Folding an infinitely long polypeptide into a helical conformation

The potential-energy surface and harmonic vibrational analysis of an infinitely long polypeptide are studied using density- functional theory in the Perdew, Burke, and Ernzerhof approximation to the exchange-correlation functional. We find that the $\pi$-helix, $\alpha$-helix, and $3_{10}$-helix are stable respect to the fully extended structure (FES) at 0 K, both in right- and left-handed conformations. Accounting for the temperature effects it is found that the left-handed helices are energetically degenerated respect to FES and the right-handed helices slightly more stable than FES, at room temperature. The minimum-energy pathway along the potential- energy surface shows that the barrier to fold a FES into a left- handed helix is at least three times larger than the barrier to fold it into a right-handed helix. This suggests that the very low occurrence of left-handed helices in protein structures is due to both thermodynamic and kinetic effects.