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We study how Cas9, a central component of the CRISPR/Cas9 system, searchesfor a target sequence on the DNA. We propose a model that includes as keyingredients 3D diffusion, 1D sliding along the DNA, and the effect of shortbinding sequences preceding the target (protospacer adjacent sequences --PAMs). This latter aspect constitutes the main difference with traditionalfacilitated diffusion of transcription factors. We solve our model, obtainingan expression for the average search time of Cas9 for its target. We find thatexperimentally measured kinetic parameters are close to the values yielding anoptimal search time. Our results rationalize the role of PAMs in guiding thesearch process, and show that Cas9 searches for its targets in a nearly optimalway.

Target search in the CRISPR/Cas9 system: Facilitated diffusion with target cues