Unraveling the Stability of Polypeptide Helices: Critical Role of van der Waals Interactions

Folding and unfolding processes are important for the functional capability of polypeptides and proteins. In contrast with a physiological environment (solvated or condensed phases), an in vacuo study provides well-defined “clean room” conditions to analyze the intramolecular interactions that largely control the structure, stability, and folding or unfolding dynamics. Here we show that a proper consideration of van der Waals (vdW) dispersion forces in density-functional theory (DFT) is essential, and a recently developed $\mathrm{DFT}+\mathrm{vdW}$ approach enables long time-scale ab initio molecular dynamics simulations at an accuracy close to “gold standard” quantum-chemical calculations. The results show that the inclusion of vdW interactions qualitatively changes the conformational landscape of alanine polypeptides, and greatly enhances the thermal stability of helical structures, in agreement with gas-phase experiments.

Figure 1

Energy per added alanine peptide unit for idealized polyalanine $\alpha$ helices as a function of peptide length, referenced to an infinite fully extended polyalanine structure. Circles and squares: neutral helices. Diamonds: ${\mathrm{Li}}^{+}$-capped helices. A cartoon of the ${\mathrm{Li}}^{+}$-capped C-terminus structure is shown on the right. The labels 1, 2, 3 indicate the dangling hydrogen bonds saturated by the ionic termination.

Figure 2

The upper left and center panels show the overall number of hydrogen bonds throughout the simulation for the $\mathrm{PBE}+\mathrm{vdW}$ and PBE methods, respectively, counting separately $\alpha$-helical bonds (red) and $3_{10}$-helical bonds (blue). $\pi$, $2_7$ and non-bonded residues are not counted. The lower left and center panels show snapshots from the corresponding MD simulations at different times. The right panel shows the ”Ramachandran map” in cylindrical pitch-twist coordinates [20, 22] for all MD simulations. The color code corresponds to the probability (from 0 to 1) of visiting a certain conformation.