Icosahedral Symmetry

Electronics Repair Manuals

Schematic Diagrams and Service Manuals

Get Instant Access

Virions can be approximately spherical in shape, based on icosahedral symmetry. Since the time of Euclid, there have been known to exist only five regular solids in which each face of the solid is a regular polygon: the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosa-hedron. The icosahedron has 20 faces, each of which is a regular triangle, and each face thus has threefold rotational symmetry (Fig. 2.3A). There are 12 vertices where 5 faces meet, and thus each vertex has fivefold rotational symmetry. There are 30 edges in which 2 faces meet, and each edge possesses twofold rotational symmetry. Thus the icosahedron is characterized by twofold, threefold, and fivefold symmetry axes. The dodecahedron, the next simpler regular solid, has the same symmetry axes as the icosahedron and is therefore isomorphous with it in symmetry: the dodecahedron has 12 faces which are regular pentagons, 20 vertices where three faces meet, and 30 edges with twofold symmetry. The three remaining regular solids have different symmetry axes. The vast majority of regular viruses that appear spherical have icosahedral symmetry.

In an icosahedron, the smallest number of subunits permissible to form the three-dimensional structure is 60 (5 subunits at each of the 12 vertices, or viewed slightly differently, 3 units on each of the 20 triangular faces). Some viruses do in fact use 60 subunits, but most use more sub-units in order to provide a larger shell capable of holding more nucleic acid. The number of subunits in an icosahedral

A POX- HERPES- AO ENG. PAPOVA- PARYO-

FIGURE 2.1 Relative size and shape of representative (A) DNA-containing and (B) RNA-containing viruses. In each panel the top row shows negatively stained virus preparations, the second row shows thin sections of virus-infected cells, and the bottom row illustrates schematic diagrams of the viruses. Magnification of the electron micrographs is 50,000. [From Granoff and Webster (1999, Vol. 1, p. 401).]

B myxo-

FIGURE 2.1 Relative size and shape of representative (A) DNA-containing and (B) RNA-containing viruses. In each panel the top row shows negatively stained virus preparations, the second row shows thin sections of virus-infected cells, and the bottom row illustrates schematic diagrams of the viruses. Magnification of the electron micrographs is 50,000. [From Granoff and Webster (1999, Vol. 1, p. 401).]

FIGURE 2.2 Structure of TMV a helical plant virus. (A) Schematic diagram of a TMV particle showing about 5% of the total length. (B) Electron micrograph of negatively stained TMV rods. [From Murphy et al. (1995, p. 434).]

structure is 60T, where the permissible values of Tare given by T = H2 + HK + K2, where H and K are integers, and T is called the triangulation number. Permissible triangulation numbers are 1, 3, 4, 7, 9, 12, 13, 16, and so forth. Note that a subunit defined in this way is not necessarily formed by one protein molecule, although in most cases this is how a structural subunit is in fact formed. Some viruses that form regular structures that are constructed using icosahedral symmetry principles do not possess true icosahedral sym metry. In such cases they are said to have pseudo-triangulation numbers. Examples are described below.

Structural studies of viruses have shown that the capsid proteins that form the virions of many plant and animal icosahedral viruses have a common fold. This fold, an eight-stranded antiparallel ß sandwich, is illustrated in Fig. 2.3B. The presence of a common fold suggests that these capsid proteins have a common origin even if no sequence identity is detectable. The divergence in sequence

FIGURE 2.3 A simple icosahedral virus. (A) Diagram of an icosahedral capsid made up of 60 identical copies of a protein subunit, shown as blue trapezoids labeled "A." The twofold, threefold, and fivefold axes of symmetry are shown in yellow. This is the largest assembly in which every subunit is in an identical environment. (B) Schematic representation of the subunit building block found in many RNA viruses, known as the eight-stranded antiparallel /} sandwich. The /} sheets, labeled B though I from the N terminus of the protein, are shown as yellow and red arrows; two possible a helices joining these sheets are shown in green. Some proteins have insertions in the C-D, E-F, and G-H loops, but insertions are uncommon at the narrow end of the wedge (at the fivefold axis). [From Plate 31 in color, Granoff and Webster (1999, Vol. 3), contributed by Johnson (1996).]

FIGURE 2.3 A simple icosahedral virus. (A) Diagram of an icosahedral capsid made up of 60 identical copies of a protein subunit, shown as blue trapezoids labeled "A." The twofold, threefold, and fivefold axes of symmetry are shown in yellow. This is the largest assembly in which every subunit is in an identical environment. (B) Schematic representation of the subunit building block found in many RNA viruses, known as the eight-stranded antiparallel /} sandwich. The /} sheets, labeled B though I from the N terminus of the protein, are shown as yellow and red arrows; two possible a helices joining these sheets are shown in green. Some proteins have insertions in the C-D, E-F, and G-H loops, but insertions are uncommon at the narrow end of the wedge (at the fivefold axis). [From Plate 31 in color, Granoff and Webster (1999, Vol. 3), contributed by Johnson (1996).]

FIGURE 2.4 Structure of three vertebrate virus protein subunits that assemble into icosahedral shells. The N and C termini are labeled with the residue number in parentheses. The /} barrels are shown as red arrows, a helices are gray coils, and the subunit regions involved in quasi-symmetric interactions that are critical for assembly are colored green. SV40 and poliovirus have triangulation numbers of "pseudo-T = 7" or P = 7 and "pseudo-T = 3" or P = 3, respectively. [Adapted from Plate 32, Granoff and Webster (1999, Vol. 3).]

SV40 VP1 P = 7 Poliovîrus 1 VP3 P = 3 Bluetongue virus

FIGURE 2.4 Structure of three vertebrate virus protein subunits that assemble into icosahedral shells. The N and C termini are labeled with the residue number in parentheses. The /} barrels are shown as red arrows, a helices are gray coils, and the subunit regions involved in quasi-symmetric interactions that are critical for assembly are colored green. SV40 and poliovirus have triangulation numbers of "pseudo-T = 7" or P = 7 and "pseudo-T = 3" or P = 3, respectively. [Adapted from Plate 32, Granoff and Webster (1999, Vol. 3).]

while maintaining this basic fold is illustrated in Fig, 2,4, where capsid proteins of three viruses are shown, SV40 (family Polyomaviridae), poliovirus (family Picornaviridae), and bluetongue virus (family Reoviridae) are a DNA virus, a single-strand RNA virus, and a double-strand RNA virus, respectively, Their capsid proteins have insertions into the basic eight-stranded antiparallel [ -sandwich structure and serve important functions in virus assembly, However, they all possess a region exhibiting the common [ -sandwich fold, and may have originated from a common ancestral protein, Thus, once a suitable capsid protein arose that could be used to construct simple icosahedral particles, it may ultimately have been acquired by many viruses, The viruses that possess capsid proteins with this fold may be related by descent from common ancestral viruses, or recombination may have resulted in the incorporation of this successful ancestral capsid protein into many lines of viruses,

Because the size of the icosahedral shell is fixed by geometric constraints, it is difficult for a change in the size of a viral genome to occur, A change in size will require a change in the triangulation number or changes in the capsid proteins sufficient to produce a larger or smaller internal volume, In either case, the changes in the capsid proteins required are relatively slow to occur on an evolutionary timescale and the size of an icosahedral virus is "frozen" for long periods of evolutionary time, For this reason, as well as for other reasons, most viruses have optimized the information content in their genomes, as will be clear when individual viruses are discussed in the following chapters,

Was this article helpful?

0 0

Post a comment