Host-Guest Interactions of Plumbagin with β-Cyclodextrin, Dimethyl-β-Cyclodextrin and Hydroxypropyl-β-Cyclodextrin: Semi-Empirical Quantum Mechanical PM6 and PM7 Methods

Molecular interactions of plumbagin inclusion complexes with β-cyclodextrin (BCD), dimethyl-β-cyclodextrin (MBCD), and hydroxypropyl-β-cyclodextrin (HPBCD) were investigated by semi-empirical, Parameterization Method 6 and 7 (PM6, and PM7) in the aqueous phase using polarizable continuum calculations. The results revealed two different binding modes of the plumbagin molecule inside the BCD cavity with a negative value of the complexation energy. In conformation-I, the hydroxyl phenolic group of plumbagin was placed in the BCD cavity near the narrow-side of the host molecule. In the other model, conformation-II, the methyl quinone group of plumbagin was placed in the cavity of BCD near the narrow-side of the host molecule. The higher the negative value of the complexation energy, the more favorable is the pathway of inclusion-complex formation.


Introduction
Molecular modeling techniques are currently widely used in chemistry and pharmacology to obtain insight into information at the molecular level of systems of interest. The computational results help explain the molecular interactions and suggest the mechanisms that govern the processes when experimental techniques are insufficient. The calculation models are able to predict and screen the results when varying the compounds or the system conditions prior to laboratory tests. Semi-empirical quantum mechanical calculations have been successful for descriptions in organic chemistry because some parameters are approximated or generalized to simplify the calculation or to yield a result based on experimental data. Modern semi-empirical quantum mechanical models such as Parameterization Method 6 and 7 (PM6 and PM7) are often used to explore the electronic structure dependent properties of large molecules, where ab initio electronic structure methods (without approximations) are too expensive [1]. The PM7 method improved the description of some properties such as the heats of formation or the height of the reaction barriers for reactions and included them into the description of the dispersion interaction and hydrogen bonding in the parameterization [2], which is suitable for a description of noncovalent interactions. In this work, the molecular   Schematic representations of glucose unit and atomic numbering of β-cyclodextrin (BCD), dimethyl-β-cyclodextrin (MBCD) and hydroxypropyl-β-cyclodextrin (HPBCD). All R1 and R2 are substituted by methyl groups on all of the glucose units in MBCD. In HPBCD, only the hydroxyl group at the R1 position of one glucose unit is substituted by a hydroxypropyl group. Figure 2. Chemical structure of plumbagin (C11H8O3) and the dimensions of its minimized molecular conformation.
The first step was to prepare the guest (plumbagin) and host (BCDs) coordinate files to include the information needed by AutoGrid and AutoDock. The non-polar hydrogens were deleted and their charges were merged with the carbon atoms. The atom types were assigned, defining hydrogen bond acceptors and donors and aromatic and aliphatic carbon atoms. The rotatable bonds of the guests were defined while the hosts were kept fixed. AutoGrid was used to calculate the grid maps, one for each atom type present in the guest being docked. The systems were investigated in a threedimensional volume divided into many small grid boxes with a grid spacing of 0.375 Å. The grid center of the boxes were set at the center of the host molecules. The box has x × y × z dimensions of 14
The first step was to prepare the guest (plumbagin) and host (BCDs) coordinate files to include the information needed by AutoGrid and AutoDock. The non-polar hydrogens were deleted and their charges were merged with the carbon atoms. The atom types were assigned, defining hydrogen bond acceptors and donors and aromatic and aliphatic carbon atoms. The rotatable bonds of the guests were defined while the hosts were kept fixed. AutoGrid was used to calculate the grid maps, one for each atom type present in the guest being docked. The systems were investigated in a three-dimensional volume divided into many small grid boxes with a grid spacing of 0.375 Å. The grid center of the boxes were set at the center of the host molecules. The box has x × y × z dimensions of 14.25 Å × 14.25 Å × 7.50 Å, 15.75 Å × 14.25 Å × 9.75 Å and 18.75 Å × 14.25 Å × 9.00 Å for BCD, MBCD, and HPBCD, respectively. AutoDock used the Lamarckian genetic algorithm to calculate the conformational states of a flexible guest, using the grid maps generated by AutoGrid to evaluate the guest-host interaction at each point in the docking simulation. One hundred docking calculations were performed on each guest-host complex. The results were clustered to identify similar conformations based on all-atom root mean square deviation within 2 Å. At the end of molecular docking calculations, AutoDockTools was used to perform a cluster analysis of the different docked conformations. The lowest energy representative docked conformation from molecular docking was selected for further full geometry optimization.

Complexation Energy Calculation
The selected docked conformation of plumbagin/BCD inclusion complexes was then fully geometry optimized by the PM6 and PM7 methods. All atoms were allowed to move freely in an aqueous environment. The most stable conformation of the plumbagin/BCD, plumbagin/MBCD, and plumbagin/HPBCD inclusion complexes were selected by considering the complexation energy (∆E) as being the difference between the heat of formation of the complex and the heat of formation of the involved free molecules where E PL/BCD , E PL , and E BCD represent the heat of formation of the complex, isolated plumbagin molecule, and isolated BCD molecule, respectively.

Molecular Docking Calculation
Molecular docking was used to calculate the possibility of binding between a plumbagin molecule complex with each BCD by fixing the host structure and allowing the guest to be flexible in the specified grid box. The calculations indicated two possible conformations of the 1:1 guest:host ratio for all systems, as shown in Tables 1 and 2. In conformation-I, the hydroxyl phenolic group of plumbagin was placed in the BCD cavity near the narrow-side of the host molecule. In the other model, conformation-II, the methyl quinone group of plumbagin was placed in the BCD cavity near the narrow-side of the host molecule, as illustrated in Figure 3.

Molecular Docking Calculation
Molecular docking was used to calculate the possibility of binding between a plumbagin molecule complex with each BCD by fixing the host structure and allowing the guest to be flexible in the specified grid box. The calculations indicated two possible conformations of the 1:1 guest:host ratio for all systems, as shown in Tables 1 and 2. In conformation-I, the hydroxyl phenolic group of plumbagin was placed in the BCD cavity near the narrow-side of the host molecule. In the other model, conformation-II, the methyl quinone group of plumbagin was placed in the BCD cavity near the narrow-side of the host molecule, as illustrated in Figure 3.   Molecular docking results indicated that plumbagin/BCD and plumbagin/MBCD complexes in conformation-I were favorable while the plumbagin/HPBCD complex preferred conformation-II, using both of PM6 and PM7 minimized starting geometries. However, the rigidity of the host molecule in the docking calculations was not realistic. Therefore, the semi-empirical PM6 and PM7 methods in the aqueous phase using polarizable continuum calculations, were used to further investigate the molecular interactions of plumbagin with three different BCD hosts.

Complexation Energy Calculation
An inclusion complex of plumbagin with each of the BCD systems from docking calculations was generated. Both conformation-I and conformation-II, were then fully optimized by the PM6 and PM7 methods, which provide free motions for host and guest molecules in an aqueous environment. From PM6 and PM7 results (Table 3), the heat of formation of the minimized structure of the complex was always lower than that of the sum of the heat of formation of the isolated guest and host molecules indicating the formation of a favorable complex in all models. The complexation energy (∆E), according to Equation (1), is also shown in Table 3. The more negative the value of the complexation energy, the more favorable the pathway of inclusion-complex formation. Table 3 shows the favorable formation of a 1:1 guest:host ratio of plumbagin with three type of BCD in both possible conformations. The values of complexation energy (∆E) from PM7 (−41.41 to −30.10 kcal/mol) were considerably lower than PM6 (−12.78 to −5.70 kcal/mol). The PM7 method includes the description of the dispersion interaction and hydrogen bonding [2] in the parameterization, and thus, should be suitable for the description of noncovalent interactions in plumbagin/BCD complexes.
The difference in ∆E between the two conformations (conformation-I-conformation-II), is also presented in Table 3. The obtained results indicated that plumbagin/BCD inclusion complexes prefer conformation-I (BCD-I) in a water environment. For the inclusion complex formation of plumbagin with modified β-cyclodextrins (MBCD and HPBCD), both conformation-I and conformation-II are favorable. Table 4 presents the distance of the intermolecular hydrogen bonds, which are found in PM6 and PM7 minimized inclusion complex structures. Three types of hydrogen bonds were established. The first one, which is often found in inclusion complex systems, is between an ether-like anomeric oxygen atom of the host molecule and a hydrogen atom of plumbagin's hydroxyl group (O4 (host) . .  H (O2H-HPBCD) ). The molecular interactions of each host-guest system in an aqueous environment are further discussed below.

Plumbagin/β-cyclodextrin Inclusion Complex
Two conformations of a plumbagin/BCD inclusion complex can be formed in an aqueous environment, as shown in Figure 4. The intermolecular hydrogen bonds between plumbagin and BCD are depicted in Figure 5. BCD-I has a 0.03 and 2.37 kcal/mol lower complexation energy from the PM6 and PM7 methods, respectively, than BCD-II. The minimized plumbagin/BCD conformations obtained from the two methods were similar. However, in BCD-I from the PM7 calculation, the plumbagin molecule dipped deeper into the BCD cavity than the structure from the PM6 calculation. This occurred due to the hydrogen bond between the oxygen atom of plumbagin's carbonyl group and the hydrogen atom of the secondary hydroxyl group at O3 of BCD-I (O (CO-PL) ···H (O3H-BCD) ), as shown in Figure 5a.

Plumbagin/β-cyclodextrin Inclusion Complex
Two conformations of a plumbagin/BCD inclusion complex can be formed in an aqueous environment, as shown in Figure 4. The intermolecular hydrogen bonds between plumbagin and BCD are depicted in Figure 5. BCD-I has a 0.03 and 2.37 kcal/mol lower complexation energy from the PM6 and PM7 methods, respectively, than BCD-II. The minimized plumbagin/BCD conformations obtained from the two methods were similar. However, in BCD-I from the PM7 calculation, the plumbagin molecule dipped deeper into the BCD cavity than the structure from the PM6 calculation. This occurred due to the hydrogen bond between the oxygen atom of plumbagin's carbonyl group and the hydrogen atom of the secondary hydroxyl group at O3 of BCD-I (O(CO-PL)···H(O3H-BCD)), as shown in Figure 5a.

Plumbagin/Dimethyl-β-cyclodextrin Inclusion Complex
The plumbagin molecule is located near the wide-side of the MBCD molecule in all complex conformations, as shown in Figures 6 and 7. These occurred due to the presence of methyl groups at the primary hydroxyl group of all glucose units (C6 position), condensing the cavity near the narrowside of MBCD. In MBCD-I, without the steric hindrance from the guest molecule, all seven methoxy groups at the C6 position can be accommodated. After insertion of a plumbagin molecule in MBCD-II, two of the methoxy groups at the C6 position of MBCD move away from the cavity due to the presence of the methyl group of the plumbagin molecule, located at the narrow-side of MBCD, as seen in Figure 6, (b) and (d). According to the steric and electronic hindrances, plumbagin should enter into MBCD at the wide side to form the inclusion complexes MBCD-I and MBCD-II. The plumbagin/MBCD inclusion complex structures are very complicated. Using the same initial starting geometry, the energy-minimized conformations obtained from the PM6 and PM7 calculations were altered.

Plumbagin/Dimethyl-β-cyclodextrin Inclusion Complex
The plumbagin molecule is located near the wide-side of the MBCD molecule in all complex conformations, as shown in Figures 6 and 7. These occurred due to the presence of methyl groups at the primary hydroxyl group of all glucose units (C6 position), condensing the cavity near the narrow-side of MBCD. In MBCD-I, without the steric hindrance from the guest molecule, all seven methoxy groups at the C6 position can be accommodated. After insertion of a plumbagin molecule in MBCD-II, two of the methoxy groups at the C6 position of MBCD move away from the cavity due to the presence of the methyl group of the plumbagin molecule, located at the narrow-side of MBCD, as seen in Figure 6b,d. According to the steric and electronic hindrances, plumbagin should enter into MBCD at the wide side to form the inclusion complexes MBCD-I and MBCD-II. The plumbagin/MBCD inclusion complex structures are very complicated. Using the same initial starting geometry, the energy-minimized conformations obtained from the PM6 and PM7 calculations were altered.

Plumbagin/Hydroxypropyl-β-cyclodextrin Inclusion Complex
The inclusion complex of plumbagin and HPBCD in conformation-I and conformation-II were stabilized in a water environment, as shown in Figures 8 and 9. The presence of the hydroxypropyl group at the C2 position on a glucose unit in HPBCD enlarges the width of the wide-side. The energy-minimized structures of HPBCD-I from the PM6 and PM7 methods were similar. The hydroxypropyl group of HPBCD lined up in the parallel direction with the methyl group of the plumbagin molecule. The guest molecule is located inside the HPBCD's cavity with an H-bond between the hydrogen atom of plumbagin's hydroxy group and the ether-like anomeric oxygen atom of HPBCD.
PM6 and PM7 calculations yield different HPBCD-II energy-minimized structures in a water environment. In HPBCD-II, for the PM6 calculation, the guest molecule is located near the wide-side of HPBCD (Figure 8b), due to the H-bond which formed between the hydroxyl group of plumbagin and the secondary hydroxyl group at O2 of HPBCD (O (OH-PL) . . . H (O2H-HPBCD) ), as mentioned in Table 4 and depicted in Figure 9b. Therefore, the guest molecule could not go deeper inside the HPBCD's cavity, yielding HPBCD-I as the preferable complex with a lower complexation energy (3.38 kcal/mol) than HPBCD-II in the PM6 calculations. In the PM7 calculations, HPBCD-II was more favorable with a lower complexation energy (9.54 kcal/mol) than HPBCD-I. The methyl part of the hydroxypropyl group substituent falls into the HPBCD's cavity and pushes the plumbagin molecule deeper inside the cavity due to the hydrophobic interaction.

Plumbagin/Hydroxypropyl-β-cyclodextrin Inclusion Complex
The inclusion complex of plumbagin and HPBCD in conformation-I and conformation-II were stabilized in a water environment, as shown in Figures 8 and 9. The presence of the hydroxypropyl group at the C2 position on a glucose unit in HPBCD enlarges the width of the wide-side. The energyminimized structures of HPBCD-I from the PM6 and PM7 methods were similar. The hydroxypropyl group of HPBCD lined up in the parallel direction with the methyl group of the plumbagin molecule. The guest molecule is located inside the HPBCD's cavity with an H-bond between the hydrogen atom of plumbagin's hydroxy group and the ether-like anomeric oxygen atom of HPBCD.
PM6 and PM7 calculations yield different HPBCD-II energy-minimized structures in a water environment. In HPBCD-II, for the PM6 calculation, the guest molecule is located near the wide-side of HPBCD (Figure 8b), due to the H-bond which formed between the hydroxyl group of plumbagin and the secondary hydroxyl group at O2 of HPBCD (O(OH-PL) … H(O2H-HPBCD)), as mentioned in Table 4 and depicted in Figure 9b. Therefore, the guest molecule could not go deeper inside the HPBCD's cavity, yielding HPBCD-I as the preferable complex with a lower complexation energy (3.38 kcal/mol) than HPBCD-II in the PM6 calculations. In the PM7 calculations, HPBCD-II was more favorable with a lower complexation energy (9.54 kcal/mol) than HPBCD-I. The methyl part of the hydroxypropyl group substituent falls into the HPBCD's cavity and pushes the plumbagin molecule deeper inside the cavity due to the hydrophobic interaction.

Conclusions
The complexation energy values of each system obtained by the PM7 method are significantly lower than those obtained by the PM6 method. The obtained results agree with the experimental data for a 1:1 guest:host ratio of plumbagin with BCD and HPBCD inclusion complexes. We predict that by using MBCD to increase the solubility and reduce the cytotoxicity of the plumbagin compound, a 1:1 guest:host inclusion complex can be produced. Our results revealed two different binding modes of the plumbagin molecule inside the BCD cavity. In conformation-I, the hydroxyl phenolic group of plumbagin was placed in the BCD cavity near the narrow-side of the host molecule. In the other model, conformation-II, the methyl quinone group of plumbagin was placed in the cavity of BCD near the narrow-side of the host molecule. The intermolecular hydrogen bond, van der Waals, and hydrophobic interactions play an important role in complexation process of plumbagin with BCDs.

Conclusions
The complexation energy values of each system obtained by the PM7 method are significantly lower than those obtained by the PM6 method. The obtained results agree with the experimental data for a 1:1 guest:host ratio of plumbagin with BCD and HPBCD inclusion complexes. We predict that by using MBCD to increase the solubility and reduce the cytotoxicity of the plumbagin compound, a 1:1 guest:host inclusion complex can be produced. Our results revealed two different binding modes of the plumbagin molecule inside the BCD cavity. In conformation-I, the hydroxyl phenolic group of plumbagin was placed in the BCD cavity near the narrow-side of the host molecule. In the other model, conformation-II, the methyl quinone group of plumbagin was placed in the cavity of BCD near the narrow-side of the host molecule. The intermolecular hydrogen bond, van der Waals, and hydrophobic interactions play an important role in complexation process of plumbagin with BCDs.