(Un)folding of a high-temperature stable polyalanine helix from first principles

Peptides \emph{in vacuo} offer a unique, well-defined testbed to match experiments directly against first-principles approaches that predict the intramolecular interactions that govern peptide and protein folding. In this respect, the polyalanine-based peptide Ac-Ala$_{15}$-LysH$^+$ is particularly interesting, as it is experimentally known to form helices \emph{in vacuo}, with stable secondary structure up to $\approx$ 750~K [1]. Room-temperature folding and unfolding timescales are usually not accessible by direct first-principles simulations, but this high $T$ scale allows a rare direct first-principles view. We here use van der Waals corrected [2] density functional theory in the PBE generalized gradient approximation as implemented in the all-electron code FHI-aims [3] to show by Born-Oppenheimer \emph{ab initio} molecular dynamics that Ac-Ala$_{15}$-LysH$^+$ indeed unfolds rapidly (within a few ps) at $T$=800~K and 1000~K, but not at 500~K. We show that the structural stability of the $\alpha$ helix at 500~K is critically linked to a correct van der Waals treatment, and that the designed LysH$^+$ ionic termination is essential for the observed helical secondary structure. [1] M. Kohtani \emph{et al.}, JACS \textbf{126}, 7420 (2004). [2] A. Tkatchenko, M. Scheffler, PRL \textbf{102}, 073005 (2009). [3] V. Blum \emph{et al}, Comp. Phys. Comm. \textbf{180}, 2175 (2009).