Fig. 1.

(A) CRISPR locus. Small ($\sim$30 nt) samples of invasive phage DNA called spacers (colored rectangles) are incorporated into the CRISPR genetic locus. Spacers are separated by short ($\sim$30 nt) sequences called repeats (black diamonds). Multiple spacers can be stored at a CRISPR locus, resulting in a genetic record of immunization (42). In our analysis of the experimental data shown in Fig. 3 A–C, we identify spacers with a type $i$, a locus position $j$, and a bacterium $k$. (B) In our model, bacteria and phages interact in a chemostat (flow cell) with a constant inflow and outflow rate $F$. Nutrients flow into the chemostat at a fixed concentration $C_0$. Phages are assumed to be identical with a large, fixed number of possible protospacers. Phages adsorb to bacteria with rate $\alpha$ and successfully infect and kill naive bacteria with probability $p_V$. Each bacterium can acquire a single spacer ($j=1$). Spacers are tracked in the population as the number of bacteria containing a spacer of type $i$, $n_B^i$. If a naive bacterium survives an infection, it can acquire a spacer with probability $\eta$. All spacers are assumed to be equally effective: The probability of phage success in an infection is reduced by $e$ if a bacterium has a spacer. Bacteria with spacers revert to naive bacteria by losing a spacer with rate $r$.