  We study how Cas9, a central component of the CRISPR/Cas9 system, searches
for a target sequence on the DNA. We propose a model that includes as key
ingredients 3D diffusion, 1D sliding along the DNA, and the effect of short
binding sequences preceding the target (protospacer adjacent sequences --
PAMs). This latter aspect constitutes the main difference with traditional
facilitated diffusion of transcription factors. We solve our model, obtaining
an expression for the average search time of Cas9 for its target. We find that
experimentally measured kinetic parameters are close to the values yielding an
optimal search time. Our results rationalize the role of PAMs in guiding the
search process, and show that Cas9 searches for its targets in a nearly optimal
way.
