Editing Dihedral angle (section)

===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]].