The many faces of membrane tension for biomembranes and vesicles

Membrane tension is generated by external forces and constraints that affect the membrane's surface area. Many studies have been pursued to elucidate this intuitive concept. Here, we focus on biomimetic model systems, for which the notion of membrane tension can be elaborated in a quantitative manner. Bottom-up, these membrane systems are planar bilayers, unilamellar nanovesicles, and giant unilamellar vesicles (GUVs). For planar bilayers and nanovesicles, we need to distinguish the mechanical bilayer tension within the whole bilayer from the mechanical leaflet tensions within the individual bilayer leaflets. In addition, the fluctuation spectrum of the bilayer defines the bilayer's fluctuation tension. These different tensions can be determined by molecular dynamics simulations. On the micron-scale, GUV membranes as observed by light microscopy, experience both a mechanical and a curvature-elastic tension, as follows from the theory of curvature elasticity. The curvature-elastic tension represents a material parameter, whereas the mechanical tension is a kind of hidden variable that depends on the size and shape of the membrane as demonstrated for multispherical shapes of GUVs. Furthermore, the excess membrane area stored in the shape fluctuations is again governed by a fluctuation tension. Many membrane systems exhibit characteristic tension thresholds. Examples include, the shapes of tubular membranes and the morphological responses of vesicle membranes to condensate droplets.