Spatial effects on the speed and reliability of protein-DNA search
Abstract
Transcription factors and other specific DNA-binding proteins find their sites using a two-mode search: alternating between 3D diffusion through the cell and 1D sliding along the DNA. Some theoretical models assume that 3D excursions are large-scale movements, jumps, in which the protein is equally likely to bind any site along the chromosome. However, recent experiments suggest that most 3D movements are hops, small moves in which the dissociation and landing sites are correlated. We model the TF search as a combination of 1D sliding and 3D diffusion, with both hops and jumps. Through simulation and analytical work, we show that hops are short and frequent and that the addition of hops makes the length of the search depend on the starting point of the search. The addition of hops creates two types of searches: fast searches and slow searches. In a fast search, the TF starts near its binding site and is able to find its site before jumping, using only hops and slides. In a slow search, the TF jumps before finding its binding site. We show that fast and slow searches differ significantly in average search time and the variability of search time. We also use experimentally measured parameter values to estimate the balance between time spent in 3D and 1D diffusion and the total search time. We use the analytical model to consistently interpret several recently published experimental results, some of which contradict each other, and also find that the elimination of the optimality assumption results in much larger estimates of search time. Together, these results help us understand observations about the structure of prokaryotic chromosomes.Keywords
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