Abstract

This QSAR study concerns a set of nineteen (19) 5-cyano thiouracil synthesized by Fanté et al. It reveals importance of three (3) major descriptors in inhibiting antibacterial activity of SecA. These are lipophilicity, electrophilicity index and dipole moment, which has a greater contribution. First, molecular descriptors were determined by DFT method associated with theory level B3LYP/6-31+G(d,p). Then, theoretical lipophilia was calculated with Kowwin/LogP software. Thus, these molecular descriptors were combined with biological activities of said molecules by multiple linear regressions (MLR) to obtain the model. Finally, domain of applicability (DA) was defined by presentation of new compounds with improved biological activity. These must have key groups such as nitrosyl or nitro in their respective structures to have optimal activity.

1. Introduction

In recent decades, emergence of drug-resistant bacterial strains has become a major public health problem ^{1, 2}. Antibiotic resistance is worrying and could be, in near future, one of main causes of death in world ². Development of new drugs to prevent this antibiotic resistance is therefore paramount ^{3, 4}. Indeed, bacterial viability and virulence are essentially linked to SecA secretion pathway. Central driving force of this secretory pathway is critical for survival of bacterium ⁵. Thus, a drug capable of inhibiting this driving force would be potentially toxic for bacterium. The SecA protein is therefore the ideal target for design and development of new antibacterial therapies ^{5, 6}. Work has shown that 5-cyano thiouracil derivatives constitute a new family of molecules with SecA inhibitory activity ^{7, 8}. Quantitative Structure-Activity Relationship (QSAR) studies are often adopted for design and synthesis of more efficient bioactive molecules. In this fact, this work is proposed to determine a QSAR model of antibacterial activity of a series of derivatives of 5-cyano thiouracil using QSAR methodology. This QSAR study establishes quantitative correlation between structure of the compounds and their biological activities through a mathematical model. This model makes it possible to predict the activities and properties of new compounds, and to guide the synthesis of new molecules with improved antibacterial activities in order to effectively fight against antibiotic resistance. A series of 5-cyano thiouracil derivatives were synthesized and evaluated for their in vitro antibacterial activities against bacterial resistant strains by Fanté and al ⁸. These molecules showed significant inhibitory activity against SecA. Improving SecA inhibitory activity of 5-cyano thiouracil derivatives requires mastery of physico-chemical properties that govern it. This would help to effectively direct synthesis of new molecules based on the structure of 5-cyano thiouracil. This work is a descriptive and predictive study of SecA inhibitory activity of nineteen (Table 1) derivatives of 5-cyano thiouracil by applying quantum chemical method in order to model their biological activities. Calculations were performed at theoretical level B3LYP/6-31+G(d,p) using DFT method.

2. Material and Calculation Methods

This study was performed on a set of 19 molecules whose structures are reported in Table 1. Thirteen (13) molecules are used for the training set and six (6) for the validation with concentrations ranging from 6.25 to 50 µM. The range of concentration of these molecules allows us to define a quantitative relationship between antibacterial activities and molecular descriptors. Biological data are usually expressed as the opposite of the logarithm to base 10 of the activity (Log (MIC)). This allows us to have large numerical values when these molecules are highly active ^{9, 10}.

The calculations were performed with the Gaussian 09 software ¹¹. DFT methods are generally known to generate a variety of molecular properties [12-19] in QSAR studies. Except for lipophilicity which was calculated with KowWin/logP software, all other descriptors are determined from a B3LYP/6-31+G(d,p) level of theory optimization calculation. As for the modeling, it was performed using the multilinear regression method implemented in Excel ²⁰ and XLSTAT ²¹.

For the development of the QSAR model, eleven theoretical descriptors were calculated such as electronic energy (Eelectr), HOMO energy (E_HOMO), LUMO energy (E_LUMO), chemical hardness (ɳ), chemical softness (S), electrophilicity index (ω), chemical potential (µpot), dipole moment (μ_D), lipophilicity (LogP), ionization potential (PI), and electronic affinity (AE). Among these descriptors, the combination of three of them provided a good model. We have lipophilicity (logP), dipole moment (μD) and electrophilicity index (ω). According to the rule of Lipinski's rule, lipophilicity (LogP) is important for identifying similarity to a drug ²². The dipole moment (μD), on the other hand, reflects the intermolecular interaction ²³. Electrophilicity evaluates the ability of a molecule to promote electron transfer ²⁴. The calculation of the partial correlation coefficient between the studied descriptors is less than 0.70 (aij < 0.70); this means that these different descriptors are independent from each other ²⁵.

The quality of a model is determined according to certain criteria such as the coefficient of determination R², the standard deviation S, the correlation coefficients of cross-validation Q²_CV and Fischer coefficient F. The statistical indicators R², S and F relate to the adjustment of calculated and experimental values. They describe the predictive capacity within the model limits and allow to estimate the precision of values calculated on the training set ^{26, 27}. The cross-validation coefficient gives information on the predictive power of the model. The coefficients R² express the dispersion of theoretical values around the experimental ones. The quality of a model is better when the points are close to the adjustment line ²⁸. The adjustment of the points to the line can be evaluated by the coefficient of determination.

(1)

Experimental value of antibacterial activity

Theoretical value of antibacterial activity

The mean of the experimental values of antibacterial activity

The closer the value of R² to 1, the more the theoretical and experimental values are correlated. In addition, the variance σ² is determined by the following relationship (2):

(2)

Where is the number of independent variables (descriptors) is, the number of molecules in the test or learning set and the degree of freedom.

The standard deviation S is another statistical indicator used to evaluate the reliability and precision of a model:

(3)

The Fischer coefficient F is also used to express the level of statistical significance of the model, that is to say the quality of the choice of the descriptors constituting the model.

(4)

The coefficient of determination of cross-validation Q²_CV, which allows evaluating the accuracy of the prediction on the test set and is calculated by using the following equation:

(5)

The performance of a model, according to Eriksson and al ²⁹. is characterized by a value of Q²_CV ˃ 0.5 for a satisfactory model when for the excellent model Q²_CV is higher than 0.9. A training set of a model will perform well if the acceptance criterion R² - Q²_CV ˂ 0.3 is respected. Moreover, the predictive power of a model can be obtained from the value of the log (1/CMI)_theo/log (1/CMI)_exp ratio for the test set. The model is acceptable when the value of the ratio of theoretical and experimental activity tends towards unity.

The final step in model development is to define the domain in which a compound can be in which a compound can be predicted with confidence ^{30, 31}. The AD allows defining the area in which a compound can be predicted with confidence and avoiding hazardous extrapolation. The AD can also be defined in terms of activity value and type of molecules ^{30, 32}.

The Cook’s distance method is used. It is a measure of the influence of a suspicious point (outlier) in the results of a certain regression and is given by ^{33, 34}.

Where and are the vectors of the predicted observations for the entire data set and for the data set without the ith observation, respectively, and k is the number of parameters adjusted by the linear model with a variance The specific criterion used to exclude a supposed outlier was Di > 4/(n – k – 1), where n is the number of experimental points. The cutoff is determine of the Cook’s distance is expressed by Compounds that are Cook’s distance higher than the cutoff are highly influential points of the model.

3. Results and Discussions

The value of molecular descriptors and antibacterial activity nineteen (19) molecules are reported in Table 2.

The contribution of a descriptor to antibacterial activity in correlation with other descriptors in the regression equation depends not only on the sign of its coefficient but also on its own sign. When the descriptor and its coefficient have the same sign, the descriptor improves the biological activity. On the other hand, if they have opposite signs, the descriptor weakens the activity. Equation (6) below represents the best model based on the data in Table 2.

The model was obtained by combining the antibacterial activity to thirteen (13) molecules for the training set and six (6) for the validation.

(6)

With μ_D (expressed in Debye) and ω (expressed in eV)

According to this model, a low lipophilicity (Lo𝑔𝑃 < 0) contributes to improve the antibacterial activity of a molecule in the studied series. This is the case for molecules 13, 15 and 19. The model predicts that a high electrophilicity (ω) will improve the antibacterial activity of any molecule in the series. To help improve activity, the dipole moment (μD) must be low. Therefore, the molecule must be minimally polar.

The value of the partial correlation coefficients of the descriptors (aij) in the model, external validation log (1/CMI)_theo/log (1/CMI)_exp are reported respectively in Table 3 and Table 4.

The partial correlation aij between the descriptors is less than 0.70. This shows the independence of the descriptors used in the model.

External validation of the model was performed with molecules 6, 14,15,16,18 and 19.

The values of Log(1/CMI)theo/Log(1/CMI)exp ratios are close to 1, indicating the good correlation between the theoretical and experimental antibacterial activity of the studied molecules. The regression line between the experimental and theoretical antibacterial activity of the training set (blue dots) and the test set (red dots) is shown in Figure 2.

This model exalts four (03) descriptors which are the lipophilicity, the dipole moment and the electrophilicity index. Figure 3 below shows the coefficients (sign and importance) assigned to these descriptors.

According to Cook’s distances (Figure 4), only compounds 1, 15 and 19 are highly influential points of the model.

In addition, the diagram of coefficients (Figure 3) defining the contributions of the three descriptors in antibacterial activity in the model reveals that the contribution of dipole moment (μD) is very important. It is followed by electrophilicity (ω) and lipophilicity (𝐿𝑜gP). Therefore, the dipole moment is the priority descriptor in describing the antibacterial activity of 5-cyano thiouracil derivatives.

Thus, the 5-cyano thiouracil derivatives developed according to the QSAR model should be low polar, highly electrophilic and low lipophilic. In this perspective, we propose the following groups to improve the antibacterial activity:

- electroattractants such as nitrosyl NO, nitro NO₂ and carbonyl CO. In addition, the presence of these groups would give a strong electrophilic character to these molecules.

-The phenyl group

4. Conclusion

Quantitative structure-activity relationships, as a tool for rational molecular modeling, play an important role in the conceptualization of molecular leads in targeted and pharmacotherapeutic compound series. This requires the construction of a QSAR model from a chemically homogeneous series of compounds based on processes coordinated by internationally accepted principles. Therefore, the QSAR model must meet established standards in terms of reliability, reproducibility, robustness and predictability. In this study, the aim was to build a QSAR model around a series of 5-cyano thiouracil derivatives for antibacterial use. This work allowed us to identify lipophilicity, dipole moment and electrophilicity as predictive descriptors of the activity of these derivatives. This work gives us a direction for the design of new more active analogues. These will have to present in their respective structures key groups such as nitrosyl, or nitro to have an optimal activity. This study plays an important role in understanding the relationship between the physicochemical parameters of the structure and the biological activity. The analysis and use of the QSAR model, allows us to select the appropriate substituent and design new compounds with improved biological activity.

References