Role of van der Waals interactions for the intrinsic stability of polyalanine helices

The helical motif is an ubiquitous conformation adopted by aminoacid residues in a protein structure and helix formation is the simplest example of the protein folding process. How stable is the folded peptide helix in comparison to a random coil structure? What are the interactions responsible for stabilizing the helical conformation? Answering these questions has thus a direct implication for understanding protein folding. In this work we use density functional theory (DFT) augmented with a non-empirical correction for van der Waals (vdW) forces to study the stability of alanine polypeptide helices \textit{in vacuo}. We find a large stabilization of the native helical forms when vdW correction is used. It amounts to 121\%, 157\% and 83\% on top of the Perdew-Burke-Ernzerhof (PBE) functional in the case of infinite $\alpha$, $\pi$ and 3$_{10}$ helices, respectively. Thus, the experimentally observed $\alpha$ helix is significantly stabilized by vdW forces both over the fully extended and the 3$_{10}$ conformations. Our findings also suggest an explanation to the remarkable stability of gas-phase alanine helices up to high temperatures [M. Kohtani \textit{et al.} JACS 126, 7420 (2004)].