Shitong Luo

Shitong Luo, Jiahan Li, Jiaqi Guan et al. · mit

Equivariance has been a long-standing concern in various fields ranging from computer vision to physical modeling. Most previous methods struggle with generality, simplicity, and expressiveness -- some are designed ad hoc for specific data types, some are too complex to be accessible, and some sacrifice flexible transformations. In this work, we propose a novel and simple framework to achieve equivariance for point cloud analysis based on the message passing (graph neural network) scheme. We find the equivariant property could be obtained by introducing an orientation for each point to decouple the relative position for each point from the global pose of the entire point cloud. Therefore, we extend current message passing networks with a module that learns orientations for each point. Before aggregating information from the neighbors of a point, the networks transforms the neighbors' coordinates based on the point's learned orientations. We provide formal proofs to show the equivariance of the proposed framework. Empirically, we demonstrate that our proposed method is competitive on both point cloud analysis and physical modeling tasks. Code is available at https://github.com/luost26/Equivariant-OrientedMP .

Xingang Peng, Shitong Luo, Jiaqi Guan et al. · mit

Deep generative models have achieved tremendous success in designing novel drug molecules in recent years. A new thread of works have shown the great potential in advancing the specificity and success rate of in silico drug design by considering the structure of protein pockets. This setting posts fundamental computational challenges in sampling new chemical compounds that could satisfy multiple geometrical constraints imposed by pockets. Previous sampling algorithms either sample in the graph space or only consider the 3D coordinates of atoms while ignoring other detailed chemical structures such as bond types and functional groups. To address the challenge, we develop Pocket2Mol, an E(3)-equivariant generative network composed of two modules: 1) a new graph neural network capturing both spatial and bonding relationships between atoms of the binding pockets and 2) a new efficient algorithm which samples new drug candidates conditioned on the pocket representations from a tractable distribution without relying on MCMC. Experimental results demonstrate that molecules sampled from Pocket2Mol achieve significantly better binding affinity and other drug properties such as druglikeness and synthetic accessibility.

Shitong Luo, Jiaqi Guan, Jianzhu Ma et al. · mit

We study a fundamental problem in structure-based drug design -- generating molecules that bind to specific protein binding sites. While we have witnessed the great success of deep generative models in drug design, the existing methods are mostly string-based or graph-based. They are limited by the lack of spatial information and thus unable to be applied to structure-based design tasks. Particularly, such models have no or little knowledge of how molecules interact with their target proteins exactly in 3D space. In this paper, we propose a 3D generative model that generates molecules given a designated 3D protein binding site. Specifically, given a binding site as the 3D context, our model estimates the probability density of atom's occurrences in 3D space -- positions that are more likely to have atoms will be assigned higher probability. To generate 3D molecules, we propose an auto-regressive sampling scheme -- atoms are sampled sequentially from the learned distribution until there is no room for new atoms. Combined with this sampling scheme, our model can generate valid and diverse molecules, which could be applicable to various structure-based molecular design tasks such as molecule sampling and linker design. Experimental results demonstrate that molecules sampled from our model exhibit high binding affinity to specific targets and good drug properties such as drug-likeness even if the model is not explicitly optimized for them.

Ruidong Wu, Ruihan Guo, Rui Wang et al.

Despite the striking success of general protein folding models such as AlphaFold2(AF2, Jumper et al. (2021)), the accurate computational modeling of antibody-antigen complexes remains a challenging task. In this paper, we first analyze AF2's primary loss function, known as the Frame Aligned Point Error (FAPE), and raise a previously overlooked issue that FAPE tends to face gradient vanishing problem on high-rotational-error targets. To address this fundamental limitation, we propose a novel geodesic loss called Frame Aligned Frame Error (FAFE, denoted as F2E to distinguish from FAPE), which enables the model to better optimize both the rotational and translational errors between two frames. We then prove that F2E can be reformulated as a group-aware geodesic loss, which translates the optimization of the residue-to-residue error to optimizing group-to-group geodesic frame distance. By fine-tuning AF2 with our proposed new loss function, we attain a correct rate of 52.3\% (DockQ $>$ 0.23) on an evaluation set and 43.8\% correct rate on a subset with low homology, with substantial improvement over AF2 by 182\% and 100\% respectively.

Jiahan Li, Tong Chen, Shitong Luo et al.

Peptides, short chains of amino acids, interact with target proteins, making them a unique class of protein-based therapeutics for treating human diseases. Recently, deep generative models have shown great promise in peptide generation. However, several challenges remain in designing effective peptide binders. First, not all residues contribute equally to peptide-target interactions. Second, the generated peptides must adopt valid geometries due to the constraints of peptide bonds. Third, realistic tasks for peptide drug development are still lacking. To address these challenges, we introduce PepHAR, a hot-spot-driven autoregressive generative model for designing peptides targeting specific proteins. Building on the observation that certain hot spot residues have higher interaction potentials, we first use an energy-based density model to fit and sample these key residues. Next, to ensure proper peptide geometry, we autoregressively extend peptide fragments by estimating dihedral angles between residue frames. Finally, we apply an optimization process to iteratively refine fragment assembly, ensuring correct peptide structures. By combining hot spot sampling with fragment-based extension, our approach enables de novo peptide design tailored to a target protein and allows the incorporation of key hot spot residues into peptide scaffolds. Extensive experiments, including peptide design and peptide scaffold generation, demonstrate the strong potential of PepHAR in computational peptide binder design. Source code will be available at https://github.com/Ced3-han/PepHAR.

Jiahan Li, Shitong Luo, Congyue Deng et al.

By folding into particular 3D structures, proteins play a key role in living beings. To learn meaningful representation from a protein structure for downstream tasks, not only the global backbone topology but the local fine-grained orientational relations between amino acids should also be considered. In this work, we propose the Orientation-Aware Graph Neural Networks (OAGNNs) to better sense the geometric characteristics in protein structure (e.g. inner-residue torsion angles, inter-residue orientations). Extending a single weight from a scalar to a 3D vector, we construct a rich set of geometric-meaningful operations to process both the classical and SO(3) representations of a given structure. To plug our designed perceptron unit into existing Graph Neural Networks, we further introduce an equivariant message passing paradigm, showing superior versatility in maintaining SO(3)-equivariance at the global scale. Experiments have shown that our OAGNNs have a remarkable ability to sense geometric orientational features compared to classical networks. OAGNNs have also achieved state-of-the-art performance on various computational biology applications related to protein 3D structures. The code is available at https://github.com/Ced3-han/OAGNN/tree/main.

Shitong Luo, Wei Hu

Point clouds acquired from scanning devices are often perturbed by noise, which affects downstream tasks such as surface reconstruction and analysis. The distribution of a noisy point cloud can be viewed as the distribution of a set of noise-free samples $p(x)$ convolved with some noise model $n$, leading to $(p * n)(x)$ whose mode is the underlying clean surface. To denoise a noisy point cloud, we propose to increase the log-likelihood of each point from $p * n$ via gradient ascent -- iteratively updating each point's position. Since $p * n$ is unknown at test-time, and we only need the score (i.e., the gradient of the log-probability function) to perform gradient ascent, we propose a neural network architecture to estimate the score of $p * n$ given only noisy point clouds as input. We derive objective functions for training the network and develop a denoising algorithm leveraging on the estimated scores. Experiments demonstrate that the proposed model outperforms state-of-the-art methods under a variety of noise models, and shows the potential to be applied in other tasks such as point cloud upsampling. The code is available at \url{https://github.com/luost26/score-denoise}.

Minkai Xu, Wujie Wang, Shitong Luo et al.

Predicting molecular conformations (or 3D structures) from molecular graphs is a fundamental problem in many applications. Most existing approaches are usually divided into two steps by first predicting the distances between atoms and then generating a 3D structure through optimizing a distance geometry problem. However, the distances predicted with such two-stage approaches may not be able to consistently preserve the geometry of local atomic neighborhoods, making the generated structures unsatisfying. In this paper, we propose an end-to-end solution for molecular conformation prediction called ConfVAE based on the conditional variational autoencoder framework. Specifically, the molecular graph is first encoded in a latent space, and then the 3D structures are generated by solving a principled bilevel optimization program. Extensive experiments on several benchmark data sets prove the effectiveness of our proposed approach over existing state-of-the-art approaches. Code is available at https://github.com/MinkaiXu/ConfVAE-ICML21

Shitong Luo, Wei Hu

We present a probabilistic model for point cloud generation, which is fundamental for various 3D vision tasks such as shape completion, upsampling, synthesis and data augmentation. Inspired by the diffusion process in non-equilibrium thermodynamics, we view points in point clouds as particles in a thermodynamic system in contact with a heat bath, which diffuse from the original distribution to a noise distribution. Point cloud generation thus amounts to learning the reverse diffusion process that transforms the noise distribution to the distribution of a desired shape. Specifically, we propose to model the reverse diffusion process for point clouds as a Markov chain conditioned on certain shape latent. We derive the variational bound in closed form for training and provide implementations of the model. Experimental results demonstrate that our model achieves competitive performance in point cloud generation and auto-encoding. The code is available at \url{https://github.com/luost26/diffusion-point-cloud}.

Shitong Luo, Wei Hu

3D point clouds are often perturbed by noise due to the inherent limitation of acquisition equipments, which obstructs downstream tasks such as surface reconstruction, rendering and so on. Previous works mostly infer the displacement of noisy points from the underlying surface, which however are not designated to recover the surface explicitly and may lead to sub-optimal denoising results. To this end, we propose to learn the underlying manifold of a noisy point cloud from differentiably subsampled points with trivial noise perturbation and their embedded neighborhood feature, aiming to capture intrinsic structures in point clouds. Specifically, we present an autoencoder-like neural network. The encoder learns both local and non-local feature representations of each point, and then samples points with low noise via an adaptive differentiable pooling operation. Afterwards, the decoder infers the underlying manifold by transforming each sampled point along with the embedded feature of its neighborhood to a local surface centered around the point. By resampling on the reconstructed manifold, we obtain a denoised point cloud. Further, we design an unsupervised training loss, so that our network can be trained in either an unsupervised or supervised fashion. Experiments show that our method significantly outperforms state-of-the-art denoising methods under both synthetic noise and real world noise. The code and data are available at https://github.com/luost26/DMRDenoise

Jiahan Li, Chaoran Cheng, Zuofan Wu et al.

Peptides, short chains of amino acid residues, play a vital role in numerous biological processes by interacting with other target molecules, offering substantial potential in drug discovery. In this work, we present PepFlow, the first multi-modal deep generative model grounded in the flow-matching framework for the design of full-atom peptides that target specific protein receptors. Drawing inspiration from the crucial roles of residue backbone orientations and side-chain dynamics in protein-peptide interactions, we characterize the peptide structure using rigid backbone frames within the $\mathrm{SE}(3)$ manifold and side-chain angles on high-dimensional tori. Furthermore, we represent discrete residue types in the peptide sequence as categorical distributions on the probability simplex. By learning the joint distributions of each modality using derived flows and vector fields on corresponding manifolds, our method excels in the fine-grained design of full-atom peptides. Harnessing the multi-modal paradigm, our approach adeptly tackles various tasks such as fix-backbone sequence design and side-chain packing through partial sampling. Through meticulously crafted experiments, we demonstrate that PepFlow exhibits superior performance in comprehensive benchmarks, highlighting its significant potential in computational peptide design and analysis.

Haolan Chen, Bi'an Du, Shitong Luo et al.

3D point clouds acquired by scanning real-world objects or scenes have found a wide range of applications including immersive telepresence, autonomous driving, surveillance, etc. They are often perturbed by noise or suffer from low density, which obstructs downstream tasks such as surface reconstruction and understanding. In this paper, we propose a novel paradigm of point set resampling for restoration, which learns continuous gradient fields of point clouds that converge points towards the underlying surface. In particular, we represent a point cloud via its gradient field -- the gradient of the log-probability density function, and enforce the gradient field to be continuous, thus guaranteeing the continuity of the model for solvable optimization. Based on the continuous gradient fields estimated via a proposed neural network, resampling a point cloud amounts to performing gradient-based Markov Chain Monte Carlo (MCMC) on the input noisy or sparse point cloud. Further, we propose to introduce regularization into the gradient-based MCMC during point cloud restoration, which essentially refines the intermediate resampled point cloud iteratively and accommodates various priors in the resampling process. Extensive experimental results demonstrate that the proposed point set resampling achieves the state-of-the-art performance in representative restoration tasks including point cloud denoising and upsampling.

Jiaxiang Wu, Shitong Luo, Tao Shen et al.

Accurate protein structure prediction from amino-acid sequences is critical to better understanding the protein function. Recent advances in this area largely benefit from more precise inter-residue distance and orientation predictions, powered by deep neural networks. However, the structure optimization procedure is still dominated by traditional tools, e.g. Rosetta, where the structure is solved via minimizing a pre-defined statistical energy function (with optional prediction-based restraints). Such energy function may not be optimal in formulating the whole conformation space of proteins. In this paper, we propose a fully-differentiable approach for protein structure optimization, guided by a data-driven generative network. This network is trained in a denoising manner, attempting to predict the correction signal from corrupted distance matrices between Ca atoms. Once the network is well trained, Langevin dynamics based sampling is adopted to gradually optimize structures from random initialization. Extensive experiments demonstrate that our EBM-Fold approach can efficiently produce high-quality decoys, compared against traditional Rosetta-based structure optimization routines.

Chence Shi, Shitong Luo, Minkai Xu et al.

We study a fundamental problem in computational chemistry known as molecular conformation generation, trying to predict stable 3D structures from 2D molecular graphs. Existing machine learning approaches usually first predict distances between atoms and then generate a 3D structure satisfying the distances, where noise in predicted distances may induce extra errors during 3D coordinate generation. Inspired by the traditional force field methods for molecular dynamics simulation, in this paper, we propose a novel approach called ConfGF by directly estimating the gradient fields of the log density of atomic coordinates. The estimated gradient fields allow directly generating stable conformations via Langevin dynamics. However, the problem is very challenging as the gradient fields are roto-translation equivariant. We notice that estimating the gradient fields of atomic coordinates can be translated to estimating the gradient fields of interatomic distances, and hence develop a novel algorithm based on recent score-based generative models to effectively estimate these gradients. Experimental results across multiple tasks show that ConfGF outperforms previous state-of-the-art baselines by a significant margin.

Minkai Xu, Shitong Luo, Yoshua Bengio et al.

We study how to generate molecule conformations (i.e., 3D structures) from a molecular graph. Traditional methods, such as molecular dynamics, sample conformations via computationally expensive simulations. Recently, machine learning methods have shown great potential by training on a large collection of conformation data. Challenges arise from the limited model capacity for capturing complex distributions of conformations and the difficulty in modeling long-range dependencies between atoms. Inspired by the recent progress in deep generative models, in this paper, we propose a novel probabilistic framework to generate valid and diverse conformations given a molecular graph. We propose a method combining the advantages of both flow-based and energy-based models, enjoying: (1) a high model capacity to estimate the multimodal conformation distribution; (2) explicitly capturing the complex long-range dependencies between atoms in the observation space. Extensive experiments demonstrate the superior performance of the proposed method on several benchmarks, including conformation generation and distance modeling tasks, with a significant improvement over existing generative models for molecular conformation sampling.