^{1}

^{1}

^{1}

^{1}

Development of more potent antituberculosis agents is as a result of emergence of multidrug resistant strains of^{2} test) of 0.8034 and Y-randomization coefficient (

Tuberculosis (TB) is the most deadly bacterial disease caused by specie of bacteria known as

The resistance of the

Meanwhile, a theoretical approach, quantitative structure activity relationships (QSARs), is one of the most widely used computational method which helps in designing drugs and predicting drugs activities [

The derivatives of 2,4-disubstituted quinoline as potent anti-

Molecular structures of inhibitory compounds and their derivatives as antitubercular agents.

S/N | Molecular structure | Observed Activity | Observed Activity | Calculated Activity | Residual | Leverage |
---|---|---|---|---|---|---|

| | 11 | 6.8191 | 7.22456 | -0.40546 | 0.186966 |

| | 12 | 6.8418 | 6.713561 | 0.128239 | 0.267393 |

| | 11 | 6.8601 | 6.664744 | 0.195356 | 0.072612 |

| | 99 | 9.4979 | 9.73193 | -0.23403 | 0.15548 |

| | 14 | 6.9772 | 6.896778 | 0.080422 | 0.328411 |

| | 23 | 7.2608 | 6.510442 | 0.750358 | 0.055405 |

| | 20 | 7.1707 | 6.972982 | 0.197718 | 0.407733 |

| | 30 | 7.4233 | 7.152527 | 0.270773 | 0.378878 |

| | 20 | 7.2838 | 6.985668 | 0.298132 | 0.085176 |

| | 16 | 7.1472 | 7.67865 | -0.53145 | 0.343511 |

| | 42 | 7.6035 | 7.71263 | -0.10913 | 0.084914 |

| | 27 | 7.2938 | 6.495725 | 0.798075 | 0.096543 |

| | 99 | 9.6090 | 9.62779 | -0.01879 | 0.089973 |

| | 21 | 7.2630 | 7.88645 | -0.62345 | 0.067538 |

| | 30 | 7.4772 | 7.411826 | 0.065374 | 0.101346 |

| | 10 | 6.8909 | 6.781862 | 0.109038 | 0.218861 |

| | 15 | 7.0807 | 7.17282 | -0.09212 | 0.090942 |

| | 21 | 7.2747 | 7.224153 | 0.050547 | 0.079898 |

| | 23 | 7.4091 | 7.67409 | -0.26499 | 0.075513 |

| | 40 | 7.7412 | 7.3187 | 0.4225 | 0.154686 |

| | 42 | 7.6688 | 7.273758 | 0.395042 | 0.0423 |

| | 21 | 6.2688 | 6.3256 | -0.0568 | 0.05984 |

| | 40 | 7.6970 | 7.73765 | -0.04065 | 0.357197 |

| | 7 | 6.7741 | 5.816571 | 0.957529 | 0.214607 |

| | 3 | 6.2513 | 6.039603 | 0.211697 | 0.200793 |

| | 10 | 6.8414 | 6.809542 | 0.031858 | 0.432707 |

| | 28 | 7.3673 | 7.357741 | 0.009559 | 0.263698 |

| | 21 | 7.1891 | 7.39202 | -0.20292 | 0.255295 |

| | 10 | 6.8291 | 6.508441 | 0.320659 | 0.06229 |

| | 10 | 6.9253 | 6.914677 | 0.010623 | 0.81434 |

| | 18 | 7.2022 | 7.50052 | -0.29832 | 0.279776 |

| | 52 | 7.7696 | 7.486908 | 0.282692 | 0.409976 |

| | 9 | 6.7716 | 7.25273 | -0.48113 | 0.25708 |

| | 30 | 7.4420 | 7.49224 | -0.05024 | 0.055855 |

| | 26 | 7.3209 | 7.025132 | 0.295768 | 0.517231 |

| | 14 | 6.9809 | 7.16429 | -0.18339 | 0.249575 |

Note. Superscript “a” represents the test set.

In order for the molecules to attain a stable conformer at a minimal energy, all the molecules were geometrically optimized with the aid of Spartan 14 V1.1.4 by employing Molecular Mechanics Force Field (MMFF) count to remove strain energy and later subjected to Density Functional Theory (DFT) by utilizing the (B3LYP) basic set [

Descriptor is a mathematical logic that describes the properties of a molecule based on the correlation between the structure of the compound and its biological activity. Descriptors calculation for all the inhibitory compounds were achieved using PaDEL-Descriptor software V2.20.

The values for the calculated descriptors were normalized using (

Kennard and Stone’s algorithm approach was employed in this study to divide the data set into two compounds, a training set and a test, in proportion of 70 to 30%. The training set was used to develop the QSAR model while the test was used to confirm the developed model [

Multilinear regression (MLR) approach is a strategy used to develop the QSAR. MLR approach displays a direct relationship between the dependent variable Y (activity) and independent variable X (descriptors). In MLR analysis, the mean of the dependent variable Y relies on X. MLR equation below is used to incorporate more than one independent variable (descriptors) with a single response variable (activity):

The combinations of the optimum descriptors for the training set were obtained from the descriptor pool using the Genetic Function Approximation technique. Their anti-lung cancer activities were placed as the last column in their respective spread sheets in Microsoft Excel 2010 which were later imported into the Material Studio software version 8.0 to generate the QSAR model by employing multilinear regression (MLR) approach and to evaluate the internal validation parameters [

The applicability domain approach was employed for the determination of outlier and influential molecule. Any compound outside the applicability domain space of

Y-Randomization test is a confirmatory test to show that the developed QSAR model is reliable, strong, and robust and not gotten by chance. This test was performed on the training set data as described by [

The external validation test for the developed QSAR model was further subjected to Golbraikh and Tropsha criteria listed below:

k (threshold value 0.85 ≤ k ≤ 1.15)

where

The fitting ability, stability, reliability, predictiveness, and robustness of the developed models were evaluated by internal and external validation parameters. The validation parameters were compared with the accepted threshold value for any QSAR model [

A theoretical approach was employed to derive a QSAR model for predicting the activities of 2,4-disubstituted quinoline analogues against

The best descriptors that could better predict the activities of the inhibitory compounds were selected with the approach of Genetic Function Algorithm (GFA) while multilinear regression (MLR) method was used as modeling technique in generating the QSAR model. GFA-MLR led to selection of five

Calculated descriptors for training set in generating model 1.

Molecule | Descriptor | Calculated | ||||
---|---|---|---|---|---|---|

| | | | | ||

| ||||||

| 2.311547 | 0.504055 | 64.51552 | 0.52720052 | 0.3506263 | 7.67865 |

| 2.67309 | 0 | 62.68136 | 34.2771775 | 9.04275631 | 7.71263 |

| 2.520833 | 0.501468 | 57.73972 | 1.29188967 | 2.96E-69 | 6.495725 |

| 2.070513 | 0.399144 | 57.39682 | 2.43835699 | 0.19620218 | 9.62779 |

| 4.712551 | 0.452852 | 66.02774 | 6.52104829 | 0.35850313 | 7.88645 |

| 2.834823 | 0.442816 | 68.01063 | 4.11533689 | 3.17070944 | 7.411826 |

| 2.250086 | 0.432569 | 69.73224 | 4.34519754 | 2.69686082 | 7.17282 |

| 1.96649 | 0.413777 | 63.86202 | 0.96785765 | 0.09769294 | 7.224153 |

| 1.739712 | 0.413777 | 62.70525 | 4.06551831 | 1.08768086 | 6.713561 |

| 2.017931 | 0.413777 | 57.96774 | 3.16024723 | 4.02E-05 | 6.3256 |

| 3.22053 | 0.467485 | 63.01904 | 6.86345924 | 5.29270652 | 7.73765 |

| 2.44322 | 0.451824 | 59.42026 | 18.6036361 | 1.72012023 | 6.039603 |

| 1.951968 | 0.504055 | 63.87078 | 2.64230219 | 0.48013813 | 6.809542 |

| 2.25 | 0.41119 | 52.98339 | 1.4003672 | 1.32E-178 | 7.39202 |

| 2.136752 | 0.41119 | 56.14089 | 1.68288294 | 1.32E-85 | 6.508441 |

| 2.540368 | 0.449237 | 62.49834 | 6.73439658 | 1.56941859 | 6.664744 |

| 2.33007 | 0.438991 | 61.12375 | 3.13665526 | 0.39982877 | 6.914677 |

| 2.282051 | 0.717269 | 69.05135 | 0.80040463 | 2.87E-17 | 7.486908 |

| 4.491667 | 0.717269 | 70.41345 | 2.29283468 | 1.64E-05 | 7.25273 |

| 2.69287 | 0 | 59.10399 | 37.2430978 | 3.36924597 | 7.49224 |

| 4.934998 | 0.755316 | 72.89643 | 8.05935217 | 1.92231371 | 7.025132 |

| 4.808826 | 0.745069 | 77.78529 | 8.30282769 | 0.38052686 | 7.16429 |

| 2.177338 | 0.504055 | 60.25478 | 2.27249229 | 0.00190267 | 9.73193 |

| 2.497643 | 0 | 63.1492 | 13.5710409 | 4.02422392 | 6.896778 |

| 2.329602 | 0.423236 | 57.11063 | 3.94385694 | 0.2244206 | 6.510442 |

| ||||||

| 1.843137 | 0.399144 | 58.85983 | 0.588352 | 7.75E-101 | 7.22456 |

| 2.535225 | 0 | 66.26276 | 8.996374 | 2.6504165 | 6.781862 |

| 2.16617 | 0.441577 | 58.02257 | 9.241266 | 0.6230199 | 7.67409 |

| 3.573278 | 0.464899 | 63.50165 | 5.442846 | 2.6206016 | 7.3187 |

| 6.729842 | 0.770977 | 78.82503 | 7.631746 | 6.2504921 | 7.273758 |

| 2.223039 | 0.501468 | 58.21113 | 9.046209 | 0.0037305 | 5.816571 |

| 2.031111 | 0.41119 | 56.34657 | 5.880833 | 0.2562624 | 7.357741 |

| 2.499622 | 0.422785 | 59.88793 | 2.565246 | 0.22884 | 7.50052 |

| 2.911765 | 0.501468 | 55.17425 | 1.262144 | 2.64E-182 | 6.972982 |

| 1.571429 | 0.588889 | 0 | 6.09E-17 | 4.24E-298 | 7.152527 |

| 2.568603 | 0 | 63.93143 | 7.576514 | 1.2281457 | 6.985668 |

The names and symbols of each descriptors selected by GFA approach were presented in Table

List of some descriptors used in the QSAR optimization model.

S/NO | Descriptors symbols | Name of descriptor(s) | Class |
---|---|---|---|

| | Average Broto-Moreau autocorrelation - lag 5 / weighted by Sanderson electronegativities | 2D |

| | Randic-like eigenvector-based index from Barysz matrix / weighted by I-state | 2D |

| | Smallest absolute eigenvalue of Burden modified matrix - n 7 / weighted by relative Sanderson electronegativities | 2D |

| | 3D topological distance based autocorrelation - lag 9 / weighted by Sanderson electronegativities | 3D |

| | Radial distribution function - 110 / weighted by relative I-state | 3D |

Statistics and correlation matrix of the selected descriptors that were reported in model 1 were presented in Table

Statistical parameters that influence the model.

Descriptor | Standard regression coefficient | Mean Effect (ME) | P- Value | VIF | Standard Error |
---|---|---|---|---|---|

| -0.3532 | -0.4429 | 0.000546 | 2.1943 | 0.00654 |

| 0.2376 | 0.3552 | 0.0236 | 2.3743 | 0.53182 |

| -0.1343 | -0.8826 | 4.34E-04 | 1.6456 | 0.7866E-05 |

| 0.5789 | 0.5196 | 2.12E-05 | 1.0491 | 0.00867 |

| 0.94224 | -0.4405 | 0.0135 | 2.7860 | 3.65E-05 |

The mean effect (ME) and standard regression coefficient (

Pearson’s correlation coefficient for the descriptor used in the QSAR model.

Inter-correlation | |||||
---|---|---|---|---|---|

| | | | | |

| 1 | ||||

| 0.414812 | 1 | |||

| 0.668151 | 0.498043 | 1 | ||

| 0.1092 | -0.67462 | -0.04264 | 1 | |

| 0.061763 | -0.6067 | 0.095274 | 0.0728009 | 1 |

Validation parameters for each model using multilinear regression (MLR).

S/NO | Validation Parameters | Formula | Threshold | Model 1 | Model 2 | Model 3 | Model 4 |
---|---|---|---|---|---|---|---|

| |||||||

| Friedman LOF | | 0.03167 | 0.03253 | 0.03561 | 0.04567 | |

| R-squared | | | 0.9265 | 0.8765 | 0.8454 | 0.8123 |

| Adjusted | | | 0.9045 | 0.8464 | 0.8277 | 0.7800 |

| Cross validated R-squared ( | | | 0.8512 | 0.8154 | 0.7574 | 0.7245 |

| Significant Regression | Yes | Yes | Yes | Yes | ||

| Critical SOR F-value (95%) | | | 3.6465 | 3.6542 | 3.75443 | 3.8743 |

| Replicate points | 0 | 0 | 0 | 0 | ||

| Computed observed error | 0 | 0 | 0 | 0 | ||

| Min expt. error for non-significant LOF (95%) | 0.03432 | 0.0354 | 0.04632 | 0.0485 | ||

| |||||||

| Average of the correlation coefficient for randomized data ( | | 0.3866 | 0.3265 | 0.4644 | 0.4875 | |

| Average of determination coefficient for randomized data ( | | 0.1465 | 0.1843 | 0.2541 | 0.2533 | |

| Average of leave one out cross-validated determination coefficient for randomized data ( | | -1.3325 | -1.3522 | -1.4023 | -1.4854 | |

| Coefficient for Y-randomization (c | | | 0.7443 | 0.7103 | 0.6587 | 0.5873 |

| |||||||

| Slope of the plot of Observed activity against Calculated activity values at zero intercept | | 0.85<k<1.15 | 1.0016 | 1.04732 | 1.0054 | 1.1134 |

| Slope of the plot of Calculated against Observed activity at zero intercept | | 0.85<k<1.15 | 0.81233 | 0.9432 | 0.6432 | 0.96433 |

| | <0.3 | 0.01643 | 0.07433 | 0.05322 | 0.04324 | |

| | <0.1 | 0.00243 | 0.00573 | 0.07843 | 0.0643 | |

| | <0.1 | 0.05332 | 0.06453 | 0.07637 | 0.8633 | |

| | | | 0.8034 | 0.75433 | 0.6765 | 0.6123 |

External validation and internal validation parameters used to assure that the developed models are stable and robust were reported in Table

The QSAR model generated in this research was compared with the models obtained in the literature [^{2}^{2}

From the above models the validation parameters reported in this work and those reported in the literature were all in agreement with the parameters presented in Table

Y-Randomization coefficient

Y-randomization parameters test.

Model | | | |
---|---|---|---|

Original | 0.9265 | 0.9045 | 0.8512 |

Random 1 | 0.3454 | 0.1193 | -1.0841 |

Random 2 | 0.4868 | 0.2370 | -1.0985 |

Random 3 | 0.4408 | 0.1943 | -0.9815 |

Random 4 | 0.5575 | 0.3108 | -0.5503 |

Random 5 | 0.2957 | 0.0874 | -1.1088 |

Random 6 | 0.5562 | 0.3093 | -0.7285 |

Random 7 | 0.7724 | 0.5966 | 0.0328 |

Random 8 | 0.2752 | 0.0757 | -1.1166 |

Random 9 | 0.74823 | 0.5598 | -0.0362 |

Random 10 | 0.5557 | 0.3088 | -0.4448 |

| |||

Average | 0.3866 | ||

Average | 0.1465 | ||

Average | -0.3325 | ||

| 0.7443 |

The graphs of calculated activities plotted against observed activities of the training and test set are presented in Figures

Plot of calculated activity against observed activity of training set.

Plot of calculated activity against observed activity of test set.

Plot of standardized residual activity versus observed activity.

The standardized residual activities plotted against the leverage value, known as the Williams plot, are shown in Figure

The Williams plot of the standardized residuals versus the leverage value.

D-Optimal design was carried out in order to determine optimal design location and maximize the efficiency of estimating a specified model. This was achieved using Statgraphics 18 software.

From the results presented in Table

D optimal validation parameters.

D optimal Validation parameters | Value |
---|---|

Correlation Coefficient | 0.899599 |

R-squared | 80.9278 percent |

R-squared (adjusted for d.f.) | 80.0986 percent |

Standard Error of Est. | 0.345508 |

Mean absolute error | 0.25514 |

Durbin-Watson statistic | 1.81474 (P=0.3302) |

Lag 1 residual autocorrelation | 0.0925989 |

Correlation Coefficient | 0.899599 |

The

Plot of observed versus predicted values.

Variance plot shows how the standard error of the predicted response varies across the design region.

Prediction profile graph displays the standard error of the predicted response.

A theoretical approach was employed in this study on selected molecular descriptors to derive a model that could be used to correlate the structure of 2,4-disubstituted quinolone derivatives as potent inhibitors against

The derivatives of 2,4-disubstituted quinoline as potent anti-

The authors declare that they have no conflicts of interest.

The authors wish to acknowledge the statgraphics team for providing statgraphics software used in the research.