Title:  Mathematical Virology in the Fight against Viral Infection
Abstract:  The Covid-19 pandemic has highlighted the need for novel antiviral strategies that also provide protection against newly emerging strain variants. Insights into the geometric principles underpinning viral geometry provide a key to uncovering the mechanisms by which viruses replicate and infect their hosts, and thus pave the way to the discovery of novel antiviral solutions. Using geometric and topological descriptors of virus architecture in combination with stochastic simulations, I will demonstrate how a virus navigates the knifeā€™s edge between stability and instability. This reveals how a virus provides sufficient protections for its genetic cargo, while allowing its timely release during a viral infection. I will also address a number of open problems in the assembly of viruses through the lens of viral geometry. This includes the origin and control of polymorphic particle assembly, which arises, amongst others, when virus-derived protein containers are functionalised to present antigens for applications in vaccinology. I will also cover the role of viral geometry in the discovery of genome-encoded assembly instructions, that occur in major viral pathogens and explain the experimental outcome of directed evolution of a bacterial system that has been engineered to package its own messenger RNA. These results shed new light on the early stages of viral evolution and open up novel opportunities in antiviral therapy and virus nanotechnology.