Electrostatic interactions between DNA molecules have been extensively studied experimentally and theoretically, but several aspects (e.g. its role in determining the pitch of the cholesteric DNA phase) still remain unclear. Here, we performed large-scale all-atom molecular dynamics simulations in explicit water and 150 mM sodium chloride, to reconstruct the potential of mean force (PMF) of two DNA oligomers 24 base pairs long as a function of their interaxial angle and intermolecular distance. We find that the potential of mean force is dominated by total DNA charge, and not by the helical geometry of its charged groups. The theory of homogeneously charged cylinders fits well all our simulation data, and the fit yields the optimal value of the total compensated charge on DNA to ≈65% of its total fixed charge (arising from the phosphorous atoms), close to the value expected from Manning's theory of ion condensation. The PMF calculated from our simulations does not show a significant dependence on the handedness of the angle between the two DNA molecules, or its size is on the order of [Formula: see text]. Thermal noise for molecules of the studied length seems to mask the effect of detailed helical charge patterns of DNA. The fact that in monovalent salt the effective interaction between two DNA molecules is independent on the handedness of the tilt may suggest that alternative mechanisms are required to understand the cholesteric phase of DNA.

This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231. RC was supported by the United Kingdom Engineering and Physical Sciences Research Council (grant No. EP/H004319/1), the French Institut National du Cancer, Grant No. INCa 5960, by the French Agence Nationale de la Recherche, Grant No. ANR-13-BSV5-0010-03, and the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n 608959. We acknowledge support of the Spanish Ministry of Economy and Competitiveness, 'Centro de Excelencia Severo Ochoa 2013-2017'. We acknowledge the support of the CERCA Programme/Generalitat de Catalunya.