The MD simulation is a computer approach for describe the position changes of particles (atoms and molecules). In this type of simulations, particles are allowed to interact for a defined time steps, giving a view of the time evolution of the total compound [17–19]. Because atombase compounds consist of a vast number of atoms, it is impossible to describe the physical performance of such complex samples analytically. MD approach fixes this problem by using numerical methods. This approach based on particle representations are among the exact methods used to describe drug delivery of CPT(OH)2 drug via MPEG1 based nanosome as nanoscale protein carrier (PDB ID: 6U2W) in current research [20]. In our simulations, determination of the evolution of the atoms is carried out by using Newton's equation for a system of atoms, where the interatomic forces are most commonly estimated by applying force field concept [20]. Here, force field between various particles inside computational box defined by DREIDING force field [21]. From this force field, atomic interactions classified in to main group; nonbonded interactions and bonded interactions. For nonbond interactions in DREIDING force field, the LennardJones (LJ) formalism is used as below [22],
\({\phi _{}}({r_{ij}})=4{\varepsilon _{}}\left[ {{{\left( {\frac{\sigma }{{{r_{ij}}}}} \right)}^{12}}  {{\left( {\frac{{{\sigma _{}}}}{{{r_{ij}}}}} \right)}^6}} \right]\) \({r_{ij}} \leqslant {r_c}\) (1)
where, epsilon constant represents the depth of the potential, sigma constant introduce the finite distance at which the net potential disappeared, r is the distance between modeled atoms. The epsilon and sigma parameter for simulated structures listed in Table 1 [21].
Table 1
The ε and σ constants for nonbond interactions in modeled CPT(OH)2 drugnanosome system. The cutoff radius set to 12 Å inside computational box [21].
Element

σ(Å)

ε(kcal/mol)

C

0.305

4.18

H

0.010

3.20

N

0.415

3.995

O

0.415

3.710

S

0.305

4.240

For bonded interactions, a simple harmonic formalism with the following equation has been implemented [23],
$$E{\text{ }}={\text{ }}\raise.5ex\hbox{$\scriptstyle 1$}\kern.1em/ \kern.15em\lower.25ex\hbox{$\scriptstyle 2$} {\text{ }}{k_r}{\left( {r  {r_0}} \right)^2}$$
2
where, kr is a harmonic constant, and r0 shows the equilibrium length. These parameters for various simple bonded interactions defined from DREIDING reference [21]. Additionally, an angular harmonic formalism has been implemented to introduce the anglebase interactions inside computational box [24],
$$E{\text{ }}={\text{ }}\raise.5ex\hbox{$\scriptstyle 1$}\kern.1em/ \kern.15em\lower.25ex\hbox{$\scriptstyle 2$} {\text{ }}{k_\theta }{\left( {\theta  {\theta _0}} \right)^2}$$
3
in Eq. (3), kθ defines the oscillator constant and θ0 parameter represents the equilibrium angle which defined in DREIDING force field. After force field settings to nanosomedrug system, the classical simulation steps followed. To describe the atomic evolution as a function of MD simulation time, Newton’s second law's equation is solved as the gradient of the defined force field function [25, 26],
$${F_i}=\sum\limits_{{i \ne j}} {{F_{ij}}={m_i}\frac{{{d^2}{r_i}}}{{d{t^2}}}={m_i}\frac{{d{v_i}}}{{dt}}}$$
4
The energy of the modeled structure can be estimated in the form of Hamilton as below [25, 26],
In current computational work, MD simulations done by using LAMMPS package [27–29]. In this computational package, the VelocityVerlet method used to compute integrationbase equations [30–32]. Technically, by using described MD simulation details, our study done in two main steps:
Phase A
Nanosomedrug system was equilibrated at 300 K and 1 bar as initial condition. For this equilibrium procedure, NPT algorithm used with 0.1 and 1 ratios for temperature and pressure damping ratios [33]. Our designed system modeled inside computational box with 1000 Å length in all directions which periodic boundary condition implemented to them [34]. The atomic representation of modeled nanosomedrug system in initial time step depicted in Fig. 1. In equilibrium process, MD simulations continued for 10 ns (by setting time step to 1 fs) and potential/kinetic energy quantity changes calculated for atomic stability description.
Phase B
Next, NPT algorithm changed to NVE one and drug delivery performance of CPT(OH)2 drug via MPEG1 based nanosome simulated [35]. This atomistic process reported by drug release ratio, root mean square displacement (RMSD), charge density, and Zeta function calculation for 10 ns. Computational settings in these two main steps listed in Table 2.
Table 2
MD simulation settings in our defined atomic sample.
MD Simulation Parameter

Value/Setting

MD Box Length

1000×1000×1000 Å3

Boundary Condition

Periodic

Defined Temperature

300 K

Defined Pressure

1 bar

Time Step

1 fs

Computational Algorithm

NPT/NVE

Damping Ratio of Temperature

0.1

Damping Ratio of Pressure

1

Total MD Time

20 ns
