Hidden Complexity of Protein Free-Energy Landscapes Revealed by Principal Component Analysis by Parts

A method to analyze molecular dynamics (MD) simulations of protein folding is proposed, which is based on a principal component analysis (PCA) of the protein's backbone dihedral angles. The protein is first partitioned into parts (e.g., its secondary structure elements), for each of which a separate PCA is performed. On the basis of these PCAS, the free-energy landscapes of each part are constructed and used to determine their metastable conformational states. In a second step, the various states of each protein part are employed to construct a product basis, which now represent the metastable conformational states of the full protein. Adopting extensive MD simulations of the villin headpiece by Pande and co-workers, it is shown that this PCA by parts allows us to characterizes the free-energy landscape of the protein with unprecedented detail.