DNA-protein interactions under random jump conditions.

We model the site-specific association of a protein molecule with DNA as a random walk with random jumps. Results show that the simultaneous occurrence of processes such as sliding, hopping, and intersegmental transfer can facilitate the diffusion-controlled site-specific association rate. We have also shown that sliding would dominate at lower DNA length, whereas at higher lengths hopping and intersegmental transfer would dominate. Apart from this, we predict that the association rate is directly proportional to the size of nonspecific DNA that flanks the specific site. These results are consistent with the experimental observations.