Helical secondary structure of polyalanine peptides in vacuo: Ac-Ala$_n$-LysH$^+$ ($n$=5,10,15), experiment and theory

The presence of a solvent is often viewed as indispensable to explain the structure of peptides and proteins. However, well defined \emph{secondary} structure motifs (helices, sheets, ...) also exist \emph{in vacuo}, offering a unique ``clean room'' condition to quantify the stabilizing interactions. We here unravel the structure of LysineH$^+$ capped polyalanine peptides Ac-Ala$_n$-LysH$^+$ ($n$-5,10,15), by combining experimental multi-photon IR spectra obtained using the FELIX free-electron laser at room-temperature with van der Waals-corrected all-electron density-functional theory (DFT) in the generalized gradient approximation in the FHI-aims code [1]. Earlier ion mobility studies of these molecules indicate helical structure [2], which we here demonstrate quantitatively. For $n$=5, we find a close energetic competition of different helix motifs ($\alpha$, 3$_{10}$), with similar and good agreement between measured and calculated vibrational spectra. We show how the LysH$^+$ termination acts to induce helices also for longer peptides, and how vibrational modes develop with helix length ($n$=10,15), yielding, e.g., a softening of collective modes towards the infinite helix limit. [1] V. Blum \emph{et al}, Comp. Phys. Comm. (2008), accepted. [2] M. Kohtani \emph{et al.}, JACS 120, 12975 (1998).