Theory of site-specific DNA-protein interactions in the presence of nucleosome roadblocks

Abstract We show that nucleosomes can efficiently control the relative search times spent by transcription factors (TFs) on one- (1D) and three-dimensional (3D) diffusion routes towards locating their cognate sites on DNA. Our theoretical results suggest that the roadblock effects of nucleosomes are dependent on the relative position on DNA with respect to TFs and their cognate sites. Especially, nucleosomes exert maximum amount of hindrance to the 1D diffusion dynamics of TFs when they are positioned in between TFs and their cognate sites. The effective 1D diffusion coefficient (χTF) associated with the dynamics of TFs in the presence of nucleosome decreases with the free energy barrier (μ) associated the sliding dynamics of nucleosomes as . Subsequently the mean first passage time (ηL) that is required by TFs to scan L number of binding sites on DNA via 1D diffusion increases with μ as . When TFs move close to nucleosomes then they exhibit a typical sub-diffusive dynamics. Nucleosomes can enhance the search dynamics of TFs when TFs present in between nucleosomes and transcription factor binding sites (TFBS). The level of enhancement effects of nucleosomes seems to be much lesser than the level of retardation effects when nucleosomes present in between TFs and their cognate sites. These results suggest that nucleosome depleted regions around the cognate sites of TFs is mandatory for an efficient site-specific interactions of TFs with DNA. Remarkably the genome wide positioning pattern of TFs shows maximum at their specific binding sites and the positioning pattern of nucleosome shows minimum at the specific binding sites of TFs under in vivo conditions. This seems to be a consequence of increasing level of breathing dynamics of nucleosome cores and decreasing levels of fluctuations in the DNA binding domains of TFs as they move across TFBS. Since the extent of breathing dynamics of nucleosomes and fluctuations in the DBDs of TFs are directly linked with their respective 1D diffusion coefficients, the dynamics of TFs becomes slow as they approach their cognate sites so that TFs form tight site-specific complex. Whereas the dynamics of nucleosomes becomes rapid so that they pass through the cognate sites of TFs. Several in vivo datasets on genome wide positioning pattern of nucleosomes as well as TFs seem to agree well with our arguments. We further show that the condensed conformational state of DNA can significantly decrease the retarding effects of nucleosome roadblocks. The retarding effects of nucleosomes on the 1D diffusion dynamics of TFs can be nullified when the degree of condensation of the genomic DNA is such that it can permit a jump size associated with the dynamics of TFs beyond k > 150 bps.