Existing molecular machine learning force fields (MLFFs) generally focus on the learning of atoms, molecules, and simple quantum chemical properties (such as energy and force), but ignore the importance of electron density (ED) $\rho(r)$ in accurately understanding molecular force fields (MFFs). ED describes the probability of finding electrons at specific locations around atoms or molecules, which uniquely determines all ground state properties (such as energy, molecular structure, etc.) of interactive multi-particle systems according to the Hohenberg-Kohn theorem. However, the calculation of ED relies on the time-consuming first-principles density functional theory (DFT), which leads to the lack of large-scale ED data and limits its application in MLFFs. In this paper, we introduce EDBench, a large-scale, high-quality dataset of ED designed to advance learning-based research at the electronic scale. Built upon the PCQM4Mv2, EDBench provides accurate ED data, covering 3.3 million molecules. To comprehensively evaluate the ability of models to understand and utilize electronic information, we design a suite of ED-centric benchmark tasks spanning prediction, retrieval, and generation. Our evaluation of several state-of-the-art methods demonstrates that learning from EDBench is not only feasible but also achieves high accuracy. Moreover, we show that learning-based methods can efficiently calculate ED with comparable precision while significantly reducing the computational cost relative to traditional DFT calculations. All data and benchmarks from EDBench will be freely available, laying a robust foundation for ED-driven drug discovery and materials science.

MOTIVATION: Accurate prediction of protein-ligand binding (PLB) relationships plays a crucial role in drug discovery, which helps identify drugs that modulate the activity of specific targets. Traditional biological assays for measuring PLB relationships are time consuming and costly. In addition, models for predicting PLB relationships have been developed and widely used in drug discovery tasks. However, learning more accurate PLB representations is essential to meet the stringent standards required for drug discovery. RESULTS: We propose an image-based PLB representation learning framework, called ImagePLB, which equips ligand representation learner (LRL) and protein representation learner (PRL) to accept 3D multi-view ligand images and protein graphs as input, respectively, and learns rich interaction information between ligand and protein through a binding representation learner (BRL). Considering the scarcity of protein-ligand pairs, we further propose a multi-level next trajectory prediction (MLNTP) task to pre-train ImagePLB on the 4D flexible dynamics trajectory of 16 972 complexes, including ligand level, protein level, and complex level, to learn information related to trajectories. Besides, by introducing trajectory regularization (TR), we effectively alleviate the problem of high (even almost identical) feature similarity caused by adjacent trajectories. Compared with the current state-of-the-art methods, ImagePLB has achieved competitive improvements on PLB-related prediction tasks, including protein-ligand affinity and efficacy prediction tasks. This study opens the door to the image-based PLB learning paradigm. AVAILABILITY AND IMPLEMENTATION: All data and implementation details of code can be obtained from https://github.com/HongxinXiang/ImagePLB.

Accurate prediction of the drug binding between proteins and ligands can significantly advance the development of structure-based drug design. Recent advances have shown great potential in applying equivariant graph neural network (EGNN) -based methods to learn representations of protein-ligand (PL) complexes. However, most of them typically focus on atom-level graph representations and omit the residue-level information in PL complexes, which are considered essential for understanding the binding mechanism. In this article, we develop a SO(3)-equivariant hierarchical graph neural network (EHGNN) that effectively captures the intrinsic hierarchy of biomolecular structures to enhance the predictive performance of PL interactions. Based on the SO(3)-EHGNN, we further propose a molecular dynamics-powered and energy-guided deep learning framework, called Dynamics-PLI, to capture the spatial structures and energetic information inside molecular dynamic (MD) trajectories. Extensive experimental results show significant improvements over current state-of-the-art methods, with a decrease of 4.03% in RMSE for the binding affinity problem and an average increase of 3.95% in AUROC and AUPRC for the ligand efficacy problem, demonstrating the superiority of Dynamics-PLI for PL interaction prediction. Our findings indicate that the SO(3)-EHGNN exhibits enhanced performance without the necessity of pre-training, emphasizing the inherent analytical strength of SO(3)-EHGNN.