标题： OTMol：通过最优传输的鲁棒分子结构比较 显示英文标题

标题： OTMol: Robust Molecular Structure Comparison via Optimal Transport

摘要： 均方根偏差（RMSD）被广泛用于评估从柔性配体构象到复杂分子簇构型的系统结构相似性。 尽管RMSD应用广泛，但其计算常常面临原子顺序不一致、分子簇中难以区分的构型以及对齐过程中可能发生的立体化学反转等问题。 这些问题突显了准确的原子对应关系作为有意义对齐的前提条件的必要性。 传统方法通常依赖于启发式的成本矩阵结合匈牙利算法，然而这些方法未能充分利用丰富的分子内结构信息，并且在化学多样性系统中可能无法推广。 在本工作中，我们引入了OTMol，这是一种将分子对齐任务形式化为融合监督Gromov-Wasserstein（fsGW）最优传输问题的方法。 通过利用每个分子内部的固有几何和拓扑关系，OTMol消除了对手动定义的成本函数的需求，并实现了原则性的、数据驱动的匹配策略。 重要的是，OTMol保留了分子立体化学和键连接一致性等关键化学特征。 我们在包括三磷酸腺苷、伊马替尼、脂质、小肽和水簇在内的多种分子系统上评估了OTMol，并证明它在保持计算效率的同时始终能够实现低RMSD值。 重要的是，OTMol通过强制整个分子之间的一一映射来保持分子完整性，从而避免了在比较分子簇时经常出现的错误多对一对齐。 我们的结果强调了最优传输理论在分子对齐中的实用性，并提供了一个可推广的框架，适用于化学生物信息学、分子建模及相关领域的结构比较任务。 显示英文摘要

摘要： Root-mean-square deviation (RMSD) is widely used to assess structural similarity in systems ranging from flexible ligand conformers to complex molecular cluster configurations. Despite its wide utility, RMSD calculation is often challenged by inconsistent atom ordering, indistinguishable configurations in molecular clusters, and potential chirality inversion during alignment. These issues highlight the necessity of accurate atom-to-atom correspondence as a prerequisite for meaningful alignment. Traditional approaches often rely on heuristic cost matrices combined with the Hungarian algorithm, yet these methods underutilize the rich intra-molecular structural information and may fail to generalize across chemically diverse systems. In this work, we introduce OTMol, a method that formulates the molecular alignment task as a fused supervised Gromov-Wasserstein (fsGW) optimal transport problem. By leveraging the intrinsic geometric and topological relationships within each molecule, OTMol eliminates the need for manually defined cost functions and enables a principled, data-driven matching strategy. Importantly, OTMol preserves key chemical features such as molecular chirality and bond connectivity consistency. We evaluate OTMol across a wide range of molecular systems, including Adenosine triphosphate, Imatinib, lipids, small peptides, and water clusters, and demonstrate that it consistently achieves low RMSD values while preserving computational efficiency. Importantly, OTMol maintains molecular integrity by enforcing one-to-one mappings between entire molecules, thereby avoiding erroneous many-to-one alignments that often arise in comparing molecular clusters. Our results underscore the utility of optimal transport theory for molecular alignment and offer a generalizable framework applicable to structural comparison tasks in cheminformatics, molecular modeling, and related disciplines.