Investigation of Pharmaceutical Importance of 2 H -Pyran-2-One Analogues via Computational Approaches

: Highly functionalized spirocyclic ketals were synthesized through asymmetric oxidative spiro-cyclization via carbanion-induced ring transformation of 2 H -pyran-2-ones with 1,4-cyclohexandione monoethyleneketal under alkaline conditions. Further acidic-hydrolysis of obtained spirocyclic ketals yields highly substituted 2-tetralone in good yield. Computational analysis based on the DFT calculations and MD simulations has been performed in order to predict and understand global and local reactivity properties of newly synthesized derivatives. DFT calculations covered fundamental reactivity descriptors such as molecular electrostatic potential and average local ionization energies. Nitrogen atom and benzene rings have been recognized as the most important molecular sites from these aspects. Additionally, to predict whether studied compounds are stable towards the autoxidation mechanism, we have also studied the bond dissociation energies for hydrogen abstraction and identiﬁed the derivative which might form potentially genotoxic impurities. Interactions with water, including both global and local aspects, have been covered thanks to the MD simulations and calculations of interaction energies with water, counting of formed hydrogen interactions, and radial distribution functions. MD simulations were also used to identify which excipient could be used together with these compounds, and it has been established that the polyvinylpyrrolidone polymer could be highly compatible with these compounds, from the aspect of calculated solubility parameters.


Introduction
A well-known aromatic bicyclic ketone derived from tetralin, 2-Tetralone, has been identified as an essential intermediate for the synthesis of natural products and biologically valuable compounds [1][2][3][4]. Moreover, tetralone-derived polyaromatic compounds with donor and acceptor groups exhibit amazing absorption and emission properties [5,6]. Further phenanthridine based fluorescent chemosensors have been designed for the detection of heavy metal ions such as Hg 2+ and Ru +3 using β-tetralone as key precursor [7,8]. Additionally, dihydrophenanthrenes synthesized via ring transformation of 2H-pyran-2-ones with 2-tetralone under basic condition have been successfully utilized in fabricating blue, sky-blue, and green color light-emitting devices [9]. Apart from this, 2-tetralones are potential precursors for the construction of tetrahydronaphthalene-based naturally occurring and pharmacologically active molecules. Tetrahydronaphthalene-cored compounds are well known for their interesting anti-tumor [10], antimicrobial [11], antidepressant [12], and anti-inflammatory activities [13]. Idarubicine, an antileukemic glycoside [14], and (±) daunomycinone [15], a potent antibiotic with anticancer activity, are tetralin-cored drug molecules derived from 2-tetralones. Another interesting drug molecule, Nepinalone, synthesized by reacting 1-methyl-2-tetralone with 1-N-(2-chloroethyl)piperidine, is a compound exhibiting antitussive activity [16]. Furthermore, rotigotine is as a dopamine agonist used in the treatment of Parkinson's disease [17] while treprostinil is used to treat pulmonary hypertension [18]. Thus, compounds of this type are potential candidates for the development of drug molecules for the treatment of different diseases related to the central nervous system (CNS). In view of the above important facts, a number of organic chemists are actively engaged in the asymmetric synthesis of spirocyclic skeletons having cyclohexane, cyclohexene, and cyclohexanone motifs.
In this work, a set of first principles and classical calculations have been performed in order to understand global and local reactivity properties of the as-synthesized molecules. Computational modelling of organic molecules with pharmaceutical potential has been recognized as one of the most important steps in the development of novel pharmaceutical products, due to its ability to predict important physical and chemical properties and, in this way, to accelerate the drug design process [19]. As evidenced by numerous publications, the combination of DFT calculations and MD simulations have been proven to be particularly useful for these purposes [20][21][22][23][24], which was a clear motivation for the application of these methods in this study as well.

General Procedure for the Synthesis of Functionalized Spirocyclic Ketals 7
To a 25 mL round bottom flask, containing 2H-pyran-2-one 5 (1.0 mmol, 1.0 equiv) and 1,4-cyclohexanedione monoethylene ketal 6 (1.2 mmol, 1.2 equiv), was added powdered KOH (1.2 mmol) in dry DMSO (3.0 mL) and the resulting reaction mixture was placed in in an ultrasonic bath for 26 to 37 min for irradiation at room temperature. The course of the reaction completion was monitored by TLC and the spots were visualized under UV light. The reaction was quenched by the addition of ice-cold H 2 O (10 mL) and the mixture was neutralized with dilute HCl, followed by extraction with EtOAc (3 × 10 mL) and the combined organic layer was dried over Na 2 SO 4 , filtered, and evaporated under vacuum. The crude product obtained was then purified using column chromatographic technique using EtOAc/hexane (1:4) as the eluent. Finally, the desired products, ketals 7, were characterized by spectroscopic analysis.

General Procedure for the Synthesis of Functionalized 2-Tetralone 11
A solution of spirocyclic ketal 7 (0.25 mmol) in 4% ethanolic-HCl (5 mL) was refluxed for 1 h. The progress of above reaction was checked by TLC. Upon completion, the reaction mixture was brought down to room temperature and solvent was evaporated under vacuum. The residue obtained was diluted with water (5 mL) and extracted in dichloromethane (3 × 5 mL). The combined organic layers were dried on Na 2 SO 4 , filtered, and concentrated under reduced pressure. The crude product was then purified through silica-gel chromatography using EtOAc:hexane (1:4) as an eluent to give functionalized 2-tetralone 11.

Computational Details
In order to study the title compounds, quantum mechanical calculations and molecular dynamics simulations have been performed by employing the programs from Schrödinger Materials Science Suite 2020-3 (SMSS). Quantum mechanical calculations were based on the DFT approach, and for these purposes, Jaguar [25][26][27] program was used for all DFT calculations. MD simulations were based on the OPLS3e force field [28][29][30][31], and for these purposes, the Desmond [32,33] program was used.
DFT calculations were done with combination of B3LYP [34][35][36][37] and CAM-B3LYP [38] exchange-correlation functionals, together with 6-31G(d,p), 6-311G(d,p) and 6-311++G(d,p) basis sets. B3LYP functional and 6-31G(d,p) basis set was used for geometrical optimizations of all molecules, followed by the vibrational analysis to check that the true ground states had been reached. In all cases, the vibrational analysis yielded only positive frequencies. Properties such as molecular electrostatic potential (MEP) and average local ionization energy (ALIE) have been calculated at the same level of theory by single-point energy calculations. Improved accuracy for self-consistent field procedure and grids was used. B3LYP/6-311G(d,p) level of theory was used for calculations of bond dissociation energy for hydrogen abstraction (H-BDE), while the simulation of UV spectra and analysis of excitations have been performed thanks to a time-dependent DFT (TD-DFT) approach at CAM-B3LYP/6-311++G(d,p) level of theory. To identify the molecular sites responsible for light absorption, natural transition orbital (NTO) formalism has been used [39].
For MD simulations, simulation time was set to 10 ns, while other parameters included a temperature of 300 K, normal pressure, and cut-off radius equal to 10 Å. In these simulations, the solvent was treated by a simple point charge (SPC) model [40]. After the MD simulations were performed, a simulation quality analysis was performed in order to assure that the selected MD parameters yielded reliable results.

Local Reactivity Properties-MEP and ALIE Surfaces
Fundamental parameters related to the reactivity, such as MEP and ALIE, have proven to be amongst the most important quantum molecular descriptors. They are fundamental since they are tightly connected to the electron density, a fundamental quantity within the DFT approach. Thanks to these descriptors, one can predict and analyze the local reactivity properties, i.e., to identify the most reactive molecular sites.
If the polarization and the nuclear rearrangement effects as a consequence of presence of a unit test charge at distance are neglected, the equation for calculation of MEP ( ( )) can be written in the following form: In Equation (1), summation is performed over all nuclei. ( ) denotes the electron density of a molecule, while ( ) denotes the potential exerted at coordinate .
According to Murray et al., ALIE is defined as a sum of orbital energies weighted by the orbital densities. With this being stated, ALIE can be calculated according to the following equation:

Local Reactivity Properties-MEP and ALIE Surfaces
Fundamental parameters related to the reactivity, such as MEP and ALIE, have proven to be amongst the most important quantum molecular descriptors. They are fundamental since they are tightly connected to the electron density, a fundamental quantity within the DFT approach. Thanks to these descriptors, one can predict and analyze the local reactivity properties, i.e., to identify the most reactive molecular sites.
If the polarization and the nuclear rearrangement effects as a consequence of presence of a unit test charge at distance r are neglected, the equation for calculation of MEP (V(r)) can be written in the following form: In Equation (1), summation is performed over all nuclei. ρ(r ) denotes the electron density of a molecule, while V(r) denotes the potential exerted at coordinate r.
According to Murray et al., ALIE is defined as a sum of orbital energies weighted by the orbital densities. With this being stated, ALIE can be calculated according to the following equation: In Equation (2) electronic density of the i-th orbital at the point → r is denoted as ρ i → r , while the ε i and ρ i → r denote the orbital energy and total electronic density respectively. From the aspect of visualization, these descriptors are most frequently presented by mapping their values on the electron density surface, which has been done in this work as well, taking into account the isosurface value of 0.001. MEP and ALIE surfaces of all studied molecules in this work have been presented in Figure 1.
While MEP quantity resembles the charge distribution with the studied molecules, ALIE quantity shows molecular sites where electrons are least tightly bonded. This means that the MEP surface indicates the molecular sites that are abundant or deficient with electrons, showing where the molecule is susceptible to electrostatic interactions with other molecules. On the other side, ALIE indicates where it is the easiest to remove an electron, therefore revealing the molecular sites that are sensitive towards electrophilic attacks.
In terms of charge distribution, MEP surfaces presented in Figure 1 indicate that the lowest MEP value is practically the same for all but one of the derivatives investigated in this work. Namely, the lowest MEP value of the RS-6 derivative is characterized by the value which is 5 kcal/mol lower than the other lowest MEP values, designating it as a derivative that is the least susceptible to interactions with electron-deficient molecular sites. On the other side, the same derivative has the highest value of MEP quantity, designating it as a derivative that could be the most sensitive towards the electron abundant molecular sites of other molecules. In general, the distribution of maximal and minimal MEP values is practically the same for all derivatives. The minimal MEP value has been always calculated for nitrogen atom; however, besides this molecular site, locations above benzene rings in all cases were also characterized by the lowest ALIE values. Therefore, these molecular sites are designated as being sensitive towards electrophilic attacks. The lowest ALIE value of 184.26 kcal/mol has been calculated for the RS-4 derivative, which is 7 kcal/mol lower than in the case of RS-2 derivative. In general, RS-1 and RS-2 are grouped around the value of 192 kcal/mol, while derivatives RS-3 to RS-6 are grouped around the value of 185 kcal/mol.

Sensitivity towards Autoxidation
The stability of active components in the pharmaceutical formulations is one of the main concerns during the development of novel drugs. This type of stability is greatly influenced by the autoxidation mechanism, which might lead to the generation of genotoxic impurities [53,54], which do not just limit the overall applicability but also threaten the health. In terms of experimental activities, the identification of molecules prone to the autoxidation mechanism is tedious and time-consuming processes. Fortunately, it has been concluded that the sensitivity towards autoxidation is closely related to the H-BDe parameter, which allows scientists to predict sensitivity towards this important mechanism employing computational analysis. If some bonds are characterized by the H-BDE values in the range between 70 kcal/mol and 85 kcal/mol [55,56], then such molecular site is most probably susceptible to the autoxidation mechanism. The most important H-BDE values of all studied molecules have been summarized in Figure 2.  Figure 2 contains only H-BDE values that are close to the border threshold. All other H-BDE values are much higher than the defined threshold and are therefore not significant for further discussion. Results presented in Figure 2 indicate that only one derivative   Figure 2 indicate that only one derivative violates the criteria for autoxidation, with respect to the upper border value of H-BDE. This derivative is denoted as RS-6 and is characterized by one H-BDE value equal tõ 83 kcal/mol. This is certainly below the upper border level of 85 kcal/mol, meaning that it could be susceptible to autoxidation and produce genotoxic impurities during the shelf storage. On the other side, all other molecules are characterized by the H-BDE values higher than the upper threshold, indicating that they should be stable during the storage. Gathered results regarding H-BDE values indicate that all but one of the derivatives (RS-6) have suitable values of H-BDE, indicating stability with respect to the autoxidation mechanism.

Interactions with Water
In this work, MD simulations were used to investigate the reactivity of title compounds with water molecules, which is one of the most important aspects of the pharmaceutical potential of the mentioned molecules. For these purposes, MD simulations are important because they allow one to explicitly involve water molecules and investigate rather large systems that would be impossible to treat with quantum-mechanical calculations.
In our MD simulations, for each studied molecule, we have run a separate MD simulation on a simulation box that consists of that molecule surrounded by approximately 2500 water molecules. For these purposes, a System Builder tool SMSS was used. The number of added water molecules was controlled by variating the dimensions of a cubic simulation box. Other MD details were as described in the Computational Details section. Simulation boxes were cubic.
Interactions with water were studied both globally, through calculations of interaction energy and an average number of the hydrogen bonds between selected molecule and water (Table 2), and locally through calculations of radial distribution functions (RDF) which indicate the atoms of molecules with the pronounced interactions with water ( Figure 3).
For each MD frame, interaction energy has been calculated by subtracting the total energies of selected molecule and solvent, from the total energy of the molecule + solvent system. Then, the interaction energy was averaged over all frames. According to the interaction energies with water, presented in Table 2, it can be seen that there is a significant difference between studied molecules in the extent to which they interact with water. The magnitude of this parameter took values in the range between 63 kcal/mol to almost 77 kcal/mol. The lowest interaction energies with water have been calculated for RS-1, RS-2, and RS-6 molecules, while RS-3 and RS-4 molecules were characterized by the strongest interactions with water. RS-5 molecule was somewhere between, with the magnitude of interaction energy equal to~70 kcal/mol. It was interesting also to note that all but one derivative on average formed~3 hydrogen bonds with water molecules. The only exclusion was the RS-4 molecule, which formed more than 4 hydrogen bonds with water molecules on average, which explains why this molecule had the highest interaction energies with water. In order to investigate the local reactivity of studied molecules with water, we have calculated the RDFs. The most representative RDFs are presented in Figure 3.
Results presented in Figure 3 indicate the absence of atoms that have significant interactions with water molecules, since all g(r) curves are characterized by the low g(r) values whose maximal values are located at high distances, well above the 2 Å. Additionally, although the studied molecules are relatively large, it has been observed that all of them have only 2-4 atoms with RDFs worth of mentioning when the size and profile of g(r) curves are taken into account. In all cases, nitrogen and oxygen were identified as the ones with relatively important RDFs, with the small exception of the chlorine atom in the case of the RS6 molecule. It is also worthy of mentioning that the RS4 molecule, characterized by the highest interaction energy with water is characterized by the three relatively decent RDFs, belonging to two oxygen and one nitrogen atoms.  Results presented in Figure 3 indicate the absence of atoms that have significant interactions with water molecules, since all g(r) curves are characterized by the low g(r) values whose maximal values are located at high distances, well above the 2 Å. Additionally, although the studied molecules are relatively large, it has been observed that all of them have only 2-4 atoms with RDFs worth of mentioning when the size and profile of g(r) curves are taken into account. In all cases, nitrogen and oxygen were identified as the ones with relatively important RDFs, with the small exception of the chlorine atom in the

Identification of Suitable Excipients
Improvement of stabilization, solubility, delivery, and other properties is another important challenge during the development of novel pharmaceutical formulations, once the suitable active components are identified. To achieve this, it is necessary to combine active components with compounds, called excipients that have suitable properties. Since there is no universal excipient, it is necessary to select one.
The selection of suitable excipient might be a tedious and time-consuming process; however, thanks to the MD simulations, the selection of adequate excipient can be significantly narrowed. The key goal in the identification of suitable excipient is to identify the one which is compatible with the active component in terms of solubility parameters. If they have similar values of the solubility parameter, then they are compatible and can be combined in a novel pharmaceutical formulation [57][58][59].
For these purposes, the solubility parameter can be calculated by using the MD simulations and by applying the following Equation (3): where ∆H V denotes heat of vaporization and V m denotes the molar volume. In order to calculate the solubility parameter for all studied compounds, for each compound separate MD simulation was performed, on the cubic box containing 32 such molecules. All other parameters were the same as mentioned in the Computational Details section. Additionally, the solubility parameters were calculated for the frequently used excipients, to be able to compare the solubility parameters of studied compounds and identify which type of excipient could be potentially suitable. Frequently used excipients studied in this work were polyvinylpyrrolidone polymer (PVP), maltose, and sorbitol. Solubility parameters of RS1-6 molecules and frequently used excipients are summarized in Table 3. Results presented in Table 3 indicate that all studied molecules in this work have rather similar values, ranging between 18.6 and 19.5, indicating that modifications do not cause significant changes in this parameter. Additionally, by comparing the solubility parameters of frequently used excipients, it is evident that the PVP excipient is the most compatible with studied compounds. Namely, the solubility parameters of studied compounds are very similar to that of PVP, indicating that this compound could be potentially practically applied for the development of novel pharmaceutical formulations based on studied derivatives.

Conclusions
In summary, the DFT calculations were used to identify the molecular sites prone to electrostatic interactions with other molecules by MEP surfaces, while ALIE surfaces were used to identify the molecular sites sensitive to the electrophilic attacks. It has been shown by our calculations that the nitrogen atom is crucial for the characteristic MEP surface, while the lowest ALIE values have been identified above benzene rings as well. H-BDE values indicated that one of the studied compounds, namely the RS6 molecule, dangerously violates the upper border threshold of 85 kcal/mol, meaning that potentially genotoxic impurities could be formed in case of the formulation based on this derivative. All other derivatives seem to be stable towards the autoxidation mechanism. Furthermore, MD simulations indicated that, of all studied molecules, RS4 is characterized by the highest interaction energies with water, and at the same time, this molecule is characterized by the highest number of hydrogen bonds formed between the observed molecule and water molecules. RDFs did not indicate that any of the atoms of studied compounds have particularly strong interactions with water molecules since there were no g(r) curves characterized by the highest g(r) values at distances of around 2 Å. MD simulations also helped in identifying which frequently used excipient could be used in the case of title compounds. Namely, the calculations of solubility parameters indicated that the studied compounds could be highly compatible with the PVP excipient, as their solubility parameters are very similar.