  The problem of inhibiting viral DNA ejection from bacteriophages by
multivalent counterions, specifically Mg$^{+2}$ counterions, is studied.
Experimentally, it is known that MgSO$_4$ salt has a strong and non-monotonic
effect on the amount of DNA ejected. There exists an optimal concentration at
which the minimum amount of DNA is ejected from the virus. At lower or higher
concentrations, more DNA is ejected from the capsid. We propose that this
phenomenon is the result of DNA overcharging by Mg$^{+2}$ multivalent
counterions. As Mg$^{+2}$ concentration increases from zero, the net charge of
DNA changes from negative to positive. The optimal inhibition corresponds to
the Mg$^{+2}$ concentration where DNA is neutral. At lower/higher
concentrations, DNA genome is charged. It prefers to be in solution to lower
its electrostatic self-energy, which consequently leads to an increase in DNA
ejection. By fitting our theory to available experimental data, the strength of
DNA$-$DNA short range attraction energies, mediated by Mg$^{+2}$, is found to
be $-$0.004 $k_BT$ per nucleotide base. This and other fitted parameters agree
well with known values from other experiments and computer simulations. The
parameters are also in aggreement qualitatively with values for tri- and
tetra-valent counterions.
