arXiv:2608.05336physics.chem-phcs.LG2026-08

用三维谱图理论生成可解释的分子指纹,高效区分立体异构体。

Physics-Based Molecular Fingerprints from Spectral Graph Theory Provide Efficient Geometry-Aware Measures of Chemical Similarity

  • 基于3D图拉普拉斯矩阵的特征值分解,生成固定长度指纹。
  • 能准确区分2D结构相同但3D构型不同的分子,计算效率高。
  • 适合大规模化学空间筛选,兼具可解释性与物理对称性约束。

分子表示对评估分子相似性和构建结构-性质关系至关重要。尽管3D结构对化学和物理性质有决定性影响,但广泛使用的分子指纹仅编码二维连接信息,无法区分结构相似但构型不同的立体异构体和构象异构体。现有3D方法通常为成对定义,难以应用于大规模化学空间;深度学习嵌入虽表达能力强,但缺乏可解释性且受限于训练数据多样性。本文提出基于谱图理论的新型物理解析分子指纹:将分子建模为3D空间中的完全图,边权重体现启发式物理相互作用。对所得图拉普拉斯矩阵进行特征值分解,得到一种计算高效、固定长度的化学指纹,既能编码3D结构,又满足置换不变性和E(3)对称性。该谱指纹可区分具有相同2D连通性但不同3D结构的分子,克服了传统2D描述符的局限性,同时保持大规模化学空间筛查所需的低计算成本。我们在有机、无机、生物、框架及反应化学数据集上,通过社区发现算法验证其性能,结果优于代表性基线。最近邻性质预测与适用域分析表明该表示在机器学习与化学生物信息学中具有实用性。我们预计该谱指纹将成为通用、可解释、高效的3D化学相似性度量,在极低成本下融入3D信息。

原文摘要 · Abstract (English)

Molecular representations are essential for the evaluation of molecular similarity and the development of structure-property relationships. Despite the known importance of 3D structure to determine chemical and physical properties, the most widely used molecular fingerprints encode only two-dimensional connectivity. Such representations fail to distinguish similar but distinct stereoisomers and conformers. Alternative 3D methods are typically defined pairwise, making their application to large chemical spaces prohibitive, while deep learning embeddings are expressive but uninterpretable and limited by their training data diversity. Here, we introduce novel physics-inspired molecular fingerprints based on principles from spectral graph theory. We represent molecules as a complete graph in 3D space, with edge weights encoding heuristic physical interactions. Eigenvalue decomposition of the resulting graph Laplacian matrix results in a computationally efficient fixed-length chemical fingerprint that encodes 3D structure while obeying necessary physical symmetries of permutation and E(3) invariance. Spectral fingerprints differentiate between unique molecular structures with identical 2D connectivity, overcoming a limitation of 2D descriptors, while maintaining the low computational cost needed for efficient screening of vast chemical spaces. We evaluate our fingerprints with community detection algorithms and observe strong performance against representative baselines across datasets from organic, inorganic, biological, reticular, and reaction chemistry. Nearest-neighbor property estimation and applicability domain analyses reveal the utility of our molecular representation in machine learning and cheminformatics. We anticipate that spectral fingerprints will serve as generalizable, interpretable, and efficient measures of chemical similarity that incorporate 3D information at minimal cost.

分子指纹三维结构谱图理论可解释性

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