  We derive formulae for the electrostatic interaction between two long, rigid
macromolecules that may have arbitrary surface charge patterns and cross at an
arbitrary interaxial angle. We calculate the dependence of the interaction
energy on the interaxial angle, on the separation, and on the precise alignment
of the charge pattern on one molecule with respect to the other. We focus in
particular on molecules with helical charge patterns. We report an exact,
explicit expression for the energy of interaction between net-neutral helices
in a nonpolar medium as well as an approximate result for charged helices
immersed in an electrolyte solution. The latter result becomes exact in the
asymptotic limit of large separations. Molecular chirality of helices manifests
itself in a torque that tends to twist helices in a certain direction out of
parallel alignment and that has a nontrivial behavior at small interaxial
angles. We illustrate the theory with the calculation of the torque between
layers of idealized, DNA-like double helices in cholesteric aggregates. We
propose a mechanism of the observed cholesteric-to-columnar phase transition
and suggest an explanation for the observed macroscopic (0.4-5 um) pitch of the
cholesteric phase of B-DNA.
