An experimental test of the discreteness-of-charge effect in positive and negative lipid bilayers

The electrostatic properties of charged bilayers and the bilayer component of biological membranes are often described theoretically by assuming the charge is smeared uniformly over the surface. This is one of the fundamental assumptions in the Gouy-Chapman-Stern (GCS) theory. However, the average distance between the charged phospholipids in a typical biological membrane is 2-3 nm, which is 2-3 times the Debye length in a 0.1 M salt solution. Existing discreteness-of-charge theories predict significant deviations from the GCS theory for the adsorption of ions to such membranes. We considered the predictions of the simplest discreteness-of-charge theory [Nelson, A. P., & McQuarrie, D. A. (1975) J. Theor. Biol. 55, 13-27], in which the charges are assumed to be fixed in a square lattice and the potential is described by the linearized Poisson-Boltzmann relation. This theory predicts deviations that are larger for counterions than for co-ions and much larger for divalent than for monovalent counterions. We tested these predictions by measuring the adsorption of a fluorescent monovalent anion and a paramagnetic divalent cation to both positive and negative membranes, which we demonstrated experimentally had the same average surface potential. All our experimental results with probes, including those obtained on membranes in the gel rather than in the liquid-crystalline state, agreed with the predictions of the GCS theory rather than with the discreteness-of-charge theory. A simple calculation indicates that the agreement between the experimental results and the predictions of the GCS theory could be due to the finite size of the lipids.