The ionic atmosphere around nucleic acids remains only partially understood at atomic level detail in a quantitative sense. Ion counting (IC) experiments provide a quantitative measure of the ionic atmosphere around nucleic acids and, as such, are a natural route for testing quantitative theoretical approaches. In this paper we replicate IC experiments involving duplex DNA in NaCl (aq) using molecular dynamics (MD), three dimensional interaction site model (3D-RISM) and non-linear Poisson-Boltzmann (NLPB) and test against recent buffer-equilibration atomic emission spectroscopy measurements. Near physiological concentrations, MD and 3D-RISM estimates are close to experiment, but at higher concentrations (<0.7 M) both methods underestimate the number of condensed cations. NLPB calculations systematically underestimate the amount of condensed cations at almost all concentrations. The effect of DNA charge on ion and water atmosphere extends 20-25 A from its surface, yielding layered density profiles in the case of MD and 3D-RISM but less structured for NLPB. Ion distributions from 3D-RISM are relatively close to those from corresponding MD simulations, with less Na + binding in grooves and tighter binding to phosphates. We outline the statistical mechanical basis of interpreting ion counting experiments and clarify the use of specific concentration scales.
