Editing Protein secondary structure (section)

== Types ==
{| class="wikitable sortable floatright"
|+ Structural features of the three major forms of protein helices<ref>{{cite web | url = http://www.biomed.curtin.edu.au/biochem/tutorials/prottute/helices.htm | title = Interactive Protein Structure Tutorial | vauthors = Bottomley S | year = 2004 | access-date = January 9, 2011 | archive-url = https://web.archive.org/web/20110301175611/http://www.biomed.curtin.edu.au/biochem/tutorials/prottute/helices.htm | archive-date = March 1, 2011 | url-status = dead }}</ref><ref>{{Cite book| vauthors = Schulz GE, Schirmer RH |url=https://www.worldcat.org/oclc/4498269|title=Principles of protein structure|date=1979|publisher=Springer-Verlag |isbn=0-387-90386-0|location=New York|oclc=4498269}}</ref>
!Geometry attribute
!α-helix
!3<sub>10</sub> helix
!π-helix
|-
|Residues per turn ||align="right"| 3.6 ||align="right"| 3.0 ||align="right"| 4.4
|-
|Translation per residue ||align="right"| {{convert|1.5|Å|nm|abbr=on}} ||align="right"| {{convert|2.0|Å|nm|abbr=on}} ||align="right"| {{convert|1.1|Å|nm|abbr=on}}
|-
|Radius of helix ||align="right"| {{convert|2.3|Å|nm|abbr=on}} ||align="right"| {{convert|1.9|Å|nm|abbr=on}} ||align="right"| {{convert|2.8|Å|nm|abbr=on}}
|-
|Pitch ||align="right"| {{convert|5.4|Å|nm|abbr=on}} ||align="right"| {{convert|6.0|Å|nm|abbr=on}} <!-- 3.0 r/t * 2.0Å trans --> ||align="right"| {{convert|4.8|Å|nm|abbr=on}} <!-- 4.4 r/t * 1.1Å trans -->
|}
{{Alpha beta structure}}
The most common secondary structures are [[alpha helix|alpha helices]] and [[beta sheet]]s. Other helices, such as the [[310 helix|3<sub>10</sub> helix]] and [[pi helix|π helix]], are calculated to have energetically favorable hydrogen-bonding patterns but are rarely observed in natural proteins except at the ends of α helices due to unfavorable backbone packing in the center of the helix. Other extended structures such as the [[polyproline helix]] and [[alpha sheet]] are rare in [[native state]] proteins but are often hypothesized as important [[protein folding]] intermediates. Tight [[turn (biochemistry)|turns]] and loose, flexible loops link the more "regular" secondary structure elements. The [[random coil]] is not a true secondary structure, but is the class of conformations that indicate an absence of regular secondary structure.

[[Amino acid]]s vary in their ability to form the various secondary structure elements. [[Proline]] and [[glycine]] are sometimes known as "helix breakers" because they disrupt the regularity of the α helical backbone conformation; however, both have unusual conformational abilities and are commonly found in [[turn (biochemistry)|turns]]. Amino acids that prefer to adopt [[alpha helix|helical]] conformations in proteins include [[methionine]], [[alanine]], [[leucine]], [[glutamate]] and [[lysine]] ("MALEK" in [[amino acid|amino-acid]] 1-letter codes); by contrast, the large aromatic residues ([[tryptophan]], [[tyrosine]] and [[phenylalanine]]) and C<sup>β</sup>-branched amino acids ([[isoleucine]], [[valine]], and [[threonine]]) prefer to adopt [[beta sheet|β-strand]] conformations. However, these preferences are not strong enough to produce a reliable method of predicting secondary structure from sequence alone.

Low frequency collective vibrations are thought to be sensitive to local rigidity within proteins, revealing beta structures to be generically more rigid than alpha or disordered proteins.<ref>{{cite journal | vauthors = Perticaroli S, Nickels JD, Ehlers G, O'Neill H, Zhang Q, Sokolov AP | title = Secondary structure and rigidity in model proteins | journal = Soft Matter | volume = 9 | issue = 40 | pages = 9548–56 | date = October 2013 | pmid = 26029761 | doi = 10.1039/C3SM50807B | bibcode = 2013SMat....9.9548P }}</ref><ref>{{cite journal | vauthors = Perticaroli S, Nickels JD, Ehlers G, Sokolov AP | title = Rigidity, secondary structure, and the universality of the boson peak in proteins | journal = Biophysical Journal | volume = 106 | issue = 12 | pages = 2667–74 | date = June 2014 | pmid = 24940784 | pmc = 4070067 | doi = 10.1016/j.bpj.2014.05.009 | bibcode = 2014BpJ...106.2667P }}</ref>  Neutron scattering measurements have directly connected the spectral feature at ~1 THz to collective motions of the secondary structure of beta-barrel protein GFP.<ref>{{cite journal | vauthors = Nickels JD, Perticaroli S, O'Neill H, Zhang Q, Ehlers G, Sokolov AP | title = Coherent neutron scattering and collective dynamics in the protein, GFP | journal = Biophys. J. | volume = 105 | issue = 9 | pages = 2182–87 | year = 2013 | pmid = 24209864 | pmc = 3824694 | doi = 10.1016/j.bpj.2013.09.029 | bibcode = 2013BpJ...105.2182N }}</ref>

Hydrogen bonding patterns in secondary structures may be significantly distorted, which makes automatic determination of secondary structure difficult.  There are several methods for formally defining protein secondary structure (e.g.,  [[DSSP (hydrogen bond estimation algorithm)|DSSP]],<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 = Dec 1983 | pmid = 6667333 | doi = 10.1002/bip.360221211 | s2cid = 29185760 }}</ref> DEFINE,<ref>{{cite journal | vauthors = Richards FM, Kundrot CE | title = Identification of structural motifs from protein coordinate data: secondary structure and first-level supersecondary structure | journal = Proteins | volume = 3 | issue = 2 | pages = 71–84 | year = 1988 | pmid = 3399495 | doi = 10.1002/prot.340030202 | s2cid = 29126855 }}</ref> [[STRIDE (algorithm)|STRIDE]],<ref>{{cite journal | vauthors = Frishman D, Argos P | title = Knowledge-based protein secondary structure assignment | journal = Proteins | volume = 23 | issue = 4 | pages = 566–79 | date = Dec 1995 | pmid = 8749853 | doi = 10.1002/prot.340230412 | url = http://nook.cs.ucdavis.edu/~koehl/Classes/ECS289/reprints/Paper_Stride.pdf | url-status = dead | archive-url = https://web.archive.org/web/20100613184204/http://nook.cs.ucdavis.edu/~koehl/Classes/ECS289/reprints/Paper_Stride.pdf | archive-date = 2010-06-13 | citeseerx = 10.1.1.132.9420 | s2cid = 17487756 }}</ref>   ScrewFit,<ref>{{cite journal | vauthors = Calligari PA, Kneller GR | title = ScrewFit: combining localization and description of protein secondary structure | journal = Acta Crystallographica Section D | volume = 68 | issue = Pt 12 | pages = 1690–3 | date = December 2012 | pmid = 23151634 | doi = 10.1107/s0907444912039029 }}</ref> [http://lcb.infotech.monash.edu.au/sst SST]<ref name=":0">{{cite journal | vauthors = Konagurthu AS, Lesk AM, Allison L | title = Minimum message length inference of secondary structure from protein coordinate data | journal = Bioinformatics | volume = 28 | issue = 12 | pages = i97–i105  | date = Jun 2012 | pmid = 22689785 | pmc = 3371855 | doi = 10.1093/bioinformatics/bts223 }}</ref>).

=== DSSP classification ===
{{Main|DSSP (algorithm)}}

[[Image:SegmentLengths.dist.png|thumb|200px|Distribution obtained from non-redundant pdb_select dataset (March 2006); Secondary structure assigned by DSSP; 8 conformational states reduced to 3 states: H=HGI, E=EB, C=STC. Visible are mixtures of (gaussian) distributions, resulting also from the reduction of DSSP states.]]

The Dictionary of Protein Secondary Structure, in short DSSP, is commonly used to describe the protein secondary structure with single letter codes. The secondary structure is assigned based on hydrogen bonding patterns as those initially proposed by Pauling et al. in 1951 (before any [[protein structure]] had ever been experimentally determined). There are eight types of secondary structure that DSSP defines:

* G = 3-turn helix ([[3 10 helix|3<sub>10</sub> helix]]). Min length 3 residues.
* H = 4-turn helix ([[α helix]]). Minimum length 4 residues.
* I = 5-turn helix ([[π helix]]). Minimum length 5 residues.
* T = hydrogen bonded turn (3, 4 or 5 turn)
* E = extended strand in parallel and/or anti-parallel [[β-sheet]] conformation. Min length 2 residues.
* B = residue in isolated β-bridge (single pair β-sheet hydrogen bond formation)
* S = bend (the only non-hydrogen-bond based assignment).
* C = coil (residues which are not in any of the above conformations).

'Coil' is often codified as '&nbsp;' (space), C (coil) or '–' (dash). The helices (G, H and I) and sheet conformations are all required to have a reasonable length. This means that 2 adjacent residues in the primary structure must form the same hydrogen bonding pattern. If the helix or sheet hydrogen bonding pattern is too short they are designated as T or B, respectively. Other protein secondary structure assignment categories exist (sharp turns, [[Omega loop]]s, etc.), but they are less frequently used.

Secondary structure is defined by [[hydrogen bond]]ing, so the exact definition of a hydrogen bond is critical. The standard hydrogen-bond definition for secondary structure is that of [[DSSP (algorithm)|DSSP]], which is a purely electrostatic model. It assigns charges of ±''q''<sub>1</sub>&nbsp;≈&nbsp;0.42[[elementary charge|''e'']] to the carbonyl carbon and oxygen, respectively, and charges of ±''q''<sub>2</sub>&nbsp;≈&nbsp;0.20''e'' to the amide hydrogen and nitrogen, respectively. The electrostatic energy is

:<math>
E = q_{1} q_{2} 
\left( \frac{1}{r_\mathrm{ON}} + \frac{1}{r_\mathrm{CH}} - \frac{1}{r_\mathrm{OH}} - \frac{1}{r_\mathrm{CN}} \right) \cdot 332 \text{ kcal/mol}.
</math>

According to DSSP, a hydrogen-bond exists if and only if ''E'' is less than {{cvt|-0.5|kcal/mol|kJ/mol}}. Although the DSSP formula is a relatively crude approximation of the ''physical'' hydrogen-bond energy, it is generally accepted as a tool for defining secondary structure.

=== SST classification ===
SST<ref>{{cite web | url=http://lcb.infotech.monash.edu.au/sstweb2 | title=SST (Web server): Secondary STructure assignment to protein coordinates using MML inference -- Submission page }}</ref><ref name=":0" /> is a Bayesian method to  assign secondary structure to protein coordinate data using the Shannon information criterion of Minimum Message Length ([[Minimum message length|MML]]) inference.  [http://lcb.infotech.monash.edu.au/sstweb2 SST]  treats any assignment of secondary structure as a potential hypothesis that attempts to explain ([[Lossless compression|compress]]) given protein coordinate data. The core idea is that the '''''best''''' secondary structural assignment is the one that can explain ([[Lossless compression|compress]]) the coordinates of a given protein coordinates in the most economical way, thus linking the inference of secondary structure to [[lossless data compression]]. SST accurately delineates any protein chain into regions associated with the following assignment types:<ref>{{Cite web|url=http://lcb.infotech.monash.edu.au/sst|title=SST web server|access-date=17 April 2018}}</ref>

* E = (Extended) strand of a '''[[Beta sheet|β-pleated sheet]]'''
* G = Right-handed '''[[310 helix|3<sub>10</sub> helix]]''' 
* H = Right-handed [[Alpha helix|'''α-helix''']]
* I = Right-handed [[Pi helix|'''π'''-'''helix''']]
* g = Left-handed '''[[310 helix|3<sub>10</sub> helix]]''' 
* h = Left-handed [[Alpha helix|'''α-helix''']]
* i = Left-handed [[Pi helix|'''π'''-'''helix''']]
* 3 = '''3<sub>10</sub>'''-like [[Turn (biochemistry)|'''Turn''']] 
* 4 = '''α'''-like [[Turn (biochemistry)|'''Turn''']] 
* 5 = '''π-'''like  [[Turn (biochemistry)|'''Turn''']] 
* T = Unspecified [[Turn (biochemistry)|'''Turn''']]
* C = '''Coil'''
* - = Unassigned residue

SST<ref>{{cite web | url=http://lcb.infotech.monash.edu.au/sstweb2 | title=SST (Web server): Secondary STructure assignment to protein coordinates using MML inference -- Submission page }}</ref>   detects '''π''' and '''3<sub>10</sub>''' helical caps to standard '''α'''-helices, and automatically assembles the various extended strands into consistent β-pleated sheets. It provides a readable output of dissected secondary structural elements, and a corresponding [[PyMOL|PyMol]]-loadable script to visualize the assigned secondary structural elements individually.