Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane

Abstract

We discuss the electrostatic contribution to the elastic moduli of a cell or artificial membrane placed in an electrolyte and driven by a DC electric field. The field drives ion currents across the membrane, through specific channels, pumps or natural pores. In steady state, charges accumulate in the Debye layers close to the membrane, modifying the membrane elastic moduli. We first study a model of a membrane of zero thickness, later generalizing this treatment to allow for a finite thickness and finite dielectric constant. Our results clarify and extend the results presented in [D. Lacoste, M. Cosentino Lagomarsino, and J. F. Joanny, Europhys. Lett., {\bf 77}, 18006 (2007)], by providing a physical explanation for a destabilizing term proportional to $\kps^3$ in the fluctuation spectrum, which we relate to a nonlinear ($E^2$) electro-kinetic effect called induced-charge electro-osmosis (ICEO). Recent studies of ICEO have focused on electrodes and polarizable particles, where an applied bulk field is perturbed by capacitive charging of the double layer and drives flow along the field axis toward surface protrusions; in contrast, we predict "reverse" ICEO flows around driven membranes, due to curvature-induced tangential fields within a non-equilibrium double layer, which hydrodynamically enhance protrusions. We also consider the effect of incorporating the dynamics of a spatially dependent concentration field for the ion channels.

22 pages, 10 figures. Under review for EPJE

References in corpus (4)

• Induced-charge Electrophoresis of Metallo-dielectric Particles
• Hindered mobility of a particle near a soft interface
• Applying a potential across a biomembrane: electrostatic contribution to the bending rigidity and membrane instability
• Effect of an electric field on a floating lipid bilayer: a neutron reflectivity study

Cited by in corpus (15)

• Electrohydrodynamic model of vesicle deformation in alternating electric fields
• A perturbative path integral study of active and passive tracer diffusion in fluctuating fields
• Effective zero-thickness model for a conductive membrane driven by an electric field
• A Poisson-Boltzmann approach for a lipid membrane in an electric field
• The Heat of Nervous Conduction: A Thermodynamic Framework
• Lipid membrane instability and poration driven by capacitive charging
• A planar lipid bilayer in an electric field: membrane instability, flow field and electrical impedance
• Peptide pores in lipid bilayers : voltage facilitation pleads for a revised model
• Tension moderation and fluctuation spectrum in simulated lipid membranes under an applied electric potential
• A model for the electric field-driven deformation of a drop or vesicle in strong electrolyte solutions
• The $(2+\delta )$-dimensional theory of the electromechanics of lipid membranes: I. Electrostatics
• Exponential decay estimates for the stability of boundary layer solutions to Poisson-Nernst-Planck systems: one spatial dimension case
• A vesicle microrheometer for high-throughput viscosity measurements of lipid and polymer membranes
• Boundary Layer Solutions of Charge Conserving Poisson-Boltzmann Equations: One-Dimensional Case
• Ion pump activity generates fluctuating electrostatic forces in biomembranes