Dynamic Regulation of the Immune Repertoire of Bacteria

The CRISPR-Cas system provides adaptive immunity in many bacteria and archaea by storing short fragments of viral DNA, known as spacers, in dedicated genomic arrays. A longstanding question in CRISPR-virus coevolution is the optimal number of spacers for each bacterium to maintain proper phage coverage. In this study, we investigate the optimal CRISPR memory size by combining steady-state immune models with dynamical antigenic traveling wave theory to obtain both analytic and numerical results of coevolutionary dynamics. We focus on two experimentally supported phenomena that shape immune dynamics: primed acquisition, where partial spacer-protospacer matches boost acquisition rates, and memory size fluctuations, where a short-term increase in memory size drives population dynamics. We find that under primed acquisition, longer optimal arrays benefit from maintaining multiple, partially matching spacers. In contrast, dynamic memory fluctuations favor shorter arrays by amplifying the fitness advantage of acquiring a few highly effective new spacers. Together, our results highlight that memory optimality is not fixed, but instead shaped by the interaction of acquisition dynamics and population-level immune pressures.