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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. [ 24 ]
Various arrangements of capsomeres are: 1) Icosahedral, 2) Helical, and 3) Complex. 1) Icosahedral- An icosahedron is a polyhedron with 12 vertices and 20 faces. Two types of capsomeres constitute the icosahedral capsid: pentagonal (pentons) at the vertices and hexagonal at the faces. There are always twelve pentons, but the number of hexons ...
This resultant helical structure is the case due to the geometric limitations and symmetrical nature necessitated by the protein sub-assembly array and its protein-protein interactions. [11] The Tobacco Mosaic Virus studied by Caspar and Klug in their 1962 crystallisation study was discovered to be composed of a '2 to 5 capsid protein subunit ...
Icosahedral symmetry fundamental domains A soccer ball, a common example of a spherical truncated icosahedron, has full icosahedral symmetry. Rotations and reflections form the symmetry group of a great icosahedron. In mathematics, and especially in geometry, an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron.
Capsomeres can arrange into an icosahedral, helical, or complex capsid, but in many viruses, such as the herpes simplex virus, an icosahedral capsid is assembled. [2] Three asymmetric and nonidentical viral protein units make up each of the twenty identical triangular faces in the icosahedral capsid.
The icosahedral symmetry can still be maintained with more than 60 subunits, but only in multiples of 60. For example, the T=3 Tomato bushy stunt virus has 60x3 protein subunits (180 copies of the same structural protein). [11] [12] Although these viruses are often referred to as 'spherical', they do not show true mathematical spherical symmetry.
The viral particle is about 30 nm in diameter with icosahedral symmetry. Because of its short genome and its simple composition—only a strand of RNA and a nonenveloped icosahedral protein coat encapsulating it—poliovirus is widely regarded as the simplest significant virus. [3]
Convex regular icosahedron A tensegrity icosahedron. In geometry, an icosahedron (/ ˌ aɪ k ɒ s ə ˈ h iː d r ən,-k ə-,-k oʊ-/ or / aɪ ˌ k ɒ s ə ˈ h iː d r ən / [1]) is a polyhedron with 20 faces.