310 helix



A 310 helix is a type of secondary structure found (rarely) in proteins.

Structure
The amino acids in a 310-helix are arranged in a right-handed helical structure. Each amino acid corresponds to a 120° turn in the helix (i.e., the helix has three residues per turn), and a translation of 2.0 Å (= 0.2 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 three residues earlier; this repeated i + 3 &rarr; i hydrogen bonding defines a 310-helix. Similar structures include the α-helix (i + 4 &rarr; i hydrogen bonding) and the &pi;-helix i + 5 &rarr; i hydrogen bonding).



Residues in 310-helices typically adopt (φ, ψ) dihedral angles near (&minus;49°, &minus;26°). 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 &minus;75°. For comparison, the sum of the dihedral angles for an α-helix is roughly &minus;105°, whereas that for a π-helix is roughly &minus;125°.

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(\frac{\varphi + \psi}{2} \right). $$