Competitive Effects of 2+ and 3+ Cations on DNA Compaction
  By using single-DNA observation with fluorescence microscopy, we observed the effects of divalent and trivalent cations on the higher-order structure of giant DNA (T4 DNA with 166 kbp). It was found that divalent cations, such as Mg(2+) and Ca(2+), inhibit DNA compaction induced by a trivalent cation, spermidine (SPD(3+)). On the other hand, in the absence of SPD(3+), divalent cations cause the shrinkage of DNA. These experimental observations are inconsistent with the well-established Debye-Huckel scheme regarding the shielding effect of counter ions, which is given as the additivity of contributions of cations with different valences. We interpreted the competition between 2+ and 3+ cations in terms of the change in the translational entropy of the counter ions before and after the folding transition of DNA. For the compaction with SPD(3+), we considered the increase in translational entropy due to the ion-exchange of the intrinsic monovalent cations condensing on a highly-charged polyelectrolyte, double-stranded DNA, by the 3+ cations. In contrast, the presence of 2+ cation decreases the gain of entropy owe to the ion-exchange between monovalent and 3+ ions. 
C. Tongu, T. Kenmotsu, Y. Yoshikawa, A. A. Zinchenko, N. Chen and K.   Yoshikawa
physics.bio-ph