Physical Model of the Co-evolution of Bacteria and Viruses Mediated by CRISPR

Bacteria and archaea have evolved an adaptive, heritable immune system that recognizes and protects against viruses or plasmids. This system, known as the CRISPR/Cas system, allows the host to recognize and incorporate short foreign DNA or RNA sequences, called 'spacers' into its CRISPR system. Spacers in the CRISPR system provide a record of the history of bacteria and phage coevolution. We use a physical model to study the dynamics of this coevolution as it evolves stochastically over time. We focus on the impact of mutation and recombination on the evolution and evasion of bacteria and phages. We discuss the effect of different spacer deletion mechanisms on the coevolutionary dynamics. We make predictions about bacteria and phage population growth, spacer diversity within the CRISPR locus, and spacer protection against the phage population. An important feature of this coevolution is the multiple loci in the phages from which CRISPR may sample genetic material. We construct a model with multiple loci, in a two dimensional geometry. We show that to match recent experimental observations on the waves of replacement of spacers in CRISPR, multiple protospacer loci must be considered. With parameter values taken from the literature, the results are in agreement with experimental measurements of spacer abundance and turnover. We show that immune pressure upon the phages leads to greater rates of phage evolution, by comparison to a neutral model, and we show a novel mechanism by which recombination in the phages leads to more effective phage escape from CRISPR recognition when there are multiple phage proto-spacer loci. We investigate the sensitivity of these results to model parameters, highlighting impacts on the immune pressure on the phages and to the evolvability of the phages. The conditions for coexistence of bacteria and viruses is an interesting problem in evolutionary biology. In this thesis, we show an intriguing phase diagram of the virus extinction probability, which is more complex than that of the classical predator-prey model. As the CRISPR incorporates genetic material, viruses are under pressure to evolve to escape the recognition by CRISPR. When bacteria have a small rate of deleting spacers, this co-evolution leads to a non-trivial phase diagram of the virus extinction probability. For example, when the virus mutation rate is low, the virus extinction probability changes non-montonically with the bacterial exposure rate. The virus and bacteria co-evolution not only alters the virus extinction probability, but also changes the bacterial population structure. Additionally, we show that recombination is a successful strategy for viruses to escape from CRISPR recognition when viruses have multiple proto-spacers