Regulated CRISPR Modules Exploit a Dual Defense Strategy of Restriction and Abortive Infection in a Model of Prokaryote-Phage Coevolution
The infected cell population (and its associated CRISPR spacer content) is created from the growing free cell population (and its corresponding CRISPR content) through phage infections. The overall CRISPR spacer content in each cell population is abstractly partitioned into active, inactive and self-targeting. Active spacers elicit phage restriction, while self-targeting spacers cause cell death (autoimmunity). While both the free and infected cell populations have genomic protospacers that contribute to the creation of self-targeting spacers, only the infected cell population has access to the released phage protospacers for the creation of active spacer content. At any given time, the CRISPR induced rate of immunity for an infected cell is proportional to its per capita quota of active spacer content associated with the population at that time. Similarly, we use the corresponding self-targeting spacer content to define the rates of autoimmunity for both the infected and free cell populations. In our equations, we directly model these per capita quotas. Thus the rates of CRISPR induced immunity and autoimmunity for a cell population are reflective of its associated spacer content at any given time, which in turn is determined by the kinetics of CRISPR and prokaryote-phage interaction.