MATVIR · Mathematical Virology: A classification of virus architecture and the structural transitions important for maturation and infection

This project in Mathematical Biology addresses two important questions concerning the structure and life cycle of viruses: -) The classification of the possible three-dimensional shapes of the capsid proteins compatible with icosahedral symmetry (the most common symmetry of viral capsids) by means of group theory and tiling theory; -) The modeling and prediction of the structural transitions of the viral capsids (protein containers encapsidating the genome) involved in the maturation of the viral particles, using ideas and techniques of the mathematical theory of phase transitions in crystals. The expected results will clarify, on a geometrical basis, the spectrum of structural features that can occur in the viral capsids with icosahedral symmetry (such as the shape and the bonds between the proteins) and elucidate the mechanisms essential for their maturation and infectivity. Such insights have relevant implications for the design of antiviral drugs that inhibit the assembly or the maturation of viral capsids, and the manufacture of self-assembling virus-like containers for drug delivery.