The (2+δ)-dimensional theory of lipid membranes: Application to measurements of surface tension and bending rigidity

Capturing the effects of electric fields on the mechanical behavior of lipid membranes requires resolving the electric potential through their thickness. Current continuum approaches, however, treat lipid membranes as two-dimensional manifolds, making them unsuitable for describing their electromechanical behavior. Thus, we propose a new dimension reduction procedure for differential equations on thin bodies. Using this approach, new surface theories for the electrostatics and mechanics of lipid membranes are derived. Combining them, we obtain a novel continuum model for the electromechanics of lipid membranes. Using this new model, we show that accounting for charged lipids is necessary to correctly determine surface tension from height fluctuations and bending rigidity from tube-pulling experiments. Thus, our new theory illustrates that standard continuum theories of lipid membranes are not suitable for studying lipid membranes in the presence of electromechanical effects and suggests the reinterpretation of lipid membrane experiments in the presence of charged lipids.