Search and Localization Dynamics of the CRISPR-Cas9 System

The CRISPR/Cas9 system acts as the prokaryotic immune system and has important applications in gene editing. The protein Cas9 is one of its crucial components. The role of Cas9 is to search for specific target sequences on the DNA and cleave them. We introduce a model of facilitated diffusion for Cas9 and fit its parameters to single-molecule experiments. Our model confirms that Cas9 search for targets by sliding, but shows that its sliding length is rather short. We then investigate how Cas9 explores a long stretch of DNA containing randomly placed targets. We solve this problem by mapping it into the theory of Anderson localization in condensed matter physics. We expand our model with hopping mechanism to rationalize experimental evidence on the distribution of Cas9 molecules along the DNA. The mapping to Anderson localization can be applied to other proteins that perform facilitated diffusion, to shed light on their dynamics and distribution along the DNA.