Superelasticity of Plasma- and Synthetic Membranes Resulting from Coupling of Membrane Asymmetry, Curvature, and Lipid Sorting.

Biological cells are contained by a fluid lipid bilayer (plasma membrane, PM) that allows for large deformations, often exceeding 50% of the apparent initial PM area. Isolated lipids self-organize into membranes, but are prone to rupture at small (<2-4%) area strains, which limits progress for synthetic reconstitution of cellular features. Here, it is shown that by preserving PM structure and composition during isolation from cells, vesicles with cell-like elasticity can be obtained. It is found that these plasma membrane vesicles store significant area in the form of nanotubes in their lumen. These act as lipid reservoirs and are recruited by mechanical tension applied to the outer vesicle membrane. Both in experiment and theory, it is shown that a "superelastic" response emerges from the interplay of lipid domains and membrane curvature. This finding allows for bottom-up engineering of synthetic biomaterials that appear one magnitude softer and with threefold larger deformability than conventional lipid vesicles. These results open a path toward designing superelastic synthetic cells possessing the inherent mechanics of biological cells.

Faceting and Flattening of Emulsion Droplets: A Mechanical Model.

When cooled down, emulsion droplets stabilized by a frozen interface of alkane molecules and surfactants have been observed to undergo a spectacular sequence of morphological transformations: from spheres to faceted liquid icosahedra, down to flattened liquid platelets. While generally ascribed to the interplay between the elasticity of the frozen interface and surface tension, the physical mechanisms underpinning these transitions have remained elusive, despite different theoretical pictures having been proposed in recent years. In this Letter, we introduce a comprehensive mechanical model of morphing emulsion droplets, which quantitatively accounts for various experimental observations, including the size scaling behavior of the faceting transition. Our analysis highlights the role of gravity and the spontaneous curvature of the frozen interface in determining the specific transition pathway.

Measuring Gaussian Rigidity Using Curved Substrates.

The Gaussian (saddle splay) rigidity of fluid membranes controls their equilibrium topology but is notoriously difficult to measure. In lipid mixtures, typical of living cells, linear interfaces separate liquid ordered (LO) from liquid disordered (LD) bilayer phases at subcritical temperatures. Here, we consider such membranes supported by curved substrates that thereby control the membrane curvatures. We show how spectral analysis of the fluctuations of the LO-LD interface provides a novel way of measuring the difference in Gaussian rigidity between the two phases. We provide a number of conditions for such interface fluctuations to be both experimentally measurable and sufficiently sensitive to the value of the Gaussian rigidity, while remaining in the perturbative regime of our analysis.

Geometric pinning and antimixing in scaffolded lipid vesicles.

Previous studies on the phase behaviour of multicomponent lipid bilayers found an intricate interplay between membrane geometry and its composition, but a fundamental understanding of curvature-induced effects remains elusive. Thanks to a combination of experiments on lipid vesicles supported by colloidal scaffolds and theoretical work, we demonstrate that the local geometry and global chemical composition of the bilayer determine both the spatial arrangement and the amount of mixing of the lipids. In the mixed phase, a strong geometrical anisotropy can give rise to an antimixed state, where the lipids are mixed, but their relative concentration varies across the membrane. After phase separation, the bilayer organizes in multiple lipid domains, whose location is pinned in specific regions, depending on the substrate curvature and the bending rigidity of the lipid domains. Our results provide critical insights into the phase separation of cellular membranes and, more generally, two-dimensional fluids on curved substrates.

Dislocation screening in crystals with spherical topology.

Whereas disclination defects are energetically prohibitive in two-dimensional flat crystals, their existence is necessary in crystals with spherical topology, such as viral capsids, colloidosomes, or fullerenes. Such a geometrical frustration gives rise to large elastic stresses, which render the crystal unstable when its size is significantly larger than the typical lattice spacing. Depending on the compliance of the crystal with respect to stretching and bending deformations, these stresses are alleviated either by a local increase of the intrinsic curvature in proximity of the disclinations or by the proliferation of excess dislocations, often organized in the form of one-dimensional chains known as "scars." The associated strain field of the scars is such as to counterbalance the one resulting from the isolated disclinations. Here we develop a continuum theory of dislocation screening in two-dimensional closed crystals with genus one. Upon modeling the flux of scars emanating from a given disclination as an independent scalar field, we demonstrate that the elastic energy of closed two-dimensional crystals with various degrees of asphericity can be expressed as a simple quadratic function of the screened topological charge of the disclinations, at both zero and finite temperature. This allows us to predict the optimal density of the excess dislocations as well as the minimal stretching energy attained by the crystal.

Lipid exchange enhances geometric pinning in multicomponent membranes on patterned substrates.

Experiments on supported lipid bilayers featuring liquid ordered/disordered domains have shown that the spatial arrangement of the lipid domains and their chemical composition are strongly affected by the curvature of the substrate. Furthermore, theoretical predictions suggest that both these effects are intimately related with the closed topology of the bilayer. In this work, we test this hypothesis by fabricating supported membranes consisting of colloidal particles of various shapes lying on a flat substrate. A single lipid bilayer coats both colloids and substrate, allowing local lipid exchange between them, thus rendering the system thermodynamically open, i.e. able to exchange heat and molecules with an external reservoir in the neighborhood of the colloid. By reconstructing the Gibbs phase diagram for this system, we demonstrate that the free-energy landscape is directly influenced by the geometry of the colloid. In addition, we find that local lipid exchange enhances the pinning of the liquid disordered phase in highly curved regions. This allows us to provide estimates of the bending moduli difference of the domains. Finally, by combining experimental and numerical data, we forecast the outcome of possible experiments on catenoidal and conical necks and show that these geometries could greatly improve the precision of the current estimates of the bending moduli.

Thermodynamic equilibrium of binary mixtures on curved surfaces.

We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and conservation laws, we identify several model-independent phenomena, such as a curvature-dependent line tension and local shifts in the binodal concentrations. To shed light on the origin of the phenomenological parameters appearing in the effective free energy, we further construct a lattice-gas model of binary mixtures on nontrivial substrates, based on the curved-space generalization of the two-dimensional Ising model. This allows us to decompose the interaction between the local concentration of the mixture and the substrate curvature into four distinct contributions, as a result of which the phase diagram splits into critical subdiagrams. The resulting free energy landscape can admit, as stable equilibria, strongly inhomogeneous mixed phases, which we refer to as "antimixed" states below the critical temperature. We corroborate our semianalytical findings with phase-field numerical simulations on realistic curved lattices. Despite this work being primarily motivated by recent experimental observations of multicomponent lipid vesicles supported by colloidal scaffolds, our results are applicable to any binary mixture confined on closed surfaces of arbitrary geometry.