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.     

Membrane bending by protein-protein crowding

Curved membranes are an essential feature of dynamic cellular structures, including endocytic pits, filopodia protrusions and most organelles. It has been proposed that specialized proteins induce curvature by binding to membranes through two primary mechanisms: membrane scaffolding by curved proteins or complexes; and insertion of wedge-like amphipathic helices into the membrane. Recent computational studies have raised questions about the efficiency of the helix-insertion mechanism, predicting that proteins must cover nearly 100% of the membrane surface to generate high curvature, an improbable physiological situation. Thus, at present, we lack a sufficient physical explanation of how protein attachment bends membranes efficiently. On the basis of studies of epsin1 and AP180, proteins involved in clathrin-mediated endocytosis, we propose a third general mechanism for bending fluid cellular membranes: protein-protein crowding. By correlating membrane tubulation with measurements of protein densities on membrane surfaces, we demonstrate that lateral pressure generated by collisions between bound proteins drives bending. Whether proteins attach by inserting a helix or by binding lipid heads with an engineered tag, protein coverage above ~20% is sufficient to bend membranes. Consistent with this crowding mechanism, we find that even proteins unrelated to membrane curvature, such as green fluorescent protein (GFP), can bend membranes when sufficiently concentrated. These findings demonstrate a highly efficient mechanism by which the crowded protein environment on the surface of cellular membranes can contribute to membrane shape change.     

Crowding-induced membrane remodeling: Interplay of membrane tension,polymer density,architecture

The plasma membrane hosts a wide range of biomolecules, mainly proteins and carbohydrates, that mediate cellular interactions with its environment. The crowding of such biomolecules regulates cellular morphologies and cellular trafficking. Recent discoveries have shown that the structure and density of cell surface polymers and hence the signaling machinery change with the state of the cell, especially in cancer progression. The alterations in membrane-attached glycocalyx and glycosylation of proteins and lipids are common features of cancer cells. The overexpression of glycocalyx polymers, such as mucin and hyaluronan, strongly correlates with cancer metastasis. Here, we present a mesoscale biophysics-based model that accounts for the shape regulation of membranes by crowding of membrane-attached biopolymer-glycocalyx and actin networks. Our computational model is based on the dynamically triangulated Monte Carlo model for membranes and coarse-grained representations of polymer chains. The model allows us to investigate the crowding-induced shape transformations in cell membranes in a tension- and graft polymer density-dependent manner. Our results show that the number of membrane protrusions and their shape depend on membrane tension, with higher membrane tension inducing more tubular protrusions than the vesicular shapes formed at low tension at high surface coverage of polymers. The shape transformations occur above the threshold density predicted by the polymer brush theory, but this threshold also depends on the membrane tension. Increasing the size of the polymer, either by changing the length or by adding side chains, is shown to increase the crowding-induced curvature. The effect of crowding is more prominent for flexible polymers than for semiflexible rigid polymers. We also present an extension of the model that incorporates properties of the actin-like filament networks and demonstrate how tubular structures can be generated by biopolymer crowding on the cytosolic side of cell membranes.     

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.     

Membrane shape changes at initial stage of membrane fusion under the action of proteins inducing spontaneous curvature

This paper studies change of membrane shape at the initial stage of the fusion process due to the fusion proteins inducing spontaneous curvature in the membrane. As protein inclusions are embedded into the membrane, a highly curved surface forms in the center of the membrane; it facilitates the formation of short-lived hydrophobic defects and leads to the merger of the contact monolayers of the membranes. Membrane is considered as continuous liquid-crystal medium subject to elastic deformations. One deformational mode of splay is taken into account; energy is calculated in the quadratic approximation on this deformation. In case of positive spontaneous curvature induced by the protein there is no bulge on the top of the membrane despite high deviation of membrane shape from the equilibrium state. In case of negative spontaneous curvature a bulge is formed and its height and curvature increase with the increase of the membrane curvature in the initial state.     

Diffusion on Membrane Domes,Tubes, and Pearling Structures

Diffusion is a fundamental mechanism for protein distribution in cell membranes. These membranes often exhibit complex shapes, which range from shallow domes to elongated tubular or pearl-like structures. Shape complexity of the membrane influences the diffusive spreading of proteins and molecules. Despite the importance membrane geometry plays in these diffusive processes, it is challenging to establish the dependence between diffusion and membrane morphology. We solve the diffusion equation numerically on various static curved shapes representative for experimentally observed membrane shapes. Our results show that membrane necks become diffusion barriers. We determine the diffusive half-time, i.e., the time that is required to reduce the amount of protein in the budded region by one half, and find a quadratic relation between the diffusive half-time and the averaged mean curvature of the membrane shape, which we rationalize by a scaling law. Our findings thus help estimate the characteristic diffusive timescale based on the simple measure of membrane mean curvature.     

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.     

AMPs and OMPs: Is the folding and bilayer insertion of β-stranded outer membrane proteins governed by the same biophysical principles as for α-helical antimicrobial peptides?

The folding and function of membrane proteins is controlled not only by specific but also by unspecific interactions with the constituent lipids. In this review, we focus on the influence of the spontaneous lipid curvature on the folding and insertion of peptides and proteins in membranes. Amphiphilic α-helical peptides, as represented by various antimicrobial sequences, are compared with β-barrel proteins, which are found in the outer membrane of Gram-negative bacteria. It has been shown that cationic amphiphilic peptides are always surface-bound in lipids with a negative spontaneous curvature like POPC, i.e. they are oriented parallel to the membrane plane. On the other hand, in lipids like DMPC with a positive curvature, these peptides can get tilted or completely inserted in a transmembrane state. Remarkably, the folding and spontaneous membrane insertion of β-barrel outer membrane proteins also proceeds more easily in lipids with a positive intrinsic curvature, while it is hampered by negative curvature. We therefore propose that a positive spontaneous curvature of the lipids promotes the ability of a surface-bound molecule to insert more deeply into the bilayer core, irrespective of the conformation, size, or shape of the peptide, protein, or folding intermediate. This article is part of a Special Issue entitled: Lipid-protein interactions.     

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.     

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.     

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.     

Observed steric crowding at modest coverage requires a particular membrane-binding scheme or a complementary mechanism

Membrane shape transitions, including fusion and fission, play an important role in many biological processes. It is therefore essential to understand mechanisms of “curvature generation,” the mathematical quantification of membrane shape. Among the different mechanisms is the effect of steric pressure between proteins crowded on a surface. At a higher curvature, there is more space for the crowders and less steric pressure. Currently, the physical model of curvature induction by crowding views the proteins as being bound to the surface as a whole rather than to the underlying lipids. Here, we split the previously understood model into two pieces: first, the reduction in steric pressure due to reduced collisions between proteins, and second, the increased area available to the protein that is independent of other crowders. The cases are distinguished by how the crowder is attached to the membrane. When a protein is attached to a specific lipid, as is the case in a typical crowding experiment, one should not model its lateral entropy; this has already been accounted for by the underlying lipid. The Carnahan-Starling pressure includes this lateral entropy. The revised theory predicts that a purely entropic crowding mechanism is inconsistent with observations of reshaping at the lower range of surface coverage, suggesting that an additional mechanism is at play.     

Modeling protein-mediated morphology in biomembranes

The equilibrium theory for lipid membranes is used to describe the structure of nuclear pores and the membrane shapes accompanying endocytosis. The commonly used variant of the theory contains a fixed parameter called the spontaneous curvature which accounts for asymmetry in the bending response of the membrane. This is replaced here by a variable distribution of spontaneous curvature representing the influence of attached proteins. The required adjustments to the standard theory are described and the resulting model is applied to the study of membrane morphology at the cites of protein-assisted nuclear pore formation and endocytosis.     

Spontaneous local membrane curvature induced by transmembrane proteins

The (local) curvature of cellular membranes acts as a driving force for the targeting of membrane-associated proteins to specific membrane domains, as well as a sorting mechanism for transmembrane proteins, e.g., by accumulation in regions of matching spontaneous curvature. The latter measure was previously experimentally employed to study the curvature induced by the potassium channel KvAP and by aquaporin AQP0. However, the direction of the reported spontaneous curvature levels as well as the molecular driving forces governing the membrane curvature induced by these integral transmembrane proteins could not be addressed experimentally.Here, using both coarse-grained and atomistic molecular dynamics (MD) simulations, we report induced spontaneous curvature values for the homologous potassium channel Kv 1.2/2.1 Chimera (KvChim) and AQP0 embedded in unrestrained lipid bicelles that are in very good agreement with experiment. Importantly, the direction of curvature could be directly assessed from our simulations: KvChim induces a strong positive membrane curvature ($\approx 0.036$ nm^?1) whereas AQP0 causes a comparably small negative curvature ($\approx ?0.019$ nm^?1).Analyses of protein-lipid interactions within the bicelle revealed that the potassium channel shapes the surrounding membrane via structural determinants. Differences in shape of the protein-lipid interface of the voltage-gating domains between the extracellular and cytosolic membrane leaflets induce membrane stress and thereby promote a protein-proximal membrane curvature. In contrast, the water pore AQP0 displayed a high structural stability and an only faint effect on the surrounding membrane environment that is connected to its wedge-like shape.     

Elastic energy of curvature-driven bump formation on red blood cell membrane.

Model calculations were performed to explore quantitative aspects of the discocyte-echinocyte shape transformation in red blood cells. The shape transformation was assumed to be driven by changes in the preferred curvature of the membrane bilayer and opposed by the elastic shear rigidity of the membrane skeleton. The energy required for echinocyte bump formation was calculated for a range of bump shapes for different preferred curvatures. Energy minima corresponding to nonzero bump heights were found when the stress-free area difference between the membrane leaflets or the spontaneous curvature of the membrane became sufficiently large, but the calculations predict that the membrane can tolerate significant differences in the resting areas of the inner and outer leaflets or significant spontaneous curvature without visible changes in shape. Thus, if the cell is near the threshold for bump formation, the calculations predict that small changes in membrane properties would produce large changes in cellular geometry. These results provide a rational framework for interpreting observations of shape transformations in red cells and for understanding the mechanism by which small changes in membrane elastic properties might lead to significant changes in geometry.     

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.     

Modeling membrane shaping by proteins: Focus on EHD2 and N-BAR domains

Cellular membranes are highly dynamic, undergoing both persistent and dynamic shape changes driven by specialized proteins. The observed membrane shaping can be simple deformations of existing shapes or membrane remodeling involving fission or fusion. Here we describe several mechanistic principles by which membrane shaping proteins act. We especially consider models for membrane bending and fission by EHD2 proteins and membrane bending by N-BAR domains. There are major challenges ahead to understand the general principles by which diverse membrane bending proteins act and to understand how some proteins appear to span multiple modes of action from driving curvature to inducing membrane remodeling.     

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.     

Entropic tension in crowded membranes

Unlike their model membrane counterparts, biological membranes are richly decorated with a heterogeneous assembly of membrane proteins. These proteins are so tightly packed that their excluded area interactions can alter the free energy landscape controlling the conformational transitions suffered by such proteins. For membrane channels, this effect can alter the critical membrane tension at which they undergo a transition from a closed to an open state, and therefore influence protein function in vivo. Despite their obvious importance, crowding phenomena in membranes are much less well studied than in the cytoplasm. Using statistical mechanics results for hard disk liquids, we show that crowding induces an entropic tension in the membrane, which influences transitions that alter the projected area and circumference of a membrane protein. As a specific case study in this effect, we consider the impact of crowding on the gating properties of bacterial mechanosensitive membrane channels, which are thought to confer osmoprotection when these cells are subjected to osmotic shock. We find that crowding can alter the gating energies by more than [Formula: see text] in physiological conditions, a substantial fraction of the total gating energies in some cases. Given the ubiquity of membrane crowding, the nonspecific nature of excluded volume interactions, and the fact that the function of many membrane proteins involve significant conformational changes, this specific case study highlights a general aspect in the function of membrane proteins.     

Prefission constriction of Golgi tubular carriers driven by local lipid metabolism: a theoretical model

Membrane transport within mammalian cells is mediated by small vesicular as well as large pleiomorphic transport carriers (TCs). A major step in the formation of TCs is the creation and subsequent narrowing of a membrane neck connecting the emerging carrier with the initial membrane. In the case of small vesicular TCs, neck formation may be directly induced by the coat proteins that cover the emerging vesicle. However, the mechanism underlying the creation and narrowing of a membrane neck in the generation of large TCs remains unknown. We present a theoretical model for neck formation based on the elastic model of membranes. Our calculations suggest a lipid-driven mechanism with a central role for diacylglycerol (DAG). The model is applied to a well-characterized in vitro system that reconstitutes TC formation from the Golgi complex, namely the pearling and fission of Golgi tubules induced by CtBP/BARS, a protein that catalyzes the conversion of lysophosphatidic acid into phosphatidic acid. In view of the importance of a PA-DAG cycle in the formation of Golgi TCs, we assume that the newly formed phosphatidic acid undergoes rapid dephosphorylation into DAG. DAG possesses a unique molecular shape characterized by an extremely large negative spontaneous curvature, and it redistributes rapidly between the membrane monolayers and along the membrane surface. Coupling between local membrane curvature and local lipid composition results, by mutual enhancement, in constrictions of the tubule into membrane necks, and a related inhomogeneous lateral partitioning of DAG. Our theoretical model predicts the exact dimensions of the constrictions observed in the pearling Golgi tubules. Moreover, the model is able to explain membrane neck formation by physiologically relevant mole fractions of DAG.