Large divalent cations and electrostatic potentials adjacent to membranes. A theoretical calculation.

We have extended the Gouy-Chapman theory of the electrostatic diffuse double layer by considering the finite size of divalent cations in the aqueous phase adjacent to a charged surface. The divalent cations are modeled as either two point charges connected by an infinitely thin, rigid "rod" or two noninteracting point charges connected by an infinitely thin, flexible "string." We use the extended theory to predict the effects of a cation of length 10 A (1 nm) on the zeta and surface potentials of phospholipid bilayer membranes. The predictions of the rod and string models are similar to one another but differ markedly from the predictions of the Gouy-Chapman theory. Specifically, the extended model predicts that a large divalent cation will have a smaller effect on the potential adjacent to a negatively charged bilayer membrane than a point divalent cation, that the magnitude of this discrepancy will decrease as the Debye length increases, and that a large divalent cation will produce a negative zeta potential on a membrane formed from zwitterionic lipids. These predictions agree qualitatively with the experimental results obtained with the large divalent cation hexamethonium. We discuss the biological relevance of our calculations in the context of the interaction of cationic drugs with receptor sites on cell membranes.