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| {{DISPLAYTITLE:3<sub>10</sub> helix}}
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| [[Image:3 10 helix neg49 neg26 sideview.png|thumb|right|250px|Side view of a 3<sub>10</sub>-helix of [[alanine]] residues in [[atom]]ic 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.]]
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| A '''3<sub>10</sub> helix''' is a type of [[secondary structure]] found (rarely) in [[protein]]s.
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| ==Structure==
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| The amino acids in a 3<sub>10</sub>-helix are arranged in a right-handed [[helix|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 [[amine|N-H]] group of an amino acid forms a [[hydrogen bond]] with the [[carbonyl|C = O]] group of the amino acid ''three'' residues earlier; this repeated ''i'' + 3 → ''i'' hydrogen bonding '''defines''' a 3<sub>10</sub>-helix. Similar structures include the [[Alpha_helix|α-helix]] (''i'' + 4 → ''i'' hydrogen bonding) and the [[Pi_helix|π-helix]] ''i'' + 5 → ''i'' hydrogen bonding).
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| [[Image:310 helix topview.png|thumb|left|225px|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|amino-acid]] residues per turn of the helix.]]
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| Residues in 3<sub>10</sub>-helices typically adopt (φ, ψ) [[dihedral angle]]s 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°.
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| The general formula for the rotation angle Ω per residue of any polypeptide helix with ''trans'' isomers is given by the equation
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| :<math>
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| 3 \cos \Omega = 1 - 4 \cos^{2} \left(\frac{\varphi + \psi}{2} \right).
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| </math>
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| ==See also== | |
| * [[alpha helix]]
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| * [[pi helix]]
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| * [[secondary structure]]
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| ==References==
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| * 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.
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| {{Protein secondary structure}}
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| [[Category:Protein structural motifs]]
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| [[Category:Helices]]
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| {{protein-stub}}
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