Cyclic peptides, characterized by geometric constraints absent in linear peptides, offer enhanced biochemical properties, presenting new opportunities to address unmet medical needs. However, designing target-specific cyclic peptides remains underexplored due to limited training data. To bridge the gap, we propose CP-Composer, a novel generative framework that enables zero-shot cyclic peptide generation via composable geometric constraints. Our approach decomposes complex cyclization patterns into unit constraints, which are incorporated into a diffusion model through geometric conditioning on nodes and edges. During training, the model learns from unit constraints and their random combinations in linear peptides, while at inference, novel constraint combinations required for cyclization are imposed as input. Experiments show that our model, despite trained with linear peptides, is capable of generating diverse target-binding cyclic peptides, reaching success rates from 38% to 84% on different cyclization strategies.

The design of target-specific molecules such as small molecules, peptides, and antibodies is vital for biological research and drug discovery. Existing generative methods are restricted to single-domain molecules, failing to address versatile therapeutic needs or utilize cross-domain transferability to enhance model performance. In this paper, we introduce Unified generative Modeling of 3D Molecules (UniMoMo), the first framework capable of designing binders of multiple molecular domains using a single model. In particular, UniMoMo unifies the representations of different molecules as graphs of blocks, where each block corresponds to either a standard amino acid or a molecular fragment. Based on these unified representations, UniMoMo utilizes a geometric latent diffusion model for 3D molecular generation, featuring an iterative full-atom autoencoder to compress blocks into latent space points, followed by an E(3)-equivariant diffusion process. Extensive benchmarks across peptides, antibodies, and small molecules demonstrate the superiority of our unified framework over existing domain-specific models, highlighting the benefits of multi-domain training.

Cyclic peptides exhibit better binding affinity and proteolytic stability compared to their linear counterparts. However, the development of cyclic peptide design models is hindered by the scarcity of data. To address this, we introduce **CPSea**(**C**yclic **P**eptide **Sea**), a dataset of 2.71 million cyclic peptide-receptor complexes, curated through systematic mining of the AlphaFold Database (AFDB). Our pipeline extracts compact domains from AFDB, identifies cyclization sites using the $\beta$-carbon (C$_\beta$) distance thresholds, and applies multi-stage filtering to ensure structure fidelity and binding compatibility. Compared with experimental data of cyclic peptides, CPSea shows similar distributions in metrics on structure fidelity and wet-lab compatibility. To our knowledge, CPSea is the largest cyclic peptide-receptor dataset to date, enabling end-to-end model training for the first time. The dataset also showcases the feasibility of simulating inter-chain interactions using intra-chain interactions, expanding available resources for machine-learning models on protein-protein interactions. The dataset and relevant scripts are accessible on GitHub ([https://github.com/YZY010418/CPSea](https://github.com/YZY010418/CPSea)).

Designing protein binders targeting specific sites, which requires to generate realistic and functional interaction patterns, is a fundamental challenge in drug discovery. Current structure-based generative models are limited in generating nterfaces with sufficient rationality and interpretability. In this paper, we propose **R**etrieval-**A**ugmented **Di**ffusion for **A**lig**n**ed interfa**ce** (**RADiAnce**), a new framework that leverages known interfaces to guide the design of novel binders. By unifying retrieval and generation in a shared contrastive latent space, our model efficiently identifies relevant interfaces for a given binding site and seamlessly integrates them through a conditional latent diffusion generator, enabling cross-domain interface transfer. Extensive exeriments show that **RADiAnce** significantly outperforms baseline models across multiple metrics, including binding affinity and recovery of geometries and interactions. Additional experimental results validate cross-domain generalization, demonstrating that retrieving interfaces from diverse domains, such as peptides, antibodies, and protein fragments, enhances the generation performance of binders for other domains. Our work establishes a new paradigm for protein binder design that successfully bridges retrieval-based knowledge and generative AI, opening new possibilities for drug discovery.

Abstract Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections, making them ineffectively processed by current Graph Neural Networks (GNNs). To address this issue, researchers proposed a variety of geometric GNNs equipped with invariant/equivariant properties to better characterize the geometry and topology of geometric graphs. Given the current progress in this field, it is imperative to conduct a comprehensive survey of data structures, models, and applications related to geometric GNNs. In this paper, based on the necessary but concise mathematical preliminaries, we formalize geometric graph as the data structure, on top of which we provide a unified view of existing models from the geometric message passing perspective. Additionally, we summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation. We also discuss the challenges and future potential directions of geometric GNNs at the end of this survey.

Many processes in biology and drug discovery involve various 3D interactions between molecules, such as protein and protein, protein and small molecule, etc. Given that different molecules are usually represented in different granularity, existing methods usually encode each type of molecules independently with different models, leaving it defective to learn the various underlying interaction physics. In this paper, we first propose to universally represent an arbitrary 3D complex as a geometric graph of sets, shedding light on encoding all types of molecules with one model. We then propose a Generalist Equivariant Transformer (GET) to effectively capture both domain-specific hierarchies and domain-agnostic interaction physics. To be specific, GET consists of a bilevel attention module, a feed-forward module and a layer normalization module, where each module is E(3) equivariant and specialized for handling sets of variable sizes. Notably, in contrast to conventional pooling-based hierarchical models, our GET is able to retain fine-grained information of all levels. Extensive experiments on the interactions between proteins, small molecules and RNA/DNAs verify the effectiveness and generalization capability of our proposed method across different domains.

Predicting high-fidelity 3D structures of atomic systems is a fundamental yet challenging problem in scientific domains. While recent work demonstrates the advantage of generative models in this realm, the exploration of different probability paths are still insufficient, and hallucinations during sampling are persistently occurring. To address these pitfalls, we introduce FlowDPO, a novel framework that explores various probability paths with flow matching models and further suppresses hallucinations using Direct Preference Optimization (DPO) for structure generation. Our approach begins with a pre-trained flow matching model to generate multiple candidate structures for each training sample. These structures are then evaluated and ranked based on their distance to the ground truth, resulting in an automatic preference dataset. Using this dataset, we apply DPO to optimize the original model, improving its performance in generating structures closely aligned with the desired reference distribution. As confirmed by our theoretical analysis, such paradigm and objective function are compatible with arbitrary Gaussian paths, exhibiting favorable universality. Extensive experimental results on antibodies and crystals demonstrate substantial benefits of our FlowDPO, highlighting its potential to advance the field of 3D structure prediction with generative models.

Peptide design plays a pivotal role in therapeutics, allowing brand new possibility to leverage target binding sites that are previously undruggable. Most existing methods are either inefficient or only concerned with the target-agnostic design of 1D sequences. In this paper, we propose a generative model for full-atom Peptide design with Geometric LAtent Diffusion (PepGLAD) given the binding site. We first establish a benchmark consisting of both 1D sequences and 3D structures from Protein Data Bank (PDB) and literature for systematic evaluation. We then identify two major challenges of leveraging current diffusion-based models for peptide design: the full-atom geometry and the variable binding geometry. To tackle the first challenge, PepGLAD derives a variational autoencoder that first encodes full-atom residues of variable size into fixed-dimensional latent representations, and then decodes back to the residue space after conducting the diffusion process in the latent space. For the second issue, PepGLAD explores a receptor-specific affine transformation to convert the 3D coordinates into a shared standard space, enabling better generalization ability across different binding shapes. Experimental Results show that our method not only improves diversity and binding affinity significantly in the task of sequence-structure co-design, but also excels at recovering reference structures for binding conformation generation.

Antibody design is an essential yet challenging task in various domains like therapeutics and biology. There are two major defects in current learning-based methods: 1) tackling only a certain subtask of the whole antibody design pipeline, making them suboptimal or resource-intensive. 2) omitting either the framework regions or side chains, thus incapable of capturing the full-atom geometry. To address these pitfalls, we propose dynamic Multi-channel Equivariant grAph Network (dyMEAN), an end-to-end full-atom model for E(3)-equivariant antibody design given the epitope and the incomplete sequence of the antibody. Specifically, we first explore structural initialization as a knowledgeable guess of the antibody structure and then propose shadow paratope to bridge the epitope-antibody connections. Both 1D sequences and 3D structures are updated via an adaptive multi-channel equivariant encoder that is able to process protein residues of variable sizes when considering full atoms. Finally, the updated antibody is docked to the epitope via the alignment of the shadow paratope. Experiments on epitope-binding CDR-H3 design, complex structure prediction, and affinity optimization demonstrate the superiority of our end-to-end framework and full-atom modeling.

Molecule generation is central to a variety of applications. Current attention has been paid to approaching the generation task as subgraph prediction and assembling. Nevertheless, these methods usually rely on hand-crafted or external subgraph construction, and the subgraph assembling depends solely on local arrangement. In this paper, we define a novel notion, principal subgraph that is closely related to the informative pattern within molecules. Interestingly, our proposed merge-and-update subgraph extraction method can automatically discover frequent principal subgraphs from the dataset, while previous methods are incapable of. Moreover, we develop a two-step subgraph assembling strategy, which first predicts a set of subgraphs in a sequence-wise manner and then assembles all generated subgraphs globally as the final output molecule. Built upon graph variational auto-encoder, our model is demonstrated to be effective in terms of several evaluation metrics and efficiency, compared with state-of-the-art methods on distribution learning and (constrained) property optimization tasks.