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

• Received 4 December 2001

DOI:https://doi.org/10.1103/PhysRevLett.89.018303