Abstract
A growing number of physical and biological nanostructures are characterized by non-crystallineorder and by unconventional physical and biological properties. Among these systems one can distinguish viral capsids. These solid shells formed by a certain number of copies of the same protein protect viruses from aggressions and facilitate infection of the host cell. Protein distributionin a capsid is quite regular and shows high degree of order, both orientational and positional. Viral capsids with spherical topology have icosahedral symmetry compatible with local crystalline orderbut incompatible with the global one and forbidden in periodic structures.Here, on the example of Papovaviruses we show the existence of a new type of organization whichresults in the chiral pentagonal quasicrystalline order of proteins in capsids with spherical topology and dodecahedral geometry. The formation of this order is described in the frame of the Landau theory of crystallization. The theory of elasticity of quasicrystals is used to show that the structure peculiarities result from the non-linear phason strain.Generalization of the proposed Landau theory of crystallization allows us to describe octagonal and decagonal quasicrystalline structures using constrained minimization of the free energy, thus giving a new physical sense to the « projection window » notion used in multi-dimensionalcrystallography.