Lattice-gas model of DNA charge inversion by a positively charged polyelectrolyte.

The model of DNA charge inversion by Nguyen and Shklovskii [T. T. Nguyen and B. I. Shklovskii, Phys. Rev. Lett. 89, 018101 (2002)] is extended. A single double-helix strand of DNA is represented by a lattice of negative charges at the positions of the protruding oxygens of the phosphates along the DNA backbone, and the adsorbed polyelectrolyte molecules are represented by charged dimers. A lattice-gas model is used in which dimers adsorbing either parallel or perpendicular to the lattice are treated as separate species, and the model allows for vacancies between adsorbed species. The mean field theory used is formulated as a saddle-point approximation of the exact functional integral representation of the grand canonical partition function, opening the way for the inclusion of the effects of charge fluctuation corrections.