# Capsid

Schematic of a cytomegalovirus
Illustration of geometric model changing between two possible capsids. A similar change of size has been observed as the result of a single amino-acid mutation[1]

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[2][3] structure. Some viruses, such as bacteriophages, have developed more complicated structures due to constraints of elasticity and electrostatics.[4] The icosahedral shape, which has 20 equilateral triangular faces, approximates a sphere, while the helical shape resembles the shape of a spring, taking the space of a cylinder but not being a cylinder itself.[5] 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.[6]

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; examples include the inner nuclear membrane, the golgi membrane, and the cell's outer membrane.[7]

Once the virus has infected a cell and begins replicating itself, 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.[8]

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.[9][10]

## Specific shapes

### Icosahedral

Virus capsid T-numbers

The icosahedral structure is extremely common among viruses. The number and arrangement of capsomeres in an icosahedral capsid can be classified using the "quasi-equivalence principle" proposed by Donald Caspar and Aaron Klug.[11] 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 ${\displaystyle h\geq 1}$ and ${\displaystyle k\geq 0}$; 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:

${\displaystyle T=h^{2}+h\cdot k+k^{2}}$

Icosahedral capsids contain 12 pentamers plus 10(T − 1) hexamers. [12][13] The T-number is representative of the size and complexity of the capsid proteins: all know viruses with T > 7 require auxiliary proteins for assembly.[14] Geometric examples for many values of h, k, and T can be found at List of geodesic polyhedra and Goldberg polyhedra. Although this classification can be applied to the majority of known viruses, exceptions are known including the retroviruses where point mutations disrupt the symmetry.[13]

T-numbers can be represented in different ways, for example T = 1 can only be represented as an 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.[15][clarification needed]

### Prolate

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 triangles. The Q number, which can be any positive integer[dubious ], 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 number.[16]

### Helical

3D model of a helical capsid structure of a virus

Many rod-shaped and filamentous plant viruses have capsids with helical symmetry.[17] The helical structure can be described as a set of n 1-D molecular helices related by an n-fold axial symmetry.[18] The helical transformation are classified into two categories: one-dimensional and two-dimensional helical systems.[18] Creating an entire helical structure relies on a set of translational and rotational matrices which are coded in the protein data bank.[18] Helical symmetry is given by the formula P = μ x 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.[19] The most understood helical virus is the tobacco mosaic virus.[17] The virus is a single molecule of (+) strand RNA. Each coat protein on the interior of the helix bind 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,[17] while the influenza A virus has a 28 amino acid tail loop.[citation needed]

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