Biology Reference
In-Depth Information
1962; Johnson & Speir, 1997). There are a few viruses whose capsids indeed
consist of 60 coat protein subunits, for example, the mammalian virus
Canine
parvovirus
(CPV) (2.2.15) (see the VIPER; http://viperdb.scripps.edu).
However, most viruses form larger structures and consist of more than
60 coat protein subunits. Particles that are formed by more than 60 units
are described to have quasi-equivalent symmetry because the subunits
cannot be placed at equivalent positions (they are placed at quasi-equivalent
positions). To assemble quasi-equivalent particles, conformational switching
of the subunits is required (Johnson & Speir, 1997). The geometric design
principles for quasi-equivalence of larger virus capsids were developed by
Caspar and Klug in 1962 when they introduced the concept of
triangulation
(T) numbers
(Caspar & Klug, 1962).
The triangulation (
T
) numbers.
According to Caspar and Klug's theory
(Caspar & Klug, 1962), the icosahedral virus capsid consists of pentamers
and hexamers. A virus particle looks pretty much like a football (soccer ball).
A football can be regarded as a spherically truncated icosahedron consisting
of pentagons and hexagons (Fig. 2.3).
Figure 2.3
Schematic of a football with pentagons (black) and hexagons (white).
In the viral capsid, the same coat protein forms the pentamers and
hexamers; the bonding relation and their environment are thus not identical.
This distortion is called quasi-equivalence. Pentamers are inserted in place
of certain hexamers, in accordance with selection rules described by the
T
number. If we assume a flat sheet of hexamers (Fig. 2.4), the relative position
of the hexamers can be indexed along the axis denoted by
h
and
k
related by
a 60
rotation. The mathematical relation is given in the following formula
(Caspar & Klug, 1962):
°
T
=
h
+
hk
+
k
(2.1)
2
2
with
numbers can thus only
adopt positive integer values. The size of the capsid is proportional to the
h
and
k
being any positive integer or zero.
T
T
number. The larger the
T
number, the larger the capsid (Fig. 2.5).
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