# 310 helix

A **3 _{10} helix** is a type of secondary structure found (rarely) in proteins.

## Structure

The amino acids in a 3_{10}-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 → *i* hydrogen bonding **defines** a 3_{10}-helix. Similar structures include the α-helix (*i* + 4 → *i* hydrogen bonding) and the π-helix *i* + 5 → *i* hydrogen bonding).

Residues in 3_{10}-helices typically adopt (φ, ψ) dihedral angles near (−49°, −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 −75°. For comparison, the sum of the dihedral angles for an α-helix is roughly −105°, whereas that for a π-helix is roughly −125°.

The general formula for the rotation angle Ω per residue of any polypeptide helix with *trans* isomers is given by the equation

- <math>

3 \cos \Omega = 1 - 4 \cos^{2} \left(\frac{\varphi + \psi}{2} \right). </math>

## See also

## 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.