Multivariate frequency domain analysis (MFDA) is proposed to characterize collective vibrationaldynamics of protein obtained by a molecular dynamics (MD) simulation. MFDA performs principalcomponent analysis (PCA) for a bandpass filtered multivariate time series using the multitapermethod of spectral estimation. By applying MFDA to MD trajectories of bovine pancreatic trypsininhibitor, we determined the collective vibrational modes in the frequency domain, which wereidentified by their vibrational frequencies and eigenvectors. At near zero temperature, the vibrationalmodes determined by MFDA agreed well with those calculated by normal mode analysis. At 300 K,the vibrational modes exhibited characteristic features that were considerably different from theprincipal modes of the static distribution given by the standard PCA. The influences of aqueousenvironments were discussed based on two different sets of vibrational modes, one derived from aMD simulation in water and the other from a simulation in vacuum. Using the varimax rotation, analgorithm of the multivariate statistical analysis, the representative orthogonal set of eigenmodeswas determined at each vibrational frequency.
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