The Geometries and Nomenclature of Peptide Helices

The a-helix is a right-handed helix with 3.6 residues per turn. Its backbone C=O group at residue n accepts a 2.8 Å-long hydrogen bond from the N–H group at residue n+4 (see Fig. 6-7). Because the a-helix is a right-handed helix, we refer to it in this exercise as an a_R helix. Its backbone torsion angles of f = –57° and y = –47° place it in an allowed region in the lower left quadrant of the Ramachandran diagram (Fig.6-6).

This exercise examines four other polypeptide helices that have allowable hydrogen bonding distances. These are:

1.The 2.2₇ helix, in which the backbone C=O group at residue n accepts a hydrogen bond from the N–H group at residue n+2. The 2.2₇ helix, which is really a ribbon, is so-named because it has 2.2 residues per helical turn and the hydrogen bonded ring of atoms containing the C=O group at residue n and the N–H group at residue n+2 consists of 7 atoms (using this nomenclature, the a_R helix is called a 3.6₁₃ helix). Its backbone torsion angles are f = –78° and y = +59°, which place it in a forbidden region in the upper left quadrant of the Ramachandran diagram. Hence, the 2.2₇ helix has never been observed.

2.The 3₁₀ helix, in which the backbone C=O group at residue n accepts a hydrogen bond from the N–H group at residue n+3. The 3₁₀ helix has 3.0 residues per turn and its hydrogen bonded ring of atoms containing the C=O group at residue n and the N–H group at residue n+3 consists of 10 atoms. Hence, as can be seen in this exercise, the 3₁₀ helix is thinner and rises more steeply than the a_R helix. The backbone torsion angles of the 3₁₀ helix are f = –49° and y = –26°, which place it in a mildly forbidden zone of the Ramachandran diagram, near the position of the a_R helix. Consequently, 3₁₀ helices only occasionally occur in proteins and then mostly in short segments that are located at the ends of a_R helices.

3.The p-helix, in which the backbone C=O group at residue n accepts a hydrogen bond from the N–H group at residue n+5. In the above nomenclature, the p-helix is called a 4.4₁₆ helix because it has 4.4 residues per turn and a 16-atom hydrogen bonded ring containing the C=O group at residue n and the N–H group at residue n+5. Its backbone torsion angles of f = –57° and y = –70°, also place it in a mildly forbidden zone of the Ramachandran diagram near the position of the a_R helix. Because the p-helix is shorter and fatter than the a_R helix, it has an axial hole that is too small to admit water molecules but too wide to permit stabilizing van der Waals associations across the helix axis as occurs in the a_R helix. Consequently, p-helices rarely occur in proteins and then only as segments of longer helices.

4.The a_L helix, which is a left-handed helix whose helical parameters are otherwise identical to those of the a_R helix. Its torsion angles of f = +57° and y = +47° place it in the mildly forbidden zone in the upper right quadrant of the Ramachandran diagram. However, whereas the side chains in the a_R helix all project outward and downward so as to avoid steric interference with the polypeptide backbone (Fig. 6-7), those of the a_L helix contact its backbone too closely. Consequently, the a_L helix has never been observed (although 1-2% of individual non-Gly residues assume this unusual conformation).