Applications of dimensionally reduced theory of lipid bilayers: Fluctuation spectra and shear-induced hydrodynamic instabilities

Lipid bilayers are fundamental to a plethora of cellular phenomena, often displaying unique physics owing to their behaving as in-plane fluids and out-of-plane elastic solids. Typically, a direct two-dimensional approach is used in order to obtain a computationally and analytically tractable theory. However, such an approach cannot capture some experimentally and computationally observed phenomena such as Kelvin-Helmholtz-like instabilities or electromechanical coupling in lipid bilayers. Here, we apply an “effective” two-dimensional framework that explicitly includes membrane thickness while retaining the amenability of previous theories. We find that the membrane thickness acts to slow the linear response of lipid bilayers to external perturbations. This novel dependence on thickness alters the behavior of the fluctuation spectrum in the short wavelength regime, where bending effects are relevant. We also study the effects of thickness on the development of shear-induced Kelvin-Helmholtz-like hydrodynamic instabilities.