LacI finds its target operator DNA surprisingly fast. In vitro the search is 10-100 times faster than the theoretical upper limit for two particles searching for each other via diffusion in three dimensions (3D). To explain the fast search, it was hypothesized that LacI and other transcription factors (TFs) find their binding sites by facilitated diffusion, a combination of free diffusion in 3D and 1D-sliding on the DNA. During sliding the repressor is in contact with the DNA helix, sliding around and tracking its major groove, which speeds up the search process by extending the target length when the TF slides in onto the operator from the side. In vivo single-molecule experiments with E.coli cells have now tested and verified the facilitated diffusion model, and shown that the TF scans on average 45 bp during each sliding event, before the TF detaches spontaneously and resumes exploring the genome in 3D. These experiments also suggest that LacI slides over the O operator several times before binding, meaning that different DNA sequences can have different probabilities to be recognized at each encounter with the TF. This implies a trade-off between fast search on nonspecific sequences and binding to specific sequences. In vivo and in vitro experiments have shown that it is this probability to recognize the operator that changes with DNA sequence, while the time the TF remains in the bound conformation on the operator changes less with sequence. The TF often leaves the sequence it is intended to regulate, but at a strong target site, it almost always make a very short journey before finding the way back again. On the macroscopic scale, this looks like a stable interaction. This binding mechanism explains how DNA binding proteins manage to quickly search through the genome of the cell without getting stuck too long at sequences that resemble the true target.
An all-atom molecular dynamics simulation suggests that the transcription factor encounters a barrier of 1 kT during sliding and 12 kT for dissociation, implying that the repressor will slide over 8 bp on average before dissociating. The in vivo search model for the lac repressor includes intersegment transfer and hopping as well as crowding by other proteins which make the genome in E.coli cells less accessible for the repressor. The existence of hopping, where the protein slips out of the major groove of DNA to land in another nearby groove along the DNA chain, has been proven more directly in vitro, where the lac repressor has been observed to bypass operators, flip orientation, and rotate with a longer pitch than the 10.5 bp period of DNA while moving along it.