Protein pocket detection is an essential step in structure-based virtual screening methods for identifying potential drug targets. To facilitate eficient molecular docking, an accurate determination of target binding sites is indispensable. In this study, we present GENEOnet, an innovative machine learning model based on Group Equivariant Non-Expansive Operators (GENEOs) for protein pocket detection. Our proposed method sets itself apart from other artificial intelligence techniques in the domain due to its reduced number of parameters, increased transparency, and integration of prior knowledge. The experimental assessment validates GENEOnet's eficacy with a limited training dataset, surpassing several established state-of-the-art methods based on multiple critical performance indicators computed using extensive public datasets of ligand-protein complexes. GENEOnet, the result of an ongoing collaborative efort between Italian universities and the pharmaceutical company Dompé Farmaceutici S.p.A., is accessible as a web service at https://geneonet.exscalate.eu to enable the scientific community to evaluate the pre-trained model for pocket detection.
Molecular docking, a critical research area in both pharmaceuticals and academia, is a simulation
technique utilized to predict the binding mode of small molecules with respect to specific
target proteins based on their three-dimensional structures [
Blind docking involves the tentative to accommodate the ligand trying anywhere on the protein surface. However, blind docking comes with challenges like false positives, where ligands may score well but have no experimental binding afinity to the target due to limitations in scoring functions.
To address these concerns, “informed” docking [
In this paper, we present some recent findings relative to GENEOnet [
In this study, we further investigate GENEOnet a shallow network composed of Group
Equivariant Non-Expansive Operator units, whose architecture is depicted in Figure 1a. For a
comprehensive understanding of GENEOs, we refer the reader to [
Equivariance [
Non-expansivity means that the outputs of a GENEO should not be further apart than their respective inputs with respect to an appropriate distance metric. This property can be read as a form of theoretical stability, ensuring that small input perturbations result in minimal output changes.
In this regard, adversarial attacks [
GENEOnet, with a representative output displayed in Figure 2a, is broken down into six steps: 1. Data preprocessing: Given an input protein , GENEOnet first computes a voxelization of the space enclosed within a bounding box surrounding the protein surface. Subsequently, eight potential functions are computed on the resulting voxel grid, each one modeling essential aspects of the protein structure from geometrical, physical and chemical viewpoints. 2. GENEO layer: A convolutional rigid motion equivariant operator (mostly based on gaussian kernels), depending on a shape parameter , is applied to each potential function.
The resulting function is normalized between 0 and 1. 3. Convex combination: The eight GENEO outputs are combined via convex combination with weights . The resulting combination output, denoted as , is normalized between 0 and 1 and encodes the probability that a voxel belongs to a pocket. 4. Thresholding: The final output is obtained by considering the connected components of the set of voxels where the value of is above a threshold parameter . 5. Evaluation: If the ground truth (i.e., the co-crystallized ligand) is accessible, the output can be compared against it using a volumetric accuracy function. 6. Scoring: Each predicted pocket is assigned a score, computed as a weighted average of within the spatial region identified by a pocket, enabling ranking of pockets from the most promising to the least promising.
F σ1
Our study employed PDBbind, a publicly accessible database of curated protein-ligand complexes for binding afinity analysis, as the primary data source (available at http://pdbbind.org.cn/). We retrieved 12330 complexes from the 2020 version for evaluation and analysis.
Steps 1 through 5 were considered during the training process, with backpropagation used to optimize parameters to optimize accuracy (introduced in Step 5). GENEOnet was trained on a set of 200 molecules extracted from the retrieved complexes. However, this method did not address the challenge of identifying true pockets within high-ranked predictions (as per Step 6).
To tackle this issue, we generated multiple models by repeating the optimization process while maintaining the same initial parameter settings but varying the training sets (each comprising of 200 complexes). The final model was selected based on maximizing its ability to identify true pockets at the highest rank using a Validation set consisting of nearly 3000 complexes.
Moreover, we compared GENEOnet’s performance against other state-of-the-art methods
(see [
In this section, our aim is to provide an additional in-depth analysis that underscores the explainability and robustness characteristics of GENEOnet, many of which can be attributed to the adoption of GENEOs as building blocks.
In the context of developing GENEO-based models, the selection and design of an appropriate pool of operators can be considered as a crucial step of information engineering for the problem at hand.
In the case of GENEOnet, experts in molecular docking identified lipophilicity, hydrophilicity, hydrogen bond acceptor or donor atoms, etc. (see Table 1b) as essential features to identify potential pockets. For example, regarding the lipophilicity potential, it was argued that a favorable pocket candidate should exhibit an average high value of this quantity. Thus, a GENEO from the family of convolutional operators with a Gaussian kernel was chosen to process this potential. The tunable shape parameter in this case is linked to the shape of the Gaussian. Analogous considerations were used to select the remaining seven GENEOs for the other potentials.
GENEOnet, as described in Section 2.2, includes a total of seventeen trainable parameters: eight shape coeficients for operator kernels, eight coeficients for the convex combination, and one threshold coeficient.
We believe that Equivariance is a primary factor contributing to GENEOnet’s relatively
few trainable parameters versus other CNN-based methods like DeepSite[
Indeed, GENEOnet’s limited trainable parameters facilitate precise interpretation of each of them: shape parameters influence operator kernels; convex combination coeficients serve as feature importances for potentials (Table 1b); and the threshold coeficient determines the significance of voxel activation. The convex combination coeficients warrant further exploration. The lipophilic potential, essential for pockets due to their need to exhibit lipophilic properties, receives the highest score. Surprisingly, potentials linked to hydrogen bonds, despite being biologically significant, have very low scores. As already noticed, this may be a result of the convex constraint: indeed, these potentials tend to be more concentrated in small regions surrounding acceptor or donor atoms, and thus other potentials, such as the polar potential, which might be strongly correlated with hydrogen bonds, are preferred. This could be the case with the selected model where the polar operator has a convex combination weight which is the third highest.
During the model selection process, parameter sensitivity analyses were performed as byproducts when generating 200 models from diferent training sets (Figure 2b shows boxplots of the convex combination coeficients). The findings largely confirm the conclusions of the previous paragraphs: on average, hydrogen bonds play a role but are outweighed by other operators, such as lipophilicity, which exhibit a coeficients distribution with a box containing higher values ( 4). If this analysis confirms the importance of potentials like those related to hydrogen bonds, it also reveals that the Gravitational and Hydrophilic potentials are given very little importance, a result that was somewhat anticipated given the nature of these potentials in connection to pocket detection.
(a) The input protein is depicted in white, while predicted pockets with colors. A zoom shows the true pocket containing the ligand.
(b) Sensitivity analysis of convex combination coeficients. Lines indicate median values, whereas stars represent means. The order is the same as in Table 1b.
Here we tested robustness to perturbations. In our context, robustness is strictly related to the Non-Expansivity property of GENEOs, and it is very important for pocket identification since proteins may exhibit extremely dynamic shapes, while in the data, they are frozen until crystallizing to capture an image of the structure. To test robustness, six proteins were selected: two belonging to the set of those whose true pocket was matched by the top-ranked prediction (proteins 2IGV, 4B0C), another two from the set of pockets matched by the second-ranked prediction (proteins 1L83, 3PCB), and the remaining two from those matched by the thirdranked predicted pocket (proteins 1IIH, 4TIM). White noise was introduced by summing i.i.d. Gaussian r.v. (0, 2) with zero mean and variance 2 to every voxel. Although i.i.d. noise is not realistic, as perturbations in the protein conformation are likely correlated because of atom interactions, it serves as a global test for robustness. We conducted multiple experiments by varying the standard deviation in the set {0.01, 0.03, 0.05}, each time generating 200 diferent perturbations. Figure 3 shows that overlaps and scores distributions of perturbations exhibit great robustness for all values of standard deviation . Figure 4 indicates greater robustness for rankings of top and second-ranked pockets while a mildly lower degree of stability is showed for third-ranked pockets.
The analysis presented in the preceding section provides an initial understanding of GENEOnet’s explainability and trustworthiness, summarised as follows: • GENEOnet can incorporate prior knowledge not only during feature selection but also in operator pool selection. Although feature selection is common in machine learning algorithms, this second step is less frequently considered, making the choice of operators more complex and less stable for methods like Convolutional Neural Networks. • GENEOnet has a smaller number of parameters than other protein pocket detection methods based on deep learning architectures. This attribute allows us to perform sensitivity analysis and provides interpretability by design rather than using post hoc explanation techniques. • GENEOnet’s equivariance with respect to rigid motions allows us to overlook the input protein’s spatial pose and helps to reduce the number of parameters. • GENEOnet’s non-expansivity provides the model with a reasonable degree of robustness against small physiological modifications in the input protein’s spatial conformation. The model shows great robustness for lower noise standard deviations when analysing the identifications made by the first or second predicted pockets. However, larger input changes may influence the final prediction. We leave this study to subsequent work. • The reduced data requirements for training GENEOnet (200 complexes) compared to deep learning methods help decrease computational costs and processing times. This attribute is not directly related to explainability but makes the model more accessible as fewer resources are needed to reproduce its results or delve deeper into its analysis.
In conclusion, GENEOs hold promise for building explainable and robust models such as
GENEOnet. Future work includes creating more instances of GENEO-based models [
Availability: GENEOnet can be tested at the following URL: https://geneonet.exscalate.eu