The classical Kirchhoff elastic-rod model applied to DNA is extended to account
for sequence-dependent intrinsic twist and curvature, anisotropic bending rigidity,
electrostatic force interactions, and overdamped Brownian motion in a solvent. The
zero-temperature equilibrium rod model is then applied to study the structural basis
of the function of the lac repressor protein in the lac operon of Escherichia coli. The
structure of a DNA loop induced by the clamping of two distant DNA operator sites
by lac repressor is investigated and the optimal geometries for the loop of length
76 bp are predicted. Further, the mimicked binding of catabolite gene activator protein (CAP) inside the loop provides solutions that might explain the experimentally
observed synergy in DNA binding between the two proteins. Finally, a combined
Monte Carlo and Brownian dynamics solver for a worm-like chain model is described
and a preliminary analysis of DNA loop-formation kinetics is presented.