Origin of icosahedral symmetry in viruses

Abstract

With few exceptions, the shells (capsids) of sphere-like viruses have the symmetry of an icosahedron and are composed of coat proteins (subunits) assembled in special motifs, the T-number structures. Although the synthesis of artificial protein cages is a rapidly developing area of materials science, the design criteria for self-assembled shells that can reproduce the remarkable properties of viral capsids are only beginning to be understood. We present here a minimal model for equilibrium capsid structure, introducing an explicit interaction between protein multimers (capsomers). Using Monte Carlo simulation we show that the model reproduces the main structures of viruses in vivo (T-number icosahedra) and important nonicosahedral structures (with octahedral and cubic symmetry) observed in vitro. Our model can also predict capsid strength and shed light on genome release mechanisms.

Fig. 1.

Icosahedral symmetry of a viral capsid. (a) Cryo-TEM reconstruction of CCMV. (b) Arrangement of subunits on a truncated icosahedron; A, B, and C denote the three symmetry nonequivalent sites. [Reproduced with permission from ref. (Copyright 1998, Elsevier)].

Fig. 2.

Energy per capsomer for ΔE = 0 (black curve) and |ΔE/ε_o| large compared to one (dotted curve).

Fig. 3.

Minimum energy structures produced by Monte Carlo simulation, with P-state capsomers shown in black. (a) The P and H states here have the same energies. The resulting N = 12, 32, 42, and 72 structures correspond to T = 1, T = 3, T = 4, and T = 7 C-K icosahedra. (b) Minimum energy structures for |ΔE/ε_o|>>1, i.e., only one size of capsomer. The N = 24 and 48 structures have octahedral symmetry, and N = 32 is icosahedral, whereas N = 72 is highly degenerate, fluctuating over structures with different symmetry, including T = 7.

Fig. 4.

Minimum energy structure as in Fig. 3a, but for N = 73; see text.

Fig. 5.

Image reconstitution (30) showing the special structure associated with 72 pentamers (T = 7) in the case of genome-free polyoma capsids.

Fig. 6.

Capsid bursting. (a) Expanded N = 32/T = 3 capsid just before bursting (compare with N = 32 in Fig. 3a). (b) Burst capsid with a radius R just exceeding 1.107 times the equilibrium radius R^*.