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 \textit{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. The source code will be available at https://github.com/Ced3-han/PepHAR.

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.

Discovering new drug molecules is a pivotal yet challenging process due to the near-infinitely large chemical space and notorious demands on time and resources. Numerous generative models have recently been introduced to accelerate the drug discovery process, but their progression to experimental validation remains limited, largely due to a lack of consideration for synthetic accessibility in practical settings. In this work, we introduce a novel framework that is capable of generating new chemical structures while ensuring synthetic accessibility. Specifically, we introduce a postfix notation of synthetic pathways to represent molecules in chemical space. Then, we design a transformer-based model to translate molecular graphs into postfix notations of synthesis. We highlight the model’s ability to: (a) perform bottom-up synthesis planning more accurately, (b) generate structurally similar, synthesizable analogs for unsynthesizable molecules proposed by generative models with their properties preserved, and (c) explore the local synthesizable chemical space around hit molecules.

Despite the striking success of general protein folding models such as AlphaFold2 (AF2), 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 improvement over AF2 by 182% and 100% respectively.

Predicting the effects of protein mutations is crucial for analyzing protein functions and understanding genetic diseases. However, existing models struggle to effectively extract mutation-related local structure motifs from protein databases, which hinders their predictive accuracy and robustness. To tackle this problem, we design a novel retrieval-augmented framework for incorporating similar structure information in known protein structures. We create a vector database consisting of local structure motif embeddings from a pre-trained protein structure encoder, which allows for efficient retrieval of similar local structure motifs during mutation effect prediction. Our findings demonstrate that leveraging this method results in the SOTA performance across multiple protein mutation prediction datasets, and offers a scalable solution for studying mutation effects.

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.

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.

Deep generative models have achieved tremendous success in designing novel drug molecules in recent years. A new thread of works have shown 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 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 drug-likeness and synthetic accessibility.

Antibodies are immune system proteins that protect the host by binding to specific antigens such as viruses and bacteria. The binding between antibodies and antigens is mainly determined by the complementarity-determining regions (CDR) of the antibodies. In this work, we develop a deep generative model that jointly models sequences and structures of CDRs based on diffusion probabilistic models and equivariant neural networks. Our method is the first deep learning-based method that generates antibodies explicitly targeting specific antigen structures and is one of the earliest diffusion probabilistic models for protein structures. The model is a "Swiss Army Knife" capable of sequence-structure co-design, sequence design for given backbone structures, and antibody optimization. We conduct extensive experiments to evaluate the quality of both sequences and structures of designed antibodies. We find that our model could yield competitive results in binding affinity measured by biophysical energy functions and other protein design metrics.

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 https://github.com/luost26/diffusion-point-cloud.

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.

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.

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 \url{https://github.com/MinkaiXu/ConfVAE-ICML21}.

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.

Predicting stable 3D conformations from 2D molecular graphs has been a long-standing challenge in computational chemistry. Recently, machine learning approaches have demonstrated very promising results compared to traditional experimental and physics-based simulation methods. These approaches mainly focus on modeling the local interactions between neighboring atoms on the molecular graphs and overlook the long-range interactions between non-bonded atoms. However, these non-bonded atoms may be proximal to each other in 3D space, and modeling their interactions is of crucial importance to accurately determine molecular conformations, especially for large molecules and multi-molecular complexes. In this paper, we propose a new approach called Dynamic Graph Score Matching (DGSM) for molecular conformation prediction, which models both the local and long-range interactions by dynamically constructing graph structures between atoms according to their spatial proximity during both training and inference. Specifically, the DGSM directly estimates the gradient fields of the logarithm density of atomic coordinates according to the dynamically constructed graphs using score matching methods. The whole framework can be efficiently trained in an end-to-end fashion. Experiments across multiple tasks show that the DGSM outperforms state-of-the-art baselines by a large margin, and it is capable of generating conformations for a broader range of systems such as proteins and multi-molecular complexes.

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