How curvature-generating proteins build scaffolds on membranenanotubes

Simunovic, M., Evergren, E., Golushko, I., Prévost, C., Renard, H-F., Johannes, L., McMahon, H. T., Lorman, V.,Voth, G. A., & Bassereau, P. (2016). How curvature-generating proteins build scaffolds on membranenanotubes. Proceedings of the National Academy of Sciences, 113(40), 11226-11231.https://doi.org/10.1073/pnas.1606943113

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How curvature-generating proteins build sca�olds onmembrane nanotubesMijo Simunovic 1,2 †, Emma Evergren 3‡, Ivan Golushko 4 , Coline Pr évost 1 , Henri-Fran çois Renard 5¶, Ludger Johannes 5 ,Harvey T. McMahon 3 , Vladimir Lorman 4 , Gregory A. Voth 2 , and Patricia Bassereau 1,6

1 Laboratoire Physico Chimie Curie, Institut Curie, PSL Research University, CNRS UMR168, 75005, Paris, France 2 Department of Chemistry, Institute forBiophysical Dynamics, James Franck Institute and Computation Institute, The University of Chicago, 5735 S Ellis Avenue, Chicago, IL 60637, USA 3 MedicalResearch Council Laboratory of Molecular Biology, Francis Crick Avenue, Cambridge CB2 0QH, UK 4 Laboratoire Charles Coulomb, UMR 5221 CNRSUniversit é de Montpellier, F-34095, Montpellier, France 5 Institut Curie, PSL Research University, Chemical Biology of Membranes and Therapeutic Deliveryunit, CNRS UMR3666, INSERM U1143, F-75248 Paris, France 6 Sorbonne Universit és, UPMC Univ Paris 06, 75005, Paris, France

Submitted to Proceedings of the National Academy of Sciences of the United States of America

Bin/Amphiphysin/Rvs (BAR) domain proteins control the curvatureo� ipid membranes in endocytosis, traf�cking, cell motility, theformation of complex sub-cellular structures, and many other cel-lular phenomena. They form three-dimensional assemblies, whichact as molecular sca�olds to reshape the membrane and alter itsmechanical properties. It is unknown, however, how a proteinsca�old forms and how BAR domains interact in these assembliesat protein densities relevant for a cell. In this work, we em-ploy various experimental, theoretical and simulation approachesto explore how BAR proteins organize to form a sca�old ona membrane nanotube. By combining quantitative microscopywith analytical modeling, we demonstrate that a highly curvingBAR protein endophilin nucleates its sca�olds at the ends of amembrane tube, contrary to a weaker curving protein centaurin,which binds evenly along the tube’s length. Our work implies thatthe nature o� ocal protein-membrane interactions can a�ect thespeci�c localization of proteins on membrane-remodeling sites.Furthermore, we show that amphipathic helices are dispensable informing protein sca�olds. Finally, we explore a possible molecularstructure of a BAR-domain sca�old using coarse-grained moleculardynamics simulations. Together with �uorescence microscopy, thesimulations show that proteins need only to cover 30–40% ofa tube ’s surface to form a rigid assembly. Our work providesmechanical and structural insights into the way BAR proteins maysculpt the membrane as a high-order cooperative assembly inimportant biological processes.

protein sca�old | BAR proteins | coarse-grained simulations

IntroductionCurvature o� ipid membranes plays important roles in the cell.It allows dynamic cellular phenomena, such as tra�cking orcell division, and it can also mediate the interactions amongmany membrane-bound proteins (1, 2). Proteins containing aBin/Amphiphysin/Rvs (BAR) domain participate in numerousmembrane-curving processes, such as endocytosis, tra�cking,motility, the formation of T-tubules, cytokinesis, etc. (3, 4). BARdomains are characterized by a crescent shape whose curvature,length, and binding a�nity to the membrane are distinct amongdi�erent members (4-6). Many BAR proteins also contain am-phipathic helices that shallowly insert into the bilayer.

BAR proteins generate curvature as a combination of (a),adhesive electrostatic interactions via their BAR domain and (b),the insertion of amphipathic helices. Additionally, BAR proteinscan associate into highly ordered assemblies on the membranethus collectively altering its shape andmechanics (7-10). Preciselyhow they assemble and a�ect the membrane is argued to dependon the surface density of proteins, membrane tension, and mem-brane shape (11). On a �at membrane at a low surface density,BAR proteins can form strings and a mesh-like network, whichcan give rise to budding and tubulation (12-16). At a su�cientlyhigh protein density, they impact themechanical properties of themembrane and stabilize membrane nanotubes (7, 10, 17-20).

An assembly of BAR proteins on cylindrical membranes hasso far only been visualized using electron microscopy (EM), e.g.(8, 9, 21). While these studies provide important and detailed as-sessments of how BAR domainsmay interact with one another oncurved membranes as a packed protein arrangement, membranetubules in those experiments were generated typically from highlycharged liposomes exposed to very high protein concentrations.In the cell, especially in the context of endocytosis, protein con-centration is not high enough to induce appreciable spontaneoustubulation, nor would such a mechanism be bene�cial to the cell.Importantly, a tightly packed assembly of BAR proteins wouldpreclude the recruitment of many other proteins required inendocytosis and tra�cking.

To achieve close packing, protein-protein interactions wereimplicated to be important, namely the lateral interactions be-tween neighboring BAR domains in F-BAR proteins (8) or be-tween N-terminal amphipathic helices in N-BAR proteins (9). Itis unclear whether BAR proteins in endocytosis and tra�ckingcooperatively shape the membrane by virtue of speci�c protein-protein interactions or if they assemble as a result of a more gen-eral membrane-mediated mechanism. Moreover, it is importantto understand how BAR proteins assemble at much lower proteinsurface densities and onmembrane compositions thatmuchmorelikely resemble those found within the cell.

We hypothesize that BAR proteins can oligomerize on amembrane nanotube at densities much lower than close packing

Signi�cance

Lipid membranes are dynamic assemblies, changing shape onnano- to micron-sized scales. Some proteins can sculpt mem-branes by organizing into a molecular sca�old, dictating themembrane ’s shape and properties. We combine microscopy,mathematical modeling, and simulations to explore how BARproteins assemble to form sca�olds on nanotubes. We showthat the way protein locally deforms the membrane a�ectswhere it will nucleate before making a sca�old. In this process,the protein ’s amphipathic helices —which shallowly insert intothe membrane —appear dispensable. Surprisingly, the sca�oldforms at low protein density on the nanotube. We simulatea structure of protein sca�olds at molecular resolution, shed-ding light on how these proteins may sculpt the membrane tofacilitate important dynamic events in cells.

Fig. 1. Sca�olding by endophilin A2. (A) Endophilin A2 N-BAR domain (aa1–247) binds to the tube ’s base and forms a sca�old that continuously growsalong the tube (note the progressive constriction in the tube radius fromthe GUV toward the OT). White circle = OT. (B) A kymogram of sca�oldgrowth from the GUV to the bead (�uorescence dims near the end as thetube buckles in and out o� ocus). Lipid and protein channels are overlaid.The plot shows tube-retraction force, f , as a function of time, t . The x-axisof the kymogram coincides with the x-axis of the plot. (C) Time lapse of astriated pattern induced by endophilin A2 N-BAR domain. In all: scale bar,2 μm; GUV, giant unilamellar vesicle; OT, optical trap; endo, endophilin A2N-BAR domain; t = 0 marks the time when protein was detected on the tube.

Fig. 2. Sca�olding by N-BAR versus BAR domains. (A) β2 centaurin BARdomain (aa 1-384) binds evenly along the tube (red: lipid; green: protein) andcauses a decrease in tube-retraction force, f , just like endophilin. Scale bar, 2μm. (B) Dilation of a narrow tube induced by a sca�old of β2 centaurin BARdomain (overlaid are �uorescence intensity of the protein on the tube, Itub ,and the tube radius, r , deduced from lipid �uorescence). (C) The mechanicsof the reference membrane ( N = 45) and after the formation of a sca�oldby endophilin A2 WT (endo WT, N = 7) and β2 centaurin (centa, N = 5). Tubeforce, f, measured from the optical trap; tube radius, r , measured from lipid�uorescence.

Table 1. Radius ( r ) of sca�olded tubes measured from lipid�uorescence. Mean ±SD (N measurements). Endo WT = wild-typeendophilin A2 (data from the full length protein and the N-BARdomain is pooled); endo ΔH0 = endophilin A2 with truncatedN-terminal helices; endo mut = endophilin A2 N-BAR domainE37K, D41K.

endo WT endo ΔH0 endo mut centa

r (nm) 9.8 ±2.8 (10) 21.4 ±11.6 (7) 19.9 ±3.0 (7) 42.5 ±7.0 (5)

Fig. 3. Amphipathic helices do not determine the sca�old initiation site.Shown are force plots (white) overlaid on kymograms o� ipid �uorescenceof a membrane nanotube (red marker) during binding and sca�olding byendophilin mutants. As before, the formation of a sca�old is evident fromtube constriction. Endo ΔH0 = endophilin A2 with truncated N-terminalhelices; endo mut = endophilin A2 N-BAR domain E37K, D41K.

Fig. 4. Strongly-curving proteins nucleate at the base of a pinned and�uctuating tube. Mathematical model: strain energy variation pro�le, E, as afunction of the axial position on the tube, z (in percentage of total length),plotted using = 0.25% (orange) and 0.05% (blue), = 50 kBT , = 100.

Fig. 5. Simulation of N-BAR domains on nanotubes. Shown are �nalsnapshots of CG MD simulations of membrane tubes coated with N-BARproteins at the indicated protein surface densities. Scale bar, 20 nm.

owing to membrane-mediated attractions. We refer to this struc-ture as a protein sca�old. It is to be noted that the term sca�old isoften used to describe a single BAR domain, imprecisely termedthe sca�olding domain. Here, a sca�old represents a three-dimensional rigid assembly of multiple proteins that adheresto the membrane and a�ects the shape and properties of themembrane.

In this work, we combine in vitro reconstitution, �uorescentmicroscopy, mechanical measurements, and analytical modeling

to describe the mechanism by which BAR proteins assemble onmembrane nanotubes to form a sca�old. We also demonstratethat rigid protein sca�olds form at much lower surface densitiesthan full packing. We simulate the protein sca�old at molecularresolution using coarse-grained (CG) molecular dynamics (MD).

Finally, as the relative contribution of BAR domain versusamphipathic helices in inducing curvature is still highly debated,we explore how these domains contribute to the sca�old forma-tion. To this end, we tested three proteins with well-distinguishedstructural features: endophilin A2 (an N-BAR protein containingfour amphipathic helices), endophilin A2 mutants, β2-centaurin(a classical BAR domain with no amphipathic helices), and epsin1 (a protein that binds membranes via an amphipathic helix in itsepsin N-terminal homology domain).

ResultsEndophilin sca�old initiates at the base of a tube. To study theinteractions of BAR proteins with a cylindrical membrane, weused a previously developed micromanipulation setup (7). In theexperiment, we pull a nanotube from a giant unilamellar vesicle(GUV) using optical tweezers. A nanotube connected to thebase membrane is a typical con�guration characteristic of someendocytic processes, such as in a clathrin-independent endocyticmechanism mediated by endophilin (22, 23). The vesicle is heldby a micropipette whose aspiration pressure sets the membranetension, implicitly tube radius, in the absence of proteins (24, 25)(see SI Text). Thus, we have a direct control of the initial radiusof curvature, which in our case ranges from � 10 nm to � 100 nm(7). With another micropipette, we inject the protein near thetube, starting from low vesicle tension. The N-BAR domain ofthe wild-type endophilin A2 and β2 centaurin (BAR + pleckstrinhomology domain) were �uorescently labeled so that we coulddirectly observe their binding to the membrane with confocalmicroscopy. By measuring the lipid and the protein �uorescence,we can calculate the tube radius and the protein’s surface density,respectively (7) (see Fig. S1 and SI Text). Therefore, at the sametime, we observe how proteins a�ect the shape of the membrane,while controlling membrane tension and membrane curvature.

We prepared GUVs using a total lipid brain extract, supple-mented with 5% PI(4,5)P 2. As such a natural composition hasnot yet been used for quantitative mechanical measurements (26,27), we con�rmed that the membrane curvature scales with GUVtension as theoretically expected for �uid membranes (25) andthat these vesicles are not undergoing phase separation (28) (seeSI Text, Figs. S2 and S3).

First, we studied how the N-BAR of endophilin A2 (29, 30)(Fig. S4) forms a sca�old on a membrane tube, by injecting theprotein at 0.5–2 5 µM (dimeric concentration in the pipette). Notethat due to di�usion, the concentration of the protein near theGUV is approximately half that in the pipette (31). Endophilinshowed a remarkable speci�city for the base of a pulled nanotube,binding �rst either at the interface with the vesicle or with thetrapped bead (Fig. 1A). Note that the two interfaces are mor-phologically equivalent, having the same saddle-like membranegeometry. Out of 59 experiments, endophilin �rst bound to theGUV-tube interface in 53 of them, while also simultaneouslybinding to the interface with the bead in 27 experiments. In fourcases, endophilin appeared to bind homogeneously along the tubewhere, possibly, the initial binding was not recorded su�cientlyfast. Only in the two remaining cases considered as negative, theprotein �rst bound to a region other than the interface.

Shortly after binding, the region covered by endophilin con-tinuously grew along the tube eventually partially or fully coveringit (Fig. 1 A and B; see SI Text for additional statistics). In mostcases, the growth of the endophilin sca�old was linear and itranged from � 20 nm.s−1 to � 300 nm.s−1 (Fig. 1 B , see also Fig.S5 and Movie S1).

The marked reduction of the lipid �uorescence intensityunderneath the protein (Fig. 1 A , lipid channel) indicates that en-dophilin changes the tube radius independently of GUV tension.Hence, it forms a stable three-dimensional structure that dictatesthe membrane curvature. Tube constriction has previously beenobserved with other members of the BAR family (7, 22, 32), al-though the dynamics of sca�old formation has not been captured.Binding and constriction under the sca�old are concomitant withthe progressive drop in force required to hold the nanotube (Fig.1B ). A fully covered tube at low GUV tension imposes no forceon the optical trap and undergoes buckling (see the deformationof the tube in the bottom panel of Fig. 1A , also see Movie S1). Ofnote, in the experiments, the proteins are also bound to the GUV(see e.g. Fig. 1 A).

We observed no di�erence in the tube-binding behavior be-tween the full-length endophilin A2 (N-BAR + SH3 domain) andonly its N-BAR domain, indicating that the location of sca�oldinitiation is not determined by the protein ’s SH3 domain (Fig. S5).

Interestingly, sometimes at higher injected concentrations(>1 5 µM in the injection pipette), endophilin initially formed astriated pattern on the nanotube, marked by a brief (few seconds)beading instability (Fig. 1 C , observed in six out of 31 experi-ments). The striation rapidly coarsened leading to a growth of thesca�old fromboth bases of the tube. To some extent, this behavioris reminiscent of the way dynamin binds to membrane tubes.Dynamin binds in a striated pattern and a�ects the membraneforce. In the case of dynamin, however, the membrane forcechanges only after the entire tube is covered with the protein (33,34), contrary to endophilin, in which case a decrease in the forceis seen immediately upon binding.

Role of protein subdomains in sca�olding. We then aimed toexamine how changing the intrinsic curvature and the presence ofamphipathic helices a�ect the sca�olding dynamics. β2 centaurinprovides a good testing ground, as it is one o� ew BAR pro-teins without an N-terminal amphipathic helix (35). Additionally,the BAR domain of centaurin is much shallower than that ofendophilin, as judged by their atomic models (see SI Text, Fig.S4). Contrary to endophilin, centaurin bound homogeneouslyalong the nanotube, with no detectable preference to the neck(Fig. 2 A). Nevertheless, there was a reduction in the membraneforce during binding, leading to a buckling instability at lowtension (Fig. 2 A). Importantly, binding of the protein changedthe curvature of the tube, even though the aspiration pressureremained the same. Figure 2 B shows an example where bindingof β2 centaurin dilates a 30-nm tube by � 20 nm. Furthermore,once the sca�old forms, either by centaurin or endophilin, thetube radius remains constant; its magnitude is characteristic ofthe protein, but independent of GUV tension (Fig. 2 C ). Namely,the tube sca�olded by centaurin is approximately four timeswiderthan the one sca�olded by endophilin (42.5 nm compared to 10nm, see Table 1). This observation is in line with the di�erence inintrinsic curvatures of their BAR domains (Fig. S4).

The formation of a sca�old by either endophilin or centaurinalso drastically changes the mechanics of the membrane, evidentfrom the systematic reduction in the equilibrium tube force for alltestedmembrane tensions (Fig. 2C ). Based on previous analyticalmodeling, the force of a sca�olded tube—characterized by aconstant radius—is expected to linearly depend on GUV tension,whereas a bare membrane is expected to have a square-rootdependence (7, 25). Indeed, membrane force of protein-coveredtubes in experiments shown in Fig. 2C display a linear dependenceon tension (Fig. S6), thus con�rming the formation of a sca�oldby a measurement independent of tube radius.

These experiments demonstrate that both BAR domains thatcontain membrane inserting amphipathic helices (endophilin)and those that do not (β2 centaurin) are capable o� orming arigid structure that controls the curvature of the membrane. They

also show that proteins from the same family may bind to themembrane at di�erent locations (we explore this point in the nextsection).

To further investigate the role of amphipathic helices versusthe BAR domain in sca�olding, we constructed two endophilinmutants. In the �rst, we truncated the N-terminal amphipathichelix of the full-length endophilin A2 (endo △H0). In the sec-ond, we mutated one glutamate and one aspartate from themembrane-binding region of endophilin A2 N-BAR domain intolysines (E37K, D41K) (endo mut), which enhances the bindingstrength of the BAR domain to the membrane. Both variantsconstricted the tube starting from an interface (Fig. 3, red �uo-rescence) and decreased the force (Fig. 3, white plot) and tuberadius (Table 1), in the same manner as the WT. This observa-tion con�rms that the N-terminal amphipathic helices are notnecessary for the formation of the sca�old or, interestingly, forthe preferential binding to the tube’s base in these experiments,although the sca�olding rate appears slower (Fig. 3).

Finally, we tested the full-length epsin 1, another impor-tant endocytic protein, which participates in the initial stagesof clathrin-mediated endocytosis (36). Epsin does not containa BAR domain; instead, it binds and bends the membrane viaan amphipathic helix. There was a clear mechanical e�ect uponthe injection of epsin 1, characterized by a systematic reductionin both the equilibrium tube force and the tube radius for awide range of membrane tensions, indicating that the proteininduces positive spontaneous curvature (7) (Fig. S7). Similarly tocentaurin, the constriction did not start from the base; rather itappeared homogenous along the tube length. Unlike endophilinand centaurin, the force never decreased to zero and so we neverobserved buckling. The square-root scaling of the force withmembrane tension (Fig. S6) indicates that no sca�old forms, evenat very high protein concentration (ten-fold higher than minimalendo WT concentration that makes a sca�old). In summary,amphipathic helices alone may remodel the membrane, as in thecase of epsin. However, the anisotropic BAR domain is criticalfor forming a rigid sca�old.

Pinning a �uctuating tube determines the protein ’s bindingsite. So far, we demonstrated that BAR proteins lacking am-phipathic helices may form sca�olds just as N-BAR proteins,however it is still unclear what determines the nucleation site ofthe protein. Our experiments cannot provide a general mecha-nism to answer this question and so we developed a mathemat-ical model of BAR proteins interacting with a membrane tube.Several models have already been proposed for an equivalentsystem (7, 37), but those models did not capture the location ofprotein nucleation. We extend these models in two ways. First,we generalize the protein-membrane interactions by assumingthat the proteins induce a local perturbation, expressed in termsof a tension or a pressure variation. Second, instead of takingperiodic boundary conditions, wemodel amembrane tube pinnedat its ends assuming that the radial displacement of the bilayer isstrongly limited at the one end by the optical trap and on the otherby the vesicle.

As we show in the SI Text in detail, we decompose the freeenergy into the costs of (a) bending and (b) stretching the mem-brane, supplemented by (c) a term accounting for membrane-protein interactions, and (d) the energy associated with a pointforce keeping the membrane tubular (Eq. S14) (25, 37, 38).Solving the equation in the limit o� ow protein concentration, weobtain the mechanical strain energy variation (Eq. S17) inducedby membrane-protein interactions, whose minima essentially in-dicate the binding sites of the protein. Importantly, the shapeof this function strongly depends on the protein-induced localtension (or curvature) perturbation. When taking a local tensionvariation of 0.25%, the energy pro�le has a minimum at eachof the tube’s ends separated by a very high energy barrier at the

tube’s center (Fig. 4). Reducing the local perturbation �ve-foldto 0.05% lowers the barrier to

aggregation previously predicted for N-BAR proteins and, to aweaker degree, spherical particles (12-14, 41). Under con�ne-ment (on a �at or spherical surface), the proteins pack into amesh(12), however it appears that a tubular surface directs the proteinsinto a helix, with 7–8 N-BAR domains making a full helical turn(Fig. 5).

We note that in CG MD simulations the helix contiguouslywraps the tubule at 30–40% protein coverage, in excellent agree-ment with the experimentally measured sca�old density. Onceattaining this density, the proteins cease to exchange neighborsand the helix becomes quasi-static (Fig. 5, see SI Text, Fig. S9).

DiscussionTwo related curvature-generating proteins can initiate a sca�oldat di�erent membrane locations, as shown by our in vitro recon-stituted system. Namely, an N-BAR protein endophilin nucleatesat the tube’s ends, whereas a BAR protein centaurin binds evenlyalong it. Our mathematical modeling predicts that speci�c bind-ing to the saddle-shaped neck of a pinned and �uctuating mem-brane tube is a consequence of strong local membrane pertur-bations. An important conclusion from these observations is thatthe nature o� ocal protein-membrane interactions can a�ect thespeci�c initial localization of proteins on curved membranes and,thus, the dynamics of their assembly on membrane-remodelingsites.

Although the complexity ofmulti-protein interactionsmay di-vert the nucleation preference of BAR proteins in a cell, previousin vivo studies of endocytosis seem to very well agree with our�ndings. Immunoelectron microscopy of endophilin on clathrin-coated pits in cells at endogenous protein concentrations showedthat endophilin indeed sits at the base of the clathrin coat (42).In the same study, in cells treated with a non-hydrolysable GTP,which form long dynamin-covered tubes, endophilin was againonly found at the base of the coat (42). By contrast, dynamin wasfound all along the tubule’s length.

Endophilin interacts with other proteins in a dynamic way.Namely, the tubulation e�ciency and the amount of dynaminrecruited to GUVs or lipid tubules are signi�cantly increasedby endophilin, and vice versa (42, 43). Furthermore, acutelyperturbing endophilin using antibodies against the SH3- or theBAR-domain stalled the formation of clathrin-coated pits beforethe sculpting of a narrow neck and the saddle (44, 45). Hence,endophilin could potentially play important roles in directingother endocytic proteins to their binding site.

Concerning protein ’s subdomains, BAR domain appears cru-cial for the formation of a rigid sca�old. As previously demon-strated on a �at membrane, local membrane deformations me-diate the interactions among BAR proteins and induce their as-sembly. The anisotropic shape of the BAR domain likely furtherfacilitates an ordered packing and the formation of a sca�old.Therefore, a BAR domain is indeed a sca�olding domain, al-though not because a single protein imprints its shape on themembrane, but owing to a collective e�ect imposed by an orderedmembrane-mediated helical assembly. Moreover, amphipathichelices appear dispensable in sca�olding; however, their role isstill important in facilitating protein recruitment to the mem-brane (22) and in increasing the membrane ’s spontaneous cur-vature (Table 1). They may also have a role at the molecular levelto help properly orient the BAR domains into a rigid sca�old,evidenced by the wide distribution of tubular radii when they aretruncated (Table 1) (22), agreeing with previous work (9).

Importantly, our results show that a sca�old can form atmuchlower surface densities than full packing. Dense protein packingwould be problematic for endocytosis. According to previoussimulations, the shape of a basic unit of a BAR-domain lattice onthe membrane a�ects the radius of the sca�old (18). Therefore,the radius of the tubule sca�olded by the same protein would

be variable, depending on the way it formed the lattice, whichseems unfavorable for endocytosis and tra�cking that requirea tight curvature control. Indeed, tubule radii from di�erent invitro studies were infrequently di�erent for the same protein. Forexample, tubule radii formed and sca�olded by amphiphysin 1 invitro (measured between themembranemidplanes) were found tobe 21 nm (35) and � 11 nm (46), both based on EM imaging, com-pared to 7 nmmeasured by �uorescencemicroscopy (7). Based onour combined experimental and simulation data, under proteinconcentrations much lower than used in EM imaging in vitro,BAR proteins do not build lattices on pre-formed tubes. Instead,they only cover 30–45%of the surface (depending on the protein),forming a stable and a rigid sca�old with constant curvature, inresemblance to in vivo EM images in which membrane tubuleswere created in the cell by endogenous protein concentrations(42, 47). In turn, this assembly provides structural integrity forendocytosis and leaves su�cient membrane area for the bindingof accessory proteins crucial in the process (42, 46, 48).

Based on our work, we can propose di�erent biologically rel-evant purposes for the N-BAR domain sca�olds. First, in endo-cytosis, they constrict the membrane tube between the endocyticvesicle and the underlying membrane, thus reducing the energybarrier for scission by dynamin (33) or by elongation forces (22).Second, highly curving proteins like endophilin are speci�callyrecruited to the neck and so in clathrin-dependent endocytosis,where endophilin recruits dynamin to the tube (43), the scissionsite will be highly localized to the base of the coat. Third, sca�oldsprovide a powerful control of membrane curvature that maybe used in forming complex cellular architectures, such as inthe formation of T-tubules or the maintenance of mitochondrialshape, which require N-BAR proteins amphiphysin 2 (49) andendophilin B1 (50), respectively. The subtle di�erences in struc-tures of these proteins give rise to a complexity in intracellulararchitectures and the highly dynamic behavior of the membrane.These di�erences are also likely the key way of modulatingthe function and localization of BAR proteins. We also expectthat in the near future, the higher-order organization of BARproteins will be shown crucial in additional important membrane-remodeling phenomena.

MethodsPulling nanotubes and making protein sca�olds. GUVs (95% total lipidbrain extract (26), 5% PI(4,5)P 2 , supplemented with 0.1% di-stearoyl phos-phatidyl ethanolamine-PEG(2000)-biotin and 1% BODIPY TR ceramide) wereprepared by electroformation on Pt-wires over night at 4 °C in a salt-containing bu�er (51). To pull a tube, the GUV was aspirated in a mi-cropipette, brought in contact with a streptavidin-coated optically trappedbead then gently pulled away. Proteins were injected near the tube withanother micropipette. The aspiration pressure sets the membrane tension

and the tube radius, r , in the absence of proteins, as , whereis membrane sti�ness and is membrane tension (7, 24, 52-54). The tubeforce, f , was measured by video-microscopy as , where isthe trap sti�ness and and are the current and the equilibrium beadpositions, respectively. The r (in the presence or absence of proteins) wasmeasured from lipid �uorescence as , where and arethe �uorescence intensities o� ipids in the tube and in the GUV, respectively,and = 200±50 nm is a previously measured calibration constant (7, 32).

CGMD simulations. We used a solvent-free three-site CG lipidmodel (55)and a 26-site elastic network model of an N-BAR domain dimer of endophilinA1 (9), with protein-membrane interactions modeled using a Lennard-Jonespotential as described previously (12). We simulated N-BARs on a lipid bilayertube (150 nm in length and 20 nm in diameter interacting with its periodicimages in the tube direction) at 5%, 10%, 30%, and 40% surface coverage.The simulations were carried at constant number of molecules, box volumeand temperature ( NVT ) for � 30 million time steps at a time step of 12 fsusing LAMMPS (56).

Acknowledgements.We thank A. Callan-Jones for insightful discussions. M.S. and G.A.V.

were supported by the National Institutes of Health (grant R01-GM063796)and the National Science Foundation (Xsede computational resources grantTG-MCA94P017, supercomputer Stampede), P.B. and L.J. by the AgenceNationale pour la Recherche (ANR-11BSV201403 to P.B. and ANR-09BLAN283to H.F.R. and L.J.), L.J. of the European Research Council advanced grant

(project 340485), E.E. and H.T.M by the Medical Research Council UK (grantU105178795). M.S. was funded in part by the Chateaubriand fellowship,France and Chicago Collaborating in the Sciences grant, and the UniversityParis Diderot. The P.B. group belongs to the CNRS consortium CellTiss, P.B.

and L.J. groups to the Labex CelTisPhyBio (ANR-11-LABX0038), and to ParisSciences et Lettres (ANR-10-IDEX-0001-02). The V.L. group belongs to theLabex NUMEV.

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