Ion repulsion within membranes.

The adsorption of hydrophobic ions such as tetraphenylborate to thin lipid membranes is known to saturate at approximately 0.1 ion/(nm)2. This saturation can be quantitatively explained by electrostatic repulsion between the ions if they are treated as discrete, mobile particles that adsorb within the lipid at least partially removed from the aqueous phases. The electrochemical potential of the ions as a function of their surface density can be expressed as a virial expansion, which in principle exactly describes the equilibrium properties of the physical model. The first few terms of the virial expansion are calculated and an approximation is considered for higher-order terms. The model has only two adjustable parameters, the depth of the adsorption sites into the lipid and the adsorption constant in the absence of repulsion. The mobile, discrete charge model can give much better fits to the equilibrium data for tetraphenylborate adsorbed at up to 0.1 ion/(nm)2 to membranes and monolayers. (Andersen et al., 1978) than those obtainable from either the smeared charge or hexagonal lattice models.