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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.
The role of thermal pressure fluctuation excited within tightly packaged DNA prior to ejection from protein capsid shells is discussed in a model calculation. At equilibrium before ejection we assume the DNA is folded many times into a bundle of para
The distance-resolved effective interaction potential between two parallel DNA molecules is calculated by computer simulations with explicit tetravalent counterions and monovalent salt. Adding counterions first yields an attractive minimum in the pot
We generalize the Poland-Scheraga (PS) model to the case of a circular DNA, taking into account the twisting of the two strains around each other. Guided by recent single-molecule experiments on DNA strands, we assume that the torsional stress induce
We investigate the ejection dynamics of a ring polymer out of a cylindrical nanochannel using both theoretical analysis and three dimensional Langevin dynamics simulations. The ejection dynamics for ring polymers shows two regimes like for linear pol
The effective force between two parallel DNA molecules is calculated as a function of their mutual separation for different valencies of counter- and salt ions and different salt concentrations. Computer simulations of the primitive model are used an