Mathematical Modeling of CRISPR-CAS system effects on biofilm formation

Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR), linked with CRISPR associated (CAS) genes, play a profound role in the interactions between phage and their bacterial hosts. It is now well understood that CRISPR-CAS systems can confer adaptive immunity against bacteriophage infections. However, the possibility of failure of CRISPR immunity may lead to a productive infection by the phage (cell lysis) or lysogeny. Recently, CRISPR-CAS genes have been implicated in changes to group behaviour, including biofilm formation, of the bacterium Pseudomonas aeruginosa when lysogenized. For lysogens with a CRISPR system, another recent experimental study suggests that bacteriophage re-infection of previously lysogenized bacteria may lead to cell death. Thus CRISPR immunity can have complex effects on phage-host-lysogen interactions, particularly in a biofilm. In this contribution, we develop and analyse a series of models to elucidate and disentangle these interactions. From a therapeutic standpoint, CRISPR immunity increases biofilm resistance to phage therapy. Our models predict that lysogens may be able to displace CRISPR-immune bacteria in a biofilm, and thus suggest strategies to eliminate phage resistant biofilms.