Molecular structure, drug likeness and QSAR modeling of 1,2-diazole derivatives as inhibitors of enoyl-acyl carrier protein reductase

3.3.1 Rules of thumb

We used various ‘rules of thumb’ in MPO methods, namely, the Lipinski (Lipinski et al., 1997), Veber rules (Veber et al., 2002), to study the oral bioavailability of the series of diazole derivatives. We also considered the oldest and most commonly used metrics, which are the ligand efficiency (LE) and the lipophilic efficiency of the ligand (LLE) (Segall, 2012) (Table 4).

The Lipinski and Veber rules are used to identify compounds that could pose absorption and permeability problems, with the Lipinski rule being used most often to characterize drug-like compounds. Compounds that do not exhibit at least two of the criteria of the Lipinski rules are very likely to present absorption or permeability issues. Lipinski's rules are: Molecular Weight (MW) < 500 Da, water partition coefficient (log P) < 5, Number of Hydrogen Bond Donors (NHD) < 5, number of Hydrogen Bond Acceptors (NHA) < 10. Veber rules: Rotatable bonds (NBR) < 10 and Polar surface area (TPSA) < 140 Ǻ².

The parameters relevant to the Lipinski rule are shown in Table 4. All the studied compounds had lipophilicity values of log P less than 5 (−5.43 to 3.19); therefore, they should present acceptable solubility in aqueous and lipid solutions. A negative value of log P indicates that a compound is very hydrophilic, and should have good solubility in water, gastric tolerance, and elimination by the kidneys. Conversely, a positive value of log P indicates that the compound is highly lipophilic, and should exhibit good permeability across the biological membrane, binding to plasma proteins, and elimination by metabolism, but low aqueous solubility and gastric tolerance (Ertl et al., 2000). Among the pyrazole derivatives in our series, compounds 15, 26, and 32 have log P values of −5.12, −4.32, and −5.43, respectively, suggesting that these compounds would have good solubility and gastric tolerance. Compound 18, which has the maximum log P value among the series (3.19), would be assumed to have good permeability across biological membranes. All the studied compounds had less than 10 hydrogen acceptors (O) and less than 5 hydrogen donors (OH, NH). Some compounds had molecular weights of less than 500 Da, indicating that they could easily cross cell membranes. The total number of violations of the Lipinski rule was tabulated for each compound; all compounds have either zero or one violation. Thus, all the compounds meet the Lipinski rule (rule of five), suggesting that theoretically, they would not present oral bioavailability issues.

In terms of Veber’s rule, the number of rotational bonds is less than 10 for all the compounds. The low number of rotational bonds (reduced flexibility) in the test compounds indicates that these ligands would change confirmation only slightly during binding to a protein. All compounds except for 32 have a PSA value lower than 140 Å², which predicts good oral bioavailability and the transport through membranes.

The LE and LLG values are also collected in Table 5. The ligand (LE) efficiency decreases with increasing number of heavy atoms. Obtaining high ligand efficiency requires compounds with few heavy atoms; this can be explained by the correlation between the size of the compound and its physicochemical properties. It has been suggested that one typical factor contributing to the decreased LE in larger ligands could be the less favorable binding entropies for larger and more flexible ligands (Loving et al., 2012). For example, Table 5 clearly shows that the compounds 1, 10, and 17, which have few heavy atoms, showed efficiencies of 0.309, 0.317, and 0.267, respectively, while compound 21, which has the greatest number of heavy atoms (34), exhibited a low ligand efficiency value of 0.215, and may have poor physicochemical and ADME (adsorption, distribution, metabolism, and excretion) properties. On the other hand, the efficiency varied proportionally with the values of the lipophilicity index pIC₅₀.

LLE provides a means of assessing the affinity of a compound for its target relative to its lipophilicity. The aim is to increase the affinity without increasing lipophilicity at the same time. Since lipophilicity is the main promissory factor for compounds, LLE-optimized compounds should be more selective. It has been suggested that LLEs in the range 5–7 or even higher should be targeted (Hopkins et al., 2004). If LipE is between 5 and 7 or more than 7, the optimized compounds will be more selective (Pliska et al., 1996). The LLE values of the compound in this series were found to range between 2.01 and 10.93. For example, compounds 11, 13, and 33have LLE values of 5–7 (5.08, 6.73, and 6.94, respectively), indicating that these compounds have been successfully optimized. On the other hand, the LLE values of the compounds 2, 7, and 18are all less than 5 (2.58, 3.63, and 2.01, respectively). In these cases, the affinity gain was accompanied by an increase in lipophilicity, making them less optimal than the compounds above.

3.3.2 Golden Triangle

The Golden Triangle is a visualization tool that was developed using in vitro permeability, in vitro clearance, and computational data to aid medicinal chemists in achieving metabolically stable, permeable, and potent drug candidates. Analysis of two or more orthogonal trends, such as permeability and clearance, is known to be an extremely effective strategy for balancing and optimizing multiple properties. In particular, molecular weight and log D impact potency-efficiency calculations, allowing potency, clearance, and permeability to be optimized simultaneously (Johnson et al., 2009).

Log D and molecular weight (MW) have been identified as properties that show correlations with permeability and stability. Using large data sets, compounds with good in vitro permeability and low clearance have been found to concentrate in the area with a baseline from log D = −2.0 to log D = 5.0 at MW = 200, and a vertex between log D = 1.0 and 2.0 at MW = 450. These trends lead to a triangle-shaped area known as the Golden Triangle; molecules within this area are low clearance and good permeability (Fig. 2).

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Fig. 2

Golden triangle: In vitro permeability and clearance trends across MW and log D.

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Johnson and co-workers reported that molecular weight (MW) and lipophilicity (log D at pH 7.4) can be used as surrogates of many different molecular descriptors; this fact has been used to develop the useful Golden Triangle visualization tool. Compounds that reside inside the Golden Triangle are more likely to be both metabolically stable and to possess good membrane permeability than those outside. The Golden Triangle (Fig. 2) shows that compounds 1, 4, 8, 10, 11, 12, 13, and 14 lie inside the triangle, and thus should show good permeability and clearance (Beale et al., 2010). In general, compounds with lower log D and higher molecular weight molecules fail due to low permeability, while higher log D and higher MW compounds fail due to elevated in vitro clearance (Johnson et al., 2009).

3.4.1 Construction of the QSAR model

The best QSAR model was develop to explain the correlations between the physicochemical parameters and the biological activities (pIC₅₀ values) of the 1,2-diazole derivatives. Various physical and chemical properties, known as physicochemical descriptors, as well as the Lipinski and Veber parameters were used as independent variables, and were correlated with the biological activities of pyrazole derivatives using multiple linear regression analyzes (MLR) to generate the QSAR model. Several QSAR equations were tested, and the best QSAR models were selected on the basis of various statistical parameters, namely, the correlation coefficient R, which measures the degree of linear association between two variables; the squared correlation coefficient (R² > 0.6), which is a relative measure of quality of fit; the standard error of the estimate, which represents an absolute measure of the quality of fit; and Fischer’s value (F). F is the Fisher ratio, which reflects the ratio of the variance explained by the model to the variance due to the error in the regression. High F values indicate that the model is statistically significant (Sanmati et al., 2012). The most statistically significant correlation generated after multiple regression analysis using the software SPSS is given below, along with the relevant statistical parameters:

The values of the variance of the fractions can range between 0 and 1 Only QSAR models with R² > 0.6 were considered for validation. For example, in the correlation above, the values R = 0.887 and R² = 0.786 indicated a strong correlation between the different parameters (independent variables) and the inhibitory activity of the compound towards enoyl acyl carrier protein reeducates. The calculated F value of the generated QSAR model exceeded the F value tabulated by a large margin, indicating the significance of the regression. In addition, the F-value was found to be statistically significant at the 95% level for this model. The positive value of the quality factor (Q) for this OSAR model suggested its high predictive power and its lack of adaptation. The low standard deviation also demonstrated the accuracy of this model.

In the model in Eqn (1) the positive coefficient of log P indicates that increased lipophilicity (hydrophobicity) of the molecules correlates with increased biological activity, while the negative coefficient of the log D term indicates that more positive molar refractivity values lead to a decrease in the biological activity; i.e., the pyrazole nucleus should be functionalized with one or the other electron or free electronic pairs.

3.4.2 Model validation

The predictive powers of the equations were validated using the “leave-one-out” (LOO) (Tetko et al., 2001) cross-validation method. Cross-validation is a convenient and reliable way to test the significance of a model. Therefore, to validate the final models individually generated for different activities properties, a one-out method was used to perform cross-validation In order to test the validity of the predictive power of the selected MLR model (eq. log (l/IC₅₀)), the LOO technique was used.

The developed model was validated by calculating the following statistical parameters: P_RESS (sum of predicted residual squares), SSY (sum of squares of response value), and R2CV (global predictive ability), adjusted R², PE (predictive error correlation coefficient), and S_PRESS (prediction uncertainty); the values of these parameters are given in (Table 5).

P_RESS is an important cross validation parameter because it provides a good approximation of the actual predictive error of the model. A P_RESS value that is lower than the SSY value indicates that the predictions of the model are better than chance, and can be considered statistically significant. The obtained P_RESS value of 2.540 indicates that the model is statistically significant. In addition, for a reliable QSAR model, the P_RESS/SSY ratio should be less than 0.4 (Podunavac-Kuzmanovi et al., 2009). As shown in Table 5, the ratio for the developed model is 0.213. An indication of the performance of the model can be obtained from its R²_CV value (the overall prediction capability). To ensure good performance of the QSAR model, high R²_CV and R²_adj values are essential; values of 0.773 and 0.746 were obtained for the present QSAR model, respectively. S_PRESS (predictive uncertainty) is another important parameter for the determination of the uncertainty in the prediction. Lower S_PRESS values indicate better predictive power. The low value of 0.311 indicates the predictive ability of this model is good. The predictive error of the correlation coefficient (PE) also evaluates the predictive power of a model. The present model satisfies the condition R > 6PE, and can therefore be said to have good predictive power. The experimental, predicted, and residual ENR inhibitory activity of 1,2-diazole and its derivatives were determined using the software SPSS, and are listed in Table 6.

Fig. 3 shows a plot of the linear regression between the predicted and experimental values of biological activity of the 1,2-diazole derivatives. The plot shows a good correlation of R² = 0.786. The evaluation set has a good distribution along the range of values of the training set. Thus, the QSAR model developed in the current study can be successfully applied to predict the inhibitory activities of this series of molecules against mycobacterium tuberculosis.

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Fig. 3

Linear regression of the plot of the predicted values against the experimental values of log (I/IC₅₀).

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To investigate the presence of systematic error in the developed QSAR model, the residuals of the predicted values of the biological activity (log(I/IC₅₀))were plotted against the experimental values, as shown in Fig. 4. The propagation of the residuals on both sides of zero indicates that no systemic error exists.

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Fig. 4

Plot of the residual values relative to the experimentally observed values.

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