Topological data analysis gives two folding paths in HP35(nle-nle), double mutant of villin headpiece subdomain

The folding dynamics of proteins is a primary area of interest in protein science. We carried out topological data analysis (TDA) of the folding process of HP35(nle-nle), a double-mutant of the villin headpiece subdomain. Using persistent homology and non-negative matrix factorization, we reduced the dimension of protein structure and investigated the flow in the reduced space. We found this protein has two folding paths, distinguished by the pairings of inter-helix residues. Our analysis showed the excellent performance of TDA in capturing the formation of tertiary structure.