Algebraic Topological Approaches to Protein Structure Analysis

在本研究中，我们发展了一些基于代数拓扑的方法来解决蛋白质结构分析的几个问题。我们成功地利用蛋白质数据库中的数据开发了一种新的蛋白质可压缩性定量方法。关键的工具是持久同源性和持久图，它使我们能够检测具有某些属性的空腔的信息。此外，我们还提出了一种利用持久图上的距离函数从几何结构对蛋白质进行分类的技术。

In this research, we developed some approaches based on algebraic topology to several problems of protein structure analysis. We succeeded in developing a new quantification of protein compressibility by using data in Protein Data Bank. The key tool is persistent homology and persistent diagrams, which enable us to detect information on cavities with certain properties. In addition, we also proposed a technique to classify proteins from their geometric structure by means of distance functions on persistent diagrams.