Abstract
A linear quantitative structure–activity relationship (QSAR) study that encodes various aspects of physicochemical, topological and electronic descriptors has been developed for a series of 1,3,4-thiadiazole-2-thione derivatives (1a-r and 2a-c). The carbonic anhydrase IX inhibitory activity of the candidates under study (1a-r and 2a-c) were correlated to the selected parameters using stepwise linear regression analyses to achieve the best QSAR model. Promising results were obtained with the employed tetra-parametric model indicating that the information approach used in the present investigation is quite useful for modeling carbonic anhydrase IX inhibitors.
Introduction
QSAR has been considered a major tool in drug discovery since the work of Hansch almost 40 years ago [Citation1]. At the present time the QSAR study is one of the major fields of research in medicinal chemistry and drug design. QSAR is an effective way of optimizing or correlating certain structural features or molecular descriptors, such as lipophilicity, polarizability, or electronic and steric properties within a congeneric series of molecules with their biological activities. A better understanding of the modes of actions, prediction of newer analogs with better activity, classification of active/inactive compounds, and optimization of the lead compound to reduce toxicity and increase selectivity are the main goals of QSAR studies [Citation2]. In addition, the methodology of QSAR is very helpful in screening a large library of possible drug candidates for selectivity and potency Citation3Citation4Citation5Citation6Citation7Citation8.
The carbonic anhydrases (CAs, EC 4.2.1.1) Citation9Citation10Citation11Citation12 constitute interesting targets for the design of pharmacological agents useful in the treatment or prevention of a variety of disorders [Citation13,Citation14]. A quite new and unexpected application of the CA inhibitors (CAIs) regard their potential use in the management (imaging and treatment) of hypoxic tumors Citation15Citation16Citation17Citation18Citation19Citation20Citation21Citation22, since at least two CA isozymes of the 15 presently known in humans Citation9Citation10Citation11Citation12Citation13, CA IX and XII, are predominantly found in tumor cells and lack (or are present in very limited amount) in normal tissues Citation14Citation23Citation24Citation25Citation26.
Most of the potent CAIs investigated up to now belong to the aromatic/heterocyclic sulfonamide or sulfamate classes Citation9Citation10Citation11Citation12Citation13Citation27Citation28, although compounds incorporating other zinc-binding groups have also been investigated Citation9Citation10Citation11Citation12Citation13Citation29Citation30. Due to the biological importance of such agents as potent CAIs, many QSAR models have been proposed for the prediction of CA inhibitory activity of different aromatic and heterocyclic sulfonamides using different molecular descriptors.
Recently, we have reported the first thiadiazole-thione non-sulfonamide CAIs (1a-r and 2a-c) showing inhibitory activity against the tumor-associated CA IX in low micromolar range [Citation31]. In the present study, a QSAR model is investigated in order to predict the CA IX inhibitory activity of certain thiadiazole-thione derivatives (1a-r and 2a-c) using different groups of molecular descriptors. Our objective is to develop a rapid and reliable method to predict the CA inhibition activity of this new group of candidates. In addition, we aim to gain more information that could be used in further development and optimization of such CA IX inhibitors.
Materials and methods
Data set
In this investigation, twenty one non-sulfonamide CAIs (1a-r and 2a-c), that were recently synthesized and reported by our group, are used and their structures are depicted in . In vitro inhibitory activity of these structures (1a-r and 2a-c) against human tumor-associated carbonic anhydrase isozyme IX (hCA IX) are expressed as log IC50 in .
Figure 1. The structures of 1,3,4-thiadiazole-2-thione derivatives (1a-r and 2a-c) under study.
Descriptors calculations
Electronic descriptors calculations were carried out using “Chem. Draw Ultra” version 8.0 and MOPAC package included in “Chem. 3D Ultra” version 8.0, Cambridge Software Corporation, USA.
The structures of the compounds (1a-r and 2a-c) were drawn in Chem. Draw and saved as a template structure. For every compound, the template structure was suitably changed considering its structural features, copied to Chem. 3D to create the 3D model and finally the model was cleaned up. The energy minimization was carried out under a Molecular Orbital Package (MOPAC) module (CS MOPAC 2000) of Chem. 3D Ultra version 8.0. The energy minimized geometry was used for the calculation of polarizability (П), dipole moment (μ), Connolly Accessible Area (CAA) and ionization potential (IP) of the molecules using PM3 Hamiltonian.
Physicochemical and topological descriptors calculations were carried out using “Molecular Operating Environment (MOE) version 2006.02”, Chemical Computing Group Inc., 1010 Sherbrooke Street West, Suite 910, Montreal, H3A 2R7, Canada.
The fourth-order valence connectivity index was calculated according to the dissection rule applied by Kier and Hall [Citation34].
Statistical analyses were carried out using “Microsoft Excel XP” software in “Microsoft Office XP” version 2002, Microsoft Corporation, USA and SPSS software, version 10.0, SPSS Inc., USA.
Results and discussion
In an effort to determine the role of structural features of the investigated derivatives (1a-r and 2a-c), QSAR studies were undertaken using the linear regression analysis model. Carbonic anhydrase inhibitory activity expressed as log IC50 was used as a dependent variable in this study.
Molecular descriptors
Three groups of molecular descriptors of the synthesized compounds (1a-r and 2a-c) were selected and calculated to cover a wide range of electronic, hydrophobic and topological characters of the molecules. shows the descriptors used in this study together with the tools used for their calculation.
Table I. Calculated molecular descriptors used in this study.
In addition to the calculated descriptors an indicator variable (I), was used to indicate the presence (1.0) or absence (0.0) of hydrogen atom at the benzylic carbon in compounds 1a-r. The calculated descriptors, indicator variable (I) and log IC50 values against hCA IX are listed in .
Table II. The inhibitory activity (log IC50) and the structural descriptors of the selected compounds (1a-r and 2a-c).
Correlation matrix of the calculated descriptors
Multicolinearity occurs when two independent variables are correlated with each other and therefore contribute redundant information to the model. However, the multicolinearity problem was recently discussed by Randic; his recommendations were used in discussing our results [Citation36].
The simplest method of investigating occurrence of multicolinearity is to obtain the correlation matrix which indicates that most of the descriptors used are not highly correlated (). We decide to avoid the combinations between the highly intercorrelated descriptors with |r| ≥ 0.90, where r is the simple linear coefficient.
Table III. Intercorrelation matrix of the molecular descriptors.
For the moderately intercorrelated descriptors we have to seriously consider Randic recommendations [Citation36]. Randic stated that selection of the descriptors to be used in QSAR studies should not be delegated solely to the computers, although the statistical criteria will continue to be useful for preliminary screening of the descriptors taken from a large pool. Often in an automated selection of parameters, a descriptor will be discarded because it is highly correlated with another descriptor already selected. But what is important is not a descriptor parallel one another, but whether the two descriptors differ in those parts that are important for the activity under concern or not. Accordingly, if the two descriptors differ in the domain, which is important for the property/activity considered then both descriptors will be retained in the same model. On the other hand, if they differ in parts that are not relevant for the correlation of considered property/activity then one of them can be discarded and only the other could be used for further calculation.
These recommendations of Randic will be applied later in the generation of the multi-parametric models.
Stepwise linear regression analyses
For the current data set of 21 compounds (1a-r and 2a-c), the QSAR model development was restricted to a maximum of four variables in accordance to the generaly accepted rule of thumb. Based on this rule for a QSAR model development, one should use five compounds for each parameter selected (5:1 for compounds:descriptor) [Citation37,Citation38].
Mono-parametric models
The simple linear regression analysis yields two statistically significant correlations, one contains the polarizability parameter (П) and the other includes the indicator variable (I). However, both models showed weak correlation with the inhibitory activity, where the former model shows better statistical results (Model 1).
n = 21, Se = 0.2435, r = 0.6931, 
= 0.4530, F = 17.5660, Q = 2.8459.
Here and thereafter:
n: number of compounds
Se: standard error of estimation
r (R):simple (multiple) correlation coefficient
: adjustable R2F: Fisher's statistics
Q: quality factor
Bi-parametric models
Stepwise regression analyses using different combinations of two structural descriptors resulted into seven bi-parametric models (), which having significantly better statistics than the mono-parametric model discussed above. It was noticed that the polarizability is a common descriptor in all of the produced bi-parametric models.
Table IV. Regression parameters for the bi-parametric models.
Out of these combinations, the bi-parametric model that contains the polarizability and the Wiener polarity number was the best one (Model 2).
n = 21, Se = 0.2010, R = 0.8154, 
= 0.6277, F = 17.8609, Q = 4.0567.
This model showed a good correlation between the inhibitory activity (log IC50) and the selected (П, Wp) descriptors with a significant improvement in its statistical parameters compared with (Model 1).
Tri-parametric models
Trials were made to correlate three combined descriptors with the biological activity (log IC50) aiming to improve the statistical parameters of the obtained models. Five tri-parametric models were obtained from stepwise regression analyses ().
Table V. Regression parameters for the tri-parametric models.
Two out of these tri-parametric models showed excellent statistics (Models 3 and 4), where the former is slightly better.
n = 21, Se = 0.1527, R = 0.9040, 
= 0.7850, F = 25.3341, Q = 5.9201.
n = 21, Se = 0.1642, R = 0.8882, 
= 0.7516, F = 21.1671, Q = 5.4080.
The results indicated that the inclusion of the indicator variable I with certain topological descriptors produces better correlations.
In the above tri-parametric models 3 and 4, the correlation parameter I has a positive coefficient indicating that derivatives contain a hydrogen atom on the benzylic carbon (1a-r) generally have better inhibitory activity. On the other hand, increasing molecular branching and complexity enhances the biological activity as indicated from the positive coefficient of Zagreb index (Model 4).
Tetra-parametric models
Finally, successive stepwise regression yielded one tetra-parametric model (model 5) of slight improvement in statistical parameters.
n = 21, Se = 0.1512, R = 0.9120, 
= 0.7894, F = 19.7397, Q = 6.0304.
It is noteworthy that, in this model the fourth-order valence connectivity index (
) appears for the first time in the multi-parametric models. This index encodes the orientation, the length and the presence of heteroatom in ring substituent. The positive coefficient of this index indicates that increasing the number and length of ring substituents as well as the presence of heteroatom containing substituents is favored for the inhibitory activity.
Validation and cross-validation of model (5)
Cross-validation statistical technique has been applied to estimate the quality with regard to predictive ability of the generated model (model 5) using MOE 2005.06 software [Citation32]. The simplest and most general cross-validation procedure is the leave-one-out technique (LOO technique), where each object of the data set is taken away, one at a time. In this case, given n objects, n reduced models are developed [Citation39].
The observed activity (Obs. log IC50) together with the predicted activity (Pred. log IC50) for the tested compounds calculated using multi-linear regression (MLR) and LOO techniques are listed in . All compounds showed very good results with Z-scores not exceed the value of 2.5 indicating high predictive ability of the model. The observed log IC50 is plotted against their predicted values (calculated by MLR method) with a value of R2 found to be 0.8331 ().
Table VI. Validation and cross-validation parameters for model (5).
Figure 2. Correlation of observed and predicted log IC50 using model 5 (R2 = 0.8331, MLR method).
Statistical features
It is now important to discuss the significant of some statistical parameters to judge the quality of our work and support the obtained results. These parameters include probable error of correlation (PE), adjustable R2 (
) and the quality parameter (Q).
Probable error of correlation (PE); () is calculated by the following expression:
Table VII. Some statistical parameters of the generated models.
It is recommended that:
If, r < PE, it is not statistically significant
r > PE several times, at least three times greater, the correlation is statistically significant and
r > 6 PE, correlation is definitely significant.
For all the proposed models r values were found to be highly greater than 6PE. Thus all the correlations attempted are definitely acceptable.
The statistical parameter adjustable R2 (
) takes into account of adjustment of R2 and the statistical significance of stepwise regression (). Therefore, if a variable is added that does not contribute its fair share, the 
will actually decline. If 
values goes on increasing as we pass from bi- to higher parametric regressions, then the added parameters have favorable contribution in the exhibition of log IC50.
It is necessary that, the proposed model should have both statistical quality as well as better predictive power. The simplest parameter to decide the predictive power of the model is the quality parameter Q, the highest value of which indicates best predictive power. In all the models discussed above Q goes on increasing as we pass from mono- to higher parametric regressions (). Consequently, all the models generated here are quality models having quality predictive power.
Conclusion
The QSAR studies performed on a small series of thiadiazole CA inhibitors (1a-r and 2a-c) produced five statistically acceptable models. The produced models presented some information about the importance of some structural descriptors for the biological activity of the compound under study. It was found that molecular polarizability is not a favorable contributor for activity. On the other hand, branching, increasing the length and complexity of ring substituent as well as the presence of hydrogen atom on the benzylic carbon could increase the CA IX inhibitory activity of the synthesized compounds (1a-r and 2a-c).
Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.
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