Conformational Analysis of Topiramate and Related Anion in the Solution and Interaction Between the Most Stable Conformer of Topiramate with Active Center of Carbonic Anhydrase Enzyme

GRAPHICAL ABSTRACT Density functional theory using the B3LYP/6-311++G** method was employed to calculate the details of the electronic structure and electronic energy of the carbonic anhydrase enzyme active center (CA); topiramate, a sulfamate substituted monosaccharide; and the complex between topiramate and CA. The calculated results indicate that topiramate appears to adopt a twist-boat conformation in the solution. The conformational analysis around the S-N bond (H-N-S-O dihedral angle) in deprotonated topiramate shows that the conformers with a H-N-S-O torsion of 270, 0, and 180 degrees are the minimum, transition state, and maximum energy conformers, respectively. The deprotonated form of topiramate is coordinated to the Zn2+ ion.


INTRODUCTION
Carbonic anhydrases (CAs) are zinc-containing enzymes, which present in plants, animals, and humans. [1][2][3][4][5][6] These enzymes catalyze a simple but important physiological reaction, the interconversion of carbon dioxide and carbonic acid. In all known isozymes of CA, the Zn(II) ion is responsible for catalytic activity. The Zn 2+ ion is located at the bottom of a conical cavity that binds to three histidins from their imidazole nitrogens, with the water molecule as the fourth ligand [7][8][9][10][11][12] (Sch. 1). The compounds with sulfonamide moiety, R 1 -SO 2 -NR 2 R 3 , can replace this hydroxyl in the anionic form and inhibit the CA enzyme. [13,14] Epilepsy is a neurological disorder that ranges from a brief cessation of responsiveness to severe spasms with a lack of consciousness. In recent years, some drugs, called anticonvulsants, have been tailored with the objective of controlling epileptic symptoms. [15][16][17][18] Among different classes of pharmacological agents, topiramate (TPM), [19][20][21][22][23][24] a sulfamate substituted monosaccharide (Sch. 2), has antiepileptic effects. One main class of CA inhibitors (CAIs) is known as the metal complexing anions, which bind to the Zn(II) ion of the enzyme by substituting the nonprotein zinc ligand (Eq. 1), generating tetrahedral geometry of the Zn(II) ion. Thus, the CA-inhibitor interaction constitutes the initial stage of the mechanism of inhibitory action: The results of experimental studies indicate that topiramate has inhibitory activity against the CA enzyme. [25,26] In addition, X-ray crystallographic studies show the binding mode of deprotonated topiramate to the active site of CA. [27,28] The complex between topiramate and different isoforms of the CA enzyme is studied experimentally or theoretically, [29][30][31] but unfortunately, there are 82 M. Ghiasi

and S. Kamalinahad
Scheme 1: Presentation of the catalytic mechanism for the CA-catalyzed CO 2 hydration. few or no experimental and theoretical studies about rotational isomerism in sulfonamide moiety and the fructopyranose ring of topiramate. [32] In the present study, conformational analysis of the topiramate and topiramate anion (TPM − ) in the solution and binding of TPM − to the CA active center was performed using a quantum mechanical approach.

Preparation of Topiramate
The crude product obtained above was dissolved in acetone (7 mL) and sodium acetate-acetic acid buffer solution (pH = 3.5). The reaction mixture was heated at 70 • C for 2 h. The cooled mixture was diluted with water (7 mL) and 10 M NaOH was added to reach a pH of 13 to 14. Then, it was extracted with t-butyl methyl ether (3 × 5 mL). The aqueous phase was treated with 85% phosphoric acid to adjust the pH to 5.5 to 6, and white crystals precipitated upon cooling to 10 • C. The product was collected by filtration and washed with cold water. The purity was improved by recrystallization from a mixture of acetone and water.

NMR Measurements
1 H NMR, 13 C NMR, COSY, and HMQC spectra of topiramate were obtained at 298 K in CDCl 3 (99.99% D) on a Bruker DRX500 operating at 500.133 MHz for 1 H and 125.770 MHz for 13 C, using a 5-mm broadband inverse probe. All 2D NMR spectra were acquired by the pulsed field gradient method. Two-dimensional correlation spectroscopy ( 1 H-1 H COSY) was used to confirm 1 H signal assignments (Fig. 1). Heteronuclear multiple quantum correlation (HMQC) and heteronuclear multiple bond correlation (HMBC) were used for 13 C signal assignments (Figs. 2 and 3). HMQC and HMBC spectra were recorded using 2048Í 1024 data matrices; the number of scans and dummy scans was 48 and 16, respectively, in all cases. The HMQC and HMBC were recorded with a 2-s interpulse delay. The spectral width was sw 1 ×sw 2 = 3255 × 22,123 Hz for all 2D experiments. For Z-only gradients, the G1:G2:G3 = 50:30:40.1 gradient ratios were used for both HMQC and HMBC spectra.

Computational Details
Ab initio calculations were carried out with the Gaussian program series 1998. [34] The geometries of the CA enzyme active site, topiramate and its related anion, and the complex between topiramate and CA were fully optimized employing a hybrid Hartree-Fock density functional scheme and the adiabatic connection method-Becke three-parameter with Lee-Yang-Parr (B3LYP) functional [35] -of density functional theory (DFT) [36] with the standard 6-311++G * * basis set. Full optimizations were performed without any symmetry constraints. The harmonic vibrational frequencies were computed 86 M. Ghiasi  to confirm that an optimized geometry correctly corresponds to a local minimum that has only real frequencies. The QST2 method was used to search for the transition state. TS geometry was double-checked by using IRC and FREQ calculations. In addition, the thermodynamic properties of all compounds were obtained from frequency calculations at 298.15 K and 1.0 atmosphere pressure. All reported enthalpies were zero-point (ZPE) corrected with unscaled frequencies. The partial charges were obtained using the NBO method. The solvent effects on the conformational equilibrium were investigated with a PCM method [37] at the B3LYP/6-311++G * * level.

Calculation of Binding Energy
To quantify the interaction between the topiramate inhibitor and CA active site in the optimized geometries, the binding energy (BE) and complexation According to Eq. 3, the complexation energy was defined as the difference in energies of the isolated inhibitor and CA active site, at their optimized conformations, from that of the complex.

Geometry Optimization of CA Active Center
The structure of the CA active center was fully optimized with the B3LYP method using the 6-311++G * * basis set without initial symmetry restrictions and assuming the C 1 point group. The optimized geometry of the CA active center in the gas phase was optimized again by considering the solvent effect ( = 78.9) using the PCM method. [37] Figure 4 shows the optimized structure and some structural details of the CA active center in the solvent. Calculation of vibrational frequencies confirmed the stationary point without the negative eigenvalue observed in the force constant matrix.

Geometry Optimization of Topiramate
Topiramate's structure was also fully optimized with the B3LYP method using the 6-311++G * * basis set without initial symmetry restrictions and assuming the C 1 point group. The optimized geometry of topiramate in gas phase was optimized again in water at the same level of calculations. Figure  distances, bond angles, and dihedral angles are compiled in Table 1. Calculation of vibrational frequencies has confirmed the stationary point without the negative eigenvalue observed in the force constant matrix.

Calculation of Chemical Shifts and NMR Spin-Spin Coupling
Constants of Topiramate NMR computations of absolute shieldings were performed using the GIAO method [39] at the DFT optimized structure in the presence of chloroform solvent. The 1 H and 13 C chemical shifts were calculated by using the corresponding absolute shielding calculated for Me 4 Si at the same level of theory ( Table 2). The good agreement between experimental and theoretical chemical shifts shows the reliability of DFT calculations for these series of molecules.
Recent investigations have shown that DFT can be used to calculate reliable J CH , J HH , and J CC values in carbohydrates without scaling. [40,41] In the present work, we extend this approach to calculate the J-coupling constants using the DFT method. 1 H and 13 C NMR spin-spin coupling constants in the DFT optimized structure in the presence of solvent were obtained by finitefield (Fermi-contact) double perturbation theory [42] calculated at the B3LYP level using the 6-311++G * * basis set. Appropriate values for the perturbing fields imposed on the coupled nuclei were chosen to ensure sufficient numerical precision, while still allowing a satisfactory low-order finite-difference representation of the effect of the perturbation. The result of a recent study on heparin disaccharide with O-or N-sulfated (OSO 3 − or NSO 3 − ) residues showed that the Fermi contact (FC) term was not always dominant and that paramagnetic spin-orbit (PSO), diamagnetic spin-orbit (DSO), and spin-dipolar (SD)  contributions considerably influenced magnitudes of proton-proton spin-spin coupling constants. [43] Therefore, we consider all contributions to calculate the coupling constants in the topiramate molecule.

Conformational Properties of Pyranose Ring in the Topiramate Molecule
According to Figure 6, the pyranose ring in the topiramate molecule could exist in three conformations. The critical parameters are the coupling constants for proton on the pyranose ring: 2 J H7,H14 = 2.7 Hz, 2 J H14,H13 = 7.9 Hz, 2 J H13,H12 = 0.8 Hz, and 2 J H13,H12' = 1.9 Hz. For chair conformation, B, one would expect 2 J H7,H14 to be a large "anticoupling" of about 10 Hz and 2 J H14,H13 to be a small "gauche coupling" of 2 to 3 Hz, which is not the case for topiramate. The alternative chair, C, would exhibit a large coupling for one of the 2 J H13,H12 values and a small coupling for 2 J H14,H13 . Neither situation is observed in the data for topiramate. To confirm twist-boat conformation for topiramate in solution, the geometry of three conformers, A, B, and C, was optimized, and coupling constants of them were calculated in solution. Table 3 indicates some structural details and some calculated proton-proton spin-spin coupling constants in the pyranose ring for the three conformers. Comparison between experimental and calculated coupling constants for the three conformers shows good agreement between conformer A, twist-boat, and experimental data. Thus, topiramate appears to adopt a twist-boat structure in solution. A single-crystal Xray analysis of topiramate shows a similar twist structure in the solid state. [44] The results of previous 1 H NMR studies in cyclic diacetals of pyranose with a "cis-anti-cis" arrangement [45] and topiramate [46] showed that it tends to adopt a twist-boat conformation, which is in agreement with our results. It appears that the molecule is a combination of a large, globular hydrophobic region and a small hydrophilic SO 2 NH 2 unit. We suggest that the nature and disposition of these two segments are important for the biological activity of topiramate.

Calculation of Deprotonation Enthalpy of Topiramate
According to reaction 1, the anionic form of topiramate binds to the Zn 2+ ion to form the complex between the active center of the CA enzyme and inhibitor, so in the next step, the anionic form of topiramate is constructed by detaching the proton from the NH 2 group. Total enthalpy of the studied species M and H(M) at the temperature T is usually estimated from Eq. 4: [47][48][49] where E 0 is the calculated total electronic energy; ZEP stands for zero-point energy; and E trans , E rot , and E vib are the translational, rotational, and vibrational contributions to the enthalpy, respectively. Finally, RT represents the PV-work term and is added to convert the energy to enthalpy. The DE is equal to H a + H p -H ih , where H a is the enthalpy of the anion generated by proton abstraction, H p is the enthalpy of proton, and H ih is the enthalpy of the inhibitor, which is calculated by considering the solvent effect. The DE value for the anion formed by proton abstraction from topiramate by considering the zero-point energy equals -307.45 kcal/mol, so deprotonation of topiramate is exothermic and topiramate has an acidic property.

Conformational Analysis Around the S-N Bond in Deprotonated Topiramate
Since very little is known experimentally or theoretically about the sulfonamide anion in the topiramate molecule, we focused on the conformational preferences of the anion. By employing a scan procedure, the potential energy variations were obtained while the H-N-S-O dihedral angle, as a proper reaction coordinate, was changed from 0 to 360 degrees in steps of 10 degrees with the results pictured in Figure 7. Figure 7 indicates that the minimum energy for the topiramate anion would have a H-N-S-O torsion angle of approximately 270 degrees. To ensure that the stationary points have been identified correctly, the geometry of structures with a torsion angle H-N-S-O of 0, 180, and 270 degrees was fully optimized in the gas phase and then in water. The results of frequency calculations confirm that the two conformers with a torsion angle H-N-S-O of 270 and 180 degrees without imaginary frequency refer to local minimum and intermediate, respectively, whereas the 0-degree conformer with one imaginary frequency refers to the transition state. Comparison of energy levels between different conformers after full optimization in water is shown in Figure 8. Some structural details of these three conformers are presented in Table 4.
It is noticeable that the valence geometry of the topiramate anion is rather different from the neutral molecule. [50,51] For example, the S-N1 bond length decreases from 1.68Å in neutral molecules (Table 1) to 1.56Å in the anionic form of topiramate (Table 4), while the S O bonds decrease from 1.47Å in the anion to 1.44Å in the neutral topiramate molecule. In addition, the O2 S O3 bond angle in the anionic form of topiramate is 118 degrees, as opposed to 122 degrees in the neutral molecule. All of these differences are consistent with an increased S-N bond character and delocalization of the negative charge in the anion. Therefore, the lone pairs on the nitrogen anion can be delocalized into the σ * orbital of the S-O bond.

DFT Calculations for Complexes Between CA Active Center and Topiramate
To follow the complexation process between the inhibitor and CA active site, the potential energy variations were obtained using the B3LYP/6-311++G * method while the distance between the N atom of the most stable conformer of the topiramate anion and Zn 2+ , as a proper reaction coordinate, was decreased from 5Å in steps of 0.3Å. The binding energy with respect to change in distance is presented in Figure 9. The negative BE change upon complexation clearly demonstrates that the CA active site can form a stable complex with inhibitor. Therefore, in the presence of a deprotonated inhibitor, an enzyme/inhibitor complex forms (Eq. 1). According to Figure 9, the optimum distance between Zn 2+ and the N atom is 1.93Å. To calculate the complexation energy, the geometry of the complex was fully optimized at the Zn-N optimum distance (Fig. 10B). As the calculated results indicate, substitution of the anionic form of inhibitor in place of the water molecule at the CA enzyme active center is energetically exothermic, E = -192.85 kcal/mol. Optimized geometry of the complex indicates that the CA/TPM complex has a tetrahedral geometry. Table 5 shows some structural details of this complex according to numbering in Figure 10A.
A comparison of some structural details of the CA/TPM complex with a native active center of CA indicates that a significant conformational rearrangement is necessary in the active site to allow binding of the inhibitor. This has never been evidenced in CA-inhibitor adducts before, as the active site of this protein is highly rigid. [52] For example, according to Table 5, the average bond angle between nitrogen atoms of histidine and zinc, N-Zn-N, is about 107 degrees rather than 119.74 degrees in CA-OH 2 ; the average bond angle of N(TPM)-Zn-N(His) is about 114 degrees as compared to 92.3 degrees, which is the bond angle of O(OH2)-Zn-N(His) in CA-OH 2 . Therefore, inhibitor binding to the zinc ion generates a structure that closely resembles a tetrahedral geometry.

Analysis of Thermodynamic Properties of CA/TPM Complexes
No experimental data of thermodynamic functions such as standard enthalpies of complexation ( H • com ) and the standard Gibbs free energies of  According to the thermodynamic equation, G = H -T S, the G • com was calculated. The computed thermodynamic properties for the CA/TPM complex are reported in Table 6. The results indicate that substitution of the anionic form of inhibitor in place of the water molecule at the active center of the CA enzyme is energetically exothermic.

CONCLUSION
Ab initio calculations have been carried out to study the complexation between the most stable conformer of the topiramate anion in solution, a potent inhibitor, with the active site of the CA enzyme. The results show that the sulfonamide anion moiety of topiramate binds to the Zn 2+ ion in CA through electrostatic interaction. The results of conformational analysis of the pyranose ring in topiramate and sulfonamide moiety in the topiramate anion indicate that the twist-boat conformer is the most stable conformer of the pyranose ring as compared to the chair and alternative chair conformers in the solvent. We hope that these data may be useful for the design of new CAIs.