Insights into the Sliding Movement of the Lac Repressor Nonspecifically Bound to DNA

The Lac repressor finds its DNA binding sequences with an association rate 2 orders of magnitude higher than what is expected for a random diffusive process. This experimental data stimulated numerous theoretical and experimental studies, which led to the facilitated diffusion model. In facilitated diffusion, the Lac repressor binds nonspecifically to DNA. This nonspecific binding is followed by an exploration of the DNA molecule in a reduced space. Single-molecule imaging confirmed that the Lac repressor may move along the DNA molecule; however, it is still under debate whether the LacI movement proceeds through sliding, with a continuous close contact between the protein and DNA, or through hopping between adjacent binding sites. We have investigated the one-dimensional sliding movement of the Lac repressor along nonspecific DNA by full-atomistic molecular dynamics simulations and free-energy calculations based on the umbrella sampling technique. The computed free-energy profile along a helical trajectory was periodic, with periodicity equal to the distance between successive nucleotides and an energy barrier between successive minima of 8.7 ± 0.7 kcal/mol. The results from the molecular simulations were subsequently used in a Langevin dynamics framework to estimate the diffusion coefficient of the Lac repressor sliding along nonspecific DNA. The computed diffusion coefficient is close to the lower limit of the experimental range.