The electromechanics of lipid membranes: A dimensionally-reduced theory.

Abstract

Lipid membranes separate the interior and exterior of a biological cell and its organelles. Their viscous-elastic material behavior gives rise to intriguing lipid membrane dynamics. However, lipid membrane dynamics are also affected by the presence of an electric field. For instance, lipid vesicles deform into prolates, oblates, and other shapes and even form pores when an electric field is applied. Furthermore, varying ionic concentrations across the boundary and within the interior of cells and organelles expose lipid membranes to electric fields in physiological conditions. Thus, understanding the electromechanics of lipid membranes is essential for many biological and experimental processes, such as the propagation of action potentials and the electroformation of lipid vesicles. Studying the electromechanics of lipid membranes on long lengths- and timescales requires a continuum physics framework. While continuum models are well-established for the pure mechanics of lipid membranes, a continuum model that captures the coupling between mechanical deformations and electric fields is currently missing. Capturing the effects of electric fields requires resolving the electric potential through the thickness of the lipid membrane. Current continuum approaches, however, treat lipid membranes as two-dimensional manifolds, making them unsuitable for describing the electromechanics of lipid membranes. Thus, we propose a new dimension reduction procedure for differential equations on thin bodies. Using this approach, we derive new surface theories for the electrostatics and mechanics of lipid membranes. Combining them, we obtain a novel continuum model for the electromechanics of lipid membranes. After discussing the new model, we apply it to a fluctuating lipid membrane in an external electric field and demonstrate the effect of accounting for the finite thickness of lipid membranes.