Low-frequency vibrations in alpha-helices: helicoidal analysis of polyalanine and deoxymyoglobin molecular dynamics trajectories.

We present an approach to the analysis of low-frequency (0-200 cm-1) alpha-helix vibrations in molecular dynamics simulations. The approach employs the P-Curves algorithm [H. Sklenar, C. Etchebest, and R. Lavery, (1989) Proteins: Structure, Function and Genetics, Vol. 6, pp. 46-60] to determine the helical axis and a set of helicoidal parameters describing the axis curvature and the position of the repeating units with respect to the axis and each other. The vibrations are analyzed in terms of time correlation functions of the fluctuations of P-Curves parameters and their Fourier transforms. Simulations of polyalanine and myoglobin are analyzed. For polyalanine, global twisting, bending, and stretching vibrations are found at 11, 20, and 40 cm-1, respectively. In myoglobin, the spectra of the global helix vibrations are qualitatively different from those of polyalanine and considerably more complicated. Local vibrations of individual amino acid units in the helix backbones are also analyzed with P-Curves and compared.