Applying a potential across a biomembrane: electrostatic contribution to the bending rigidity and membrane instability

Abstract

We investigate the effect on biomembrane mechanical properties due to the presence an external potential for a non-conductive non-compressible membrane surrounded by different electrolytes. By solving the Debye-Huckel and Laplace equations for the electrostatic potential and using the relevant stress-tensor we find: in (1.) the small screening length limit, where the Debye screening length is smaller than the distance between the electrodes, the screening certifies that all electrostatic interactions are short-range and the major effect of the applied potential is to decrease the membrane tension and increase the bending rigidity; explicit expressions for electrostatic contribution to the tension and bending rigidity are derived as a function of the applied potential, the Debye screening lengths and the dielectric constants of the membrane and the solvents. For sufficiently large voltages the negative contribution to the tension is expected to cause a membrane stretching instability. For (2.) the dielectric limit, i.e. no salt (and small wavevectors compared to the distance between the electrodes), when the dielectric constant on the two sides are different the applied potential induces an effective (unscreened) membrane charge density, whose long-range interaction is expected to lead to a membrane undulation instability.

16 pages, 3 figures, some revision

References in corpus (6)

• Collapse of Stiff Polyelectrolytes due to Counterion Fluctuations
• Undulation instability of lipid membranes under an electric field
• Budding and Domain Shape Transformations in Mixed Lipid Films and Bilayer Membranes
• Dynamics of shape fluctuations of quasi-spherical vesicles revisited
• Descriptions of membrane mechanics from microscopic and effective two-dimensional perspectives
• Fluctuations of a driven membrane in an electrolyte

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• On well-posedness of variational models of charged drops
• Lipid membrane instability and poration driven by capacitive charging
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• Reduction in Tension and Stiffening of Lipid Membranes in an Electric Field Revealed by X-ray Scattering
• Elastic moderation of intrinsically applied tension in lipid membranes
• Tension moderation and fluctuation spectrum in simulated lipid membranes under an applied electric potential
• Ion pump activity generates fluctuating electrostatic forces in biomembranes