r constants values are listed in Table 1 from DREIDING reference [24]. Also, Columbic formalism is used in the current study represented by equation (2) where q i and q j are the charges on the two particles, k is an energyconversion constant, and e 0 is the dielectric constant. Furthermore, the bonded forces consist of bond angle bend, dihedral angle torsion terms, and bond strength. Harmonic oscillator formalisms calculate the bond and angle strength in DREIDING force field. After forcefield setting for modeled structures, the atomic behavior of defined systems can be calculated. Newton's second law implemented as the gradient of the defined force field as below to compute these atomic evolutions [28][29][30], The total energy of atomic compounds is another important parameter that can be estimated in the form of Hamilton as equation (4) [30], In common MD simulations, the Velocity-Verlet algorithm was used to associate described equations which are reported in this section [31][32][33]. Below formalisms show the Velocity-Verlet algori thm for position and velocity calculation in the MD simulations, where Þand r i t ð Þ,v i t ð Þ represent the initial value of these parameters, respectively. According to the described details in this section, MD simulations in our study carried out in two main steps: Step A: The initial arrangement of coronavirus and the aqueous environment was simulated with DREIDING and TIP4P model and equilibrated by NPT ensemble for t = 10 ns. For this purpose, the initial value of atomic temperature and pressures set at 300 K and 1 bar, respectively. After equilibrium phase detection in the atomic compound, simulated structures' physical stability was reported by calculating the temperature and total energy.
Step B: Interaction process between virus and H 2 O molecules implemented by using NVE ensemble for t = 20 ns. After destruction process detection in coronavirus, physical parameters such as interaction energy, potential energy, entropy, volume, and radius of gyration were reported to the physical stability of simulated virus in the aqueous environment.

Discussions and results
In this step, the virus's atomic arrangement and aqueous environment are defined in the MD box. For this computational step, coronavirus was fixed in the middle region of the molecular dynamics box, while the surrounding region of volume was filled by water. Technically, this atomic compound was prepared by Avogadro and Packmol packages [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. Fig. 1 shows the modeled atomic arrangement for virus stability description. This figure dis- Table 1 r and e constants value for various atomic interactions in coronavirus arrangement [24]. plays the MD box at the front, top, and perspective views, visualized by OVITO software. Figs. 2 and 3 show the temperature and total energy difference of simulated structures versus molecular dynamics time. As depicted in these Figs., the temperature and total energy of atomic compounds converged to 300 K and À33919.2 eV after t = 10 ns. These calculated results indicated the MD simulation time in the equilibrium process is sufficient, and modeled structures reach physical stability after defined simulation time. Furthermore, total energy variation in simulated compounds shows matching between particle positions and defined interatomic force fields. Physically, by MD time passing, the total energy value converged to negative values. This negative convergence arises from the attraction force between various atomic units in the MD box.
After equilibrium phase detection in simulated structures, ensemble change implemented to the MD box. In this step, NPT ensemble is converted to NVE one, and simulations continued to 20 ns later for atomic destruction process description in coronavirus. By implementing atomic structures, the interatomic distance between various virus sections gets to bigger ratios (see Fig. 4). This behavior would be considered in a way similar to particles being dispersed inside the base fluids [49][50][51][52][53][54][55][56][57][58][59]. Hence the atomic behavior arises from virus destruction in the aqueous environment. The potential energy in virus structure can be described this phenomenon. Numerically, by molecular dynamics time passing from t = 10 ns to t = 30 ns, the potential energy of simulated virus varies from À25001 eV to À7263 eV, respectively. Fig. 5 shows these parameter changes versus MD time. Furthermore, potential energy drop in virus structure was detected in t = 25.33 ns for the first time, which represents the destruction time of virus in an aqueous environment. After this time, the interaction force between the various section of the virus decreases by high intensity, and the structural uniformity in this virus is lost. The interaction energy is another important parameter that show the destruction process of coronavirus in an aqueous environment. Exactly, the calculation interaction energy between coronavirus and H 2 O molecules is provided. Fig. 6 and Table 2 show this physical parameter varies from À12387 eV to À251 eV. By convergence of interaction energy to zero values show virus atoms dispersing in the MD box (between H 2 O molecules).
It can be said that the volume of virus structure is proportional to atomic stability of them. From the physical point of view, the volume of atomic systems is proportional to the distance between their atoms. On the other hand, by atomic distance variation, the bonding energy of the structure changes. So, in our computational study, coronavirus volume variation can show this atomic arrangement stability in an aqueous environment versus molecular dynamics time. Our outcomes in this calculation are indicated by simulation time passing from t = 10 ns to t = 30 ns, the volume of virus increases, as shown in Fig. 7. By increasing the coronavirus volume, the atomic distance in this structure converges to larger values. Numerically, by MD time increasing from t = 10 ns to t = 30 ns, the volume of coronavirus enhances from 182397 Å 3 to 372589 Å 3 value (see Fig. 8 and Table 3). The concept of entropy is described by two principal approaches, the microscopic description central to statistical mechanics and the macroscopic perspective of classical thermodynamics [37]. The statistical definition of entropy defines it versus the statistics of the motions of the atomic constituents of a system mechanically. So this physical parameter can be described as an atomic disorder in the MD box. The increasing entropy of simulated structures in the current system can show their destruction      Fig. 9. The entropy of atomic structures variation versus MD time at P 0 = 1 bar and T 0 = 300 K.  Table 4 and Fig. 9). Finally, the virus radius of gyration in the presence of an aqueous environment is reported. This parameter is the root mean square distance of the virus atoms [38]. Based on Table 4, time passing of simulation from t = 10 ns to t = 30 ns, the radius of gyration in coronavirus enhances from 41.78 Å to 78.32 Å, respectively as depicted in Fig. 10. Furthermore, by virus structure enlarging more than critical volume, the radius of gyration increases rapidly. This atomic evolution displays the destruction procedure in coronavirus in the presence of H 2 O molecules in the MD box.

Conclusion
Our research describes the destruction process of coronavirus in P 0 = 1 bar and T 0 = 300 K with the Molecular Dynamics (MD) approach. Coronavirus is represented by N, O, S, and C atoms in the MD box. Also, to simulate interatomic force, DREIDING and TIP4P models have been used in virus and aqueous environments, respectively. The MD results indicated the coronavirus structures could be destroyed in the vicinity of H 2 O molecules, which can be used for clinical purposes to COVID-19 disease treatment. Numerically, the results are as follows: DREIDING and TIP4P models are appropriate for MD simulation of coronavirus and aqueous environment, respectively. From the numerical point of view, the total energy of these atomic structures converges to À33919.2 eV after 10 ns. Potential energy and interaction energy of simulated structures decrease by molecular dynamics simulations time passing from À25001 eV and À12387 eV to À7263 and À251 eV. Generally, by molecular dynamics simulation time increasing, the volume of coronavirus changes from 182397 Å 3 to 372589 Å 3 . The entropy of simulated structures (coronavirus and aqueous environment) increases from 293.21 kcal/mol.K to 336.97 kcal/mol.K value by MD simulation running with micro-canonical ensemble after t = 20 ns. The radius of gyration in simulated coronavirus changes from 41.78 Å to 78.32 Å by molecular dynamics simulation time varies from t = 10 ns to t = 30 ns, respectively

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.