Schematic of a Cytomegalovirus

3D model of Helical capsid structure

For the leaf bug, see Miridae.

A capsid is the protein shell of a virus. It consists of several oligomeric structural subunits made of protein called protomers. The observable 3-dimensional morphological subunits, which may or may not correspond to individual proteins, are called capsomeres. The capsid encloses the genetic material of the virus.

Capsids are broadly classified according to their structure. The majority of viruses have capsids with either helical or icosahedral ^[1][2] structure. Some viruses, such as bacteriophages, have developed more complicated structures due to constraints of elasticity and electrostatics.^[3] The icosahedral shape, which has 20 equilateral triangular faces, approximates a sphere, while the helical shape is cylindrical.^[4] The capsid faces may consist of one or more proteins. For example, the foot-and-mouth disease virus capsid has faces consisting of three proteins named VP1–3.^[5]

Icosahedral capsid of an Adenovirus

Some viruses are enveloped, meaning that the capsid is coated with a lipid membrane known as the viral envelope. The envelope is acquired by the capsid from an intracellular membrane in the virus' host; some examples would include the inner nuclear membrane, the golgi membrane, and the cell's outer membrane.^[6]

Once the virus has infected the cell, it will start replicating itself, using the mechanisms of the infected host cell. During this process, new capsid subunits are synthesized according to the genetic material of the virus, using the protein biosynthesis mechanism of the cell. During the assembly process, a portal subunit is assembled at one vertex of the capsid. Through this portal, viral DNA or RNA is transported into the capsid.^[7]

Structural analyses of major capsid protein (MCP) architectures have been used to categorise viruses into families. For example, the bacteriophage PRD1, Paramecium bursaria Chlorella algal virus, and mammalian adenovirus have been placed in the same family.^[8]

Triangulation number[link]

Virus capsid T-numbers

Icosahedral virus capsids are typically assigned a triangulation number (T-number) to describe the relation between the number of pentagons and hexagons i.e. their quasi-symmetry in the capsid shell. The T-number idea was originally developed to explain the quasi-symmetry by Caspar and Klug in 1962.^[9]

For example, a purely dodecahedral virus has a T-number of 1 (usually written, T=1) and a truncated icosahedron is assigned T=3. The T-number is calculated by (1) applying a grid to the surface of the virus with coordinates h and k, (2) counting the number of steps between successive pentagons on the virus surface, (3) applying the formula:

Failed to parse (Missing texvc executable; please see math/README to configure.): T = h^2 + h \cdot k + k^2

= Failed to parse (Missing texvc executable; please see math/README to configure.):  (h+k)^2 - hk

where Failed to parse (Missing texvc executable; please see math/README to configure.): h \ge k

and h and k are the distances between the successive pentagons on the virus surface for each axis (see figure on right). The larger the T-number the more hexagons are present relative to the pentagons.[10][11]

Representation of Viral Capsid T-numbers up to (6,6)

capsid parameters		hexagon/pentagon system				triangle system
(h,k)	T	# hex	Conway notation	image	geometric name	# tri	Conway notation	image	geometric name
(1,0)	1	0	D		Dodecahedron	20	I		Icosahedron
(1,1)	3	20	tI dkD		Truncated icosahedron	60	kD		Pentakis dodecahedron
(2,0)	4	30	cD=t5daD		Truncated rhombic triacontahedron	80	k5aD		Pentakis icosidodecahedron
(2,1)	7	60	dk5sD		Truncated pentagonal hexecontahedron	140	k5sD		Pentakis snub dodecahedron
(3,0)	9	80	dktI		Hexapentatruncated pentakis dodecahedron	180	ktI		Hexapentakis truncated icosahedron
(2,2)	12	110	dkt5daD			240	kt5daD		Hexapentakis truncated rhombic triacontahedron
(3,1)	13	120				260
(4,0)	16	150	ccD			320	dccD
(3,2)	19	180				380
(4,1)	21	200	dk5k6stI tk5sD			420	k5k6stI kdk5sD		Hexapentakis snub truncated icosahedron
(5,0)	25	240				500
(3,3)	27	260	tktI			540	kdktI
(4,2)	28
(5,1)	31
(6,0)	36	350	tkt5daD			720	kdkt5daD
(4,3)	37
(5,2)	39
(6,1)	43
(4,4)	48	470	dadkt5daD			960	k5k6akdk5aD
(6,2)	48
(5,3)	49
(5,4)	61
(6,3)	64
(5,5)	75
(6,4)	76
(6,5)	91
(6,6)	108
...

T-numbers can be represented in different ways, for example T=1 can only be represented as a icosahedron or a dodecahedron and, depending on the type of quasi-symmetry, T=3 can be presented as a truncated dodecahedron, an icosidodecahedron, or a truncated icosahedron and their respective duals a triakis icosahedron, a rhombic triacontahedron, or a pentakis dodecahedron. ^[12]

References[link]