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A DFT and QSAR Study of Several Sulfonamide Derivatives in Gas and Solvent
A DFT and QSAR Study of Several Sulfonamide Derivatives in Gas and Solvent
Journal of the Korean Chemical Society. 2016. Aug, 60(4): 225-234
Copyright © 2016, Korean Chemical Society
  • Received : January 15, 2016
  • Accepted : June 02, 2016
  • Published : August 20, 2016
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About the Authors
Robabeh Sayyadi kord Abadi
Department of Chemistry, Rasht Branch, Islamic Azad University, P.O. Box 41335-3516, Rasht, Iran.
Asghar Alizadehdakhel
Department of Chemical Engineering, Islamic Azad University, Rasht Branch, P.O. Box 41335-3516, Rasht, Iran.
Soghra Tajadodi Paskiabei
Department of Chemistry, Rasht Branch, Islamic Azad University, P.O. Box 41335-3516, Rasht, Iran.

Abstract
The activity of 34 sulfonamide derivatives has been estimated by means of multiple linear regression (MLR), artificial neural network (ANN), simulated annealing (SA) and genetic algorithm (GA) techniques. These models were also utilized to select the most efficient subsets of descriptors in a cross-validation procedure for non-linear -log (IC50) prediction. The results obtained using GA-ANN were compared with MLR-MLR, MLR-ANN, SA-ANN and GA-ANN approaches. A high predictive ability was observed for the MLR-MLR, MLR-ANN, SA-ANN and MLR-GA models, with root mean sum square errors (RMSE) of 0.3958, 0.1006, 0.0359, 0.0326 and 0.0282 in gas phase and 0.2871, 0.0475, 0.0268, 0.0376 and 0.0097 in solvent, respectively (N=34). The results obtained using the GA-ANN method indicated that the activity of derivatives of sulfonamides depends on different parameters including DP03, BID, AAC, RDF035v, JGI9, TIE, R7e+, BELM6 descriptors in gas phase and Mor 32u, ESpm03d, RDF070v, ATS8m, MATS2e and R4p, L1u and R3m in solvent. In conclusion, the comparison of the quality of the ANN with different MLR models showed that ANN has a better predictive ability.
Keywords
INTRODUCTION
The sulfonamide group is considered as a pharmacopoeia which is present in a number of biologically active molecules, particularly in antimicrobial agents. 15 It is also present in inhibitors of carbonic anhydrase, 610 anticancer 11 and anti-inflammatory agents, 12 which are derivatives of sulfonamides.
Most diseases that involve G-protein receptors in the central nervous system cause abnormal behavior, due to drug addiction to sulfonamides. Recent studies have shown that in regulating other receptors that interact with drug and other substance abuse, the opioid receptors play an important role. 1316
One of the most important aspects in chemometrics that provide important information useful for molecular design and medicinal chemistry is the Quantitative structure activity relationship (QSAR). 1719 QSAR models are mathematical equations that create a relationship between chemical structures and biological activities. The first step in the QSAR study is to find a set of descriptors with higher impact on biological activity. 2023 In QSAR models, a wide range of descriptors are used, which can be constitutional, geometrical etc.
Several QSAR studies 26,27 have been carried out involving the use of an effective computational method to examine the inhibition mechanism.
In the present study, the multiple linear regressions (MLR) as linear models, and artificial neural networks (ANN), simulated annealing (SA) and genetic algorithm (GA) 2125 as non-linear models were applied to investigate the QSAR in sulfonamide derivatives. Various QSAR models have been used to select the best descriptors for the important prediction of inhibitory activity of sulfonamide compounds, and then these models were compared.
THEORY AND COMPUTATIONAL METHODS
- General methods
The geometric optimizations of sulfonamide compounds were carried out using Gaussian 03W at B3lyp/6-31g. 28 Polarized continuum model (PCM) was applied to consider the non-specific solvent effect, and all molecules were optimized in H 2 O solvent.
3226 molecular descriptors in topological, geometrical, MoRSE, 30,31 RDF, 31,32 GETAWAY, 33,23 auto-correlations 34 and WHIM 35, 36 groups were calculated using the Dragon program. 29 In three steps, the number of descriptors was reduced through an objective feature selection.
At first, in the dataset of sulfonamide compounds, the descriptors that had the same value of at least 70% were removed. and thereafter, the descriptors with correlation coefficient less than 0.25 with the dependent variable (-log IC50) were considered redundant and removed. 37 After these two steps, the number of descriptors was reduced to 1047 in the gas phase and 1110 in the solvent phase. Stepwise multiple linear regression procedure was used for rejection of descriptors. The QSAR method with high correlation coefficient (R), low standard deviation, least numbers of independent variables, high ability to predict and high F statistic value is an ideal method. 38
The best subset of descriptors selected in (MLR) was fed into neural networks in the MLR-ANN method. The neural networks used in this study were all three-layer feed-forward network. The networks were trained using the TSET members with Levenberg-Marquart algorithm. 39 In SA-ANN and GA-ANN methods, 1047 and 1110 descriptors in the gas and solvent phase were considered as possible input of the ANN and fed into the input layer of the ANNs in GA-ANN and SA-ANN models ( . 1 ). All calculations in the present study were done in Matlab environment (V 7.12, The Mathworks,Inc), SA, GA and Neural Fitting toolbox.
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The employed procedure for finding optimum descriptors of the ANN models.
The mean square error of all the models was calculated using the following equation:
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where yi is the desired output, yo is the predicted value by model, and n is the number of molecules in this study’s data set.
RESULTS AND DISCUSSION
Thirty four different sulfonamide derivatives were selected as a sample set, and the geometry of the compounds was optimized using Gaussian 09W at B3LYP/6-31 g. All the optimized Sulfonamide compounds are shown in . 2 .
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Optimized structure of the compounds used to build QSAR models with B3lyp/6-31g in gas phase.
Linear and non-linear feature selection methods, such as MLR-MLR (stepwise-MLR), MLR-ANN, SA-ANN, MLR-GA and GA-ANN, were used to select the most significant descriptor.
SPSS 40 software was used for stepwise MLR models as shown in 10 . The RMSE in MLR-MLR for predicted activity was found to be 0.39576 in gas phase and 0.2871 in solvent phase. Also, the correlation coefficient (R 2 ) calculated for the PSET was 0.8226 in gas phase and 0.90671 in solvent phase.
10 shows that MLR-MLR method is better than other linear methods (MLR-PLS1 and MLR-PCR). The definition of the descriptors in the MLR-MLR method is shown in 1 .
The best selected descriptors using MLR-MLR method in gas phase
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The best selected descriptors using MLR-MLR method in gas phase
The descriptors, which were selected using the MLR-MLR model were fed into the neural networks to establish the MLR-ANN model. In this model, the RMSE for predicted activity and TSET compounds were found to be 0.1006, 0.0475 and 0.1162, 0.0458 in gas and solvent phase, respectively ( 9 ).
To establish the SA-ANN, MLR-GA and GA-ANN models, the 1047 and 1110 descriptors in gas and solvent phase were fed into the neural network to select the best descriptors, also 3 neurons in the hidden layer of the GA-ANN model were used in this study ( . 1 ).
The descriptors, which were selected using the QSAR models are shown in 1 - 8 . These parameters relate the structure to the activity of the optimized compounds.
The best selected descriptors using MLR-MLR method in solvent phase
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The best selected descriptors using MLR-MLR method in solvent phase
The best selected descriptors using SA-ANN method in gas phase
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The best selected descriptors using SA-ANN method in gas phase
The best selected descriptors using SA-ANN method in solvent phase
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The best selected descriptors using SA-ANN method in solvent phase
The best selected descriptors using MLR-GA method in gas phase
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The best selected descriptors using MLR-GA method in gas phase
The best selected descriptors using MLR-GA method in solvent phase
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The best selected descriptors using MLR-GA method in solvent phase
The best selected descriptors using GA-ANN method in gas phase
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The best selected descriptors using GA-ANN method in gas phase
The best selected descriptors using GA-ANN method in solvent phase
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The best selected descriptors using GA-ANN method in solvent phase
MATS5e and GATS2p ( 1 and 2 ), GATS3e and ATS4v ( 4 ), ATS8m, and MATS2e ( 8 ) are 2D autocorrelation descriptors. The 2D-autocorrelation descriptors explain how the values of certain functions, at intervals equal to the lag, are correlated. 41
EEig0 ( 1 ), EEig13d ( 2 and 5 ) and ESPm03d ( 8 ) are Edge adjacency indices. The Edge adjacency relationships in molecular graphs have been used to define a new topographic index. 41
RDF 130p, RDF 115v, RDF095v, RDF035v, RDF070v, and RDF 115p ( 1 , 2 , 5 , 7 , 8 , and 6 ) are RDF descriptors. The radial distribution function (RDF) descriptors are based on the distance distribution in the molecule. 42
IC5 ( 2 ) and IC0 ( 5 ), and AAC ( 7 ) are information indices. The total information content (I) is obtained by multiplying the mean information content by the number of elements: 43
G1s and G1v ( 1 ), L1m ( 3 ), KM ( 6 ), L1u ( 6 ), and TP ( 5 ) are WHIM descriptors. WHIM descriptors are built in such a way to capture the relevant molecular 3D information regarding molecular size, shape, symmetry and atom distribution with respect to invariant reference frames. 31
R4e+ and R5p+ ( 1 ), R7u+ ( 2 ) and H6v, RTe, R6u+ ( 3 ), H5m ( 4 ), R7e+ ( 7 ) and R4p, R3m ( 8 ) are GETAWAY descriptors. GETAWAY (Geometry, Topology, and Atom-Weights Assembly) descriptors encode the geometrical information obtained from the molecular matrix, the topological information obtained from the molecular graph and the information obtained from atomic weights, which are specially designed with the aim of matching the 3D-molecular geometry. 31
Mor08u, Mor17v, Mor23e ( 2 ) and Mor02v, Mor17u ( 4 ) and Mor 17e ( 5 ), and Mor 32u ( 8 ) are 3D-MoRSE descriptors. The 3D-MoRSE descriptors were obtained through the molecular transformation employed in electron diffraction studies. 43
GGI6 ( 3 ), JGI9 ( 7 ) are topology charge indices. The Topological Charge Indices were proposed to evaluate the charge transfer between pairs of atoms and therefore, the global charge transfer in the molecule. 31
MPC05 ( 3 ), MWC03 ( 6 ), BID ( 7 ) are walk and path count. The molecular walk count of kth order (MWCk) is the total number of walks of the kth length in the hydrogen suppressed molecular graph. 31
F06[C-C] ( 6 ) and F09[C-O] are 2D frequency fingerprints descriptors. Fragment descriptors are representations of local atomic environments. 31
BEHm6 ( 3 ), Belem ( 4 ), BEHp6 ( 6 ), and BELm6 are Burden eigenvalue descriptors. The B matrix has been defined as the number of atoms, bond order between two atoms or the electronegativity of the atoms. 31
VED2 ( 4 ), Eig1m ( 5 ), and Adige ( 6 ) are eigenvalue based indices descriptors. The Eigenvalue Sum Descriptors are computed from Weighted Distance Matrices of a Hydrogen-depleted Molecular Graph.
QYYM ( 5 ) and DP03 ( 7 ) are geometrical and Rancid molecular profiles. The Rancid molecular profile DP k is derived from the distance distribution moments of the geometric matrix G as the average row sum of its entries raised to the k th power and normalized by the factor k!. 31
The geometrical variables incorporate information about the magnitude of the displacement between the molecular centroid (center of mass) and the polarizability-field (center of charge). 4
SOK, TI2 ( 6 ), J ( 5 ) and TIE ( 7 ) are topological descriptors. Topological index mathematically encode information regarding the structure of molecules, which have been depicted as graphs and are often sensitive to size, shape, branching, cyclicity and, to a certain extent, the electronic characteristics of molecules. 31
The statistical parameters of all QSAR models are shown in 9 and 10 . In train, a computation of 80% sulfonamid compounds is used. In the GA-ANN model, the RMSE and R-square were calculated as 0.0282 and 0.9716 in gas phase and 0.0097 and 0.9894 in the solvent phase, respectively, therefore, GA-ANN model was better than the other models and as such, only the descriptors used in this model were evaluated in this study. These descriptors are shown in 7 and 8 . The observed and predicted values of - logIC50 using Matlab program are shown in 11 and 12 . The plot showing the variation of observed versus predicted -logIC50 values are shown in . 3 and 4 .
Statistical parameters of different nonlinear QSAR models
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Statistical parameters of different nonlinear QSAR models
Statistical parameters of different linear QSAR models in gas and solvent phase
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Statistical parameters of different linear QSAR models in gas and solvent phase
Observed and predicted values of -logIC50 by using GA- ANN in gas phase
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Observed and predicted values of -logIC50 by using GA- ANN in gas phase
Observed and predicted values of –logIC50 by using GA-ANN in solvate phase
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Observed and predicted values of –logIC50 by using GA-ANN in solvate phase
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Plot between observed vs predicted -log (/IC50) by using GA-ANN descriptors in gas phase.
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Plot between observed vs predicted -log (IC50) by using GA-ANN descriptors in solvate phas.
The plots of the DP03, BID, AAC, RDF035v, JGI9, TIE, R7e+, and BELm6 descriptors ( . 5 ) in the gas phase and Mor 32u, ESPm03d, RDF070v, ATS8m and MATS2e, R4p, L1u, and R3m descriptors in solvent phase ( . 6 ) versus the experimental negative logarithm half maximal inhibitory concentration (-logIC50) values were plotted using Excel program. The descriptors values in GA-ANN method in gas and solvent phase were normalized using the equation (2) in Excel program.
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Plot between -log IC50 experimental versus the DP03, BID, AAC, RDF035v, JGI9, TIE, R7e+, and BELm6 normalized descriptors in the gas phase.
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Plot between experimental -log IC50 value versus the Mor32u, ESpm03d, RDF070v, ATS8m, MATS2e, R4p, L1u, and R3m normalized descriptors in the solvent phase.
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The charts in gas phase show that the experimental negative logarithm half maximal inhibitory concentration (-logIC50) value increases with increasing DP03 (Molecular profile no.3), BID (Balaban ID number), R7e+ (weighted by atomic Sanderson electronegativities), and BElm6 (Weighted by atomic masses) descriptors. Thus the half maximal inhibitory concentration (IC50) value is reduced. Therefore, the aforementioned descriptors are the best among the eight descriptors in the gas phase. As the RDF035v (weighted by atomic polarizabilities) descriptor increased, the experimental negative logarithm half maximal inhibitory concentration (-logIC50) value decreased. In JGI9 (topological charge index) descriptor of about 0.8, response do not change. But between 0.8-1 values, an increased experimental negative logarithm half maximal inhibitory concentration rate is shown in the bar chart. As the TIE (E-state topological parameter) descriptor increased up to 0.4, the experimental negative logarithm half maximal inhibitory concentration (-log IC50) value increased and then, the increased TIE (that are sensitive to size, shape, and the electronic characteristics of molecules) descriptor decreased the experimental negative logarithm half maximal inhibitory concentration value. Charts in solvent show that as Mor 32u (indicates that the size of the inhibitor molecule has certain effect on the extent of the interaction between the drug and molecule), RDF070v (weighted by atomic van der waals volumes), R4p (weighted by atomic polarizabilities), L1u (size direction index), and R3m (weighted by atomic masses) descriptors are increased, the experimental negative logarithm half maximal inhibitory concentration (-logIC50) value is reduced. However, with an increase in ATS8m (Broto-Moreau autocorrelation of a topological structure), the amount of experimental negative logarithm half maximal inhibitory concentration is first increased and then reduced, and finally a sharp increase is achieved. In increased ESPm03d (Spectral momen 03 edge adj. matrix weighted by dipole moments), a constant process experimental negative logarithm half maximal inhibitory concentration (-logIC50) is seen, and then subsequently increased. MATS2e (weighted by atomic Sanderson electronegativities) descriptor, which increased the amount of 0.8 changes in the experimental negative logarithm half maximal inhibitory concentration (-logIC50), cannot be seen. But from 0.8 to 1, an increase probe was seen in the experimental negative logarithm half maximal inhibitory concentration (-log IC50) value.
Selected descriptors that are common between all the QSAR methods are shown in 14 . The GETAWAY descriptors played an important role in predicting the -log-IC50 of Sulfonamide compounds. The plots of the GET-AWAY descriptors versus the experimental negative logarithm half maximal inhibitory concentration (-logIC50) values were plotted using Excel program.
Physico-chemical descriptors in GA-ANN method in gas and solvent phase
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Physico-chemical descriptors in GA-ANN method in gas and solvent phase
The common selected descriptors using QSAR methods
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The common selected descriptors using QSAR methods
. 7 shows that the -logIC50 value increase with increasing R5p, R7u+, H5m, R7e+ descriptors. As the R3m descriptor increased the –log IC50 value decreased.
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Plot between GETAWAY descriptors versus -log (IC50).
However, with an increased in RTe and R6u+ descriptors the amount of -logIC50 is first increased and then reduced ( Fig. 7 ). In R4p descriptor the amount of -logIC50 is first decreased and then increased. In increased R4e+, a constant process -logIC50 is seen. R5p, H5m, R7e+, RTe, R4p, R3m are physico-chemical descriptors and These are polarizability, weighted by atomic masses and sanderson electronegativities.
13 shows physico-chemical descriptors in GA-ANN method in gas and solvent phase.the physico-chemical descriptors were found to have an important role in change in activity ( . 5 , 6 ). These descriptors reduce the half maximal inhibitory concentration (IC50).
Statistical parameter and QSAR model of the sulfonamide compounds from the previous literatures are presented on the 15 . 4548 It shows that the results of GA-ANN method in this work ( 9 ) is better than the other QSAR models in previous studies.
Statistical parameter and QSAR model from the previous literatures
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Statistical parameter and QSAR model from the previous literatures
CONCLUSION
Among the QSAR models used in this study, the nonlinear feature selection models were demonstrated to be better than their linear methods, and the results of GA-ANN method were better than the other non-linear models used. These results also proved that DP03, BID, AAC, RDF035v, JGI9, TIE, R7e + , BELm6 descriptors in the gas phase and Mor32u, ESpm03d, RDF070v, ATS8m, MATS2e, R4p, L1u, R3m descriptors in the solvent phase were more significant than other descriptors in building this QSAR model and predicting the biological activity of Sulfonamides substitution patterns.
Acknowledgements
Publication cost of this paper was supported by the Korean Chemical Society.
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