# 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.[1] Although once thought to be rare, short π-helices are 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.[2] Because such insertions are highly destabilizing,[3] 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.[2][4][5]

## Standard structure

The amino acids in a standard π-helix are arranged in a right-handed helical structure. Each amino acid corresponds to an 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 (φψ) dihedral angles throughout the entire structure like that of α-helices or β-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

${\displaystyle 3\cos \Omega =1-4\cos ^{2}\left({\frac {\phi +\psi }{2}}\right).}$

## Left-handed structure

In principle, a left-handed version of the π-helix is possible by reversing the sign of the (φψ) 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 Å [150 pm]). 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°.

## π-helices in nature

A short, 7 residue π-helix (orange) is embedded within a longer, α-helix (green). The "bulge" of the π-helix can be clearly seen, and was created as the result of a single amino acid that has been inserted into an α-helix. PDB code 3QHB.

Commonly used automated secondary structure assignment programs, such as DSSP, suggest <1% of proteins contain a π-helix. This mis-characterization results from the fact that naturally occurring π-helices are typically short in length (7 to 10 residues) and are almost always associated with (i.e. flanked by) α-helices on either end. Nearly all π-helices are therefore cryptic in that the π-helical residues are incorrectly assigned as either α-helical or as "turns". Recently developed programs have been written to properly annotate π-helices in protein structures and they have found that 1 in 6 proteins (around 15%) do in fact contain at least one π-helical segment.[2]

Natural π-helices can easily be identified in a structure as a "bulge" within a longer α-helix. Such helical bulges have previously been referred to as α-aneurisms, α-bulges, π-bulges, wide-turns,looping outs and π-turns, but in fact are π-helices as determined by their repeating i + 5 → i hydrogen bonds.[2] Evidence suggests that these bulges, or π-helices, are created by the insertion of a single additional amino acid into a pre-existing α-helix. Thus, α-helices and π-helices can be inter-converted by the insertion and deletion of a single amino acid.[2][3] Given both the relatively high rate of occurrence of π-helices and their noted association with functional sites (i.e. active sites) of proteins, this ability to interconvert between α-helices and π-helices has been an important mechanism of altering and diversifying protein functionality over the course of evolution.[2]

One of the most notable group of proteins whose functional diversification appears to have been heavily influenced by such an evolutionary mechanism is the ferritin-like superfamily, which includes ferritins, bacterioferritins, rubrerythrins, class I ribonucleotide reductases and soluble methane monooxygenases. Soluble methane monooxygenase is the current record holder for the most number of π-helices in a single enzyme with 13 (PDB code 1MTY). However, the bacterial homologue of a Na+/Cl dependent neurotransmitter transporter (PDB code 2A65) holds the record for the most π-helices in a single peptide chain with 8.[2]