Time-Series Analysis of Molecular Dynamics: Conformational Change and Dynamics of Collective Behavior

Abstract

Proteins have complex energy landscapes because of their specific three-dimensional structures determined by the heterogeneous interactions between different types of atoms, resulting in complex and functional motions. On the computational sides, it is important to characterize such energy landscapes with use of reaction coordinates, because it gives us a comprehensive view of protein dynamics and some connections to experiment. To this end, molecular dynamics (MD) simulation has been commonly employed, and from a sufficiently long MD run, we can characterize the energy landscape. A conventional tool to analyze the energy landscape is the principal component analysis (PCA), which utilizes the variance-covariance matrix for the fluctuations of a protein, and assuming the principal modes as the reaction coordinates, the free energy profile can be analyzed. However, the truly dynamic nature of protein is lost in this type of analysis because the time information is neglected. In this presentation, we develop a new method to analyze the dynamic nature by combining the wavelet transformation, a well-established tool to analyze time-frequency information of any types of dynamics, and PCA. We will call this method wPCA and apply it to a long time (∼ one microsecond) MD simulation of a small protein, chignolin (PDBid:1UAO). Chignolin is so small and flexible that it is better to use internal coordinates such as dihedral angles to analyze the conformational dynamics. We here use the dihedral PCA combined with the wavelet analysis and try to extract some collective and time-dependent nature of the protein dynamics. We found that the tryptophan residue has a strong feature around 10 to 50 ns timescales, and such a frequency-dependence of the dynamics within the native state is different from the one within the misfolded state.