1. The support vector machine (SVM) is a supervised learning algorithm applied to both classification and regression problems. The fundamental objective of this process is to determine an optimal hyperplane that separates at most two classes in a p-dimensional feature space. This improves the overall ability of the model to generalize when dealing with unknown data¹⁶. For a dataset of labeled pairs ) …… ) where  and , the decision function or optimal separating hyper plane: is obtained by estimating the weight vector  and the intercept. For linear SVM, support vectors that meet the conditions and , define the outer limits of the two classes, and the separation distance between these two hyperplanes given by, , is maximized. Once the parameters w and b have been determined, any input vector  can be classified using the function:; a positive result assigns the sample to the positive class (BBB+), while a negative value corresponds to the negative class (BBB-).When the training data is not linearly separable, a non-linear SVM projects the input vectors into a higher dimensional feature space using a kernel function.

2. k-nearest neighbors (k-NN) algorithm is a supervised non-parametric approach used for both classification and regression modeling. Unlike parametric methods, it assumes no underlying data distribution. For a given input, x_j, the algorithm identifies the k-nearest training data points according to a predefined distance metric and assigns a class label or predicted value based on the majority vote or average response of these neighbors. In the present study, the nearness is measured by the Euclidean distance between  and as follows:

The 1-NN algorithm represents the simplest form of k-NN, where only one neighbor is considered. The input x_j is classified by assigning it the same label as its nearest sample¹⁷.

3. A decision tree (DT) can be defined as a flexible supervised learning algorithm that is used for classification and regression, based on the division of the data. The process of partitioning the data, which is carried out recursively, involves subdividing the dataset according to the feature that allows the most efficient division at each stage. This approach results in a hierarchical tree structure, where internal nodes represent feature-based decisions and leaf nodes correspond to final predictions. Over the last few decades, a set of algorithmic methods dedicated to the construction of decision trees has emerged. The aim of these algorithms is twofold: firstly, to increase the accuracy of the models, and secondly, to adapt to the diversity of data sources¹⁸. Among them an optimized version of CART (Classification and Regression Tree), implemented as Decision Tree Classifier, is available in scikit-learn python package. 
4. The Random Forest (RF) algorithm is an ensemble-based machine learning approach that aggregates the predictions of multiple decision trees to improve accuracy and minimize overfitting. The tree generation process relies on random sampling of subsets of the training data and features available for each tree. This random process has the effect of increasing model diversity and consolidating generalization performance. During prediction, each tree contributes to a result. The final result is obtained by averaging the predictions in regression tasks or by applying majority voting in classification. As a result, Random Forest models demonstrate greater robustness and generalization capability than individual decision trees.
5. The concept of “boost” refers to a set of algorithms designed to optimize the predictive capabilities of a learning system by increasing its performance, from weak to strong. Intuitively, these algorithms merge a number of weak performance learnings into a single strong performance model, significantly improving the results. Thus, boosting algorithms work by sequentially training a set of weak learning models and combining them for prediction where subsequent learners focus more on the errors of previous learners improving prediction performance to ultimately obtain, through this model, strong learners. The superiority of boosting lies in its serial learning nature, which enables excellent approximation and generalization¹⁹. Among the various kinds of boosting approaches, the highly effective tree boosting methods, Gradient Boosting Machine (GBM), have been used for binary classification-based QSAR models of logBB permeability predictions.

Binary classification assessment methods

Internal 10 fold cross-validation scheme was applied to the training dataset in order to identify the models with the best predictive performance. The final evaluation of the classifiers was carried out using an independent test set, the aim of which was to assess their generalization capability. For binary classification performance evaluation, several scalar measures were considered, including accuracy (Q), precision (Pr), recall (Re), specificity (Sp), F-score (F) and Matthews correlation coefficient (MCC). These measures are defined mathematically as follows:

The quantities TP, FN, TN and FP are defined as true positives, false negatives, true negatives and false positives respectively. Beyond standard metrics, model performance was also assessed using the receiver operating characteristic (ROC) curve and its associated area under the curve (AUC), which provides a summary measure of classification accuracy.

Models explainability

“Black box” models are characterized by their inability to provide decisions that can be clearly interpreted and/or explained. Transparent models, on the other hand, have the ability to allow direct understanding of their internal reasoning. In drug research, for example, the explainability of models plays a crucial role, as the decisions taken must be justifiable. Interpretability is therefore just as important as the accuracy of predictions²⁰. In recent years, Lundberg and Lee have developed a unified framework for interpretability prediction namely SHAP (SHapley Additive exPlanations)²¹. This explanation model suggests taking an additive feature contribution method as a weighted sum of the binary features:

With M, the number of simplified input features, and the shapely values (weights) are defined as follow:

Where is the original model,is the number of non-zero entries in , and represents all vectors where the non-zero entries are a subset of the non-zero entries in a simplified input . According to Lundberg et al., only one possible explanation model  satisfies equation 18 and three properties (local accuracy, missingness and consistency)²¹. SHAP, based on a concept from the field of cooperative game theory (Eq.19), provides model transparency for any machine-learning algorithm to define feature influence at the individual prediction level (i.e., local interpretability). In the perspective of BBB permeability prediction, Shapley values are assigned to each feature in order to estimate their importance and the direction of their impact for a particular prediction. Strongly positive SHAP values indicate that the molecular descriptor helps to predict molecules that cross the BBB, whereas strongly negative SHAP values indicate that the molecular descriptor helps to predict molecules that do not cross the BBB. Several variants of the SHAP algorithm have been reported: Kernel SHAP (model-agnostic), Tree SHAP (specifically applicable to model derived from trees) and Deep SHAP (specialized for deep learning models). Model explanation and analysis were performed using the SHAP package in Python (v. 0.43.0), which enables the quantification of each contribution of feature to model predictions²².

 

RESULTS AND DISCUSSION

 

Data set distribution analysis

According to data gathered from published studies, a total of 1,000 compounds linked to BBB permeability were compiled with 137 BBB- and 863 BBB+ after data separation. The chemical diversity of the compounds used in both the training and external validation sets was extensively analyzed by Shaker and coworkers to support the construction of a robust and reliable binary classification model. Thus, similar compounds were discarded on the basis of Tanimoto similarity, preserving the uniqueness of the compounds and avoiding biased and over fitted models with an abundance of similar compounds¹. The success of the machine-learning algorithms depends on the quality of the data in order to obtain a generalized predictive model of the classification problem. Therefore, to ensure optimum data quality and optimize the performance of the machine learning models, a rigorous normalization procedure was implemented. This involved centering each feature around a mean equal to zero and scaling it to a standard deviation of one. Like redundancy and non-standardizing, unbalanced datasets have a serious impact on the optimization performance of binary classification machine learning models. Thus, using the SMOTE method, we obtained 1,726 compounds (1000 evaluated chemicals and 726 synthethic compounds), divided into two balanced groups for the implementation of models to assess the ability of drugs to penetrate the BBB. Three hundred and forty-six (346) molecules (166 BBB- and 180 BBB+) serve as the test set to evaluate the generalization ability and reliability of the model and the remaining 1,380 molecules were used to build the prediction models, which were divided into 697 BBB+ and 683 BBB.

Feature involved in models

Feature selection methods have been used for dimension reduction, and this technique is essential for mitigating the effects of the curse of dimensionality and improving the performance of algorithms⁹. The tree-like diagram, constructed using squared Pearson correlation coefficients, was divided horizontally to form forty (40) clusters of descriptors, each containing strongly correlated variables sharing similar information¹⁰. After grouping the descriptors, we selected one variable from each group, i.e. the one that best correlated with its centroid. Thus, the gain in cohesion was 50.77%. This percentage measures the correspondence between the descriptors of the cluster and its centroid (the first PC obtained by applying PCA to it). ClustOfVar algorithm for detecting a partition extracted from a tree-like diagram obtained by hierarchical representation of quantitative variables have been used. Each stage of the hierarchy is thus created by successively merging the clusters of the lower stage. This merge is initiated by the lowest stage with the most homogeneous partition, i.e. the partition whose cluster contains only one variable¹⁰. The difference between PCA and our clustering method built using the ClustOfVar algorithm is that the centroids of the obtained clusters can be correlated. Therefore, the correlation matrix of the 40 descriptors was performed to detect residual correlations, which could negatively affect the models by increasing variance. Finally, after removing redundant, non-informative and irrelevant descriptors from the original high-dimensional dataset, we obtained 10 informative descriptors for BBB permeability prediction. The correlation matrix of the ten most informative and best selected descriptors was then constructed using the method described by N’guessan et al.⁹ 

It appears highly improbable that any of the selected descriptors will be correlated with another, with all R² measuring no more than 0.40 (Figure 1). This suggests that multi-collinearity, a consequence of the curse of dimensionality, has been addressed. 

Table 1 shows the 10 molecular descriptors obtained using a data mining procedure that integrates hierarchical clustering and correlation-based analysis. This approach allows us to assess both the strength and direction of relationships between variables. These descriptors are similar to those used in previously published qualitative QSAR models designed to predict the permeability of pharmaceutical compounds across the blood-brain barrier^1,23. As shown in Table 1, a large proportion of the obtained descriptors belong to the autocorrelation descriptor class, with descriptors VSA_Estate8, AATSC0c, ATSC5pe, GATS1pe, ATSC3pe, and GATS2are. 

In molecular modelling and QSAR, it is common practice to use autocorrelation descriptors to describe how the physicochemical properties of molecules vary according to their spatial distribution structure. These descriptors are derived from a conceptual partitioning of the structure of the molecule and the application of an autocorrelation function. Typically, spatial autocorrelation descriptors are computed by considering the atoms of a molecule as discrete spatial points, with an atomic property assigned to each point. The descriptors are then weighted according to physicochemical parameters such as atomic weight, volume of van der Waals of considered atom, atomic electronegativity, atomic polarizability, atomic charge, or covalent radius²⁴. In this work, E-state indices (SdO and SsssN) that encode electronic and topological environment of each atom are used as the most informative descriptors in classification-based QSAR models predicting blood-brain barrier permeability (logBB)²⁵.

Class imbalance handling

As indicated in the previous study, we use the SMOTE approach to solve the class imbalance problem. We then proceed to a quantitative and qualitative assessment of its impact on the initial or original dataset⁹. A quantitative comparison between the synthetic (Ds) and true (Do) probability distributions was performed using the Jensen–Shannon Distance (JSD) across the ten most informative molecular descriptors. The resulting JSD scores, reflecting the degree of similarity between synthetic and original distributions, are presented in Table 2. As outlined in Table 2, the two distributions – the original one prior to SMOTE and the synthetic one following SMOTE algorithm are indistinguishable, with all JSD values approaching 0. Before modeling, a qualitative comparison between the two minority class distributions was performed for two informative descriptors selected based on their JSD scores (minimum and maximum) to further study the impact of the SMOTE algorithm. 

Kernel density estimation (KDE), a technique that estimates and plots probability distribution functions, was applied⁹. As demonstrated in Figure 2, there is a significant overlap in the probability distribution functions between the original and synthetic distributions. This indicates that the SMOTE algorithm effectively preserves data quality and maintains the local structure of features⁹. The finalized dataset encompasses a total of 1,726 molecular observations, which are associated with 10 informative descriptors. As illustrated in Table 3, a concise overview of the samples employed in the experimental procedures, both for training and testing, is provided. 

Hyperparameter values of ML models

Following the identification of the optimal methods for dimensionality reduction and handling class imbalance problem, ML-based QSAR models for BBB penetration prediction were implemented. Prior to model development, a deep grid search with 10-fold cross-validation was constructed to adjust the hyperparameters of each classifier, except for the RF model where default values were used⁹. Table 4 provides the best hyperparameters that gave the best QSAR performance based on the statistical training of the models used. 

Performance of ML models

In this study, classification models were constructed utilizing five distinct machine learning (ML) algorithms. After model construction, both internal and external validation schemes were employed to assess model reliability. 10-fold cross-validation scheme was used for internal validation using training dataset consists of 1,380 molecular observations divided into 697 BBB+ and 683 BBB- compounds (Table 3) and 10 descriptors. In this procedure, the training dataset is stochastically partitioned into ten distinct splits. For each iteration, nine of these splits are used for training the model, while the remaining split is used to assess its performance. This process is repeated ten times so that every split was used once for validation, and the average of all results was taken as the final performance measure.

The performance of ML binary classifiers was compared based on an internal validation scheme using the training dataset. As shown in Table 5, the results of the five ML binary classification models are presented according to the evaluation measures defined and used in equations 12 to 17. The table clearly reveal that the decision tree classifier exhibits the weakest performance across all evaluation measures. Conversely, SVM and k-NN classifiers appear to have similar performance, although they differ in their ability to correctly classify BBB+ molecules. According to Table 5, GBM model outperforms all other binary classifiers in terms of Q (92.90%), Pr (94.84%), Re (90.61%), Sp (92.65%), and MCC (0.86). The next best classifier is RF with Q = 91.74% for10-fold internal cross-validation. Considering Q (%), Pr (%), F (%), and MCC, the classifiers were ranked in descending order of performance as GBM, RF, k-NN, SVM, and CART-DT. Based on the evaluation metrics, the GBM estimator was identified as the most effective logBB permeability prediction model of drug molecules. To further confirm its stability and predictive strength, GBM model was tested on an independent dataset that had not been used during training.  As shown in Table 5, he GBM classifier achieved a correct classification rate of 91.04% on the test dataset, accurately identifying 88.89% of the BBB+ molecular observations.   The Ability of recommended classifier to recognize false-alarm molecule on the test dataset is good with Sp = 91.17 %; and the Pr, F and MCC scores are 93.57%, 93.37% and 0.82 respectively.

As illustrated in Figure 3, the ROC curves of each classifier on the external test set are presented. It appears that all classifiers demonstrate superior performance in comparison to the random classifier, which is represented by the diagonal line . Therefore, the area AUC scores are as follows: 0.85 for the CART-DT classifier, 0.90 for the SVM and k-NN classifiers, 1.0 for the RF and GBM classifiers. The study exhibits the effectiveness of our classifiers, particularly ensemble models, in accurately 

between blood-brain barrier permeable and non-permeable pharmaceutical compounds. This result therefore highlights the crucial role of effective feature engineering methodologies in improving model accuracy and overall predictive performance.

Applicability domain

In this study, binary classification-based ML models were designed to evaluate the blood-brain barrier (BBB) penetration potential of pharmaceutical compounds encompassing broad-spectrum chemical diversity. Since QSAR models are not universal, defining the applicability domain AD is essential to distinguish reliable interpolations from less reliable extrapolations. Following validation, the applicability domain of GBM classifier was analyzed through the PCA bounding box method. The first three principal components (PCs), derived from the ten most informative descriptors obtained, capture more than half of the total variance of the dataset²⁶. As can be seen in Figure 4, test set observation points are colored in red and the molecular observations of training dataset are colored in blue. An analysis of the prediction reliability using PCA bonding box shows that only a few molecular observations reside outside the AD. This incorrect prediction could be a consequence of the oversampling method implementing by SMOTE algorithm that inserts synthetic examples on the original dataset. Consequently, it is assumed that the predictions for 3 of the 346 compounds will be incorrect, thereby suggesting that the selected model captures the majority of the information present in the ten informative features. Furthermore, this result reveals that the test set molecular observations exhibit a structural similarity greater than 99% to those in the training set molecular observations, confirming strong overlap between the two datasets and reliable representation within the applicability domain of classification-based ML models.

In conclusion, we can say that our models can be used with high accuracy to predict whether a compound can effectively penetrate the brain or not.

Model comparisons

Using a larger number of descriptors (features) when training machine-learning models can introduce several important drawbacks especially in drug discovery. Although the models display satisfactory predictive performance, binary classification approaches that incorporate a large number of descriptors are susceptible to overfitting and exhibit limited generalization to unseen data. This is because high-dimensional descriptors often contain redundant or highly correlated variables, a phenomenon that is often referred to as the curse of dimensionality. Therefore, in our study, we trained our models with the few descriptors make it simpler to extract biological or chemical meaning from model outputs. Thus, the predictive capabilities of our binary classification-based GBM model exceed those of previously published ML models for blood–brain barrier (BBB) penetration prediction, highlighting its improved accuracy and robustness (Table 6).

Explaining ML model

In recent years, the need for interpretable models has been increasingly recognized in research, industry, and regulatory contexts²⁷. Given the potential risks of deploying opaque or “black box” models in clinical and preclinical applications, explainable artificial intelligence (XAI) approaches have become a top priority. The practice of XAI models is essential to justify predictive results and ensure the reliability, safety and transparency of preclinical or clinical decision-making²⁸. In order to meet this objective, SHAP was developed and validated to interpret how the proposed GBM estimation algorithm predicts class labels for chemical compounds. Here, Tree-SHAP, a variant of SHAP algorithm, is applied to study the effect or influence of selected informative descriptors on the prediction of chemical class (BBB+ vs BBB-) of pharmaceutical compounds studied with GBM model. Thus, multiple visualization techniques can be applied to examine and illustrate the distribution of SHAP values, providing both local (instance-level) and global (model-level) explanations of the predictive behavior. As illustrated in Figure 5(a), a sample-wise SHAPE summary plot is employed to demonstrate which features are the most significant overall. In this plot, the x-axis represents the Shapley values, whereas the y-axis lists the descriptors and their corresponding value distributions, sorted according to their mean absolute Shapley values, highlighting the relative importance of each feature. Each point represents a Shapley value corresponding to a specific molecular observation, with the color indicating the magnitude of the associated descriptor. As shown in the color bar, sky blue indicates the lowest values and magenta the highest. The descriptors are displayed along the y-axis in descending order of importance, reflecting their relative contribution to the model’s predictions²⁹. With GBM classifier, averaged and centered Moreau-Broto autocorrelation of lag 0 weighted by Gasteiger charge (AATSCOc), geary coefficient of lag 2 weighted by Allred-Rochow EN (GATS2are) and geary coefficient of lag 1 weighted by Pauling EN (GATS1pe) are the top three important descriptors.

Furthermore, Figure 5(b) shows the MAS (mean absolute SHAP) value for specific informative descriptors, serving as a metric of feature importance. MAS values provide an effective measure of the effect of selected informative descriptors in decision making to classify a query compound. The more the mean absolute values, the more the selected descriptors influence overall in separating compounds into class BBB- vs class BBB+. This will help interpret the sample-wise SHAP values shown in Figure 5(a). Shapley values are a means to describe the influence of selected descriptors in the model prediction, and the direction of this influence can be determined using the positive or negative values assigned to a particular descriptor for each molecular observation²⁹. As the SHAP values indicate the direction of the predictions (towards BBB- for negative values and towards BBB+ for positive values), it can be concluded that compounds with higher AATSCOc values decrease the probability of the BBB+ class, while lower values of this descriptor appear to increase the probability of the BBB+ class. In the other words, it appears that highly charged molecules, such as macromolecular drugs, recombinant proteins and nucleic acid, are not likely to cross the blood-brain barrier³⁰. Electronegativity auto-correlation is a graph-based molecular descriptor that quantifies how the electronegativity values of atoms in a molecule are correlated at a specific topological distance (number of bonds apart)²⁴. In this work, GATS2are and GATS1pe are identified as the next most influential descriptors for predicting BBB permeability, reflecting electronegativity auto-correlation. These two descriptors are slightly correlated with  because they reflect the same properties calculated in two different scales³¹. Electronegativity scale formulated by Pauling analyses or reflects single or multiple bond dissociation energies. And, as we can see in Figure 5(a), GBM classifier concludes that lower values of GATS1pe have high SHAP values. Therefore, the likelihood of BBB+ permeability increases as the amount of energy required to break a bond decreases. Electronegativity molecular property implemented in GATS2are uses the formulation of Allred and Rochow electronegativity that measures an atom’s tendency to attract electrons in a chemical bond. It defined in terms of the electrostatic force or Coulombic attraction exerted by the effective nuclear charge () on valence electrons located at the covalent radius () of the atom³¹. Therefore, the higher the effective nuclear charge of the atom, the higher the electronegativity. If atoms with a high electronegativity value are often connected at a distance d = 2 Å in the molecular graph, the value of the descriptor will be high and the autocorrelation will be strong, which will increase the probability of BBB+. Whilst the general trend between the top three descriptors values and the Shapley values allows for the identification of linear relationships, saturation effects emerge in the impact of these characteristics on the model's predictions.

Limitations of the study

The first limitation of this study is its dependence on a single dataset from Shaker et al.¹ Although GBM classifier achieved strong predictive performance, its clinical or preclinical relevance remains limited by the dataset’s size and diversity. While the dataset provides a solid foundation for algorithm development, its restricted scope warrants caution when generalizing these findings to real-world settings^3,6. The second limitation of this QSAR investigation pertains to the quality of the underlying data, which is inherently dependent on the accuracy and reliability of the molecular descriptors employed in model development. Molecular descriptors mathematically capture the chemical information embedded in molecular structures. As molecules may exist in various conformations, choosing the correct conformer is as important as selecting suitable descriptors, since conformational changes can alter descriptor values. Therefore, accurate molecular geometries are fundamental to constructing reliable QSAR models, particularly those employing quantum-chemical or 3D descriptors, as they ensure several benefits: (i) enhances data quality and model robustness; (ii) reduces overfitting and training complexity by avoiding the time-consuming hyper-parameter adjustment process; (iii) provides better biological relevance for structure–activity relationships and (iv) improves comparability and transparency of model development³². Another notable limitation of this study stems from the approach used to balance the dataset. Specifically, the application of the SMOTE algorithm, while effective in mitigating class imbalance, may introduce synthetic samples that do not fully represent the actual data distribution or the fit between the training and test data. This may increase the risk of overfitting and potentially distort class boundaries, thus affecting the generalizability of the model to unobserved data. 

 

CONCLUSIONS

 

In this study, we developed non-animal predictive models to assess the ability of drug or pharmaceutical compounds to penetrate the blood–brain barrier (BBB), providing an alternative to traditional in vivo testing. The construction of robust and accurate predictive models necessitates the use of a dataset that is sufficiently large, chemically diverse, and well-balanced across classes. Using ClustOfVar algorithm and correlation matrix technique, only 10 molecular informative descriptors of 1,726 (original and synthetic) compounds with different structures were used. Then, five binary machine learning classifiers (SVM, k-NN, CART-DT, RF and GBM) used to predict whether a query compound is BBB permeable or not were developed and validated using 10-fold cross-validation. Since with a large or very large number of descriptors the risk of likelihood of overfitting and unexplainability increases, our models were trained with the few descriptors to make it simpler to extract relevant biological or chemical meaning from model outputs. The accuracy of these classifiers ranged from 77.68 () to 92.90% (, and the MCC ranged from 0.57( to 0.86 ( in internal cross-validation.

The best model, GBM, has a Q of 91.04%, a Pr of 93.57%, a Re of 88.89%, a F-score of 93.37%, a Sp of 91.17%, a MCC 0.82 and AUC of 1.0 in external validation demonstrating that the collection of few and more informative descriptors can more accurately distinguish whether pharmaceutical compound can cross the blood-brain barrier. Additionally, the SHAP interpretability framework was employed to enhance model transparency and to elucidate the relative importance of key molecular descriptors influencing prediction results. The SHAP analysis revealed that two primary factors, such as the spatial distribution of atomic charges and atomic electronegativity, play a critical role in determining BBB penetration predictions. Overall, the explainable GBM classification model developed in this study shows strong potential as a predictive and screening tool to identify drug candidates targeting the central nervous system (CNS) or having a better pharmacokinetic profile.

 

ACKNOWLEDGEMENTS

 

The authors wish to thank the Laboratory of Fundamental and Applied Physics (LFAP) at Nangui ABROGOUA University, Côte d’Ivoire, for making available the facilities that supported this research.

 

AUTHOR’S CONTRIBUTION

 

N’guessan A: performing the data collection, curation, the study, and writing the original draft. Mélèdje D:  checking and correcting python code.  Akonan L:  supervision methodology and intellectual input. Kouakou JLK: literature review, research analysis and data inspection. Moussé L:  formal analysis and conceptualization. Kéita M: formal analysis and conceptualization. Kré R: data investigation and intellectual input. Ziao N: supervision methodology and review. Megnassan E: formal analysis, supervision methodology and review. All authors have read and agreed to the published version of the manuscript.

 

DATA AVAILABILITY

 

The empirical data used to support the study's results can be obtained upon request from the corresponding author.

 

CONFLICT OF INTEREST

 

The authors declare that no conflict of interest is associated with this study.

 

REFERENCES