Counterion condensation on a helical charge lattice

We extend the theory of counterion condensation from the standard represent ation of a locally stiff rodlike polyion as a line of discrete charges to a helical lattice of charges. The number of counterions condensing on a heli x with given axial charge density is the same as on a line of the same char ge density, but the electrostatic free energy is substantially less for the helix than for the line. In fact, the free energy of assembling the helica l charge lattice becomes negative at higher salt concentrations, indicating electrostatic stabilization of the helix due to the mixing entropy of cond ensed counterions. The electrostatic persistence lengths of the line and he lix subjected to locally elastic thermal bending fluctuations differ only s lightly. They have the same kappa (-2) dependence as the Odijk-Skolnick-Fix man persistence length but a different prefactor. It is commonly believed t hat elastic bending models for the persistence length are applicable to dou ble-helical DNA, but we point out that DNA apparently has unique mechanical properties that do not conform to the elastic model of bending. On the oth er hand, the helical model and its subsequent generalization to a double he lix will serve as a basis for the electrostatic free energy of DNA conforma tional transitions.