A theory for the effects of neutral carriers such as the macrotetralide actin antibiotics on the electric properties of bilayer membranes

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Abstract
To develop a quantitiative theoretical treatment for the effects of neutral macrocyclic antibiotics on the electrical properties of phospholipid bilayer membranes, this paper proceeds from the known ability of such molecules to form stoichiometric, lipid-soluble complexes with cations and deduces the electrical properties that a simple organic solvent phase would have if it were made into a membrane of the thinness of the phospholipid bilayer. In effect, we postulate that the essential barrier to ion movement across a bilayer membrane is its liquid-like hydrocarbon interior and that the neutral macrocyclic antibiotics bind monovalent cations and solubilize them in the membrane as mobile positively charged complexes. Using the Poisson-Boltzmann equation to describe the equilibrium profile of the electrical potential, it is shown that an excess of the positive complexes over all the other ions is expected in the membrane as a net space charge for appropriate conditions of membrane thickness and values of the partition coefficients of the various ionic species and without requiring the presence of fixed charges. Describing the fluxes of these complexes by the Nernst-Planck equation and neglecting the contribution to the electric current of uncomplexed ions, theoretical expressions are derived for the membrane potential in ionic mixtures, as well as for the limiting value of the membrane conductance at zero current when the membrane is interposed between identical solutions. The expressions are given in terms of the ionic activities and antibiotic concentrations in the aqueous solutions so as to be accessible to direct experimental test. Under suitable experimental conditions, the membrane potential is described by an equation recognizible as the Goldman-Hodgkin-Katz equation, in which the permeability ratios are combinations of parameters predicted from the present theory to be independently determinable from the ratio of membrane conductances in single salt solutions. Since this identity between permeability and conductance ratios is expected also for systems obeying the "Independence Principle" of Hodgkin and Huxley, the applicability of this principle to membranes exposed to antibiotics is discussed, and it is shown that this principle is compatible with the permeation mechanism proposed here.