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.

First-principles free-energy analysis of helix stability: the origin of the low entropy in pi helices.

The temperature dependence of the stability of infinite poly-L-alanine alpha, pi, and 310 helices with respect to the fully extended structure (FES) is calculated using density functional theory and the harmonic approximation. We find that the vibrational entropy strongly reduces the stability of the helical conformations with respect to the FES. By mapping the ab initio data on an approximate mechanical model, we show that this effect is exclusively due to the formation of hydrogen bonds, whereas changes in the backbone stiffness are practically negligible. We furthermore observe that the temperature dependence is largest for the pi helix and smallest for the 310 helix and demonstrate that these trends are a generic behavior related to the geometric peculiarities of the respective helical conformations and independent of the specific amino acid sequence.

Phonon spectra and thermodynamic properties of the infinite polyalanine alpha helix: a density-functional-theory-based harmonic vibrational analysis.

We have performed a density-functional theory harmonic vibrational analysis of the infinite polyalanine alpha helix. The calculated phonon dispersion spectrum shows excellent agreement to available experimental data, except for the high frequency hydrogen stretching modes which show characteristic shifts due to anharmonic effects. A major advantage compared to previously performed empirical force field studies is that long range effects such as electrostatic interaction and polarization are intrinsically taken into account for characterizing hydrogen bond formation in the helix. Our results indicate that these effects are crucial to accurately describe the low frequency acoustical branches and lead to a significantly better agreement with experiment for the specific heat in the low temperature range.