Space charge-limited conductance in lipid bilayer membranes

A mathematical treatment is given for the flux of ions of one charge sign across lipid bilayer membranes. This treatment is a generalization of a previous analysis of the membrane conductance by D. Walz, E. Bamberg and P. Läuger which was restricted to systems with negligible space charge in the membrane. The present theory includes space charge effects, and it is no longer assumed that the electric field strength in the membrane is constant. It is found that the ohmic membrane conductivity λ0 is reduced by space charges; if only ions of one charge sign are soluble in the membrane, λ0 approaches a limiting value for increasing concentration of the permeable ion in the aqueous solution. The theory also predicts the range in which the constant field approximation is valid. It is found that space charge effects become predominant when the mean concentration of the permeable ion in the membrane exceeds 5×10(-5) M. The currentvoltage characteristic of the membrane remains practically linear even in the presence of a high space charge. It is therefore concluded that the experimentally observed nonlinearity is caused mainly by the distortion of the potential energy profile of an ion due to image forces.