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Background Accurate identification of protein-protein interaction sites (PPIS) is critical for elucidating biological mechanisms and advancing drug discovery. However, existing methods still face significant challenges in leveraging structural information, including inadequate equivariant modeling, coarse graph representations, and limited multimodal fusion strategies. Results In this study, we propose a novel multimodal and multiscale deep learning framework, EDG-PPIS, that achieves efficient PPIS prediction by jointly enhancing structural and geometric representations. Specifically, a 3D equivariant graph neural network (LEFTNet) is employed to capture the global spatial geometry of proteins. For structural modeling, a dual-scale graph neural network is constructed to extract protein structural features from both local and remote perspectives. Finally, an attention mechanism is utilized to dynamically fuse structural and geometric features, enabling cross-modal integration. Experimental results demonstrate that EDG-PPIS achieves superior performance across multiple benchmark datasets. Conclusions EDG-PPIS provides an effective and robust computational tool for target identification and protein function analysis, addressing existing challenges in PPIS prediction and offering a promising approach for advancing the understanding of PPIS.

Ligand-based virtual screening (LBVS) is a promising approach for rapid and low-cost screening of potentially bioactive molecules in the early stage of drug discovery. Compared with traditional similarity-based machine learning methods, deep learning frameworks for LBVS can more effectively extract high-order molecule structure representations from molecular fingerprints or structures. However, the 3D conformation of a molecule largely influences its bioactivity and physical properties, and has rarely been considered in previous deep learning-based LBVS methods. Moreover, the relative bioactivity benchmark dataset is still lacking. To address these issues, we introduce a novel end-to-end deep learning architecture trained from molecular conformers for LBVS. We first extracted molecule conformers from multiple public molecular bioactivity data and consolidated them into a large-scale bioactivity benchmark dataset, which totally includes millions of endpoints and molecules corresponding to 954 targets. Then, we devised a deep learning-based LBVS called EquiVS to learn molecule representations from conformers for bioactivity prediction. Specifically, graph convolutional network (GCN) and equivariant graph neural network (EGNN) are sequentially stacked to learn high-order molecule-level and conformer-level representations, followed with attention-based deep multiple-instance learning (MIL) to aggregate these representations and then predict the potential bioactivity for the query molecule on a given target. We conducted various experiments to validate the data quality of our benchmark dataset, and confirmed EquiVS achieved better performance compared with 10 traditional machine learning or deep learning-based LBVS methods. Further ablation studies demonstrate the significant contribution of molecular conformation for bioactivity prediction, as well as the reasonability and non-redundancy of deep learning architecture in EquiVS. Finally, a model interpretation case study on CDK2 shows the potential of EquiVS in optimal conformer discovery. The overall study shows that our proposed benchmark dataset and EquiVS method have promising prospects in virtual screening applications.

Background Protein–protein interactions regulate the dynamic operation of intracellular molecular networks, serving as the molecular basis for revealing protein functions and disease mechanisms. Recently, several computational methods for predicting protein–protein interaction sites (PPIs) have been presented as alternatives to costly and labor-intensive traditional experiments. However, existing methods generally ignore the inherent hierarchical structure of protein chains. Furthermore, the equivariance of graph structure during spatial transformations is often neglected when applying graph neural networks to modeling. Therefore, accurately identifying PPIs remains a challenging task. Results In this work, we propose an end-to-end GNN-based computational method, EGCPPIS, for efficiently identifying protein–protein interaction sites. First, we construct a hierarchical graph representation of the protein chain, including residue-level graph and atom-level graph. Next, EGCPPIS designs an E(n) Equivariant Graph Neural Network (EGNN) module to learn residue-level embeddings with equivariant features. After further extracting atom-level embeddings using the GraphSAGE module, we introduce the contrastive learning strategy to integrate hierarchical graph features. This strategy enables us to learn consistent embeddings between residue-level and atom-level representations. Finally, the fused embeddings are weighted using an improved gated multi-head attention mechanism. Conclusion Comprehensive evaluation results on multiple datasets demonstrate that EGCPPIS significantly outperforms state-of-the-art methods. Extensive comparative experiments and case studies further confirm that EGCPPIS can reveal the decision-making patterns in PPIs prediction, facilitating the discovery of potential PPIs. The original datasets and code of EGCPPIS are available at https://github.com/GuicongSun/EGCPPIS .

Background Peptide-based therapeutics have great potential due to their versatility, high specificity, and suitability for a variety of therapeutic applications. Despite these advantages, the inherent toxicities of some peptides pose challenges in drug development. Several computational methods have been developed to allow rapid and efficient large-scale screening of peptide toxicity. However, these methods mainly rely on the primary sequence and often ignore critical structural information, which limits their predictive accuracy. Results In this study, we introduce a novel framework named StrucToxNet that integrates a pre-trained protein language model with an equivariant graph neural network to improve peptide toxicity prediction. By combining sequence embeddings from the ProtT5 language model and 3D structural data predicted by ESMFold, StrucToxNet can capture both sequential and spatial characteristics of peptides. Testing on the independent dataset indicates that StrucToxNet outperforms existing sequence-based models in various metrics, achieving higher balanced accuracy and overall performance. Conclusions The results demonstrate the robustness and generalizability of StrucToxNet, marking it a reliable tool in the computational screening of toxic peptides and facilitating safer peptide-based drug development.

Graph neural networks (GNNs) are widely used as surrogates for costly experiments and first-principles simulations to study the behavior of compounds at atomistic scale, and their architectural complexity is constantly increasing to enable the modeling of complex physics. While most recent GNNs combine more traditional message passing neural networks (MPNNs) layers to model short-range interactions with more advanced graph transformers (GTs) with global attention mechanisms to model long-range interactions, it is still unclear when global attention mechanisms provide real benefits over well-tuned MPNN layers due to inconsistent implementations, features, or hyperparameter tuning. We introduce the first unified, reproducible benchmarking framework–built on HydraGNN–that enables seamless switching among four controlled model classes: MPNN, MPNN with chemistry/topology encoders, GPS-style hybrids of MPNN with global attention, and fully fused localglobal models with encoders. Using seven diverse open-source datasets for benchmarking across regression and classification tasks, we systematically isolate the contributions of message passing, global attention, and encoder-based feature augmentation. Our study shows that encoder-augmented MPNNs form a robust baseline, while fused localglobal models yield the clearest benefits for properties governed by long-range interaction effects. We further quantify the accuracycompute trade-offs of attention, reporting its overhead in memory. Together, these results establish the first controlled evaluation of global attention in atomistic graph learning and provide a reproducible testbed for future model development. Scientific contribution This work provides the first unified and reproducible empirical framework to systematically evaluate when global attention mechanisms yield measurable benefits over well-tuned message passing neural networks for atomistic graph learning. By implementing all combinations of message passing, encoder-based feature augmentation, and global attention within a single HydraGNN pipeline and under identical training and hyperparameter optimization protocols, we eliminate confounding effects present in prior comparisons. The results transform widely stated but weakly verified assumptions about long-range modeling in molecular GNNs into empirically testable conclusions, clarifying when global attention is beneficial and when expressive MPNNs remain sufficient.

Graph convolutional neural networks have been instrumental in machine learning of material properties. When representing tensorial properties, weights and descriptors of a physics-informed network must obey certain transformation rules to ensure the independence of the property on the choice of the reference frame. Here we explicitly encode such properties using an equivariant graph convolutional neural network. The network respects rotational symmetries of the crystal throughout by using equivariant weights and descriptors and provides a tensorial output of the target value. Applications to tensors of atomic Born effective charges in diverse materials including perovskite oxides, Li 3 PO 4 , and ZrO 2 , are demonstrated, and good performance and generalization ability is obtained.

Representations are a foundational component of any modeling protocol, including on molecules and molecular solids. For tasks that depend on knowledge of both molecular conformation and 3D orientation, such as the modeling of molecular dimers, clusters, or condensed phases, we desire a rotatable representation that is provably complete in the types and positions of atomic nuclei and roto-inversion equivariant with respect to the input point cloud. In this paper, we develop, train, and evaluate a new type of autoencoder, molecular O(3) encoding net (Mo3ENet), for multi-type point clouds, for which we propose a new reconstruction loss, capitalizing on a Gaussian mixture representation of the input and output point clouds. Mo3ENet is end-to-end equivariant, meaning the learned representation can be manipulated on O(3), a practical bonus. An appropriately trained Mo3ENet latent space comprises a universal embedding for scalar, vector, and tensorial molecule property prediction tasks, as well as other downstream tasks incorporating the 3D molecular pose, and we demonstrate its fitness on several such tasks.

This study introduces a novel contrastive learning-based X-ray diffraction (XRD) analysis framework, an SE(3)-equivariant graph neural network (E3NN) based Atomic Cluster Expansion Neural Network (EACNN), which reduces the strong dependency on databases and initial models in traditional methods. By integrating E3NN with atomic cluster expansion (ACE) techniques, a dual-tower contrastive learning model has been developed, mapping crystal structures and XRD patterns to a continuous embedding space. The EACNN model retains hierarchical features of crystal systems through symmetry-sensitive encoding mechanisms and utilizes relationship mining via contrastive learning to replace rigid classification boundaries. This approach reveals gradual symmetry-breaking patterns between monoclinic and orthorhombic crystal systems in the latent space, effectively addressing the recognition challenges associated with low-symmetry systems and small sample space groups. Our investigation further explores the potential for model transfer to experimental data and multimodal extensions, laying the theoretical foundation for establishing a universal structure–property mapping relationship.

Background Molecular biology is crucial for drug discovery, protein design, and human health. Due to the vastness of the drug-like chemical space, depending on biomedical experts to manually design molecules is exceedingly expensive. Utilizing generative methods with deep learning technology offers an effective approach to streamline the search space for molecular design and save costs. This paper introduces a novel E(3)-equivariant score-based diffusion framework for 3D molecular generation via SDEs, aiming to address the constraints of unified Gaussian diffusion methods. Within the proposed framework EMDS, the complete diffusion is decomposed into separate diffusion processes for distinct components of the molecular feature space, while the modeling processes also capture the complex dependency among these components. Moreover, angle and torsion angle information is integrated into the networks to enhance the modeling of atom coordinates and utilize spatial information more effectively. Results Experiments on the widely utilized QM9 dataset demonstrate that our proposed framework significantly outperforms the state-of-the-art methods in all evaluation metrics for 3D molecular generation. Additionally, ablation experiments are conducted to highlight the contribution of key components in our framework, demonstrating the effectiveness of the proposed framework and the performance improvements of incorporating angle and torsion angle information for molecular generation. Finally, the comparative results of distribution show that our method is highly effective in generating molecules that closely resemble the actual scenario. Conclusion Through the experiments and comparative results, our framework clearly outperforms previous 3D molecular generation methods, exhibiting significantly better capacity for modeling chemically realistic molecules. The excellent performance of EMDS in 3D molecular generation brings novel and encouraging opportunities for tackling challenging biomedical molecule and protein scenarios.

Accurate and interpretable modeling of crystalline materials is essential for understanding the structure–property relationships in materials critical in accelerating materials discovery. While recent graph neural networks (GNNs) have achieved high predictive accuracy, they often struggle to provide physical interpretability and fail to explicitly model the hierarchical and symmetrical nature of crystals. In this work, we introduce Capsule Graph Networks with E(3)-Equivariance (CGN-e3), a novel deep learning framework that integrates equivariant message passing with capsule networks to capture both geometric symmetries and hierarchical motif structures. CGN-e3 leverages E(3)-equivariant message passing to learn physically consistent features and organize them into capsule representations that can disentangle local motifs, such as polyhedral environments, and connects them to global properties. We validate the effectiveness of our framework on bandgap and formation energy prediction, as well as material classification using Materials Project and Matbench datasets. Our model achieves a MAE of 0.054 eV/atom and 0.379 eV on formation energy and bandgap prediction, respectively, outperforming CGCNN and matching the performance of MEGNet on the same dataset, while also providing insightful interpretations of the learned capsule representations. Scientific contribution : We present the first integration of E(3)-equivariant graph neural networks with capsule networks for modeling crystalline materials. This unified architecture captures both the fundamental physical symmetries of 3D space; rotation, translation, reflection and the intrinsic hierarchical part-whole relationships e.g., atoms to polyhedra to extended motifs found in crystal structures. The framework provides an unsupervised pathway for interpretable motif discovery. The dynamic routing-by-agreement mechanism identifies and aggregates structurally significant local environments such as the T i O 6 octahedra into higher-order graph-level capsules. This process yields human-intelligible insights by explicitly quantifying the contribution of specific structural motifs to target material properties, moving beyond \"black-box\" predictions. We validate our framework on key property prediction tasks and provide capsule-level interpretation of the results.