Systematic Study of Anharmonic Features in a Principal Component Analysis of Gramicidin A

We use principal component analysis (PCA) to detect functionally interesting collective motions in molecular-dynamics simulations of membrane-bound gramicidin A. We examine the statistical and structural properties of all PCA eigenvectors and eigenvalues for the backbone and side-chain atoms. All eigenvalue spectra show two distinct power-law scaling regimes, quantitatively separating large from small covariance motions. Time trajectories of the largest PCs converge to Gaussian distributions at long timescales, but groups of small-covariance PCs, which are usually ignored as noise, have subdiffusive distributions. These non-Gaussian distributions imply anharmonic motions on the free-energy surface. We characterize the anharmonic components of motion by analyzing the mean-square displacement for all PCs. The subdiffusive components reveal picosecond-scale oscillations in the mean-square displacement at frequencies consistent with infrared measurements. In this regime, the slowest backbone mode exhibits tilting of the peptide planes, which allows carbonyl oxygen atoms to provide surrogate solvation for water and cation transport in the channel lumen. Higher-frequency modes are also apparent, and we describe their vibrational spectra. Our findings expand the utility of PCA for quantifying the essential features of motion on the anharmonic free-energy surface made accessible by atomistic molecular-dynamics simulations.