A Poisson-Boltzmann approach for a lipid membrane in an electric field

Abstract

The behavior of a non-conductive quasi-planar lipid membrane in an electrolyte and in a static (DC) electric field is investigated theoretically in the nonlinear (Poisson-Boltzmann) regime. Electrostatic effects due to charges in the membrane lipids and in the double layers lead to corrections to the membrane elastic moduli which are analyzed here. We show that, especially in the low salt limit, i) the electrostatic contribution to the membrane's surface tension due to the Debye layers crosses over from a quadratic behavior in the externally applied voltage to a linear voltage regime. ii) the contribution to the membrane's bending modulus due to the Debye layers saturates for high voltages. Nevertheless, the membrane undulation instability due to an effectively negative surface tension as predicted by linear Debye-Hückel theory is shown to persist in the nonlinear, high voltage regime.

15 pages, 4 figures

References in corpus (6)

• Electrohydrodynamic model of vesicle deformation in alternating electric fields
• Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane
• Effective zero-thickness model for a conductive membrane driven by an electric field
• Applying a potential across a biomembrane: electrostatic contribution to the bending rigidity and membrane instability
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Cited by in corpus (3)

• A planar lipid bilayer in an electric field: membrane instability, flow field and electrical impedance
• Reduction in Tension and Stiffening of Lipid Membranes in an Electric Field Revealed by X-ray Scattering
• The $(2+\delta )$-dimensional theory of the electromechanics of lipid membranes: I. Electrostatics