What matters for lac repressor search in vivo--sliding, hopping, intersegment transfer, crowding on DNA or...

We have investigated which aspects of transcription factor DNA interactions are most important to account for the recent in vivo search time measurements for the dimeric lac repressor. We find the best agreement for a sliding model where non-specific binding to DNA is improbable at first contact and the sliding LacI protein binds at high probability when reaching the specific Osym operator. We also find that the contribution of hopping to the overall search speed is negligible although physically unavoidable. The parameters that give the best fit reveal sliding distances, including hopping, close to what has been proposed in the past, i.e. ∼40 bp, but with an unexpectedly high 1D diffusion constant on non-specific DNA sequences. Including a mechanism of inter-segment transfer between distant DNA segments does not bring down the 1D diffusion to the expected fraction of the in vitro value. This suggests a mechanism where transcription factors can slide less hindered in vivo than what is given by a simple viscosity scaling argument or that a modification of the model is needed. For example, the estimated diffusion rate constant would be consistent with the expectation if parts of the chromosome, away from the operator site, were inaccessible for searching.