Random Matrix Theory Analysis of Cross Correlations in Molecular Dynamics Simulations of Macro-Biomolecules

Abstract

We apply the random matrix theory to analyze the molecular dynamics simulation of macromolecules, such as proteins. The eigensystem of the cross-correlation matrix for the time series of the atomic coordinates is analyzed. We study a data set with seven different sampling intervals to observe the characteristic motion at each time scale. In all cases, the unfolded eigenvalue spacings are in agreement with the predictions of random matrix theory. In the short-time scale, the cross-correlation matrix has the universal properties of the Gaussian orthogonal ensemble. The eigenvalue distribution and inverse participation ratio have a crossover behavior between the universal and nonuniversal classes, which is distinct from the known results such as the financial time series. Analyzing the inverse participation ratio, we extract the correlated cluster of atoms and decompose it to subclusters.