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A series of ruthenium azopyridine complexes have recently been investigated due to their potential cytotoxic activities against renal cancer (A498), lung cancer (H226), ovarian cancer (IGROV), breast cancer (MCF-7) and colon cancer (WIDR). Thus, in order to predict the cytotoxic potentials of these compounds, quantitative structure-activity relationship studies were carried out using the methods of quantum chemistry. Five Quantitative Structure Activity Relationship (QSAR) models were obtained from the determined quantum descriptors and the different activities. The models present the following statistical indicators: regression correlation coefficient
R
^{2} = 0.986 - 0.905, standard deviation
S = 0.516 - 0.153, Fischer test
F = 106.718 - 14.220, correlation coefficient of cross-validation
= 0.985- 0.895 and
= 0.010 - 0.001. The statistical characteristics of the established QSAR models satisfy the acceptance and external validation criteria, thereby accrediting their good performance. The models developed show that the variation of the free enthalpy of reaction
, the dipole moment μ and the charge of the ligand in the complex
Q_{l}, are the explanatory and predictive quantum descriptors correlated with the values of the anti-cancer activity of the studied complexes. Moreover, the charge of the ligand is the priority descriptor for the prediction of the cytotoxicity of the compounds studied. Furthermore, QSAR models developed are statistically significant and predictive, and could be used for the design and synthesis of new anti-cancer molecules.

The satisfaction obtained in the use of cisplatin for the treatment of tumours stimulated research on transition metal complexes. Many organometallic compounds have been synthesized and tested [_{3}, 3H_{2}O reactive by only the lone electron pairs of the nitrogen atoms of the pyridine ring and the azo group, thereby forming a 5-membered stable ring of chelation. Thus, this reaction provides metal with excellent stability. In addition, the complexation of ruthenium (Reaction 1) by the asymmetric bidentate ligands leads to five isomers named α-Cl, β-Cl, γ-Cl, δ-Cl and ε-Cl [

The recent discovery of anticancer activity azopyridine complex ruthenium [_{2}L_{2}] where L stands for 2-phenylazopyridine, o-tolylazopyridine and 4-methyl-2-phenylazopyridine isomers were synthesized and tested in a series of cells line of renal cancer (A498), lung cancer (H226), ovarian cancer

code | Ligand | R Substituent | R1 Substituent |
---|---|---|---|

1 | 2-phenylazopyridine | -H | |

2 | o-tolylazopyridine | -H | |

3 | 4-methyl-2-phenylazopyridine | CH_{3 } |

(IGROV), breast cancer (MCF-7) and colon cancer (WIDR) [

The Quantitative Structure Activity Relationship (QSAR) study is one of the most widely used methods to design new therapeutic agents [

The six molecules of the training set and the three other external validation set molecules used in this study have IC_{50} ranging from 0.045 to 74 μM. Here, the term IC_{50} means the median concentration of molecules determined experimentally to inhibit 50% of cancer cells in a population of cancer cells. This range of concentrations makes it possible to define a quantitative relationship between the anticancer activity and the theoretical descriptors. According to Aldrik et al. the experimentation of the cytotoxicity of the aforementioned human tumor cell lines was made in vitro using the microculture sulforhodamine B test (SRB) for the estimation of the cell viability [_{50} that is defined in Equation (1):

DFT methods are generally known to generate a variety of molecular properties [

For the development of QSAR models, some theoretical descriptors related to the conceptual DFT were determined. In particular, the variation of the formation free enthalpy ΔG˚, the natural ligand charge in the complex Q_{L} and the dipole moment μ. These descriptors are all determined from the optimized molecules. Here, the variation of free enthalpy of the reaction indicates the spontaneity of the reaction. It was calculated according to Equation (2).

The ligand charge, which corresponds to the sum of the ligand’s natural atomic charges within the complex obtained by the NPA calculation, reflects the electrophilic or nucleophilic character of this entity. The dipole moment (μ) indicates the stability of a molecule in water. Thus, a high dipole moment will result in poor solubility in organic solvents and high solubility in water. Moreover, the interdependence of descriptors is evaluated by a linear correlation coefficient R between the pairs of the set of descriptors. Here, two descriptors are said to be independent when R < 0.95 [

A QSAR model is developed on the basis of statistical indicators. The quality of a model is determined on the basis of these various analysis statistical indicators, including the correlation coefficient R^{2}, the standard deviation S, the correlation coefficients of cross validation ^{2}, S and F relate to the adjustment of the calculated and experimental values: they describe the predictive capacity within the limits of the model and allow to estimate the precision of the values calculated on the learning set [

The squared correlation coefficient R² gives an evaluation of the dispersion of theoretical values around the experimental data. The quality of the modelling is improved when the points are close to the fitting line [^{2} was given by the following Equation (3):

where:

More the R² value will be closer to 1 more the theoretical and experimental values will be assumed to correlate. In addition, the variance

where k is the number of independent descriptors, n is the number of molecules of the training set and

The Fisher test F was also used to measure the level of statistical significance of the model, i.e. quality of the choice of descriptors constituting the model. The Fisher test F is defined from Equation (6):

The correlation coefficient of cross-validation

The performance of a mathematical model, for Eriksson et al. [

Moreover, the prediction power of a model can be obtained from five Tropsha’s criteria [

1)

2)

3)

4)

5)

In this QSAR study, the training set consisting of six molecules and the three other ruthenium azopyridine complexes forming the validation set are presented in

The calculated linear correlation coefficients R of the series of descriptors are less than 0.95 (R < 0.95). This demonstrates the non-dependence of the descriptors used to develop the models.

The best QSAR models obtained for the various anti-cancer activities as well as

Code | Descriptors | pIC50 exp | ||||||
---|---|---|---|---|---|---|---|---|

ΔG˚ | Q_{l} | µ | A498 | H226 | IGROV | MCF-7 | WIDR | |

Training Set | ||||||||

^{b}2α | −16.077 | 0.471 | 7.858 | 6.444 | 7.523 | 8.056 | 7.678 | 7.347 |

^{b}2β | −14.336 | 0.428 | 8.612 | 4.131 | 4.538 | 4.523 | 4.495 | 4.284 |

^{b}2γ | −11.267 | 0.486 | 2.547 | 5.921 | 7.081 | 7.114 | 7.032 | 6.638 |

^{c}3α | −13.142 | 0.466 | 7.513 | 5.959 | 6.337 | 6.658 | 6.377 | 6.097 |

^{c}3β | −10.369 | 0.432 | 9.382 | 4.367 | 4.745 | 4.854 | 4.824 | 4.678 |

^{c}3γ | −6.086 | 0.486 | 2.845 | 6.301 | 6.770 | 6.854 | 7.102 | 6.699 |

Validation Set | ||||||||

^{a}1α | −16.989 | 0.430 | 7.261 | 6.569 | 6.319 | 6.569 | 6.569 | 6.569 |

^{a}1β | −13.796 | 0.420 | 8.835 | 5.056 | 4.886 | 5.469 | 5.208 | 4.959 |

^{a}1γ | −9.010 | 0.480 | 1.674 | 6.699 | 6.770 | 7.387 | 7.284 | 7.187 |

^{a}1α, 1β and 1γ correspond respectively to α-, β- and γ-RuCl_{2}(2-phenylazopyridine)_{2}; ^{b}2α, 2β and 2γ correspond respectively to α-, β- and γ-RuCl_{2}(o-tolylazopyridine)_{2}; ^{c}3α, 3β and 3γ correspond respectively to α-, β- and γ-RuCl_{2}(4-methyl-2-phenylazopyridine)_{2}._{ }

ΔG˚ | Q_{l} | µ | |
---|---|---|---|

ΔG˚ | 1.000 | ||

Q_{l} | 0.331 | 1.000 | |

µ | 0.600 | 0.846 | 1.000 |

Cell line | Regression equations | R² | S | F | ||
---|---|---|---|---|---|---|

A498 | 0.986 | 0.985 | 0.153 | 106.718 | 0.001 | |

H226 | 0.953 | 0.951 | 0.348 | 30.479 | 0.002 | |

IGROV | 0.915 | 0.907 | 0.516 | 16.205 | 0.008 | |

MCF-7 | 0.922 | 0.916 | 0.470 | 17.763 | 0.007 | |

WIDR | 0.906 | 0.897 | 0.481 | 14.520 | 0.010 |

the statistical indicators are given in

It should be noted that the negative or positive sign of the model descriptor’s coefficient reflects the proportionality effect between the biological activity evolution of interest and this parameter of the regression equation. Thus, the negative sign indicates that when the value of the descriptor is high, the biological activity decreases while the positive sign translates the opposite effect.

The negative sign of the coefficient of the free enthalpy variation or the dipole moment indicates that the cytotoxic activity will be improved for a low value of the free enthalpy variation or the dipole moment. On the other side, the positive sign of the coefficient of the ligand charge means that the cytotoxic activity will be improved for a high value of the ligand charge. Also, the significance of the models is reflected by the Fisher coefficient F which is between 14.22 and 106.718 and the cross-validation correlation coefficient

Cell line | |||||||
---|---|---|---|---|---|---|---|

A498 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |

H226 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |

IGROV | 1 | 1 | 0 | 0 | 0 | 1 | 1 |

MCF-7 | 1 | 1 | 0 | 0 | 0.002 | 1.001 | 0.999 |

WIDR | 1 | 1 | 0 | 0 | 0.001 | 1 | 1 |

The Tropsha criteria for the different models are presented in

All values respect the Tropsha criteria, so these models are acceptable for predicting the ruthenium azopyridine complexes cytotoxic activity.

The study of the relative descriptors contribution in the prediction of the compounds cytotoxicity was carried out for each type of cancer cells. The different contributions are shown in

The charge of the ligand has a large contribution than the free enthalpy variation or the dipole moment. Thus, the charge of the ligand is revealed to be the priority descriptor in the prediction of the cytotoxic activity of the ruthenium azopyridine complexes studied.

In this work, the cytotoxic activities of six ruthenium azopyridine complexes on cancer cells that comprise renal cancer (A498), lung cancer (H226), ovarian cancer (IGROV), breast cancer (MCF-7) and colon cancer (WIDR) were correlated with the theoretical descriptors calculated by the DFT methods. The cytotoxic activities of three other ruthenium azopyridine complexes were selected to form the external validation sets for the calculated models. Multiple Linear Regression (MLR) was used to quantify the relationships between molecular descriptors and the properties of the azopyridine derivatives cytotoxic activity. A strong correlation was observed between the experimental values and the predicted values of the cytotoxic activity, indicating the validity and quality of the QSAR models obtained. The quantum descriptors of the optimized molecules, the free enthalpy variation of reaction, the dipole moment and the ligand charge, made it possible to predict the cytotoxicity of the ruthenium azopyridine complexes studied on cancer cells. Among all these descriptors the ligand charge is the descriptor which influences the cytotoxicity activ-

ity. The QSAR models present a robustness, with good internal and external predictive capabilities.

N’guessan, K.N., Guy-Richard Koné, M., Bamba, K., Patrice, O.W. and Ziao, N. (2017) Quantitative Structure Anti-Cancer Activity Relationship (QSAR) of a Series of Ruthenium Complex Azopyridine by the Density Functional Theory (DFT) Method. Computational Molecular Bioscience, 7, 19-31. https://doi.org/10.4236/cmb.2017.72002