  The effective DNA-DNA interaction force is calculated by computer simulations
with explicit tetravalent counterions and monovalent salt. For overcharged DNA
molecules, the interaction force shows a double-minimum structure. The
positions and depths of these minima are regulated by the counterion density in
the bulk. Using two-dimensional lattice sum and free energy perturbation
theories, the coexisting phases for DNA bundles are calculated. A
DNA-condensation and redissolution transition and a stable mesocrystal with an
intermediate lattice constant for high counterion concentration are obtained.
