Spatio-temporal hierarchy in the dynamics of a minimalist protein model.

A method for time series analysis of molecular dynamics simulation of a protein is presented. In this approach, wavelet analysis and principal component analysis are combined to decompose the spatio-temporal protein dynamics into contributions from a hierarchy of different time and space scales. Unlike the conventional Fourier-based approaches, the time-localized wavelet basis captures the vibrational energy transfers among the collective motions of proteins. As an illustrative vehicle, we have applied our method to a coarse-grained minimalist protein model. During the folding and unfolding transitions of the protein, vibrational energy transfers between the fast and slow time scales were observed among the large-amplitude collective coordinates while the other small-amplitude motions are regarded as thermal noise. Analysis employing a Gaussian-based measure revealed that the time scales of the energy redistribution in the subspace spanned by such large-amplitude collective coordinates are slow compared to the other small-amplitude coordinates. Future prospects of the method are discussed in detail.