Density-Wave Theory of the Capsid Structure of Small Icosahedral Viruses

We apply Landau theory of crystallization to explain and to classify the capsid structures of small viruses with spherical topology and icosahedral symmetry. We develop an explicit method which predicts the positions of centers of mass for the proteins constituting the viral capsid shell. Corresponding density distribution function which generates the positions has a universal form without any fitting parameter. The theory describes in a uniform way both the structures satisfying the well-known Caspar and Klug geometrical model for capsid construction and those violating it.

Figure 1

(a)–(e) The first five irreducible icosahedral density functions with the wave numbers $l=15$, 21, 25, 27, and 31, respectively. Corresponding numbers of different 60-fold positions of density maxima are $N=1$, 2, 3, 3, and 4. (f) Function with $l=37$ and $N=6$.

Figure 2

Comparison of the positions of protein centers predicted by our model (left panel) with the experimental viral structures [15] (right panel) for the capsids which cannot be explained by the CK geometrical model. Capsids of L-A virus (a), dengue virus (b), and murine polyoma virus (c) are presented. The corresponding density functions for $l=21$, $l=25$, and $l=37$, respectively, are shown in Figs. 1b, 1c, 1f.