Research investigating lipid membrane curvature generation and sensing is a rapidly developing frontier in membrane physical chemistry and biophysics. The fast recent progress is based on the discovery of a plethora of proteins involved in coupling membrane shape to cellular membrane function, the design of new quantitative experimental techniques to study aspects of membrane curvature, and the development of analytical theories and simulation techniques that allow a mechanistic interpretation of quantitative measurements. The present review first provides an overview of important classes of membrane proteins for which function is coupled to membrane curvature. We then survey several mechanisms that are assumed to underlie membrane curvature sensing and generation. Finally, we discuss relatively simple thermodynamic/mechanical models that allow quantitative interpretation of experimental observations.

The importance of curvature as a structural feature of biological membranes has been recognized for many years and has fascinated scientists from a wide range of different backgrounds. On the one hand, changes in membrane morphology are involved in a plethora of phenomena involving the plasma membrane of eukaryotic cells, including endo- and exocytosis, phagocytosis and filopodia formation. On the other hand, a multitude of intracellular processes at the level of organelles rely on generation, modulation, and maintenance of membrane curvature to maintain the organelle shape and functionality. The contribution of biophysicists and biologists is essential for shedding light on the mechanistic understanding and quantification of these processes.

Endocytosis is a ubiquitous eukaryotic membrane budding, vesiculation and internalization process fulfilling numerous roles including compensation of membrane area increase after bursts of exocytosis. The mechanism of the coupling between these two processes to enable homeostasis is not well understood. Recently, an ultrafast endocytosis (UFE) pathway was revealed with a speed significantly exceeding classical clathrin-mediated endocytosis (CME). Membrane tension reduction is a potential mechanism by which endocytosis can be rapidly activated at remote sites. Here, we provide experimental evidence for a mechanism whereby membrane tension reduction initiates membrane budding and tubulation mediated by endocytic proteins, such as endophilin A1. We find that shape instabilities occur at well-defined membrane tensions and surface densities of endophilin. From our data, we obtain a membrane shape stability diagram that shows remarkable consistency with a quantitative model. This model applies to all laterally diffusive curvature-coupling proteins and therefore a wide range of endocytic proteins.

Line tension is a determinant of fluid phase domain formation kinetics and morphology in lipid bilayer membranes, which are models for biological membrane heterogeneity. We describe the first direct measurement of this line tension by micropipette aspiration. Our data are analyzed with a model that does not rely on independently measured (and composition dependent) secondary parameters, such as bending stiffness or membrane viscosities. Line tension is strongly composition dependent and decreases towards a critical consolute point in a quasiternary room temperature phase diagram.