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RESEARCH ARTICLE SPECIAL ISSUE: RECONSTITUTING CELL BIOLOGY Drp1 polymerization stabilizes curved tubular membranes similar to those of constricted mitochondria Begon ̃ a Ugarte-Uribe 1,2 , Coline Pre ́ vost 3,4 , Kushal Kumar Das 1 , Patricia Bassereau 3,4 and Ana J. Garcı ́ a-Sa ́ ez* ,1,5 ABSTRACT Dynamin-related protein 1 (Drp1), an 80 kDa mechanochemical GTPase of the dynamin superfamily, is required for mitochondrial division in mammals. Despite the role of Drp1 dysfunction in human disease, its molecular mechanism remains poorly understood. Here, we examined the effect of Drp1 on membrane curvature using tubes pulled from giant unilamellar vesicles (GUVs). We found that GTP promoted rapid rearrangement of Drp1 from a uniform distribution to discrete foci, in line with the assembly of Drp1 scaffolds at multiple nucleation sites around the lipid tube. Polymerized Drp1 preserved the membrane tube below the protein coat, also in the absence of pulling forces, but did not induce spontaneous membrane fission. Strikingly, Drp1 polymers stabilized membrane curvatures similar to those of constricted mitochondria against pressure changes. Our findings support a new model for mitochondrial division whereby Drp1 mainly acts as a scaffold for membrane curvature stabilization, which sets it apart from other dynamin homologs. KEY WORDS: Dynamin-related protein 1, Membrane biophysics, Protein self-assembly, Membrane curvature, Curvature stabilizer, Mitochondrial fission INTRODUCTION Mitochondria are eukaryotic organelles that host key cellular processes and metabolic reactions (Glancy and Balaban, 2012; Osman et al., 2011). They present an elaborate structure based on a branched and tubular network that undergoes continuous fission and fusion. The balance between fusion and fission events is crucial for the maintenance of functional mitochondrial structure, size, distribution, homogeneity and inheritance (Friedman and Nunnari, 2014; Okamoto and Shaw, 2005; Youle and van der Bliek, 2012). In addition, mitochondrial dynamics are directly linked to apoptosis (Chan, 2006; Detmer and Chan, 2007; Martinou and Youle, 2011) and emerging evidence suggests that defects in mitochondrial dynamics can lead to neurodegenerative diseases (Chen and Chan, 2009; Wilson et al., 2013; Zorzano and Claret, 2015). Over the past two decades, advances in light microscopy and genetic techniques have provided an unprecedented insight into mitochondrial dynamics. Current models include a number of key proteins that control mitochondrial shape, size and position (Friedman et al., 2011; Labbé et al., 2014; Ugarte-Uribe and García-Sáez, 2014). For example, both the fusion and fission of mitochondrial proteins are mediated by large GTPases of the dynamin family, such as mitofusin-1 and mitofusion-2, OPA1 and Drp1 (Chen et al., 2003; Cipolat et al., 2004; Legros et al., 2002; Smirnova et al., 2001), as well as regulatory factors such as Mff, Fis1, MiD49 or MiD51, known as Drp1 adaptors (Gandre-Babbe and van der Bliek, 2008; Koirala et al., 2013; Loson et al., 2013; Otera et al., 2010; Palmer et al., 2011). Yet, the molecular mechanisms of action of these proteins, and how their activities are coordinated to regulate mitochondrial dynamics remain elusive. The function of dynamin-related protein 1 (Drp1), an 80 kDa mechanochemical GTPase of the dynamin superfamily, is required for mitochondrial division of eukaryotic cells. Similarly to other members of this family, Drp1 adopts a four-domain architecture that includes a GTPase domain, a bundle-signaling element, a stalk and a B insert (Faelber et al., 2011; Fröhlich et al., 2013; Gao et al., 2010). Drp1 monomers assemble in a crisscross fashion via a contact interface found at the center of the stalk. Interactions via two additional interfaces are also required for Drp1 oligomerization, which leads to the formation of filaments around mitochondria (Bui and Shaw, 2013). According to this model, the GTPase domains in Drp1 oligomers are located on one side of the filament and opposite to the membrane, whereas the B-inserts face the membrane (Fröhlich et al., 2013). In contrast to classical dynamins, Drp1 does not contain a PH domain for membrane binding or curvature sensing and generation (Srinivasan et al., 2016). Instead, Drp1 includes a region known as a variable domain, whose function is still debated but has been related to membrane binding and negative regulation of cytosolic Drp1 assembly (Francy et al., 2015). Drp1 is recruited from the cytosol to the mitochondrial outer membrane in response to physiological cues. At the membrane, Drp1 forms large helical rings that wrap the organelle at discrete and predetermined fission sites (Smirnova et al., 2001). Then, Drp1 is believed to constrict the mitochondrial double membrane via its mechanochemical activity, leading to fission. However, this view has been extrapolated from molecular models of fission involving the Drp1 yeast homolog Dnm1 and other dynamin family members (Faelber et al., 2012, 2011; Ford et al., 2011; Mears et al., 2011). Structural studies have revealed a fourth interaction surface in Drp1 that is necessary for assembling two neighboring Drp1 filaments to give a broader filament size (14.4 nm). This filament size is similar to that in the model proposed for Dnm1 but differs from that of dynamin (10.6 nm) (Fröhlich et al., 2013; Mears et al., 2011). Thus, two double filaments of Drp1 that extend next to each other around the membrane tubule account for a two-start helix with a 28.8 nm helical pitch (Fröhlich et al., 2013). Recent reports have identified new adaptors in Drp1-mediated membrane fission, which mainly help in Received 14 July 2017; Accepted 5 December 2017 1 Interfaculty Institute of Biochemistry, University of Tu ̈ bingen, 72076 Tu ̈ bingen, Germany. 2 Biofisika Institute (CSIC, UPV/EHU), Department of Biochemistry and Molecular Biology, University of the Basque Country, 48940 Leioa, Spain. 3 Laboratoire Physico Chimie Curie, Institut Curie, PSL Research University, CNRS UMR168, 75005 Paris, France. 4 Sorbonne Université s, UPMC Univ Paris 06, 75005 Paris, France. 5 Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany. *Author for correspondence ([email protected]) A.J.G.-S., 0000-0002-3894-5945 1 © 2018. Published by The Company of Biologists Ltd | Journal of Cell Science (2019) 132, jcs208603. doi:10.1242/jcs.208603 Journal of Cell Science

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RESEARCH ARTICLE SPECIAL ISSUE: RECONSTITUTING CELL BIOLOGY

Drp1 polymerization stabilizes curved tubular membranes similarto those of constricted mitochondriaBegon a Ugarte-Uribe1,2, Coline Prevost3,4, Kushal Kumar Das1, Patricia Bassereau3,4 andAna J. Garcıa-Saez*,1,5

ABSTRACTDynamin-related protein 1 (Drp1), an 80 kDa mechanochemicalGTPase of the dynamin superfamily, is required for mitochondrialdivision in mammals. Despite the role of Drp1 dysfunction in humandisease, its molecular mechanism remains poorly understood. Here,we examined the effect of Drp1 on membrane curvature using tubespulled from giant unilamellar vesicles (GUVs). We found that GTPpromoted rapid rearrangement of Drp1 from a uniform distribution todiscrete foci, in line with the assembly of Drp1 scaffolds at multiplenucleation sites around the lipid tube. Polymerized Drp1 preservedthe membrane tube below the protein coat, also in the absence ofpulling forces, but did not induce spontaneous membrane fission.Strikingly, Drp1 polymers stabilized membrane curvatures similar tothose of constricted mitochondria against pressure changes. Ourfindings support a newmodel for mitochondrial division wherebyDrp1mainly acts as a scaffold for membrane curvature stabilization, whichsets it apart from other dynamin homologs.

KEY WORDS: Dynamin-related protein 1, Membrane biophysics,Protein self-assembly, Membrane curvature, Curvature stabilizer,Mitochondrial fission

INTRODUCTIONMitochondria are eukaryotic organelles that host key cellularprocesses and metabolic reactions (Glancy and Balaban, 2012;Osman et al., 2011). They present an elaborate structure based on abranched and tubular network that undergoes continuous fissionand fusion. The balance between fusion and fission events is crucialfor the maintenance of functional mitochondrial structure, size,distribution, homogeneity and inheritance (Friedman and Nunnari,2014; Okamoto and Shaw, 2005; Youle and van der Bliek, 2012). Inaddition, mitochondrial dynamics are directly linked to apoptosis(Chan, 2006; Detmer and Chan, 2007; Martinou and Youle, 2011)and emerging evidence suggests that defects in mitochondrialdynamics can lead to neurodegenerative diseases (Chen and Chan,2009; Wilson et al., 2013; Zorzano and Claret, 2015).Over the past two decades, advances in light microscopy and

genetic techniques have provided an unprecedented insight into

mitochondrial dynamics. Current models include a number of keyproteins that control mitochondrial shape, size and position(Friedman et al., 2011; Labbé et al., 2014; Ugarte-Uribe andGarcía-Sáez, 2014). For example, both the fusion and fission ofmitochondrial proteins are mediated by large GTPases of thedynamin family, such as mitofusin-1 and mitofusion-2, OPA1 andDrp1 (Chen et al., 2003; Cipolat et al., 2004; Legros et al., 2002;Smirnova et al., 2001), as well as regulatory factors such as Mff,Fis1, MiD49 or MiD51, known as Drp1 adaptors (Gandre-Babbeand van der Bliek, 2008; Koirala et al., 2013; Loson et al., 2013;Otera et al., 2010; Palmer et al., 2011). Yet, the molecularmechanisms of action of these proteins, and how their activities arecoordinated to regulate mitochondrial dynamics remain elusive.

The function of dynamin-related protein 1 (Drp1), an 80 kDamechanochemical GTPase of the dynamin superfamily, is requiredfor mitochondrial division of eukaryotic cells. Similarly to othermembers of this family, Drp1 adopts a four-domain architecture thatincludes a GTPase domain, a bundle-signaling element, a stalk anda B insert (Faelber et al., 2011; Fröhlich et al., 2013; Gao et al.,2010). Drp1 monomers assemble in a crisscross fashion via acontact interface found at the center of the stalk. Interactions via twoadditional interfaces are also required for Drp1 oligomerization,which leads to the formation of filaments around mitochondria (Buiand Shaw, 2013). According to this model, the GTPase domains inDrp1 oligomers are located on one side of the filament and oppositeto the membrane, whereas the B-inserts face the membrane(Fröhlich et al., 2013). In contrast to classical dynamins, Drp1does not contain a PH domain for membrane binding or curvaturesensing and generation (Srinivasan et al., 2016). Instead, Drp1includes a region known as a variable domain, whose function isstill debated but has been related to membrane binding and negativeregulation of cytosolic Drp1 assembly (Francy et al., 2015).

Drp1 is recruited from the cytosol to the mitochondrial outermembrane in response to physiological cues. At the membrane, Drp1forms large helical rings that wrap the organelle at discrete andpredetermined fission sites (Smirnova et al., 2001). Then, Drp1 isbelieved to constrict the mitochondrial double membrane via itsmechanochemical activity, leading to fission. However, this view hasbeen extrapolated from molecular models of fission involving theDrp1 yeast homolog Dnm1 and other dynamin family members(Faelber et al., 2012, 2011; Ford et al., 2011; Mears et al., 2011).Structural studies have revealed a fourth interaction surface in Drp1that is necessary for assembling two neighboring Drp1 filaments togive a broader filament size (14.4 nm). This filament size is similar tothat in the model proposed for Dnm1 but differs from that of dynamin(10.6 nm) (Fröhlich et al., 2013; Mears et al., 2011). Thus, twodouble filaments of Drp1 that extend next to each other around themembrane tubule account for a two-start helix with a 28.8 nm helicalpitch (Fröhlich et al., 2013). Recent reports have identified newadaptors in Drp1-mediated membrane fission, which mainly help inReceived 14 July 2017; Accepted 5 December 2017

1Interfaculty Institute of Biochemistry, University of Tubingen, 72076 Tubingen,Germany. 2Biofisika Institute (CSIC, UPV/EHU), Department of Biochemistry andMolecular Biology, University of the Basque Country, 48940 Leioa, Spain.3Laboratoire Physico Chimie Curie, Institut Curie, PSL Research University,CNRS UMR168, 75005 Paris, France. 4Sorbonne Universites, UPMC Univ Paris 06,75005 Paris, France. 5Max Planck Institute for Intelligent Systems, 70569 Stuttgart,Germany.

*Author for correspondence ([email protected])

A.J.G.-S., 0000-0002-3894-5945

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the recruitment of Drp1 to the mitochondrial outer membrane andrearrange the helical structure of the Drp1 scaffold (Gandre-Babbeand van der Bliek, 2008; Koch et al., 2005; Loson et al., 2013; Palmeret al., 2011; Zhao et al., 2011). Drp1 has also been proposed topromote membrane tethering as a mechanism for stabilizing themembrane topologies involved in membrane fission (Ugarte-Uribeet al., 2014). Together, these studies have revealed a complexscenario, but additional research is required to uncover the role ofDrp1 in mitochondrial division. One key issue is the mechanism ofDrp1 as a minimal machinery in the series of membrane alterationsnecessary to catalyze membrane division. If Drp1 alone is not able tomediate spontaneous membrane division, what is it doing?Here, in order to shed light on the membrane activity of Drp1, we

have visualized the assembly of fluorescently labeled Drp1 on lipidtubes pulled from giant unilamellar vesicles (GUVs) and quantifiedthe effect of Drp1 scaffolds on tube diameter. We report that thelipid membrane plays an essential role in Drp1 assembly byregulating its supramolecular organization in the absence andpresence of GTP and that this nucleotide is essential for Drp1 clusterformation on membrane tubes. We also show that Drp1polymerization alone can stabilize a narrow range of tube radiithat are similar in size to the Drp1 foci found in mitochondria. Thisnew function of Drp1 as curvature stabilizer, rather than curvaturesensor or generator, demonstrates that Drp1 follows a differentmechanism of action compared with dynamin 1.

RESULTSCardiolipinmodulatesDrp1membranebinding andassemblyCardiolipin (CL) is an important anionic phospholipid specificallyfound in the mitochondria of eukaryotic cells. Previous studies havereported a role of CL in Drp1 GTPase activity and oligomerization,as well as in direct protein–lipid interactions (Bustillo-Zabalbeitiaet al., 2014; Macdonald et al., 2014; Stepanyants et al., 2015). Inaddition, Drp1-induced tubulation and membrane tethering wererecently observed in GUVs containing CL (Ugarte-Uribe et al.,2014). However, it is unclear whether Drp1 needs to oligomerize insolution before binding to membranes or whether it self-assemblesonce it is bound to the membrane, and how this depends on CL. Wetherefore evaluated the self-assembly and binding behavior of Drp1using supported bilayers with excess of reservoir (SUPER)templates (Neumann et al., 2013) in the absence and presence ofGTP, a nucleotide required for Drp1 oligomerization. We usedmembranes of four different lipid compositions: one mimicking themitochondrial outer membrane [mitochondria-like lipids (MLL),with 4.35% CL; see Materials and Methods] and the otherscontaining 10%, 20% or 30% CL. We found that Drp1 bound to theSUPER templates in a CL-dependent manner, which was enhancedby the presence of GTP (Fig. 1A). Surprisingly, the macromolecularassembly of Drp1 on the membrane was largely affected by CLconcentration. At lower CL concentrations (i.e. MLL and 10% CL),Drp1 formed heterogeneous clusters, as visualized by confocalmicroscopy, whereas in the presence of 20% and 30% CL Drp1exhibited a more homogeneous distribution on the membrane(Fig. 1B). We observed a few brighter foci in both channels at highCL concentrations, indicative of lipid and protein enrichment,which suggests the formation of budding-like structures induced bylocal accumulation and/or oligomerization of Drp1.It is important to note that SUPER templates enable the

quantification of membrane fission and have been efficiently usedto measure the fission activity of dynamin 1 (Neumann et al., 2013;Pucadyil and Schmid, 2008). However, we could not detect anymembrane fission using this model membrane system with either

MLL or 30% CL compositions or with Drp1 concentrations up to1 µM, suggesting that membrane tension and/or additional playerscould be required for Drp1-mediated membrane scission to occur.

To determine whether membrane association alone plays a role inDrp1 assembly, we examined the oligomeric state of Drp1 insolution and in the membrane by fluorescence cross-correlationspectroscopy (FCCS), a technique with single molecule sensitivitythat quantifies the dynamic co-diffusion of biomolecules either insolution or in membranes of GUVs (Bleicken et al., 2013b; García-Sáez and Schwille, 2008). For this purpose, we selected conditionsof homogeneous Drp1 distribution in the absence of GTP, in orderto avoid big bright aggregates (i.e. high-order oligomers that cannotbe analyzed by this method). We quantified complex formation ofDrp1 with Alexa Fluor 488 (Drp1–Al488) and with Atto 655 dye(Drp1–A655) in solution and in GUVs with high CL concentration(Fig. 1C–E). As shown in Fig. 1E, the positive values of cross-correlation indicate that Drp1 self-assembled in both situations, butto a higher extent when bound to the membrane. In agreement withthis, we calculated that the diffusion coefficient of Drp1 particles inthe membrane was 3.0±1.5 µm2 s−1 (mean±s.d.). This is slowerthan that of membrane-inserted Bcl-xL/cBid complexes (4.4±0.6 µm2 s−1) (García-Sáez et al., 2009) and Bax oligomers (4.1±1.5 µm2 s−1) (Bleicken et al., 2017), suggesting a higher assemblystate of Drp1 on the membrane. From these experiments, we couldnot distinguish whether Drp1 oligomers form in solution and bind tothe membrane or whether this oligomerization occurs directly on themembrane after binding. However, these findings reveal that boththe membrane environment and its composition (CL content)modulate Drp1 oligomerization, which is probably important for themolecular mechanism of oligomerization.

Drp1 self-assembly stabilizes membrane nanotubesMost previous studies of Drp1-induced membrane remodeling havefocused on static structural aspects, using harsh conditions ofelectron microscopy and non-physiological lipid compositions (suchas pure phosphatidylserine or very high CL concentrations) (Francyet al., 2015; Fröhlich et al., 2013; Koirala et al., 2013; Macdonaldet al., 2014; Stepanyants et al., 2015; Ugarte-Uribe et al., 2014). Toprovide insight into the dynamic aspects of membrane remodelingby Drp1 under more physiological conditions, we used membranetubes pulled from GUVs with MLL lipid composition. Wevisualized Drp1 binding to the tube in the absence and presence ofGTP and analyzed the putative role of Drp1 in membrane tubeconstriction, twisting and fission. In contrast to SUPER templates,this system allows us to control membrane tension and to measurethe radii of the tubes during experiments. The same approach wasused to study membrane constriction and scission by dynamin in acontrolled manner (Morlot et al., 2012; Roux et al., 2010).

After pulling a tube from a single MLL GUV with the opticaltrap, a second pipette filled with Drp1-Al488 was carefullypositioned near the tube to release small amounts of protein (seeMaterials and Methods). Drp1-Al488 bound homogeneously toboth the GUV and tube surfaces in the absence of GTP; in thepresence of GTP, it adopted a heterogeneous distribution with brightfoci along the tube (Fig. 2A). Remarkably, in the presence of GTPthe tube did not fully retract when the optical tweezers (OT) wereswitched off, although we repeatedly observed rapid retraction ofthe tube in the absence of nucleotides (Fig. 2B). The bead was stillconnected to the vesicle through the Drp1-coated tubule in thepresence of GTP (Fig. 2B), showing that, despite the absence ofexternal forces, Drp1 assembly preserved the membrane tube withinit. This also suggested that, in the presence of GTP, Drp1 did not

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simply adsorb onto the tube but rather polymerized around it. Takentogether, these observations demonstrate the ability of Drp1 tostabilize the curved membrane of lipid tubes in a process dependenton GTP-induced self-assembly.

GTP-induced assembly drives Drp1 rearrangement intodistinct clusters on the membraneNext, we used live microscopy to study the assembly of Drp1 coatson the membrane by following cluster formation and growth on thelipid tubes in the presence of GTP (Fig. 3). Two minutes afterinjection, Drp1 fluorescence concentrated only on some parts of thetube (Fig. 3A). As shown in the lipid channel, the tube radius underthe scaffold was different from that of the bare tube radius. Thekinetics of cluster rearrangement and growth into randomlydistributed distinct structures is shown in the kymograph inFig. 3B. The high speed of foci formation and growth suggests

that Drp1 nucleation is the result of association of dimers or tetramersalready adsorbed on the membrane (Roux et al., 2010). In addition,heterogeneous Drp1 binding could be visualized on the surface ofthe GUV (Fig. 3A), in agreement with previous work (Ugarte-Uribeet al., 2014). After a series of intermittent Drp1 injections, all clustersshowed similar growth rates with no predominant nucleation point,implying that there is no specific hotspot where nucleation occurs(Fig. 3A). The length of the small Drp1 clusters steadily increasedat an average rate of 1.25±0.31 nm s−1 (Fig. 3C). These resultsdemonstrate that the binding of Drp1 on membranes proceeds via anucleation and growth mechanism rather than by simple adsorption.

Drp1 polymers mechanically stabilize membrane curvaturewithout a preference for a specific tube diameterBy changing the aspiration pressure on the GUVs, the radius ofthe tube could be decreased or increased. We then measured the

Fig. 1. Cardiolipin induces Drp1-mediated vesiclebudding and Drp1 self-assembly. (A) Proteinbinding to SUPER templates in the absence orpresence of GTP was plotted by dividing thefluorescence intensity at the bead rim (IFmemb) by thebackground fluorescence (IFback) (n=3). (B) Confocalimages of Drp1 oligomerization on SUPER templatesin the presence of GTP (3D reconstruction). Lipidcompositions tested: MLL (mitochondrial-like lipids),PC:CL (90:10, 80:20 and 70:30) (mol:mol). (C) Drp1binding kinetics in solution by FCCS (50 nM of eachlabeled species, n=3). CC% stands for cross-correlation percentage. (D) Representative schemewith confocal images, auto-correlation (green andmagenta), and cross-correlation (orange) curves fromFCCS measurements in membranes of PC:CL(70:30, mol:mol) GUVs using Drp1–Al488 and Drp1–A655. Solid lines correspond to fitted curves anddotted lines to the raw data. (E) Percentage complexformation between Drp1 molecules in solution (n=11,14, 12, 13, 17, 19, 13) or in individual GUVs (n=44) asmeasured by FCCS. Drp1 concentration in solutionstands for each labeled Drp1 species. In membranes,complex formation was reduced in the presence ofunlabeled Drp1 (n=21). Mb stands for FCCS inmembranes (20 nM of each labeled Drp1 species);Comp stands for competition in membranes withunlabeled Drp1 (100 nM). Unpaired two-tail t-test,P<0.001 for Mb versus Comp. Scale bars: 10 µm.

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fluorescence intensity ratio between the tube and the GUV surfacein the lipid channel, from which we quantified the radii of the tubesas described by Prévost et al. (2015) (see Materials and Methods).We found that Drp1 self-assembly was not dependent on thecurvature of the lipid tubes, as it polymerized on lipid tubes of alldiameters accessible with our method (from about 20 nm to about80 nm). Drp1 was also able to self-assemble on the flat surface ofGUVs, indicating that scaffold formation did not exhibit curvature-selectivity.Then, we increased or decreased the aspiration pressure of GUVs

decorated with discrete Drp1 scaffolds in order to examine theresponse of the tube radius under the Drp1 coat to changes inmembrane tension. By slowly varying the aspiration pressure (withstabilization pauses of 0.5–2.5 min), we were able to explore aphysiologically relevant range of tube diameters, and explicitlyanalyze the effect of Drp1 clusters on the curvature of preformedtubes of different sizes while varying their diameter. To oursurprise, instead of readily adapting to the pressure changes, wefound that membrane curvature under the Drp1 clusters oftenresponded differently to alterations in membrane tension comparedwith bare lipid tube regions. With increased aspiration, the radiusof the bare parts of the tube became smaller than the radius of

Drp1-covered parts (Fig. 4A). This is because the increase inaspiration and, correspondingly, in membrane tension reduced thediameter of bare tube regions, whereas Drp1 scaffolds helpedpreserve the curvature of the membrane underneath. With decreasedaspiration, corresponding to lower membrane tensions that resultedin an increase in the diameter of bare lipid tubes, we observed theopposite effect (Fig. 4A). As an example, results presented inFig. 4B indicate that a bare tube responds to an increase or decreasein membrane tension by undergoing thinning or expansion. In thepresence of Drp1 clusters, an increase in membrane tension causestube thinning, implying that the scaffold is not rigid but can adapt.However, a subsequent lowering of membrane tension produceslittle change to tube dimensions, suggesting that the scaffoldstabilizes or preserves membrane curvature upon reaching a certaingeometry (or packing). Thus, curvature stabilization is apparentonly after the scaffold has reached a critical limit of curvature orpacking (equivalent to an inner radius of about 20 nm). Also, Drp1polymer clusters did not inhibit lipid advection between the GUVand the bare parts of the tube, thereby permitting fast tensionequilibration. Together, these results show that GTP–Drp1 scaffoldshave unique mechanical properties, being able to both adapt to andstabilize the curvature of the membrane under the coat againstmechanical forces (similar to stiff scaffolds). In addition, thedistribution of radii of Drp1 clusters correlates with super-resolutionimaging data of Drp1 rings on mitochondria (Rosenbloom et al.,2014).

Continuous Drp1 scaffolds generate rigid membranestructuresIn addition to growth of Drp1 clusters along the tube duringcontinued Drp1 addition (Fig. 3A), Drp1 density on the GUV alsoincreased, eventually saturating the surface. Thus, we decided toperform tube length elongation and shortening experiments to testthe following: (i) whether the protein pool bound to the GUVsurface was able to occupy newly elongated tube zones and (ii)whether Drp1 clusters could further assemble into a complete,continuous scaffold on the tube once they came into contact witheach other.

First, we observed that the lipid tube could be easily elongatedwithout any incorporation of the Drp1-bound fraction from theGUV surface to the newly generated tube zone. This suggests thatDrp1 assemblies cannot rearrange into higher membrane curvaturesonce Drp1 has polymerized on a flat membrane and adopted aspecific structure there (Fig. 5A). In contrast, subsequent Drp1injection led to homogeneous binding to the newly extended tubesurface, followed byDrp1 rearrangement into new clusters along theuncoated tube part (Fig. 5A).

Next, we shortened the tube by moving the GUV closer to thebead in order to establish cluster–cluster contact. In this case, allthe clusters present on the tube associated with each other,resulting in a continuous Drp1 scaffold covering the entiremembrane surface (GUV and tube; Fig. 5A). This scaffoldprevented further tube shortening. Moving the GUV even closerto the bead led to tube buckling (indicated by the filled arrowheadin Fig. 5A).

This scaffold also blocked tube elongation: pulling on the GUVas strongly as possible while keeping the bead in the trap (i.e. with aforce lower than the trapping force of the OT) did not result in anyelongation of the tube (Fig. 5A), suggesting that the protein hadformed a rigid shell all over the membrane. Upon switching off theOT, the tube did not retract into the GUV, indicating that the Drp1continuous scaffold was stabilizing it. This effect was observed

Fig. 2. GTP-induced Drp1 polymerization on lipid tubes enables tubestabilization. (A) Drp1 binding to GUV surface and preformed tubes in theabsence (left, n=12) and presence (right, n=28) of GTP. (B) Drp1-inducedeffect on tube stabilization in the absence (left) or presence (right) of GTP.Images were acquired a few seconds after switching off the optical tweezers. Inboth cases, GUV lipid composition was MLL with 1% Rhod-PE and 0.1%biotin-PE. The bead appears with different levels of green fluorescence as aresult of adsorption of labeled Drp1. Scale bars: 10 µm.

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during the whole duration of our experiments (at least 5–10 minafter switching off the OT).Last, we attempted to promote tube scission in our system.

As mentioned above, when pulling on the GUV in the absenceof a continuous Drp1 scaffold, the membrane can flow from theGUV to the tube. We reasoned that this prevented build-up of stresswithin the tube, stress that would possibly favor scission. Therefore,we repeated the tube-shortening experiment (starting from atube with discrete protein clusters) to obtain a complete proteinscaffold. We then attempted to pull on the GUV using increasedpower of the trapping laser (from 2 W to 2.5 W, which results in aproportional increase in trap stiffness and enables probing higherlevels of membrane stress). Doing so, we were able to generate abreak in the scaffold (indicated by the open arrowhead in Fig. 5B),but not of the membrane tube. However, additional pulling resultedin the bead being pulled out of the trap, suggesting that the stressincrease was not sufficient to promote scission. In summary, tubescission did not occur under all conditions tested, suggesting thatadditional components are most probably required for catalysis ofmembrane fission.

DISCUSSIONHere, we examined the mechanism of Drp1 self-assembly onmembranes and its mechanical effect on membrane shape todecipher Drp1 function in mitochondrial fragmentation. We foundthat the lipid composition not only regulated the binding affinity ofDrp1 to membranes, but also subsequent clustering of Drp1 onthe lipid bilayer. On the one hand, association of Drp1 with themembrane increased with CL concentration. Additionally,membrane binding promoted Drp1 oligomerization, as revealed byFCCS experiments. This is in line with previous reports on themembrane binding and GTPase activity of Drp1 (Bustillo-Zabalbeitia et al., 2014; Macdonald et al., 2014). On the otherhand, bright Drp1–Al488 clusters formed efficiently only onmembranes mimicking the composition of the mitochondrial outermembrane or containing similarly low CL concentrations. At higherCL levels, close to those thought to be present at contact sitesbetween mitochondrial outer and inner membranes (i.e. 20% and30% CL), Drp1 distribution was generally homogeneous. Underthese conditions, most Drp1-containing SUPER templates alsopresented fewer bud-like structures enriched in both lipid and

Fig. 3. Drp1 redistribution from homogeneousbinding to discrete nucleated clusters on themembrane in the presence of GTP. (A) Confocalimages of Drp1 binding kinetics to amembrane tube.Filled and open circles stand for presence orabsence of Drp1 injection, respectively. GUV lipidcomposition was MLL with 1% Rhod-PE and 0.1%biotin-PE. Scale bars: 10 µm. (B) Representativekymograph (derived from images in A) showingDrp1binding to the membrane tube and cluster growthwith time. (C) Growth kinetics of individual Drp1scaffolds on a lipid tube.

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protein, suggesting that CL has a relevant effect on Drp1-mediatedmembrane remodeling. These findings demonstrate that themembrane plays an active role in the self-assembly of Drp1, whichis linked to its membrane remodeling activity. They also revealan unprecedented level of regulation, whereby the formation ofDrp1 scaffolds could be modulated by dynamic changes inmembrane composition. Elucidating how lipid distributionprecisely tunes Drp1 assembly and its functional consequencesrequires further investigation.Our results also show that the presence of GTP is crucial for the

self-assembly and membrane activity of Drp1. We observed thatGTP was not necessary for membrane binding, but that it enhancedthe association of Drp1 with the lipid bilayer at all lipid compositionstested, in agreement with previous studies (Bustillo-Zabalbeitiaet al., 2014; Stepanyants et al., 2015; Ugarte-Uribe et al., 2014).Most importantly, we found that GTP was required for the assemblyof Drp1 into protein scaffolds that stabilized curved membranes. Inthe absence of nucleotides, Drp1 simply adsorbed on the membraneand was unable to stabilize curvature. Drp1 polymerization alsostabilized the lipid tubes even in the absence of complete Drp1coverage (i.e. no continuous Drp1 scaffold). This indicates that smallnucleation sites are sufficient for tube stabilization, in the sense thatthe tubes did not fully retract when releasing the bead from the

optical trap. Mechanistically, our results demonstrate that theclustering of membrane-bound Drp1 particles in the presence ofGTP leads to assembly into microscopic nucleation sites, without theneed for pre-oligomerization in solution.

The kinetic analysis of Drp1 scaffold assembly on the membranetubes showed that, once formed, Drp1 clusters were stable and grewat a similar rate (75±19 nm min−1 under our experimentalconditions), with no predominant cluster along the tube. Based onexisting structural data (Fröhlich et al., 2013; Mears et al., 2011), ifwe assume that the size of the helical Drp1 pitch is 14.4 nm, we canestimate that (under our experimental conditions) Drp1 clusters grewby 5.2±1.3 helical turns per minute. This corresponds to the additionof 2.1±0.5 tetramers s−1 or 4.2±1.0 dimers s−1 to the Drp1 coat(Fröhlich et al., 2013). Previous reports showed similar distributionpatterns for dynamin 1 onmembrane tubes, suggesting that Drp1 anddynamin 1 clusters have similar properties and that these sites mightrepresent potential nucleation points for subsequent membranefission (Morlot et al., 2012; Roux et al., 2010). Shlomovitz andcolleagues proposed a model whereby the dynamic couplingbetween protein adsorption, oligomerization and condensation ona membrane tube explains why linear assemblies of proteins such asdynamin and FtsZ lead to regular patterns on membrane tubes(Shlomovitz and Gov, 2009; Shlomovitz et al., 2011). Accordingly,

Fig. 4. Drp1 polymerization stabilizes different tube radii. (A) Confocal images and tube intensity plots (corresponding to the arrows shown in the images) ofDrp1 (green) andmembrane (magenta); the membrane below Drp1 clusters shows a different curvature compared with the bare tube. GUV lipid composition wasMLL with 1% Rhod-PE and 0.1% biotin-PE. Scale bars: 10 µm. (B) Data from a representative vesicle showing membrane curvature variations in the bare tubeand in the areas underneath Drp1 clusters (mean±s.d., n=5) upon tension changes. (C) Analysis of the lipid tube curvature stabilized by Drp1 clusters versus thetube radii of the bare tube regions (132 tubes and 417 clusters analyzed). The gray panel highlights the range of tube radii accessed in this assay. Deviations fromthe diagonal black line indicate the preservation of membrane curvature under Drp1 coats against tension changes that modify the curvature of the surroundingbare tube areas.

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membrane-mediated interactions drive the spontaneous nucleationof condensed protein domains. Our data suggest that a similarmechanism probably also applies in the case of Drp1.The range of radii of tubular segments covered with Drp1 coats is

in line with current super-resolution imaging data for Drp1 rings onmitochondria (69±30 nm for the mitochondrial membrane pre-constriction step, 52±24 nm for the intermediate constricted stateand 38±19 nm for post-constriction membrane scission)(Rosenbloom et al., 2014). These values are also similar to thosefound for Dnm1 helical rings (pre, 60±12 nm; post, 35±11 nm)(Berman et al., 2008; Friedman et al., 2011). However, Drp1 coatingdid not show any preference for the stabilization of specific tubediameters, suggesting that Drp1 could form scaffolds that adapt tothe curvature of the target membrane. This is in accordance with thevariability in the diameters of Drp1 helical coats measured byelectron microscopy (i.e. from 30 nm to more than 150 nm) whenincubated in the absence or presence of GTP analogs (Bossy et al.,2010; Fröhlich et al., 2013; Koirala et al., 2013; Macdonald et al.,2014; Stepanyants et al., 2015; Yoon et al., 2001), or even atdifferent time points in the presence of GTP (Francy et al., 2015).The same experimental approach applied to dynamin 1 revealed

two different features for this protein at the membrane: curvaturesensing (i.e. nucleation dependent on membrane curvature), and

curvature generation (i.e. constriction of the tube) followed bymembrane scission (Roux et al., 2010). In contrast, Drp1 was able tobind to and polymerize on both flat and curvedmembranes (i.e. GUVsurface and tube) independently of the curvature. Moreover, we didnot detect any membrane fission under any of the experimentalconditions tested. These observations are consistent with the diameterof the mitochondrial sites where Drp1 is recruited being much biggerthan that of the neck of endocytic vesicles where dynamin 1 operates(Friedman et al., 2011; Ingerman et al., 2005). It could also reflect thefact that Drp1 is being continuously recruited to a number ofmitochondrial foci, with only a small fraction of these actuallyundergoing mitochondrial division (Smirnova et al., 2001). Incontrast, dynamin 1 is recruited to the neck of endocytic vesicles aftertheir maturation, immediately prior to membrane fission (Ehrlichet al., 2004; Merrifield et al., 2002; Rappoport et al., 2008).

It is important to mention that we could not detect any membranefission, even when assisting Drp1 complete scaffolds by exertingpulling forces externally with the OTs. This is an unexpectedphenomenon because, once the protein scaffold is formed, pullingusually leads to membrane scission, as in the case of the BARdomain protein endophilin-A2 (Renard et al., 2015). In fact,endophilin-A2 scaffolding sensitizes membrane tethers to pullingforce-induced scission, even if the protein scaffold does not

Fig. 5. Formation of complete Drp1 scaffoldsleads to rigid membrane structures withoutmembrane fission. Tube elongation and shorteningexperiments (n=14). (A) Confocal images of Drp1behavior on membrane tubes after tube elongationand shortening (see arrows in opposite directions) inthe presence of GTP. Filled circles and arrowheadsindicate Drp1 injection and tube buckling,respectively. GUV lipid composition was MLL with1% Rhod-PE and 0.1% biotin-PE. (B) Confocalimages of the formation of complete Drp1 scaffoldand its effect after tube elongation. Filled and openarrowheads indicate tube buckling and Drp1 scaffoldbreak, respectively. Scale bars: 10 µm.

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completely cover the tube surface. This has been attributed to thehigh friction between the protein scaffold and the membrane tubeand to the mechanical connection between protein assemblies on thetube and on the GUVmembrane. If we also consider that membranetension can be equilibrated between the GUV and the baremembrane regions in the tube despite the presence of Drp1(which is not observed in the case of BAR domain proteins), ourfindings indicate that Drp1 follows a completely different molecularmechanism when assembling on the tube and probably inducesmuch lower friction with the lipid bilayer.Thus, Drp1 membrane activity is different from that of other

dynamin homologs. In the context of mitochondrial division in thecell, our data suggest that additional components are necessary tofurther constrict or tense the membrane in order to drivemitochondrial fission. One possibility is that Drp1 requiresadaptors such as Mff or MiD49/51 to mediate membrane fission.We find this unlikely because current studies show that, althoughadaptors are able to modulate membrane constriction, the tubediameters observed by electron microscopy are still too large forspontaneous membrane fission. Alternatively, a very recent studyhas reported that dynamin 2 acts in concert with Drp1 to coordinatemitochondrial division (Lee et al., 2016). One interesting aspect ofthis model is that dynamin 2 depends heavily on a narrow curvaturefor membrane binding, which is in good agreement with thedistribution of Drp1-stabilized tube diameters detected here.Consistent with this, we found that Drp1 self-assembly was

sufficient for membrane tube stabilization, indicating that it behavesas a curvature stabilizer, although having some plasticity. Ourobservations also suggest that the Drp1 scaffold might have non-constant mechanical properties over time. Coat and tubewidth couldbe affected by changing the aspiration at the beginning of theexperiment, but seems to become less likely with time, as if theDrp1 structure was initially soft and adjustable and graduallybecomes more rigid and stiff over time. This would potentially allowremodeling if additional proteins bind and further constrict themembrane, or otherwise keep the structure constricted, which couldbe related to the role of Drp1 in stabilizing platforms duringapoptosis (Prudent et al., 2015). The versatility of the GTP–Drp1assembly for a large range of curvatures could allow pre-constriction of the membrane to facilitate dynamin 2 recruitment,while not resisting further constriction by dynamin.Our finding that the main activity of Drp1 is as a stabilizer of

membrane curvature could have physiological implications, becauseit sheds new light on the core mechanisms that control mitochondrialdynamics and function. Our data provide strong support for a recentmodel for mitochondrial fission that involves the concerted action ofmultiple cellular machineries (Lee et al., 2016). According to thismodel, the endoplasmic reticulum first constricts mitochondria atspecific sites to ∼130 nm diameter, where Drp1 is subsequentlyrecruited, probably with the help of specific adaptors (Friedmanet al., 2011; Morlot et al., 2010). The assembly of Drp1 probablyfurther constricts these foci and, importantly, stabilizes membranecurvature, as we show here. The stabilization of a high membranecurvature at mitochondrial fission sites is a requisite for therecruitment of dynamin 2 (similar to the case of dynamin 1binding at the endocytic vesicle neck), which eventually mediatesthe final step of membrane fission (Friedman et al., 2011; Hoppinset al., 2007; Lee et al., 2016; Mears et al., 2011).In summary, we have directly visualized the dynamics of Drp1

assembly on lipid tubes and evaluated its effect on membranecurvature. We found that the formation of Drp1 scaffolds on themembrane surface requires GTP and that it can be modulated by CL

levels. Drp1 associates with lipid bilayers independently ofcurvature, which did not lead to membrane fission under theexperimental conditions tested. Unexpectedly, Drp1 forms clusterswith very original mechanical properties: they stabilize lipid tubesas do other protein scaffolds but, instead of imposing a prescribedcurvature, Drp1 clusters can set a large range of curvatures thatdepend on the initial conditions of assembly. Nevertheless, the Drp1assembly can preserve membrane curvature against changesinduced by external forces. The molecular origin of these peculiarproperties of the Drp1 assembly in its GTP form has still to beunderstood. To conclude, in contrast to other proteins of thedynamin family, our results support a new function of Drp1 as astabilizer of curved membrane and not as a direct membrane scissor,in agreement with a model whereby Drp1 requires cooperation withother cellular components to mediate mitochondrial division.

MATERIALS AND METHODSDrp1 purification and fluorescent labelingDrp1 was purified from Escherichia coli BL21 (DE3)-RIPL cells containingpCal-n-EK-Drp1 as previously described (Ugarte-Uribe et al., 2014). pCal-n-EK-Drp1 (isoform 1) constructs were provided by Dr C. Blackstone (CellBiology Section, Neurogenetics Branch, National Institute of NeurologicalDisorders and Stroke, National Institutes of Health, Bethesda) (Chang et al.,2010; Zhu et al., 2004). Alexa Fluor 488 or Atto 655 maleimide (Invitrogen)were covalently attached to cysteine residues in Drp1 bound to resin, asdescribed by the manufacturer. The labeling efficiencies of the purifiedprotein were 2 and 1.5 mol dye/mol protein for Alexa Fluor 488 and Atto655, respectively. Purified fluorescent protein (Drp1–Al488 or Drp1–A655)was storedwith 50% (v/v) glycerol in dialysis buffer (25 mMHEPES pH 7.4,500 mMNaCl, 2 mMMgCl2). Although we could not control the location ofthe labeling reaction (i.e. whether the maleimide dyes were located in theGTPase domain or in the stalk region of the protein), dye-labeled Drp1 wasenzymatically active in the absence and presence of membrane, similar tounlabeled Drp1, as previously shown (Ugarte-Uribe et al., 2014).

Lipid composition of model membranesAll lipids were from Avanti Polar Lipids. The lipid mixture mimicking themitochondrial outer membrane composition, called hereMLL, was preparedwith egg L-α-phosphatidylcholine (PC), egg L-α-phosphatidylethanolamine(PE), bovine liver L-α-phosphatidylinositol, 18:1 phosphatidylserine andCL (48.5:27.2:9.9:10.05:4.35, mol:mol) (Bleicken et al., 2012, 2013a,b;Lovell et al., 2008; Ugarte-Uribe et al., 2014). CL-containing samples werealso used (90:10, 80:20 and 70:30 PC:CL, mol:mol). For membranevisualization, 0.5% (for SUPER templates) or 1% (for GUVs) of L-α-phosphatidylethanolamine N (lissaminerhodamine B sulfonyl) lipid (Rhod-PE) was used, replacing part of the mol ratio of PE (in MLL samples) or PC(in the rest of samples) in the lipid mixture.

SUPER template formation and vesicle release assayThe formation of the SUPER (supported bilayers with excess membranereservoir) templates was carried out as previously described (Neumann et al.,2013), but with incubation time modifications. Briefly, 5-µm silica beads(5×106 beads) were incubated for 1 h in 1 M NaCl solution with 200 µMlarge unilamellar vesicles (final concentration), previously extruded with a100-nm filter followed by four washing steps with Milli Q water. Drp1binding experiments were carried out by mixing 50 nM Drp1–Al488 with10 µl of SUPER templates in a final volume of 100 µl in GTPase buffer(20 mM HEPES pH 7.4, 150 mM KCl, 1 mM MgCl2) in the absence orpresence of GTP (1 mM final concentration) (n=3). The vesicle release assaywas performed as previously described (Neumann et al., 2013) (n=3).

Visualization of SUPER templates by fluorescence confocalmicroscopyImages of SUPER template and membrane-coated capillaries were acquiredwith a commercial LSM710 microscope (Carl Zeiss, Jena, Germany). Theexcitation light was reflected by a dichroic mirror (MBS 488/561/633) and

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focused through a Zeiss C-Apochromat 40× (Zeiss, Oberkochen, Germany),numerical aperture 1.2 water immersion objective onto the sample. Thefluorescence emission was collected by the objective and directed byspectral beam guides to photomultiplier tube detectors. Images wereprocessed with ImageJ (http://rsbweb.nih.gov/ij/).

Image analysis of radial profile measurementsQuantitative analysis of fluorescent intensities of Drp1 bound to themembrane of the SUPER templates (IFmemb) in the confocal images wasperformed using ImageJ and the ‘radial profile’ extended plugin fromPhilippe Carl available from the ImageJ homepage. The integration angleselected was 60 in order to avoid non-membrane coated zones of the beads.Intensity was plotted as IFmemb/IFback, where IFback is the backgroundintensity.

Experimental setup and sample preparation with GUVsGUVs were produced by electroformation (García-Sáez et al., 2009;Ugarte-Uribe et al., 2014). MLL with 1% Rhod-PE and 0.1%biotin-PE (1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[biotinyl(polyethylene glycol)-2000]) or PC:CL (70:30, mol:mol) lipid mixture inchloroform was dried on platinum wires (2.5 µl per wire from 2 mg/mlstock), which were immersed in 350 µl of 300 mM sucrose solution in theelectroformation chamber. Electroformation proceeded for 2 h at 10 Hz atroom temperature, followed by 1 h at 2 Hz.

Our tube-pulling setup has been described previously (Sorre et al., 2009).It comprises a custom-built optical trap implemented on a confocalmicroscope (eC1 confocal system with two excitation lines of 488and 543 nm) connected to a TE2000 inverted microscope (Nikon).Micromanipulators on either side of the stage allowed us to perform bothmicromanipulation of the GUVs and microinjection of proteins. Eachmicropipette was back-connected to a mobile water tank for pressureadjustment.

The experimental chamber andmicromanipulation pipette were incubatedwith 5 mg ml−1 β-casein (Sigma) to prevent non-specific adhesion of thevesicles to the glass. Meanwhile, the tip of the microinjection pipette wasfilled with <1 µl of protein solution (1 µM) and the rest of the pipette wasback-filled with mineral oil. The experimental chamber was rinsed and filledwith GTPase buffer (with or without 1 mM GTP), then GUVs andstreptavidin-coated polystyrene beads (3.2 μm diameter; Spherotech) wereadded to the solution. The concentration of the bead solution and thevolumes added to the chamber were adjusted to obtain dilute experimentalconditions (no more than an average of 1 GUV/bead per field of view toavoid pollution of the optical trap). Because of the higher density of theGUV growth buffer compared with experimental buffer, the GUVs fall tothe bottom of the chamber, where all manipulations and imaging areperformed. The protein flow from the injection pipette was visually adjustedto as low as possible (using Alexa Fluor 488 fluorescence) and the tip of thepipette was kept away from the chamber surface while selecting a GUV andpulling a tube. Tube pulling was achieved by holding the GUV in themicromanipulation pipette under very low aspiration pressure, approachingit to a trapped bead, gently contacting the bead to establish biotin–streptavidin bonding, and finally moving the GUV away from the trap.Once the tube was pulled, the tip of the microinjection pipette was broughtback into focus and the evolution of protein fluorescence on the GUV andtube was monitored over time. Changes in tube radius were achieved byadjusting the aspiration pressure of the micromanipulation pipette.

The radius of the tube was calculated from Rhod-PE fluorescence using a

previously established calibration Rtube ¼ RcalIRhod�PEtube

IRhod�PEGUV

, where Rtube is the

tube radius, IRhod�PEtube is the fluorescence of Rhod-PE in the tube, IRhod�PE

GUV isthe fluorescence of Rhod-PE in the GUV and Rcal is a calibration constantthat does not depend on the lipid composition (taken as Rcal=200 nm)(Prévost et al., 2015).

Fluorescence cross-correlation spectroscopyAll experiments were performed at 22°C on an LSM710 microscope with aC-Apochromat 40×1.2 water immersion objective (Zeiss, Oberkochen,Germany). Excitation light came from Ar ion (488 nm) or HeNe lasers

(633 nm). We performed FCCS and two-focus scanning FCCSmeasurements using a Confocor 3 module as described (Bleicken et al.,2013b). Photon arrival times were recorded with a hardware correlator Flex02-01D/C (http://correlator.com). For protein interaction in solution (1, 5,10, 25, 50, 100 and 150 nM of each labeled Drp1 species; n=11, 14, 12, 13,17, 19 and 13, respectively), FCCS analysis was carried out with FluctuationAnalyzer 4G software (http://www.embl.de/~wachsmut/downloads.html).For scanning FCCS [20 nM of each labeled Drp1 species with (n=44) orwithout (n=21) 100 nM unlabeled Drp1], the detection volume with twoperpendicular lines across a GUV equator was repeatedly scanned (thedistance between the two lines, d, was measured by photobleaching on afilm of dried fluorophores). Data analysis was performed with our ownsoftware (García-Sáez et al., 2009). The photon stream was binned in 2 µsand arranged as a matrix such that every row corresponded to one line scan.We corrected for membrane movements by calculating the maximum of arunning average over several hundred line scans and shifting it to the samecolumn. An average over all rows was fitted with a Gaussian and we addedonly the elements of each row between −2.5σ and 2.5σ to construct theintensity trace. We computed the autocorrelation and spectral and spatialcross-correlation curves from the intensity traces and excluded irregularcurves resulting from instability and distortion. We fitted the auto- andcross-correlation functions with a nonlinear least-squares global fittingalgorithm (García-Sáez et al., 2009).

AcknowledgementsWe thank Carolin Stegmueller for technical assistance.

Competing interestsThe authors declare no competing or financial interests.

Author contributionsConceptualization: B.U.-U., P.B., A.J.G.-S.; Methodology: C.P., K.K.D., P.B.,A.J.G.-S.; Formal analysis: B.U.-U., C.P., K.K.D.; Investigation: B.U.-U., C.P.;Resources: B.U.-U., A.J.G.-S.; Data curation: B.U.U.;Writing - original draft: B.U.-U.,A.J.G.-S.; Writing - review & editing: B.U.-U., C.P., P.B., A.J.G.-S.; Visualization:B.U.-U., A.J.G.-S.; Supervision: P.B., A.J.G.-S.; Project administration: A.J.G.-S.;Funding acquisition: A.J.G.-S.

FundingThis work was supported by Deutsche Forschungsgemeinschaft (DFG; FOR2036),the European Research Council (ERC; 309966) and the Government of the BasqueCountry (fellowship for B.U.-U.). C.P. received a PhD grant from the Universite ParisDiderot and support from the Fondation pour la RechercheMedicale. The P.B. groupbelongs to the CNRS consortium CellTiss, to the Labex CelTisPhyBio (ANR-11-LABX0038), and to Paris Sciences et Lettres (ANR-10-IDEX-0001-02) funded bythe Agence nationale de la recherche.

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