Quantifying hopping and jumping in facilitated diffusion of DNA-binding proteins

Facilitated diffusion of DNA-binding proteins is known to speed up target site location by combining three dimensional excursions and linear diffusion along the DNA. Here we explicitly calculate the distribution of the relocation lengths of such 3D excursions, and we quantify the short-range correlated excursions, also called hops, and the long-range uncorrelated jumps. Our results substantiate recent single-molecule experiments that reported sliding and 3D excursions of the restriction enzyme EcoRV on elongated DNA molecules. We extend our analysis to the case of anomalous 3D diffusion, likely to occur in a crowded cellular medium.