  The mechanism allowing a protein to search of a target sequence on DNA is
currently described as an intermittent process composed of 3D diffusion in bulk
and 1D diffusion along the DNA molecule. Due to the relevant charge of protein
and DNA, electrostatic interaction should play a crucial role during this
search. In this paper, we explicitly derive the mean field theory allowing for
a description of the protein-DNA electrostatics in solution. This approach
leads to a unified model of the search process, where 1D and 3D diffusion
appear as a natural consequence of the diffusion on an extended interaction
energy profile.
