Interaction of Tamoxifen Analogs With the Pocket Site of Some Hormone Receptors. A Molecular Docking and Density Functional Theory Study

In this paper, the antiestrogenic properties of Tamoxifen analogs have been investigated and a theoretical report of its analogs interaction with the pocket site of some hormone receptors are presented. Analogs were generated by modification of the hydrophilic functional group of Tamoxifen by hydroxyl, amide, carboxyl, and sulfhydryl functional groups, in an attempt to improve their activity and selectivity. The analogs exhibit a negative binding energy in the estrogen and progesterone receptors, which indicates a spontaneous interaction between the analogs and the pocket site in the hormone receptors. The values of the molecular polar surface area indicate that the analogs have good permeability and are strong electrophiles. The couplings showed electrostatic interactions such as hydrogen bond and π-π interactions. According with the Lipinsky Rule of Five, the four analogs presented a good biodistribution, permeability, and pharmacological action on the hormone receptors. The analysis of the charge transfer suggests a limited enhanced oxidative damage in the estrogen receptor that not takes place with the progesterone receptor.


INTRODUCTION
Tamoxifen (TAM) is a drug widely prescribed as chemopreventive for women to prevent and to treat all stages of breast cancer (Jordan, 2007;Esteve-Romero et al., 2010). TAM is a Selective Estrogen Receptor Modulator (SERM) (Boyd and Coner, 1996;Jordan, 2003), which acts as a blockage for the effects of estrogen in the breast tissue by attaching to the estrogen receptors in breast cells.The targets for this drug are some hormone receptors [estrogen receptors (ER) and progesterone receptors (PR)]. This drug is a prodrug and can be metabolically activated to 4-hydroxytamoxifen (4OHTAM) (Jordan et al., 1977;Borgna and Rochefort, 1981) or alternatively can be metabolically routed via N-desmethyltamoxifen (NDTAM) to 4-hydroxy-N-desmethyltamoxifen also known as endoxifene (END) (Irarrazával, 2011;Sanyakamdhorn et al., 2016). The hydroxyl metabolites of tamoxifen have a high binding affinity for the ER (Jordan et al., 1977).
The recent exponential growth of computational resources has facilitated successful development of theoretical algorithms that can also be used to study the electronic effects (Brewerton, 2008). These algorithms can also be used to calculate other physical and chemical properties of ligands using semiempirical and Density Functional Theory (DFT) methods (Correa-Basurto et al., 2012). The theoretical results obtained with these methods have been successfully compared with experimental results (Ravna et al., 2007).
A huge amount of theoretical studies on TAM has already been carried out to describe its interaction with ER. Using calculations of molecular dynamics, semiempirical, and DFT in conformational analysis of TAM and Toremifene (TOR), it was predicted that TOR conformations were slightly different from those of TAM owing to the effect of the chlorine atom at chloroethyl group (Kuramochi, 1996). In a recent research, Landeros-Martinez et al. analyzed the molecular docking of TAM in ER and PR in which the active site of the hormone receptors were determined, as well as the charge transfer of the TAM to the residues of the active sites in the hormone receptors . Other theoretical studies analyzed the metabolism of TAM using semiempirical (PM3) and DFT with B3LYP/6-31G * methods (Hariharan and Pople, 1973;Francl et al., 1982). Also a study of the molecular conformations and the vibrational NMR spectra of TAM performed with B3LYP/6-311(d,p) has been reported (Badawi and Khan, 2016). Another theoretical IR and ultraviolet-visible (UV-Vis) spectra of TAM drug were compared with the experimental data where the methodology that have been found in a better correlation with experimental data is M06/6-31G(d) (Landeros-Martínez et al., 2017).
On the other hand, the molecular docking is an operation in which one molecule is brought into the vacancy of another while calculating the interaction energies of the numerous mutual orientations and conformations of the two interacting species (Bultinck et al., 2003). This technique allows predicting the preferred conformations of a molecule, being bonded to another (Lengauer and Rarey, 1996), and it is widely used in drug design (Kitchen et al., 2004). Mathew et al. have employed a molecular docking procedure to estimate the analogs of TAM and Reloxifen (REL) with high affinity, which could be considered a possible lead molecule for drug design (Mathew and Raj, 2009).
The aim of this work is to modify the hydrophilic functional groups of the TAM by the hydroxyl, amide, carboxyl, and sulfhydryl functional groups to achieve better activity improvement and selectivity. These analogs were studied to determine the binding activity into the hormone receptor by molecular docking and DFT analysis that allowed to decide which analog generates more oxidative damage at the active site. Also, the study of the molecular polar surface area (PSA) permitted to quantify if Tamoxifen analogs (TAM-analogs) have good permeability in cell.

Optimization, Frontier Molecular Orbitals, and Electronic Structure Calculations
The optimized structures of the different TAM-analogs were calculated by means of the hybrid meta-GGA M06 density functional (Zhao and Truhlar, 2008a,b) developed by the Truhlar group from the University of Minnesota, combined with the 6-31G (d) basis set proposed by the Pople group (Hariharan and Pople, 1973;Francl et al., 1982) and the continuous polarizable solvent model (CPCM) (Tomasi and Persico, 1994) using water as a solvent. The latter was used to obtain the Highest Occupied Molecular Orbital (HOMO) and Lower Unoccupied Molecular Orbital (LUMO) of each of the analogs, respectively. These calculations were carried out using the Gaussian 09 suite of programs (Frisch et al., 2018). The energy calculations of the amino acids that make up the active site on the estrogen, progesterone and TAM-analogs as well as the chemical reactivity descriptors are calculated with the M06/6-31G(d) model chemistry and CPCM using water as a solvent. All calculations were performed using DFT (Hohenberg and Kohn, 1964;Kohn and Sham, 1965;Parr and Yang, 1989). The charge distributions for the amino acids and TAM-analogs were obtained through the Hirshfeld population analysis (Hirshfeld, 1977).
Density functional methodology provides an excellent framework to define a set of known chemical concepts such as ionization potential (I) (Foresman and Frisch, 1996;Lewars, 2003), electron affinity (A) (Foresman and Frisch, 1996;Lewars, 2003), chemical hardness (η) (Parr and Pearson, 1983;Parr and Yang, 1984), electronegativity (χ) (Parr and Pearson, 1983;Parr and Yang, 1984), and electrophilicity (ω) (Parr et al., 1999). These reactivity descriptors were obtained by means of energy difference calculations. The chemical hardness, electronegativity, and electrophilicity are defined as: where µ is the chemical potential (Parr and Pearson, 1983;Parr and Yang, 1984) and ǫ H and ǫ L are the energies of the HOMO and LUMO, respectively. The overall interaction between the TAM-analogs and the amino acids that make up the active site on ER and PR can be quantified through the charge transfer between the chemical species. This parameter determines the behavior of the different molecular systems as a donor or as an acceptor system. In this case, the electrons were transferred from the TAM-analogs to the amino acids of the active site of receptors or vice versa. The global interactions between two constituents has been calculated using the charge transfer parameter ( N) which is given by Padmanabhan et al. (2007): The molecular polar surface area (PSA) was obtained through Molinspiration, a free software readily available on the Web (Molinspiration, 2018). To obtain PSA, the TAM-analogs were encoded with SMILES (Simplified Molecular Input Line System), which is a chemical notation system designed for modern chemical information processing (Weininger, 1988).

Molecular Docking
The crystal structures of the estrogen and progesterone receptor were retrieved from the Protein Data Bank PDB: 1A52 and 1A28 respectively. The molecular docking was calculated with the specially tailored AutoDock 4.2 software with the Lamarckian Genetic Algorithm (LGA) (Morris et al., 2009)  The geometry optimization and frequency calculation of the TAM-analogs were performed to make sure that the molecules were at their lowest energy level. Figure 1 shows the optimized geometries of the studied molecules. The optimized TAManalogs show a non-planar geometry due to the four dihedral angles in their structures as we can see in Table 1 The evaluation of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) in each of the ligands were carried out to identify the zone that is richer in electrons. This analysis of the molecular orbitals allowed to explore the pharmacophore of the analogs. Figure 2 shows the HOMO and LUMO for the different ligands. In all cases, the pharmacophore of the TAM-analogs remains in the same area (phenyl, ethyl, and alkene functional groups) reported for the TAM drug . This study was also used to explain which zone of the ligands has the recognition ability in the hormone receptors. Furthermore, the electrostatic potential surface (EPS) maps were adequate for analyzing the binding sites on the basis of the recognition of one molecule by another, which is very important for drug design (Li et al., 2013). The maps in Figure 3 show in red the region with the most electronegative electrostatic potential and blue region for the most positive electrostatic potential. It can be observed that atoms that are more electronegative in TAM-Hydroxyl, TAM-Amide, and TAM-Carboxyl are the oxygen atoms while in TAM-Sulfihydryl are the oxygen and sulfur atoms.

Reactivity Parameters
Chemical reactivity parameters such as electron affinity, ionization potential, chemical hardness, electronegativity, chemical potential, and electrophilicity index obtained with energy differences approximation as well as HOMO-LUMO approximation are presented in Table 2. These values suggest that TAM-Amide has the greater ease to react in the presence of the hormonal receptors according to the chemical hardness in both approximations. Also, the electrophilicity index information allowed to determinate that all TAM-analogs are strong electrophiles with ω > 1.5 eV for both approximations in accordance with Domingo et al. (2016). In addition, the nucleophilicity index was calculated by Tetracyanoethylene (TCE) was used as a reference for these scales of nucleophilicity because it presents the lowest HOMO energy in a large series of molecules previously studied, being the E HOMO of the TCE of −9.13 eV. The values of nucleophilicity of the TAM drug, TAM-Hydroxyl, TAM-Amide, TAM-Carboxyl, and TAM-Sulfhydryl are 3.42, 3.40, 3.43, 3.41, and 3.38 eV, respectively. All the molecules have a strong nucleophiliic character with N > 3.0 eV according to the scale proposed by Domingo et al. (2016). Another important result of the TAM-analogs is the molecular polar surface area (PSA), which allows the prediction of the transport properties of drugs through membranes. PSA consists of the sum of all polar atoms, including the oxygen, nitrogen and hydrogen attached to these atoms (Ertl, 2008). The results were 29.46 , 29.54 46.53 , and 9.63 Å 2 for TAM-Hydroxyl, TAM-Amide, TAM-Carboxyl, and TAM-Sulfhydryl, respectively.
According to Clark, the drugs with a value less than 90 Å 2 are completely absorbed in the cell membranes, while those drugs with values greater than 140 Å 2 are poorly cell permeable (Clark, 1999).

Analysis of the Hormone Receptors With the Tamoxifen Analogs
The binding modes of a series of TAM-analogs were estimated by means of molecular docking calculations. The value of the root mean square deviation (RMSD) was considered as a measure of the accuracy of the docking results. The optimal RMSD value must be lower than 2 Å (Samanta and Das, 2016). Figure 4 shows the alignments to the native co-crystallized structure TAM (gray) with each one TAM-analogs (blue). Therefore, the RMSD in the estrogen receptor obtained between TAM with TAM-Hydroxyl, TAM-Amide, TAM-Carboxyl, and TAM-Sulfhydryl are 3.03 , 1.824 , 19.67 , and 2.272 Å, respectively, while for the progesterone receptor the RMSD value between TAM and TAM-Hydroxyl, TAM-Amide, TAM-Carboxyl, and TAM-Sulfhydryl are 2.082 , 3.445, 0.148, and 0.949 Å.

Docking Analysis of the Estrogen Receptor
All the TAM-analogs were successfully docked into the binding pocket of ER. In this work, the attention has been focused on the estrogen receptor-ligand because this analysis allows to determine which of these analogs are the most or least active. The binding energy of TAM-Hydroxyl, TAM-Amide, TAM-Carboxyl, and TAM-Sulfhydryl with the ER are −9.63 , −10.79, −10.80, and −10.23 kcal/mol, respectively. Figure 5 shows the optimal docking position and binding energy into the binding pocket of ER. It has been observed that each of the TAM-analogs is located at the pocket site of the ER. Furthermore, based on our previous experience, it can be said that in spite of the differences between the G values in each case being small, the results of the binding energies are significant enough to assert that the TAM-Amide and TAM-Carboxyl species are the most active while the least active is TAM-Hydroxyl in the pocket site of the ER.
After successful analysis of the bonding mode of TAM analogs, the hydrogen bond and π-π interaction were analyzed in each of the couplings. TAM-Hydroxyl has one π-π interaction and one hydrogen bond between hydroxyl of the analog and the oxygen atom of Lys 529 (OH-O, 1.94 Å); TAM-Amide formed one hydrogen bond with the oxygen atom of the ligand and the NH of Lys 529 (O-NH, 2.078 Å); TAM-Carboxyl present one π-π interaction and one hydrogen bond between oxygen atom of the analog and NH of Lys 529 (O-NH, 1.845 Å) and finally TAM-Sulfhydryl has one π-π interaction and one hydrogen bond between sulfhydryl (SH) of the ligand and the oxygen atom of Asp 351 (SH-O, 1.759 Å). In all cases, the TAM-analogs analyzed follow the Lipinsky Rule of Five which    is used to predict whether a compound has or not has a druglike character (Leeson, 2012). Additionally, when there are five or fewer hydrogen bonds, it can be said that the drug have good absorption or permeation and will be more active (Lipinski et al., 2001). Figure 6 shows the TAM-analogs in ball and stick and the amino acids of the pocket site in tube. The hydrogen bonds are showed in green dots and π-π interactions are the area in yellow.

Reactivity Parameters
The values of reactivity parameters calculated for each of the TAM-analogs and the amino acids of the pocket site of the ER were estimated using the vertical A and I and are given in Tables 3, 4

Charge Transfer in the Estrogen Receptor
The interaction between the TAM-analogs and the amino acids of the pocket site was calculated by means of the parameter N which determines the fractional number of electrons transferred form a system A to a system B with N described by Equation (4). In this formula, µ A is for the TAM-analogs and µ B is for the amino acids of the active site. η A and η B represent the chemical hardness of the TAM-analogs and the amino acids of the   (Wan et al., 2000;Kanvah and Schuster, 2005). According to the results of Table 5 (Lipinski et al., 2001). Figure 8 shows the TAM-analogs in ball and stick and the amino acids of the pocket site in tube. The hydrogen bonds are showed in green dots.

Reactivity Parameters
After having obtained the most stable structure of TAM-analogs in the pocket site, an analysis of the chemical reactivity of TAManalogs and progesterone residues was performed by means of the reactivity descriptors. The results for these calculations are presented in Tables 6, 7, respectively.   The

Charge Transfer in the Progesterone Receptor
The amount of charge transfer between the TAM-analogs and the amino acids of the pocket site was estimated with the parameter N described with Equation (4). The values of N are shown in Table 8

CONCLUSIONS
In this work, the replacement of polar groups, such as the hydroxyl, amide, carboxyl, and sulfhydryl in the hydrophilic zone of the TAM drug did not modified the pharmacophore. According to the PSA values, the permeability in cell of the TAM-analogs decreases in the order: TAM-Sulfhydryl > TAM-Hydroxyl > TAM-Amide > TAM-Carboxyl. The scale of The coupling of ER with each of the TAM-analogs showed that TAM-Carboxyl and TAM-Amide are the most active in the pocket site while TAM-Hydroxyl is the least active in the pocket site and in both cases the couplings have one hydrogen bond and one π-π interaction. According to the charge transfer descriptor, the coupling ER-TAM-Sulfhydryl and ER-TAM-Amide presented the greatest oxidative damage. In turn, the coupling of PR with the TAM-analogs showed that the most active analog is TAM-Sulfhydryl and the least active is TAM-Carboxyl, presenting in both cases one hydrogen bond. The charge transfer descriptor shows that the TAM-Sulfhydryl and TAM-Hydroxyl are more damage oxidative in the pocket site of the PR. The four TAM-analogs have a good biodistribution, permeability, and pharmacological action on the hormone receptors, according to the Lipinsky Rule of Five.
The values of the chemical hardness for TAM into the pocket site of ER and PR have been calculated earlier by us as being 2.40 and 2.33 eV, respectively. Thus, according with the chemical hardness values, TAM has a greater ease to react than the analogs in presence of both hormonal receptors. We can conclude that the activity has been not improved with any of the the TAManalogs.
If we consider the selectivity or the degree to which the analogs acts in the active site, TAM-amide and TAM-carboxyl analogs improved the binding energy regarding with TAM in less than 0.5 kcal/mol for the case of the ER receptor for which was calculated as −10.38 Kcal/mol. In turn, for the PR case, there is an improvement in the binding energy exclusively with TAM-Sulfhydryl with −9.50 kcal/mol compared with −9.38 Kcal/mol of TAM calculated previously. However, due to the small difference between the two values, it can be concluded that this is a rather limited improvement. The main conclusion is that a marked better activity and selectivity improvement is not achieved through the studied TAM-analogs.
The reasoning behind the election of the different radical groups for building the different TAM-analogs was based on the previous knowledge of the improvement in the binding energy of hydroxyl-TAM metabolites. Nevertheless, the improvement was not significant. We believe that this behavior can be related with the low number of H-bonds because the studied TAM-analogs have only one of these bonds with either of the receptors. For this reason, the future design of potential TAM-analogs should include radical groups that make easier the formation of these kind of bonds.
Moreover, it is of outermost importance to increase the electron donor ability of the ligands and this could be probably achieved by including radical groups containing a larger number of polar atoms.
Finally, although the number of π-π bonds need to be larger in order to improve the interaction of the receptors with the TAM-analogs, this is not a fundamental issue because that interaction takes place between the rings of the pharmacophore and the receptor and our intention is to modify only the hydrophilic functional group.