A Mathematical Approach to Structural Transitions in Viral Capsids

Abstract

The majority of viruses have protein containers, called capsids, in which proteins are arranged with icosahedral symmetry. The capsids of these viruses follow structural blueprints that can be modelled as subsets of 3-dimensional aperiodic lattices called quasicrystals. These, in turn, can be obained by projection from 6-dimensional Bravais lattices. In this work we apply the crystallographic theory of phase transitions to these 6D lattices, and via projection of these results derive information on the structural transitions of viruses important for infection.