Simple model for overcharging of a sphere by a wrapped oppositely charged asymmetrically neutralized polyelectrolyte: Possible effects of helical charge distribution

We investigate the complexation of a polyelectrolyte bendable rod with an oppositely charged spherical macroion. We take into account electrostatic bending of the rod and its asymmetric charge neutralization by sphere charges. The spontaneous curvature of the rod toward the sphere results in a substantial overcharging of such polyelectrolyte complex with a possible phase transition. Assuming a discrete helical charge distribution on the rod surface, we calculate the electrostatic energy of the helix and the electrostatic contribution to its bending and twisting elasticity. We show that the latter may change sign when the helical pitch is changed. For a DNA-relevant case, these corrections appear to be small compared to the corresponding mechanical elastic moduli. We discuss possible applications of our results to the description of overcharging of the nucleosome core particles.