Membrane shape remodeling by protein crowding

The steric repulsion between proteins on biological membranes is one of the most generic mechanisms that cause membrane shape changes. We present a minimal model in which a spontaneous curvature is induced by asymmetric protein crowding. Our results show that the interplay between the induced spontaneous curvature and the membrane tension determines the energy-minimizing shapes, which describes the wide range of experimentally observed membrane shapes, i.e., flat membranes, spherical vesicles, elongated tubular protrusions, and pearling structures. Moreover, the model gives precise predictions on how membrane shape changes by protein crowding can be tuned by controlling the protein size, the density of proteins, and the size of the crowded domain.     

Nonlinear sorting, curvature generation, and crowding of endophilin N-BAR on tubular membranes

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.     

Membrane Morphology Is Actively Transformed by Covalent Binding of the Protein Atg8 to PE-Lipids

Autophagy is a cellular degradation pathway involving the shape transformation of lipid bilayers. During the onset of autophagy, the water-soluble protein Atg8 binds covalently to phosphatdylethanolamines (PEs) in the membrane in an ubiquitin-like reaction coupled to ATP hydrolysis. We reconstituted the Atg8 conjugation system in giant and nm-sized vesicles with a minimal set of enzymes and observed that formation of Atg8-PE on giant vesicles can cause substantial tubulation of membranes even in the absence of Atg12-Atg5-Atg16. Our findings show that ubiquitin-like processes can actively change properties of lipid membranes and that membrane crowding by proteins can be dynamically regulated in cells. Furthermore we provide evidence for curvature sorting of Atg8-PE. Curvature generation and sorting are directly linked to organelle shapes and, thus, to biological function. Our results suggest that a positive feedback exists between the ubiquitin-like reaction and the membrane curvature, which is important for dynamic shape changes of cell membranes, such as those involved in the formation of autophagosomes.     

The hydrophobic insertion mechanism of membrane curvature generation by proteins

A wide spectrum of intracellular processes is dependent on the ability of cells to dynamically regulate membrane shape. Membrane bending by proteins is necessary for the generation of intracellular transport carriers and for the maintenance of otherwise intrinsically unstable regions of high membrane curvature in cell organelles. Understanding the mechanisms by which proteins curve membranes is therefore of primary importance. Here we suggest, for the first time to our knowledge, a quantitative mechanism of lipid membrane bending by hydrophobic or amphipathic rodlike inclusions which simulate amphipathic α-helices—structures shown to sculpt membranes. Considering the lipid monolayer matrix as an anisotropic elastic material, we compute the intramembrane stresses and strains generated by the embedded inclusions, determine the resulting membrane shapes, and the accumulated elastic energy. We characterize the ability of an inclusion to bend membranes by an effective spontaneous curvature, and show that shallow rodlike inclusions are more effective in membrane shaping than are lipids having a high propensity for curvature. Our computations provide experimentally testable predictions on the protein amounts needed to generate intracellular membrane shapes for various insertion depths and membrane thicknesses. We also predict that the ability of N-BAR domains to produce membrane tubules in vivo can be ascribed solely to insertion of their amphipathic helices.     

Protein shape and crowding drive domain formation and curvature in biological membranes

Folding, curvature, and domain formation are characteristics of many biological membranes. Yet the mechanisms that drive both curvature and the formation of specialized domains enriched in particular protein complexes are unknown. For this reason, studies in membranes whose shape and organization are known under physiological conditions are of great value. We therefore conducted atomic force microscopy and polarized spectroscopy experiments on membranes of the photosynthetic bacterium Rhodobacter sphaeroides. These membranes are densely populated with peripheral light harvesting (LH2) complexes, physically and functionally connected to dimeric reaction center-light harvesting (RC-LH1-PufX) complexes. Here, we show that even when converting the dimeric RC-LH1-PufX complex into RC-LH1 monomers by deleting the gene encoding PufX, both the appearance of protein domains and the associated membrane curvature are retained. This suggests that a general mechanism may govern membrane organization and shape. Monte Carlo simulations of a membrane model accounting for crowding and protein geometry alone confirm that these features are sufficient to induce domain formation and membrane curvature. Our results suggest that coexisting ordered and fluid domains of like proteins can arise solely from asymmetries in protein size and shape, without the need to invoke specific interactions. Functionally, coexisting domains of different fluidity are of enormous importance to allow for diffusive processes to occur in crowded conditions.     

Protein-Induced Membrane Curvature Alters Local Membrane Tension

Adsorption of proteins onto membranes can alter the local membrane curvature. This phenomenon has been observed in biological processes such as endocytosis, tubulation, and vesiculation. However, it is not clear how the local surface properties of the membrane, such as membrane tension, change in response to protein adsorption. In this article, we show that the partial differential equations arising from classical elastic model of lipid membranes, which account for simultaneous changes in shape and membrane tension due to protein adsorption in a local region, cannot be solved for nonaxisymmetric geometries using straightforward numerical techniques; instead, a viscous-elastic formulation is necessary to fully describe the system. Therefore, we develop a viscous-elastic model for inhomogeneous membranes of the Helfrich type. Using the newly available viscous-elastic model, we find that the lipids flow to accommodate changes in membrane curvature during protein adsorption. We show that, at the end of protein adsorption process, the system sustains a residual local tension to balance the difference between the actual mean curvature and the imposed spontaneous curvature. We also show that this change in membrane tension can have a functional impact such as altered response to pulling forces in the presence of proteins.     

Simulations of (an)isotropic diffusion on curved biological surfaces

We present a computational particle method for the simulation of isotropic and anisotropic diffusion on curved biological surfaces that have been reconstructed from image data. The method is capable of handling surfaces of high curvature and complex shape, which are often encountered in biology. The method is validated on simple benchmark problems and is shown to be second-order accurate in space and time and of high parallel efficiency. It is applied to simulations of diffusion on the membrane of endoplasmic reticula (ER) in live cells. Diffusion simulations are conducted on geometries reconstructed from real ER samples and are compared to fluorescence recovery after photobleaching experiments in the same ER samples using the transmembrane protein tsO45-VSV-G, C-terminally tagged with green fluorescent protein. Such comparisons allow derivation of geometry-corrected molecular diffusion constants for membrane components from fluorescence recovery after photobleaching data. The results of the simulations indicate that the diffusion behavior of molecules in the ER membrane differs significantly from the volumetric diffusion of soluble molecules in the lumen of the same ER. The apparent speed of recovery differs by a factor of approximately 4, even when the molecular diffusion constants of the two molecules are identical. In addition, the specific shape of the membrane affects the recovery half-time, which is found to vary by a factor of approximately 2 in different ER samples.     

Protein-Induced Membrane Curvature Alters Local Membrane Tension

Adsorption of proteins onto membranes can alter the local membrane curvature. This phenomenon has been observed in biological processes such as endocytosis, tubulation, and vesiculation. However, it is not clear how the local surface properties of the membrane, such as membrane tension, change in response to protein adsorption. In this article, we show that the partial differential equations arising from classical elastic model of lipid membranes, which account for simultaneous changes in shape and membrane tension due to protein adsorption in a local region, cannot be solved for nonaxisymmetric geometries using straightforward numerical techniques; instead, a viscous-elastic formulation is necessary to fully describe the system. Therefore, we develop a viscous-elastic model for inhomogeneous membranes of the Helfrich type. Using the newly available viscous-elastic model, we find that the lipids flow to accommodate changes in membrane curvature during protein adsorption. We show that, at the end of protein adsorption process, the system sustains a residual local tension to balance the difference between the actual mean curvature and the imposed spontaneous curvature. We also show that this change in membrane tension can have a functional impact such as altered response to pulling forces in the presence of proteins.     

Lipids in biological membrane fusion

The results reviewed suggest that membrane fusion in diverse biological fusion reactions involves formation of some specific intermediates: stalks and pores. Energy of these intermediates and, consequently, the rate and extent of fusion depend on the propensity of the corresponding monolayers of membranes to bend in the required directions.Proteins and peptides can control the bending energy of membrane monolayers in a number of ways. Monolayer lipid composition may be altered by different phospholipases [50, 85, 90], flipases and translocases [4, 50]. Proteins and peptides can change monolayer spontaneous curvature or hydrophobic void energy by direct interaction with membrane lipids [20, 32, 111]. Proteins may also provide some barriers for lipid diffusion in the plane of the monolayer [83, 141]. If diffusion of lipids at some specific membrane sites (e.g., in the vicinity of fusion protein) is somehow hindered, the energy of the bent fusion intermediates would reflect the elastic properties of these particular sites rather than the spontaneous curvature of the whole monolayers. Proteins may deform membranes while bringing them locally into close contact. The alteration of the geometric (external) curvature will certainly change the elastic energy of the initial state and, thus affect the energetic barriers of the formation of the intermediates [143]. In addition, the area and the energy of the stalk can be reduced by preliminary bending of the contacting membranes [111]. The possible effects of proteins and polymers on local elastic properties and local shapes of the membranes have been recently analyzed [22, 39, 45, 63]. These studies may provide a good basis for future development of theoretical models of protein-mediated fusion.     

Sensing Membrane Stresses by Protein Insertions

Protein domains shallowly inserting into the membrane matrix are ubiquitous in peripheral membrane proteins involved in various processes of intracellular membrane shaping and remodeling. It has been suggested that these domains sense membrane curvature through their preferable binding to strongly curved membranes, the binding mechanism being mediated by lipid packing defects. Here we make an alternative statement that shallow protein insertions are universal sensors of the intra-membrane stresses existing in the region of the insertion embedding rather than sensors of the curvature per se. We substantiate this proposal computationally by considering different independent ways of the membrane stress generation among which some include changes of the membrane curvature whereas others do not alter the membrane shape. Our computations show that the membrane-binding coefficient of shallow protein insertions is determined by the resultant stress independently of the way this stress has been produced. By contrast, consideration of the correlation between the insertion binding and the membrane curvature demonstrates that the binding coefficient either increases or decreases with curvature depending on the factors leading to the curvature generation. To validate our computational model, we treat quantitatively the experimental results on membrane binding by ALPS1 and ALPS2 motifs of ArfGAP1.     

Erythrocyte shape simulation by numerical optimization

In a recent paper we examined the morphology of erythrocytes in terms of the mean mean curvature (MMC) of their cell membranes. A computer simulation of these shapes based on the different geometries showed that the MMC increased from the sphero-stomatocyte to the spheroechinocyte via the discocyte. In this work we extend this analysis by using a numerical optimization method based on importance sampling and the principle of adiabatic cooling. The erythrocyte membrane is treated as a single closed fluid lamina exhibiting viscoelastic characteristics. The energy function of the lamina includes the following terms: (i) Curvature-elastic energy terms which depend on both local and global curvature. (ii) A term describing the compression elasticity of the lamina. (iii) A term which depends on the volume of the cell and which is related to the osmotic pressure across the membrane. In the simulation the cell is assumed to have axial symmetry and it can therefore be described by a finite set of conic sections. So far we have been able to obtain an energy minimum corresponding to a discocyte shape using a sphere as the initial configuration. Our results therefore imply that the well-known sequence of erythrocyte shapes could solely be governed by the above mentioned properties of an ideal fluid forming a closed singly connected lamina.     

The Vesicle Trafficking Protein Sar1 Lowers Lipid Membrane Rigidity

The sculpting of membranes into dynamic, curved shapes is central to intracellular cargo trafficking. Though the generation of membrane curvature during trafficking necessarily involves both lipids and membrane-associated proteins, current mechanistic views focus primarily on the formation of rigid cages and curved scaffolds by protein assemblies. Here we report on a different mechanism for the control of membrane deformation, unrelated to the imposition of predefined curvature, involving modulation of membrane material properties: Sar1, a GTPase that regulates vesicle trafficking from the endoplasmic reticulum, lowers the rigidity of the lipid bilayer membrane to which it binds. In vitro assays in which optically trapped microspheres create controlled membrane deformations revealed a monotonic decline in bending modulus as a function of Sar1 concentration, down to nearly zero rigidity, indicating a dramatic lowering of the energetic cost of curvature generation. This is the first demonstration that a vesicle trafficking protein lowers the rigidity of its target membrane, leading to a new conceptual framework for vesicle biogenesis.     

Membrane-Mediated Interaction between Strongly Anisotropic Protein Scaffolds

Specialized proteins serve as scaffolds sculpting strongly curved membranes of intracellular organelles. Effective membrane shaping requires segregation of these proteins into domains and is, therefore, critically dependent on the protein-protein interaction. Interactions mediated by membrane elastic deformations have been extensively analyzed within approximations of large inter-protein distances, small extents of the protein-mediated membrane bending and small deviations of the protein shapes from isotropic spherical segments. At the same time, important classes of the realistic membrane-shaping proteins have strongly elongated shapes with large and highly anisotropic curvature. Here we investigated, computationally, the membrane mediated interaction between proteins or protein oligomers representing membrane scaffolds with strongly anisotropic curvature, and addressed, quantitatively, a specific case of the scaffold geometrical parameters characterizing BAR domains, which are crucial for membrane shaping in endocytosis. In addition to the previously analyzed contributions to the interaction, we considered a repulsive force stemming from the entropy of the scaffold orientation. We computed this interaction to be of the same order of magnitude as the well-known attractive force related to the entropy of membrane undulations. We demonstrated the scaffold shape anisotropy to cause a mutual aligning of the scaffolds and to generate a strong attractive interaction bringing the scaffolds close to each other to equilibrium distances much smaller than the scaffold size. We computed the energy of interaction between scaffolds of a realistic geometry to constitute tens of k_BT, which guarantees a robust segregation of the scaffolds into domains.     

Effect of surface curvature on the rate of cholesterol transfer between lipid vesicles.

The effect of surface curvature on the spontaneous movement of cholesterol between membranes was investigated by measuring the rates of cholesterol transfer from donor vesicles of various sizes to a common acceptor vesicle. Donor vesicles of size in the range 40-240 nm were prepared by extruding multilamellar dispersions through polycarbonate filters of different pore sizes under pressure. The smallest donor vesicle and the acceptor vesicles were obtained by the normal sonication procedures. The rate of cholesterol transfer, as measured by the movement of [3H]cholesterol, decreases with increasing size of the donor vesicle in an almost linear fashion. The extrapolation of the results gave a half-time (t1/2) of 16-20 h of the desorption of cholesterol from a planar bilayer, and this can be considered as a reference value for most cellular membranes which are characterized by very low curvatures. Our earlier studies have shown that the t1/2 for cholesterol efflux is influenced by the presence of gangliosides and phosphatidylethanolamine, and the asymmetric distribution of these lipids in the plasma membrane could partially account for the large difference in the rates of cholesterol movement from the two sides of the plasma membrane. The small differences in rates arising from asymmetric distribution will be magnified by the longer t1/2 obtained here for membranes of low curvatures, so that the large difference in rates might be a coupled effect of lipid asymmetry and low curvature of the plasma membrane. This, in turn, may have a role in maintaining the large differences in cholesterol/phospholipid molar ratios observed between plasma membrane and intracellular membranes.     

Spectrin, red cell shape and deformability. II. The antagonistic action of spectrin and sialic acid residues in determining membrane curvature in genetic spectrin deficiency in mice

In a companion paper, the shapes of spectrin deficient mouse erythrocytes were described; in contrast to previous assumptions, spherules with tethered microvesicles rather than true "spherocytes" were found. Thence, spectrin deficient mouse erythrocytes are endowed with an excess of surface area for the given volume but the membrane is assuming a highly positive curvature. Observations during and after the action of enzymes cleaving the red cell surface charge (Neuraminidase, Trypsin, Chymotrypsin) showed that the previously positive membrane curvature, as well as the tendency of the membrane to flow into fingerlike protrusions was completely abolished. The erythrocytes of the spectrin deficient, desialylated mouse erythrocytes assumed a variety of shapes, often discocytic or even stomatocytic, i.e. their membrane presented with negative curvature. However, while these desialylated membranes could be easily deformed (elongated) by shear flow they did not recoil elastically into any definitive configuration after removal of the deforming forces. It is concluded from these observations that spectrin (acting on the inner interface between membrane and cytoplasm) and sialic acid residues (acting on the outer interface between membrane and plasma) exert antagonizing effects on membrane curvature and membrane bending elasticity. Sialic acid residues, strongly charged and situated on the outer side of the cell, produce positive membrane curvature; this observation can most readily be explained by assuming that this mechanical effect is caused by repulsive coulombic forces expanding the outer half of the bilayer. To explain the effect of the spectrin-complex in counteracting positive or in producing negative membrane curvature, a similar expansive coulombic force acting between the highly charged residues has been postulated. Thence, a model for explaining the overall elastic behaviour of the normal mammalian red cell is developed which is based on the assumption of elastic interactions of proteinacous membrane components coupled to the lipid bilayer of the membrane.     

Dynamic Partitioning of a Glycosyl-Phosphatidylinositol-Anchored Protein in Glycosphingolipid-Rich Microdomains Imaged by Single-Quantum Dot Tracking

Recent experimental developments have led to a revision of the classical fluid mosaic model proposed by Singer and Nicholson more than 35 years ago. In particular, it is now well established that lipids and proteins diffuse heterogeneously in cell plasma membranes. Their complex motion patterns reflect the dynamic structure and composition of the membrane itself, as well as the presence of the underlying cytoskeleton scaffold and that of the extracellular matrix. How the structural organization of plasma membranes influences the diffusion of individual proteins remains a challenging, yet central, question for cell signaling and its regulation. Here we have developed a raft-associated glycosyl-phosphatidyl-inositol-anchored avidin test probe (Av-GPI), whose diffusion patterns indirectly report on the structure and dynamics of putative raft microdomains in the membrane of HeLa cells. Labeling with quantum dots (qdots) allowed high-resolution and long-term tracking of individual Av-GPI and the classification of their various diffusive behaviors. Using dual-color total internal reflection fluorescence (TIRF) microscopy, we studied the correlation between the diffusion of individual Av-GPI and the location of glycosphingolipid GM1-rich microdomains and caveolae. We show that Av-GPI exhibit a fast and a slow diffusion regime in different membrane regions, and that slowing down of their diffusion is correlated with entry in GM1-rich microdomains located in close proximity to, but distinct, from caveolae. We further show that Av-GPI dynamically partition in and out of these microdomains in a cholesterol-dependent manner. Our results provide direct evidence that cholesterol-/sphingolipid-rich microdomains can compartmentalize the diffusion of GPI-anchored proteins in living cells and that the dynamic partitioning raft model appropriately describes the diffusive behavior of some raft-associated proteins across the plasma membrane.     

A unifying mechanism accounts for sensing of membrane curvature by BAR domains,amphipathic helices and membrane-anchored proteins

The discovery of proteins that recognize membrane curvature created a paradigm shift by suggesting that membrane shape may act as a cue for protein localization that is independent of lipid or protein composition. Here we review recent data on membrane curvature sensing by three structurally unrelated motifs: BAR domains, amphipathic helices and membrane-anchored proteins. We discuss the conclusion that the curvature of the BAR dimer is not responsible for sensing and that the sensing properties of all three motifs can be rationalized by the physicochemical properties of the curved membrane itself. We thus anticipate that membrane curvature will promote the redistribution of proteins that are anchored in membranes through any type of hydrophobic moiety, a thesis that broadens tremendously the implications of membrane curvature for protein sorting, trafficking and signaling in cell biology.     

Lateral diffusion anisotropy and membrane lipid/skeleton interaction in outer hair cells

The organization of the plasma membrane of cells in lipid domains affects the way the membrane interacts with the underlying protein skeleton, which in turn affects the lateral mobility of lipid and protein molecules in the membrane. Membrane fluidity properties can be monitored by various approaches, the most versatile of which is fluorescence recovery after photobleaching (FRAP). We extended previous FRAP experiments on isolated cochlear outer hair cells (OHCs) by analyzing the two-dimensional pattern of lipid diffusion in the lateral membrane of these cells. We found that membrane lipid mobility in freshly isolated OHCs is orthotropic, diffusion being faster in the axial direction of the cell and slower in the circumferential direction. Increasing the cell's turgor pressure by osmotic challenge reduced the axial diffusion constant, but had only a slight effect on circumferential diffusion. Our results suggest that lipid mobility in the OHC plasma membrane is affected by the presence of the cell's orthotropic membrane skeleton. This effect could reflect interaction with spectrin filaments or with other membrane skeletal proteins. We also performed a number of FRAP measurements in temporal bone preparations preserving the structural integrity of the hearing organ. The diffusion rates measured for OHCs in this preparation were in good agreement with those obtained in isolated OHCs, and comparable to the mobility rates measured on the sensory inner hair cells. These observations support the idea that the plasma membranes of both types of hair cells share similar highly fluid phases in the intact organ. Lipid mobility was significantly slower in the membranes of supporting cells of the organ of Corti, which could reflect differences in lipid phase or stronger hindrance by the cytoskeleton in these membranes.     

The diffusive vesicle supply center model for tip growth in fungal hyphae

We propose the diffusive vesicle supply center model for tip growth in fungal hyphae. The model is based on the three-dimensional vesicle supply center (VSC) model [Gierz, G., Bartnicki-García, S., 2001. A three-dimensional model of fungal morphogenesis based on the vesicle supply center concept: J. Theor. Biol. 208, 151-164], but incorporates two aspects of a more realistic vesicle delivery mechanism: vesicle diffusion from the VSC and a finite rate constant for vesicle fusion with the cell membrane. We develop a framework to describe tip growth for a general class of models based on the vesicle supply center concept. Combining this with a method for calculating the steady state distribution of diffusive vesicles we iteratively solve for stationary cell shapes. These show a blunter tip than predicted by the original VSC model, which we attribute to increased forward-directed vesicle delivery via diffusion. The predicted distance between the VSC and the utmost tip of the cell is set by the ratio between the diffusion constant and the rate constant for vesicle exocytosis. Combined with the cell radius, these define the only dimensionless parameter for our model.