Embryos allocate cells to the three germ layers in a spatially ordered sequence. Human embryonic stem cells (hESCs) can generate the three germ layers in culture, however, differentiation is typically heterogeneous and spatially disordered. Here we show that geometric confinement is sufficient to trigger self-organized patterning in hESCs. In response to BMP4, these colonies reproducibly differentiate to an outer trophectoderm-like ring, an inner ectodermal circle and a ring of mesendoderm expressing primitive-streak markers in between. Fates are defined relative to the boundary with a fixed length scale: small colonies correspond to the outer layers of larger ones. Inhibitory signals limit the range of BMP4 signaling to the colony edge and induce a gradient of Activin/Nodal signaling that patterns mesendodermal fates. These results demonstrate that the intrinsic tendency of stem cells to make patterns can be harnessed by controlling colony geometries, and provide a quantitative assay for studying paracrine signaling.

Cells are populated by a vast array of membrane-binding proteins that execute critical functions. Functions, like signaling and intracellular transport, require the abilities to bind to highly curved membranes and to trigger membrane deformation. Among these proteins is amphiphysin 1, implicated in clathrin-mediated endocytosis. It contains a Bin-Amphiphysin-Rvs membrane-binding domain with an N-terminal amphipathic helix that senses and generates membrane curvature. However, an understanding of the parameters distinguishing these two functions is missing. By pulling a highly curved nanotube of controlled radius from a giant vesicle in a solution containing amphiphysin, we observed that the action of the protein depends directly on its density on the membrane. At low densities of protein on the nearly flat vesicle, the distribution of proteins and the mechanical effects induced are described by a model based on spontaneous curvature induction. The tube radius and force are modified by protein binding but still depend on membrane tension. In the dilute limit, when practically no proteins were present on the vesicle, no mechanical effects were detected, but strong protein enrichment proportional to curvature was seen on the tube. At high densities, the radius is independent of tension and vesicle protein density, resulting from the formation of a scaffold around the tube. As a consequence, the scaling of the force with tension is modified. For the entire density range, protein was enriched on the tube as compared to the vesicle. Our approach shows that the strength of curvature sensing and mechanical effects on the tube depends on the protein density.curvature-inducing | curvature-sensing | membrane nanotube | membrane physics

Sorting of lipids and proteins is a key process allowing eukaryotic cells to execute efficient and accurate intracellular transport and to maintain membrane homeostasis. It occurs during the formation of highly curved transport intermediates that shuttle between cell compartments. Protein sorting is reasonably well described, but lipid sorting is much less understood. Lipid sorting has been proposed to be mediated by a physical mechanism based on the coupling between membrane composition and high curvature of the transport intermediates. To test this hypothesis, we have performed a combination of fluorescence and force measurements on membrane tubes of controlled diameters pulled from giant unilamellar vesicles. A model based on membrane elasticity and nonideal solution theory has also been developed to explain our results. We quantitatively show, using 2 independent approaches, that a difference in lipid composition can build up between a curved and a noncurved membrane. Importantly, and consistent with our theory, lipid sorting occurs only if the system is close to a demixing point. Remarkably, this process is amplified when even a low fraction of lipids is clustered upon cholera toxin binding. This can be explained by the reduction of the entropic penalty of lipid sorting when some lipids are bound together by the toxin. Our results show that curvature-induced lipid sorting results from the collective behavior of lipids and is even amplified in the presence of lipid-clustering proteins. In addition, they suggest a generic mechanism by which proteins can facilitate lipid segregation in vivo. cholera toxin ͉ giant unilamellar vesicle ͉ membrane curvature ͉ membrane nanotube ͉ optical tweezers L ipids and proteins are not homogeneously distributed among cell membranes (1). How intracellular trafficking maintains the composition differences between the various membrane compartments of the cell is still poorly understood. In many cases, trafficking intermediates are tubular structures with radii typically in the range of 50 nm (2). It has been suggested that lipid sorting could be mediated by a physical mechanism based on the coupling between membrane composition and the high curvature of these intermediates (refs. 3-6; and see refs. 7-12 for theoretical papers) and on solid substrate topography (13). Added lipid or protein dyes have been shown to be sorted into or out of highly curved regions but without a systematic study of the influence of the underlying membrane composition on the sorting process (3,14). It is crucial from a biological point of view to know whether the native membrane lipids themselves can be sorted by curvature and if so, whether or not the mechanism is robust for variable membrane compositions. In fact, a recent theoretical paper predicts a weak effect of curvature on membrane composition because of the overwhelming cost of mixing entropy, suggesting that curvature does not significantly contribute to sorting (15). In contrast, we demonstrate in the present work that cooperative behavior be...