Measurements of the effect of DNA on rates of bimolecular energy transfer between ions provide a direct indication of how cations cluster in regions near DNA and how anions are repelled from the same regions. Energy transfer from luminescent lanthanide ions (in the "rapid-diffusion" limit) probes collision frequencies that are dependent on the equilibrium spatial distributions of ions. The addition of 1 mM DNA (phosphate) to a 2 mM salt solution increases the overall collision frequency between monovalent cations by a factor of 6 +/- 1.5; it increases the divalent-monovalent cation collision frequency by a factor of 29 +/- 3; and it decreases the divalent cation-monovalent anion collision frequency by a factor of 0.24 +/- 0.03. Comparisons are made with the changes in collision frequencies predicted by several different theoretical descriptions of ion distributions. The closest agreement with experimental results for monovalent ions at 1 mM DNA is obtained with a static accessibility-modified discrete charge calculation, based on a detailed molecular model of B-DNA. At high DNA concentration (10 mM), the best results are obtained by numerical solutions of the Poisson-Boltzmann equation for a "soft-rod" model of DNA. Poisson-Boltzmann calculations for a "hard-rod" model greatly overestimate the effects of DNA on collision frequencies, as does a calculation based on counterion-condensation theory.

Wensel, T. G., Meares, C. F., Vlachy, V., & Matthew, J. B. (1986). Distribution of ions around DNA, probed by energy transfer. Proceedings of the National Academy of Sciences, 83(10), 3267–3271.