Theory of morphological transformation of viral capsid shells during maturation process

In the frame of the Landau-Ginzburg formalism we propose a minimal phenomenological model for a morphological transformation in viral capsid shells. The transformation takes place during virus maturation process which renders virus infectious. The theory is illustrated on the example of the HK97 bacteriophage and viruses with similar morphological changes in the protective protein shell. The transformation is shown to be a structural phase transition driven by two order parameters. The first order parameter describes the isotropic expansion of the protein shell while the second one is responsible for the shape symmetry breaking and the resulting shell faceting. The group theory analysis and the resulting thermodynamic model make it possible to choose the parameter which discriminates between the icosahedral shell faceting often observed in viral capsids and the dodecahedral one observed in viruses of the Parvovirus family. Calculated phase diagram illustrates the discontinuous character of the virus morphological transformation and shows two qualitatively different paths of the transformation in a function of two main external thermodynamic parameters of the in vitro and in vivo experiments.