Highlights at the FHI Theory Department

Unraveling the Structure, Stability, and Dynamics of
Polyalanines in Vacuo, October 2010

Figure 1: Molecular dynamics simulations of unfolding of the Ac-Ala15LysH+ peptide using DFT with (PBE+vdW) and without (PBE) van der Waals forces at different temperatures. The plots show the conformational region explored by the peptide throughout the molecular dynamics simulation. The color corresponds to the probability (from 0 to 1) of visiting a given point. Representative geometry snapshots from the simulations are also shown.

Predicting how biopolymers, e.g. proteins, DNAs, and RNAs, fold from a simple sequence of aminoacid residues (primary structure) to the complex three dimensional form (tertiary structure) is a problem that has puzzled scientists for many years. Starting from hundreds or thousands of atoms, the protein's final and unique native state determines its function. Many diseases are known to be caused by changes (misfolding) of this native state, including, but not limited to Alzheimer's disease, Creutzfeld-Jacob's disease and some types of diabetes. To achieve quantitative understanding and disentangle the forces responsible for protein folding, a full quantum-mechanical treatment of protein structure and stability is required.

This task is computationally prohibitive in the present days. However, first-principles prediction of the secondary structure, i.e. the helices and sheets that compose the native protein structure of small biopolymers (polypeptides) is possible. The formation of such structures is a fundamental step in the overall folding process.

Figure 2: The structure of the most stable Ac-Ala5LysH+ peptide conformation from PBE+vdW simulations. The calculated anharmonic vibrational spectrum (black) is compared to experiment (orange).

Ultimately, the protein formation and stability have to be understood under physiological conditions (in solvent environment). However, the primary stabilizing interactions for protein formation [e.g., protein backbone hydrogen bonds and van der Waals (vdW) interactions] are intramolecular forces, whose quantitative role can be directly assessed in vacuo. Such studies correspond to ideal well-defined "clean room" conditions, and recent progress in experimental gas-phase spectroscopies yields increasingly refined vibrational spectra for peptides and proteins [1,2]. In particular, it has been recently shown [3,4] that typical secondary structure motifs, like helices, are observed also in the gas phase. This gives an excellent testbed for theoretical methods to dissect the interactions responsible for this primary step of the full folding process. In the Fritz Haber Institute (FHI), we are studying the sequence of polyalanine-based peptides Ac-AlanLysH+, which form a helical structure in the gas phase up to 750 Kelvin [3,4]. For comparison, alanine polypeptides in water unfold already at 340 Kelvin. Using the all-electron code FHI-aims [5], we perform density-functional theory (DFT) calculations adding the important van der Waals (vdW) interactions using the recently developed PBE+vdW approach [6]. For the longer molecules (n=10,15) we find that α-helical models provide good qualitative agreement between theoretical and vibrational spectra already in the harmonic approximation. For n=5, the lowest energy conformer is not a simple helix, but competes closely with α-helical motifs at room temperature. The inclusion of van der Waals is critical for the observed energetic hierarchy. Close agreement between infrared spectra from experiment and ab initio molecular dynamics (including anharmonic effects) supports our findings [7].

For Ac-Ala15LysH+, we performed long (~ 65 picoseconds) ab initio molecular dynamics simulations at various temperatures (500, 700, 800, and 1000 Kelvin) in order to identify the reasons of its high temperature stability. We could show that although the hydrogen bonds and the electrostatic dipole of the molecule are important, van der Waals interactions are essential to describe not only the correct temperature stability of this helix, but also the correct α-helical preference [8]. Our study offers quantitative first-principles insight into the structure, stability, and dynamics of helical motifs in proteins. References

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[2] J. P. Simons, Mol. Phys. 107, 2435 (2009).
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[5] V. Blum, R. Gehrke, F. Hanke, P. Havu, V. Havu, X. Ren, K. Reuter, and M. Scheffler, Comp. Phys. Comm. 180, 2175 (2009).
[6] A. Tkatchenko and M. Scheffler, Phys. Rev. Lett. 102, 073005 (2009).
[7] M. Rossi, V. Blum, P. Kupser, G. von Helden, F. Bierau, K. Pagel, G. Meijer and M. Scheffler, submitted.
[8] A. Tkatchenko, M. Rossi, V. Blum, J. Ireta and M. Scheffler, submitted.