Abstract
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.
Highlights
The folding dynamics of proteins is a primary area of interest in protein science
We proposed a feature construction method based on persistent homology (PH), the most widely used topological data analysis (TDA) m ethod[10]
We carried out negative matrix factorization (NMF) decomposition for L = 4, 5, and 6, and we found no quantitative changes
Summary
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. Data-scientific methods, such as principal component analysis (PCA) or k-means clustering have been used to study the folding structures. A small change in the local bending angle causes a large change in the position of all residues; linear analysis, such as PCA or k-means, sometimes provide insufficient information. To overcome this difficulty, complex procedures are often needed. Jain and Stock used a combination of dihedral PCA, k-means clustering, Markov state modeling, and hierarchical clustering to analyze the folding of protein HP353 Another approach is the application of non-linear analysis, such as kernel PCA, isomap, or t-distributed stochastic neighbor embedding. Yao et al analyzed the folding path of RNA using Mapper, a popular TDA m ethod[6]
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