Inner voltage clamping. A method for studying interactions among hydrophobic ions in a lipid bilayer

Ketterer, et al. (1971) have suggested that a combination of electrostatic and chemical interactions may cause hydrophobic ions absorbed within a bilayer lipid membrane to reside in two potential wells, each close to a membrane surface. The resulting two planes of charges would define three regions of membrane dielectric: two identical outer regions each between a plane of absorbed charges and the plane of closest approach of ions in the aqueous phase; and the inner region between the two planes of adsorbed charges. The theory describing charge translocation across the inner region is based on a simple three-capacitor model. A significant theoretical conclusion is that the difference between the voltage across the inner region, V(i), and the voltage across the entire membrane, V(m), is directly proportional to the amount of charge that has flowed in a voltage clamp experiment. We demonstrate that we can construct an "inner voltage clamp" that can maintain, with positive feedback, a constant inner voltage, V(i). The manifestation of proper feedback is that the clamp current (after a voltage step) will exhibit pure (i.e., single time-constant) exponential decay, because the voltage dependent rate constants governing translocation will be independent of time. The "pureness" of the exponential is maximized when the standard deviation of the least-square fit of the appropriate exponential equation to the experimental data is minimized. The concomitant feedback is directly related to the capacitances of the inner and outer membrane regions, C(i) and C(o).Experimental results with tetraphenylborate ion adsorbed in bacterial phosphatidylethanolamine/n-decane bilayers indicate C(i) approximately 5 . 10(-7)F/cm(2) and C(o) approximately 5 . 10(-5)F/cm(2).