Protein Diffusion on Heterogeneous DNA

A lot of vital biological processes require recognition and binding of specific sites on DNA, by proteins, in order to work properly. For proteins to find their specific site, called the target site, on DNA, it has been shown that they alternate between 1D diffusion, on the DNA, and 3D diffusion off the DNA. The 3D excursion can be divided into two groups, hops, where the protein re-binds to the DNA immediately, corresponding to a small relocation on the DNA, and jumps, long 3D excursions, where the protein binds the DNA far from where it dissociated. In this report we investigate the effects of uncorrelated and correlated rebinding to the DNA after a 3D excursion, on both a uniform DNA chain, and a DNA chain with a rough, sequence-dependent, energy landscape. A well known problem with searching in an energy landscape is that a realistic energy landscape cannot provide both rapid search and stability of the protein-DNA complex. By using a search-and-fold mechanism, here called the two mode model, this inconsistency can be resolved. We compare the effects on the mean search time of the two mode model with both correlated and uncorrelated rebinding, to show that, in some cases, correlations in rebinding to the DNA can have the same effect