要旨
Peptides and proteins fulfil crucial tasks enabling and maintaining life. Their function is directly correlated with their three-dimensional structure, which is in turn determined by their chemical composition, the amino-acid sequence. Predicting the structure of a peptide based only on its sequence information is of fundamental interest. A fully first-principles treatment free of empirical parameters would be ideal. However, this presents an ongoing challenge, due to the large system size and conformational space of most peptides.
In the present work, we address this challenge concentrating on the example of polyalanine-based
peptides in the gas phase. Such studies under isolated conditions follow a bottom-up approach that allows one to investigate the intramolecular interactions important for secondary structure separate from environmental effects. Furthermore, direct benchmarks of theoretical structure predictions against experiment are facilitated.
The peptide series Ac-Alan-Lys(H+), (n > 6), forms α-helices in the gas phase due to a favorable interaction of the helix dipole with the positive charge at the C-terminal lysine residue. Using this design principle as a template, we explore the impact of increased structural flexibility on the conformational space due to (i) sequence length [Ac-Alan-Lys(H+), n = 19], (ii) charge placement [Ac-Ala19-Lys(H+) versus Ac-Lys(H+)-Ala19], and (iii) backbone elongation of the monomer units as represented by β-amino acids [Ac-β2hAla6-Lys(H+)]. To address the large conformational space, we develop a three-step structure-search strategy employing an unprecedented first-principles screening effort. After pre-sampling of the conformational space using a force field, thousands of structures are optimized employing density-functional theory (DFT). For this, the PBE functional is used, coupled with a pairwise correction for van der Waals interactions. For the best few structure candidates, ab initio replica-exchange molecular-dynamics simulations are performed in order to refine the local structural environment. It is shown that these can yield lower-energy conformations and lead to rearrangements of the hydrogen-bonding network. In order to connect to experiment, collision cross sections are calculated that link to ion mobility-mass spectrometry. Furthermore, infrared spectra are derived from ab initio Born-Oppenheimer molecular-dynamics simulations accounting for anharmonicities within the classical-nuclei approximation.
As expected, the 20-residue peptide Ac-Ala19-Lys(H+) forms helical structures. In contrast, placing the charge at the N-terminus [Ac-Lys(H+)-Ala19], leads to several different compact structures, which are close in energy. Such small energy differences present a challenge to the theoretical approach. Incorporating exact exchange and many-body van der Waals effects predicts the presence of only one dominant conformer, which is compatible with both experimental datasets.
In comparison to Ac-Ala6-Lys(H+), the β-peptide Ac-β2hAla6-Lys(H+) exhibits increased conformational flexibility due to an extended monomer backbone. Out of the almost 15,000 structures optimized with DFT, no helical conformers are found in the low-energy regime. This is changed when considering vibrational free energy (300K, harmonic approximation), which strongly favors helical conformations due to softer vibrational modes. One possible structure candidate is the H16-helix, which is compatible with both experiments. It is a unique structure as it exhibits a hydrogen-bonding pattern equivalent to the helix of natural peptides.
The systems considered here highlight the advances of current DFT functionals to address
the large conformational space of peptides, but also the need for further development.
