Vibrational Approach to the Dynamics of an a-Helix

The dynamics of a finite a-helix have been studied in the harmonic approximation by a vibrational analysis of the atomic motions about their equilibrium positions. The system was represented by an empirical potential energy function, and all degrees of freedom (bond lengths, bond angles, and torsional angles) were allowed to vary. The complete results were compared with a more restrictive model in which the peptide dihedral angle was kept rigid; also, a model potential excluding hydrogen bonds was examined. Thermal fluctuations in the backbone dihedral angles ~b and ~b are l2O to l5o. The fluctuations of adjacent dihedral angles are highly correlated, and the correlation pattern is affected by the flexibility of the pel~tide dihedral angle. Time-dependent autocorrelations in the motion of € and ~b appear to decay due to dephasing in less than 1 psec, while the motions of the carbonyl oxygen and amide hydrogens out of the peptide plane are more harmonic. Length fluctuations have been evaluated and exhibit a strong end effect; the calculated elastic modulus is ih agreement with " other values. Rigid and adiabatic total energy surfaces corresponding to dihedral angle rotations in the middle of the helix have been obtained and compared with the quadratic approximation to those surfaces. The magnitudes and correlations between the fluctuations obtained by averaging over the adiabatic energy surface most closely resemble the vibrational results. Of particular interest is the fact that hydrogen bonds play a relatively small r°le in the local dihedral angle fluctuations, though the hydrogen bonds are important in the energy of overall length changes.