Editing Dihedral angle (section)

==In stereochemistry==
{{see also|Alkane stereochemistry|Conformational isomerism}}
{| style="margin: 0 auto;"
| [[File:Synantipericlinal.svg|200px]]
| [[File:Newman projection butane -sc.svg|200px]]
|[[File:Sawhorse projection butane -sc.svg|200px]]
|-
|Configuration names<br />according to dihedral angle
| ''syn'' ''n-''[[Butane]] in the<br />''gauche<sup>−</sup>'' conformation (−60°)<br /> [[Newman projection]]
| ''syn'' ''n-''[[Butane]]<br /> sawhorse projection
|}
[[File:Dihedral angles of Butane.svg|alt=|thumb|400x400px|Free energy diagram of [[butane|''n''-butane]] as a function of dihedral angle.]]
In [[stereochemistry]], a '''torsion angle''' is defined as a particular example of a dihedral angle, describing the geometric relation of two parts of a molecule joined by a [[chemical bond]].<ref>{{GoldBookRef|file=T06406|title=Torsion angle}}</ref><ref>{{GoldBookRef|file=D01730|title=Dihedral angle}}</ref> Every set of three non-colinear atoms of a [[molecule]] defines a half-plane. As explained above, when two such half-planes intersect (i.e., a set of four consecutively-bonded atoms), the angle between them is a dihedral angle. Dihedral angles are used to specify the [[Conformational isomerism|molecular conformation]].<ref name="dougherty">{{cite book|last=Anslyn|first=Eric|title=Modern Physical Organic Chemistry|year=2006|publisher=University Science|isbn=978-1891389313|page=95|author2=Dennis Dougherty}}</ref> [[Stereochemical]] arrangements corresponding to angles between 0° and ±90° are called ''syn'' (s), those corresponding to angles between ±90° and 180° ''anti'' (a). Similarly, arrangements corresponding to angles between 30° and 150° or between −30° and −150° are called ''clinal'' (c) and those between 0° and ±30° or ±150° and 180° are called ''periplanar'' (p).

The two types of terms can be combined so as to define four ranges of angle; 0° to ±30° synperiplanar (sp); 30° to 90° and −30° to −90° synclinal (sc); 90° to 150° and −90° to −150° anticlinal (ac); ±150° to 180° antiperiplanar (ap). The synperiplanar conformation is also known as the ''syn''- or ''cis''-conformation; antiperiplanar as ''anti'' or ''trans''; and synclinal as ''gauche'' or ''skew''.

For example, with ''n''-[[butane]] two planes can be specified in terms of the two central carbon atoms and either of the methyl carbon atoms. The ''syn''-conformation shown above, with a dihedral angle of 60° is less stable than the ''anti''-conformation with a dihedral angle of 180°.

For macromolecular usage the symbols T, C, G<sup>+</sup>, G<sup>−</sup>, A<sup>+</sup> and A<sup>−</sup> are recommended (ap, sp, +sc, −sc, +ac and −ac respectively).

===Proteins===
[[Image:Protein backbone PhiPsiOmega drawing.svg|thumb|175px|Depiction of a [[protein]], showing where ω, φ, & ψ refer to.]]
A [[Ramachandran plot]] (also known as a Ramachandran diagram or a [''φ'',''ψ''] plot), originally developed in 1963 by [[G. N. Ramachandran]], C. Ramakrishnan, and V. Sasisekharan,<ref>{{cite journal |pages=95–9 |doi=10.1016/S0022-2836(63)80023-6 |title=Stereochemistry of polypeptide chain configurations |year=1963 |last1=Ramachandran |first1=G. N. |last2=Ramakrishnan |first2=C. |last3=Sasisekharan |first3=V. |journal=Journal of Molecular Biology |volume=7 |pmid=13990617}}</ref> is a way to visualize energetically allowed regions for backbone dihedral angles ''ψ'' against ''φ'' of [[amino acid]] residues in [[protein structure]].
In a [[protein]] chain three dihedral angles are defined:
* ω (omega) is the angle in the chain C<sup>α</sup> − C' − N − C<sup>α</sup>,
* φ (phi) is the angle in the chain C' − N − C<sup>α</sup> − C'
* ψ (psi) is the angle in the chain N − C<sup>α</sup> − C' − N (called ''φ′'' by Ramachandran)

The figure at right illustrates the location of each of these angles (but it does not show correctly the way they are defined).<ref>{{cite book |year=1981 |last1=Richardson |first1=J. S. |title=Anatomy and Taxonomy of Protein Structures |chapter=The Anatomy and Taxonomy of Protein Structure |volume=34 |pages=167–339 |doi=10.1016/S0065-3233(08)60520-3 |pmid=7020376 |series=Advances in Protein Chemistry |isbn=9780120342341}}</ref>

The planarity of the [[peptide bond]] usually restricts ''ω'' to be 180° (the typical ''[[Cis-trans isomerism|trans]]'' case) or 0° (the rare ''[[Cis-trans isomerism|cis]]'' case).  The distance between the C<sup>α</sup> atoms in the ''trans'' and ''cis'' [[geometric isomerism|isomers]] is approximately 3.8 and 2.9&nbsp;Å, respectively.  The vast majority of the peptide bonds in proteins are ''trans'', though the peptide bond to the nitrogen of [[proline]] has an increased prevalence of ''cis'' compared to other amino-acid pairs.<ref>{{Cite journal|vauthors=Singh J, Hanson J, Heffernan R, Paliwal K, Yang Y, Zhou Y|date=August 2018|title=Detecting Proline and Non-Proline Cis Isomers in Protein Structures from Sequences Using Deep Residual Ensemble Learning|journal=Journal of Chemical Information and Modeling|volume=58|issue=9|pages=2033–2042|doi=10.1021/acs.jcim.8b00442|pmid=30118602|s2cid=52031431}}</ref>

The side chain dihedral angles are designated with ''χ<sub>n</sub>'' (chi-''n'').<ref>{{Cite web|url=http://www.cryst.bbk.ac.uk/PPS95/course/3_geometry/conform.html|title=Side Chain Conformation}}</ref> They tend to cluster near 180°, 60°, and −60°, which are called the ''trans'', ''gauche<sup>−</sup>'', and ''gauche<sup>+</sup>'' conformations.  The stability of certain sidechain dihedral angles is affected by the values ''φ'' and ''ψ''.<ref>{{cite journal|last1=Dunbrack|first1=RL Jr.|last2=Karplus|first2=M|title=Backbone-dependent rotamer library for proteins. Application to side-chain prediction.|journal=Journal of Molecular Biology|date=20 March 1993|volume=230|issue=2|pages=543–74|pmid=8464064|doi=10.1006/jmbi.1993.1170}}</ref> For instance, there are direct steric interactions between the C''γ'' of the side chain in the ''gauche<sup>+</sup>'' rotamer and the backbone nitrogen of the next residue when ''ψ'' is near −60°.<ref>{{cite journal|last1=Dunbrack|first1=RL Jr|last2=Karplus|first2=M|title=Conformational analysis of the backbone-dependent rotamer preferences of protein sidechains.|journal=Nature Structural Biology|date=May 1994|volume=1|issue=5|pages=334–40|pmid=7664040|doi=10.1038/nsb0594-334|s2cid=9157373}}</ref> This is evident from statistical distributions in [[Backbone-dependent rotamer library|backbone-dependent rotamer libraries]].