Abstract

This QSAR study was carried out on a series of twenty-five (25) amides herbicides and highlights the importance of four (4) key descriptors that contribute to the lethal dose . These are polarizability (Pol), lipophilicity (LogP), total energy (), and chemical potential (µ). First, the molecular descriptors were determined using the DFT method with the B3LYP/6-31+G(d,p) theory level. Next, the theoretical lipophilicity was calculated using the open-source software A/LogPS 2.1. These descriptors were combined with biological activity using multiple linear regression (MLR) to develop the model. Finally, the domain of applicability (DA) was defined to avoid any hazardous extrapolation, and it appears that all molecular structures can be used through modulation for the prediction of new analogs. These must contain key groups such as halogens (I, Br, Cl), delocalized π systems (benzene ring, conjugated double bonds), and sulfur- or phosphorus-containing groups in their respective structures in order to exhibit optimal activity.

1. Introduction

Today’s intensive agriculture use 90% of the pesticides available on the market, which comprise a range of more than 8,000 products sold worldwide ¹. In particular, herbicides play a crucial role in weed control and in optimizing crop yields ². In fact, herbicide residues can persist in the soil, seep into groundwater, and accumulate in the food chain, thereby exposing humans to various health risks ³. Several studies have identified links between chronic exposure to certain herbicides and adverse health effects, such as endocrine disruption, carcinogenic effects, and immune system dysfunction ⁴.

Given that there is a correlation between molecular structures and biological activity or toxicity, a QSAR study is conducted in this research to develop a mathematical model capable of predicting or explaining the toxicity of new compounds. This helps limit the excessive number of experiments—which can be time-consuming and costly—and reduces production costs ^{5, 6}. The agrochemists can then use the model to synthesize new herbicides with improved biological activity. This descriptive and predictive study was conducted on a series of 25 amide herbicide molecules with lethal doses () ⁷. Improving the LD₅₀ of the amide series requires the determination of certain descriptors through calculations performed at the B3LYP/6-31+G(d,p) theoretical level using the DFT method. These descriptors will then be combined with the lethal dose to develop a predictive model.

2. Materials and Calculation methods

This study was carried out on a set of 25 molecules, whose structures are shown in Figure 1. Seventeen (17) molecules were used for the training set and eight (8) for validation. The is used to measure a substance’s toxicity and is expressed in units of substance mass per body mass, i.e., mg/kg. It values range from 3.80 mg/kg to 416.87 mg/kg. Biological data are generally expressed as the negative of the decimal logarithm of the activity (). This allows us to obtain high numerical values when these molecules are highly active ^{8, 9}. The toxicity indicator is expressed by the potential defined by equation (1):

(1)

Where is the dose of a substance that causes the death of 50% of the test animal population (mg/kg).

The calculations were performed using the Gaussian 09 software in the gas-phase mode ¹⁰. DFT methods are generally known to generate various molecular properties ^{11, 12, 13, 14, 15} in QSAR studies. With the exception of lipophilicity, which was calculated using the A/logPS 2.1 software, all other descriptors are determined from a frequency-following optimization calculation at the B3LYP/6-31+G(d,p) theory level. As for the modeling, it was performed using the multiple linear regression method implemented in Excel ¹⁶ and XLSTAT ¹⁷.

Thirteen (13) theoretical descriptors were calculated for the development of the QSAR model. This includes: total energy (), HOMO energy (), LUMO energy (), energy gap (ΔE), chemical hardness (ɳ), chemical potential (μ), electrophilicity index (ω), ionization energy (EI), dipole moment (), electronegativity (χ), lipophilicity (LogP), polarizability (Pol), and electronaffinity (AE). Among these descriptors, we found that a combination of four (4) key ones allowed us to develop a reliable model. These are lipophilicity (logP), polarizability (Pol), total energy (), and chemical potential (μ). Lipophilicity is an important parameter that can aid in predicting a compound’s pharmacological activity, as its transport, its passage through membranes, and its pharmacological activity may be influenced by its partition between a lipid phase and an aqueous phase ^{18, 19}. Chemical potential is the variation in free enthalpy (G) upon the addition of a substance ; it plays a key role in the equilibrium of biological systems and the activity of molecules. It reflects a molecular system’s tendency to attract electrons or electron-rich-systems. Polarizability is one of the parameters that reflect molecular properties related to hydrophobicity and, consequently, to biological activities ¹⁸. The partial correlation coefficient calculated between the descriptors studied is less than 0.70 (aij< 0.70) ; this means that these different descriptors are independent of one another ²⁰.

3. Estimation of Predictive Power

The quality of a model is determined by certain criteria, such as the coefficient of determination R², the standard deviation S, the cross-validation correlation coefficients Q²_CV, and Fischer’s F-coefficient. The statistical indicators R², S, and F relate to the fit between the calculated and experimental values. They describe the model’s predictive capability within its parameters and allow for an estimation of the accuracy of the values calculated on the training set ^{21, 22}. The cross-validation coefficient provides information on the model’s predictive power. R² indicates the dispersion of the theoretical values around the experimental values. The quality of the model is better when the data points lie close to the fitted line ²³. The fit of the data points to the line can be assessed using the coefficient of determination

Where

The closer the value of R² is to 1, the better the correlation between the experimental and theoretical values.

Furthermore, the variance σ² isdetermined by equation 1:

(3)

Where k is the number of independent variables (descriptors) and n is the number of molecules in the test or training set, and n-k-1 is the number of degrees of freedom. The standard deviation S is another statistical measure used. It assesses the reliability and accuracy of a model:

(4)

The Fischer F-coefficient is also used to measure the statistical significance of the model, that is, the quality of the choice of descriptors that make up the model.

(5)

The cross-validation coefficient of determination (Q²_CV) is used to evaluate the accuracy of predictions on the test set and is calculated using the following equation:

(6)

According to Eriksson and al. ²⁴, a model’s performance is characterized by a Q²_CV value greater than 0.5 for a satisfactory model, and for an excellent model, Q²_CV is greater than 0.9. A model’s training set is considered to perform well if the acceptance criterion R²- Q²_CV< 0.3 is satisfied.

This validation is characterized by the R² (test) and R²_cv (test) statistics. Recently, several studies ^{25, 26} have shown that the R², R, and R²_cvstatistics are insufficient for assessing the predictive power of RQSA models. Consequently, other statistics must be examined. These parameters are known as “external validation criteria.” They are the criteria proposed by Tospha and Roy and Roy.

1),

2),

3)

4),

5)

In addition, Roy and Roy refined the prediction method for an RQSA model ^{27, 28}. They developed the metrics and ΔThese are metric values ; measures the proximity between the observed activity and the prediction. The metric values are calculated based on the observed and predicted activities.The advantage of metric values is that they can be used for both internal and external validation.

According to Roy and Roy, an RQSA model is acceptable if both criteria are met :

1)

2)

With:

and

: Coefficient of determination for molecules in the test or training set.

: Coefficient of determination for the regression between the experimental values and the predicted values for the test or training set.

: Coefficient of determination for the regression between predicted values and experimental values for the test or training set.

4. Applicability domain (AD)

The final step in model development is to define the domain within which a compound can be predicted with certainty ^{29, 20}. The domain of applicability (DA) allows us to define the range within which a compound can be predicted with certainty and to avoid any risky extrapolation. The AD can also be defined in terms of activity values and molecular types ^{29, 30}. The Cook's distance method is used. This is a measure of the influence of a suspect point (outlier) on the results of a given regression, as described in ^{31, 32}.

Where and are the 𝑛×1 vectors of predicted observations for the entire dataset and for the dataset excluding observation i, respectively, and k is the number of parameters estimated by the linear model with variance σ².The specific criteria used to exclude a suspected outlier was Di > 4/(n – k – 1), where n is the number of experimental data points. This threshold is determined by the Cook’s distance, which is expressed as 4/((n-p-1)). Data points with a Cook’s distance greater than this threshold are considered highly influential in the model.

5. Results and Discussion

Of the thirteen (13) calculated descriptors, only five (5) were significant in the model development using multiple linear regression (MLR). All descriptor values for the seventeen (17) molecules in the test set and the eight (8) molecules in the validation set are presented in Table 1

The contribution of a descriptor to , when correlated with other descriptors in the regression equation, depends not only on the sign of its coefficient but also on the sign of the descriptor it self. When the descriptor and its coefficient have the same sign, the descriptor enhances biological activity. Conversely, if they have opposite signs, the descriptor weakens the activity. Equation (2) below represents the best model based on the data in Table 1.

N=17; R²= 0.824; Q²_CV = 0.653; S= 0.921; F= 10.21; R² – Q²_CV = 0.171

According to the model, a high polarizability (Pol) value helps improve the.Additionally, lipophilicity, total energy, and chemical potential must be low to enhance this activity.

The values of the partial correlation coefficients for the descriptors (aij) in the model are shown in Table 2.

The partial correlation coefficients between the descriptors studied are less than 0.70, indicating that the descriptors are independent of one another.

The regression line between the experimental and the theoretical for the training set (blue points) and the test or validation set (red points) is shown in Figure 2.

The robustness and predicted reliability of the developed QSAR model were evaluated using the criteria proposed by Trospha and Roy.

Trospha’s Criteria

1),

2) ,

3)

4) ,

5)

All criteria have been verified and confirm that the model is suitable for predicting . Let’s check Roy’s criteria.

Roy and Roy's Criteria

1)

2)

With: = 0.679 et = 0.523

Criterias are also verified.

External validation also confirms the validity of the QSAR model.

The model highlights five (5) descriptors, four (4) of which are significant: lipophilicity, total energy, and chemical potential. Figure 3 below shows the coefficients (sign and importance) assigned to these descriptors.

An order of decreasing importance of the descriptors gives us: lipophilicity (LogP) > polarizability (Pol) > chemical potential (µ) > total energy.

For a better understanding of the model’s predictive power, plots showing the agreement between the experimental and theoretical values have been generated. Figure 4 shows these plots.

These curves show minimal deviation. The model is therefore acceptable for prediction purposes.

To clarify the model’s limits of application, its domain of applicability has been determined. The Cook distance provides further details.

With p denoting the number of descriptors in the model and n denoting the number of molecules in the training set.

This demonstrates the absence of outliers. The results of the various validations and the analysis of the applicability domain show that these molecules have a significant structural influence on the model. They can be used to predict the of amides herbicides and their derivatives using the established model.

6. Conclusion

The QSAR study on the series of amide herbicides allowed us to identify four (4) key descriptors for predicting the of these molecules and the results of the internal and external validation criteria suggest that the model is predictive. Among these descriptors are polarizability (Pol), lipophilicity (LogP), total energy (), and chemical potential (µ). In addition, it is clear that lipophilicity plays a key role in this model, followed by polarizability. Since the polarizabilities of the molecules must be high, modulation with electron-rich groups such as halogens (I, Br, Cl) and delocalized π systems (benzene ring, conjugated double bonds), as well as groups containing sulfur or phosphorus, could improve activity. The domain of applicability indicates the absence of outliers. All of these molecules can therefore be used in the prediction. Thus, this study opens the way for the synthesis of new amide herbicides with improved activity.

References