Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore.
School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK.
Sci Rep. 2023 Jul 11;13(1):11183. doi: 10.1038/s41598-023-37853-z.
Molecular representations are of fundamental importance for the modeling and analysing molecular systems. The successes in drug design and materials discovery have been greatly contributed by molecular representation models. In this paper, we present a computational framework for molecular representation that is mathematically rigorous and based on the persistent Dirac operator. The properties of the discrete weighted and unweighted Dirac matrix are systematically discussed, and the biological meanings of both homological and non-homological eigenvectors are studied. We also evaluate the impact of various weighting schemes on the weighted Dirac matrix. Additionally, a set of physical persistent attributes that characterize the persistence and variation of spectrum properties of Dirac matrices during a filtration process is proposed to be molecular fingerprints. Our persistent attributes are used to classify molecular configurations of nine different types of organic-inorganic halide perovskites. The combination of persistent attributes with gradient boosting tree model has achieved great success in molecular solvation free energy prediction. The results show that our model is effective in characterizing the molecular structures, demonstrating the power of our molecular representation and featurization approach.
分子表示对于分子系统的建模和分析至关重要。分子表示模型为药物设计和材料发现的成功做出了巨大贡献。在本文中，我们提出了一种基于持久 Dirac 算子的数学上严格的分子表示计算框架。系统地讨论了离散加权和非加权 Dirac 矩阵的性质，并研究了同调和非同调特征向量的生物学意义。我们还评估了各种加权方案对加权 Dirac 矩阵的影响。此外，还提出了一组物理持久属性，用于表征 Dirac 矩阵在过滤过程中谱性质的持久性和变化，作为分子指纹。我们的持久属性用于对九种不同类型的有机-无机卤化物钙钛矿的分子构型进行分类。持久属性与梯度提升树模型的结合在分子溶剂化自由能预测方面取得了巨大成功。结果表明，我们的模型在表征分子结构方面非常有效，展示了我们的分子表示和特征化方法的强大功能。
