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 conformational space of these molecules, we find that helices emerge as alanine-based polypeptides, Ac-Ala(n)-LysH(+). By exhaustively exploring the 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.