Biological membranes are known to contain compositional heterogeneities, often termed rafts, with distinguishable composition and function, and these heterogeneities participate in vigorous transport processes. Membrane lipid phase coexistence is expected to modulate these processes through the differing mechanical properties of the bulk domains and line tension at phase boundaries. In this contribution, we compare the predictions from a shape theory derived for vesicles with fluid phase coexistence to the geometry of giant unilamellar vesicles with coexisting liquid-disordered (L(d)) and liquid-ordered (L(o)) phases. We find a bending modulus for the L(o) phase higher than that of the L(d) phase and a saddle-splay (Gauss) modulus difference with the Gauss modulus of the L(o) phase being more negative than the L(d) phase. The Gauss modulus critically influences membrane processes that change topology, such as vesicle fission or fusion, and could therefore be of significant biological relevance in heterogeneous membranes. Our observations of experimental vesicle geometries being modulated by Gaussian curvature moduli differences confirm the prediction by the theory of Juelicher and Lipowsky.

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 curvature of biological membranes is controlled by membrane-bound proteins. For example, during endocytosis, the sorting of membrane components, vesicle budding, and fission from the plasma membrane are mediated by adaptor and accessory proteins. Endophilin is a peripherally binding membrane protein that functions as an endocytic accessory protein. Endophilin's membrane tubulation capacity is well known. However, to understand the thermodynamic and mechanical aspects of endophilin function, experimental measurements need to be compared to quantitative theoretical models. We present measurements of curvature sorting and curvature generation of the endophilin A1 N-BAR domain on tubular membranes pulled from giant unilamellar vesicles. At low concentration, endophilin functions primarily as a membrane curvature sensor; at high concentrations, it also generates curvature. We determine the spontaneous curvature induced by endophilin and observe sigmoidal curvature/composition coupling isotherms that saturate at high membrane tensions and protein solution concentrations. The observation of saturation is supported by a strong dependence of lateral diffusion coefficients on protein density on the tether membrane. We develop a nonlinear curvature/composition coupling model that captures our experimental observations. Our model predicts a curvature-induced phase transition among two states with varying protein density and membrane curvature. This transition could act as a switch during endocytosis.

We investigate the adhesion of vesicles, under the influence of a contact potential, to substrates with various geometry. For axisymmetric configurations, we find that the transition from a free vesicle to a bound state depends significantly on the substrate shape. In general, the critical values of the contact potential at which these transitions take place are lower for a concave-shaped substrate than that for a flat-shaped substrate investigated in earlier studies. We observe that the transitions happen at higher critical values of the contact potential when the substrate is convex and illustrate how these critical values depend on the curvature of the substrate. In addition, we construct an approximate analytical solution that predicts the shape of the vesicle for large internal excess pressure and contact potential. The analytical solution leads to an inequality that relates the surface tension with the contact potential.

Membrane curvature of a biological cell is actively involved in various fundamental cell biological functions. It has been discovered that membrane curvature and binding of peripheral membrane proteins follow a symbiotic relationship. The exact mechanism behind this interplay of protein binding and membrane curvature has not yet been properly understood. To improve understanding of the mechanism, we study curvature sorting of proteins in a model system consisting of a tether pulled from a giant unilamellar vesicle using mechanical-thermodynamic models. The concentration of proteins bound to the membrane changes significantly due to curvature. This has also been observed in experiments by other researchers. We also find that there is a phase transition based on protein concentration and we discuss the coexistence of phases and stability of solutions. Furthermore, when sorting is favorable, the increase in protein concentration stabilizes the tether in the sense that less pulling force is required to maintain the tether. A similar mechanism may be in place, when motor proteins pull tethers from donor membranes.