Pi helix

Side view of a standard π-helix of L-alanine residues in atomic detail. Two hydrogen bonds to the same peptide group are highlighted in magenta; the oxygen-hydrogen distance is 1.65 Å (165 pm). The protein chain runs upwards, i.e., its N-terminus is at the bottom and its C-terminus at the top of the figure. Note that the sidechains point slightly downwards, i.e., towards the N-terminus.

A pi helix (or π-helix) is a type of secondary structure found in proteins. Although thought to be rare, π-helices are actually found in 15% of known protein structures and are believed to be an evolutionary adaptation derived by the insertion of a single amino acid into an α-helix. Because such insertions are highly destabilizing, the formation of π-helices would tend to be selected against unless it provided some functional advantage to the protein. π-helices therefore are typically found near functional sites of proteins.

Standard structure

The amino acids in a standard π-helix are arranged in a right-handed helical structure. Each amino acid corresponds to a 87° turn in the helix (i.e., the helix has 4.1 residues per turn), and a translation of 1.15 Å (=0.115 nm) along the helical axis. Most importantly, the N-H group of an amino acid forms a hydrogen bond with the C=O group of the amino acid five residues earlier; this repeated i+5→i hydrogen bonding defines a π-helix. Similar structures include the 3₁₀ helix (i+3→i hydrogen bonding) and the α-helix (i+4→i hydrogen bonding).

Top view of the same helix shown above. Four carbonyl groups are pointing upwards towards the viewer, spaced roughly 87° apart on the circle, corresponding to 4.1 amino-acid residues per turn of the helix.

The majority of π-helices are only 7 residues in length and do not adopt regularly repeating (φ, ψ) dihedral angles throughout the entire structure like that of α-helices or ß-sheets. Because of this, textbooks that provide single dihedral values for all residues in the π-helix are misleading. Some generalizations can be made, however. When the first and last residue pairs are excluded, dihedral angles exist such that the ψ dihedral angle of one residue and the φ dihedral angle of the next residue sum to roughly -125°. The first and last residue pairs sum to -95° and -105°, respectively. For comparison, the sum of the dihedral angles for a 3₁₀ helix is roughly -75°, whereas that for the α-helix is roughly -105°. Proline is often seen immediately following the end of π-helices. The general formula for the rotation angle Ω per residue of any polypeptide helix with trans isomers is given by the equation

$3 \cos \Omega = 1 - 4 \cos^{2} \left[ \left(\phi + \psi \right)/2 \right]$

Left-handed structure

In principle, a left-handed version of the π-helix is possible by reversing the sign of the (φ, ψ) dihedral angles to (55°, 70°). This pseudo-"mirror-image" helix has roughly the same number of residues per turn (4.1) and helical pitch (1.5 angstroms or 150 picometers). It is not a true mirror image, because the amino-acid residues still have a left-handed chirality. A long left-handed π-helix is unlikely to be observed in proteins because, among the naturally occurring amino acids, only glycine is likely to adopt positive φ dihedral angles such as 55°.

See also

• alpha helix
• 3_10 helix
• secondary structure