Editing Capsid (section)

==Specific shapes==

===Icosahedral===
[[File:Adenovirus 3D schematic.png|thumb|Icosahedral capsid of an [[Adenoviridae|adenovirus]]]]
[[File:Virus capsid T number.tif|thumb|right|Virus capsid T-numbers]]
The icosahedral structure is extremely common among viruses. The [[icosahedron]] consists of 20 triangular faces delimited by 12 fivefold vertexes and consists of 60 asymmetric units. Thus, an icosahedral virus is made of 60N protein subunits. The number and arrangement of [[capsomere]]s in an icosahedral capsid can be classified using the "quasi-equivalence principle" proposed by [[Donald Caspar]] and [[Aaron Klug]].<ref name=Caspar1962>{{cite journal | vauthors = Caspar DL, Klug A | title = Physical principles in the construction of regular viruses | journal = Cold Spring Harbor Symposia on Quantitative Biology | volume = 27 | pages = 1–24 | year = 1962 | pmid = 14019094 | doi = 10.1101/sqb.1962.027.001.005 }}</ref> Like the [[Goldberg polyhedra]], an icosahedral structure can be regarded as being constructed from pentamers and hexamers. The structures can be indexed by two integers ''h'' and ''k'', with <math>h \ge 1</math> and <math>k \ge 0</math>; the structure can be thought of as taking ''h'' steps from the edge of a pentamer, turning 60 degrees counterclockwise, then taking ''k'' steps to get to the next pentamer. The triangulation number ''T'' for the capsid is defined as:
:<math> T = h^2 + h \cdot k + k^2 </math>
In this scheme, icosahedral capsids contain 12 pentamers plus 10(''T''&nbsp;−&nbsp;1) hexamers.<ref>{{cite journal | vauthors = Carrillo-Tripp M, Shepherd CM, Borelli IA, Venkataraman S, Lander G, Natarajan P, Johnson JE, Brooks CL, Reddy VS | display-authors = 6 | title = VIPERdb2: an enhanced and web API enabled relational database for structural virology | journal = Nucleic Acids Research | volume = 37 | issue = Database issue | pages = D436-42 | date = January 2009 | pmid = 18981051 | pmc = 2686430 | doi = 10.1093/nar/gkn840 | url = http://viperdb.scripps.edu/virus.php | access-date = 2011-03-18 | archive-date = 2018-02-11 | archive-url = https://web.archive.org/web/20180211191026/http://viperdb.scripps.edu/virus.php | url-status = dead }}</ref><ref name="Johnson, J. E. and Speir, J.A. 2009 115–123">{{cite book | vauthors = Johnson JE, Speir JA |title=Desk Encyclopedia of General Virology|publisher=Academic Press |location=Boston |year=2009 |pages=115–123 |isbn=978-0-12-375146-1}}</ref> The ''T''-number is representative of the size and complexity of the capsids.<ref>{{cite journal | vauthors = Mannige RV, Brooks CL | title = Periodic table of virus capsids: implications for natural selection and design | journal = PLOS ONE | volume = 5 | issue = 3 | pages = e9423 | date = March 2010 | pmid = 20209096 | pmc = 2831995 | doi = 10.1371/journal.pone.0009423 | bibcode = 2010PLoSO...5.9423M | doi-access = free }}</ref> Geometric examples for many values of ''h'', ''k'', and ''T'' can be found at [[List of geodesic polyhedra and Goldberg polyhedra]].

Many exceptions to this rule exist: For example, the [[polyomavirus]]es and [[papillomaviruses]] have pentamers instead of hexamers in hexavalent positions on a quasi T = 7 lattice. Members of the double-stranded RNA virus lineage, including [[reovirus]], [[rotavirus]] and bacteriophage φ6 have capsids built of 120 copies of capsid protein, corresponding to a T = 2 capsid, or arguably a T = 1 capsid with a dimer in the asymmetric unit. Similarly, many small viruses have a pseudo T = 3 (or P = 3) capsid, which is organized according to a T = 3 lattice, but with distinct polypeptides occupying the three quasi-equivalent positions <ref>{{cite web | first = Jean-Yves | last = Sgro | work = Institute for Molecular Virology | publisher = University of Wisconsin-Madison | title=Virusworld | url=http://www.virology.wisc.edu/virusworld/tri_number.php }}</ref>

===Prolate===
[[Image:PhageExterior.svg|thumb|left|The prolate structure of a typical head on a [[bacteriophage]]]]
An elongated icosahedron is a common shape for the heads of bacteriophages. Such a structure is composed of a cylinder with a cap at either end. The cylinder is composed of 10 elongated triangular faces. The Q number (or T<sub>mid</sub>), which can be any positive integer,<ref>{{cite journal | vauthors = Luque A, Reguera D | title = The structure of elongated viral capsids | journal = Biophysical Journal | volume = 98 | issue = 12 | pages = 2993–3003 | date = June 2010 | pmid = 20550912 | pmc = 2884239 | doi = 10.1016/j.bpj.2010.02.051 | bibcode = 2010BpJ....98.2993L }}</ref> specifies the number of triangles, composed of asymmetric subunits, that make up the 10 triangles of the cylinder. The caps are classified by the T (or T<sub>end</sub>) number.<ref>{{cite book | vauthors = Casjens S |title=Desk Encyclopedia of General Virology|publisher=Academic Press |location=Boston |year=2009 |pages=167–174 |isbn=978-0-12-375146-1}}</ref>{{clear}}

The bacterium ''E. coli'' is the host for [[Escherichia virus T4|bacteriophage T4]] that has a prolate head structure. The bacteriophage encoded gp31 protein appears to be functionally homologous to ''E. coli'' chaperone protein GroES and able to substitute for it in the assembly of bacteriophage T4 virions during infection.<ref name = Marusich1998>Marusich EI, Kurochkina LP, Mesyanzhinov VV. Chaperones in bacteriophage T4 assembly. Biochemistry (Mosc). 1998;63(4):399-406</ref> Like GroES, gp31 forms a stable complex with [[GroEL]] [[chaperone (protein)|chaperonin]] that is absolutely necessary for the folding and assembly ''in vivo'' of the bacteriophage T4 major capsid protein gp23.<ref name = Marusich1998/>

===Helical===
[[File:Helical capsid with RNA.png|thumb|left|3D model of a helical capsid structure of a virus]]

Many rod-shaped and filamentous plant viruses have capsids with [[Symmetry (geometry)#Helical symmetry|helical symmetry]].<ref name="autogenerated9">{{cite journal | vauthors = Yamada S, Matsuzawa T, Yamada K, Yoshioka S, Ono S, Hishinuma T | title = Modified inversion recovery method for nuclear magnetic resonance imaging | journal = The Science Reports of the Research Institutes, Tohoku University. Ser. C, Medicine. Tohoku Daigaku | volume = 33 | issue = 1–4 | pages = 9–15 | date = December 1986 | pmid = 3629216 }}</ref> The helical structure can be described as a set of ''n'' 1-D molecular helices related by an ''n''-fold axial symmetry.<ref name="autogenerated84"/> The helical transformation are classified into two categories: one-dimensional and two-dimensional helical systems.<ref name="autogenerated84">{{cite journal | vauthors = Aldrich RA | title = Children in cities--Seattle's KidsPlace program | journal = Acta Paediatrica Japonica | volume = 29 | issue = 1 | pages = 84–90 | date = February 1987 | pmid = 3144854 | doi = 10.1111/j.1442-200x.1987.tb00013.x | s2cid = 33065417 }}</ref> Creating an entire helical structure relies on a set of translational and rotational matrices which are coded in the protein data bank.<ref name="autogenerated84"/> Helical symmetry is given by the formula ''P''&nbsp;=&nbsp;''μ''&nbsp;x&nbsp;''ρ'', where ''μ'' is the number of structural units per turn of the helix, ''ρ'' is the axial rise per unit and ''P'' is the pitch of the helix.  The structure is said to be open due to the characteristic that any volume can be enclosed by varying the length of the helix.<ref name="virology">{{cite book | vauthors = Racaniello VR, Enquist LW |title=Principles of Virology, Vol. 1: Molecular Biology |publisher=ASM Press |location=Washington, D.C. |year=2008 |isbn=978-1-55581-479-3 }}</ref> The most understood helical virus is the tobacco mosaic virus.<ref name="autogenerated9"/> The virus is a single molecule of (+) strand RNA.  Each coat protein on the interior of the helix binds three nucleotides of the RNA genome. Influenza A viruses differ by comprising multiple ribonucleoproteins, the viral NP protein organizes the RNA into a helical structure.  The size is also different; the tobacco mosaic virus has a 16.33 protein subunits per helical turn,<ref name="autogenerated9"/> while the influenza A virus has a 28 amino acid tail loop.<ref>{{cite journal|vauthors=Ye Q, Guu TS, Mata DA, Kuo RL, Smith B, Krug RM, Tao YJ|date=26 December 2012|title=Biochemical and structural evidence in support of a coherent model for the formation of the double-helical influenza A virus ribonucleoprotein|journal=mBio|volume=4|issue=1|pages=e00467–12|doi=10.1128/mBio.00467-12|pmc=3531806|pmid=23269829}}</ref>