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A pentagonal order formed by 360 proteins in the bovine papilloma viralcapsid and structures of some smaller viral capsids are considered from aunified point of view based on the Landau crystallization theory. To simulatethe capsid structures we map the planar pentagonal Penrose quasilattice (PPQ)constructed in the frames of the Landau theory onto a sphere through thedodecahedron nets of different sizes. Six different simplest nets containingfrom 60 to 360 positions occupied by proteins are proposed. Buckling of theinitially planar capsid faces and a smooth conjugation of the protein orders atthe adjacent faces are taken into account by means of two conditions imposed onthe minimization of the capsid free energy. This conditional minimizationresults in two-component phason strain field, which describes theself-consistent reconstruction of quasicrystalline orders located at twelvefaces of spherical dodecahedron. All six chiral structures obtained in this wayare very similar to those of well-known spherical viral capsids. The theoryproposed explains some general peculiarities of protein organization in capsidsof small and medium-sized viruses.

Density waves, dodecahedral geometry and structures of some spherical viral capsids