Algebraic Topological Approaches to Protein Structure Analysis

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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.