Artificial intelligence-assisted drug design is revolutionizing the pharmaceutical industry. Effective molecular features are crucial for accurate machine learning predictions, and advanced mathematics plays a key role in designing these features. Persistent homology theory, which equips topological invariants with persistence, provides valuable insights into molecular structures. The calculation of Betti numbers is based on differential that typically satisfy \(d^2 = 0\). Our recent work has extended this concept by employing Mayer homology with a generalized differential that satisfies \(d^N = 0\) for \(N \geq 2\), leading to the development of persistent Mayer homology (PMH) theory and richer topological information across various scales. In this study, we utilize PMH to create a novel multiscale topological vectorization for molecular representation, offering valuable tools for descriptive and predictive analysis in molecular data and machine learning prediction. Specifically, benchmark tests on established protein-ligand datasets, including PDBbind-2007, PDBbind-2013, and PDBbind-2016, demonstrate the superior performance of our Mayer homology models in predicting protein-ligand binding affinities.
Persistent local Laplacian prediction of protein-ligand binding affinities
Mathematical Science Research Center, Chongqing University of Technology（重庆理工大学数学科学研究中心）；Department of Mathematics and Statistics, University of North Carolina at Charlotte（北卡罗来纳大学夏洛特分校数学与统计系）
From Static to Dynamic Structures: Improving Binding Affinity Prediction with Graph-Based Deep Learning
Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；School of Medicine, Tsinghua University（清华大学医学院）；KTH Stockholm（瑞典皇家理工学院）；Microsoft Research Asia（微软亚洲研究院）；School of Life Science and Technology, Xidian University（西安电子科技大学生命科学技术学院）；School of Engineering, Westlake University（西湖大学工程学院）
DEL-Ranking: Ranking-Correction Denoising Framework for Elucidating Molecular Affinities in DNA-Encoded Libraries
CUHK（香港中文大学）；College of Chemistry and Chemical Engineering, Lanzhou University（兰州大学化学化工学院）；HKUST（香港科技大学）；College of Pharmaceutical Sciences, Zhejiang University（浙江大学药学院）
针对 DEL 筛选读取计数噪声问题，提出结合排序损失、自训练与一致性损失的 DEL-Ranking 去噪框架，并发布三个多表征数据集，显著提升结合亲和力预测与零样本泛化能力。
Electrostatic Affinities and Binding Kinetics among $α_2\textrm{I}$ Integrin Domains, Divalent Cations and 21-mer Collagen Fragment
本文比较了$α_2β_1$整合素与胶原蛋白相互作用的模拟结果和实验数据，发现整合素与胶原蛋白的相互作用表现为空间位阻、相互取向约束和长程静电力之间的竞争。已发表的实验结果表明，对于42聚体胶原片段和$α_2\textrm{I}$整联蛋白结构域复合物，$\textrm{k}_{\textrm{on}}$比率的范围为$10^4-10^5$ M $^{-1}$ s $^{-1}$的数量级。这是由扩散限制制度和取向约束定义的区间的下限。由于二价阳离子（$\textrm{Mg}^{2+}$、$\textrm{Co}^{2+}$、$\textrm{Mn}^{2+}$和$\textrm{Ca}^{2+}$），21-mer胶原片段和$α_2\textrm{I}$整联蛋白结构域之间的静电亲和力已用配体的静电去溶剂化电位和受体的静电相互作用电位之间的Pearson相关系数表示。所获得的Pearson系数值清楚地揭示了$α_2\textrm{I}$整联蛋白结构域与金属离子依赖性位点中的21-mer胶原之间的互补性。根据已发表的实验数据，在扩散限制方案中应用的原子布朗动力学模拟正确地再现了在$\textrm{Mg}^{2+}$、$\textrm{Co}^{2+}$和$\textrm{Mn}^{2+}$存在下$α_2\textrm{I}$整联蛋白结构域和21-mer胶原的结合动力学。
A Multi-Grained Symmetric Differential Equation Model for Learning Protein-Ligand Binding Dynamics
University of California Berkeley（加州大学伯克利分校）；DAMO Academy（达摩院）；University of Oxford（牛津大学）；California Institute of Technology（加州理工学院）；University of Toronto（多伦多大学）；National Research Council Canada（加拿大国家研究委员会）
FLOWR.root: A flow matching based foundation model for joint multi-purpose structure-aware 3D ligand generation and affinity prediction
Machine Learning & Computational Sciences, Pfizer Worldwide R&D（辉瑞全球研发 机器学习与计算科学部）；Computational Chemistry, Medicine Design, Pfizer Worldwide R&D（辉瑞全球研发 计算化学与医学设计部）；Doctoral School of Medical and Health Sciences, Jagiellonian University Medical College（杰拉西利昂大学医学院医学与健康科学博士学院）；Department of Physicochemical Drug Analysis, Faculty of Pharmacy, Jagiellonian University Medical College（杰拉西利昂大学医学院药物物理化学分析系）；Institute of Structural Biology, Molecular Targets and Therapeutics Center, Helmholtz Munich（海德堡-慕尼黑分子靶点与治疗中心 结构生物学研究所）；TUM School of Natural Sciences, Department of Bioscience, Bayerisches NMR Zentrum, Technical University of Munich（慕尼黑技术大学自然科学学院 生物科学系，拜耳核磁共振中心）
Binding-Adaptive Diffusion Models for Structure-Based Drug Design
Tsinghua University（清华大学）；Peng Cheng Laboratory（鹏城实验室）；Peking University（北京大学）；University of Science and Technology of China（中国科学技术大学）；University of Chinese Academy of Sciences（中国科学院大学）；ByteDance（字节跳动）
Deep learning is competing random forest in computational docking
Egypt-Japan University of Science and Technology (E-JUST)（埃及日本科技大学）；Alexandria University（亚历山大大学）
Computational docking is the core process of computer-aided drug design; it aims at predicting the best orientation and conformation of a small drug molecule when bound to a target large protein receptor. The docking quality is typically measured by a scoring function: a mathematical predictive model that produces a score representing the binding free energy and hence the stability of the resulting complex molecule. We analyze the performance of both learning techniques on the scoring power, the ranking power, docking power, and screening power using the PDBbind 2013 database. For the scoring …
