310-helices in proteins are parahelices

The 3(10)-helix is characterized by having at least two consecutive hydrogen bonds between the main-chain carbonyl oxygen of residue i and the main-chain amide hydrogen of residue i + 3. The helical parameters - pitch, residues per turn, radius, and root mean square deviation (rmsd) from the best-fit helix - were determined by using the HELFIT program. All 3(10)-helices were classified as regular or irregular based on rmsd/(N - 1)(1/2) where N is the helix length. For both there are systematic, position-specific shifts in the backbone dihedral angles. The average phi, psi shift systematically from similar to z-58 degrees, similar to -32 degrees to similar to -90 degrees, similar to -4 degrees for helices 5, 6, and 7 residues long. The same general pattern is seen for helices, N = 8 and 9; however, in N = 9, the trend is repeated with residues 6, 7, and 8 approximately repeating the phi, psi of residues 2, 3, and 4. The residues per turn and radius of regular 3(10)-helices decrease with increasing length of helix, while the helix pitch and rise per residue increase. That is, regular 3(10)-helices become thinner and longer as N increases from 5 to 8. The fraction of regular 31,helices decreases linearly with helix length. All longer helices, N >= 9 are irregular. Energy minimizations show that regular helices become less stable with increasing helix length. These findings indicate that the definition of 3(10)-helices in terms of average, uniform dihedral angles is not appropriate and that it is inherently unstable for a polypeptide to form an extended, regular 3(10)-helix. The 3(10)-helices observed in proteins are better referred to parahelices.