1
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Gainza P, Bunker RD, Townson SA, Castle JC. Machine learning to predict de novo protein-protein interactions. Trends Biotechnol 2025:S0167-7799(25)00158-1. [PMID: 40425414 DOI: 10.1016/j.tibtech.2025.04.013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2024] [Revised: 04/23/2025] [Accepted: 04/23/2025] [Indexed: 05/29/2025]
Abstract
Advances in machine learning for structural biology have dramatically enhanced our capacity to predict protein-protein interactions (PPIs). Here, we review recent developments in the computational prediction of PPIs, particularly focusing on innovations that enable interaction predictions that have no precedence in nature, termed de novo. We discuss novel machine learning algorithms for PPI prediction, including approaches based on co-folding and atomic graphs. We further highlight methods that learn from molecular surfaces, which can predict PPIs not found in nature including interactions induced by small molecules. Finally, we explore the emerging biotechnological applications enabled by these predictive capabilities, including the prediction of antibody-antigen complexes and molecular glue-induced PPIs, and discuss their potential to empower drug discovery and protein engineering.
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Affiliation(s)
- Pablo Gainza
- Monte Rosa Therapeutics, Klybeckstrasse 191, 4057 Basel, Switzerland.
| | - Richard D Bunker
- Monte Rosa Therapeutics, Klybeckstrasse 191, 4057 Basel, Switzerland
| | - Sharon A Townson
- Monte Rosa Therapeutics, Klybeckstrasse 191, 4057 Basel, Switzerland
| | - John C Castle
- Monte Rosa Therapeutics, Klybeckstrasse 191, 4057 Basel, Switzerland.
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2
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Li H, Nithin C, Kmiecik S, Huang SY. Computational methods for modeling protein-protein interactions in the AI era: Current status and future directions. Drug Discov Today 2025; 30:104382. [PMID: 40398752 DOI: 10.1016/j.drudis.2025.104382] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2025] [Revised: 04/30/2025] [Accepted: 05/14/2025] [Indexed: 05/23/2025]
Abstract
The modeling of protein-protein interactions (PPIs) has been revolutionized by artificial intelligence, with deep learning and end-to-end frameworks such as AlphaFold and its derivatives now dominating the field. This review surveys the current computational landscape for predicting protein complex structures, outlining the role of traditional docking approaches as well as focusing on recent advances in AI-driven methods. We discuss key challenges, including protein flexibility, reliance on co-evolutionary signals, modeling of large assemblies, and interactions involving intrinsically disordered regions (IDRs). Recent innovations aimed at improving sampling diversity, integrating experimental data, and enhancing robustness are also highlighted. Although classical methods remain relevant in specific contexts, the continued evolution of AI-based tools offers transformative potential for structural biology. These advances are poised to deepen our understanding of biomolecular interactions and accelerate the design of therapeutic interventions.
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Affiliation(s)
- Hao Li
- School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
| | - Chandran Nithin
- University of Warsaw, Biological and Chemical Research Centre, Faculty of Chemistry, Warsaw, Poland
| | - Sebastian Kmiecik
- University of Warsaw, Biological and Chemical Research Centre, Faculty of Chemistry, Warsaw, Poland.
| | - Sheng-You Huang
- School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China.
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3
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Zhang X, Jiang L, Weng G, Shen C, Zhang O, Liu M, Zhang C, Gu S, Wang J, Wang X, Du H, Zhang H, Zhang K, Wang E, Hou T. HawkDock version 2: an updated web server to predict and analyze the structures of protein-protein complexes. Nucleic Acids Res 2025:gkaf379. [PMID: 40326522 DOI: 10.1093/nar/gkaf379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2025] [Revised: 04/14/2025] [Accepted: 04/24/2025] [Indexed: 05/07/2025] Open
Abstract
Protein-protein interactions (PPIs) are fundamental to cellular functions, yet predicting and analyzing their 3D structures remains a critical and computationally demanding challenge. To address this, the HawkDock web server was developed as an integrated computational platform for predicting and analyzing protein-protein complexes. Over the past 6 years, HawkDock has successfully processed >234 000 computational tasks. In this study, an updated version of HawkDock was developed with the following advancements: (1) a deep learning-based flexible docking method, GeoDock, has been integrated to improve docking accuracy, particularly for apo-protein structures; (2) the VD-MM/GBSA method, which outperforms conventional MM/GBSA approaches in predicting binding affinities, has been implemented; (3) a new Mutation Analysis Module has been added to systematically evaluate the energetic impacts of amino acid mutations on protein-protein binding; (4) the server has been migrated to a high-performance cluster with Amber upgraded to version 24. Here, we describe the general protocol of HawkDock2, with a particular focus on its new features related to flexible docking, VD-MM/GBSA affinity prediction, and amino acid residue mutations. Comprehensive validation studies have demonstrated the reliability and effectiveness of these new features. HawkDock2 will remain freely accessible to all users at http://cadd.zju.edu.cn/hawkdock/.
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Affiliation(s)
- Xujun Zhang
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Linlong Jiang
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Gaoqi Weng
- Vollum Institute, Oregon Health and Science University, Portland, OR 97239, United States
| | - Chao Shen
- Department of Clinical Pharmacy, The First Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou 310003, Zhejiang, China
| | - Odin Zhang
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Mingquan Liu
- College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, Hunan, China
| | - Chen Zhang
- College of Animal Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Shukai Gu
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Jike Wang
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Xiaorui Wang
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Hongyan Du
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Hui Zhang
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Ke Zhang
- Polytechnic Institute, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Ercheng Wang
- Research Center for Life Science Computing, Zhejiang Lab, Hangzhou 310058, Zhejiang, China
| | - Tingjun Hou
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
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4
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Hitawala FN, Gray JJ. What does AlphaFold3 learn about antigen and nanobody docking, and what remains unsolved? BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2025:2024.09.21.614257. [PMID: 39975279 PMCID: PMC11838198 DOI: 10.1101/2024.09.21.614257] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 02/21/2025]
Abstract
Antibody therapeutic development is a major focus in healthcare. To accelerate drug development, significant efforts have been directed towards the in silico design and screening of antibodies for which high modeling accuracy is necessary. To probe AlphaFold3's (AF3) capabilities and limitations, we tested AF3's ability to capture the fine details and interplay between antibody structure prediction and antigen docking accuracy. With one seed, AF3 achieves an 11.0% and 11.4% high-accuracy docking success rate for antibodies and nanobodies, respectively, and a median unbound CDR H3 RMSD accuracy of 2.73 Å and 2.30 Å. CDR H3 accuracy boosts complex prediction accuracy, with antigen context improving CDR H3 accuracy, particularly for loops longer than 15 residues. Combining I-pLDDT with Δ G B improves discriminative power for correctly docked complexes. However, AF3's 60% failure rate for antibody and nanobody docking (with single seed sampling) demonstrates necessary refinement to improve antibody design endeavors.
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Affiliation(s)
- Fatima N. Hitawala
- Chemical and Biomolecular Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
| | - Jeffrey J. Gray
- Chemical and Biomolecular Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
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5
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Alotaiq N, Dermawan D. Evaluation of Structure Prediction and Molecular Docking Tools for Therapeutic Peptides in Clinical Use and Trials Targeting Coronary Artery Disease. Int J Mol Sci 2025; 26:462. [PMID: 39859178 PMCID: PMC11765240 DOI: 10.3390/ijms26020462] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2024] [Revised: 01/04/2025] [Accepted: 01/07/2025] [Indexed: 01/27/2025] Open
Abstract
This study evaluates the performance of various structure prediction tools and molecular docking platforms for therapeutic peptides targeting coronary artery disease (CAD). Structure prediction tools, including AlphaFold 3, I-TASSER 5.1, and PEP-FOLD 4, were employed to generate accurate peptide conformations. These methods, ranging from deep-learning-based (AlphaFold) to template-based (I-TASSER 5.1) and fragment-based (PEP-FOLD), were selected for their proven capabilities in predicting reliable structures. Molecular docking was conducted using four platforms (HADDOCK 2.4, HPEPDOCK 2.0, ClusPro 2.0, and HawDock 2.0) to assess binding affinities and interactions. A 100 ns molecular dynamics (MD) simulation was performed to evaluate the stability of the peptide-receptor complexes, along with Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) calculations to determine binding free energies. The results demonstrated that Apelin, a therapeutic peptide, exhibited superior binding affinities and stability across all platforms, making it a promising candidate for CAD therapy. Apelin's interactions with key receptors involved in cardiovascular health were notably stronger and more stable compared to the other peptides tested. These findings underscore the importance of integrating advanced computational tools for peptide design and evaluation, offering valuable insights for future therapeutic applications in CAD. Future work should focus on in vivo validation and combination therapies to fully explore the clinical potential of these therapeutic peptides.
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Affiliation(s)
- Nasser Alotaiq
- Health Sciences Research Center (HSRC), Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13317, Saudi Arabia
| | - Doni Dermawan
- Department of Applied Biotechnology, Faculty of Chemistry, Warsaw University of Technology, 00-661 Warsaw, Poland;
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Zheng J, Wang Y, Liang Q, Cui L, Wang L. The Application of Machine Learning on Antibody Discovery and Optimization. Molecules 2024; 29:5923. [PMID: 39770013 PMCID: PMC11679646 DOI: 10.3390/molecules29245923] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2024] [Revised: 11/27/2024] [Accepted: 12/11/2024] [Indexed: 01/11/2025] Open
Abstract
Antibodies play critical roles in modern medicine, serving as diagnostics and therapeutics for various diseases due to their ability to specifically bind to target antigens. Traditional antibody discovery and optimization methods are time-consuming and resource-intensive, though they have successfully generated antibodies for diagnosing and treating diseases. The advancements in protein data, computational hardware, and machine learning (ML) models have the opportunity to disrupt antibody discovery and optimization research. Machine learning models have demonstrated their abilities in antibody design. These machine learning models enable rapid in silico design of antibody candidates within a few days, achieving approximately a 60% reduction in time and a 50% reduction in cost compared to traditional methods. This review focuses on the latest machine learning-based antibody discovery and optimization developments. We briefly discuss the limitations of traditional methods and then explore the machine learning-based antibody discovery and optimization methodologies. We also focus on future research directions, including developing Antibody Design AI Agents and data foundries, alongside the ethical and regulatory considerations essential for successfully adopting machine learning-driven antibody designs.
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Affiliation(s)
- Jiayao Zheng
- School of Pharmacy & School of Biological and Food Engineering, Changzhou University, Changzhou 213164, China
| | - Yu Wang
- Protein Design Lab, Changzhou AiRiBio Healthcare Co., Ltd., Changzhou 213164, China
| | - Qianying Liang
- Protein Design Lab, Changzhou AiRiBio Healthcare Co., Ltd., Changzhou 213164, China
| | - Lun Cui
- School of Pharmacy & School of Biological and Food Engineering, Changzhou University, Changzhou 213164, China
- Protein Design Lab, Changzhou AiRiBio Healthcare Co., Ltd., Changzhou 213164, China
| | - Liqun Wang
- School of Pharmacy & School of Biological and Food Engineering, Changzhou University, Changzhou 213164, China
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Chu LS, Sarma S, Gray JJ. Unified Sampling and Ranking for Protein Docking with DFMDock. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.09.27.615401. [PMID: 39386449 PMCID: PMC11463455 DOI: 10.1101/2024.09.27.615401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/12/2024]
Abstract
Diffusion models have shown promise in addressing the protein docking problem. Traditionally, these models are used solely for sampling docked poses, with a separate confidence model for ranking. We introduce DFMDock (Denoising Force Matching Dock), a diffusion model that unifies sampling and ranking within a single framework. DFMDock features two output heads: one for predicting forces and the other for predicting energies. The forces are trained using a denoising force matching objective, while the energy gradients are trained to align with the forces. This design enables our model to sample using the predicted forces and rank poses using the predicted energies, thereby eliminating the need for an additional confidence model. Our approach outperforms the previous diffusion model for protein docking, DiffDock-PP, with a sampling success rate of 44% compared to its 8%, and a Top- 1 ranking success rate of 16% compared to 0% on the Docking Benchmark 5.5 test set. In successful decoy cases, the DFMDock Energy forms a binding funnel similar to the physics-based Rosetta Energy, suggesting that DFMDock can capture the underlying energy landscape.
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Affiliation(s)
- Lee-Shin Chu
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
| | - Sudeep Sarma
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
| | - Jeffrey J Gray
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
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8
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Nasaev SS, Mukanov AR, Mishkorez IV, Kuznetsov II, Leibin IV, Dolgusheva VA, Pavlyuk GA, Manasyan AL, Veselovsky AV. Molecular Modeling Methods in the Development of Affine and Specific Protein-Binding Agents. BIOCHEMISTRY. BIOKHIMIIA 2024; 89:1451-1473. [PMID: 39245455 DOI: 10.1134/s0006297924080066] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2024] [Revised: 06/12/2024] [Accepted: 07/11/2024] [Indexed: 09/10/2024]
Abstract
High-affinity and specific agents are widely applied in various areas, including diagnostics, scientific research, and disease therapy (as drugs and drug delivery systems). It takes significant time to develop them. For this reason, development of high-affinity agents extensively utilizes computer methods at various stages for the analysis and modeling of these molecules. The review describes the main affinity and specific agents, such as monoclonal antibodies and their fragments, antibody mimetics, aptamers, and molecularly imprinted polymers. The methods of their obtaining as well as their main advantages and disadvantages are briefly described, with special attention focused on the molecular modeling methods used for their analysis and development.
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Affiliation(s)
| | - Artem R Mukanov
- Research & Development Department, Xelari Ltd., Moscow, 121601, Russia
| | - Ivan V Mishkorez
- Research & Development Department, Xelari Ltd., Moscow, 121601, Russia
- Institute of Biomedical Chemistry, Moscow, 119121, Russia
| | - Ivan I Kuznetsov
- Research & Development Department, Xelari Ltd., Moscow, 121601, Russia
| | - Iosif V Leibin
- Skolkovo Institute of Science and Technology, Skolkovo Innovation Center, Moscow, 121205, Russia
| | | | - Gleb A Pavlyuk
- Research & Development Department, Xelari Ltd., Moscow, 121601, Russia
| | - Artem L Manasyan
- Research & Development Department, Xelari Ltd., Moscow, 121601, Russia
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9
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Kousaka S, Ishikawa T. Quantum Chemistry-Based Protein-Protein Docking without Empirical Parameters. J Chem Theory Comput 2024; 20:5164-5175. [PMID: 38845143 DOI: 10.1021/acs.jctc.4c00531] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/26/2024]
Abstract
This study developed a novel protein-protein docking approach based on quantum chemistry. To judge the appropriateness of complex structures, we introduced two criterion values, EV1 and EV2, computed using the fragment molecular orbital method without any empirical parameters. These criterion values enable us to search complex structures in which patterns of the electrostatic potential of the two proteins are optimally aligned at their interface. The performance of our method was validated using 53 complexes in a benchmark set provided for protein-protein docking. When employing bound state structures, docking success rates reached 64% for EV1 and 76% for EV2. On the other hand, when employing unbound state structures, docking success rates reached 13% for EV1 and 17% for EV2.
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Affiliation(s)
- Sumire Kousaka
- Department of Chemistry, Biotechnology, and Chemical Engineering, Graduate School of Science and Engineering, Kagoshima University, 1-21-40 Korimoto, Kagoshima 890-0065, Japan
| | - Takeshi Ishikawa
- Department of Chemistry, Biotechnology, and Chemical Engineering, Graduate School of Science and Engineering, Kagoshima University, 1-21-40 Korimoto, Kagoshima 890-0065, Japan
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10
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Zhao N, Wu T, Wang W, Zhang L, Gong X. Review and Comparative Analysis of Methods and Advancements in Predicting Protein Complex Structure. Interdiscip Sci 2024; 16:261-288. [PMID: 38955920 DOI: 10.1007/s12539-024-00626-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2023] [Revised: 02/29/2024] [Accepted: 03/01/2024] [Indexed: 07/04/2024]
Abstract
Protein complexes perform diverse biological functions, and obtaining their three-dimensional structure is critical to understanding and grasping their functions. In many cases, it's not just two proteins interacting to form a dimer; instead, multiple proteins interact to form a multimer. Experimentally resolving protein complex structures can be quite challenging. Recently, there have been efforts and methods that build upon prior predictions of dimer structures to attempt to predict multimer structures. However, in comparison to monomeric protein structure prediction, the accuracy of protein complex structure prediction remains relatively low. This paper provides an overview of recent advancements in efficient computational models for predicting protein complex structures. We introduce protein-protein docking methods in detail and summarize their main ideas, applicable modes, and related information. To enhance prediction accuracy, other critical protein-related information is also integrated, such as predicting interchain residue contact, utilizing experimental data like cryo-EM experiments, and considering protein interactions and non-interactions. In addition, we comprehensively review computational approaches for end-to-end prediction of protein complex structures based on artificial intelligence (AI) technology and describe commonly used datasets and representative evaluation metrics in protein complexes. Finally, we analyze the formidable challenges faced in current protein complex structure prediction tasks, including the structure prediction of heteromeric complex, disordered regions in complex, antibody-antigen complex, and RNA-related complex, as well as the evaluation metrics for complex assessment. We hope that this work will provide comprehensive knowledge of complex structure predictions to contribute to future advanced predictions.
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Affiliation(s)
- Nan Zhao
- Institute for Mathematical Sciences, Renmin University of China, Beijing, 100872, China
- School of Mathematics, Renmin University of China, Beijing, 100872, China
| | - Tong Wu
- Institute for Mathematical Sciences, Renmin University of China, Beijing, 100872, China
- School of Mathematics, Renmin University of China, Beijing, 100872, China
| | - Wenda Wang
- Institute for Mathematical Sciences, Renmin University of China, Beijing, 100872, China
- School of Mathematics, Renmin University of China, Beijing, 100872, China
| | - Lunchuan Zhang
- School of Mathematics, Renmin University of China, Beijing, 100872, China.
| | - Xinqi Gong
- Institute for Mathematical Sciences, Renmin University of China, Beijing, 100872, China.
- School of Mathematics, Renmin University of China, Beijing, 100872, China.
- Beijing Academy of Artificial Intelligence, Beijing, 100084, China.
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11
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Zhao N, Han B, Zhao C, Xu J, Gong X. ABAG-docking benchmark: a non-redundant structure benchmark dataset for antibody-antigen computational docking. Brief Bioinform 2024; 25:bbae048. [PMID: 38385879 PMCID: PMC10883643 DOI: 10.1093/bib/bbae048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2023] [Revised: 01/05/2024] [Accepted: 01/15/2024] [Indexed: 02/23/2024] Open
Abstract
Accurate prediction of antibody-antigen complex structures is pivotal in drug discovery, vaccine design and disease treatment and can facilitate the development of more effective therapies and diagnostics. In this work, we first review the antibody-antigen docking (ABAG-docking) datasets. Then, we present the creation and characterization of a comprehensive benchmark dataset of antibody-antigen complexes. We categorize the dataset based on docking difficulty, interface properties and structural characteristics, to provide a diverse set of cases for rigorous evaluation. Compared with Docking Benchmark 5.5, we have added 112 cases, including 14 single-domain antibody (sdAb) cases and 98 monoclonal antibody (mAb) cases, and also increased the proportion of Difficult cases. Our dataset contains diverse cases, including human/humanized antibodies, sdAbs, rodent antibodies and other types, opening the door to better algorithm development. Furthermore, we provide details on the process of building the benchmark dataset and introduce a pipeline for periodic updates to keep it up to date. We also utilize multiple complex prediction methods including ZDOCK, ClusPro, HDOCK and AlphaFold-Multimer for testing and analyzing this dataset. This benchmark serves as a valuable resource for evaluating and advancing docking computational methods in the analysis of antibody-antigen interaction, enabling researchers to develop more accurate and effective tools for predicting and designing antibody-antigen complexes. The non-redundant ABAG-docking structure benchmark dataset is available at https://github.com/Zhaonan99/Antibody-antigen-complex-structure-benchmark-dataset.
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Affiliation(s)
- Nan Zhao
- Institute for Mathematical Sciences, School of Mathematics, Renmin University of China, Beijing, China
| | - Bingqing Han
- Institute for Mathematical Sciences, School of Mathematics, Renmin University of China, Beijing, China
| | - Cuicui Zhao
- Institute for Mathematical Sciences, School of Mathematics, Renmin University of China, Beijing, China
| | - Jinbo Xu
- MoleculeMind Ltd., Beijing, China
| | - Xinqi Gong
- Institute for Mathematical Sciences, School of Mathematics, Renmin University of China, Beijing, China
- Beijing Academy of Artificial Intelligence, Beijing, China
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