The -helix and -sheet are common protein secondary structures that were originally predicted by Linus Pauling (Figure 6.3).

The -helix structure repeats after exactly 18 residues, which amounts to 5 turns. It has, therefore, 3.6 residues per turn. Since the pitch of a helix is given by p = nh, we have for the helix, with a rise of 0.15 nm/residue, p = 3.6 (res/turn) x 0.15 (nm/res) = 0.54 nm/turn. Parameters for the other helices shown in Figure 6.3 and Figure 6.4 are listed in Table 6.1.

In an -helix each carbonyl oxygen is hydrogen-bonded to the amido proton on the fourth residue up the helix. Thus, if one includes the hydrogen bond, a loop of 13 atoms is formed, as shown in Figure 6.6. Each of the helices shown in Figure 6.3 and Figure 6.4 has a different number of atoms in such a hydrogen-bonded loop. We shall call this number N. A quick way to describe a polypeptide helix, then, is by the shorthand nN, where n is the number of residues per turn. The 310 helix fits this description; it has exactly 3.0 residues per turn and a 10-member loop. The -helix could also be called a 3.613 helix, and the helix a 4.416 helix.

Sheet