Overcharging of a spherical macroion by an oppositely charged polyelectrolyte

We consider the electrostatic interaction between a spherical macroion of c harge Q(q) and an oppositely, highly charged polyelectrolyte of charge -Nq (N, Q > 0). For N less than or equal to Q the polyelectrolyte fully collaps es on the macroion, while for N > Q only a partial collapse (up to neutrali zation of the macroion) is expected. We show, however, that for N > Q, the amount of collapsed polyelectrolyte can be bigger than that required to neu tralize the macroion, i.e. the macroion can be overcharged. The overchargin g increases with the diameter of the macroion (continuously or through mult iple first-order transitions), until a total collapse of the polyelectrolyt e takes place. The predictions of this model are then compared with Monte C arlo simulations and a possible mechanism is suggested for the overcharging of the octameric histone in the nucleosome.