Manifold-Constrained Nucleus-Level Denoising Diffusion Model for Structure-Based Drug Design

Artificial intelligence models have shown great potential in structure-based drug design, generating ligands with high binding affinities. However, existing models have often overlooked a crucial physical constraint: atoms must maintain a minimum pairwise distance to avoid separation violation, a phenomenon governed by the balance of attractive and repulsive forces. To mitigate such separation violations, we propose NucleusDiff. It models the interactions between atomic nuclei and their surrounding electron clouds by enforcing the distance constraint between the nuclei and manifolds. We quantitatively evaluate NucleusDiff using the CrossDocked2020 dataset and a COVID-19 therapeutic target, demonstrating that NucleusDiff reduces violation rate by up to 100.00% and enhances binding affinity by up to 22.16%, surpassing state-of-the-art models for structure-based drug design. We also provide qualitative analysis through manifold sampling, visually confirming the effectiveness of NucleusDiff in reducing separation violations and improving binding affinities.

Sculpting Molecules in 3D: A Flexible Substructure Aware Framework for Text-Oriented Molecular Optimization

The integration of deep learning, particularly AI-Generated Content, with high-quality data derived from ab initio calculations has emerged as a promising avenue for transforming the landscape of scientific research. However, the challenge of designing molecular drugs or materials that incorporate multi-modality prior knowledge remains a critical and complex undertaking. Specifically, achieving a practical molecular design necessitates not only meeting the diversity requirements but also addressing structural and textural constraints with various symmetries outlined by domain experts. In this article, we present an innovative approach to tackle this inverse design problem by formulating it as a multi-modality guidance generation/optimization task. Our proposed solution involves a textural-structure alignment symmetric diffusion framework for the implementation of molecular generation/optimization tasks, namely 3DToMolo. 3DToMolo aims to harmonize diverse modalities, aligning them seamlessly to produce molecular structures adhere to specified symmetric structural and textural constraints by experts in the field. Experimental trials across three guidance generation settings have shown a superior hit generation performance compared to state-of-the-art methodologies. Moreover, 3DToMolo demonstrates the capability to generate novel molecules, incorporating specified target substructures, without the need for prior knowledge. This work not only holds general significance for the advancement of deep learning methodologies but also paves the way for a transformative shift in molecular design strategies. 3DToMolo creates opportunities for a more nuanced and effective exploration of the vast chemical space, opening new frontiers in the development of molecular entities with tailored properties and functionalities.

A Multi-Grained Symmetric Differential Equation Model for Learning Protein-Ligand Binding Dynamics

In drug discovery, molecular dynamics (MD) simulation for protein-ligand binding provides a powerful tool for predicting binding affinities, estimating transport properties, and exploring pocket sites. There has been a long history of improving the efficiency of MD simulations through better numerical methods and, more recently, by utilizing machine learning (ML) methods. Yet, challenges remain, such as accurate modeling of extended-timescale simulations. To address this issue, we propose NeuralMD, the first ML surrogate that can facilitate numerical MD and provide accurate simulations in protein-ligand binding. We propose a principled approach that incorporates a novel physics-informed multi-grained group symmetric framework. Specifically, we propose (1) a BindingNet model that satisfies group symmetry using vector frames and captures the multi-level protein-ligand interactions, and (2) an augmented neural differential equation solver that learns the trajectory under Newtonian mechanics. For the experiment, we design ten single-trajectory and three multi-trajectory binding simulation tasks. We show the efficiency and effectiveness of NeuralMD, with a 2000$\times$ speedup over standard numerical MD simulation and outperforming all other ML approaches by up to 80% under the stability metric. We further qualitatively show that NeuralMD reaches more stable binding predictions compared to other machine learning methods.

A quatum inspired neural network for geometric modeling

By conceiving physical systems as 3D many-body point clouds, geometric graph neural networks (GNNs), such as SE(3)/E(3) equivalent GNNs, have showcased promising performance. In particular, their effective message-passing mechanics make them adept at modeling molecules and crystalline materials. However, current geometric GNNs only offer a mean-field approximation of the many-body system, encapsulated within two-body message passing, thus falling short in capturing intricate relationships within these geometric graphs. To address this limitation, tensor networks, widely employed by computational physics to handle manybody systems using high-order tensors, have been introduced. Nevertheless, integrating these tensorized networks into the message-passing framework of GNNs faces scalability and symmetry conservation (e.g., permutation and rotation) challenges. In response, we introduce an innovative equivariant Matrix Product State (MPS)-based message-passing strategy, through achieving an efficient implementation of the tensor contraction operation. Our method effectively models complex many-body relationships, suppressing mean-field approximations, and captures symmetries within geometric graphs. Importantly, it seamlessly replaces the standard message-passing and layer-aggregation modules intrinsic to geometric GNNs. We empirically validate the superior accuracy of our approach on benchmark tasks, including predicting classical Newton systems and quantum tensor Hamiltonian matrices. To our knowledge, our approach represents the inaugural utilization of parameterized geometric tensor networks.

Molecule Joint Auto-Encoding: Trajectory Pretraining with 2D and 3D Diffusion

Recently, artificial intelligence for drug discovery has raised increasing interest in both machine learning and chemistry domains. The fundamental building block for drug discovery is molecule geometry and thus, the molecule's geometrical representation is the main bottleneck to better utilize machine learning techniques for drug discovery. In this work, we propose a pretraining method for molecule joint auto-encoding (MoleculeJAE). MoleculeJAE can learn both the 2D bond (topology) and 3D conformation (geometry) information, and a diffusion process model is applied to mimic the augmented trajectories of such two modalities, based on which, MoleculeJAE will learn the inherent chemical structure in a self-supervised manner. Thus, the pretrained geometrical representation in MoleculeJAE is expected to benefit downstream geometry-related tasks. Empirically, MoleculeJAE proves its effectiveness by reaching state-of-the-art performance on 15 out of 20 tasks by comparing it with 12 competitive baselines.

Power-law Dynamic arising from machine learning

We study a kind of new SDE that was arisen from the research on optimization in machine learning, we call it power-law dynamic because its stationary distribution cannot have sub-Gaussian tail and obeys power-law. We prove that the power-law dynamic is ergodic with unique stationary distribution, provided the learning rate is small enough. We investigate its first exist time. In particular, we compare the exit times of the (continuous) power-law dynamic and its discretization. The comparison can help guide machine learning algorithm.

Symmetry-Informed Geometric Representation for Molecules, Proteins, and Crystalline Materials

Artificial intelligence for scientific discovery has recently generated significant interest within the machine learning and scientific communities, particularly in the domains of chemistry, biology, and material discovery. For these scientific problems, molecules serve as the fundamental building blocks, and machine learning has emerged as a highly effective and powerful tool for modeling their geometric structures. Nevertheless, due to the rapidly evolving process of the field and the knowledge gap between science (e.g., physics, chemistry, & biology) and machine learning communities, a benchmarking study on geometrical representation for such data has not been conducted. To address such an issue, in this paper, we first provide a unified view of the current symmetry-informed geometric methods, classifying them into three main categories: invariance, equivariance with spherical frame basis, and equivariance with vector frame basis. Then we propose a platform, coined Geom3D, which enables benchmarking the effectiveness of geometric strategies. Geom3D contains 16 advanced symmetry-informed geometric representation models and 14 geometric pretraining methods over 46 diverse datasets, including small molecules, proteins, and crystalline materials. We hope that Geom3D can, on the one hand, eliminate barriers for machine learning researchers interested in exploring scientific problems; and, on the other hand, provide valuable guidance for researchers in computational chemistry, structural biology, and materials science, aiding in the informed selection of representation techniques for specific applications.

A Group Symmetric Stochastic Differential Equation Model for Molecule Multi-modal Pretraining

Molecule pretraining has quickly become the go-to schema to boost the performance of AI-based drug discovery. Naturally, molecules can be represented as 2D topological graphs or 3D geometric point clouds. Although most existing pertaining methods focus on merely the single modality, recent research has shown that maximizing the mutual information (MI) between such two modalities enhances the molecule representation ability. Meanwhile, existing molecule multi-modal pretraining approaches approximate MI based on the representation space encoded from the topology and geometry, thus resulting in the loss of critical structural information of molecules. To address this issue, we propose MoleculeSDE. MoleculeSDE leverages group symmetric (e.g., SE(3)-equivariant and reflection-antisymmetric) stochastic differential equation models to generate the 3D geometries from 2D topologies, and vice versa, directly in the input space. It not only obtains tighter MI bound but also enables prosperous downstream tasks than the previous work. By comparing with 17 pretraining baselines, we empirically verify that MoleculeSDE can learn an expressive representation with state-of-the-art performance on 26 out of 32 downstream tasks.

A new perspective on building efficient and expressive 3D equivariant graph neural networks

Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these networks through a local-to-global analysis lacks today. In this paper, we propose a local hierarchy of 3D isomorphism to evaluate the expressive power of equivariant GNNs and investigate the process of representing global geometric information from local patches. Our work leads to two crucial modules for designing expressive and efficient geometric GNNs; namely local substructure encoding (LSE) and frame transition encoding (FTE). To demonstrate the applicability of our theory, we propose LEFTNet which effectively implements these modules and achieves state-of-the-art performance on both scalar-valued and vector-valued molecular property prediction tasks. We further point out the design space for future developments of equivariant graph neural networks. Our codes are available at \url{https://github.com/yuanqidu/LeftNet}.

Structure-based Drug Design with Equivariant Diffusion Models

Structure-based drug design (SBDD) aims to design small-molecule ligands that bind with high affinity and specificity to pre-determined protein targets. Traditional SBDD pipelines start with large-scale docking of compound libraries from public databases, thus limiting the exploration of chemical space to existent previously studied regions. Recent machine learning methods approached this problem using an atom-by-atom generation approach, which is computationally expensive. In this paper, we formulate SBDD as a 3D-conditional generation problem and present DiffSBDD, an E(3)-equivariant 3D-conditional diffusion model that generates novel ligands conditioned on protein pockets. Furthermore, we curate a new dataset of experimentally determined binding complex data from Binding MOAD to provide a realistic binding scenario that complements the synthetic CrossDocked dataset. Comprehensive in silico experiments demonstrate the efficiency of DiffSBDD in generating novel and diverse drug-like ligands that engage protein pockets with high binding energies as predicted by in silico docking.