Pi helix

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Side view of an π-helix of 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 $\boldsymbol\pi$ -helix) is a type of secondary structure found (rarely) in proteins.

[edit] Structure

The amino acids in an $π$ -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 $i+5 \rightarrow i$ hydrogen bonding defines a $π$ -helix. Similar structures include the $310$ helix ( $i+3 \rightarrow i$ hydrogen bonding) and the α-helix ( $i+4 \rightarrow i$ 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.

Residues in $π$ -helices typically adopt (φ, ψ) dihedral angles near $(-55^{\circ}, -70^{\circ})$ . More generally, they adopt dihedral angles such that the ψ dihedral angle of one residue and the φ dihedral angle of the next residue sum to roughly $-125^{\circ}$ . For comparison, the sum of the diheral angles for a $310$ helix is roughly $-75^{\circ}$ , whereas that for the α-helix is roughly $-105^{\circ}$ . The general formula for the rotation angle $Ω$ per residue of any polypeptide helix with trans isomers is given by the equation

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

[edit] See also

[edit] References

Pauling L, Corey RB and Branson HR. (1951) "The Structure of Proteins: Two Hydrogen-Bonded Helical Configurations of the Polypeptide Chain", Proc. Nat. Acad. Sci. Wash., 37, 205.

Protein secondary structure
Helices:	α-helix \| 3₁₀ helix \| π-helix \| β-helix \| Polyproline helix \| Collagen helix
Extended:	β-strand \| Turn \| Beta hairpin \| Beta bulge
Supersecondary:	Coiled coil \| Helix-turn-helix \| EF hand
Secondary structure propensities of amino acids
Helix-favoring:	Methionine \| Alanine \| Leucine \| Glutamic acid \| Glutamine \| Lysine
Extended-favoring:	Threonine \| Isoleucine \| Valine \| Phenylalanine \| Tyrosine \| Tryptophan
Disorder-favoring:	Glycine \| Serine \| Proline \| Asparagine \| Aspartic acid
No preference:	Cysteine \| Histidine \| Arginine
←Primary structure		Tertiary structure→