基因组的拓扑序列分析：范畴论方法
Topological Sequence Analysis of Genomes: Category theory Approaches
AI总结：
本文提出基于范畴论的拓扑序列分析框架 CTSA，利用消解范畴与持续同调提取基因组多尺度特征，在 SARS-CoV-2 系统发育分析和结合亲和力预测中优于六种现有方法。
摘要：
序列数据（如 DNA、RNA 和蛋白质序列）表现出复杂的多尺度结构，这给传统分析方法（尤其是依赖比对或纯统计表示的方法）带来了重大挑战。在本工作中，我们提出了基因组的基于范畴的拓扑序列分析（CTSA）。CTSA 将序列建模为一个 resolution category（消解范畴），通过一种范畴构造捕捉其层次结构。随后，从该范畴表示中导出子结构复形，并计算其持续同调以提取多尺度拓扑特征。我们的模型通过纳入植根于序列拓扑的结构化数学形式体系，脱离了传统的无比对方法。所得拓扑特征在多种任务中提供了信息丰富的表示，包括 SARS-CoV-2 变异株的系统发育分析以及蛋白质-核酸结合亲和力的预测。我们针对六种最先进方法开展了比较研究。实验结果表明，CTSA 在这些任务中取得了优异且稳定的性能，表明其具有广泛的适用性和鲁棒性。除序列分析之外，所提出的框架还为整合范畴论与同调理论以进行生物序列分析开辟了新方向。
英文摘要：
Sequence data, such as DNA, RNA, and protein sequences, exhibit intricate, multi-scale structures that pose significant challenges for conventional analysis methods, particularly those relying on alignment or purely statistical representations. In this work, we introduce category-based topological sequence analysis (CTSA ) of genomes. CTSA models a sequence as a resolution category, capturing its hierarchical structure through a categorical construction. Substructure complexes are then derived from this categorical representation, and their persistent homology is computed to extract multi-scale topological features. Our models depart from traditional alignment-free approaches by incorporating structured mathematical formalisms rooted in sequence topology. The resulting topological signatures provide informative representations across a variety of tasks, including the phylogenetic analysis of SARS-CoV-2 variants and the prediction of protein-nucleic acid binding affinities. Comparative studies were carried out against six state-of-the-art methods. Experimental results demonstrate that CTSA achieves excellent and consistent performance in these tasks, suggesting its general applicability and robustness. Beyond sequence analysis, the proposed framework opens new directions for the integration of categorical and homological theories for biological sequence analysis.
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