QSAR, docking, dynamic simulation and quantum mechanics studies ...

Chemico-Biological Interactions 209 (2014) 1–13

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Chemico-Biological Interactions journal homepage: www.elsevier.com/locate/chembioint

QSAR, docking, dynamic simulation and quantum mechanics studies to explore the recognition properties of cholinesterase binding sites J. Correa-Basurto a,⇑, M. Bello a, M.C. Rosales-Hernández a, M. Hernández-Rodríguez a, I. Nicolás-Vázquez b, A. Rojo-Domínguez c, J.G. Trujillo-Ferrara a, René Miranda b, C.A. Flores-Sandoval d,⇑ a Laboratorio de Modelado Molecular y Bioinformática, Sección de Estudios de Posgrado e Investigación y Departamento de Bioquímica, Escuela Superior de Medicina, Instituto Politécnico Nacional, Plan de San Luis y Díaz Mirón, 11340 México, D.F., Mexico b Departamento de Ciencias Químicas, Campo 1, Facultad de Estudios Superiores Cuautitlán, Universidad Nacional Autónoma de México, Av. 1ro de Mayo s/n, Col. Santa María de las Torres, Cuautitlán Izcalli, 54740 Estado de México, Mexico c Departamento de Ciencias Naturales, Universidad Autónoma Metropolitana, Unidad Cuajimalpa, Pedro Antonio de los Santos 84, Col. San Miguel Chapultepec, 11850 México, D.F., Mexico d Programa de Ingeniería Molecular, Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, Col. San Bartolo Atepehuacan, 07730 México, D.F., Mexico

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 9 September 2013 Received in revised form 25 November 2013 Accepted 2 December 2013 Available online 7 December 2013 Keywords: Acetylcholinesterase Butyrylcholinesterase DFT QSAR MD simulation

A set of 84 known N-aryl-monosubstituted derivatives (42 amides: series 1 and 2, and 42 imides: series 3 an 4, from maleic and succinic anhydrides, respectively) that display inhibitory activity toward both acetylcholinesterase and butyrylcholinesterase (ChEs) was considered for Quantitative structure–activity relationship (QSAR) studies. These QSAR studies employed docking data from both ChEs that were previously submitted to molecular dynamics (MD) simulations. Donepezil and galanthamine stereoisomers were included to analyze their quantum mechanics properties and for validating the docking procedure. Quantum parameters such as frontier orbital energies, dipole moment, molecular volume, atomic charges, bond length and reactivity parameters were measured, as well as partition coefficients, molar refractivity and polarizability were also analyzed. In order to evaluate the obtained equations, four compounds: 1a (4-oxo-4-(phenylamino)butanoic acid), 2a ((2Z)-4-oxo-4-(phenylamino)but-2-enoic acid), 3a (2-phenylcyclopentane-1,3-dione) and 4a (2-phenylcyclopent-4-ene-1,3-dione) were employed as independent data set, using only equations with r2mðtestÞ >0.5. It was observed that residual values gave low value in almost all series, excepting in series 1 for compounds 3a and 4a, and in series 4 for compounds 1a, 2a and 3a, giving a low value for 4a. Consequently, equations seems to be specific according to the structure of the evaluated compound, that means, series 1 fits better for compound 1a, series 3 or 4 fits better for compounds 3a or 4a. Same behavior was observed in the butyrylcholinesterase (BChE). Therefore, obtained equations in this QSAR study could be employed to calculate the inhibition constant (Ki) value for compounds having a similar structure as N-aryl derivatives described here. The QSAR study showed that bond lengths, molecular electrostatic potential and frontier orbital energies are important in both ChE targets. Docking studies revealed that despite the multiple conformations obtained through MD simulations on both ChEs, the ligand recognition properties were conserved. In fact, the complex formed between ChEs and the best N-aryl compound reproduced the binding mode experimentally reported, where the ligand was coupled into the choline-binding site and stabilized through p–p interactions with Trp82 or Trp86 for BChE and AChE, respectively, suggesting that this compound could be an efficient inhibitor and supporting our model. Ó 2013 Published by Elsevier Ireland Ltd.

1. Introduction Alzheimer’s disease (AD) is the most widespread form of human dementia among elderly people worldwide, and this illness is characterized by a low concentration of acetylcholine (ACh) in

⇑ Corresponding authors. E-mail addresses: [email protected] (C.A. Flores-Sandoval).

(J.

Correa-Basurto),

cafl[email protected]

0009-2797/$ - see front matter Ó 2013 Published by Elsevier Ireland Ltd. http://dx.doi.org/10.1016/j.cbi.2013.12.001

the hippocampus and cortex [1,2], giving rise to symptoms such as loss of cerebral capability, cognition deterioration and a diversity of neuropsychiatric conditions [1–4]. ACh is a neurotransmitter that plays a role in the modulation of memory function in normal and neurodegenerative conditions [5,6]. ACh is hydrolyzed and degraded by acetylcholinesterase (AChE, E.C. 3.1.1.7) and butyrylcholinesterase (BChE, E.C. 3.1.1.8) [7–9]. AChE has been characterized as being the only target identified in the design of several drugs for AD treatment [6–9].

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J. Correa-Basurto et al. / Chemico-Biological Interactions 209 (2014) 1–13

There is considerable three-dimensional information about both cholinesterases (ChEs) in the Protein Data Bank (PDB, http:// www.pdb.org/), which also reveals structural details of both conformational states. In their free state, these enzymes are monomers whose structural topology is comprised of a 12-stranded mixed beta sheet surrounded by 14 alpha helices with a molecular weight of approximately 60 kDa; these monomers often form aggregates (dimers) that possess catalytic activity [10] as monomer. In the bound state, both ChEs have been found to form complexes with ACh, their natural inhibitor. The knowledge of the interactions that stabilize the AChE–ACh complex has been exploited for the initial coordinates in docking and molecular dynamics (MD) simulation studies for the purpose of localizing multiple binding sites for ACh and other known inhibitors, as well as for the development of new acetylcholinesterase inhibitors (AChEIs) [11]. Both the three-dimensional data and MD simulations confirm that the ChEs share a catalytic triad (Ser, His, Glu) and an anionic subsite (Trp). However, a comparison between human AChEs and BChE reveals that aromatic residues Phe295 and Phe297 in the former are exchanged for the aliphatic residues Leu286 and Val288 in the latter. Furthermore, it is worth mentioning that these residues are in close proximity to the catalytic triad in both enzymes and contribute to their specificity and selectivity [12]. The catalytic triad and other important residues that constitute functional subsites are located in a deep narrow gorge (approximately 20 Å) with an oxyanion hole (Gly121, Gly122, Ala204) and an acyl binding pocket (Trp286, Phe295, Phe297, Phe338). An anionic subsite is found at the bottom of this gorge, which is formed by Trp82 and Trp86 in human AChE and BChE, respectively, and binds the quaternary nitrogen of their substrates and other ligands [13]. This active site is characterized by a highly negative electrostatic potential. In addition, it has recently been reported that recognition processes can be achieved by another important site, known as the peripheral anionic subsite, which is located in the deep surface of this hole (Asp74, Tyr124, Ser125, Trp286, Tyr337, Tyr341) [14]. The quantitative structure–activity relationship (QSAR) has been one of the principal strategies to predict the activity of new molecules by correlating structural or property descriptors of compounds through mathematical equations [15–21]. Furthermore, QSAR methodology has led to the design of several AD inhibitors such as phenylpentenone derivatives [22], physostigmine analogs [23], indanone and tacrine [24,25]. Recently, Correa-Basurto et al. through docking and quantum mechanics studies described the activity of 88 N-aryl derivatives as inhibitors of AChE and BChE [26], where density functional theory (DFT) calculations at the B3LYP/6-31G+(d,p) level were employed to obtain the energy value of the optimized structure and the energies of the frontier orbitals to correlate them with the inhibitory effects of the compounds. However, a conformational description for the optimized structures was not obtained, nor were other quantum descriptors determined [26]. Meanwhile, Solomon et al. applied a QSAR study that derived the models for 53 compounds bound to AChE and 61 compounds bound to BChE with the aid of genetic function approximation (GFA) techniques using the logarithm of the partition coefficient (logP), the sum of chemical bonds between atoms (Wiener), the molecular Shape Kappa indices (KAPPA-1-AM), the dipole moment (l), and the molecular connectivity indices (CHI-1) [27]. In this contribution, a QSAR study for a series of 84 known Naryl derivatives that display inhibitory activity towards AChE and BChE was performed using docking and quantum mechanics to explore the recognition properties of both. Furthermore, in order to evaluate the obtained equations, compounds 1a (4-oxo-4-(phenylamino)butanoic acid), 2a ((2Z)-4-oxo-4-(phenylamino)but-

2-enoic acid), 3a (2-phenylcyclopentane-1,3-dione) and 4a (2-phenylcyclopent-4-ene-1,3-dione) were employed as independent data set [26]. ChEs. Donepezil and galanthamine were included to analyze their quantum mechanics properties and for validating the docking procedure. Furthermore, before performing the docking studies, both ChEs were submitted to MD simulations with the aim of taking into account the target flexibility properties. Therefore, our findings may provide quantum chemical details that can be used for drug design by combining different computational tools. 2. Computational procedure 2.1. Molecular dynamics Classical MD simulations were performed using the NAMD 2.6 program [28] employing the CHARMM27 force field [29]. The initial ChE coordinates were obtained from the PDB (PDB IDs: 1B41 and 1P0I). The co-crystallized ligands and water molecules of the crystal structure were removed. Hydrogen atoms were added using the psfgen program included in the VMD package [30]. Afterwards, these structures were neutralized and solvated with TIP3P water molecules. The equilibration protocol consisted of 1500 minimization steps, followed by 30 ps of MD simulations at 10 K with fixed protein atoms. Subsequently, the entire system was minimized over 1500 steps (at 0 K), followed by gradual heating from 10 to 310 K using temperature reassignment during the initial 60 ps of the 100 ps equilibration dynamics without restraints. The final step involved a 30 ps NTP simulation using the Nose– Hoover Langevin piston pressure control at 310 K and 1.0 bars for density (volume) fitting [31]. After this point, the simulation was continued using the NTV ensemble for 10 ns. Periodic boundary conditions and the particle mesh Ewald method [32,33] were applied for a complete electrostatics calculation. The dielectric water constant was used, and the temperature was maintained at 310 K using Langevin dynamics. Nonbonded interactions were calculated by applying a 10 Å cutoff with a switching function at 8 Å. The nonbonded list generation was terminated at 11.5 Å. The SHAKE method [34] was employed to provide an integration time step of 2 fs while keeping all bonds to the hydrogen atoms rigid. The trajectory was stored every 1 ps and was further analyzed with the VMD program [30]. The MD simulation output over 10 ns provided several ChE structures, which were sampled every 0.5 ns to evaluate the energetics of ligand recognition and binding modes of the target compounds (Table 1). Some average geometrical properties, such as the root-mean squared deviation (RMSD), root-mean squared fluctuation (RMSF) and radius of gyration (Rg), were evaluated using Carma software [35]. 2.2. Docking simulations For docking studies, we utilized several protein conformations previously obtained through the MD simulation procedures mentioned above. First, the initial geometry optimization of ligands was performed with HYPERCHEM (Version 7.0, Hypercube, USA, http://www.hyper.com) at the MM+ level [36]. Then, the compound was optimized at the AM1 and DFT (B3LYP/6-31G(d,p)) levels using the Gaussian 09 program [37,38]. The AutoDock (4.2) program was selected for docking studies because this algorithm maintains a rigid macromolecule while allowing ligand flexibility [39]. This program has been widely used because it displays good free energy correlation values between docking simulations and experimental data [40]. A GRID-based procedure was utilized to prepare the structural inputs and to define all of the binding sites

J. Correa-Basurto et al. / Chemico-Biological Interactions 209 (2014) 1–13 Table 1 Structures of the compounds for series 1, 2, 3, and 4.

O

R1 R1

O R2

N H

R3

HO

O

R2

HO

1

N H

R3

O

2

R1

R1

O

R2

N

O

R2

N

R3

R3

O

O

3

1a, 2a, 3a, 4a 1b, 2b, 3b, 4b 1c, 2c, 3c, 4c 1d, 2d, 3d, 4d 1e, 2e, 3e, 4e 1f, 2f, 3f, 4f 1g, 2g, 3g, 4g 1h, 2h, 3h, 4h 1i, 2i, 3i, 4i 1j, 2j, 3j, 4j 1k, 2k, 3k, 4k 1l, 2l, 3l, 4l 1m, 2m, 3m, 4m 1n, 2n, 3n, 4n 1o, 2o, 3o, 4o 1p, 2p, 3p, 4p 1q, 2q, 3q, 4q 1r, 2r, 3r, 4r 1s, 2s, 3s, 4s 1t, 2t, 3t, 4t 1u, 2u, 3u, 4u 1v, 2v, 3v, 4v

4 R1

R2

R3

H NO2 H H CO2H H H Cl H H OH H H NH2 H H OCH3 H H F H H

H H NO2 H H CO2H H H Cl H H OH H H NH2 H H OCH3 H H F H

H H H NO2 H H CO2H H H Cl H H OH H H NH2 H H OCH3 H H F

[39]. A rectangular lattice (126  126  126 Å) with points separated by 0.375 Å was superimposed on the entire protein structure to achieve a blind docking procedure. All docking simulations were conducted using the hybrid Lamarckian genetic algorithm with an initial population of 100 randomly placed individuals and a maximum of 1.0  107 energy evaluations. All other parameters were maintained at their default settings. The resulting docked orientations were clustered together, within a root mean square deviation (RMSD) of 0.5 Å. The lowest energy cluster for each ligand was subjected to further free energy and binding geometry analyses, as previously reported [41]. 2.3. Quantum studies First, the N-aryl derivative (Table 1) structures were optimized by using MM+ molecular modeling and the semi-empirical PM3 method, both of which are implemented in Hyperchem 7.0 software [36]. For these calculations, the Polak-Ribiere conjugate gradient algorithm was employed, with the RMS gradient set to 0.0001 kcal/(Å mol). Afterwards, DFT calculations implemented in the Gaussian 09 program were performed [37,38]. Thus, the structures obtained were fully optimized at the DFT/B3LYP/6-31G(d,p) level of theory [42–46], followed by single-point calculations at the DFT/B3LYP/6-311G(d,p) level of theory [47–48]. The energy values were corrected by a zero-point energy (ZPE) correction.

3

Calculated vibrational frequencies ensured that the structures were stable (with no imaginary frequencies). Natural Bond Orbital (NBO) analyses were performed using the Gaussian 03 package. Statistical parameters were obtained using the multiple linear regression (MLR) method, and the variables were entered into a regression equation through t-values of coefficients (threshold value P2). Further, some reactivity properties were determined for galanthamine and donepezil molecules by the following computational procedure. Quantum chemical calculations at the DFT/RB3LYP/6311G(d,p) (restricted B3LYP) theory [49–51] were employed for full optimization of the selected neutral compounds. During the second step, the molecular energy was differentiated twice with respect to the Cartesian coordinates of the atoms. Harmonic vibrational frequency analysis suggested that optimized geometries belong to minima at the respective potential energy surfaces. In a similar context, DFT based on the Hohenberg–Khon theorems has proven to be an important tool for several chemical concepts and ideas on reactivity. In this work, the more relevant electronic properties for galanthamine (G) and donepezil (D) stereoisomers have been calculated, including electronic chemical potential (l) [52], ionization potential (IP), electron affinity (EA), electronegativity (v) [53,54] and global hardness (g) [55–57], as well as the energy of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Using l and g, Parr et al. [53] have defined another quantum chemical descriptor known as the electrophilicity index (x) (or more accurately called the global electrophilicity) which measures the propensity to absorb electrons. That is, the electrophilicity index measures the energy stabilization when an optimal electronic charge transfer from the environment to the system occurs. On the other hand, the energy values of interaction between the N-aryl derivatives on both ChEs were taken from previously published research [26]. 2.4. Validation parameters 2.4.1. q2cv and q2lmo One of the most commonly applied internal validation techniques is the leave-one-out cross-validation (LOO-CV). The measure connected to internal validation by LOO-CV, q2cv , is defined as follows:

Pn v 2 obs  ypredo Þ i¼1 ðyi i q2cv ¼ 1  P 2 n obs obs i Þ y i¼1 ðyi

ð1Þ

where yobs is the experimental (observed) value of the property for the i v ith compound; ypredo is the predicted value for the temporarily exi obs cluded (cross-validated) ith compound; y is the mean experimental i value of the property in the training set; and n is the number of compounds in the training set. Excluding more than one element in each iteration is the leave-many-out (LMO) technique; in this case, for n = 84 compounds G = 4, whereas for n = 42 and n = 21 compounds G = 3 [58,59] LOO and LMO are highly used to evaluate whether overfitting occurs, and whether the model is robust and stable. 2.4.2. r2mðtestÞ Cross validation provides a reasonable approximation of ability with which the QSAR predicts the activity values for new compounds. However, external validation gives the ultimate proof of the true predictability of a model. In this sense, for better external predictive potential of the model, a modified r 2mðtestÞ is introduced by the following equation:

r2mðtestÞ ¼ r2  ð1 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 2  r 20 Þ

ð2Þ

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where r 2 is the square of the correlation coefficient between the observed and predicted values, and r 20 is square of the correlation coefficient between the observed and predicted values with intercept set to zero. The value of r 2mðtestÞ should be higher than 0.5 for an acceptable model; moreover, it may be used for the selection of the best prediction ability among comparable models. The concepts of absolute electronegativity, v, and absolute hardness, g, were reported by Parr [54,55]. The operational definitions of these quantities are as follows:

g ¼ ðIP  EAÞ=2

ð3Þ

v ¼ ðIP þ EAÞ=2

ð4Þ

where IP and EA are the ionization potential and electron affinity of any chemical system, atom, ion, molecule, or radical. Within the validity of Koopmans’ theorem [60], the frontier orbital energies are given by the following:

eHOMO ¼ IP  eLUMO ¼ EA

ð5Þ

The electrophilicity is a descriptor of the reactivity that allows a quantitative classification of the global electrophilic nature of a molecule within a relative scale and, effectively, is the power of a system to ‘soak up’ electrons; this parameter is defined by [53], as follows:

x¼

l2 2g

ð6Þ

where l is the electronic chemical potential and g is the hardness, in their corresponding intervals. 3. Results and discussion 3.1. Molecular dynamics and docking simulations MD simulations serve to study protein flexibility properties, as has been discussed elsewhere [61]. The RMSD values for AChE oscillate between 2.5 and 9 Å with a median value of 8.5 Å (Fig. 1a), reaching convergence after 5 ns. These RMSD values indicate that AChE experiences several conformational changes before arriving at a stable structure. Fig. 1b shows the Rg value, which is a measure of protein compactness that ranged from 11 to 17 Å with

a median value of 10.5 Å for AChE, showing that the protein tends toward compactness in short MD simulation periods. On the other hand, the RMSF analysis over the alpha carbon atoms shows that the regions with the lowest RMSF values oscillated from 3.0 to 3.7 Å, whereas the regions with the highest RMSF values were those corresponding to loop regions (Fig. 1c). For the case of BChE, it can be seen that RMSD oscillated from 1 to 3.5 Å with a mean value of 3.3 Å (Fig. 1d), reaching equilibrium after 5.0 ns as observed for AChE; however, for the latter case, convergence was reached at higher RMSD values (Fig. 1a), which is in agreement with the higher conformational fluctuations observed in different protein sections (Fig. 1c). Rg values oscillated between 22.7 to 23.7 Å with an average value of 23.4 Å, indicating that BChE compactness is twice that of AChE and therefore, despite the fact that BChE shows a lower conformational fluctuation (Fig. 1f), this protein could be more unstable in water. Overall, the two ChEs did not share similar geometrical behavior, despite being very similar with respect to their biological properties. Regarding docking procedure, compared to simply using the crystallized protein as the initial structure, important improvements are gained by using several conformations obtained through MD simulation procedures, as has been reported elsewhere [61]. Furthermore, because validation of the docking procedure is required, we utilized galanthamine and donepezil, both of which recognize AChE as has been reported elsewhere [62]. As shown in Fig. 2a, galanthamine binds to AChE, interacting with both the choline-binding site by p–p interactions with Trp86 and the acyl-binding pocket (Phe338). The tertiary amine makes a hydrogen bond via its N-methyl group with Asp74, near the top of the gorge. The hydroxyl group of the galanthamine establishes hydrogen bond interactions with Glu202. The binding of galanthamine to AChE is the result of a great number of weak interactions with the protein because of the rigid nature of the inhibitor, as reported by Greenblatt et al. [63]. Fig. 2b shows that the binding mode for donepezil into AChE is in agreement with that reported by Sugimoto et al. [64], which reports the interaction between the NH group in the protonated piperidine, the carboxyl group of Asp74, and the phenyl ring of Phe330, as well as the interaction between the phenyl ring in the benzyl piperidine and the indole ring of Trp86. In this sense, the validation of the docking procedure was realized because the binding modes for galanthamine or donepezil on AChE are reproducible,

Fig. 1. Geometrical parameters calculated through the 10 ns-long MD simulations of both ChEs, (a) root mean square deviations (RMSD), (b) radius of gyration (Rg) and (c) root mean square fluctuations (RMSF) for AChE. While for BChE simulations: (d) RMSD, (e) Rg and (f) RMSF.

J. Correa-Basurto et al. / Chemico-Biological Interactions 209 (2014) 1–13

5

Fig. 2. The binding poses of AChEIs. (a) Galanthamine on AChE, (b) donepezil on AChE and (c) the best N-aryl compound (2F) on BChE. Both reported (galanthamine) and aryl derivatives reach Trp86 for AChE and Trp82 for BChE through p–p interactions. (d) galanthamine (red) with the AChE snapshot obtained at 2 ns, (e) galanthamine (blue) at 6 ns, (f) galanthamine (purple) at 10 ns, (g) donepezil (red) on AChE snapshot obtained at 2 ns, (h) donepezil (blue) at 6 ns and (i) donepezil (purple) at 10 ns. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

according to previous data [62]. Furthermore, for BChE, the binding mode was reproduced, and Fig. 2c shows the interaction of the best N-aryl compound (Compound 2F), where the principal interactions are mainly p–p interactions with Trp82, suggesting that, despite the fact that the three ChEIs underwent many structural orientations, their recognition properties are maintained. It is important to mention that despite the fact that the protein experienced several conformational changes, the interactions observed with the protein before submitting to MD simulations are maintained. This similarity is shown in the binding of galanthamine, which is maintained near Trp86, His443 and Ser203 at different MD simulation times (2, 6 and 10 ns, Fig. 2d–f); a similar behavior was observed with donepezil (Fig. 2g–i). 3.2. Conformational analysis of N-aryl compounds First, the energy of each series of compounds was obtained from the single-point calculations performed at the DFT/B3LYP/6311G(d,p) theory level with the B3LYP/6-31G(d,p) geometries. Using a higher basis set in the single point calculations, we obtained a better energy value that those reported in the literature [26]. Table 2 lists the bond lengths of the aromatic carbon atom to the amidic or imidic nitrogen atom (CAr–N) and the nitrogen atom to the carbon atom of the carbonyl (N–CO). For series 1 and 2, considering the compounds 1a and 2a, the bond lengths N–CO and CAr–N for 1a are lower than those in 2a because of a notable electronic delocalization for the 2-buten-1,4-dicarbonyl fragment (OC1–C@C–C4O). With respect to the CAr–N bond in series 1, the compounds with electron-withdrawing groups in the positions 1, 2 and 1, 4, excluding 1t and 1v, show a shorter bond length than for 1a. For 1t and 1v, the bond lengths are similar compared to 1a; therefore, these compounds could be excluded from this

comparison. In series 2, decreases were only observed in the bond lengths of the compounds 2d, 2e, 2g and 2v. In 2b, a second-order perturbation theory analysis of the Fock matrix in the NBO basis was performed, with the results showing that the nN ? p⁄CC interaction was 8.43 kcal/mol lower than for 1b, which explains the lower bond length in 1b in comparison with 2b. For 2t, the nN ? p⁄CC interaction was 19.82 kcal/mol lower than that of 2v; this energy difference mainly occurs because the 2t dihedral angle for the H–N–CAr1–CAr2 fragment is 57.35°, whereas in 2v the angle is 18.44°. In 2t, it is not possible to have a good interaction with the lone pair from the nitrogen atoms; therefore, the bond length is higher in this compound in comparison with 2v. Taking into consideration 1k and 1q, where an electron-donating group is presented, there is an elongation of the CAr–N bond in comparison with 1a. From the NBO analysis, in 1k the interaction nO ? p⁄CC was 28.56 kcal/mol and nN ? p⁄CC 8.06 kcal/mol, while in 1q nO ? p⁄CC was 30.54 kcal/mol and nN ? p⁄CC was 8.76 kcal/ mol. The difference of 1.98 kcal/mol in the nO ? p⁄CC interactions was mainly due to the methyl group, which is a more effective electron-donating group than a hydrogen atom. In the case of 1n, the nN ? p⁄CC interaction was 27.39 kcal/mol, due to the nitrogen atom of the NH2 group. However, in this compound, the CAr–N bond is shorter with respect to 1k and 1q because 1n shows a strong interaction nN ? p⁄CC of 15.74 kcal/mol. Therefore, even an oxygen atom is a better electron-donating group than a nitrogen atom in inhibitors of AChE and BChE, and it is preferable to have a NH2 group over an OH or OCH3 group. On the other hand, considering the succinimide (series 3) or maleimide (series 4) fragments in relation to the substituents on an aromatic ring, for the derivatives with a 1,4 relationship, the oxygen atoms are equivalent because of the presence of a symmetry plane (Fig. 3a). However, for the derivatives with 1,2 and 1,3

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J. Correa-Basurto et al. / Chemico-Biological Interactions 209 (2014) 1–13

Table 2 Bond lengths of CAr–N and N–CO (Å). Series

1

2

3

4

CAr–N

N–CO

CAr–N

N–CO

CAr–N

N–CO

CAr–N

N–CO

a b c

1.4163 1.4013 1.4133

1.3812 1.3911 1.3882

1.4128 1.4135 1.4200

1.3724 1.3837 1.3809

1.4378 1.4313 1.4321

1.4282 1.4055 1.4223

d

1.3909

1.3936

1.3966

1.3817

1.4239

e f

1.4118 1.4195

1.3869 1.3835

1.4121 1.4245

1.3777 1.3774

1.4340 1.4353

g

1.4061

1.3869

1.3972

1.3805

1.4309

h i

1.4139 1.4184

1.3833 1.3844

1.4200 1.4251

1.3741 1.3774

1.4355 1.4352

j

1.4113

1.3807

1.4234

1.3811

1.4298

k l

1.4271 1.4193

1.3742 1.3823

1.4264 1.4250

1.3705 1.3760

1.4367 1.4367

m

1.4216

1.3775

1.4099

1.3708

1.4429

n o

1.4092 1.4265

1.3849 1.3785

1.4276 1.4228

1.3692 1.3710

1.4372 1.4400

p

1.4330

1.3799

1.4331

1.3773

1.4421

q r

1.4268 1.4148

1.3742 1.3815

1.4389 1.4258

1.3694 1.3754

1.4369 1.4372

s

1.4085

1.3812

1.4239

1.3756

1.4301

t u

1.4196 1.4171

1.3804 1.3842

1.4291 1.4247

1.3749 1.3768

1.4360 1.4350

v

1.4154

1.3825

1.4086

1.3749

1.4264

1.4139 1.4200 1.4181s 1.4160ª 1.4143s 1.4116ª 1.4175 1.4154s 1.4141ª 1.4094s 1.4081ª 1.4157 1.4164s 1.4160ª 1.4116s 1.4116a 1.4128 1.4149s 1.4140ª 1.3948s 1.4283ª 1.4113 1.4126s 1.4140ª 1.3990s 1.4223ª 1.4127 1.4145s 1.4134ª 1.4101s 1.4079ª 1.4147 1.4162s 1.4160ª 1.4146s 1.4110ª

1.4119 1.4337 1.4161s 1.4145ª 1.4344s 1.4319a 1.4156 1.4134s 1.4126ª 1.4100s 1.4086a 1.4133 1.4142s 1.4139a 1.4116s 1.4105a 1.4170 1.4197s 1.4189ª 1.4000s 1.4320ª 1.4151 1.4116s 1.4121ª 1.3976s 1.4187ª 1.4170 1.4193s 1.4183ª 1.4148s 1.4135ª 1.4191 1.4211s 1.4209ª 1.4121s 1.4104ª

relationships, the oxygen atoms are asymmetric and experience different chemical environments. Thus, the oxygen atoms were labeled as Os and Oa as shown in Fig. 3b and c. In series 3 and 4, and particularly in those compounds with substituents in 1,2 and 1,3 relationships, the bond length in N–CO of the succinimidic or maleimidic fragments differs as described above, except in 3j. In this compound, the plane of the aromatic ring and the plane of the succinimidic ring are almost at 90°, having both oxygen atoms at the same bond length, from NBO analysis, the nN ? p⁄CC interaction is zero. The same interaction value is observed in compound 4j, where the dihedral angles of (Cl) C–C– N–CO fragments are 72° and 109°. With the exception of compounds 3m, 3o, 3p, 4m, 4o and 4p, it was observed that the N–COs bond is higher than the N–COa, which could be attributed to no-bonding repulsive through space interactions (steric effects). In the compounds 3m, 3p, 4m and 4p, the N–COs bond is shorter because of the formation of a hydro-

1.4034 1.4240 1.4260 1.4224 1.4256 1.4254 1.4212 1.4320 1.4315 1.4380 1.4330 1.4298 1.4327 1.4323 1.4320 1.4261 1.4309 1.4296 1.4191

gen bond. Table 3 lists the interatomic distances of COHR (R@O,N) and the values of the nO ? r⁄HR interaction. A sevenmembered ring is formed for the four compounds, in which 3m showed the highest interaction value and thus a shorter OH distance. Tables S1–S4 (Supplementary information) list the absolute electronegativity (v), the chemical hardness (g) and the global electrophilicity index (x) for each series. As is shown, there is not a linear correlation between the reactivity parameters and inhibitor activity. However, a comparison could be made between the compounds that are the most efficient and the least efficient inhibitors. Therefore, for AChE, the most efficient compounds were 1n, 2e, 3i and 4i, whereas for BChE, they were 1p, 2p, 3o and 4f. With respect to the worst inhibitor compounds, 1d, 2o, 3a and 4a were for AChE, and 1o, 2b, 3d and 4d were for BChE. Regarding AChE, for series 1 and 2, only the c value shows an inverse order, therefore, the presence of a double bond does not affect the order for g, l and x. However, between 1n and 2e, the latter showed

Table 3 Interatomic distances and nO ? r⁄HR interactions for 3m, 3p, 4m and 4p.

Fig. 3. Spatial conformation of the oxygen atoms in series 3 and 4.

a

Compound

Interatomic distance O–H (Å)

Interaction (kcal/mol) nO ? r⁄HRa

3m 3p 4m 4p

1.7563 2.0065 2.1062 2.0496

3.72 0.96 0.54 0.76

R = O,N.

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more negative values than the former; as a result, the presence of a double bond has an important effect on the values of these reactivity parameters. In series 3, v and g show an inverse order; nonetheless, the compound with the highest activity should have a negative v value of approximately 0.002. As in aliphatic systems, the presence of a double bond, specifically in 4i, has an important effect on the reactivity parameters, most importantly in the hardness values of the systems with double bonds. The hardness value is greater in systems with a double bond; furthermore, these systems are more efficient as cholinesterase inhibitors, according to their inhibition constant (Ki) values, with Ki = 0.17 in 4i versus Ki = 0.23 in 3i. On the other hand, for the BChE in series 1 and 2, all of the reactivity parameters showed an inverse order. As inhibitors of the BChE, the compounds of these series should be less hard than those for the AChE, whereas for series 3 and 4, the compounds should be harder.

Table 4 Significance of descriptors mentioned or used in this study. Descriptors

Type

Significance

LogP

Thermodynamic descriptor

Logarithm of the partition coefficient a Obtained using Hyperchem 7.0 [36]) b Obtained using Molinspiration methodology 7.0 [26]) Sum of chemical bonds between atoms Molecular shape kappa indices Molecular electrostatic potential Dipole moment Molecular connectivity indices Energy of the frontier molecular orbitals Energetic difference between orbitals Molecular volume Electrostatic potential

a

LogPH=

b

LogPM=

Wiener KAPPA-1-AM MEP

l CHI-1 EHOMO and ELUMO GAP VM ESP

Graph theoretical descriptor Topological descriptor Electronic descriptor Electronic descriptor Topological descriptor Quantum-chemical descriptor Quantum-chemical descriptor Topological descriptor Electronic descriptor

3.3. QSAR study Solomon et al. described a QSAR study of 53 compounds for AChE and 61 compounds for BChE, obtaining only one equation for each target [27]. Therefore, we decided to perform a QSAR study in three different ways: (1) considering 84 compounds for each target, similar to Solomon’s approach [27]; (2) considering 42 compounds for series 1–2, and 42 for series 3–4, and finally; (3) considering each series independently (21 compounds each) for each target. N-aryl derivatives 1a, 2a, 3a, and 4a were used in order to evaluate the obtained equations. The parameters considered in our study, with the exception of logP and dipole moment (l), are different from those considered in Solomon’s study [27]. The quantum chemical parameters taken into consideration for this study for each series are as follows: energy of the frontier molecular orbitals (EHOMO and ELUMO), energetic difference between orbitals (GAP), l, molecular volume (VM), electrostatic potential (ESP) and molecular electrostatic potential (MEP) that considered the steric effects [26]. This last parameter was taken from the literature in which it was obtained using the Suresh methodology [65]. The atomic charge for the nitrogen atom was obtained by employing the Mulliken population analysis (CAMLK) and the Merz–Singh–Kollman population analysis (CAESP) (data not shown). Two population analyses were considered because the Mulliken analysis is sensitive to the basis set. The partition coefficient values logPH, the molar refractivity (MR) and the polarizability (a) were obtained from the software Hyperchem 7.0 [36], whereas the logPM values were taken from the work of Correa-Basurto et al. in which the Molinspiration methodology was employed [26]. The subscript of log P is referring to the software employed to obtain this value. The physical, chemical or physiochemical significance of each of the descriptors appearing in the QSAR equations or mentioned along this contribution are given in Table 4. In addition, the lengths of the CAr–N and N–CO bonds were considered. As mentioned above, regarding the N–CO bonds for series 3 and 4, N–COs and N–COa were taken into account. Finally, the reactivity parameters of v, g and x were considered in this analysis. Conversely, because there are two logP (H or M) and CA (MLK or ESP) parameters, the MLR was performed by making a combination of the four parameters to avoid repetitions in the runs on the same parameter. 3.3.1. QSAR for the AChE The determination coefficient (R2), the adjusted determination coefficient (R2ajus) and the standard deviation (SD) were the statistical parameters obtained in each equation. The variables were entered into a regression equation through t-values of coefficients

(threshold value P2), and the Fisher criterion (F) was considered to be the parameter that best reflected the fit of the equation. For the AChE target, when n = 84, the equation was as follows: log Ki = 3.5784–0.5710 logPH + 0.1902 MR  0.5912 a + 0.5579 CAESP  2.7438 MEP R2 = 0.3025, R2adj = 0.2578, SD = 0.4311, F = 6.8, q2cv = 0.1052, 2 qlmo = 0.3306, r2mðtestÞ = 0.2412. The inclusion of 84 compounds did not provide a fitted correlation in comparison with the results described by Solomon et al. [27], furthermore, the r2mðtestÞ value was low at 0.5, hence, performing a QSAR study is not recommended for this target and with these molecular parameters. Taking into account series 1–2, with n = 42, the equation was as follows: log Ki = 2.2544–0.00969 VM + 0.1048 MR  0.2579 a  24.9687

g R2 = 0.2382, R2adj = 0.1558, SD = 0.3882, F = 2.9, q2cv = 0.3025, q2lmo = 0.3546, r 2mðtestÞ = 0.1689. For series 3–4 with n = 42, the equation obtained was as follows: log Ki = 11.0465 + 12.7373 GAP  1.4596 logPH + 0.4356 MR  1.2790 a + 12.4017 CAMLK  5.8635 MEP R2 = 0.8106, R2adj = 0.7781, SD = 0.2666, F = 25.0, q2cv = 0.8106, 2 qlmo = 0.8731, r 2mðtestÞ = 0.8066. For n = 42, series 3–4 gave a better fit in comparison to series 1– 2, giving a r 2mðtestÞ >0.5. Thus, when n = 42 was employed, the statistical values dropped because of the low correlation observed in series 1–2. Thus, it is necessary to treat each series individually. The equations obtained for the four series, n = 21, are as follows: Series 1: log Ki = 125.6397–0.00707 VM + 0.3168 logPM + 0.1624 MR  0.4763 a  10.1741 CAMLK + 1.7706 MEP  27.9435 CAr– N  63.1731 N–CO R2 = 0.7327, R2adj = 0.5544, SD = 0.1677, F = 4.1, q2cv = 0.7327, 2 qlmo = 0.8698, r 2mðtestÞ = 0.7046. Series 2: log Ki = 0.5497–0.0178 VM + 0.4336 MR  1.0032 a  7.5257 MEP + 22.5256 v R2 = 0.4909, R2adj = 0.3212, SD = 0.4532, F = 2.8, q2cv = 0.4909, 2 qlmo = 0. 5704, r2mðtestÞ = 0.4418. Series 3: log Ki = 4.4128–14.0321 EHOMO  1.5212 logPH + 0.4101 MR  1.1650 a  6.45775 MEP R2 = 0.7629, R2adj = 0.6839, SD = 0.3095, F = 9.7, q2cv = 0.7629, 2 qlmo = 0.8211, r 2mðtestÞ = 0.7516. Series 4:

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log Ki = 946.0467–25.1090 ELUMO + 0.0065 VM  2.2561 logPH  0.3313 l + 67.4759 CAMLK + 46.8473 ESP  3.5601 MEP + 98.9023 g + 109.1875 x  32.0204 CAr–N R2 = 0.9672, R2adj = 0.9343, SD = 0.1523, F = 29.5, q2cv = 0.9672, q2lmo = 0.9124, r2mðtestÞ = 0.9660. Except for series 2, all runs gave r 2mðtestÞ >0.5, with series 1 showing a less rigorous fit in comparison to series 3 and 4; however, the correlation was better than when series 1 and 2 were considered with n = 42. Frontier orbital energies are important parameters in series 3 and 4. These energies could arise from the higher electronic delocalization in these series in comparison with series 1 or 2. Fig. 4 shows the graphics for each series, considering n = 21. Tables S5-S11 (Supplementary information) are listed the residual values for the equations considering n = 21, 42, and 84. 3.3.2. QSAR for the BChE For the BchE target, considering series 1–4 (n = 84), the equation was as follows: log Ki = 16.8092 + 0.2376 logPM + 0.6555 CAESP + 13.2110 N– COs R2 = 0.5820, R2adj = 0.5663, SD = 0.3623, F = 37.1, q2cv = 0.8041, 2 qlmo = 0.7953, r2mðtestÞ = 0.5103. For series 1–2 (n = 42), the equation was as follows: log Ki = 1.2936–0.1027 l R2 = 0.1293, R2adj = 0.1075, SD = 0.3824, F = 5.9, q2cv = 0.1293, q2lmo = 0.4342, r2mðtestÞ = 0.0947. In contrast, considering series 3–4 (n = 42), we obtain the following: log Ki = 29.4515 + 0.2378 logPM  0.1555 MR + 0.3499 a + 1.7315 CAESP  37.5771 CAr–N + 19.4543 N–COa R2 = 0.6643, R2adj = 0.6067, SD = 0.2262, F = 11.5, q2cv = 0.6643, q2lmo = 0.7811, r2mðtestÞ = 0.5963.

The BChE target with n = 84 showed better correlation than the AChE target. With regard to series 1–2, with n = 42, exhibited lower correlation than series 3–4. Therefore, in the BchE target, the four series were treated separately. Thus, the equations obtained for the four series with n = 21 are as follows: Series 1: log Ki = 540.6671–42.1316 EHOMO  109.0587 GAP  1.4862 log PH  0.3606 MR + 0.8822 a + 29.2523 ESP  7.4362 MEP + 276.8690 x R2 = 0.6721, R2adj = 0.4535, SD = 0.3856, F = 3.1, q2cv = 0.6721, q2lmo = 0.6413, r 2mðtestÞ = 0.6363. Series 2: log Ki = 32.1053–1.5026E16 ELUMO  9.8053E15 GAP + 0.4144 log PH + 0.09278 MR  0.2477 a  3.1684 MEP  1.5026E16 v + 3.4637E16 g  23.3933 N–CO R2 = 0.8976, R2adj = 0.8139, SD = 0.0987, F = 10.7, q2cv = 0.3924, 2 qlmo = 0.6601, r2mðtestÞ = 0.8908. Series 3: log Ki = 136.2426 + 22.4931 EHOMO + 0.10824 l + 0.5419 logPM  0.3315 MR + 0.7385 a + 2.3136 MEP + 43.5035 g  63.1832 CAr– N  29.9552 N–COs R2 = 0.8826, R2adj = 0.7865, SD = 0.1549, F = 9.2, q2cv = 0.8826, q2lmo = 0.6928, r 2mðtestÞ = 0.8730. Series 4: log Ki = -1036.9626 + 0.1249 l + 0.5614 logPM  0.0747 MR  52.1824 ESP  17.1103 CAr–N + 19.4185 N–COs + 58.4455 N–COa R2 = 0.8623, R2adj = 0.7882, SD = 0.1798, F = 11.6, q2cv = 0.8623, q2lmo = 0.8229, r 2mðtestÞ = 0.8492. For this target, series 2 and 3 provided a better correlation than the AChE target, whereas series 1 and 4 obtained a good fit but with lower statistical values compared to the AChE target.

Fig. 4. Plots of docking versus predicted log Kiexp vs log Kicalc for AChE: (a) series 1, (b) series 2, (c) series 3, and (d) series 4.

J. Correa-Basurto et al. / Chemico-Biological Interactions 209 (2014) 1–13

9

Fig. 5. Plots of docking versus predicted log Kiexp vs log Kicalc for BChE: (a) series 1, (b) series 2, (c) series 3, and (d) series 4.

Furthermore, in the BChE target, it was observed that the HOMO and LUMO energies were considered in series 1 to 3. CorreaBasurto et al. [26] reported that the frontier orbital energies play an important role in ligand recognition at the bottom of both ChE gorges, which was observed when these parameters were present in the equation, except for series 1 in the AChE target. Fig. 5 shows the graphics for each series with n = 21. Tables S12–S18 (Supplementary information) are listed the residual values for the equations considering n = 21, 42, and 84. In order to carry out the validation of obtained equations, firstly, compounds 1a to 4a were employed as independent data set. Log Ki experimental values in AChE for compounds 1a, 2a, 3a, and 4a were 1.19, 0.75, 1.47, and 1.47, respectively; whereas in BChE were 1.13, 1.02, 2.06, and 2.09, respectively [26]. In Table 5 is listed the log Kiexp vs log Kicalc value for AchE and BChE using only equations with r 2mðtestÞ >0.5. As it can be observed, residual values gave low va-

Table 5 Log Kicalc and residual values for AChE and BChE, using the independent data set. Equation Series

log Kicalc 1a

Res

2a

Res

3a

AchE 34 1 3 4

1.18 1.12 0.98 4.10

0.01 0.07 0.21 2.91

1.49 1.99 0.99 4.49

0.74 1.24 0.24 3.74

1.14 – 1.03 3.83

BchE 1234 34 1 3 4

0.92 – 1.04 3.87 –

0.21

0.76 – – 4.17 –

0.26

1.71 1.68 – 1.68 1.45

0.09 2.74

3.15

Res 0.33 0.44 2.36 0.35 0.38 0.38 0.61

4a

Res

1.14 – 1.05 1.33

0.33

1.60 1.55 – 2.43 1.72

0.49 0.54

0.42 0.14

0.34 0.37

lue in almost all series, excepting in series 1 for compounds 3a and 4a, and in series 4 for compounds 1a, 2a and 3a, giving a low value for 4a. Thus, the equation seems to be specific according to the structure of the evaluated compound; that means, series 1 fits better for compound 1a, series 3 or 4 fits better for compounds 3a or 4a. Same behavior is observed in the BChE. Therefore, obtained equations in this QSAR study could be employed to calculate the Ki value for compounds having a similar structure as N-aryl described here. On the other hand, the galanthamine (G) and donepezil (D) molecules studied in this work are displayed in Fig. 6. For the G-1–G-8 and D-1–D-2 stereoisomers, the geometries were fully optimized at B3LYP levels using the 6-311G(d,p) basis set. Several molecular properties derived from the principle of maximum hardness [56] were applied to the G–G-8 and D-1–D-2 stereoisomers in order to discuss their reactivity. The ionization potential, electron affinities, electronegativity, global hardness and electrophilicity index for the G1–G-8 and D-1–D-2 stereoisomers are given in Table 6. The G1/G8 and G4/G5 galanthamine stereoisomers show similar values of the properties calculated in this work. It should be noted that the eight stereoisomers of the galanthamine showed an ionization potential between 7.111 and 7.276 eV (the difference between the largest and smallest data is 0.165 eV = 3.8 kcal/mol); and considering D-1–D-2, the difference with the G-6 stereoisomer is 0.176 eV = 4.1 kcal/mol. Moreover, the eight stereoisomers of galanthamine showed electron affinities between 1.039 and 0.901 eV (the difference between the largest and smallest data is 0.138 eV = 3.2 kcal/mol), and considering D-1–D-2, the difference with respect to the G-2 stereoisomer is 0.096 eV = 23.0 kcal/mol. The stereoisomer with the lowest ionization potential is G-6, whereas G-2 has the greatest negative electron affinity and hardness. In addition, G-3 and D-1/D-2 show the highest electronegativity and electrophilicity index. According to the IP, EA, v and g of G-2, G-3 and G-6 are

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Fig. 6. a) Galanthamine molecule (b) donepezil molecule (c) eight stereoisomers of galanthamine studied in this work, fully optimized at B3LYP/6-311G(d,p) level of theory. Relative configuration of stereoisomers: G-1 (4aS,6S,8aR), G-2 (4aS,6R,8aR), G-3 (4aS,6S,8aS), G-4 (4aS,6R,8aS), G-5 (4aR,6S,8aR), G-6 (4aR,6R,8aR), G-7 (4aR,6S,8aS), G-8 (4aR,6R,8aS). (d) Two stereoisomers of donepezil, fully optimized at B3LYP/6-311G(d,p) level of theory. Relative configuration of stereoisomers: D-1 (2S), D-2 (2R).

more reactive. Furthermore, the donepezil stereoisomers D-1/D-2 show no difference in their reactive properties because one stereoisomer has a relative R configuration and the other has a relative S configuration. The most remarkable feature of these R and S enantiomers is that they have the same molecular shape except for small portions of the indanone and piperidine rings (Fig. 6d). These two conformers also have almost equal electronic energy, as computed by B3LYP/6-311G(d,p). To determine whether there was a relationship between the reactivity of the galanthamine and donepezil stereoisomers and the movements of the protein, the interactions of each of these molecules were analyzed using different AChE conformers obtained through MD simulations. Fig. 7a and h show that, although Table 6 Vertical ionization potential (IP), electron affinities (EA), electronegativity (v), global hardness (g) and electrophilicity index (x) in eV, for stereoisomers under study, at B3LYP/6-311G(d,p) level of theory of galanthamine (G) and donepezil (D). Stereoisomers

IP

EA

v

g

x

G-1 G-2 G-3 G-4 G-5 G-6 G-7 G-8 D-1 D-2

7.275 7.270 7.264 7.202 7.202 7.111 7.276 7.275 7.287 7.287

0.971 1.039 0.901 1.038 1.038 1.028 1.038 0.971 0.043 0.043

3.152 3.115 3.181 3.082 3.082 3.041 3.119 3.152 3.622 3.622

4.123 4.155 4.082 4.120 4.120 4.069 4.157 4.123 3.665 3.665

1.205 1.168 1.240 1.153 1.153 1.137 1.170 1.205 1.790 1.790

the G-1 and G-8 stereoisomers exhibit similar properties, they are recognized in different manners; while G-1 did not change its binding mode, G-8 shows different binding modes, mostly at 10 ns. However, the G-5 and G-5 stereoisomers have similar properties and similar binding modes. The stereoisomer G-6 (Fig. 7f), which has the lowest ionization potential, was recognized in the similar form to that of G-4 and G-5. Despite the fact that G-2 has more negative electron affinity and the greatest hardness, it was recognized in the similar form to that of G-4–G-6. Despite the fact that the electronic properties between the stereoisomers are different, these differences have little apparent influence because the stereoisomers are recognized in the similar form. The galanthamine stereoisomer that is employed as a drug to treat Alzheimer’s disease is G-4, which is recognized in the similar form to that of G5 and G-6; however, G-2, G-3 and G-8 are stereoisomers that exhibit greater difference and different interactions, possibly because G-3 is the most reactive stereoisomer, as mentioned above. On the other hand, donepezil stereoisomers were recognized in the similar form shown in (Fig. 7i–j) which is interesting because this drug is employed as a racemate of the R and S stereoisomers. The EHOMO and ELUMO energies and EHOMO–ELUMO gaps are provided in Table 7. The maximum hardness principle asserts that systems tend to be as hard as possible; thus, a hard molecule has a large energy gap. A larger value of g indicates a larger IP and smaller EA, which implies that the system has a lower tendency to accept and donate particles, meaning that the system is stable. The results indicate that there are no significant differences in hardness between the various galanthamine stereoisomers (0.088 eV = 2.1

J. Correa-Basurto et al. / Chemico-Biological Interactions 209 (2014) 1–13

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Fig. 7. Stereoisomers of galanthamine and donepezil binding to conformers of AChE. (a) G-1, (b) G-2, (c) G-3, (d) G-4, (e) G-5, (f) G-6, (g) G-7, (h) G-8, (i) D-1 and (j) D-2. Red (2 ns), green (4 ns), blue (6 ns), yellow (8 ns) and magenta (10 ns). Amino acid residues His443 and Ser203 are orange colored. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 7 EHOMO and ELUMO, ELUMO–EHOMO energy (GAP) in eV, for G-1–G-8 and D-1–D-2 stereoisomers, at B3LYP/6-311G(d,p) level of theory of galanthamine (G) and donepezil (D). Stereoisomers

EHOMO

ELUMO

GAP

G-1 G-2 G-3 G-4 G-5 G-6 G-7 G-8 D-1 D-2

5.63 5.64 5.68 5.64 5.64 5.55 5.64 5.63 5.86 5.86

0.51 0.46 0.59 0.47 0.47 0.46 0.47 0.51 1.54 1.54

5.12 5.18 5.09 5.17 5.17 5.09 5.18 5.12 4.31 4.31

kcal/mol between the largest and smallest data), which means that the reactivities of G-1–G-8 are similar. The calculated absolute electronegativity (v) can be correlated to the reactivity because a lower electronegativity reflects a greater tendency to lose electrons, as observed for stereoisomer G-6. Furthermore, De Vleeschouwer et al. [66] suggested that a small x-value indicates that the radical can be designated as nucleophilic. Therefore, the data for stereoisomer G-6 suggest that it is more electrophilic. The gaps of the donepezil stereoisomers are equivalent.

4. Conclusions In this study, we have explored a set of 84 N-aryl compounds under a QSAR study using quantum parameters and molecular descriptors. Multiple linear regression methodologies were employed to perform this study, considering n = 21, 42 and 84. This study is the first to report a correlation of this quality. QSAR shows that the bond lengths of CAr–N and N–CO bonds, molecular electrostatic potential, and the frontier orbital energies play an important role for ChEs recognition. Regarding evaluation carried out with four compounds, it was observed that the equations seems to be specific according to the structure of the evaluated compound in AChE and BChE. Therefore, obtained equations in this QSAR study could be employed to calculate the Ki value for compounds having a similar structure as N-aryl described here. In addition, it has been theoretically determined that the chemical parameters indicate the reactive behavior of the stereoisomers of galanthamine and donepezil. The G-6 stereoisomer could easily form a positive ion, while G-2 could form a negative ion, and G-3 can easily attract electrons. The hardest stereoisomer is G-2. The donepezil molecule showed a higher ionization potential, electronegativity and electrophilicity index, and a smaller electron affinity and hardness compared to the galanthamine stereoisomers.

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