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, $\mathrm{N,}$ 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 $N_0.$ DNA condensation takes place in the vicinity of $N_0,$ where absolute value of the DNA net charge is small and the correlation induced short range attraction dominates the Coulomb repulsion. At ${\mathrm{N>N}}_0$ 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 ${\mathrm{Spe}}^{\mathrm{4+}},$ we obtain that $N_0\text{=3.2\hspace{0.05em}}\mathrm{mM}$ and that the energy of DNA condensation per nucleotide is ${\text{0.07\hspace{0.5em}k}}_B\mathrm{T.}$