Biomembranes and vesicles cover a wide range of length scales. Indeed, small nanovesicles have a diameter of a few tens of nanometers whereas giant vesicles can have diameters up to hundreds of micrometers. The remodeling of giant vesicles on the micron scale can be observed by light microscopy and understood by the theory of curvature elasticity, which represents a top-down approach. The theory predicts the formation of multispherical shapes as recently observed experimentally. On the nanometer scale, much insight has been obtained via coarse-grained molecular dynamics simulations of nanovesicles, which provides a bottom-up approach based on the lipid numbers assembled in the two bilayer leaflets and the resulting leaflet tensions. The remodeling processes discussed here include the shape transformations of vesicles, their morphological responses to the adhesion of condensate droplets, the instabilities of lipid bilayers and nanovesicles, as well as the topological transformations of vesicles by membrane fission and fusion. The latter processes determine the complex topology of the endoplasmic reticulum.

Many biological membranes host different lipid species in their two leaflets. Since their spontaneous curvatures are typically not the same, this compositional asymmetry generally entails bending torques, which can be counteracted by differential stress-the difference between the two leaflet tensions. This stress, in turn, can affect elastic parameters or phase behavior of the membrane or each individual leaflet, or push easily flippable species, especially cholesterol, from the compressed leaflet into the tense leaflet. In short, breaking the symmetry of a single observable (to wit: composition), essentially breaks all other symmetries as well, with many potentially interesting consequences. This brief report examines the elastic aspects of this interplay, focusing on some elementary conditions of mechanical and thermodynamic equilibrium, but also shows how this poses novel questions that we are only beginning to appreciate.

Artificial or synthetic organelles are a key challenge for bottom-up synthetic biology. So far, synthetic organelles have typically been based on spherical membrane compartments, used to spatially confine selected chemical reactions. In vivo, these compartments are often far from being spherical and can exhibit rather complex architectures. A particularly fascinating example is provided by the endoplasmic reticulum (ER), which extends throughout the whole cell by forming a continuous network of membrane nanotubes connected by three-way junctions. The nanotubes have a typical diameter of between 50 and 100 nm. In spite of much experimental progress, several fundamental aspects of the ER morphology remain elusive. A long-standing puzzle is the straight appearance of the tubules in the light microscope, which form irregular polygons with contact angles close to 120°. Another puzzling aspect is the nanoscopic shapes of the tubules and junctions, for which very different images have been obtained by electron microcopy and structured illumination microscopy. Furthermore, both the formation and maintenance of the reticular networks require GTP and GTP-hydrolyzing membrane proteins. In fact, the networks are destroyed by the fragmentation of nanotubes when the supply of GTP is interrupted. Here, it is argued that all of these puzzling observations are intimately related to each other and to the dimerization of two membrane proteins anchored to the same membrane. So far, the functional significance of this dimerization process remained elusive and, thus, seemed to waste a lot of GTP. However, this process can generate an effective membrane tension that stabilizes the irregular polygonal geometry of the reticular networks and prevents the fragmentation of their tubules, thereby maintaining the integrity of the ER. By incorporating the GTP-hydrolyzing membrane proteins into giant unilamellar vesicles, the effective membrane tension will become accessible to systematic experimental studies.

Mechanical deformation of lipid membranes plays important roles in various cellular tasks. Curvature deformation and lateral stretching are two major energy contributions to the mechanical deformation of lipid membranes. In this paper, continuum theories for these two major membrane deformation events were reviewed. Theories based on curvature elasticity and lateral surface tension were introduced. Numerical methods as well as biological applications of the theories were discussed.

Biomimetic membranes are fluid and can undergo two different elastic deformations, bending and stretching. The bending of a membrane is primarily governed by two elastic parameters: its spontaneous (or preferred) curvature m and its bending rigidity κ. These two parameters define an intrinsic tension scale, the spontaneous tension 2 κm². Membrane stretching and compression, on the other hand, are determined by the mechanical tension acting within the membrane. For vesicle membranes, the two elastic deformations are coupled via the enclosed vesicle volume even in the absence of mechanical forces as shown here by minimizing the combined bending and stretching energy with respect to membrane area for fixed vesicle volume. As a consequence, the mechanical tension within a vesicle membrane depends on the spontaneous curvature and on the bending rigidity. This interdependence, which is difficult to grasp intuitively, is then illustrated for a variety of simple vesicle shapes. Depending on the vesicle morphology, the magnitude of the mechanical tension can be comparable to or can be much smaller than the spontaneous tension.