Computational evaluation on the molecular conformation, vibrational spectroscopy, NBO analysis and molecular docking of betaxolol and betaxolol-chlorthalidone cocrystals

Journal Pre-proof Computational evaluation on the molecular conformation, vibrational spectroscopy, NBO analysis and molecular docking of betaxolol and betaxolol-chlorthalidone cocrystals Khloud Mohammed, Ahmed A.K. Mohammed, Ahmed F. Abdel Hakiem, Refaat M. Mahfouz PII:

S0022-2860(20)30068-5

DOI:

https://doi.org/10.1016/j.molstruc.2020.127744

Reference:

MOLSTR 127744

To appear in:

Journal of Molecular Structure

Received Date: 16 September 2019 Revised Date:

13 January 2020

Accepted Date: 15 January 2020

Please cite this article as: K. Mohammed, A.A.K. Mohammed, A.F. Abdel Hakiem, R.M. Mahfouz, Computational evaluation on the molecular conformation, vibrational spectroscopy, NBO analysis and molecular docking of betaxolol and betaxolol-chlorthalidone cocrystals, Journal of Molecular Structure (2020), doi: https://doi.org/10.1016/j.molstruc.2020.127744. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

Computational evaluation on the molecular conformation, vibrational spectroscopy, NBO analysis and molecular docking of betaxolol and betaxolol-chlorthalidone cocrystals

Khloud Mohammed1, Ahmed A. K. Mohammed1, Ahmed F. Abdel Hakiem2, Refaat M. Mahfouz1* 1

Chemistry Department, Faculty of science, Assiut University, Assiut, Egypt

2

Pharmaceutical Analytical Chemistry Department, Faculty of Pharmacy, Kafrelsheikh University, Kafrelsheikh, Egypt *E-mail: [email protected]

Abstract: In this work, we will report a combined experimental and theoretical study on the molecular structures of betaxolol and betaxolol.HCl drug in monomeric and dimeric forms, and in combination with chlorthalidone. Geometry optimizations were carried out in the gas phase by B3LYP-D3BJ/6-311++G(d,p) level of DFT. The electronic properties were performed by time-dependent DFT (TD-DFT) approach. Global reactivity descriptors (ionization potential, electron affinity, electronegativity, electrophilicity index, global hardness, global softness and chemical potential) were predicted with the help of HOMO/LUMO energy values. Experimental FT-IR spectrum of betaxolol was recorded and compared with the computed values obtained by the same level of DFT. Detailed vibrational assignments of the vibrational spectrum have been made on the basis of potential energy distribution (PED) analysis. Molecular electrostatic potential map (MEP), topology analysis (AIM, ELF, LOL) and reduced density gradient (RDG) were used to detect the possible electrophilic and nucleophilic sites as well as hydrogen bonding, which elucidated the important role of the isopropylamino-2-propanol moiety of the betaxolol structure in the biological activity of the drug to block β1-adrenergic receptors. Cocrystals of betaxolol–chlorthalidone were prepared and the structure was tested by X-ray powder diffraction. Stability of the molecular structures and hydrogen bonding interactions in pure betaxolol and in betaxolol-chlorthalidone cocrystals were investigated by NBO analysis. The biological activity of the molecule in terms of molecular docking has been analyzed theoretically.

Key words:

Betaxolol, DFT calculations,

Spectroscopic studies, Betaxolol-

chlorthalidone cocrystals, NBO analysis, Molecular docking.

1. Introduction Recently, successful efforts have been done to improve the physical properties of active pharmaceutical ingredients (APIS) such as thermal stability, melting point, crystallinity and solubility[1]. These desired improvements can be often obtained by the cocrystallization technique[2, 3]. Betaxolol (BT) (1-[4-[2-(cyclopropylmethoxy)ethyl]phenoxy]-3-(1-methylethylamino) propan-2-ol) is β1-blocker used as β1-adrenergic antagonist in cardiovascular diseases, glaucoma treatment, in addition to treatment of hypertension[4, 5]. BT has two moieties, isopropylamino-2-propanol and cyclopropylmethoxyethyl, in its structure (See Fig. S1 of the supporting information). β1-adrenergic receptors are located mainly in the heart. When they get activated by epinephrine they increase the heart rate and blood pressure. Drugs such as BT block these receptors, and thus have a reverse effect: lowering blood pressure. Knowledge of the structure and properties of BT is crucial for understanding its chemical and biological impact. It can elucidate which one of the two moieties of BT is more active in the blocking of these receptors. The efficiency of the combination BT as β1-adrenergic blocker and chlorthalidone (CTD) as thiazide diuretic showed a desirable additive effect in the treatment of hypertension[6, 7]. For understanding the pharmacological reactivity and the elucidation of the geometrical structural parameters of biomolecular compounds, DFT was shown to be a powerful

tool[8, 9]. The structure of betaxolol was determined by an X-ray single crystal experiment and computationally using B3LYP/6-31G(d,p) level of DFT[10]. The title compound betaxolol in acidic and basic forms was investigated by infrared spectroscopy and NBO analysis[11]. In the present study, a detailed interpretation of the vibrational spectrum of betaxolol has been made on the basis of the calculated amounts of potential energy distribution (PED) and the results of the theoretical and experimental studies are reported. The redistribution of electron density (ED) in various bonding and anti-bonding orbitals, along with E(2) energies have been calculated by natural bond orbital (NBO) analysis to give evidence to the stabilization arising from hyperconjugative effects of various inter- and intramolecular interactions in BT and BT-CTD cocrystals. The study of HOMO-LUMO localization and energies has been used to elucidate information regarding charge transfer in BT and to calculate its reactivity parameters. The theoretical and experimental results supported each other, and the calculations are available for providing reliable insights into the vibrational spectra and molecular properties of BT and BT-CTD structures. 2. Computational Methods DFT computations have been performed using Gaussian 09 program without any constraints on the geometry. B3LYP-D3BJ level was used in our calculations with the 6-311++G(d,p) basis set to achieve the optimal conditions for structural parameters calculations and ground state optimization in the gas phase. The dispersion corrected DFT (DFT-D3) approach by Grimme et al used in this study was shown to give better results for non-covalent interactions [12-14]. Frequency calculations for the optimized structures of BT showed that there are no imaginary frequencies, which confirm that they are true minima. The VEDA program was exploited for the investigation of the different modes of vibrations by their potential energy distribution (PED), [15]. To get visual animation for the verification of the normal modes of vibrations, Avogadro

software was fallen back on[16]. The NBO analysis was performed for the optimized structures of BT and BT-CTD at the same level of calculations using the 3.1 program as implemented in the Gaussian 09 program. Atoms in molecules (AIM), electron localization function (ELF) and localization orbital locator (LOL) have been performed by Multiwfn program. Reduced density gradient (RDG) and molecular electrostatic potential maps (MEP) have been performed by Multiwfn and VMD programs. The counterpoise correction method was used to account for the basis set superposition error (BSSE). The MOE 2014 software for windows (Chemical Computing Group Inc. Montreal, Canada) was utilized for the molecular docking study. 3. Experimental Methods 3.1 Instrumentation The powder XRD diffractions were recorded on Philips Model PIV 1710 with Cu Kα radiation (λ = 1.54 Å) and operating at 30 mA. The scan mode was the continuous speed of 0.06 deg/min. FT-IR analysis was performed in the transmission mode as KBr pellets in the range of 4000-400 cm-1 using FT-IR, Nicolet IS 10. Made in USA. 3.2 Preparation of betaxolol-chlorthalidone cocrystals The cocrystals of BT-CTD were obtained by dissolving equimolar amounts of the two components in a minimum amount of hot methanol with good stirring. The cocrystals were precipitated by dropwise addition of distilled water. The system was allowed to stand for 24h, and then filtered. The cocrystals were subjected to investigation by PXRD to ensure complete cocrystallization. Fig. 1 shows the P-XRD pattern of the cocrystals of BT-CTD together with the P-XRD patterns of the pure components. As shown in Fig. 1, the P-XRD pattern of the cocrystals system shows diffraction lines of

different d-spacing values compared to the values of pure components, giving evidence of mixed crystal formation rather than crystalline mixture. Fig (1) 4. Results and Discussions Fig. 2 shows the optimized structures of the most stable conformer of betaxolol (BT) and chlorthalidone (CTD) with the numbering of atoms labeled on the figure. Fig. 3 displays the optimized structures of betaxolol.HCl dimer and betaxolol.HClchlorthalidone (BTH-CTD). The most important structural parameters of BT (bond lengths, bond angles and dihedral angles) computed by the B3LYP–D3BJ/6311++G(d,p) level of DFT are listed in Table 1. To test the validity of this DFT level and the basis set, the optimized structural parameters computed in this work were compared with the crystal structure of the cyclopropylmethoxy fragment of BT and with the optimized parameters calculated by 6-31G(d,p) method used in [10]. The data are listed in Table 1. Figs. (2) and (3), Table (1) The binding energies, ∆Eb, for BT dimer, BT–CTD and BTH-CTD were calculated according to equations 1, 2 and 3, respectively: ∆Eb = Edimer - 2Emonomer

(1)

∆Eb = EBT-CTD - (EBT + ECTD)

(2)

∆Eb = EBTH-CTD - ( EBTH + ECTD)

(3)

Table 2 lists the ground state energies of BT, BTH, CTD, BT-CTD, BTH-CTD, BTdimer, and BTH-dimer. Table (2)

From Table 2, it can be seen that the BTH-CTD has the highest binding energy. Introducing HCl to BT almost doubles its binding affinity to CTD. These results are of valuable help for the applications of this structure in biological systems.

4.1 Vibrational analysis According to the theoretical calculations, the molecular structure of BT belongs to the C1 point group symmetry. The molecule consists of 51 atoms and is expected to have 147 modes of vibrations of the same A species. All the fundamental vibrations of BT are active in both FT-IR and FT-Raman spectra. The detailed vibrational assignments of the fundamental modes of BT along with the calculated and the experimental FT-IR wavenumbers are listed in Table 3. The computed vibrational data were scaled by an 0.96 scale factor and the modes are assigned by their potential energy distribution (PED) obtained by the VEDA program. The obtained results showed that the B3LYP/6-311++G(d,p) level applied in this work gives vibrational wavenumbers in a good agreement with the experimental data. Table (3)

4.1.1 Methyl group vibrations (-CH3) In the title compound, there are two –CH3 groups. Basically nine fundamental modes of vibrations can be associated with each –CH3 group: two asymmetric stretching, one symmetric stretching, three in-plane bending (scissoring), two rocking vibrations and one torsion[17].

Two vibrations were computed at 3085 and 3014 cm-1 and assigned to asymmetric and symmetric –CH3 vibrations with ≈ 50% PED. The two in-plane deformations of the – CH3 group were calculated at 1398 and 1480 cm-1 for scissoring and rocking vibrations, respectively, compared to the observed values at 1338 and 1493 cm-1 as seen in Table 3. The PEDs of these modes show that they are not pure vibrations and are mixed with other modes of vibrations in the molecule[18]. 4.1.2 Hydroxyl group vibrations (-OH) The –OH stretching vibration is generally observed in the region around 3200-3650 cm1

[19, 20]. This band is computed at 3689 cm-1 and contributes 100% of the total PED.

4.1.3 Methylene group vibration (-CH2) Six fundamental modes of vibrations can be associated with the –CH2 group namely, asymmetric and symmetric stretching, scissoring and rocking (in-plane bending), wagging and twisting (out-of-plane bending). In the present work, the computed –CH2 symmetric and asymmetric stretching fall into 3118-2974 cm-1 and 3124-3039 cm-1, respectively, which is more than 92% PED. The vibrational frequency computed by B3LYP/6-311++G(d,p) at 1516 cm-1 is attributed to in-plane bending of -CH2 group and shows correlation with the recorded vibration at 1441 cm-1 [17]. 4.1.4 Ring vibrations The benzene ring possesses six ring stretching vibrations. The four vibrations with the highest wavenumbers, occurring respectively near 1615, 1543,1511 and 1412 cm-1, are assigned to ring vibrations and show quite agreement with the observed data at 1514, 1474 and 1311 cm-1[21]. These modes are affected by other vibrations as indicated by the low values of PED%. 4.1.5 -C-H vibrations

The heteroaromatic structure shows the presence of -C-H stretching vibrations in the region of 3100-3000 cm-1, which is a characteristic region for the identification of the C-H stretching vibration, and is not affected by the nature of the substituent group. In the present study, the -C-H stretching vibrations are observed at 3036 cm-1. Vibrations computed at 3157 and 3156 cm-1 are assigned to –C-H stretching[22]. 4.1.6 C-N vibrations The assignment of C-N stretching vibrations is a very tough task since it falls in a complex region of the vibrational spectrum, i.e., mixing of several bands are possible in this region of vibration. In the present work, the band observed at 970 cm-1 is assigned as a C-N stretching vibration. The theoretical wavenumber calculated at 949 cm-1 is assigned as C-N stretching with intensity lower than 0.1 Km/mol and is not listed in Table 3. 4.2 Frontier molecular orbitals and density of states (DOS) Frontier molecular orbitals (FMO), represented in the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), play an important role in determining physical and chemical activities of molecules, as well as electrical and optical criteria[23]. Fig. 4. shows the HOMO and LUMO of BT. The compositions of both HOMO and LUMO were calculated by the Becke method via Multiwfn program and marked in Fig. 4. Molecular orbital coefficient analysis based on the optimized structures of BT and BT-CTD indicated that FMOs are mainly composed of P-orbitals. Here, it should be emphasized that the HOMO-LUMO gap of BT-CTD (∆E = 4.34 eV) is lower than that of BT only (∆E = 5.62 eV). These results gave evidence for utilization of BT-CTD cocrystals in drug formulation and applications. Multiwfn program has been used to plot the total, partial and overlap population density of states (TDOS, PDOS, OPDOS). These plots are displayed in Fig. 5. The curve map

of broadened partial DOS (PDOS) and overlap population DOS (OPDOS) are very valuable for the visual study of atomic orbitals of different fragments for the title molecule and have significant contributions to the corresponding MOs and chemical bonding. Fig. 5 shows the fragments of the title molecule and its PDOS and OPDOS between the first two fragments only in the valence MOs range. The axis at the left side corresponds to TDOS and PDOS, while the one at right side corresponds to OPDOS and the vertical dashed line highlights the position of the HOMO. Red, blue, magenta, brown, yellow, and orange lines represent PDOS of fragments 1, 2, 3, 4, 5, and 6, respectively. It can be seen that the fragments 1, 3, and 6 have the highest contribution to valence MOs, with comparable amount of contribution. The green curve is the OPDOS between fragments 1 and 2, and its positive part implies that MOs in the corresponding energy range show bonding characters between two fragments (e.g. the one at -25.02 eV which corresponds to MO 26). There are also regions where OPDOS is negative, e.g. the HOMO-1 (-6.69 eV). MOs in this range behave as anti-bonding orbitals between two fragments. Figs. (4) and (5) 4.3 Reactivity descriptors The HOMO and LUMO energy values are used to estimate the global reactivity descriptors such as chemical hardness, chemical softness, chemical potential and electrophilicity index. Reactivity descriptors are used to predict the tendency of the drug to charge transfer processes and drug-receptor interactions [24]. Based on EHOMO and ELUMO, the following reactivity parameters are calculated as follow and tabulated in Table (4)[25][26, 27] :

Ionization potential (I) = - EHOMO

(4)

Electron affinity(A) = - ELUMO Electronegativity (χ) =

 

Chemical potential (µ) = -χ

Chemical hardness (η) =

(5)

(6)

(7)

 

(8)

Chemical softness (Ѕ) = 1/η

(9)

Electrophilicity index (ω) = µ2 /2η

(10)

Energy change (∆E) = -µ2 /2η

(11)

Maximal charge acceptance (∆Nmax) = -µ /η

(12)

The biological activity is expressed as a function of molecular descriptors, and can have a maximum or minimum value at specific descriptor values. From these values, we can explain chemical properties and activity of the title molecule. Notice that, since the chemical hardness (η) > 0 and the energy change due to charge transfer (∆E) < 0, the charge transfer process is energetically favorable, and when the ratio between energy change and maximal charge acceptance ∆(E)/∆(Nmax)=0, it means that the title compound is saturated with electrons and doesn’t have a tendency for a charge transfer process[26]. From the tabulated values in Table 4, ∆(E)/∆(Nmax) is -1.7eV, and the value of maximal charge acceptance ∆Nmax is 1.23eV. These values elucidate the intramolecular charge transfer within the drug and its ability to interact and bind with β1-adrenergic receptors. The values of chemical hardness (η) and ∆E of electron transfer are 2.81 and -2.14 eV,

respectively. These results indicate that the charge transfer process is energetically favorable in the drug and bioactivity formation of intermolecular interaction with β1adrenergic receptors and blocking it is allowed. 4.4 Molecular electrostatic potential (MEP) map Molecular electrostatic potential (MEP) is related to the electron density and can be useful to predict the reactivity, locate sites for electrophilic and nucleophilic attacks in the molecule, and finally evaluate the hydrogen bonding interactions and the biological recognition process[28]. The electrostatic potential (ESP) V(r) is also well studied in drug-receptor and enzyme substrate interactions[29] [30]. The 3D plot of the ESP of the studied molecule is illustrated in Fig. 6 to find the various values of electrostatic potential at electrophilic and nucleophilic sites. The MEP surface is mapped by different colors: blue, red and white representing the regions of most negative, most positive and zero electrostatic potential, respectively. The figure displays 15 surface minima, which indicate the negative potential sites located on oxygen atoms, as well as 24 surface maxima for positive potential sites around the hydrogen atoms. The global minimum on the surface (-35.124 kcal/mol) is owing to the O12 lone pair. The global maximum on the surface (+29.049 kcal/mol) is around H30, which is attached to N14. We observe that both global maximum and minimum, the strongest nucleophilic and electrophilic sites, are located in the region of isopropylamino-2-propanol moiety. From the MEP map, it could be concluded that isopropylamino-2-propanol moiety of BT molecule has important biological activity and plays the predominant role in the recognition of the drug in biological systems than cyclopropylmethoxyethyl. Fig (6) 4.5 Atoms in molecules (AIM)

The quantum theory of atoms in molecules (AIM) is a useful tool for the characterization of hydrogen bonding and π-π interactions within the molecule[31]. The topology analysis of BT molecule displays 53 (3,-1) bond critical points (BCPs) between attractive pairs and 3 (3,+1) ring critical points corresponding to π-π interactions. One bond critical point is associated with a very weak O12 –H27 ----N14 hydrogen bonding interaction (2.16 Å) [32] [33]. From Multiwfn we can calculate the energy of the hydrogen bond by a relationship between bond energy EHB and potential energy density at corresponding BCP as ( ) EHB =  2

(13)

The energy of the hydrogen bond O12 –H27 ----N14 was calculated to be -5.04 kcal/mol. 4.6 ELF and LOL The electron localization function (ELF) and the localized orbital locator (LOL) allow the visualization of covalent bonds, electron lone pairs, and atomic shell structure from properties of the electron density. The surface analysis performed based on the covalent bonds offers the ELF and LOL maps, which display the regions of molecular space where the probability of finding an electron pair is high [34-36]. ELF, denoted τ(r), and LOL, denoted η(r), were completed using the Multiwfn program. The chemical content of LOL is similar to that of ELF as both depend on the kinetic-energy density. However, whereas ELF is founded on consideration of the electron pair density, LOL simply displays the gradients of the localized orbitals and is maximized when localized orbitals overlap. Color shade maps and contour maps of the hydrogen bonding region (H27-O12-C11-C13-N14) are presented in Fig. 7.

The value of ELF, τ(r), ranges from 0.0 to 1.0, where relatively high values in the interval 0.5 and 0.1 indicate regions containing bonding and anti-bonding localized electrons, whereas lower values (< 0.5) describe domains where electrons are expected to be delocalized. The LOL, η(r), attains high values (> 0.5) in regions where the electron density is dominated by electron localization[37-39]. A high localization of electrons due to the presence of a covalent bond, a lone pair of electrons, or a nuclear shell is indicated by a large τ value in that region. From Fig. 7, the high ELF and LOL regions are seen around hydrogen atoms, indicating the presence of highly localized bonding and non-bonding electrons. The small blue region between H27 and N14 displays the formation of a weak hydrogen bond, which is in agreement with the AIM analysis. The 3D plot of ELF for BT is shown in Fig. 7c. In the hydrogen bonding region of BT, the lone pair domain of N14 is shaded as blue and distorted and the shape of the atomic orbital on H27 is significantly reduced which gave evidence for occurrence of interaction in this region, leading to hydrogen bonding. Fig. (7) 4.7 Reduced density gradient (RDG) Reduced density gradient (RDG) is a fundamental dimensionless quantity coming from the density and its first derivative and is given by[40]:

RDG(r ) =

∇ρ ( r )

1 2 ( 3π

1 2 3

)

ρ (r )

4 3

(14)

The RDG spikes that show large negative values of sign(λ2)ρ are indicative of attractive interactions such as dipole-dipole interactions or hydrogen bonding; if the sign(λ2)ρ is large and positive the interaction is non-bonding (steric effect). Values near zero

indicate very weak, van der Waals (vdW), interactions [40] [41]. The RDG of BT and BT-CTD are pictured in Fig. 8. The blue colors indicate the hydrogen bonding interaction, green colors are van der Waals interactions and the red color is identified as strong repulsion. Repulsive interactions were observed inside the ring while van der Waals interactions were seen between the hydrogen atoms. As can be seen from Fig. 8 (a and b), for BT, the van der Waals interaction is the predominant factor as electrostatic interaction in the molecule. The RDG also displays very weak hydrogen bonding interactions and strong steric effect as repulsive interaction. The RDG of BTCTD mixed system displays very strong van der Waals interaction with very weak hydrogen bonding interaction. Moreover, hydrogenic and van der Waals regions are more impacted in the presence of HCl moiety in the structure BTH-CTD, as can be seen in Fig. S2 (supporting information). These results gave evidence for the potential use of BTH-CTD with HCl moiety in the enhancement of drug combination formulation. From these results, we conclude that, the BTH-CTD structure is more stable compared to the BT-CTD, which is in agreement with the values of binding energies reported in Table 2. Fig. (8) 4.8 NBO analysis Natural bond orbital (NBO) calculations were performed using the NBO 3.1 program implemented in Gaussian 09 package at B3LYP/6-311++G(d,p) level of DFT. NBO analysis allows the measuring of the hybridization of atomic lone pairs and of the atoms involved in bonding orbitals. The hyperconjugative interaction energies were deduced from the second order perturbation approach[33] [42].

For each donor (i) and acceptor (j), the stabilization energy E(2) associated with the delocalization i → j is estimated as:  () = ∆ = 

(,)  

(15)

In NBO analysis, a large E(2) value shows the intensive interaction between electrondonors and electron-acceptors and a greater degree of hyperconjugation in the whole system[21]. The possible interactions in BT and BT-CTD are given in Table 5. The most important hyperconjugative interactions in BT are LP(2)O9 → σ* C3-C4, LP(2)O12 → σ* C11-H26, LP(1)N14 → σ* C15-C16 and LP(2)O40 → σ* C41-H43, with stabilization energies 28.67, 9.31, 7.59, and 6.81 kcal/mol, respectively. NBO analysis detected weak intramolecular hydrogen bonding interactions as LP(1)N14→ σ*O12H27 with stabilization energy of 3.47 kcal/mol. NBO analysis for BT-CTD system displays the most important hyperconjugative interactions as LP(1)O56 → σ*C13-H29, LP(1)O54 → σ*C13-H29, with stabilization energies of 64.82 and 41.21 kcal/mol, respectively, as listed in Table 5. From the NBO analysis of BT-CTD, the stabilization energy of intramolecular interaction of BT in hydrogen bonding region (LP(1)N14 → σ*O12-H27) is increased in the presence of betaxolol in combination by 4.31 kcal/mol. Table (5) 4.9 Electronic UV-Vis spectral analysis UV-Visible analysis of BT was carried out using the TD-DFT method at the B3LYP/6311++G(d,p) level. Electronic spectrum of BT in methanol reveals the absorption peak at 220 nm due to π-π* transition[43]. The maximum peak for BT in methanol was computed at 223 nm. This absorption wavelength corresponds to the electronic

transition from the HOMO to LUMO+4 and LUMO+6 (see Fig. S3 of the supporting information). 4.10 Molecular modeling Modeling small molecules and proteins on the atomic level by molecular docking approach allows elucidation of fundamental biochemical processes in addition to behavioral characterization of ligands at binding sites within target proteins. Docking entails two main steps: positional orientation within target sites (poses) as well as prediction of ligand conformation and binding affinity evaluation[44]. In this work, we chose the human serum albumin (HSA) because it is the most abundant plasma protein as well as it is a highly soluble negatively charged protein, and greatly improves the transport capacity of blood plasma. Additionally, its effect is exerted by reversible binding of a vast majority of chemically diverse endogenous and exogenous compounds. This astonishing binding capacity, which often seriously impacts pharmacokinetic properties of therapeutic drugs is encoded in the secondary structure of HSA[45]. Pharmaceuticals usually bind to HSA at either binding sites I or II, present in subdomains IIA and IIIA. This explanation had been confirmed by the Xray crystallographic structure of HSA[46]. Free energy (∆G°) investigations of 30 probable binding poses in the hydrophobic cavity of HSA (PDB code: 1e78) prove that pose V has the highest negative value of ∆G° of − 6.83 kcal/mol. Thus, the highest interaction capability is in subdomains IIA and IIIA, which are consistent with sites I and II according to the terminology of Sudlow et. al[47]. A close inspection of this pose reveals that betaxolol (ligand) is surrounded by 17 amino acids residues, hydrophilic (i.e. Arginine 145) and hydrophobic (i.e. Tyrosine 452), as shown in Fig. 9. One weak hydrogen bond of 2.75 Å occurs between hydroxyl

moiety of the side chain and Glutamine 459 and a π-bonding interaction of benzene ring and Histidine 146 of 4.28 Å. To the best of our knowledge, electrostatic interactions of other polar residues form additional hydrogen bonds that stabilize the ligand interactions.

5. Conclusion We report a combined experimental and theoretical study of the molecular structures of betaxolol and betaxolol.HCl, a β1-blocker drug used for the treatment of cardiovascular diseases and hypertension. The molecular structures of betaxolol (BT) and betaxolol.HCl (BTH) in monomeric, dimeric forms and with combination chlorthalidone (CTD) were optimized by B3LYP-B3BJ/6-311++G(d,p) level of DFT. The results show that the BTH-CTD has a binding energy of 31.8 kcal/mol, much higher than that of the BTH dimer, 20.3 kcal/mol, and the BT-CTD, which is 18 kcal/mol. Our results also show that the addition of HCl almost doubles the binding energy of betaxolol to chlorthalidone. The molecular structure of BT belongs to the C1 point group symmetry, consists of 51 atoms, and is expected to have 147 modes of vibrations of the same A species. All the fundamental vibrations of BT are active in both FT-IR and FT-Raman spectra. The vibrational assignments of the fundamental modes of BT showed that the B3LYP/6311++G(d,p) level applied in this work gives vibrational wavenumbers in a good agreement with the experimental data. Intra- and intermolecular non-covalent and weak interactions (van der Waals forces) of betaxolol were explored using atoms in molecules (AIM) and the reduced density

gradient (RDG) methods. AIM confirms the presence of an intramolecular hydrogen bond between O12–H27----N14 with an energy of 5.04 kcal/mol. These findings were confirmed by electron localization function (ELF) and localized orbital locator (LOL) studies. The molecular electrostatic potential (MEP) map was plotted to locate nucleophilic and electrophilic sites in betaxolol. The strongest electrophilic site is the lone pair of the O12 atom. The H30, which is attached to N14, was revealed to be the strongest nucleophilic site. Both sites are in the isopropylamino-2-propanol moiety, giving it the predominant role in the biological activity of the drug. NBO analysis confirms the existence of weak intramolecular hydrogen bonding interaction with a stabilization energy of 3.47 kcal/mol. In the NBO analysis of BTCTD system, the most important hyperconjugative interactions are LP(1) O56→C13H29 and LP(1)O54→C13-H29 with stabilization energies of 64.82 and 41.21 kcal/mol, respectively. The UV-Vis spectrum of BT was computed and compared with experiment. The maximum peak computed at 223 nm corresponds to π-π* transition from HOMO to LUMO+4 and LUMO+6. Molecular docking was used to investigate the binding of betaxolol to proteins and understand its biological activity. The highest free energies of binding for the drug to the human serum albumin (HSA) protein were in the subdomains IIA and IIIA.

Acknowledgments: This work is a part of Khloud Mohammed’s M.Sc. thesis. The authors like to thank Assiut University for the official, technical and financial support. The authors also acknowledge a generous allocation of computer time granted by SHARCNET, a partner consortium in the Compute Canada national HPC platform.

6. Reference

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Captions of figures: Fig. 1. P-XRD patterns of (a) BT, (b) BT-CTD cocrystal, and (c) CTD. Fig. 2. Optimized structures with numbering of atoms of (a) betaxolol (BT), (b) chlorthalidone (CTD). Fig. 3. Optimized structures with numbering of atoms of (a) betaxolol.HCl (BTH) dimer and (b) betaxolol.HCl-chlorthalidone (BTH-CTD). Fig. 4. The atomic orbital compositions of the frontier molecular orbitals of betaxolol calculated by the Becke method. Percentage contributions to the HOMO and LUMO are given in blue and red colors, respectively. Fig. 5. Population density of states (TDOS), partial density of states (PDOS) for fragments of betaxolol and overlap density of state (OPDOS) for frag. 1 and frag. 2. Fig. 6. 3D molecular electrostatic potential map for betaxolol along with the values of its electrostatic and vdW surfaces. Fig. 7. ELF for hydrogen bonding moiety region of betaxolol; (a) color filled map, (b) contour map and (c) 3D ELF. Fig. 8. RDG scatter graphs of (a) BT and (c) BT-CTD. (b) weak interactions in BT and (d) weak interactions in BT-CTD. Fig. 9. The active sites of human serum albumin (HSA) in complex with betaxolol.

Table (1): Selected geometrical parameters of betaxolol obtained by B3LYPD3BJ/6-311++G(d,p), B3LYP/6-31G(d,p) levels of DFT.

B3LYP/6-311++G(d,p)

X-Ray Experimental data*

6-31G(d,p)

Bond lengths(Å) N14-C15

1.47347

-

-

N14-C13

1.46745

-

-

O12-C11

1.4205

-

-

O12-H27

0.97079

-

-

O9-C10

1.42522

-

-

O9-C3

1.36741

-

-

O40-C8

1.41811

-

-

O40-C41

1.42150

1.46

1.418

C41-C44

1.50278

1.52

1.506

C44-C45

1.50678

1.54

1.508

C45-C46

1.5096

1.55

1.509

C44-C46

1.51036

1.43

1.510

Bond angles(°) C8-O40-C41

113.25

-

-

O40-C41-C44

109.499

-

-

C11-O12-H27

104.68

-

-

O12-C11-C10

106.433

-

-

C10-O9-C3

118.79

-

-

C11-C10-O9

107.85

-

-

C15-N14-C13

116.45

-

-

N14-C13-C11

108.63

-

-

C44-C45-C46

60.09

55.2

60.1

C45-C46-C44

59.86

61.9

59.9

C45-C44-C46

60.04

62.9

60

Dihedral angles (°) C16-C15-N14-C13

-62.69

-

-

N14-C13-C11-O12

52.08

-

-

C13-C14-O12-H27

-35.55

-

-

O12-C11-C10-O9

-173.82

-

-

N14-C13-C11-C10

171.08

-

-

O40-C41-C44-C46

153.89

163.9

156.8

C8-O40-C41-C44

178.63

160

178.8

O40-C41-C44-C45

83.48

96.8

86.5

*Experimental data are taken from [10].

Table (2): Ground state energies, E, and binding energies, ΔEb, for the systems under investigations calculated by B3LYP-D3BJ/6-311++G(d,p).

E(a.u)

ΔEb (kcal/mol)

BT

-984.0324

-

BTH

-1444.9866

-

CTD

-1809.2538

-

Compound

BT dimer

-1968.2618

- 14.2

BTH dimer

-2890.0056

- 17.1

BT-CTD

-2793.3993

- 14.4

BTH-CTD

-3254.2911

- 27.1

Table (3): Experimental and scaled theoretical wavenumbers (cm-1) and potential energy distribution (%PED) for BT. Computed 3689 3210 3157 3156 3124

Scaled 3541 3081 3030 3029 2999

3118 3105 3093 3085 3080 3057

2993 2980 2969 2961 2956 2934

Calculated at B3LYP \6-311++G(d,p) Experiment Intensity* Assignment (PED%) 3243 171 (O12-H27)(100%) 3135 25 (C45-H48)(27%) + (C46-H51)(16%) 3036 18 (C1-H18)(61%)+(C5-H21)(31%) 13 (C5-H21)(65%) + (C1-H18)(31%) 3008 12 (C45-H49)(35%)+(C46-H50)(10%)+(C45H48)(41%)+(C46-H51)(13%) 2984 23 (C46-H50)(32%)+(C46-H51)(45%) 2965 28 (C17-H37)(65%) 2926 36 (C16-H33)(75%) 66 (C16-H34)(15%)+(C17-H36)(24%) 20 (C7-H23)(54%) 44  (C10-H24)(55%)

3051 3039 3022

2928 2917 2901

21 29 34

3014 3006 3002 2984 2974 2960 2945 1652 1615 1543 1516 1511 1480 1460 1418

2893 2885 2881 2864 2855 2841 2827 1585 1550 1481 1455 1450 1420 1401 1361

21 25 30 27 65 38 69 65 12 146 64 19 20 25 22

1412 1407 1398

1355 1350 1342

1367 1359 1354 1335 1331 1298

1312 1304 1299 1281 1277 1246

27 18 14 21 28 37

1279 1270 1250 1199 1187 1186 1138 1132

1227 1219 1200 1151 1139 1138 1092 1086

20 344 41 25 64 11 11 71

1123 1119 1110 1161 1046 1011 962 945 859 845 838 793

1078 1074 1065 1114 1004 970 923 907 824 811 804 761

2858

1584 1514 1474 1441 1493

1311 1338

1146 1121 1089 1052

813 787

11 24 22

31 330 22 136 11 26 23 11 12 22 28 20

(C10-H24)(13%)+(C13-H28)(60%) (C7-H22)(54%)+(C7-H23)(45%) (C16-H34)(13%)+(C17-H35)(15%)+(C17H36)(32%)+(C17-H37)(10%) (C16-H32)(12%)+(C16-H33)(34%)+(C16-H34)(18%) (C10-H24))(65%)+(C10-H25)(32%) (C13-H28)(24%)+(C13-H29)(64%) (C8-H39)(50%) (C41-H42)(59%) (C11-H26)(92%) (C41-H42))(50%)+(C−)() (C1-C2)(32%)+(C5-C4)(10%) (C4-C3)(78%)+(c43-c41-c42)(12%) (H18-C1-C2)(15%) (H25-C10-H24)(79%) (H36-C17-H35))(10%) (H30-N14-C15)(27%)+(H36-C17-H35)(13%) (H27-O12-C11)(21%)+(C11-C13)(15%) (H32-C16-H34)(15%)+(H35-C17-H37)(18%)+(H36C17-H35)(21%) ţ(H24-C10-O9-C3))(17%) ţ(H38-C8-O40-C41)(16%) (H32-C16-H34)(18%)+(H33-C16-H32)(20%)+(H34C16-H33)(18%) (H42-C41-O40)(14%)+ţ(H42-C41-O40-C8)(23%) (H26-C11-O12)(26%)+OOP(C11-C13-C10-H26)(21%) ţ(H31-C15-N14-C13)(50%) ţ(H29-C13-N14-C15)(17%)+(H31-C15-C17)(26%) (C4-C3)(11%) (−−C11)(28%)+(H26-C11-O12)(21%)+OOP(C11-C13C10-H26)(20%) (H28-C13-N14)(34%) (O9-C3)(42%) (H24-C10-O9)(30%)+ţ(H25-C10-O9-C3)(12%) (H21-C5-C6)(22%) ţ(H36-C17-C15-C16)(10%)+(N14-C15)(15%) (H24-C10-O9)(24%) (H18-C1-C2)(18%)+(H19-C2-C1)(23%)+(C1-C2)(12%) (O40-C8)(10%)+ţ(H49-C45-C46-C44)(11%)+ţ(H47-C44-C46C45)(26%) (O12-C11)(30%)+(C13-C11-C10)(11%) (O40-C8)(36%) (N14-C13)(38%) (O9-C10)(57%) ţ(H50-C45-C46-C44)(18%)+ţ(H51-C46-C45-C44)(16%) (C44-C41)(17%)+(C8-C7)(19%) ţ(H28-C13-N14-C15)(10%) ţ(H48-C45-C46-C44)(10%) (C3-C2)(11%)+(C4-C3)(15%)+(C4-C3-C2)(12%) (C17-C15)(11%)+(C16-C15)(12%) (C44-C45)(21%) (C7-C6)(14%)+(C6-C5-C4)(12%)+(C4-C3-C2)(11%)

780 779 581 551

748 747 557 528

521

: stretching

: Bending

(H48-C45-C46)(35%) ţ(H30-N14-C15-C16)(37%) (H27-O12-C11-C10)(65%) OOP(O12-C11-C10-C13)(12%)+OOP(C1-C2-C4-C5)(11%)

14 52 42 25 ţ: Torsion

OOP: Out-of-plane

* Vibrations with intensities less than 10% are omitted.

Table(4):The reactivity parameters ( ionization potential (I), electron affinity (A), electronegativity (χ), chemical potential (µ), chemical hardness (η), softness (S), electrophilicity index(ω), energy change (ΔE), maximal charge acceptance (ΔNmax)) for betaxolol. Ionization potential (I)

6.094eV

Electron affinity (A)

0.470eV

Electronegativity (χ)

3.47 eV

Chemical Potential (µ) Chemical hardness (η) Chemical softness (S) Electrophilicity index(ω) Energy change (ΔE) Maximal charge acceptance(ΔNmax) ΔE/ΔNmax

-3.47eV 2.812eV 0.36 eV-1 2.14eV -2.14eV 1.23eV -1.7eV

Table(5) Selected second order perturbation theory of the Fock matrix in NBO basis of BT and BT-CTD studied at B3LYP-D3BJ/6-311++G(d,p) level. NBO of BT Donor (i)

Acceptor (j)

E(2) (kcal/mol)

Ej-Ei (a.u.)

F(i,j) (a.u.)

(1)

LPO9

C3-C4

6.66

1.11

0.077

(2)

LPO9

C3-C4

28.67

0.34

0.094

(2)

LPO9

C10-H24

5.54

0.70

0.058

(2)

LPO9

C10-H25

5.84

0.69

0.059

(2)

LPO12

C11-H26

9.31

0.66

0.070

(1)

LPN14

C13-H29

6.84

0.70

0.063

(1)

LPN14

C15-C16

7.59

0.68

0.065

(2)

LPO40

C8-H38

6.64

0.67

0.060

(2)

LPO40

C8-H39

6.39

0.67

0.059

(2)

LPO40

C41-H42

5.96

0.67

0.057

(2)

LPO40

C41-H43

6.81

0.67

0.061

(1)

LPN14

O12-H27

3.47

0.74

0.046

NBO OF BT-CTD (1)

LPN14

O12-H27

4.31

0.74

0.051

(1)

LPO12

C66-H76

7.51

0.73

0.066

(1)

LPO54

C1-C6

11.99

0.95

0.095

(1)

LPO54

C13-H29

41.21

0.43

0.119

(2)

LPO55

C13-H29

28.73

0.02

0.025

(1)

LPO56

C1-C6

6.14

1.11

0.074

(1)

LPO56

C13-H29

64.82

0.60

0.176

(2)

LPO56

C13-H29

25.53

0.07

0.0411

(1)

LPO57

C1-C6

22.94

1.14

0.144

(2)

LPO57

C16-H33

6.69

1.09

0.076

(2)

LPO57

C13-H29

13.79

0.07

0.028

(1)

LPN59

C1-C6

24.66

0.65

0.115

(1)

LPN59

C16-H33

25.10

0.60

0.112

Highlights •

Complete assignment of the various modes of vibrations of betaxolol

•

The binding energy of betaxolol to chlorthalidone is 31.8 kcal/mol

•

Electrostatic potential map reveals the main electrophilic and nucleophilic sites

•

Weak hydrogen bonding in betaxolol is confirmed by NBO, ELF and AIM studies

•

The binding sites of HSA protein to betaxolol is revealed by molecular docking

Credit author statement Khloud Mohammed: measuring IR spectrum, synthesis of cocrystals, calculation of reactivity parameters, visualization; Ahmed A. K. Mohammed: conceptualization, methodology, geometry optimization, IR and UV calculations, binding energy calculations, interpretation of data, reviewing and editing; Ahmed F. Abdel Hakiem: conceptualization, synthesis of cocrystals, docking study; Refaat M. Mahfouz: conceptualization, methodology, interpretation of data, IR assignment, supervision.

Declaration of interests ☐ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐ The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: