  DNA loop formation is one of several mechanisms used by organisms to regulate
genes. The free energy of forming a loop is an important factor in determining
whether the associated gene is switched on or off. In this paper we use an
elastic rod model of DNA to determine the free energy of forming short (50--100
basepair), protein mediated DNA loops. Superhelical stress in the DNA of living
cells is a critical factor determining the energetics of loop formation, and we
explicitly account for it in our calculations. The repressor protein itself is
regarded as a rigid coupler; its geometry enters the problem through the
boundary conditions it applies on the DNA. We show that a theory with these
ingredients is sufficient to explain certain features observed in modulation of
in vivo gene activity as a function of the distance between operator sites for
the lac repressor. We also use our theory to make quantitative predictions for
the dependence of looping on superhelical stress, which may be testable both in
vivo and in single-molecule experiments such as the tethered particle assay and
the magnetic bead assay.
