In a typical drug discovery scenario, we often deal with large numbers of compounds, their associated properties, and activities gathered from literature and/or inhouse experimental data sources. Often, we build Quantitative Structure Activity Relation (QSAR) models, an essential technique in cheminformatics, that allows us to predict the properties or activities of compounds based on molecular descriptors. In turn, this permits access to ultra-fast property/activity predictions, across ultra-large chemical spaces, amenable in both structurally-enabled and non-structurally-enabled molecule design projects.
Feature Representation for QSAR Modeling
As the first step of constructing an effective QSAR model, molecule input formats, for example the 1D-SMILES string or 2/3D molecule conformations, are converted into meaningful features, known as descriptors. These descriptors can include:
- Physicochemical properties: Scalar descriptor values derived from the physical characteristics of a molecule, such as molecular weight, logP, polar surface area, hydrogen bonding properties (acceptor/donor) etc.
- 2D fingerprints: Bit vectors encoding molecular substructures, reflecting the presence of certain substructures, paths and fragments.
- Topological and connectivity indices: Descriptors derived from a 2D-molecular graph representation of a molecule, capturing information on molecular size, shape, branching and atom connectivity (e.g. Kier-Hall connectivity indices).
- Cresset XED 3D field descriptors: Local extrema in the electrostatic and shape fields of a molecule, modeling the shape and electrostatic character of a ligand in terms of how a protein “sees” it.
QSAR modeling harnesses both linear and non-linear relationships between molecular descriptors (e.g. 3D descriptors, topological indices, 2D fingerprints, physicochemical properties) and target endpoints, to build predictive models that enable the virtual screening and prioritization of compounds.
2D-ML-QSAR Modeling in Flare
Flare is a powerful platform for building both 3D and 2D QSAR models. Electrostatic and volume descriptors generated using Cresset’s XED force field can be used to build Field QSAR1 and machine learning QSAR models, both of which are incredibly performant when seeking to predict biological activity. However, generating 3D QSAR model requires a reference bioactive 3D conformation to generate alignments for all compounds, which is an essential step in the derivation of 3D field descriptors and ‘de-noising’ the QSAR model. In cases where the 3D bioactive conformation of the reference ligand is unknown, machine learning-based QSAR models can be developed harnessing 2D descriptors, which are either calculated implicitly on-the-fly within Flare or can be imported from RDKit, or other external property services.
One challenge in QSAR modeling is avoiding overfitting. Models that use too many descriptors may perform well on the training set but often fail to predict accurately for the new compounds outside the training set. To alleviate this, we can use QSAR models which are inherently robust to collinearity and multi-collinearity such as Gradient Boosting machine learning models. As an alternative, we must carefully select relevant descriptors.
Gradient Boosting Model in Flare
Flare has further expanded its QSAR capabilities with the introduction of Gradient Boosting Machine Learning models2. Gradient boosting QSAR models capture complex and non-linear relationships between molecular descriptors and activity, inherently prioritizing important descriptors and minimizing overfitting to irrelevant ones. As such, Gradient Boosting models are inherently robust to collinearity and multi-collinearity, as their decision-tree-based architecture naturally prioritizes informative splits and down-weights redundant descriptors. This makes them well-suited to high-dimensional descriptor sets, allowing for effective model training without pre-filtering using methods such as Recursive Feature Elimination (RFE).
Case Study: hERG Ion Channel Activity Prediction
Here we present an example of building a descriptor-based Gradient Boosting machine learning QSAR model to predict cardiotoxicity related to the hERG channel inhibition potential of compounds, which is crucial for evaluating cardiac safety during drug development. In this experiment, we utilized the ToxTree hERG dataset3 for model training and evaluation. This dataset encompasses 8,877 compounds stored as SMILES strings, covering a diverse set of unique chemistries, each with an associated hERG pIC50 value. The dataset was standardized through conversion to canonical SMILES and 208 physical-chemical, topological and connectivity descriptors were calculated using RDKit.
All 208 RDKit descriptors were scaled, and a correlation matrix was generated using Python script4 to gain an initial understanding of the prevalence of multi-collinearity within the descriptor space (Figure 1). In Figure 1, each cell represents the Pearson correlation coefficient between two descriptors, with the colour scale indicating the degree of correlation. The presence of highly correlated features (red regions) suggests potential redundancy in the dataset, which may lead to overfitting in machine learning models. Low-correlation regions (green/light blue) indicate diverse, independent descriptors contributing unique information. In this case strong descriptor-descriptor correlations were not abundant, however, some descriptors are worth further monitoring. If overfitting is evident while building the final model, removal of some of the correlated descriptors could be beneficial.
Figure 1. Feature correlation matrix for the ToxTree hERG dataset2, showing a reduced number of descriptors for clarity (some of 208 RDKit descriptors are not shown). The color scale indicates the degree of correlation between descriptors. Dark red (1.0): Strong positive correlation (highly similar descriptors). Dark blue (-1.0): Strong negative correlation (one descriptor increases as the other decreases). Green (≈ 0.0): Weak or no correlation (independent descriptors).
As a diagnostic step to assess the nature of the relationship between molecular descriptors and hERG pIC50, we first trained both a 5-fold cross-validated Linear Regression model and a Gradient Boosting (GB) model on the full dataset. The goal was to determine whether the underlying structure of the data was primarily linear or non-linear or have multicollinearity problem, where two or more predictor variables are highly correlated, making it difficult to determine their individual effects on the dependent variable. The GB model significantly outperformed the linear model, achieving a notably lower root mean squared error (RMSE), suggesting that the descriptor–activity relationships are either non-linear or affected by multicollinearity. Based on this insight, we proceeded with a full model development pipeline using Gradient Boosting, including hyperparameter optimization and model validation, in Flare V10 (Figure 2). An r² test set > 0.5 indicates that the model has predictive power. The r² delta (difference between cross-validated training and testing r²) is 0.041 which, in addition to an RMSE delta of 6.59%, indicates that we have not overfitted to the training data.
Figure 2. Gradient Boosting model performance (Left). Predicted vs Experimental activity plot for Training set CV and Test set (Right).
Avoiding Overfitting and Descriptor Selection with Flare Python API
A simple alternative approach to avoid overfitting is to remove descriptors with missing values (this is done automatically in Flare), descriptors with values constant across the whole dataset, and descriptors which are multi-collinear, that being, descriptors which themselves are highly correlated.
Although intuitive and simple to implement, simply eliminating low variance and highly correlated descriptors comes with limitations, most notably neglecting the causal relationship between such descriptors and the target property, which may cause to inadvertently discard descriptors that contribute meaningfully when combined with others. An alternative approach, although more complex, is RFE. RFE offers a more informed approach to descriptor removal by incorporating descriptor selection into the model training process. It iteratively removes the least important descriptors based on their impact on model performance, retaining only those that are truly predictive in the context of the full descriptor space. This supervised approach reduces the risk of overfitting while preserving the most informative features.
Two Python scripts, written by Cresset via the Flare Python API, are available which afford the user both strategies: simple descriptor removal based on variance and multi-collinearity thresholds and descriptor removal through RFE.
Conclusion
Effectively managing descriptor intercorrelation and variance is vital for developing robust QSAR models. Advanced features offered by Flare V10, including Gradient Boosting QSAR machine learning models and scripts developed with the Flare Python API for descriptor selection, provide powerful tools to enhance model performance and reliability in drug discovery.
References
- Flare™, Cresset®, Litlington, Cambridgeshire, UK; https://www.cresset-group.com/software/flare/; Cheeseright T., Mackey M., Rose S., Vinter, A.; Molecular Field Extrema as Descriptors of Biological Activity: Definition and Validation J. Chem. Inf. Model. 2006, 46 (2), 665-676
- (a) A. Knoll, A. Natekin, Gradient Boosting Machines, a Tutorial. Front. Neurorobotics 2013, 7. (b) A. Ferrario, R. Hämmerli, On Boosting: Theory and Applications. Social Science Research Network
- Arab, I.; Barakat, K. ToxTree: descriptor-based machine learning models for both hERG and Nav1.5 cardiotoxicity liability predictions. arXiv, 2021, arXiv:2112.13467, ver. 1. DOI: 10.48550/arXiv:2112.13467v1
- Contact support@cresset-group.com for access to the Python script
