Theoretical Study of β-Peptide Models: Intrinsic Preferences of Helical Structures

β-Peptides form various secondary structures, such as 14-helix, 12-helix, 10/12-helix, 10-helix, 28-ribbon, C6-ribbon, and pleated-sheet. Thus, it is useful to understand the intrinsic backbone conformational preferences of these basic structures. By using a simple repeating-unit method, we have calculated the preferences of C6-ribbon, β-strand, 10/12-helix, 14-helix, 12-helix, 10-helix, and 28-ribbon of a series of poly-β-alanine models, Ac-(β-Ala)n-NH2, with n=1–9. Interactions among single amino acids result in cooperative residue energies. This is not found for the formations of β-strands, 28-ribbons, and C6-ribbons, which possess constant residue energies. In contrast, the 12-helix, 10-helix, and 14-helix are characterized by increasing residue energies as the peptide elongates. Therefore, there is a considerable positive cooperative impetus in the gas phase for their formation. The residue energy of the 10/12-helix increases significantly for n=2 and 3, and then displays a zigzag pattern. Meanwhile, there is a good correlation between calculated residue energies and residue dipole moments, indicating the importance of long-range electrostatic interactions to the cooperative residue energy. Efforts have been made to separate the electrostatic and torsional interactions between residues. Thereby, the 12-, 10-, and 10/12-helices all benefit from electrostatic interactions, while the 14-helix has the most intrinsic preference in terms of torsional interaction. The effect of MeOH on the secondary structures has also been evaluated by SCIPCM solvent model calculations.