PhD Public Lecture - Tyler Pattenden (AP Math)

Title: Mathematical modelling of prophage dynamics

Abstract: We use mathematical models to study prophages, viral genetic sequences carried by bacterial genomes. In this work, we first examine the role that plasmid prophage play in the survival of de novo beneficial mutations for the associated temperate bacteriophage.  Through the use of a life-history model, we determine that mutations first occurring in a plasmid prophage are far more likely to survive drift than those first occurring in a free phage.  We then analyse the equilibria and stability of a system of ordinary differential equations that describe temperate phage-host dynamics.  We elucidate conditions on dimensionless parameters to determine a parameter regime that guarantees coexistence of all populations.  We then develop a resource-explicit model to investigate further the lysis-lysogeny decision in variable environments. A novel feature of our model is the inclusion of a distinct stationary phase for the hosts and lysogens. Through the application of evolutionary invasion techniques, we determine that as variability increases, bacteriophage populations tend to evolve to a fully lysogenic state, so long as the hosts and lysogens are able to enter stationary phase.  This lead us to question the evolutionary fates of prophage in fast- and slow-growing bacterial species.  Using a partial differential equation model developed in Khan and Wahl (2019), we fit distributions of prophage lengths for both growth classes and observe several significant differences in strategies of the phage that infect both growth classes. Specifically, we demonstrate that phages infecting fast-growing hosts have a much higher rate of lysogeny. Our work sheds light on the long-standing question, ``why be temperate?'', offering novel explanations regarding the evolution of temperate bacteriophage.