Group Theory Methods in Virology: Landau Density Wave Approach

Abstract

Viruses are organized biological nanosystems which display high level of spatial organization. In the present work we focus on the group theory meth-ods application to the problems of virus self-assembly and resulting viral structure formation. The approach is based on the successive application of methods of rep-resentation theory for continuous and discrete groups and invariant theory for the groups not-generated by reflections. It generalizes the Landau density wave theory of crystallization to the case of compact crystal-like manifold assembly. To compare the predictions of the theory with the available cryoelectronic microscopy data we use the calculated density distribution functions which generate the protein posi-tions on a spherical surface of the cage protecting viral genome. We also discuss the relation between density distribution functions and viral infectivity.