Principal Component Analysis for Protein Folding Dynamics

Abstract

Protein folding is considered here by studying the dynamics of the folding of the triple β-strand WW domain from the Formin binding protein 28 (FBP). Starting from the unfolded state and ending either in the native or nonnative conformational states, trajectories are generated with the coarse-grained united residue (UNRES) force field. The effectiveness of principal component analysis (PCA), an already-established mathematical technique for finding global, correlated motions in atomic simulations of proteins, is evaluated here for coarse-grained trajectories. The problems related to PCA and their solutions are discussed. The folding and non-folding of proteins are examined with free energy landscapes. Detailed analyses of many folding and non-folding trajectories at different temperatures show that PCA is very efficient for characterizing the general folding and non-folding features of proteins. It is shown that the first principal component captures and describes in detail the dynamics of a system. Anomalous diffusion in the folding/non-folding dynamics is examined by the mean-square displacement, (MSD), and the fractional diffusion and fractional kinetic equations. The collision-less (or ballistic) behavior of a polypeptide undergoing Brownian motion along the first few principal components is accounted for.