Mathematical virology

Viruses encapsulate their genetic material into protein containers that act akin to molecular Trojan horses, protecting viral genomes between rounds of infection and facilitating their release into the host cell environment. In the majority of viruses, including major human pathogens, these containers have icosahedral symmetry. Many open questions in virology can therefore be addressed through the lens of viral geometry, and novel mathematical techniques from group, graph, tiling and lattice theory, in partnership with biophysical modelling, bioinformatics, and stochastic simulations, can act as drivers of discovery in virology. Topics of interest include the combinatorics of virus assembly, the functional roles of symmetry breaking in viral life cycles, and mathematical techniques, e.g. from percolation or lattice transition theory, to model genome release. Viruses are also ideal model systems to study the laws of evolution in a laboratory environment, where mathematical insights from viral geometry enable a novel perspective on evolutionary fitness landscapes, and can also be used to construct alternative types of function-based phylogenies. The talk will finish with applications of the geometric and mechanistic insights in the context of multi-scale models of viral infections, and discuss potential applications in anti-viral therapy, vaccination and gene therapy.