The electrophoretic mobilities of multilamellar phosphatidylserine vesicles were measured in solutions containing monovalent cations, and the xi potentials, the electrostatic potentials at the hydrodynamic plane of shear, were calculated from the Helmholtz--Smoluchowski equation. In the presence of 0.1 M lithium, sodium, ammonium, potassium, rubidium, cesium, tetraethylammonium, and tetramethylammonium chloride, the xi potentials were -60, -62, -72, -73, -77, -80, -82, and -91 mV, respectively. Similar results were obtained with phosphatidylglycerol vesicles; different results were obtained with cardiolipin, phosphatidylinositol, and phosphatidic acid vesicles. The phosphatidylserine results are interpreted in terms of the Stern equation, a combination of the Gouy equation from the theory of the diffuse double layer, the Boltzmann relation, and the Langmuir adsorption isotherm. Evidence is presented that suggests the hydrodynamic plane of shear is 2 A from the surface of the membrane in solutions containing the alkali metal cations. With this assumption, the intrinsic association constants of the above monovalent cations with phosphatidylserine are 0.8, 0.6, 0.17, 0.15, 0.08, 0.05, 0.03, and 0 M-1, respectively. The validity of this approach was tested in two ways. First, the xi potentials of vesicles formed from mixtures of phosphatidylserine and a zwitterionic lipid, phosphatidylcholine, were measured in solutions containing different concentrations of sodium. All the data could be described by the Stern equation if the "relaxation" of the ionic atmosphere, which is predicted by classic electrostatic and hydrodynamic theory to occur at low salt concentrations and high potentials, was circumvented by using only large (diameter greater than 13 micrometers) vesicles for these measurements. Second, the fluorescent probe 2-(p-toluidinyl)naphthalene-6-sulfonate was used to estimate the potential at the surface of phosphatidylserine and phosphatidylglycerol vesicles sonicated in 0.1 M NaCl. Reasonable agreement with the predicted values of the surface potential was obtained.

The Stern equation, a combination of the Langmuir adsorption isotherm, the Boltzmann relation, and the Grahame equation from the theory of the diffuse double layer, provides a simple theoretical framework for describing the adsorption of charged molecules to surfaces. The ability of this equation to describe the adsorption of divalent cations to membranes containing brain phosphatidylserine (PS) was tested in the following manner. Charge reversal measurements were first made to determine the intrinsic 1:1 association constants of the divalent cations with the anionic PS molecules: when the net charge of a PS vesicle is zero one-half of the available sites are occupied by divalent cations. The intrinsic association constant, therefore, is equal to the reciprocal of the divalent cation concentration at which the mobility of a PS vesicle reverses sign. The Stern equation with this association constant is capable of accurately describing both the zeta potential data obtained with PS vesicles at other concentrations of the divalent cations and the data obtained with vesicles formed from mixtures of PS and zwitterionic phospholipids. Independent measurements of the number of ions adsorbed to sonicated PS vesicles were made with a calcium-sensitive electrode. The results agreed with the zeta potential results obtained with multilamellar vesicles. When membranes are formed at 20~ in 0.1 M NaCI, the intrinisc 1 : 1 association constants of Ni, Co, Mn, Ba, Sr, Ca, and Mg with PS are 40, 28, 25, 20, 14, 12, respectively.