Abstract
Genes are frequently regulated by interactions between proteins that bind to the DNA near the gene and proteins that bind to DNA sites located far away, with the intervening DNA looped out. But it is not understood how efficient looping can occur when the sites are very far apart. We develop a simple theoretical framework that relates looping efficiency to the energetic cost and benefit of looping, allowing prediction of the efficiency of single or multiple nested loops at different distances. Measurements of absolute loop efficiencies for Lac repressor and λ CI using gene expression reporters in Escherichia coli cells show that, as predicted by the model, long-range DNA looping between a pair of sites can be strongly enhanced by the use of nested DNA loops or by the use of additional protein-binding sequences. A combination of these approaches was able to generate efficient DNA looping at a 200 kb distance.