Computational study of DNA condensation with divalent counterions, role of counterion size

The problem of DNA$-$DNA interaction mediated by divalent counterions is studied using computer simulation. The effect of the counterion size on the condensation behavior of the DNA bundle is investigated. Experimentally, it is known that multivalent counterions has strong effect on the DNA condensation phenomenon. While tri- and tetra-valent counterions are shown to easily condense free DNA molecules in solution into torroidal bundles, the situation with divalent counterions are not as clear cut. Some divalent counterions like Mg$^{+2}$ are not able to condense free DNA molecules in solution, while some like Mn$^{+2}$ can condense them into disorder bundles. In restricted environment such as in two dimensional system or inside viral capsid, Mg$^{+2}$ can have strong effect and able to condense them, but the condensation varies qualitatively with different system, different coions. It has been suggested that divalent counterions can induce attraction between DNA molecules but the strength of the attraction is not strong enough to condense free DNA in solution. However, if the configuration entropy of DNA is restricted, these attractions are enough to cause appreciable effects. The variations among different divalent salts might be due to the hydration effect of the divalent counterions. In this paper, we try to understand this variation using a very simple parameters, the size of the divalent counterions. We investigate how divalent counterions with different sizes can leads to varying qualitative behavior of DNA condensation in restricted environments.