Quasilattice-Based Models for Structural Constraints on Virus Architecture

Crick and Watson were the first to recognise the importance of symmetry in the structures of viral capsids. This observation was the departure point for Caspar-Klug’s theory in which the possible positions and orientations of the protein building blocks are predicted and classified in terms of T-numbers. Whilst this theory predicts the layouts of the protein containers, it provides no information on the thickness of the capsid or its surface features. The creation of icosahedrally invariant point arrays via affine extension of the icosahedral symmetry group and their mapping to viral capsids in [37] has shown that they provide geometrical constraints on viral structure that not only correlate positioning of proteins on the capsid, but also relate structural features on different radial levels including genome organisation.
In this study we have extended this approach using the quasilattices embedding these point arrays. To derive further geometric constraints on virus architecture we firstly show how classifying the possible transitions between the quasilattices modelling the structure of the virus before and after the transition allows us to derive information on the most likely transition paths taken by the protein shell during the structural transformation. Next, a new algorithm matching tile sets to viral capsids has been implemented to investigate further the geometrical constraints quasilattices place on these structures over and above the point arrays in [37].