Complexation between a Semiflexible Polyelectrolyte and an Oppositely Charged Sphere

We study theoretically the interaction of a charged, semiflexible polymer with an oppositely charged sphere. Both the effects of added salt (leading to a finite screening length) and of a bare stiffness of the polymer are taken into account. For intermediate salt concentration and high enough sphere charge we obtain a strongly bound complex where the polymer completely wraps around the sphere. The complex may or may not exhibit charge reversal, depending on the sphere charge and salt concentration. The low-salt regime is dominated by the polymer−polymer repulsion and leads to a characteristic hump shape: the polymer partially wraps around the sphere, and the two polymer arms extend parallel and in opposite directions from the sphere. In the high-salt regime we find bent solutions, where the polymer partially wraps the sphere and the polymer ends extend in arbitrary directions from the sphere; in this regime, the wrapping transition is strongly discontinuous. This wrapping behavior agrees qualitatively well with the salt-induced release of DNA from nucleosomal core particles. The salt dependence of the wrapping transition for large salt concentrations agrees with experimental results for the complexation of synthetic polyelectrolytes with charged micelles. Other applications include the complexation of polyelectrolytes with charged colloids or multivalent ions. In our analysis we calculate the classical or optimal path of the polymer, using a perturbational scheme. This calculation is confirmed and augmented by scaling arguments, which in addition allow us to consider the effect of polymer fluctuations.