In the present study, quantitative structure–activity-relationship (QSAR) study on a group of sulfonamide Schiff-base inhibitors of Carbonic Anhydrase (CA) enzyme has been carried out using Codessa Pro methodology and software. Linear regression QSAR models of the biological activity (Ki) of 38 inhibitors of carbonic anhydrase CA-II isozyme were established with 12 different molecular descriptors which were selected from more than hundreds of geometrical, topological, quantum-mechanical, and electronic types of descriptors and calculated using Codessa Pro software. Among the models presented in this study, statistically the most significant one is a five-parameter equation with correlation coefficient, R^{2} values of ca. 0.840, and the cross-validated correlation coefficient, R^{2} values of ca. 0.777. The obtained models allowed us to reveal some physicochemical and structural factors, which are strongly correlated with the biological activity of the compounds.

The metallo-protein carbonic anhydrase (CA, EC 4.2.1.1) is one of the most widely spread biological catalysts all over the phylogenetic tree. In humans, isozymes I, II, and IV are involved in respiration and regulation of the acid/base homeostasis. These complex processes involve both the transport of CO_{2}/bicarbonate between metabolizing tissues and excretion sites (lungs, kidneys), facilitate CO_{2} elimination in capillaries and pulmonary microvasculature, eliminate H^{+} ions in the renal tubules and collecting ducts, as well as help in the reabsorption of bicarbonate in the brush border and thick ascending Henle loop of the kidneys. By producing the bicarbonate-rich aqueous humor secretion (mediated by ciliary processes isozymes CA I, II, CA IV and CA XII) within the eye, CAs are involved in vision, and their misfunctioning leads to high intraocular pressure and glaucoma. CA II is also involved in the bone development and in functions such as the differentiation of osteoclasts or the provision of acid for bone resorption in osteoclasts [

Quantitative structure activity relationship (QSAR) studies are tools for predicting endpoints of interest in organic molecules acting as drugs [

In this study, we investigated QSAR for 38 sulfanilamide Schiff's base inhibitors of the physiologically relevant isozyme CAII using Codessa Pro approach [

For all the molecules studied, 3-D modeling and calculations of quantum mechanical descriptors were performed using the Gaussian 03 quantum chemistry package [^{2} _{min} 0.01 by default, (c) the parameter's t-value is less than t_{1} (where R^{2} min 0.1 by default and t_{1} 1.5 by default are user-defined values), and (d) the descriptor is highly inter-correlated (above r_{full}, where r_{full} is a user-specified value by default 0.80), with another descriptor. All the remaining descriptors are then listed in the decreasing order according to the correlation coefficient of the corresponding one-parameter correlation equation. All two parameter regression models with remaining descriptors are developed and ranked by the regression correlation coefficient R^{2}. A stepwise addition of further descriptor scales is performed to find the best multi-parameter regression models with optimum values of statistical criteria (highest values of R^{2}, the cross-validated, R^{2} _{CV,} and the F value). In addition to the descriptors calculated using Gaussian 03 and Codessa Pro, we have also added two physicochemical properties of compounds, namely, logarithm of 1-octonal/water partition coefficient (logP) and logarithm of aqueous solubility (logS) to the descriptor pool. These two parameters were calculated using WEB tool of ALOGPS 2.1 software [

The structures of 38 Schiff-base sulfonamide compounds are shown in

Using the HM, several regression equations were obtained in this study. Among the regression results, five equations (the best one, two, three, four, and five parameters) were selected as models and are given in ^{2}, is a measure of the fit of the regression equation. F, the Fisher test value, reflects the ratio of the variance explained by the model and the variance due to the error in the model. Higher values of F-test indicate the significance of the equation. s^{2} is the standard deviation of the regression. R^{2}_{CV}, the ‘leave one out’ (LOO) cross-validated coefficient, is a practical and reliable method for testing the predictive performance and stability of a regression model. LOO approach involves developing a number of models, with one sample omitted at a time. After developing each model, the omitted data are predicted and the differences between the experimental and predicted activity values are calculated. The R^{2}_{CV} values are then calculated according to the following formula [

where y_{i} is the actual experimental activity, _{î}

In the present work, more than two hundred descriptors were exploited. In Codessa Pro, descriptors are divided into groups such as constitutional, topological, geometrical, electrostatic, quantum chemical, thermodynamic, and constructed. Constitutional descriptors are related to the number of atoms and bonds in each molecule. Topological descriptors include valence and non valence molecular connectivity indices calculated from the hydrogen-suppressed formula of the molecule, encoding information about the size, composition, and the degree of branching of a molecule. Geometrical descriptors are calculated from 3-D atomic coordinates of the molecule and comprise moments of inertia, shadow indices, molecular volumes, molecular surface areas, and gravitation indices. Electrostatic descriptors reflect characteristics of the charge distribution of the molecule. Quantum chemical descriptors encode the polar interactions between molecules or their chemical reactivity and the activation energy of the corresponding chemical reaction. Thermodynamic descriptors are quantum mechanically calculated on the basis of the total partition function of the molecule

According to the preliminary regression analysis, these two compounds exhibited unusual behaviors in all the models. When the heuristic method has been run with default for 38 compounds, the best one, two, three, four and five parameter equations have shown up as the program output. In all these five equations, compounds 29 and 38 have had the largest standard residual (almost twice of mean residua). After selecting these two compounds as outliers, the statistical quality of one, two, three, four and five parameter equations were increased dramatically such as statistical parameters for five parameter equation R^{2} from 0.71 to 0.84, F from 15.96 to 31.54, and s^{2} from 0.061 to 0.034. It is worthy here mention that the descriptors involved in the best equations obtained for 38 compounds set and 36 compounds set are not the same. The best one, two, three, four and five parameter equations obtained from 36 compounds are presented as models in following.

A perusal of

Here and thereafter, N is the number of compounds, R^{2} is the correlation coefficient, R^{2} _{CV} is the ‘leave one out’ (LOO) cross-validated coefficient, F is the Fisher-statistic value, and s^{2} is the standard deviation of the regression equation. In this model, as well as the models presented below, compounds 29 and 38 are outliers. In this model, RNBR is the relative number of benzene rings. RNBR is the ratio between the numbers of benzene rings divided by the total number of atoms in the molecules. In the above equation, RNBR has a positive-sign coefficient. This means that increases in the magnitude of RNBR favors the exhibitions of the inhibitory activity of CA II-Ki.

Among the obtained two-parameter models, statistically the best one is as below:

In this model, NBR is the number of benzene rings and NCA is the number of C atoms in the molecules. These two descriptors are constitutional. NBR has a coefficient with positive sign and NCA has a coefficient with a negative sign. When models 1 and 2 are considered together, both models highlight the same features of the molecules. According to the models, substituting benzene with nitro or hydroxy groups instead of methyl groups and decreasing the number of CH_{2} bond to imine nitrogen are favorable for an increase in the inhibition activity of the compounds.

Among the obtained three-parameter models, statistically the best one is as follows:

In this model, RNDB is the relative number of double bonds, DPSA-1 is defined as the difference in CPSAs (PPSA1 (partial positive surface area) -PNSA1 (partial negative surface area)) [Zefirov's PC] and MiPCN is the Min partial charge for a N atom [Zefirov's PC]. RNDB is a constitutional descriptor and has a coefficient with a negative sign. A decrease in the magnitude of RNDB favors the exhibitions of the inhibitory activity of CA II-Ki. DPSA-1 is an electrostatically charged partial surface-area descriptor and encodes features responsible for polar interactions between molecules. The negative sign of coefficient of DPSA-1 highlights a decrease in the magnitude of RNDB, which favors the exhibitions of the inhibitory activity of CA II-Ki. MiPCN is an electrostatic descriptor and reflects minimum partial charge on the N atom in the molecules. The positive sign of the coefficient of MiPCN indicates that increases in the magnitude of MiPCN are favorable for an increase of inhibition activity of the compounds.

Among the obtained four-parameter models, statistically the best one is as shown below:

In this model, ALS is the Average LogS, ^{3}χ is the Randic index (order 3), RPCG is the Relative positive charge (QMPOS/QTPLUS) [Zefirov's PC], and RNDB is the relative number of double bonds as in model 4. ALS is the logarithm of aqueous solubility of the compounds. The negative sign of the coefficient of ALS highlights a decrease in the magnitude of ALS_{,} which favors the exhibitions of inhibitory activity of CA II-Ki. ^{3}χ is a topological descriptor, and describes the atomic connectivity and branching information of the molecules. ^{3}χ has a coefficient with a negative sign. This means that the third-order branching is not the favorable parameter for the exhibition of the inhibitory activity. RPCG, the RPCG Relative positive charge (QMPOS/QTPLUS) is an electrostatic descriptor, and reflects characteristics of the charge distribution of the molecules. The positive sign of the coefficient of RPCG indicates that increases in the magnitude of relative positive charge of molecules are favorable for an increase of the inhibition activity of the compounds.

During our regression analysis using HM, we obtained several five-parameter equations. Out of these five-parameter equations, ^{2}AIC the Average information content (order 2) is the best. This model is as shown below:

In this model, the sign of coefficients of NBR and NCA is the same as in that in the model 2 and thus they carry the same significance as in that model. NNA is a constitutional descriptor. It has a positive sign of coefficient. This means that the increase in the magnitude of NNA is the favorable parameter for the exhibition of the inhibitory activity. ALP is the logarithm of 1-octonal/water partition coefficient and exhibits hydrophobicity of compounds. The positive sign of coefficient of ALP indicates that Log CA II-Ki increases with increase in the magnitude of Average logP. ^{2}AIC is the second-order average complementary information content that could be considered an index of heterogeneity of a molecule [^{2}AIC indicates that increases in the magnitude of ^{2}AIC are favorable for an increase of inhibition activity of the compounds.

By default setting, HM uses maximum five descriptors to construct a regression model. We have changed the default setting of the software in order to allow for the use of more than five descriptors. This has yielded several six- and seven-parameter regression equations. None of those equations has better statistic parameters than the above five parameters (^{2} values of those six- and seven-parameter equations were greater than those of

Twelve types of descriptors were involved in the models. Two of the descriptors are physicochemical property, namely, ALS, average logS, and ALP, average logP. In model 4, average logS negatively contribute to the inhibitory activity. In model 5, average logP positively contributes to the inhibitory activity. This result is expected due to the fact that the average logP is inversely proportional to the average logS. Five of the involved descriptors are constitutional. RNBR, the relative number of benzene rings in model 1, and NBR, the number of benzene rings in the models 2 and 5 positively contribute to the inhibitory activity. On the contrary, NCA, the number of C atoms, negatively contribute to the inhibitory activity in the models 2 and 3. When these two results are combined together, one could draw a conclusion that one should avoid substituting benzene rings with C-containing groups and adding CH_{2} bond to imine nitrogen for designing Schiff-base sulfonamide compounds with increased inhibitory activity. Another constitutional descriptor is NNA, the number of N atoms which positively contribute to the inhibitory activity in model 5. As a consequence, substituting benzene ring with nitro groups or inserting an N-containing ring to a Schiff-base sulfonamide compound may help increase the inhibitory activity. Two descriptors, ^{3}χ and ^{2}AIC_{,} out of twelve are topological index. ^{3}χ is the third-order Randic index which negatively contributes to the inhibitory activity in model 4. This means that if one wants to design a Schiff-base sulfonamide with high inhibitory activity, it should be considered that the third-order branching is not the favorable parameter. Another topological index is ^{2}AIC, the second-order average information content. This descriptor reflects the heterogeneity of a molecule and positively contributes to the inhibitory activity in model 5. Remaining three descriptors are electrostatic index, and they characterize the charge distribution of the molecules. MiPCN, Min partial charge for a N atom [Zefirov's PC], and RPCG Relative positive charge (QMPOS/QTPLUS) [Zefirov's PC], positively contribute to the inhibitory activity in models 3 and 4, respectively. DPSA-1, Difference in CPSAs (PPSA1-PNSA1) [Zefirov's PC], negatively contributes to the inhibitory activity in model 3. The values of these electrostatic indexes of molecules are affected by substituting groups. This should be taken into account when one tries to design a new molecule.

In the present study, the structural descriptors of 36 sulfonamide Schiff-base inhibitors of Carbonic Anhydrase CA II enzyme have been correlated with the their inhibition constant Ki using Codessa Pro methodology. Among the obtained model, five-parameter equation consists of the descriptors namely the Number of benzene rings, the Number of C atoms, the Number of N atoms, the Average logP, and the Average information content (order 2) is the best one. The statistical parameters of this model are the R^{2} = 0.84, R^{2} _{CV}=0.77, F= 31.54, and s^{2} = 0.034.

The inhibition value LogCA II-Ki was adopted from the references [

Two topological indexes were involved in our models. These two indices are defined using the formula given below according to Codessa Pro reference Manual [

where _{i}_{j}^{n}^{υ} by Kier and Hall [

where _{i}_{i}

where _{i} is a number of atoms in the

where

According to Codessa Pro reference Manual [

Descriptors involved in this study are as follows:

DPSA-1 Difference in CPSAs (PPSA1-PNSA1) [Zefirov's PC].

RPCG Relative positive charge (QMPOS/QTPLUS) [Zefirov's PC].

This work has been supported by Harran University Research Council (HUBAK) Project no: 788.

Molecular structure of Schiff-base sulfonamides used in the present study

Description Plot of observed versus predicted LogKi CA II values using model 5.

Calculated descriptors involved in the models and LogCA II-Ki of 38 sulfonamides compounds predicted by model 5.

Comp. | RNBR | NBR | NCA | RNDB | DPSA-1 | MiPCN | ALS | ^{3}χ |
RPCG | NNA | ALP | ^{2}AIC |
Obs. Ki | Pre. Ki | Residue |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0.0571 | 2.0000 | 16.0000 | 0.1351 | 21.4428 | -0.0912 | -4.0600 | 8.3122 | 0.0934 | 2.0000 | 1.4900 | 4.1579 | 1.447^{a} |
1.6557 | 0.2087 |

2 | 0.0526 | 2.0000 | 17.0000 | 0.1250 | 68.0099 | -0.0967 | -4.1400 | 8.5538 | 0.0894 | 2.0000 | 1.6600 | 4.3006 | 1.146^{a} |
1.5640 | 0.418 |

3 | 0.0488 | 2.0000 | 18.0000 | 0.1163 | 105.7782 | -0.0980 | -4.1300 | 8.8038 | 0.0855 | 2.0000 | 1.9700 | 4.4307 | 1.322^{a} |
1.4996 | 0.1776 |

4 | 0.0526 | 2.0000 | 17.0000 | 0.1250 | 54.8184 | -0.0912 | -4.3100 | 8.6547 | 0.0902 | 2.0000 | 1.9000 | 4.3951 | 1.544^{a} |
1.7243 | 0.1803 |

5 | 0.0488 | 2.0000 | 18.0000 | 0.1163 | 113.8093 | -0.0967 | -4.4600 | 8.8962 | 0.0865 | 2.0000 | 2.0800 | 4.4512 | 1.740^{a} |
1.5507 | -0.1893 |

6 | 0.0455 | 2.0000 | 19.0000 | 0.1087 | 165.0231 | -0.0980 | -4.3200 | 9.1462 | 0.0828 | 5.0000 | 2.3900 | 4.5694 | 1.778^{a} |
1.4747 | -0.3033 |

7 | 0.0444 | 2.0000 | 20.0000 | 0.1042 | 59.8359 | -0.1043 | -4.7700 | 10.8703 | 0.0693 | 5.0000 | 1.7700 | 4.6356 | 1.518^{a} |
1.6333 | 0.1153 |

8 | 0.0417 | 2.0000 | 21.0000 | 0.0980 | 117.0900 | -0.1043 | -4.9300 | 11.2127 | 0.0675 | 3.0000 | 2.1800 | 4.8192 | 1.612^{a} |
1.6494 | 0.0374 |

9 | 0.0465 | 2.0000 | 17.0000 | 0.1556 | -111.7607 | -0.0872 | -5.4600 | 10.5070 | 0.1504 | 3.0000 | 2.0600 | 4.4434 | 2.008^{a} |
1.9995 | -0.0085 |

10 | 0.0435 | 2.0000 | 18.0000 | 0.1458 | -67.6019 | -0.0872 | -5.9000 | 10.8494 | 0.1474 | 2.0000 | 2.4600 | 4.6297 | 2.123^{a} |
2.0154 | -0.1076 |

11 | 0.0667 | 2.0000 | 13.0000 | 0.0968 | 31.6593 | -0.0932 | -4.2600 | 6.3063 | 0.1267 | 2.0000 | 2.3900 | 3.7736 | 2.461^{b} |
2.3724 | -0.0886 |

12 | 0.0588 | 2.0000 | 14.0000 | 0.0857 | 130.0701 | -0.0935 | -3.7900 | 6.6081 | 0.1082 | 2.0000 | 1.9000 | 3.9476 | 2.230^{b} |
2.1247 | -0.1053 |

13 | 0.0606 | 2.0000 | 14.0000 | 0.0882 | 20.6325 | -0.0986 | -4.3900 | 6.5479 | 0.1193 | 2.0000 | 2.4700 | 3.9535 | 1.954^{b} |
2.2916 | 0.3376 |

14 | 0.0541 | 2.0000 | 15.0000 | 0.0789 | 138.1794 | -0.1001 | -3.9200 | 6.8399 | 0.1040 | 3.0000 | 1.9300 | 4.0539 | 2.079^{b} |
1.9578 | -0.1212 |

15 | 0.0500 | 2.0000 | 16.0000 | 0.0976 | 111.5054 | -0.1002 | -3.8000 | 7.0673 | 0.0950 | 3.0000 | 1.2600 | 4.2531 | 2.041^{b} |
1.8666 | -0.1744 |

16 | 0.0571 | 2.0000 | 14.0000 | 0.0833 | -18.8479 | -0.0984 | -4.0900 | 7.0830 | 0.1145 | 3.0000 | 1.8300 | 4.0436 | 2.477^{b} |
2.3815 | -0.0955 |

17 | 0.0571 | 2.0000 | 14.0000 | 0.0833 | -22.6421 | -0.1000 | -4.1100 | 7.1305 | 0.1169 | 2.0000 | 1.8300 | 3.9864 | 2.146^{b} |
2.3257 | 0.1797 |

18 | 0.0444 | 2.0000 | 17.0000 | 0.0652 | 291.3417 | -0.0991 | -3.9900 | 8.2996 | 0.0693 | 2.0000 | 1.6400 | 3.9908 | 1.301^{b} |
1.2556 | -0.0454 |

19 | 0.0556 | 2.0000 | 15.0000 | 0.0811 | 65.0019 | -0.0999 | -4.4000 | 6.7979 | 0.1125 | 3.0000 | 2.8900 | 4.1144 | 2.322^{b} |
2.2884 | -0.0336 |

20 | 0.0465 | 2.0000 | 17.0000 | 0.0909 | 140.9603 | -0.1015 | -3.9200 | 7.3173 | 0.0906 | 3.0000 | 1.6000 | 4.3855 | 1.602^{b} |
1.8128 | 0.2108 |

21 | 0.0500 | 2.0000 | 15.0000 | 0.0732 | 122.8380 | -0.1001 | -4.0600 | 7.3330 | 0.1367 | 3.0000 | 1.6100 | 4.2719 | 2.397^{b} |
2.2632 | -0.1338 |

22 | 0.0588 | 2.0000 | 15.0000 | 0.1143 | 40.6266 | -0.0956 | -3.7700 | 6.2710 | 0.1287 | 2.0000 | 2.5200 | 3.7556 | 1.698^{b} |
1.8331 | 0.1351 |

23 | 0.0323 | 1.0000 | 12.0000 | 0.1250 | 90.8476 | -0.1147 | -2.5200 | 6.0563 | 0.1241 | 3.0000 | 0.6900 | 4.1682 | 1.000^{b} |
1.0004 | 0.0004 |

24 | 0.0303 | 1.0000 | 12.0000 | 0.1176 | 155.8272 | -0.1064 | -2.1200 | 6.2979 | 0.1070 | 4.0000 | -0.3000 | 4.3549 | 1.301^{b} |
1.0857 | -0.2153 |

25 | 0.0278 | 1.0000 | 13.0000 | 0.1081 | 209.1037 | -0.1064 | -2.3600 | 6.5479 | 0.1015 | 4.0000 | 0.1200 | 4.4823 | 1.000^{b} |
1.0497 | 0.0497 |

26 | 0.0645 | 2.0000 | 13.0000 | 0.0938 | 43.8927 | -0.0934 | -3.2500 | 6.3063 | 0.1498 | 2.0000 | 1.5000 | 3.8574 | 2.230^{c} |
2.2027 | -0.0273 |

27 | 0.0667 | 2.0000 | 13.0000 | 0.0968 | -5.1570 | -0.0932 | -4.2600 | 6.3063 | 0.1267 | 2.0000 | 2.4500 | 3.7736 | 2.462^{c} |
2.3894 | -0.0726 |

28 | 0.0500 | 2.0000 | 16.0000 | 0.0976 | 186.4766 | -0.0941 | -4.1900 | 7.6016 | 0.0993 | 2.0000 | 1.5200 | 4.3929 | 2.000^{c} |
1.8939 | -0.1061 |

29^{d} |
0.0625 | 2.0000 | 13.0000 | 0.0909 | -51.7829 | -0.0946 | -4.0500 | 6.8889 | 0.1241 | 3.0000 | 1.7600 | 3.8125 | 1.698^{c} |
-- | -- |

30 | 0.0667 | 2.0000 | 13.0000 | 0.0968 | -23.5748 | -0.0946 | -4.2700 | 6.1901 | 0.1294 | 2.0000 | 2.4800 | 3.7069 | 2.447^{c} |
2.3327 | -0.1143 |

31 | 0.0645 | 2.0000 | 13.0000 | 0.0938 | 32.0889 | -0.0947 | -3.3500 | 6.1901 | 0.1511 | 2.0000 | 1.3700 | 3.7929 | 2.278^{c} |
2.1029 | -0.1751 |

32 | 0.0476 | 1.0000 | 7.0000 | 0.1429 | 2.8615 | -0.0749 | -2.2300 | 3.5542 | 0.1785 | 2.0000 | 0.6400 | 3.7257 | 1.602^{c} |
1.7672 | 0.1652 |

33 | 0.0588 | 2.0000 | 14.0000 | 0.0857 | 61.6262 | -0.1001 | -3.3600 | 6.4317 | 0.1432 | 2.0000 | 1.4100 | 3.9698 | 1.845^{c} |
2.0079 | 0.1629 |

34 | 0.0500 | 2.0000 | 16.0000 | 0.0976 | 112.8082 | -0.1002 | -3.8000 | 7.0673 | 0.0950 | 3.0000 | 1.2300 | 4.2531 | 2.041^{c} |
1.8581 | -0.1829 |

35 | 0.0571 | 2.0000 | 14.0000 | 0.0833 | -22.7851 | -0.0997 | -4.1100 | 7.0624 | 0.1164 | 3.0000 | 1.8400 | 4.1007 | 2.255^{c} |
2.4402 | 0.1852 |

36 | 0.0541 | 2.0000 | 15.0000 | 0.0789 | 135.7274 | -0.1001 | -3.3700 | 6.7979 | 0.1350 | 2.0000 | 2.0600 | 4.1824 | 2.113^{c} |
2.1202 | 0.0072 |

37 | 0.0556 | 2.0000 | 15.0000 | 0.0811 | 112.8082 | -0.1017 | -3.7200 | 6.2710 | 0.1224 | 2.0000 | 2.3200 | 3.8565 | 2.146^{c} |
1.8751 | -0.2709 |

38^{d} |
0.0526 | 2.0000 | 15.0000 | 0.0769 | 8.6366 | -0.1013 | -4.1900 | 7.3805 | 0.1103 | 3.0000 | 2.2200 | 4.1427 | 1.301^{c} |
-- | -- |

RNBR, Relative number of benzene rings; NBR, Number of benzene rings; NCA, Number of C atoms; RNDB, Relative number of double bonds; DPSA-1 Difference in CPSAs (PPSA1-PNSA1) [Zefirov's PC]; MiPCN, Min partial charge for a N atom [Zefirov's PC]; ALS, Average logS; ^{3}χ, Randic index (order 3); RPCG, RPCG Relative positive charge (QMPOS/QTPLUS) [Zefirov's PC]; NNA, Number of N atoms; ALP, Average logP; and ^{2}AIC, Average Information content (order 2)

a) From Ref. [

Regression parameters and statistical quality of the correlations of the activity LogK_{i} -CAII in the present study.

Models | Descriptors involved | t-test | Coefficient_{i} |
Statistical Parameters N R^{2} R^{2} _{cv} F s^{2} | |||||
---|---|---|---|---|---|---|---|---|---|

RNBR Relative number of benzene rings | 6.163 | 32.767(5.316) | 0.180 | 36 | 0.527 | 0.488 | 37.98 | 0.090 | |

(0.280) | |||||||||

NBR Number of benzene rings | 7.590 | 1.296(0.170) | 1.245 | 36 | 0.647 | 0.599 | 30.27 | 0.069 | |

NCA Number of C atoms | -5.745 | -0.119(0.020) | (0.298) | ||||||

RNDB Relative number of double bonds | -7.939 | -16.73(2.107) | 6.182 | 36 | 0.729 | 0.618 | 28.74 | 0.055 | |

DPSA-1 Difference in CPSAs (PPSA1-PNSA1) [Zefirov's PC] | -5.458 | -0.0031(0.0005) | (0.776) | ||||||

MiPCN Minimum partial charge for a N atom [Zefirov's PC] | 3.406 | 24.276(7.127) | |||||||

ALS Average logS | -5.887 | -0.462(0.078) | 1.061 | 36 | 0.786 | 0.716 | 29.98 | 0.045 | |

^{3}χ Randic index (order 3) |
-2.571 | -0.125(0.048) | (0.330) | ||||||

RNDB Relative number of double bonds | -4.515 | -9.122(2.020) | |||||||

RPCG Relative positive charge (QMPOS/QTPLUS) [Zefirov's PC] | 3.924 | 7.577(1.930) | |||||||

NBR Number of benzene rings | 7.826 | 1.739(0.222) | -2.205 | 36 | 0.840 | 0.777 | 31.54 | 0.034 | |

NCA Number of C atoms | -7.510 | -0.279(0.037) | (0.940) | ||||||

NNA Number of N atoms | 3.578 | 0.182(0.051) | |||||||

ALP Average logP | 3.609 | 0.282(0.078) | |||||||

^{2}AIC Average Information content (order 2) |
3.488 | 0.977(0.280) |

Correlation matrix for the inter-correlation of various molecular descriptors involved in the obtained models.

RNBR | NBR | NCA | RNDB | DPSA-1 | MiPCN | ALS | ^{3}χ |
RPCG | NNA | ALP | ^{2}AIC | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

RNBR | 1.000 | |||||||||||

NBR | 0.6504 | 1.000 | ||||||||||

NCA | -0.1979 | 0.5717 | 1.000 | |||||||||

RNDB | -0.3454 | -0.3573 | 0.0337 | 1.000 | ||||||||

DPSA-1 | -0.4510 | -0.1773 | 0.2007 | -0.4079 | 1.000 | |||||||

MiPCN | 0.4106 | 0.1693 | -0.2183 | 0.4310 | -0.4810 | 1.000 | ||||||

ALS | -0.2483 | -0.3005 | 0.3372 | 0.6106 | 0.5991 | -0.6935 | 1.000 | |||||

^{3}χ |
-0.3005 | 0.4068 | -0.2031 | -0.2953 | 0.7793 | -0.0203 | -0.7565 | 1.000 | ||||

RPCG | 0.3372 | -0.2031 | -0.7013 | 0.2939 | 0.4134 | 0.7380 | 0.2244 | -0.5260 | 1.000 | |||

NNA | -0.6106 | -0.2953 | 0.2939 | 0.0882 | -0.1964 | 0.3227 | -0.0431 | 0.4294 | -0.3141 | 1.000 | ||

ALP | 0.5991 | 0.7793 | 0.4134 | -0.1964 | -0.3333 | 0.2484 | -0.7649 | 0.3105 | -0.0307 | -0.3609 | 1.000 | |

^{2}AIC |
-0.6935 | -0.0203 | 0.7380 | 0.3227 | 0.2484 | -0.2802 | -0.3572 | 0.7993 | -0.5658 | 0.6052 | -0.1155 | 1.000 |

RNBR, Relative number of benzene rings; NBR, Number of benzene rings; NCA, Number of C atoms; RNDB, Relative number of double bonds; DPSA-1 Difference in CPSAs (PPSA1-PNSA1) [Zefirov's PC]; MiPCN, Min partial charge for a N atom [Zefirov's PC]; ALS, Average logS; ^{3}χ, Randic index (order 3); RPCG Relative positive charge (QMPOS/QTPLUS) [Zefirov's PC]; NNA, Number of N atoms; ALP, Average logP; and ^{2}AIC, Average Information content (order 2).