Reentrant condensation of DNA induced by multivalent counterions

A theory of condensation and resolubilization of a dilute DNA solution with growing concentration of multivalent cations, N, is suggested. It is based on a new theory of screening of a macroion by multivalent cations, which shows that due to strong cation correlations at the surface of DNA the net charge of DNA changes sign at some small concentration of cations N₀. DNA condensation takes place in the vicinity of N₀, where absolute value of the DNA net charge is small and the correlation induced short range attraction dominates the Coulomb repulsion. At N>N₀ positive DNA should move in the opposite direction in an electrophoresis experiment. From comparison of our theory with experimental values of condensation and resolubilization thresholds for DNA solution containing Spe⁴⁺, we obtain that N₀ = 3.2mM and that the energy of DNA condensation per nucleotide is 0.07 k_BT.