  Under dilute in vitro conditions transcription factors rapidly locate their
target sequence on DNA by using the facilitated diffusion mechanism. However,
whether this strategy of alternating between three-dimensional bulk diffusion
and one-dimensional sliding along the DNA contour is still beneficial in the
crowded interior of cells is highly disputed. Here we use a simple model for
the bacterial genome inside the cell and present a semi-analytical model for
the in vivo target search of transcription factors within the facilitated
diffusion framework. Without having to resort to extensive simulations we
determine the mean search time of a lac repressor in a living E. coli cell by
including parameters deduced from experimental measurements. The results agree
very well with experimental findings, and thus the facilitated diffusion
picture emerges as a quantitative approach to gene regulation in living
bacteria cells. Furthermore we see that the search time is not very sensitive
to the parameters characterizing the DNA configuration and that the cell seems
to operate very close to optimal conditions for target localization. Local
searches as implied by the colocalization mechanism are only found to mildly
accelerate the mean search time within our model.
