How nonspecifically DNA-binding proteins search for the target in crowded environments

We investigate how a tracer particle searches a target located in DNA modeled by a stiff chain in crowded environments using theoretical analysis and Langevin dynamics simulations. First, we show that the three-dimensional (3D) diffusion coefficient of the tracer only depends on the density of crowders phi, while its one-dimensional (1D) diffusion coefficient is affected by not only phi but also the nonspecific binding energy epsilon. With increasing phi and epsilon, no obvious change in the average 3D diffusion time is observed, while the average 1D sliding time apparently increases. We propose theoretically that the 1D sliding of the tracer along the chain could be well captured by the Kramers' law of escaping rather than the Arrhenius law, which is verified directly by the simulations. Finally, the average search time increases monotonously with an increase in phi while it has a minimum as a function of epsilon, which could be understood from the different behaviors of the average number of search rounds with the increasing phi or epsilon. These results provide a deeper understanding of the role of facilitated diffusion in target search of proteins on DNA in vivo. (C) 2016 AIP Publishing LLC.