Résumé:

Viral genome is protected by a solid protein shell (capsid) self-assembled from many copies of identical subunits (one or few proteins). The positions and orientations of subunits display high level of spatial organization well suited to modern structural methods of study. The structural and biochemical data rise a whole number of questions concerning unconventional positional order of subunits in the shell, physical mechanisms of the self-assembly and its thermodynamics. In the present work we develop the theory which explains the formation and classifies the structures of viruses with spherical topology and icosahedral symmetry. We develop an explicit method based on symmetry selection rules, which predicts the positions of centers of mass for the proteins self-assembled in the viral capsid shell. The theory describes in a uniform way both the structures satisfying the well-known Caspar and Klug model for capsid construction and those violating it. The peculiarities of the assembly thermodynamics are discussed. We also show the relation between the protein density distributions obtained and the infectivity properties of several human viruses. To illustrate the notions of the theory and the results obtained we focus on the Dengue virus (DENV) capsid.