Hamiltonian Dynamics of the Protein Chain and Normal Modes of Alpha-Helix and Beta-Sheet

We use the torsional angles of the protein chain as generalized coordinates in the canonical formalism, derive canonical equations of motion, and investigate the coordinate dependence of the kinetic energy expressed in terms of the canonical momenta. We use the formalism to compute the normal-frequency distributions of the alpha-helix and the beta-sheet, under the assumption that they are stabilized purely through hydrogen bonding. Comparison of their free energies show the existence of a phase transition between the alpha-helix and the beta-sheet at a critical temperature.