Kasha's rule

Side view of a 3₁₀-helix of alanine residues in atomic detail. Two hydrogen bonds to the same peptide group are highlighted in magenta; the oxygen-hydrogen distance is 1.83 Å (183 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 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, and has 10 atoms in the ring formed by making the hydrogen bond. 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 3₁₀-helix. Similar structures include the α-helix (i + 4 → i hydrogen bonding) and the π-helix i + 5 → i hydrogen bonding).

Top view of the same helix shown to the right. Three carbonyl groups are pointing upwards towards the viewer, spaced roughly 120° apart on the circle, corresponding to 3.0 amino-acid residues per turn of the helix.

Residues in 3₁₀-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

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

See also

• alpha helix
• pi helix
• secondary structure

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.