The influence of hydrophobic ions and dipolar molecules on the electrostatic barrier in biomembranes

To calculate the electric field inside a membrane the aqueous phase can be approximated by a conductor since the dielectric constant of water is much larger than that of the membrane. Then, using the method of image charges, ions adsorbed inside the membrane can be considered as dipoles and dipolar molecules adsorbed inside the membrane may similarly be regarded as sets of two similarly oriented dipoles. The microscopic interactions and, therefore, the spatial correlations of the adsorbed species can then be obtained. Together with the Gouy theory for the diffuse double layer these results allow the determination of the adsorbed phase--aqueous phase equilibrium. From the densities and spatial correlations of the adsorbed ions and dipolar species, their influence upon the electrostatic barrier as experienced by an ion translocating the membrane can be calculated. Changes observed in the relaxation time and initial conductance of translocating hydrophobic ions in voltage-pulse experiments on bilayer membranes are predicted using this model of the electrostatic barrier. In addition, an equation giving the surface tension as a function of the (non-ideal) adsorption of hydrophobic ions and dipoles is derived.