Continuum theory of lipid bilayer electrostatics

Abstract

In order to address the concerns about the applicability of the continuum theory of lipid bilayers, we generalize it by including a film with uniaxial dielectric properties representing the polar head groups of the lipid molecules. As a function of the in-plane dielectric constant $\kappa_{{\Vert}}^{}$ of this film, we encounter a sequence of different phases. For low values of $\kappa_{{\Vert}}^{}$ , transmembrane pores have aqueous cores, ions are repelled by the bilayer, and the ion permeability of the bilayer is independent of the ion radius as in the existing theory. For increasing $\kappa_{{\Vert}}^{}$ , a threshold is reached --of the order of the dielectric constant of water-- beyond which ions are attracted to the lipid bilayer by generic polarization attraction, transmembrane pores collapse, and the ion permeability becomes sensitively dependent on the ion radius, results that are more consistent with experimental and numerical studies of the interaction of ions with neutral lipid bilayers. At even higher values of $\kappa_{{\Vert}}^{}$ , the ion/pore complexes are predicted to condense in the form of extended arrays. The generalized continuum theory can be tested quantitatively by studies of the ion permeability as a function of salt concentration and co-surfactant concentration.