A Cost–Benefit Analysis of the Physical Mechanisms of Membrane Curvature

REVIEW

A cost–benefit analysis of the physical mechanisms of membrane curvature

Jeanne C. Stachowiak, Frances M. Brodsky and Elizabeth A. Miller

Many cellular membrane-bound structures exhibit distinct curvature that is driven by the physical properties of their lipid and protein constituents. Here we review how cells manipulate and control this curvature in the context of dynamic events such as vesicle-mediated membrane traffic. Lipids and cargo proteins each contribute energy barriers that must be overcome during vesicle formation. In contrast, protein coats and their associated accessory proteins drive membrane bending using a variety of interdependent physical mechanisms. We survey the energy costs and drivers involved in membrane curvature, and draw a contrast between the stochastic contributions of molecular crowding and the deterministic assembly of protein coats. These basic principles also apply to other cellular examples of membrane bending events, including important disease-related problems such as viral egress.

Cellular membranes, which partition eukaryotic cells into distinct The current challenge is to understand how the cooperative energy compartments, possess an intrinsic simplicity that belies their com- contributions of multiple active components drive bending of complex plex gymnastics during normal cellular function. The majority of membranes composed of diverse lipids and proteins. Cellular membrane cellular membranes are planar lipid bilayers. These are influenced by bending also occurs in the context of organized tissue or in the face of intrinsic and extrinsic forces to generate the curved structures that are turgor pressure, factors that introduce additional energy barriers, neces- associated with diverse cellular architectures (Fig. 1). Curved mem- sitating additional force. Here we review the multiple physical mecha- branes can be relatively stable structures — such as those surrounding nisms that influence membrane bending and perform an accounting nuclear pores — or can be transient, such as transport vesicles that are of their relative energy contributions to cellular membrane deforma- continually produced and consumed during membrane and protein tion. We focus primarily on vesicle trafficking pathways, although the traffic. In each case, these structures form from the action of proteins same fundamental principles can also help us understand curvature in that use distinct mechanisms to exert forces that sculpt the requisite other cellular contexts. We first consider the physical properties of lipids membrane architecture1–3. Considerable insight into the mechanisms and cargo, and the barriers they pose to membrane bending. We then of membrane curvature has been gained from minimally reconstituted discuss the drivers of membrane curvature and the different physical systems, largely based on shape changes exerted on synthetic liposomes mechanisms that they employ. Together these considerations define by individual protein components. These systems have established that, an integrated set of parameters that operate during intracellular and in many instances, physical properties associated with a single protein plasma membrane bending. The energy cost-benefit analysis that we are sufficient to induce curvature. In recent years, experimental sys- describe here becomes particularly important in considering membrane tems have focused on two principles: membrane insertion and pro- curvature under pathological conditions, for example where pathogens tein scaffolding. However, more recent theoretical and experimental induce uptake by cells, or when viruses bud from the plasma membrane, analyses have suggested that molecular crowding is also an important liberating themselves for additional rounds of infection. driver of curvature, in a manner that can either augment the action of protein scaffolds, or oppose it. Finally, scaffold rigidity has also The energy costs of bending a membrane been suggested to be a key factor contributing to membrane bending. Most cellular phospholipids have a cylindrical shape and therefore self- Examples of each of these types of curvature drivers can be found at assemble into planar bilayers. According to the simplified two-dimen- different sites within the cell (Fig. 1), where different bending require- sional description of membrane mechanics by Canham4 and Helfrich5, ments are likely to be specified by the lipid and protein composition of deforming bilayers into curved shapes encounters two energy barriers: the underlying membrane. resistance to membrane bending and resistance to membrane stretching.

Jeanne C. Stachowiak is in the Department of Biomedical Engineering, Institute for Cellular and Molecular Biology, University of Texas at Austin, Austin, Texas 78712, USA. Frances M. Brodsky is in the Departments of Bioengineering and Therapeutic Sciences, Pharmaceutical Chemistry and Microbiology and Immunology, The G.W. Hooper Foundation, University of California, San Francisco, California 94143, USA. Elizabeth A. Miller is in the Department of Biological Sciences, Columbia University, New York, New York 10027, USA. e-mail: [email protected]

NATURE CELL BIOLOGY VOLUME 15 | NUMBER 9 | SEPTEMBER 2013 1019

Cilia Clathrin-coated vesicles Caveolae Viral budding Cargo oligomerization

Septins

Caveolin Secretory granules ESCRTs Retromer

Cargo aggregation COPI vesicles

Multivesicular bodies

COPII vesicles ESCRTs Mitochondrial cristae

ATP synthase Nuclear pores

ER tubules

Reticulons Nups

Figure 1 Cellular sites of membrane curvature. The membranes of eukaryotic cells often display curvature; some are dynamic (for example, transport vesicles, endosomal tubules and viral buds) and others more static (for example, nuclear pores, cilia, endoplasmic reticulum (ER) tubules and mitochondrial cristae). Each of these examples of membrane curvature is created by physical effects that derive from both lipid and protein sources. Self-assembling proteins can scaffold membranes (clathrin, COPI, COPII, nucleoporins, caveolins, reticulons, retromer, ESCRTs and septins). Asymmetric lipid and protein insertion can drive curvature by the bilayer couple model and molecular crowding effects (secretory granule cargoes, reticulons, caveolins, viral matrix proteins and mitochondrial ATP synthase). COPI structure reproduced with permission from ref. 46, © 2004 AAAS. COPII structure reproduced from ref. 45, clathrin structure from ref. 83 and retromer model from ref. 84. Septin model reproduced with permission from ref. 85, © 2009 Elsevier. ESCRT structure reproduced with permission from ref. 86, © 2013 Wiley.

As discussed below, bending rigidity generally poses the larger barrier to membrane surface. This process increases steric repulsion among cargo membrane curvature, except in cases where membrane tension is signifi- molecules that can be expected to oppose membrane curvature (Fig. 2a). cantly raised by turgor pressure6, osmotic shock, or action of the cytoskel- Such effects are amplified when cargo proteins display asymmetry across eton7. Many biological membranes, such as the plasma membranes of the bilayer such that lumenal domains are significantly larger than their red blood cells8, are thought to have significant spontaneous curvature, a corresponding cytoplasmic domains. An extreme example of this topol- preferred curvature5 that typically arises from a difference in lipid compo- ogy is the family of lipid-anchored proteins, glycosylphosphorylinosi- sition between the two leaflets of the membrane9. Spontaneous curvature is tol (GPI)-anchored proteins. These abundant and diverse cell surface likely to have a significant influence on the curvature of cellular structures, proteins expose their entire molecular mass on the lumenal surface of though this contribution remains difficult to quantify, as it arises from transport vesicles11. Concentration of these proteins at budding sites may highly localized, often transient, differences in membrane composition. create significant lateral pressure within the membrane that could induce local negative (away from the membrane) curvature (Fig. 2b). Cargo proteins The idea that unbalanced steric pressure among membrane-bound An under-appreciated player in the membrane-bending problem is the molecules can drive membranes to bend derives in part from the bilayer protein fraction embedded within the bilayer. Far from being inert vesicle couple model of Sheetz and Singer12. These authors recognized that tight passengers, cargo proteins represent major constituents of vesicles10 that coupling between the two leaflets of a lipid bilayer engenders curvature, probably contribute a significant energy barrier to membrane bending. As whereby expanding or compressing one side of the membrane would cargo concentration increases and membrane curvature progresses, the cause the other side to experience the opposite effect (i.e. compression surface area available to each protein decreases on the concave lumenal or expansion). The increased abundance of molecules and the increased

1020 NATURE CELL BIOLOGY VOLUME 15 | NUMBER 9 | SEPTEMBER 2013

© 2013 Macmillan Publishers Limited. All rights reserved REVIEW rate of collisions within or adjacent to one leaflet of the membrane causes ab the area of the leaflet to increase relative to the opposite leaflet, leading to Reduced steric pressure membrane curvature away from the source of increased steric pressure Cytosol (Fig. 2b). The phenomenon of curvature driven by steric pressure has been demonstrated for synthetic membranes with a high concentration of poly- Cytosol Lumen mer molecules attached to their outer surfaces13. More recently, it has been demonstrated that steric pressure between densely crowded, membrane- bound proteins can drive dramatic changes in membrane shape, forming Lumen narrow membrane tubules, even from stiff, solid-phase membranes14. In the first physiological example of this phenomenon, steric pressure between GPI-anchored proteins and other cargo molecules in the lumen Increased steric pressure of the endoplasmic reticulum seems to oppose the curvature enforced by the COPII vesicle coat machinery, driving a requirement for increased c d Cargo adaptors coat rigidity15. Similar costs are likely to apply to bona fide transmembrane cargo proteins, especially those with relatively small cytoplasmic domains Cytosol such as many surface receptors and Golgi glycosylation enzymes16.

Overcoming the barriers to membrane bending Lumen Cells have evolved multiple solutions to the problem of overcoming the Cytosol energy barriers associated with curving membranes (Fig. 1). Early observations of clathrin-coated vesicles17 and subsequent characterization of clathrin’s self-assembling properties18 gave rise to the long-standing Lumen premise that formation of spherical vesicles is driven by coat protein scaffolds that are capable of imposing their inherent curvature on mem- Figure 2 Steric effects during membrane curvature. (a) As curvature brane surfaces (Fig. 1). In addition to the scaffolding effects of polymeric progresses and a vesicle bud forms, the decrease in surface area on the coat structures, further mechanisms that contribute to membrane bend- lumenal face restricts mobility of lumenal protein mass, increasing the local ing have now been characterized. These include differential lipid and steric pressure to resist bending. Simultaneously, the cytoplasmic surface protein insertion into the bilayer, steric pressure among proteins bound area increases, reducing steric pressure and necessitating increased force at this face to maintain bending. (b) Complete asymmetry of lumenally oriented to membrane surfaces, oligomerization of membrane-embedded and proteins during budding could create negative spontaneous curvature by membrane-associated proteins, and actin polymerization. We consider entropic means, thus opposing the action of the coat. (c) Conversely to b, if each of these mechanisms in turn, starting with the membrane itself and lumenally oriented proteins oligomerize, their affinity for each other and the working our way out towards the cytoplasm. membrane could drive bending in the appropriate direction. (d) Recruitment of cargo adaptors to nascent budding sites could create local curvature by entropic means and thereby reverse cargo resistance. The combined mass of Lipid asymmetry cargo plus adaptor proteins creates steric pressure. Although the majority of membrane lipids are cylindrical in shape, lipids with large hydrocarbon tails (or small head groups) can take on a coni- traffic, such as epsin 1, Arf1 and Sar1, insert short amphipathic helices cal shape, and lipids with small tails (or large head groups) can adopt into one leaflet of the membrane when recruited. These proteins can an inverse conical shape. The unequal distribution of such irregularly tubulate synthetic liposomes when applied at relatively high concen- shaped lipids between the two leaflets of the membrane could impose trations26–29. However, whether it is physiologically possible to create a a distinct curvature on the bilayer. Indeed, asymmetric lipids such as high enough local density of insertions to generate a significant driving phosphatidylethanolamine and gangliosides19 and ceramides20 display force for membrane bending remains under debate30,31. Specifically, the curvature preferences. The asymmetric distribution of these lipids has physical dimensions of the proteins that contain insertable helices set been invoked to explain observations of curvature during autophago- a limit on the number of helices that can be actually be inserted at the some formation21. In the context of vesicle formation, local recruitment membrane surface. As discussed below, even when all membrane-bound of lipases and other lipid-modifying enzymes, including flippases, may proteins insert helices, the membrane area occupied by helices cannot contribute to the curvature associated with vesicle formation22. Direct fill the disparity in area between the two leaflets of highly curved mem- measurement of this effect in a cellular context has not been achieved, branes. This analysis is based on the prediction30 that insertions must making the impact of lipid asymmetry difficult to quantify. Nonetheless, cover at least 10% of the membrane surface area to drive formation of flippases are clearly implicated in post-Golgi trafficking events23 and the smallest vesicles found in cells. This situation is intractable except local release of sphingomyelinase can induce endocytosis24, suggesting for cases in which proteins that contain multiple helix insertions cover such mechanisms are physiologically relevant in cells. the entire membrane surface30. Therefore, hydrophobic insertion probably makes a relatively small contribution to the energy budget of mem- Protein asymmetry brane curvature in most settings. This is consistent with the formation Asymmetric membrane insertion of proteins should also be capable of of COPII-coated curved membranes in the absence of helix insertions27 driving membrane bending, according to the bilayer couple model25. and curvature induced by clathrin in the presence of a truncated form Indeed, a number of cytosolic proteins that are central to membrane of epsin that lacks the N-terminal amphipathic helix32.

NATURE CELL BIOLOGY VOLUME 15 | NUMBER 9 | SEPTEMBER 2013 1021

An alternative effect that may account for the observed tubulation heterogeneous population of cargo proteins would require an asymmet- following recruitment of helix-containing proteins is steric pressure ric distribution in the membrane, with the bulk of their masses facing between densely crowded membrane-bound molecules. As described the cytoplasm. Alternatively, lumenally oriented cargoes would need above with respect to asymmetric cargo proteins, this effect can itself to undergo significant intermolecular interactions that would in turn drive membrane bending when the concentration of molecules is higher reverse the spontaneous curvature of the underlying bilayer37 (Fig. 2c). on one face of the membrane than the other. In this case, the crowding Yet another alternative would invoke the molecular crowding effects of effect is achieved by local membrane association of coat assembly pro- the cargoes plus their cargo adaptors, such that the accumulated mass teins, creating curvature and contributing to vesicle formation. Indeed, on the cytoplasmic face of the bilayer creates sufficient lateral pressure membrane-bound clathrin assembly proteins, including epsin 1 and to bend the membrane in the desired direction (Fig. 2d). Such a scenario AP180, have recently been demonstrated to drive bending of model might be accelerated by curvature-sensing properties of the cargo adap- membrane vesicles by creating steric pressure, accounted for by the tors such that a positive feedback loop is created: local recruitment and reduced frequency of protein–protein collisions (i.e. increased entropy) concentration initiates curvature that is in turn sensed by additional when the membrane bends away from its more densely crowded sur- adaptors that bring in more cargo molecules, perpetuating the local cur- face31 (Fig. 2d). Instead of driving bulk curvature, coat initiation by vature25. Indeed, such positive feedback may participate in the canonical amphipathic-helix-containing proteins might generate initial local coat systems where curvature may be induced initially by steric pressure curvature and then couple this to coat propagation through recruit- among cargo adaptors, detected and propagated by accessory proteins ment of additional helix-containing (and other) proteins, leading to with amphipathic helices and concave membrane-binding surfaces, and steric pressure effects of the coat as a whole. Indeed, the amphipathic further propagated and stabilized by cargo concentration and polymeri- helix of Sar1 lowers the bending energy of the underlying lipid bilayer33, zation of a protein coat or the cargo adaptors themselves. suggesting that it makes the membrane more susceptible to remodelling by downstream coat components25. Another function for amphipathic Self-assembly of membrane-embedded proteins helices is detection rather than induction of curvature. This is almost Caveolins and reticulons are membrane-embedded proteins that certainly the case for the ALPS-domain of ARF GAP (GTPase-activating undergo oligomerization to generate curvature42,43 (Fig. 1). They both protein), which detects lipid-packing defects in the curved bilayers of have transmembrane domains that form wedge-shaped insertions COPI vesicles, inserting specifically into membranes that are under with capacity to contribute to membrane curvature. Self-assembly of curvature stress34 and thus restricting its GTPase stimulation activity caveolins and reticulons then further drives membrane remodelling to to curved membranes. create plasma membrane invaginations and tubulate the endoplasmic An extension of this protein asymmetry and molecular crowd- reticulum, respectively. By combining a wedge-shaped hydrophobic ing model may also be relevant to cargo-driven vesiculation events. structure with oligomerization, these proteins can induce significant Experiments with membrane-bound polymers revealed that self-avoid- local curvature without occupying a large amount of the membrane ing polymers create an expansive pressure that drives the membrane surface. Thus, they are effective curvature generators that are compat- to bend away from them13,35 (Fig. 2b), a finding supported by a sim- ible with recruitment of effectors for receptor signalling and other ple thermodynamic model36. Likewise, self-attracting polymers can be functions44. expected to create a compressive pressure that drives the membrane to bend toward them37 (Fig. 2c). Thus, vesiculation of the correct topology Self-assembling soluble coat scaffolds (that is towards the cytoplasm) might be induced by lumenally distrib- Moving outwards from the membrane surface, membrane-binding uted proteins if they have affinity for each other. For example, apical adaptor proteins frequently recruit coat scaffolds to the membrane sur- sorting of GPI-anchored proteins relies on their oligomerization38, rais- face. Perhaps the best-characterized examples of protein assembly driving the prospect that such sorting employs a cargo-driven budding event ing membrane curvature are two of the canonical coats, clathrin and (Fig. 2c). This phenomenon might also explain the biogenesis of secre- COPII. Both coats contain elements that polymerize into polyhedral tory granules that have long been thought to employ a concentration- structures independent of membranes45. As noted, the favourable ener- driven segregation mechanism of egress from the trans-Golgi network getics of clathrin or COPII assembly alone can induce vesicle formation (TGN)39 (Fig. 1), although the molecular details of the budding event are without membrane-inserted motifs32,27. However, the structure formed not yet fully defined. Viral budding may also employ such a mechanism by the COPII outer coat scaffold does not employ the significant inter- whereby self-association of matrix proteins — driven in some cases by twining that occurs during clathrin triskelion assembly, relying instead nucleic acid packaging — would couple with plasma membrane recruit- on less extensive interactions among coat protomers. Thus, the energy ment to drive outward budding of the enveloped virus40 (Fig. 1). derived from assembly of COPII interfaces is likely to be less than that Cargo-driven molecular crowding effects could also be relevant to derived from clathrin assembly. intracellular trafficking pathways for which cargo adaptors are known In the case of the COPI coat, self-assembly into a cage-like structure but no outer coat scaffold has been described. So far, no known coat pro- has not been observed, and electron microscopy of liposome-derived teins mediate transport between the yeast TGN and plasma membrane, COPI vesicles reveals both gaps in coat packing and alternative packing although some specialized cargo adaptors (such as exomer) regulate interactions on vesicles of different size46, suggesting a more labile scaf- selected transport steps41. Whether exomer recruits a more canonical fold. Adaptor recruitment alone could also contribute to membrane coat scaffold remains to be seen. In a cargo-driven budding model, cargo bending (Fig. 2d), especially if additional organization promotes steric concentration alone would create local shape changes in the membrane pressure. The plastic COPI coat could contribute to membrane bend- by virtue of molecular crowding (Fig. 2b). For this model to work, a ing through this mechanism, as well as by forming a rigid scaffold.

1022 NATURE CELL BIOLOGY VOLUME 15 | NUMBER 9 | SEPTEMBER 2013

Sorting events mediated by the AP3 adaptor complex, which can occur in membrane curvature. In some cellular circumstances, membrane without clathrin, may rely on Vps41 as a self-assembling element47, but deformation by the mechanisms described is not sufficient to induce whether this assembly provides a bona fide scaffold or promotes adaptor vesicle budding. In these cases, actin polymerization is coordinated aggregation remains to be established. In the case of the two COP coats, with membrane-bending proteins to generate the force required for membrane recruitment is mediated by small GTPases with amphip- budding. Actin can play three roles in budding; one role is to help the athic helices. As discussed above, it is not completely clear whether these vesicle pinching process by polymerization at the neck of a budding contribute to bending by inserting in the cytoplasmic leaflet27,48 or serv- vesicle, pushing the vesicle away from the membrane and/or providing ing as lipid interactors that alter membrane rigidity33, or both. Clathrin constricting force. For clathrin-coated vesicles forming in yeast, actin assembly at the TGN and endosome employs ARF1 (ref. 49) and ARF6 is constitutively needed at the neck of a budding coated vesicle to over- (ref. 50), respectively. The use of these accessory proteins may reflect come turgor pressure on the membrane6. Indeed, the effect of turgor, different bending challenges at the different cellular locations. combined with the small size of yeast endocytic vesicles, may form such Although no experimentally determined numbers exist for the free a strong barrier to curvature that membrane bending isn’t detected until energy generated by clathrin or COP scaffold assembly at membranes, actin polymerization occurs59. Similarly, in mammalian cell membranes it is clear that the individual interactions of scaffold components are of under tension, either induced by the presence of microvilli on apical sufficiently low affinity to be reversible51. Experimental evidence that membranes or by artificially generated tension, actin polymerization is clathrin assembly can directly vesiculate membranes32 is consistent required for budding7. These clathrin-associated actin pathways involve with higher estimates of clathrin–clathrin interactions7,52 rather than the connection between the clathrin light chain subunits and HIP (hun- lower estimates53. Further, cellular clathrin depolymerization (uncoat- tingtin interacting protein) family proteins49. Interestingly, electron ing) clearly requires ATP hydrolysis by heat-shock protein 70 (HSP70) microscopy analysis of mammalian cells60 shows actin at the neck of stimulated by the DNAJ homologue auxilin (known in yeast as Swa2), in most endocytic clathrin-coated vesicles, indicating that most plasma a process that requires direct interaction with the coat protein49. COPI membrane budding uses actin. In this particular feature, mammalian and COPII coat disassembly, on the other hand, is modulated by their endocytic clathrin-coated vesicles resemble yeast endocytic clathrin- anchoring small GTPases, and they apparently disassemble spontane- coated vesicles61, though the former has variable requirements for actin, ously following GTP hydrolysis34,54. One remaining question is whether whereas the latter has absolute requirements. Despite these findings on the energy invested in vesicle formation is sufficient to force curvature of the important role of actin in membrane bending and endocytosis, it membranes such that the closed vesicle released from the donor mem- has also been shown that depolymerization of the actin cytoskeleton brane remains under curvature stress. We speculate that such accumu- does not significantly inhibit clathrin-mediated endocytosis in multiple lated tension might ‘prime’ a vesicle for fusion such that the stored energy mammalian cell types62. However, these latter experiments involved cells will promote membrane fusion events when the vesicle docks with the in culture, so actin could be more critical for endocytosis in the context target membrane. In this model, the energy invested in forming a highly of mammalian tissue. curved vesicle could help to pay the energy cost of membrane fusion, Another mechanism by which actin contributes to endocytosis relies providing a role for curvature drivers in both vesicle biogenesis and on its ability to extend membrane protrusions by polymerization and consumption. induce localized phagocytosis. When clathrin coats are flat and cargo is A final important physical parameter associated with coat scaffolds is too large to be surrounded by a scaffold, actin operates to cause endo- the need for rigidity, which presumably translates into stronger bending cytosis. This is observed during uptake of clathrin plaques63, uptake of forces and is seemingly required to enforce curvature on certain cargo- bacteria where clathrin serves as an actin-assembly nucleator64, and with containing membranes. For example, structural modelling suggests that viral particles that are too large to fit in conventional clathrin-coated the outer COPII coat protein, Sec13, acts to rigidify the coat to enforce pits65. Uptake of virus by endocytosis in caveolae works by a similar prin- curvature on wild-type membranes. In yeast, Sec13 becomes dispensable cipal and requires actin66. A third role for actin, which is less established, when traffic of GPI-anchored cargoes is diminished, linking coat rigid- may be to contribute to vesicle biogenesis from membrane tubules67. ity to a specific cargo burden15. In support of this model, knockdown Yeast TGN-derived vesicles travel on actin cables to polarized sites of of mammalian SEC13 has minimal impact on bulk protein secretion growth and thus may also employ actin in their biogenesis. Directed but impedes endoplasmic reticulum export of collagen55, which might endosomal recycling in mammalian cells also involves actin-organizing contribute a significant barrier to curvature because of its polymeric proteins, particularly during cell migration, which could play a role in state56. Similarly, the clathrin light chain subunit, which confers rigidity generating recycling vesicles68. on the proximal leg of the triskelion, is dispensable for receptor-mediated Once these drivers have acted to generate nascent vesicle buds, addi- endocytosis of transferrin and the epidermal growth factor receptor57. tional membrane remodelling occurs during vesicle release. Pinching at However, some G-protein-coupled receptors (GPCRs) require the pres- the neck of a vesicle is a special case of extreme membrane bending to ence of clathrin light chains for their uptake58. Although this was sug- promote fusion, and involves complex curvature that seems to require gested to be an effect on clathrin uncoating, it might also reflect a need specialized protein machines69. In metazoan cells, force for this process is for greater rigidity of coats that must internalize GPCRs plus their associ- exerted by self-assembly of dynamin into collars, which can also recruit ated arrestin and signalling subunit baggage. actin70. Additional influence can come from BAR-domain-containing proteins that oligomerize to scaffold membrane curvature. In the case Actin polymerization of dynamins71 and BAR-domain proteins72, membrane insertion events Beyond membrane cargo and membrane-associated adaptors and might make an important contribution by virtue of the high surface coats, the actin cytoskeleton frequently plays an indispensable role density of these oligomeric proteins.

NATURE CELL BIOLOGY VOLUME 15 | NUMBER 9 | SEPTEMBER 2013 1023

© 2013 Macmillan Publishers Limited. All rights reserved REVIEW ) ) -2 a -2 b 1.0 Bending rigidity T nm T nm B B 0.6 50% cholesterol (50 kBT) k k ( ( 0.8 Asymmetric Bending rigidity 0.6 0.4 No cholesterol (10 kBT) Symmetric

Membrane 0.4 0.2 tension 0.2

0.0 0.0 Energy per membrane area Energy per membrane area 25 50 75 100 25 50 75 100 Vesicle diameter (nm) Vesicle diameter (nm)

c d ) ) -2 -2 0.4

T nm T nm 0.8 B B k k ( Hydrophobic insertion ( 0.3 Costs 0.6 Drivers AP crowding 0.2 0.4 Clathrin polymerization

0.1 0.2 Actin polymerization

Energy per membrane area 0.0 Energy per membrane area 0.0 25 50 75 100 25 50 75 100 Vesicle diameter (nm) Vesicle diameter (nm)

Figure 3 Energetics of coated vesicle formation. Compiling quantitative data and models from the recent literature, we estimate the energy budget responsible for formation of coated vesicles of variable size. (a) Energy costs of membrane bending, including bending rigidity and tension74. (b) Energy costs of cargo confinement in the vesicle lumen15,31, considering either asymmetrically (orange) or symmetrically (blue) distributed cargoes. (c) Energy contributions by drivers of membrane bending including actin polymerization7, clathrin coat assembly52, confinement of accessory proteins (AP) beneath coats31, and hydrophobic insertions30. The colours of each icon correspond to their energy contributions shown in the plot. (d) Comparison of energy costs with drivers during coated vesicle formation. Drivers (actin, clathrin coats and APs) are blue, and cargo- and membrane-derived costs are red. See Box 1 for further description of these energy estimates.

Compiling the forces that drive and oppose membrane curvature Returning first to the Canham and Helfrich models of membrane bend- The various mechanisms by which lipids, membrane-bound proteins, self- ing4,5, we can calculate the energy cost of bending a piece of initially flat assembling scaffolds and actin contribute to membrane bending during membrane into a spherical vesicle by understanding the bending rigidity. vesicle formation are the subject of ongoing discussion. In the cell, these This force, expressed in units of energy, ranges from 10 kBT for highly fluid mechanisms are deployed in a complementary and cooperative fashion. membranes composed entirely of lipids with unsaturated tails73 to approxi- 74 Here we provide an accounting of the energetics involved in membrane mately 50 kBT for fluid membranes containing 50% cholesterol , similar 75 bending, using the assembly of clathrin-coated vesicles as a model. Our in composition to the plasma membrane of mammalian cells (where kB estimates are based on previously published calculations of the contri- is Boltzmann’s constant and T is temperature) (Fig. 3a and Box 1). The butions of the components we have described (see Box 1). In doing so, energy barrier to membrane stretching is the product of membrane ten- we aim to approximate the relative contribution of each component to sion and membrane surface area. Membrane tension arises from thermal vesicle formation and to investigate whether our current understanding of fluctuations within the membrane74, osmotic imbalances across the mem- the physical forces underlying membrane bending is sufficient to explain brane and application of forces to the membrane by the cytoskeleton in vesicle formation. This approach does not incorporate the entire spectrum cellular structures such as villi7, and by a cell wall. Physiological values –3 −2 of physical effects, especially those driven by accessory proteins and lipid of membrane tension are in the range of 0.2–1×10 kBT nm (ref. 76). asymmetry, largely because these effects have not yet been precisely quan- For a typical vesicle of 100 nm diameter, the energy cost per mem- tified. Further, since the number of independently published quantitative brane area of overcoming membrane tension is therefore 10–100 times estimates of the individual bending effects is still quite small, we expect smaller than the energy cost per membrane area of membrane bending –3 −2 these estimates to be revised repeatedly over the next few years. In particu- (8–40×10 kBT nm ), such that membrane bending is usually cited as lar, the contribution of actin to vesicle formation is based on a single, very the most significant lipid-associated barrier to deforming membranes. recent estimate7. Nonetheless, we consider that this quantitative approach The energy costs of cargo crowding are more difficult to model, as they provides a valuable illustration of the problem of the cost-driver balance are dependent on the specific protein composition of the underlying mem- of forming highly curved vesicles from cellular membranes. brane, with asymmetrically distributed and lumenally oriented proteins

1024 NATURE CELL BIOLOGY VOLUME 15 | NUMBER 9 | SEPTEMBER 2013

BOX 1 Calculations and assumptions of approximate energy analysis for formation of coated vesicles in Fig. 3

−2 All energy costs and drivers were estimated in terms of energy per membrane area (units of kBT nm ) as a function of coated vesicle diameter ranging from 25‑100 nm.

Energetic costs of forming coated vesicles Membrane bending. Using the classic Canham, Helfrich, and Evans theory4,5, the energy cost per membrane area of creating a curved 2 sphere was estimated as Gbending = (8πκ)/(4πr ), where κ is the bending rigidity of the membrane and r is the vesicle radius. Calculations were

performed for soft fluid membranes for which κ~10 kBT and for membranes containing 50% cholesterol (typical value for mammalian plasma

membrane), for which κ~50 kBT (ref. 74).

Membrane tension. The finite tension of biological membranes opposes changes in shape. The membrane tension, which has units of energy per area, is approximately the energy required per membrane area to form a spherical vesicle from an initially flat membrane surface. A typical −2 74 value of 0.02 kBT nm was estimated based on micropipette aspiration measurements of membrane tension before significant straining .

Cargo crowding. When an initially flat region of the membrane becomes curved, the lumenal domains of cargo molecules have less space to diffuse on the membrane surface, owing to the concave curvature of the vesicle inner surface. The reduced entropy of cargo molecules leads to an increased pressure on the membrane surface that can be expressed as an energy cost per membrane area. Conversely, cargo molecules that have a domain on the coat side of the membrane will experience a reduction in steric congestion as the membrane bends, an energy contribution that encourages membrane curvature. The difference between these terms is the approximate energy cost of cargo crowding. The net energy cost per membrane area of crowding was calculated by assuming a cargo molecule with either a single lumenal domain of 5 nm diameter (asymmetric case), or independently diffusing domains of 5 nm diameter on both sides of the membrane (symmetric case), where lumenal domains cover 50% of the initially flat membrane surface area16. Surface pressures on both membrane surfaces were estimated using a nonlinear equation of state for hard discs in two dimensions as proposed by Carnahan and Starling87,88, used recently to estimate the surface pressure owing to protein crowding on membrane surfaces31,89.

Energetic drivers for forming coated vesicles Hydrophobic insertion. Clathrin assembly proteins, such as epsin 1, insert amphipathic helices when they bind to the membrane surface26. The energy contribution of helix insertion was taken from Campelo et al.30 assuming that a maximum of 2% of the membrane surface area is

covered by insertions. Under this condition, Campelo et al. predict a membrane radius of curvature of about 130 nm. Using Gbending = (8πκ)/ 2 −2 (4πr ) to calculate the bending energy and assuming a bending rigidity of 50 kBT, we arrive at a value of 0.006 kBT nm for insertions. The 2% insertion area is the maximum expected if each adaptor protein provides an insertion of approximately 2 nm2, and there are approximately three adaptor proteins per clathrin triskelia (such as AP2, AP180, epsin 1 etc).

Accessory protein crowding. When an initially flat portion of the membrane surfaces curves to form a clathrin-coated vesicle, accessory proteins beneath the clathrin lattice are able to explore a larger region of the membrane surface, owing to the positive curvature of the outer vesicle surface. This increased entropy decreases the membrane surface pressure, which can be described as a reduction in free energy per membrane area. Assuming that 75% of the membrane surface is occupied by accessory proteins90 and that an average accessory protein has a diameter of 5–10 nm, the energy contribution of accessory protein crowding was estimated using the same approach used to estimate the cost of cargo crowding.

Clathrin polymerization. Coarse-grained molecular simulations used a reasonable estimate that 25 kBT is released per clathrin triskelia when a clathrin lattice assembles52. Dividing this value by the membrane surface area occupied per triskelia of a lattice (~300 nm2; ref. 83), the energy −2 contribution of clathrin assembly per membrane area was estimated at approximately 0.08 kBT nm .

Actin polymerization. A dense collar of actin filaments surrounds clathrin-coated vesicles, contributing to vesicle formation60. Recent studies have suggested that polymerization of these filaments helps clathrin-coated vesicles to form7,59. The energy contribution of actin polymerization to vesicle budding must vary with the density and geometric arrangement of filaments, parameters that are still being defined and are likely to −2 differ from one physiological situation to another. Here we include an energy contribution of 0.13 kBT nm , based on the recent report that osmotic swelling of mammalian cells creates a requirement for actin to efficiently complete clathrin-mediated endocytosis7. In this report, the work, W, required to form a vesicle against membrane tension, σ, was estimated as W =πr 2σ. Roughly estimating the elevated membrane −2 2 tension to be approximately half the lytic limit (~0.5 kBT nm ; ref. 74), and dividing the work, W, by the vesicle surface area (4πr ), we estimate −2 the contribution of actin required to overcome high membrane tension as approximately 0.13 kBT nm . having a larger effect than those that are symmetrically proportioned. size and density of proteins bound to membrane surfaces31. Applying these However, a recently published model has estimated the energy costs of results to two hypothetical vesicle budding scenarios that contain either the entropic effects of membrane-attached proteins as a function of the asymmetrically or symmetrically distributed cargo proteins (Fig. 3b)

NATURE CELL BIOLOGY VOLUME 15 | NUMBER 9 | SEPTEMBER 2013 1025

© 2013 Macmillan Publishers Limited. All rights reserved REVIEW suggests that both orientations contribute a significant barrier, espe- example, clathrin is implicated in organizing retroviral glycoproteins dur- cially as the diameter of the vesicle decreases. It is initially surprising that ing viral budding, which might induce crowding that enforces external symmetric cargo proteins oppose curvature nearly as strongly as highly budding81. This may be comparable to the crowding effects of Herpes asymmetric ones. This behaviour is a consequence of the highly nonlinear virus capsid proteins, which may have a positive influence on budding82. increase in steric pressure with protein density. Owing to this nonlinearity, In conclusion, the simple principles of membrane bending that we have crowding effects are much stronger on the inner leaflet of a small vesicle discussed here can be orchestrated in a variety of combinations to mediate than on the outer leaflet. Therefore, crowding on the outer leaflet by sym- membrane budding in biological membranes both for normal cellular metric cargos only slightly reduces the barrier to membrane bending. function and during pathogenesis. Turning to the drivers of curvature and compiling recent estimates ACKNOWLEDGEMENTS from the literature (Fig. 3c), we find that the effect of hydrophobic inser- J.C.S. acknowledges funding from the University of Texas Austin Cockrell School tions is relatively small, even where one insertion was included for each of Engineering and the Texas 4000 Cancer Seed Grant Program. F.M.B. and E.A.M. adaptor protein with a generous stoichiometry of three adaptor proteins acknowledge support from the National Institute of General Medical Science of the National Institutes of Health under award numbers R01GM038093 (F.M.B.), per clathrin triskelia (see Box 1 for detailed analysis). Since insertions R01GM078186 (E.A.M.) and R01GM085089 (E.A.M.). We thank M. C. S. Lee contribute to membrane bending on a per area basis, their energy contri- (Columbia University), E. Schmid (University of California, Berkeley), C. Hayden bution per membrane area remains constant across vesicles of different (Sandia National Laboratories) and E. Lafer (University of Texas Health Science Center) for thoughtful discussions and comments on the manuscript. sizes. Crowding effects of the cargo-bound adaptor complexes contribute significantly, with a larger impact as vesicle diameter decreases. COMPETING FINANCIAL INTERESTS Clathrin and actin polymerization are both significant contributors that The authors declare no competing financial interests. make a fixed contribution per membrane area. These estimates rep- 1. McMahon, H. T. & Gallop, J. L. Membrane curvature and mechanisms of dynamic cell membrane remodelling. Nature 438, 590–596 (2005). resent data from diverse experiments that are likely to be refined and 2. Bigay, J. & Antonny, B. Curvature, lipid packing, and electrostatics of membrane revised by future work. Therefore, their interpretation at this stage must organelles: defining cellular territories in determining specificity. Dev. Cell 23, 886– 895 (2012). remain largely qualitative. Nonetheless, from combining these findings, 3. Zimmerberg, J. & Kozlov, M. M. How proteins produce cellular membrane curvature. it seems that the energy costs (bending rigidity and tension4,5,73,74, and Nat. Rev. Mol. Cell Biol. 7, 9–19 (2006). cargo crowding15,31) of producing vesicles of moderate size (~50 nm 4. Canham, P. B. The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J. Theoret. Biol. 26, 61–81 (1970). diameter) is offset by the energy drivers when all drivers are present 5. Helfrich, W. Elastic properties of lipid bilayers: theory and possible experiments. (coat polymerization52, accessory protein crowding31, amphipathic inser- Biochem. Biophys. Biol. Virol. 28, 693–703 (1973). 6. Aghamohammadzadeh, S. & Ayscough, K. R. Differential requirements for actin during 26,30 60,77 tion and cytoskeletal forces ), whereas producing smaller vesicles yeast and mammalian endocytosis. Nat. Cell Biol. 11, 1039–1042 (2009). and vesicle production in the absence of one or more drivers cannot 7. Boulant, S., Kural, C., Zeeh, J. C., Ubelmann, F. & Kirchhausen, T. Actin dynamics counteract membrane tension during clathrin-mediated endocytosis. Nat. Cell Biol. be fully accounted for (Fig. 3d). Synaptic vesicles represent an extreme 13, 1124–1131 (2011). example of a highly curved vesicle, measuring just 40 nm in diameter. 8. Svetina, S. & Zeks, B. Membrane bending energy and shape determination of phospholipid vesicles and red blood cells. Eur. Biophys. J. 17, 101–111 (1989). 78 Formation of these vesicles is independent of actin and thus would 9. Fuller, N. & Rand, R. P. The influence of lysolipids on the spontaneous curvature and seem to be energetically unfavourable in our analysis (Fig. 3d). However, bending elasticity of phospholipid membranes. Biophys. J. 81, 243–254 (2001). 10. Takamori, S. et al. Molecular anatomy of a trafficking organelle. Cell 127, 831–846 detailed structural and proteomic analysis of synaptic vesicles reveals (2006). that a large number of the embedded protein cargoes are cytoplasmically 11. Fujita, M. & Kinoshita, T. GPI-anchor remodeling: potential functions of GPI-anchors in intracellular trafficking and membrane dynamics. Biochim. Biophys. Acta 1821, oriented and thus may contribute positively to membrane bending rather 1050–1058 (2012). than acting as a barrier. In this example, the energy cost of membrane 12. Sheetz, M. P. & Singer, S. J. Biological membranes as bilayer couples. A molecular mechanism of drug-erythrocyte interactions. Proc. Natl Acad. Sci. USA 71, 4457–4461 bending would be overestimated and cargo itself could be considered as a (1974). driver. Indeed, the detailed molecular map of synaptic vesicles10 serves as 13. Decher, G. et al. Interaction of amphiphilic polymers with model membranes. Angew. Makromol. Chem. 166, 71–80 (1989). a benchmark that characterization of other vesicle systems might aspire 14. Stachowiak, J. C., Hayden, C. C. & Sasaki, D. Y. Steric confinement of proteins on to in order to fully appreciate the underlying costs and drivers of an lipid membranes can drive curvature and tubulation. Proc. Natl Acad. Sci. USA 107, 7781–7786 (2010). individual budding event. Our analysis demonstrates that different prop- 15. Copic, A., Latham, C. F., Horlbeck, M. A., D’Arcangelo, J. G. & Miller, E. A. ER cargo erties of cellular membranes engender distinct requirements in terms of properties specify a requirement for COPII coat rigidity mediated by Sec13p. Science 335, 1359–1362 (2012). the energetics of coat scaffold assembly, the role of actin and the need for 16. Sharpe, H. J., Stevens, T. J. & Munro, S. A comprehensive comparison of transmembrane additional accessory factors such as BAR-domain proteins and dynamin domains reveals organelle-specific properties. Cell 142, 158–169 (2010). 17. Roth, T. F. & Porter, K. R. Yolk protein uptake in the oocyte of the mosquito Aedes that can provide additional curvature and/or force. aegypti L. J. Cell Biol. 20, 313–332 (1964). Ultimately, cellular membrane curvature involves the coordination of 18. Pearse, B. M. & Crowther, R. A. Structure and assembly of coated vesicles. Annu. Rev. Biophys. Biophys. Chem. 16, 49–68 (1987). multiple complementary and cooperative mechanisms. Such coordina- 19. Thomas, P. D. & Poznansky, M. J. Curvature and composition-dependent lipid tion has been elegantly demonstrated for clathrin-coated pit formation by asymmetry in phosphatidylcholine vesicles containing phosphatidylethanolamine and gangliosides. Biochim. Biophys. Acta 978, 85–90 (1989). single-molecule imaging. Cooperative interactions between cargo-bound 20. Goni, F. M. & Alonso, A. Biophysics of sphingolipids, I. Membrane properties of adaptors recruited scaffold-forming coat molecules that in turn attracted sphingosine, ceramides and other simple sphingolipids. Biochim. Biophys. Acta 1758, 79 1902–1921 (2006). other membrane benders . Intracellular pathogens provide further exam- 21. Hailey, D. W. et al. Mitochondria supply membranes for autophagosome biogenesis ples of diverse solutions to the membrane bending problem. The outer during starvation. Cell 141, 656–667 (2010). 22. Yang, J. S. et al. A role for phosphatidic acid in COPI vesicle fission yields insights into coat of trypanosomes is formed by GPI-anchored proteins that might Golgi maintenance. Nat. Cell Biol. 10, 1146–1153 (2008). create bending challenges through leaflet asymmetry and cargo crowding. 23. Gall, W. E. et al. Drs2p-dependent formation of exocytic clathrin-coated vesicles in vivo. Curr. Biol. 12, 1623–1627 (2002). Notably, these organisms alter the packing of their surface proteins by gly- 24. Zha, X. et al. Sphingomyelinase treatment induces ATP-independent endocytosis. cosylation that could reduce crowding or rigidity80. In another pathogenic J. Cell Biol. 140, 39–47 (1998).

1026 NATURE CELL BIOLOGY VOLUME 15 | NUMBER 9 | SEPTEMBER 2013

25. Leibler, S. Curvature instability in membranes. J. Phys. 47, 507–516 (1986). 58. Ferreira, F. et al. Endocytosis of G protein-coupled receptors is regulated by clathrin 26. Ford, M. G. et al. Curvature of clathrin-coated pits driven by epsin. Nature 419, 361– light chain phosphorylation. Curr. Biol. 22, 1361–1370 (2012). 366 (2002). 59. Kukulski, W., Schorb, M., Kaksonen, M. & Briggs, J. A. G. Plasma membrane reshaping 27. Lee, M. C. S. et al. Sar1p N-terminal helix initiates membrane curvature and completes during endocytosis is revealed by time-resolved electron tomography. Cell 150, 508– the fission of a COPII vesicle. Cell 122, 605–617 (2005). 520 (2012). 28. Lundmark, R., Doherty, G. J., Vallis, Y., Peter, B. J. & McMahon, H. T. Arf family GTP 60. Collins, A., Warrington, A., Taylor, K. A. & Svitkina, T. Structural organization of the loading is activated by, and generates, positive membrane curvature. Biochem. J. 414, actin cytoskeleton at sites of clathrin-mediated endocytosis. Curr. Biol. 21, 1167–1175 189–194 (2008). (2011). 29. Krauss, M. et al. Arf1‑GTP-induced tubule formation suggests a function of Arf family 61. Idrissi, F. Z., Blasco, A., Espinal, A. & Geli, M. I. Ultrastructural dynamics of proteins proteins in curvature acquisition at sites of vesicle budding. J. Biol. Chem. 283, involved in endocytic budding. Proc. Natl Acad. Sci. USA 109, E2587–2594 (2012). 27717–27723 (2008). 62. Fujimoto, L. M., Roth, R., Heuser, J. E. & Schmid, S. L. Actin assembly plays a variable, 30. Campelo, F., McMahon, H. T. & Kozlov, M. M. The hydrophobic insertion mechanism but not obligatory role in receptor-mediated endocytosis in mammalian cells. Traffic 1, of membrane curvature generation by proteins. Biophys. J. 95, 2325–2339 (2008). 161–171 (2000). 31. Stachowiak, J. C. et al. Membrane bending by protein-protein crowding. Nat. Cell Biol. 63. Saffarian, S., Cocucci, E. & Kirchhausen, T. Distinct dynamics of endocytic clathrin- 14, 944–949 (2012). coated pits and coated plaques. PLoS Biol. 7, e1000191 (2009). 32. Dannhauser, P. N. & Ungewickell, E. J. Reconstitution of clathrin-coated bud and 64. Bonazzi, M. et al. Clathrin phosphorylation is required for actin recruitment at sites of vesicle formation with minimal components. Nat. Cell Biol. 14, 634–639 (2012). bacterial adhesion and internalization. J. Cell Biol. 195, 525–536 (2011). 33. Settles, E. I., Loftus, A. F., McKeown, A. N. & Parthasarathy, R. The vesicle trafficking 65. Cureton, D. K., Massol, R. H., Whelan, S. P. & Kirchhausen, T. The length of vesicular protein Sar1 lowers lipid membrane rigidity. Biophys. J. 99, 1539–1545 (2010). stomatitis virus particles dictates a need for actin assembly during clathrin-dependent 34. Bigay, J., Gounon, P., Robineau, S. & Antonny, B. Lipid packing sensed by ArfGAP1 couples endocytosis. PLoS Pathog. 6, e1001127 (2010). COPI coat disassembly to membrane bilayer curvature. Nature 426, 563–566 (2003). 66. Hansen, C. G. & Nichols, B. J. Exploring the caves: cavins, caveolins and caveolae. 35. Tsafrir, I., Caspi, Y., Guedeau-Boudeville, M. A., Arzi, T. & Stavans, J. Budding and Trends Cell Biol. 20, 177–186 (2010). tubulation in highly oblate vesicles by anchored amphiphilic molecules. Phys. Rev. 67. Karpova, T. S. et al. Role of actin and Myo2p in polarized secretion and growth of Lett. 91, 138102 (2003). Saccharomyces cerevisiae. Mol. Biol. Cell 11, 1727–1737 (2000). 36. Lipowsky, R. Bending of membranes by anchored polymers. Europhys. Lett. 30, 197– 68. Zech, T., Calaminus, S. D. & Machesky, L. M. Actin on trafficking: Could actin guide 202 (1995). directed receptor transport? Cell Adh. Migr. 6, 476–481 (2012). 37. Kim, Y. W. & Sung, W. Y. Membrane curvature induced by polymer adsorption. Phys. 69. Campelo, F. & Malhotra, V. Membrane fission: the biogenesis of transport carriers. Annu. Rev. E 63, 041910 (2001). Rev. Biochem. 81, 407–427 (2012). 38. Imjeti, N. S. et al. N-Glycosylation instead of cholesterol mediates oligomerization and 70. Ferguson, S. M. & De Camilli, P. Dynamin, a membrane-remodelling GTPase. Nat. Rev. apical sorting of GPI-APs in FRT cells. Mol. Biol. Cell 22, 4621–4634 (2011). Mol. Cell Biol. 13, 75–88 (2012). 39. Tooze, S. A., Martens, G. J. & Huttner, W. B. Secretory granule biogenesis: rafting to 71. Schmid, S. L. & Frolov, V. A. Dynamin: functional design of a membrane fission catalyst. the SNARE. Trends Cell Biol. 11, 116–122 (2001). Annu. Rev. Cell Dev. Biol. 27, 79–105 (2011). 40. Vennema, H. et al. Nucleocapsid-independent assembly of coronavirus-like particles 72. Boucrot, E. et al. Membrane fission is promoted by insertion of amphipathic helices by co-expression of viral envelope protein genes. EMBO J. 15, 2020–2028 (1996). and is restricted by crescent BAR domains. Cell 149, 124–136 (2012). 41. Wang, C. W., Hamamoto, S., Orci, L. & Schekman, R. Exomer: A coat complex for 73. Rawicz, W., Olbrich, K. C., McIntosh, T., Needham, D. & Evans, E. Effect of chain length transport of select membrane proteins from the trans-Golgi network to the plasma and unsaturation on elasticity of lipid bilayers. Biophys. J. 79, 328–339 (2000). membrane in yeast. J. Cell Biol. 174, 973–983 (2006). 74. Evans, E. & Rawicz, W. Entropy-driven tension and bending elasticity in condensed-fluid 42. Shibata, Y. et al. The reticulon and DP1/Yop1p proteins form immobile oligomers in membranes. Phys. Rev. Lett. 64, 2094–2097 (1990). the tubular endoplasmic reticulum. J. Biol. Chem. 283, 18892–18904 (2008). 75. Van Meer, G., Voelker, D. R. & Feigenson, G. W. Membrane lipids: where they are and 43. Walser, P. J. et al. Constitutive formation of caveolae in a bacterium. Cell 150, 752–763 how they behave. Nat. Rev. Mol. Cell Biol. 9, 112–124 (2008). (2012). 76. Hochmuth, F. M., Shao, J. Y., Dai, J. & Sheetz, M. P. Deformation and flow of membrane 44. Hu, J. et al. Membrane proteins of the endoplasmic reticulum induce high-curvature into tethers extracted from neuronal growth cones. Biophys. J. 70, 358–369 (1996). tubules. Science 319, 1247–1250 (2008). 77. Liu, J., Kaksonen, M., Drubin, D. G. & Oster, G. Endocytic vesicle scission by lipid 45. Stagg, S. M. et al. Structure of the Sec13/31 COPII coat cage. Nature 439, 234–238 phase boundary forces. Proc. Natl Acad. Sci. USA 103, 10277–10282 (2006). (2006). 78. Sankaranarayanan, S., Atluri, P. P. & Ryan, T. A. Actin has a molecular scaffolding, not 46. Faini, M. et al. The structures of COPI-coated vesicles reveal alternate coatomer propulsive, role in presynaptic function. Nat. Neurosci. 6, 127–135 (2003). conformations and interactions. Science 336, 1451–1454 (2012). 79. Cocucci, E., Aguet, F., Boulant, S. & Kirchhausen, T. The first five seconds in the life 47. Darsow, T., Katzmann, D. J., Cowles, C. R. & Emr, S. D. Vps41p function in the alkaline of a clathrin-coated pit. Cell 150, 495–507 (2012). phosphatase pathway requires homo-oligomerization and interaction with AP-3 through 80. Mehlert, A., Wormald, M. R. & Ferguson, M. A. Modeling of the N-glycosylated two distinct domains. Mol. Biol. Cell 12, 37–51 (2001). transferrin receptor suggests how transferrin binding can occur within the surface coat 48. Bielli, A. et al. Regulation of Sar1 NH2 terminus by GTP binding and hydrolysis of Trypanosoma brucei. PLoS Pathog. 8, e1002618 (2012). promotes membrane deformation to control COPII vesicle fission. J. Cell Biol. 171, 81. Zhang, F., Zang, T., Wilson, S. J., Johnson, M. C. & Bieniasz, P. D. Clathrin facilitates 919–924 (2005). the morphogenesis of retrovirus particles. PLoS Pathog. 7, e1002119 (2011). 49. Brodsky, F. M. Diversity of clathrin function: new tricks for an old protein. Annu. Rev. 82. Johnson, D. C. & Baines, J. D. Herpesviruses remodel host membranes for virus egress. Cell Dev. Biol. 28, 309–336 (2012). Nat. Rev. Microbiol. 9, 382–394 (2011). 50. Luo, Y., Zhan, Y. & Keen, J. H. Arf6 regulation of gyrating-clathrin. Traffic 14, 97–106 83. Fotin, A. et al. Molecular model for a complete clathrin lattice from electron (2012). cryomicroscopy. Nature 432, 573–579 (2004). 51. Wakeham, D. E., Chen, C. Y., Greene, B., Hwang, P. K. & Brodsky, F. M. Clathrin self- 84. Hierro, A. et al. Functional architecture of the retromer cargo-recognition complex. assembly involves coordinated weak interactions favorable for cellular regulation. EMBO Nature 449, 1063–1067 (2007). J. 22, 4980–4990 (2003). 85. Tanaka-Takiguchi, Y., Kinoshita, M. & Takiguchi, K. Septin-mediated uniform bracing 52. Den Otter, W. K. & Briels, W. J. The generation of curved clathrin coats from flat plaques. of phospholipid membranes. Curr. Biol. 19, 140–145 (2009). Traffic 12, 1407–1416 (2011). 86. Effantin, G. et al. ESCRT-III CHMP2A and CHMP3 form variable helical polymers in vitro 53. Nossal, R. Energetics of clathrin basket assembly. Traffic 2, 138–147 (2001). and act synergistically during HIV-1 budding. Cell. Microbiol. 15, 213–226 (2013). 54. Antonny, B., Madden, D., Hamamoto, S., Orci, L. & Schekman, R. Dynamics of the 87. Carnahan, N. F. & Starling, K. E. Equation of state for nonattracting rigid spheres. COPII coat with GTP and stable analogues. Nat. Cell Biol. 3, 531–537 (2001). J. Chem. Phys. 51, 635 (1969). 55. Townley, A. K. et al. Efficient coupling of Sec23–Sec24 to Sec13–Sec31 drives COPII- 88. Song, Y. H., Mason, E. A. & Stratt, R. M. Why does the Carnahan-Starling equation dependent collagen secretion and is essential for normal craniofacial development. work so well. J. Phys Chem 93, 6916–6919 (1989). J. Cell Sci. 121, 3025–3034 (2008). 89. Scheve, C. S., Gonzales, P. A., Momin, N. & Stachowiak, J. C. Steric pressure between 56. Malhotra, V. & Erlmann, P. Protein export at the ER: loading big collagens into COPII membrane-bound proteins opposes lipid phase separation. J. Am. Chem. Soc. 135, carriers. EMBO J. 30, 3475–3480 (2011). 1185–1188 (2013). 57. Huang, F. & Sorkin, A. Growth factor receptor binding protein 2-mediated recruitment 90. Blondeau, F. et al. Tandem MS analysis of brain clathrin-coated vesicles reveals their of the RING domain of Cbl to the epidermal growth factor receptor is essential and critical involvement in synaptic vesicle recycling. Proc. Natl Acad. Sci. USA 101, sufficient to support receptor endocytosis. Mol. Biol. Cell 16, 1268–1281 (2005). 3833–3838 (2004).

NATURE CELL BIOLOGY VOLUME 15 | NUMBER 9 | SEPTEMBER 2013 1027