  Understanding the protein folding process is an outstanding issue in
biophysics; recent developments in molecular dynamics simulation have provided
insights into this phenomenon. However, the large freedom of atomic motion
hinders the understanding of this process. In this study, we applied persistent
homology, an emerging methods to analyze topological features in a dataset, to
reveal protein folding dynamics. We developed a new method to characterize
protein structure based on persistent homology and applied this method to
molecular dynamics simulations of chignolin. Using principle component analysis
or non-negative matrix factorization, our analysis method revealed two stable
states and one saddle state, corresponding to the native, misfolded, and
transition states, respectively. We also identified an unfolded state with slow
dynamics in the reduced space. Our method serves as a promising tool to
understand the protein folding process.
