This models the adaptation stage of CRISPR-Cas immunity — the memory-forming step that happens before Cas9-style interference, and is usually skipped in gene-editing demos. When phage DNA enters the cell, a Cas1–Cas2 integrase complex samples short "protospacer" fragments of it:
P(select | PAM match) = s
P(select | PAM mismatch) = 1 − s
s = PAM stringency slider
Real Cas1–Cas2 strongly prefers protospacers flanked by a correct PAM (e.g. 5′-AAG for the *E. coli* Type I-E system) — a mismatched PAM is captured far less often, modeled here as the selection weight s.
A captured protospacer is then spliced into the CRISPR array as a new repeat–spacer unit. Integration is strongly polarized toward the leader end of the array — the promoter-proximal site — so the newest spacer sits first and the array reads as a chronological timeline of past infections:
P(insert at leader end) = L
P(insert at random site) = 1 − L
L = leader-end bias slider
- Inject Phage DNA — releases a new phage genome fragment; each base run is scanned for PAM-adjacent windows (highlighted) and non-PAM windows.
- PAM stringency — how strongly Cas1–Cas2 favors PAM-flanked protospacers over random ones. Real systems sit high (~70–90%); dropping it shows why off-target spacer acquisition happens.
- Leader-end bias — how consistently the new repeat–spacer unit lands next to the leader (promoter) instead of a random array position, which is what keeps the array chronologically ordered.
- Adaptation fidelity — the running fraction of acquired spacers that came from a correctly PAM-flanked protospacer, i.e. how "clean" the resulting immune memory is.
Real-world relevance: this acquisition step is why CRISPR arrays are used as literal phylogenetic timestamps of a bacterium's viral exposure history, and it is mechanistically distinct from the Cas9 cutting/repair step that most CRISPR gene-editing tools exploit.