UC Berkeley

Biological membranes form the boundaries of cells and most organelles. Therefore, they are crucial for processes such as intracellular vesicle transport, cell signaling, and endocytosis. The shape and function of cells is largely regulated by membrane-environment interactions. As such, it is important to understand the mechanical properties and behaviors of these membranes. For instance, drug delivery methods focus on targeting the cell membrane, and therefore require a detailed understanding of its physics. All biological membranes are composed of lipid bilayers. Each individual lipid has a hydrophobic tail and a hydrophilic head. Therefore, under appropriate physicochemical conditions, lipids will spontaneously assemble into bilayers. The emergent properties of these membranes is a result of the lipid chemistry. The collective in-plane motion of the lipids due to diffusion leads to membrane fluidity while the rigidity resulting from the emergence of the bilayer structure furnishes elasticity. As a result, these membranes are viscoelastic media capable of arbitrarily curved and large deformations. Therefore, a careful mathematical framework that allows for these deformations is required. Most descriptions on the continuum level have described membranes as two-dimensional sheets. More recent developments have begun to resolve the thickness of membrane but often rely on equilibrium approaches.

Here, we present a comprehensive theoretical description of lipid bilayers as three-dimensional bodies. In order to do so, we introduce a spectral methods framework to derive approximate two-dimensional equations describing the membrane that retain its thickness as an explicit parameter. We arrive at a low-order, analytically tractable theory that allows us to explore membrane thickness length scale phenomena on the continuum level. Using this description, we investigate the hydrodynamic response of a finite thickness lipid bilayer by employing the linear response framework. We show that thickness effects lead to a previously unresolved mode of viscous dissipation in the vicinity of the membrane, and finally discuss the biological implications of our findings.