Study of the Stability, Solubility and Geometry of the Complex of Inclusion β-CD with Nimesulide by Computer Chemistry Methods ^†

Abstract

During this study, a molecular system was modeled: a nimesulide, β-cyclodextrin, inclusion complex. The use of the Gaussian 16W software package allowed us to optimize geometry and determine the thermochemical characteristics of molecular systems without considering a solvent. And this was also carried out in water media, accounted for by the polarized continuum model (PCM). To confirm the accuracy of the geometry of the β-cyclodextrin molecule, a structural alignment of 46 β-cyclodextrin molecules, accessible by a corresponding search query in the RCSB database, was performed. The RSMD values of carbon and oxygen atom deviations, as well as the total number of atoms aligned, were calculated. This calculation showed a complete conformational coincidence between the β-cyclodextrin structure designed by us and the RCSB database structures. This ensures the correct approach to subsequent calculations involving this structure. Quantum-mechanical modeling of the relationship was carried out in several stages with a gradual complexity of the basic set. The hybrid method of functional density B3LYP and 6-31G(d) was used. At the end of the calculation stage, on the surface of the studied complex, the potential energy of several minimal elements was detected. This means that there are several conformational forms of the molecular system with likely differences. The change in potential energies of the investigated compounds, caused by their application to optimize the in vacuum molecules of the PCM, allowed us to determine the values of the solvatization energies. The greater magnitude of these values in the complex under consideration indicates its better solubility in water compared to nimesulide.

1. Introduction

Inclusion complexes are a little-known part of sub-molecular chemistry. The importance of studying host–guest complexes is constantly increasing due to the need for improved delivery systems and the development of new encapsulated forms of biologically active compounds. Most theoretical assumptions about complexation mechanisms are based on the results of quantum-chemical calculations. Recently, the study of these objects has been gaining popularity in molecular dynamics methods. These approaches allow us to gain an idea of the course of the process of complexation, the presence of sterile difficulties, and deformations of molecules in the course of action. Computational methods are currently extremely well known, as they help to look at the usual experiment from a different angle and find ways of creating new high-efficiency technologies. In turn, we designed β-cyclodextrin (β-CD) and ni-mesulid (Nim), as well as the proposed inclusion complex (β-CD/Nim). The optimization of geometry of structures was carried out with the help of the Gaussian16W program. The geometry of the RMSD trajectory was confirmed by the analysis of RMSD trajectories [1,2,3]. The inclusion of the complex was evaluated for its stability and solubility based on the PCM. The water solubility of nimesulide was <0.02 mg/mL, which had low bioavailability of the drug. The possibility of including nimesulide in the β-CD molecule will be assessed to identify methods for obtaining samples with improved permeability [4,5].

2. Computational Chemistry Methods Used

The modeling of the molecular systems under consideration was performed using the software package GAUSSIAN16W. Quantum-chemical calculation was performed using the hybrid method of B3LYP functional density in the base 6-31G(d). The validation of the β-CD structure was performed with the PyMOL(2.6) program and the RCSB database. Solubility was approached through the polarized continuum model (PCM) [6,7].

3. Results and Discussion

3.1. Optimization of the Geometry of the Carrier Molecule β-CD

Quantum-mechanical modeling of all connections was performed in stages with gradual complexity of the base set to reduce the computer time and improve the accuracy of results. Thus, the use of the hybrid method of the B3LYP and 6-31G(d) basis at the end of the calculation stage resulted in the detection of the potential energy of the studied complex of two minimums on the surface and what it can say about the existence of several conformational forms of data of molecular systems, formed with different probabilities (Figure 1) [8,9].

3.2. RMSD Trajectory Analysis

Using the RCSB database, 46 β-SD molecules were found. All structures, optically divided by X-ray diffraction and NMR spectroscopy, were aligned with the molecule obtained in our Gaussian 16W as a reference for comparison with experimental PBDs. RSMD values of carbon and oxygen atom deviations were calculated, as well as the total number of atoms leveled. Results are presented in

Table 1. RSMD calculation of deviations.

№	PDB ID	Method	Resolution, Å	RMSD, Å (Atoms of 77)	Atoms Aligned of 77
1	1VFO	X-ray	2.81	0.768	73
2	2V8L	X-ray	1.8	0.767	73
3	2Z1K	X-ray	2.3	0.630	74
4	3CGT	X-ray	2.40	0.000	77
5	3JUV	X-ray	3.12	0.879	73
6	5E6Z	X-ray	1.878	0.759	73
7	6JEQ	X-ray	1.802	0.846	73

.

In the end, a structure with PDB ID 3CGT was found that has full conformity with the standard. This structure shows the complete absence of atom aberration (RMSD = 0.0), with all atoms aligned (77 atoms to 77 atoms of the reference). Three more structures (PDB IDs: 2Z1K, 5E6Z, and 2V8L) have RMSD 0.630–0.767Å and alignment 73–74 out of 77 atoms (Figure 2).

The data obtained show that the β-cyclodostrin geometry from Gaussian is correct, corresponding to structures defined expressively.

3.3. Taking into Account the Effects of the Concatenation

The use of the Gaussian 16 software package allowed us to optimize geometry and determine the thermochemical characteristics of molecular systems both without the solvent and in water media accounted for by the polarized continuum model (PCM). The result is presented in

Table 2. Results of calculation in the Gaussian 16W program.

Element Name	Solvation Accounting	S, kcal/mol × K	Sum of Electronic and Thermal Free Energies, Hartree/Particle	Sum of Electronic and Thermal Enthalpies, Hartree/Particle	E(B3LYP), Hartree	Solvation Energy, Hartree
β-CD	-	383.432	−4273.99089	−4273.80871	−4275.10458	0.0696683
	PCM	386.579	−4274.06354	−4273.87986	−4275.17425
Nim	-	143.736	−1386.05638	−1385.98809	−1386.2509	0.01683559
	PCM	144.997	−1386.07425	−1386.00536	−1386.26774
Complex No.1	-	491.886	−5660.034603	−5659.800892	−5661.359932	0.08395511
	PCM	498.4	−5660.12313	−5659.88632	−5661.44389
Complex No.2	-	488.694	−5660.06363	−5659.83143	−5661.39178	0.08010679
	PCM	501.576	−5660.15194	−5659.91363	−5661.47189

. The change in potential energies of the studied compounds caused by their application to optimize in vacuum molecules of the PCM allowed us to determine values of the covalent energies, the larger size of which in the complexes under consideration indicated their better solubility in water compared to the neissulide [10].

The solvent-based free energy value of Gibbs per-sectional molecular systems still confirms their thermodynamic possibility.

4. Conclusions

Recent advances in chemical sciences open up new promising opportunities, including the ability to model molecular systems by computer software with further investigations beyond a wet lab. Among a broad range of computational approaches, quantum-mechanical calculations provide a better understanding of geomagnetic structure, solvatization energies, and thermodynamic features of compounds of interest.