A density functional theory based estimation of the anharmonic contributions to the free energy of a polypeptide helix

We have employed density functional theory to determine the temperature dependence of the intrinsic stability of an infinite poly-L-alanine helix. The most relevant helix types, i.e., the α- and the 3(10)-helix, and several unfolded conformations, which serve as reference for the stability analysis, have been included. For the calculation of the free energies for the various chain conformations we have explicitly included both, harmonic and anharmonic contributions. The latter have been calculated by means of a thermodynamic integration approach employing stochastic Langevin molecular dynamics, which is shown to provide a dramatic increase in the computational efficiency as compared to commonly employed deterministic molecular dynamics schemes. Employing this approach we demonstrate that the anharmonic part of the free energy amounts to the order of 0.1-0.4 kcal/mol per peptide unit for all analysed conformations. Although small, the anharmonic contribution stabilizes the helical conformations with respect to the fully extended structure.