A Multiscale Model To Analyze the Sliding Movement of Repressor Proteins on DNA

Repressor proteins (RP) regulate gene transcriptions by binding to target sequences, named operator sites, on the DNA molecule. Association rates higher than the diffusion limit were measured in several RP. These experimental data led to the facilitated diffusion model. Facilitated diffusion requires nonspecific binding of the RP to the DNA. Then, the searching for the target sequence proceeds in a reduced search space. In agreement with this model, a structure of the RP LacI bound to nonspecific DNA was revealed by NMR, and one-dimensional movements of the same protein along DNA were observed by single molecule imaging. Single molecule imaging cannot provide a molecular description of how the movement occurs at the molecular level, and two hypotheses were formulated: i) sliding of the RP, in continuous contact with the DNA major grove; ii) hopping of the RP between adjacent binding sites. The continuous contact between the protein and the DNA major grove can result only from a helical trajectory of the RP around the DNA molecule. We simulated the sliding motion of the LacI protein along this helical trajectory by a multiscale model than integrates data from molecular dynamics (MD) simulations in stochastic dynamics. The multiscale approach was necessary to extend the timescale accessible by brute-force MD, and simulate dynamics on the millisecond timescale. MD simulations were used to compute the local diffusion coefficient and the potential of mean force for the sliding movement. These data were then used in the stochastic simulations, to simulate the dynamics on a millisecond time scale, and identify the characteristics of the hypothetic sliding motion. Since the parameters of the stochastic equation were computed by MD simulations, the multiscale model is strictly based on the microscopic characteristics of the molecular system.