The pair interaction between two stiff parallel linear DNA molecules depends not only on the distance between their axes but on their azimuthal orientation. The positional and orientational order in columnar B-DNA assemblies in solution is investigated, based on the DNA-DNA electrostatic pair potential that takes into account DNA helical symmetry and the amount and distribution of adsorbed counterions. A phase diagram obtained by lattice sum calculations predicts a variety of positionally and azimuthally ordered phases and bundling transitions strongly depending on the counterion adsorption patterns.
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