Electromechanics of Lipid Bilayers: A Dimensionally Reduced Theory

From experiments, it is well known that electric fields affect the physics of lipid bilayers. For instance, lipid vesicles change their morphologies under an external electric field, and under physiological conditions lipid bilayers are immersed in electrolytes and are thus exposed to electric fields as well. Therefore, understanding the electromechanics of lipid bilayers is essential for many biologically relevant processes. While the continuum theory of the mechanics of lipid bilayers is well established, a unified theory that captures the coupling between electric fields and mechanical deformations is currently missing.

Lipid bilayers are commonly modeled as a two-dimensional manifold. However, in order to capture the effects of an electric field, the potential must be resolved through the thickness of the lipid bilayer, rendering existing approaches inadequate. To derive an electromechanical theory for lipid bilayers, we propose a new dimension reduction approach. This allows us to derive a surface theory for the electrostatics of thin films. Furthermore, we recover the well-known equations governing the mechanics of thin films. Finally, we combine the surface description of the electrostatics and mechanics with appropriate constitutive models to formulate a new theory for the electromechanics of lipid bilayers.