  In many cases, transcriptional regulation involves the binding of
transcription factors at sites on the DNA that are not immediately adjacent to
the promoter of interest. This action at a distance is often mediated by the
formation of DNA loops: Binding at two or more sites on the DNA results in the
formation of a loop, which can bring the transcription factor into the
immediate neighborhood of the relevant promoter. Though there have been a
variety of insights into the combinatorial aspects of transcriptional control,
the mechanism of DNA looping as an agent of combinatorial control in both
prokaryotes and eukaryotes remains unclear. We use single-molecule techniques
to dissect DNA looping in the lac operon. In particular, we measure the
propensity for DNA looping by the Lac repressor as a function of the
concentration of repressor protein and as a function of the distance between
repressor binding sites. As with earlier single-molecule studies, we find (at
least) two distinct looped states and demonstrate that the presence of these
two states depends both upon the concentration of repressor protein and the
distance between the two repressor binding sites. We find that loops form even
at interoperator spacings considerably shorter than the DNA persistence length,
without the intervention of any other proteins to prebend the DNA. The
concentration measurements also permit us to use a simple statistical
mechanical model of DNA loop formation to determine the free energy of DNA
looping, or equivalently, the J-factor for looping.
