ABSTRACT
Although some viruses indeed utilize strict icosahedral arrangement of capsid, built from chemically and structurally identical monomers, in this case, the obvious limitation is the particle size, which is restricted to 60 subunits. Although capsid size can be increased by simply utilizing larger monomers, a more economical way would be to use more monomers. Indeed, most icosahedral viruses utilize the so-called quasiequivalence principle, rst described by Caspar and Klug in 1962 [2], where chemically identical coat protein subunits pack in slightly different environments on icosahedron surface. Each icosahedral asymmetric unit is now divided into a number of smaller, quasiequivalent triangles, a process called triangulation. The consequence is that coat protein monomers are no longer structurally identical, but have slightly different (quasiequivalent) conformations. Due to geometric restrictions, icosahedral particles can be built from T × 60 monomers, where the so-called triangulation number T = h2 + hk + k2, h and k being any nonnegative integers. To understand the quasiequivalence principle, let us rst imagine that coat protein subunits are packed in hexagons, as shown in Figure 1.2a. If we now would attempt to take out one monomer from hexamer (Figure 1.2b) and join the free sides together (Figure 1.2c), we would end up
1.1 Multimeric Organization of Viral Particles ......................................................................................................................... 3 1.2 Icosahedral Capsids ............................................................................................................................................................. 3 1.3 Special Cases of T = 2 and T = 6......................................................................................................................................... 7 1.4 Pseudosymmetry .................................................................................................................................................................. 7 1.5 Prolate Icosahedrons ............................................................................................................................................................ 7 1.6 Twinned Icosahedrons ......................................................................................................................................................... 8 1.7 Viral Structural Proteins That Do Not Follow Icosahedral Symmetry .............................................................................. 8 1.8 Scaffolding Proteins ............................................................................................................................................................ 9 1.9 Helical Capsids .................................................................................................................................................................... 9 1.10 Enveloped Viruses ............................................................................................................................................................... 9 References ................................................................................................................................................................................... 10
with a concave pentamer (Figure 1.2d). Notice that contact surface between monomers in hexamers and pentamers is largely the same, so only minor changes in protein structure would be necessary to accommodate both pentameric and hexameric structures. Next, let us imagine that coat protein monomers are rst packed in a planar, hexagonal
environment, like honeycomb (Figure 1.3a, note that this is just an imagination and not necessarily the case for real virus assembly). Then, if we replace some coat protein hexamers by regularly interspersed pentamers, this results in curvature of planar surface, eventually leading to closed icosahedral structure (Figure 1.3b and c). h and k indices
FIGURE 1.2 Hexamers and pentamers. (a) Protein monomers packed in hexameric fashion. (b) If we now take one monomer out and (c) force the two free protein sides to interact each with other, the result will be a concave pentamer (d).
