Ion binding to a membrane with surface charge layers

A model for the potential distribution across a charged biological membrane proposed previously by us Biophys. J., 47 (1985) 673] is extended to a case which includes the effects of binding of monovalent cations. We assume that the membrane has a surface charge layer of thickness d which is permeable to electrolyte ions and in which the membrane-fixed charged groups are distributed at a uniform density N. We also assume that each charged group can bind one monovalent cation with an equilibrium constant K. In the limit of d → 0, keeping the product Nd constant, our model gives the most commonly used model in which ion binding is considered to occur only at the membrane surface (of zero thickness). It is shown that the amount of bound cations as well as the potential distribution are found to depend strongly on d. For example, in 0.1 M 1-1 electrolyte with K = 0.8 M⁻¹, the reduction in magnitude of the surface potential at the outer surface of the surface charge layer of 10 Å thickness is about 40 ∼ 60% of that for the membrane having the surface charge layer of zero thickness, and the deviation of the amount of bound cations for the membrane of d = 10 Å from that predicted for d = 0 is 30–40%, indicating that the conventional model assuming d = 0 leads to a serious overestimation of the surface potential as well as the amount of bound cations onto the membrane.