Allosteric interactions in DNA are crucial for various biological processes.
These interactions are quantified by measuring the change in free energy as a
function of the distance between the binding sites for two ligands. Here we
show that trends in the interaction energy of ligands binding to DNA can be
explained within an elastic birod model. The birod model accounts for the
deformation of each strand as well as the change in stacking energy due to
perturbations in position and orientation of the bases caused by the binding of
ligands. The strain fields produced by the ligands decay with distance from the
binding site. The interaction energy of two ligands decays exponentially with
the distance between them and oscillates with the periodicity of the double
helix in quantitative agreement with experimental measurements. The trend in
the computed interaction energy is similar to that in the perturbation of
groove width produced by the binding of a single ligand which is consistent
with molecular simulations. Our analysis provides a new framework to understand
allosteric interactions in DNA and can be extended to other rod-like
macromolecules whose elasticity plays a role in biological functions