Landau theory of crystallization and the capsid structures of small icosahedral viruses
Résumé
A new approach to the capsid structures of small viruses with spherical topology and icosahedral symmetry is proposed. It generalizes Landau theory of crystallization to describe icosahedral viral shells self-assembled from identical asymmetric proteins. An explicit method which predicts the positions of centers of mass for the proteins constituting the shell is discussed in detail. The method is based on irreducible density distribution function which generates the protein positions. The universal form of the density distribution function which contains no fitting parameter permits to classify the capsids structures of small viruses. 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. A group theory analysis of the Caspar and Klug model and of the “quasiequivalence” principle for protein environments in viral capsids is given. The molecular basis of difference in protein environments and peculiarities in the assembly thermodynamics are also discussed.