Epidemiological and evolutionary consequences of CRISPR-Cas reactivity

Adaptive immune systems face a control challenge: they should react with enough strength to clear an infection while avoiding to harm their organism. CRISPR-Cas systems are adaptive immune systems of prokaryotes that defend against fast evolving viruses. Here, we explore the CRISPR-Cas control challenge and look how its reactivity, i.e. its probability to acquire a new resistance, impacts the epidemiological outcome of a phage outbreak and the prokaryote9s fitness. We show that in the absence of phage evolution, phage extinction is driven by the probability to acquire at least one resistance. However, when phage evolution is fast, phage extinction is driven by an epidemiological critical threshold: any reactivity below this critical threshold leads to phage survival whereas any reactivity above it leads to phage extinction. We also show that in the absence of autoimmunity, high levels of reactivity evolve. However, when CRISPR-Cas systems are prone to autoimmune reactions, intermediate levels of reactivity are evolutionarily optimal. These results help explaining why natural CRISPR-Cas systems do not show high levels of reactivity.