Résumé
Understanding of virus capsid organization and self-assembly mechanisms helps to get an insight into the protein interactions which render virus infectious, but also to advance new methods in nanotechnology which use capsid self-assembly to produce virus-like nanoparticles. As in abiotic nanostructures, the obstacles along this way are related not only to the nanoscopic size of capsids but also to their unconventional topology and symmetry. In the present work on the example of exceptional families of viruses we : i) show the existence of a completely new type of organization, resulting in a chiral pentagonal quasicrystalline order of protein positions in a capsid with spherical topology and dodecahedral geometry; ii) generalize the classical theory of quasicrystals (QC) to explain this organization and demonstrate that a particular non-linear phason strain induces chirality in QC; and iii) establish the relation between chiral order and inhomogeneous buckling strain of the capsid shell.