Persistent homology and persistent diagrams have been developed as tools of topological data analysis. They provide a robust topological characterization of a given (discrete) geometrical data. In this talk, I will present our recent researches on applying persistent diagrams to protein structural analysis. Topological characterizations of protein compressibilities and H/D exchanges will be explained in detail. Time permitting, I will also introduce a notion of the three ladder persistence as representaions on a certain class of associative algebra, which will be useful for comparing two proteins in view of homological information.