  Allosteric interactions between molecules bound to DNA at distant locations
have been known for a long time. The phenomenon has been studied via
experiments and numerical simulations, but a comprehensive understanding
grounded in a theory of DNA elasticity remains a challenge. Here we quantify
allosteric interactions between two entities bound to DNA by using the theory
of birods. We recognize that molecules bound to DNA cause local deformations
that can be captured in a birod model which consists of two elastic strands
interacting via an elastic web representing the base-pairs. We show that the
displacement field caused by bound entities decays exponentially with distance
from the binding site. We compute the interaction energy between two proteins
on DNA as a function of distance between them and find that it decays
exponentially while oscillating with the periodicity of the double-helix, in
excellent agreement with experiments. The decay length of the interaction
energy can be determined in terms of the mechanical properties of the strands
and the webbing in our birod model, and it varies with the GC content of the
DNA. Our model provides a framework for viewing allosteric interactions in DNA
within the ambit of configurational forces of continuum elasticity.
