Editing Alpha helix (section)

=== Geometry and hydrogen bonding ===
The amino acids in an α-helix are arranged in a right-handed [[helix|helical]] structure where each amino acid residue corresponds to a 100° turn in the helix (i.e., the helix has 3.6 residues per turn), and a translation of {{cvt|1.5|Å|nm}} along the helical axis. Dunitz<ref>{{cite journal | vauthors = Dunitz J | author-link = Jack Dunitz | year = 2001 | title = Pauling's Left-Handed α-Helix | journal = Angewandte Chemie International Edition | volume = 40 | pages = 4167&ndash;4173 | doi = 10.1002/1521-3773(20011119)40:22<4167::AID-ANIE4167>3.0.CO;2-Q | issue = 22| pmid = 29712120 }}</ref> describes how Pauling's first article on the theme in fact shows a left-handed helix, the enantiomer of the true structure. Short pieces of left-handed helix sometimes occur with a large content of achiral [[glycine]] amino acids, but are unfavorable for the other normal, biological [[amino acids|{{small|L}}-amino acids]]. The pitch of the alpha-helix (the vertical distance between consecutive turns of the helix) is {{cvt|5.4|Å|nm}}, which is the product of 1.5 and 3.6. The most important thing is that the [[amine|N-H]] group of one amino acid forms a [[hydrogen bond]] with the [[carbonyl|C=O]] group of the amino acid ''four'' residues earlier; this repeated ''i''&nbsp;+&nbsp;4 → ''i'' hydrogen bonding is the most prominent characteristic of an α-helix. Official international nomenclature<ref>{{cite journal | author = IUPAC-IUB Commission on Biochemical Nomenclature | year = 1970 | title = Abbreviations and symbols for the description of the conformation of polypeptide chains | journal = Journal of Biological Chemistry | volume = 245 | issue = 24 | pages = 6489–6497| doi = 10.1016/S0021-9258(18)62561-X | doi-access = free }}</ref><ref name="qmul_ppep1">{{cite web |title=Polypeptide Conformations 1 and 2 |url=http://www.sbcs.qmul.ac.uk/iupac/misc/ppep1.html |website=www.sbcs.qmul.ac.uk |access-date=5 November 2018}}</ref> specifies two ways of defining α-helices, rule 6.2 in terms of repeating ''φ'', ''ψ'' torsion angles (see below) and rule 6.3 in terms of the combined pattern of pitch and hydrogen bonding. The α-helices can be identified in protein structure using several computational methods, such as [[DSSP (algorithm)|DSSP]] (Define&nbsp;[[Secondary structure|Secondary Structure]] of Protein).<ref>{{cite journal | vauthors = Kabsch W, Sander C | title = Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features | journal = Biopolymers | volume = 22 | issue = 12 | pages = 2577–637 | date = December 1983 | pmid = 6667333 | doi = 10.1002/bip.360221211 | s2cid = 29185760 }}</ref>

[[Image:Alpha vs 310 helix end views.jpg|thumb|left|300px|Contrast of helix end views between α (offset squarish) vs 3<sub>10</sub> (triangular)]]
Similar structures include the [[310 helix|3<sub>10</sub> helix]] (''i''&nbsp;+&nbsp;3 → ''i'' hydrogen bonding) and the [[Pi helix|π-helix]] (''i''&nbsp;+&nbsp;5 → ''i'' hydrogen bonding). The α-helix can be described as a 3.6<sub>13</sub> helix, since the ''i''&nbsp;+&nbsp;4 spacing adds three more atoms to the H-bonded loop compared to the tighter 3<sub>10</sub> helix, and on average, 3.6 amino acids are involved in one ring of α-helix. The subscripts refer to the number of atoms (including the hydrogen) in the closed loop formed by the hydrogen bond.<ref name="Anatax">{{cite journal | vauthors = Richardson JS | title = The anatomy and taxonomy of protein structure | journal = Advances in Protein Chemistry | volume = 34 | pages = 167–339 | year = 1981 | pmid = 7020376 | doi = 10.1016/S0065-3233(08)60520-3 | author-link = Jane S. Richardson | isbn = 9780120342341 }}</ref>

[[Image:Ramachandran plot general 100K.jpg|thumb|right|250px|[[Ramachandran plot]] (''φ'',&nbsp;''ψ'' plot), with data points for α-helical residues forming a dense diagonal cluster below and left of center, around the global energy minimum for backbone conformation.<ref>{{cite journal | vauthors = Lovell SC, Davis IW, Arendall WB, de Bakker PI, Word JM, Prisant MG, Richardson JS, Richardson DC | title = Structure validation by Calpha geometry: phi,psi and Cbeta deviation | journal = Proteins | volume = 50 | issue = 3 | pages = 437–50 | date = February 2003 | pmid = 12557186 | doi = 10.1002/prot.10286 | s2cid = 8358424 }}</ref>]]
Residues in α-helices typically adopt backbone (''φ'',&nbsp;''ψ'') [[dihedral angle]]s around (−60°,&nbsp;−45°), as shown in the image at right. In more general terms, 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 −105°. As a consequence, α-helical dihedral angles, in general, fall on a diagonal stripe on the [[Ramachandran diagram]] (of slope −1), ranging from (−90°,&nbsp;−15°) to (−70°,&nbsp;−35°). For comparison, the sum of the dihedral angles for a 3<sub>10</sub> helix is roughly −75°, whereas that for the π-helix is roughly −130°. The general formula for the rotation angle ''Ω'' per residue of any polypeptide helix with ''trans'' isomers is given by the equation<ref>{{citation | vauthors = Dickerson RE, Geis I | author-link2 = Irving Geis |  year = 1969 | title = Structure and Action of Proteins | publisher = Harper, New York }}</ref><ref>{{cite book|chapter = Structural Organization of Proteins|first = Matjaž|last = Zorko|pages = 36–57|title = Introduction to Peptides and Proteins|editor1-first = Ülo|editor1-last = Langel|editor2-first = Benjamin F.|editor2-last = Cravatt|editor-link2 = Benjamin Cravatt III|editor3-first = Astrid|editor3-last = Gräslund|editor4-first = Gunnar|editor4-last = von Heijne|editor-link4 = Gunnar von Heijne|editor7-first = Matjaž|editor7-last = Zorko|editor5-first = Tiit|editor5-last = Land|editor6-first = Sherry|editor6-last = Niessen|publisher = [[CRC Press]]|location = Boca Raton|year = 2010|chapter-url = https://books.google.com/books?id=GA3SBQAAQBAJ&pg=PA40|isbn = 9781439882047}}</ref>

:{{math|3 cos ''Ω'' {{=}} 1 − 4 cos<sup>2</sup> {{sfrac|''φ'' + ''ψ''|2}}}}

The α-helix is tightly packed; there is almost no free space within the helix. The amino-acid side-chains are on the outside of the helix, and point roughly "downward" (i.e., toward the N-terminus), like the branches of an evergreen tree ([[Christmas tree]] effect). This directionality is sometimes used in preliminary, low-resolution electron-density maps to determine the direction of the protein backbone.<ref>{{cite journal | vauthors = Terwilliger TC | title = Rapid model building of alpha-helices in electron-density maps | journal = Acta Crystallographica Section D | volume = 66 | issue = Pt 3 | pages = 268–75 | date = March 2010 | pmid = 20179338 | pmc = 2827347 | doi = 10.1107/S0907444910000314 | bibcode = 2010AcCrD..66..268T }}</ref>