(14g) Electromechanics of Lipid Bilayers: A Dimensionally Reduced Theory with Applications

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

Lipid membranes are commonly modeled as two-dimensional manifolds. However, in order to capture the effects of an electric field, the potential must be resolved through the thickness of the lipid membrane, rendering existing approaches inadequate. To derive an electromechanical theory for lipid membranes, 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 membranes. Finally, we will discuss the importance of accounting for the thickness of lipid membranes in biophysical applications.