Impact of Vibrational Entropy on the Stability of Unsolvated Peptide Helices with Increasing Length

Helices are a key folding motif in
protein structure. The question
of which factors determine helix stability for a given polypeptide
or protein is an ongoing challenge. Here we use van-der-Waals-corrected
density functional theory to address a part of this question in a
bottom-up approach. We show how intrinsic helical structure is stabilized
with length and temperature for a series of experimentally well-studied
unsolvated alanine-based polypeptides, Ac-Alan-LysH+. By exhaustively exploring the conformational
space of these molecules, we find that helices emerge as the preferred
structure in the length range n = 4–8 not
just due to enthalpic factors (hydrogen bonds and their cooperativity,
van der Waals dispersion interactions, electrostatics) but importantly
also by a vibrational entropic stabilization over competing conformers
at room temperature. The stabilization is shown to be due to softer
low-frequency vibrational modes in helical conformers than in more
compact ones. This observation is corroborated by including anharmonic
effects explicitly through ab initio molecular dynamics
and generalized by testing different terminations and considering
larger helical peptide models.