Curvature-driven lipid sorting in a membrane tubule

From reversible to irreversible: When the membrane nanotube pearling is coupled with phase separation

Membrane nanotubes, which are ubiquitous in biology and act as channels maintaining transport between different cells and organelles, readily undergo pearling in response to external stimuli. Membrane nanotube pearling involves generation of heterogeneous curvature coupled with redistribution of membrane components that may interfere with the shape recovery of pearled nanotubes. However, the mechanism underlying such delicate process remains unclear and difficult to study at the molecular scale in vivo. By means of molecular dynamics simulation, here we investigate pearling of multi-component membrane nanotubes and reversibility through manipulating system temperature and osmotic pressure. With the equilibrium shape of membrane nanotubes controlled by the osmotic pressure, our results demonstrate that the process of membrane nanotube pearling can be reversible or irreversible, depending on the phase segregation state. For the pearled nanotube releasing high surface energy, different lipid components redistribute along the tube axial direction. Lipids with unsaturated tails prefer gathering at the high-curvature shrinking region, whereas the swelling region is constituted by saturated lipids forming the liquid-ordered phase of a higher bending rigidity. Such curvature sensitive phase segregation minimizes the system free energy by reducing both the membrane bending energy and line tension at the phase boundary. As such, the pearled nanotube fails to recover its shape upon retracting stimuli, suggesting irreversibility of the membrane nanotube pearling coupled with phase separation. Given importance of membrane nanotube pearling in various cellular activities, these results provide a new mechanism of controlling equilibrium shapes of membrane nanotubes in complex cellular environment.

Endocytosis and Transcytosis of SARS-CoV-2 Across the Intestinal Epithelium and Other Tissue Barriers

Since 2003, the world has been confronted with three new betacoronaviruses that cause human respiratory infections: SARS-CoV, which causes severe acute respiratory syndrome (SARS), MERS-CoV, which causes Middle East respiratory syndrome (MERS), and SARS-CoV-2, which causes Coronavirus Disease 2019 (COVID-19). The mechanisms of coronavirus transmission and dissemination in the human body determine the diagnostic and therapeutic strategies. An important problem is the possibility that viral particles overcome tissue barriers such as the intestine, respiratory tract, blood-brain barrier, and placenta. In this work, we will 1) consider the issue of endocytosis and the possibility of transcytosis and paracellular trafficking of coronaviruses across tissue barriers with an emphasis on the intestinal epithelium; 2) discuss the possibility of antibody-mediated transcytosis of opsonized viruses due to complexes of immunoglobulins with their receptors; 3) assess the possibility of the virus transfer into extracellular vesicles during intracellular transport; and 4) describe the clinical significance of these processes. Models of the intestinal epithelium and other barrier tissues for in vitro transcytosis studies will also be briefly characterized.

Membrane Thinning Induces Sorting of Lipids and the Amphipathic Lipid Packing Sensor (ALPS) Protein Motif

Heterogeneities (e.g., membrane proteins and lipid domains) and deformations (e.g., highly curved membrane regions) in biological lipid membranes cause lipid packing defects that may trigger functional sorting of lipids and membrane-associated proteins. To study these phenomena in a controlled and efficient way within molecular simulations, we developed an external field protocol that artificially enhances packing defects in lipid membranes by enforcing local thinning of a flat membrane region. For varying lipid compositions, we observed strong thinning-induced depletion or enrichment, depending on the lipid's intrinsic shape and its effect on a membrane's elastic modulus. In particular, polyunsaturated and lysolipids are strongly attracted to regions high in packing defects, whereas phosphatidylethanolamine (PE) lipids and cholesterol are strongly repelled from it. Our results indicate that externally imposed changes in membrane thickness, area, and curvature are underpinned by shared membrane elastic principles. The observed sorting toward the thinner membrane region is in line with the sorting expected for a positively curved membrane region. Furthermore, we have demonstrated that the amphipathic lipid packing sensor (ALPS) protein motif, a known curvature and packing defect sensor, is effectively attracted to thinner membrane regions. By extracting the force that drives amphipathic molecules toward the thinner region, our thinning protocol can directly quantify and score the lipid packing sensing of different amphipathic molecules. In this way, our protocol paves the way toward high-throughput exploration of potential defect- and curvature-sensing motifs, making it a valuable addition to the molecular simulation toolbox.

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.

Membrane curvature induces cardiolipin sorting

Cardiolipin is a cone-shaped lipid predominantly localized in curved membrane sites of bacteria and in the mitochondrial cristae. This specific localization has been argued to be geometry-driven, since the CL's conical shape relaxes curvature frustration. Although previous evidence suggests a coupling between CL concentration and membrane shape in vivo, no precise experimental data are available for curvature-based CL sorting in vitro. Here, we test this hypothesis in experiments that isolate the effects of membrane curvature in lipid-bilayer nanotubes. CL sorting is observed with increasing tube curvature, reaching a maximum at optimal CL concentrations, a fact compatible with self-associative clustering. Observations are compatible with a model of membrane elasticity including van der Waals entropy, from which a negative intrinsic curvature of -1.1 nm-1 is predicted for CL. The results contribute to understanding the physicochemical interplay between membrane curvature and composition, providing key insights into mitochondrial and bacterial membrane organization and dynamics.

Sidewall contact regulating the nanorod packing inside vesicles with relative volumes

Intracellular packing of one-dimensional and rodlike materials plays an important role in many biological processes such as cell mimicking, microtubule protrusion, cell division, frustrated phagocytosis, and pathogenicity. To understand the mechanical interplay between cells/intracellular membranous organelles and encapsulated rodlike materials, we perform theoretical analyses to investigate how the morphologies and mechanical behaviors of lipid vesicles of given relative volumes are regulated by encapsulated rigid nanorods of finite diameters and selected geometries, including a cylindrical nanorod, a nanorod with one widened end, and a cone-shaped nanorod. The contact between the vesicle protrusion and the sidewall of the rod, neglected in most theoretical studies, is shown to play an important role in regulating vesicle tubulation, membrane tension, and axial contact force on the nanorod. As the nanorod length increases, the confining vesicle evolves from a prolate into different shapes, such as a lemon, a conga drum, a cherry, and a bowling pin, depending on the radical size of the nanorod and the relative vesicle volume. The corresponding morphological phase diagrams are determined. Moreover, phase diagrams of the buckling of the encapsulated nanorods are determined based on the classical Euler buckling theory. It is shown that there exists an optimal filament number at which the encapsulated weakly cross-linked filament bundle maintains the largest length in a mechanically stable state. Similarities and differences between the nanorod packing in vesicles at a given pressure difference and a relative volume are discussed. Our results provide valuable insight into the biophysics underlying cell interactions with one-dimensional and rodlike materials.

Relating the structure factors of two-dimensional materials in planar and spherical geometries

Scattering structure factors provide essential insight into material properties and are routinely obtained in experiments, computer simulations, and theoretical analyses. Different approaches favor different geometries of the material. In case of lipid bilayers, scattering experiments can be performed on spherical vesicles, while simulations and theory often consider planar membrane patches. We derive an approximate relationship between the structure functions of such a material in planar and spherical geometries. We illustrate the usefulness of this relationship in a case study of a Gaussian material that supports both homogeneous and microemulsion phases. Within its range of applicability, this relationship enables a model-free comparison of structure factors of the same material in different geometries.

Size-dependent formation of membrane nanotubes: continuum modeling and molecular dynamics simulations

With continuum theory and molecular dynamics simulations we demonstrated that the lipid membrane upon extraction exhibits size- and tension-dependent mechanical behaviors, and different structural lipid rearrangements in different leaflets.

Tuning interfacial patterns of molecular bonds via surface morphology

Many studies have demonstrated that the mechanical properties of the extracellular matrix can significantly influence the morphology, strength and lifetime of focal adhesions. However, how the morphology of the contact surface affects the pattern formation of the molecular bonds still remains largely unknown. Here, by simplifying the cell and extracellular matrix to two opposing elastic bodies and considering the lateral diffusion as well as the bonding/debonding of molecular bonds, we study the clustering behavior of receptor-ligand bonds between curved surfaces and the phase diagrams of cluster patterns. We reveal the important role of surface morphology and bond kinetics in regulating the patterns of bond clusters. We further investigate the segregation dynamics of the interfacial bonds under various loading speeds, and we show that the average interfacial stress is rate-dependent while the rupture stress is rate-independent. Finally, we demonstrate that programmable patterning of bond clusters can be achieved through the designed surface morphology.

Shape Transformation of the Nuclear Envelope during Closed Mitosis

The nuclear envelope (NE) in lower eukaryotes such as Schizosaccharomyces pombe undergoes large morphology changes during closed mitosis. However, which physical parameters are important in governing the shape evolution of the NE, and how defects in the dividing chromosomes/microtubules are reflected in those parameters, are fundamental questions that remain unresolved. In this study, we show that improper separation of chromosomes in genetically deficient cells leads to membrane tethering or asymmetric division in contrast to the formation of two equal-sized daughter nuclei in wild-type cells. We hypothesize that the poleward force is transmitted to the nuclear membrane through its physical contact with the separated sister chromatids at the two spindle poles. A theoretical model is developed to predict the morphology evolution of the NE where key factors such as the work done by the poleward force and bending and surface energies stored in the membrane have been taken into account. Interestingly, the predicted phase diagram, summarizing the dependence of nuclear shape on the size of the load transmission regions, and the pole-to-pole distance versus surface area relationship all quantitatively agree well with our experimental observations, suggesting that this model captures the essential physics involved in closed mitosis.

Polyunsaturated chains in asymmetric lipids disorder raft mixtures and preferentially associate with α-Synuclein

Using molecular dynamics simulations, we have explored the effect of asymmetric lipids-specifically those that contain one polyunsaturated (PUFA) and one saturated fatty acid chain-on phase separation in heterogeneous membranes. These lipids are prevalent in neuronal membranes, particularly in synaptic membranes, where the Parkinson's Disease protein α-Synuclein (αS) is found. We have therefore explored the relationship between asymmetric, PUFA-containing lipids, and αS. The simulations show that asymmetric lipids partition to the liquid disordered (Ld) phase of canonical raft mixtures because of the highly disordered PUFA chain. In the case of a membrane built to mimic the lipid composition of a synaptic vesicle, the PUFA-containing asymmetric lipids completely disrupt phase separation. Because αS is positively charged, we show that it partitions with negatively charged lipids, regardless of the saturation state of the chains. Additionally, αS preferentially associates with the polyunsaturated fatty acid tails of both charged and neutral lipids. This is a consequence of those chains' ability to accommodate the void beneath the amphipathic helix. This article is part of a Special Issue entitled: Lipid order/lipid defects and lipid-control of protein activity edited by Dirk Schneider.

Analysis of diffusion in curved surfaces and its application to tubular membranes

Diffusion of particles in curved surfaces is inherently complex compared with diffusion in a flat membrane, owing to the nonplanarity of the surface. The consequence of such nonplanar geometry on diffusion is poorly understood but is highly relevant in the case of cell membranes, which often adopt complex geometries. To address this question, we developed a new finite element approach to model diffusion on curved membrane surfaces based on solutions to Fick's law of diffusion and used this to study the effects of geometry on the entry of surface-bound particles into tubules by diffusion. We show that variations in tubule radius and length can distinctly alter diffusion gradients in tubules over biologically relevant timescales. In addition, we show that tubular structures tend to retain concentration gradients for a longer time compared with a comparable flat surface. These findings indicate that sorting of particles along the surfaces of tubules can arise simply as a geometric consequence of the curvature without any specific contribution from the membrane environment. Our studies provide a framework for modeling diffusion in curved surfaces and suggest that biological regulation can emerge purely from membrane geometry.

A model of vesicle tubulation and pearling induced by adsorbing particles

We study the basic theoretical model of a deformable vesicle immersed in a solution of particles that can adsorb onto one of the two surfaces of a membrane. The model consists of an adsorption energy gain for the adsorbing particles and the Canham-Helfrich membrane bending energy, in which the spontaneous curvature is coupled with the adsorption area. We demonstrate that bud, pearling, and tube conformations can be stabilized after minimizing the free energy and that the pearling-tubulation transition has the characteristics of an abrupt structural transition.

Aggregation dynamics of molecular bonds between compliant materials

In this paper, we develop a mechanochemical modeling framework in which the spatial-temporal evolution of receptor-ligand bonds takes place at the interface between two compliant media in the presence of an externally applied tensile load. Bond translocation, dissociation and association occur simultaneously, resulting in dynamic aggregation of molecular bonds that is regulated by mechanical factors such as material compliance and applied stress. The results show that bond aggregation is energetically favorable in the out-of-equilibrium process with convoluted time scales from bond diffusion and reaction. Material stiffness is predicted to contribute to adhesion growth and an optimal level of applied stress leads to the maximized size of bond clusters for integrin-based adhesion, consistent with related experimental observations on focal adhesions of cell-matrix interactions. The stress distribution within bond clusters is generally non-uniform and governed by the stress concentration index.

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham - Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this description, the protein is expressed in the form of a spontaneous curvature field. The approaches include field theoretical methods limited to the small deformation regime, triangulated surfaces and particle-based computational models to investigate the large-deformation regimes observed in the natural state of many biological membranes. Applications of these methods to understand the properties of biological membranes in homogeneous and inhomogeneous environments of proteins, whose underlying curvature fields are either isotropic or anisotropic, are discussed. The diversity in the curvature fields elicits a rich variety of morphological states, including tubes, discs, branched tubes, and caveola. Mapping the thermodynamic stability of these states as a function of tuning parameters such as concentration and strength of curvature induction of the proteins is discussed. The relative stabilities of these self-organized shapes are examined through free-energy calculations. The suite of methods discussed here can be tailored to applications in specific cellular settings such as endocytosis during cargo trafficking and tubulation of filopodial structures in migrating cells, which makes these methods a powerful complement to experimental studies.

Defining the free-energy landscape of curvature-inducing proteins on membrane bilayers

Curvature-sensing and curvature-remodeling proteins, such as Amphiphysin, Epsin, and Exo70, are known to reshape cell membranes, and this remodeling event is essential for key biophysical processes such as tubulation, exocytosis, and endocytosis. Curvature-inducing proteins can act as curvature sensors; they aggregate to membrane regions matching their intrinsic curvature; as well as induce curvature in cell membranes to stabilize emergent high curvature, nonspherical, structures such as tubules, discs, and caveolae. A definitive understanding of the interplay between protein recruitment and migration, the evolution of membrane curvature, and membrane morphological transitions is emerging but remains incomplete. Here, within a continuum framework and using the machinery of Monte Carlo simulations, we introduce and compare three free-energy methods to delineate the free-energy landscape of curvature-inducing proteins on bilayer membranes. We demonstrate the utility of the Widom test particle (or field) insertion methodology in computing the excess chemical potentials associated with curvature-inducing proteins on the membrane-in particular, we use this method to track the onset of morphological transitions in the membrane at elevated protein densities. We validate this approach by comparing the results from the Widom method with those of thermodynamic integration and Bennett acceptance ratio methods. Furthermore, the predictions from the Widom method have been tested against analytical calculations of the excess chemical potential at infinite dilution. Our results are useful in precisely quantifying the free-energy landscape, and also in determining the phase boundaries associated with curvature-induction, curvature-sensing, and morphological transitions. This approach can be extended to studies exploring the role of thermal fluctuations and other external (control) variables, such as membrane excess area, in shaping curvature-mediated interactions on bilayer membranes.

Multivalent immune complexes divert FcRn to lysosomes by exclusion from recycling sorting tubules

Study of receptor sorting between recycling and degradative pathways shows that sorting into the recycling pathway depends not only on recognition of sorting motifs by cytosolic adaptors, but also on the physical properties of the endosomal luminal complexes, as shown by the neonatal receptor for IgG FcRn.

The neonatal receptor for immunoglobulin G (IgG; FcRn) prevents IgG degradation by efficiently sorting IgG into recycling endosomes and away from lysosomes. When bound to IgG-opsonized antigen complexes, however, FcRn traffics cargo into lysosomes, where antigen processing can occur. Here we address the mechanism of sorting when FcRn is bound to multivalent IgG-opsonized antigens. We find that only the unbound receptor or FcRn bound to monomeric IgG is sorted into recycling tubules emerging from early endosomes. Cross-linked FcRn is never visualized in tubules containing the unbound receptor. Similar results are found for transferrin receptor, suggesting a general mechanism of action. Deletion or replacement of the FcRn cytoplasmic tail does not prevent diversion of trafficking to lysosomes upon cross-linking. Thus physical properties of the lumenal ligand–receptor complex appear to act as key determinants for sorting between the recycling and lysosomal pathways by regulating FcRn entry into recycling tubules.

Dynamic sorting of lipids and proteins in multicomponent membranes

Dynamic sorting of lipids and proteins in cellular membranes plays a critical role in establishing and maintaining distinct compositions in various organelles. Recent experiments found that the lipid sorting in a membrane tube highly depends on the pulling speed at the tip. However, the mechanism of this velocity dependence has not yet been revealed. In this Letter, we found that when a membrane is deformed rapidly, the lipid flow induced by fast membrane shape change will significantly affect the sorting results. The competition between the curvature-driven lipid sorting and the pulling-induced lipid flow leads to novel behaviors. When a membrane tube is pulled out from a liquid ordered (L(o)) domain at a constant speed, slow pulling leads to the formation of a liquid disordered (L(d)) tube, while fast pulling results in a L(o) tube. Interestingly, in a membrane tube pulled at an intermediate speed, alternate L(d) and L(o) domains appear in the tube. The sorting dynamics and the corresponding pulling force were systematically studied. The results of this study could lead to a better understanding of the dynamic sorting and traffic of lipids and proteins in living cells.

Analytical expressions for the shape of axisymmetric membranes with multiple domains

Based on the Canham-Helfrich free energy, we derive analytical expressions for the shapes of axisymmetric membranes consisting of multiple domains. We give explicit equations for both closed vesicles and almost cylindrical tubes. Using these expressions, we also find the shape of a tube attached to a spherical vesicle. The resulting shapes compare well to numerical data, and our expressions can be used to easily determine membrane parameters from experimentally obtained shapes.

Curvature-driven lipid sorting in biomembranes

It has often been suggested that the high curvature of transport intermediates in cells may be a sufficient means to segregate different lipid populations based on the relative energy costs of forming bent membranes. In this review, we present in vitro experiments that highlight the essential physics of lipid sorting at thermal equilibrium: It is driven by a trade-off between bending energy, mixing entropy, and interactions between species. We collect evidence that lipid sorting depends strongly on lipid-lipid and protein-lipid interactions, and hence on the underlying composition of the membrane and on the presence of bound proteins.

Dynamic sorting of lipids and proteins in membrane tubes with a moving phase boundary

Cellular organelle membranes maintain their integrity, global shape, and composition despite vigorous exchange among compartments of lipids and proteins during trafficking and signaling. Organelle homeostasis involves dynamic molecular sorting mechanisms that are far from being understood. In contrast, equilibrium thermodynamics of membrane mixing and sorting, particularly the phase behavior of binary and ternary model membrane mixtures and its coupling to membrane mechanics, is relatively well characterized. Elucidating the continuous turnover of live cell membranes, however, calls for experimental and theoretical membrane models enabling manipulation and investigation of directional mass transport. Here we introduce the phenomenon of curvature-induced domain nucleation and growth in membrane mixtures with fluid phase coexistence. Membrane domains were consistently observed to nucleate precisely at the junction between a strongly curved cylindrical (tube) membrane and a pipette-aspirated giant unilamellar vesicle. This experimental geometry mimics intracellular sorting compartments, because they often show tubular-vesicular membrane regions. Nucleated domains at tube necks were observed to present diffusion barriers to the transport of lipids and proteins. We find that curvature-nucleated domains grow with characteristic parabolic time dependence that is strongly curvature-dependent. We derive an analytical model that reflects the observed growth dynamics. Numerically calculated membrane shapes furthermore allow us to elucidate mechanical details underlying curvature-dependent directed lipid transport. Our observations suggest a novel dynamic membrane sorting principle that may contribute to intracellular protein and lipid sorting and trafficking.

Phospholipid demixing and the birth of a lipid droplet

The biogenesis of lipid droplets (LD) in the yeast Saccharomyces cerevisiae was theoretically investigated on basis of a biophysical model. In accordance with the prevailing model of LD formation, we assumed that neutral lipids oil-out between the membrane leaflets of the endoplasmic reticulum (ER), resulting in LD that bud-off when a critical size is reached. Mathematically, LD were modeled as spherical protuberances in an otherwise planar ER membrane. We estimated the local phospholipid composition, and calculated the change in elastic free energy of the membrane caused by nascent LD. Based on this model calculation, we found a gradual demixing of lipids in the membrane leaflet that goes along with an increase in surface curvature at the site of LD formation. During demixing, the phospholipid monolayer was able to gain energy during LD growth, which suggested that the formation of curved interfaces was supported by or even driven by lipid demixing. In addition, we show that demixing is thermodynamically necessary as LD cannot bud-off otherwise. In the case of Saccharomyces cerevisiae our model predicts a LD bud-off diameter of about 12 nm. This diameter is far below the experimentally determined size of typical yeast LD. Thus, we concluded that if the standard model of LD formation is valid, LD biogenesis is a two step process. Small LD are produced from the ER, which subsequently ripe within the cytosol through a series of fusions.

Bending stiffness depends on curvature of ternary lipid mixture tubular membranes

Lipid and protein sorting and trafficking in intracellular pathways maintain cellular function and contribute to organelle homeostasis. Biophysical aspects of membrane shape coupled to sorting have recently received increasing attention. Here we determine membrane tube bending stiffness through measurements of tube radii, and demonstrate that the stiffness of ternary lipid mixtures depends on membrane curvature for a large range of lipid compositions. This observation indicates amplification by curvature of cooperative lipid demixing. We show that curvature-induced demixing increases upon approaching the critical region of a ternary lipid mixture, with qualitative differences along two roughly orthogonal compositional trajectories. Adapting a thermodynamic theory earlier developed by M. Kozlov, we derive an expression that shows the renormalized bending stiffness of an amphiphile mixture membrane tube in contact with a flat reservoir to be a quadratic function of curvature. In this analytical model, the degree of sorting is determined by the ratio of two thermodynamic derivatives. These derivatives are individually interpreted as a driving force and a resistance to curvature sorting. We experimentally show this ratio to vary with composition, and compare the model to sorting by spontaneous curvature. Our results are likely to be relevant to the molecular sorting of membrane components in vivo.

Curvature-driven lipid sorting needs proximity to a demixing point and is aided by proteins

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.