escrt - iii ( endosomal sorting complex required for transport ) has been implicated in the formation of intralumenal vesicles ( ilvs ) during biogenesis of multi - vesicular bodies ( mvbs ) by genetic ( babst et  al . , 2002 , coonrod and stevens , 2010 ) and biochemical assays ( adell et  al . , 2014 , escrt - iii budding occurs in an opposite direction than in endocytosis : the limiting membrane is pushed outward from the cytoplasm instead of curving inward . escrt - iii has been proposed to play a role in membrane deformation ( hanson et  al . , 2008 ) and consistent with this , escrt - iii is also required for geometrically similar fission reactions such as viral budding ( von schwedler et  al . , 2003 ) and abscission during cytokinesis ( carlton et  al . , 2008 , elia et  al . , 2011 , escrt - iii nucleation is promoted by escrt - ii and its disassembly by the atpase vps4 ( lata et  al . , 2008 ) . because of their polymerization abilities , escrt - iii proteins ( vps20 , snf7 , vps2 , vps24 ) have been proposed to generate membrane curvature by scaffolding ( cashikar et  al . , 2014 , fabrikant et  al . , 2009 , hanson et  al . , 2008 , polymers coating the membrane usually adopt a single specific shape , or , at least , a set of geometrically similar shapes . escrt - iii filaments adopt instead a wide variety of shapes in  vivo and in  vitro : concentric circles , rings , spirals , helices , or linear filaments have been observed ( hanson et  al . , 2008 , furthermore , no unique shape for the assembly of escrt - iii proteins arises from the molecular structure of escrt - iii proteins ( mccullough et  al . , , curvature could be generated by other mechanisms : for example , it has been proposed that the amphipathic insertion of the n - terminal part of snf7 could participate in the generation of membrane curvature ( buchkovich et  al . , 2013 ) . we were thus interested in studying how escrt - iii polymerization could drive membrane curvature . to study the polymerization of escrt - iii , we reconstituted escrt - iii polymerization by adding purified yeast snf7 onto supported lipid membranes . supported membranes were obtained by bursting giant unilamellar vesicles ( guvs ) composed of 40% di - oleoyl - phosphatidylserine ( dops ) and 60% of di - oleoyl - phosphatidylcholine ( dopc ) on cleaned glass coverslips ( figure  s1a , movie s1 ) . these coverslips were built into a flow chamber , allowing sequential addition and exchange of solutions . first , snf7 labeled with alexa488 ( snf7-alexa488 ) was flushed into the chamber , and its association to the membrane was imaged by time - lapse spinning - disk confocal microscopy ( sdc ) . at 400  nm , snf7 formed patches evenly distributed on the membrane surface ( figure  1a ) . these circular patches ( figure  1b ) grew over the course of an hour until becoming confluent , eventually covering the membrane completely . the nucleation rate of the patches depended on snf7 bulk concentration ( figure  1c ) . patch formation and growth was so fast that individual patches could hardly be discriminated . between these limiting concentrations , we were able to follow micron - sized patches individually over several tens of minutes ( movie s2 ) . once formed , patches disassembled with a half time of approximately 15  hr upon snf7 washout ( figure  s1b ; movie s3 ) patch nucleation  this nucleation of patches in the absence of a previous snf7 structure . the patch nucleation rate was very low , less than 1 seed.m.hour , and depended on the amount of negatively charged lipids in the membrane ( figure  s1c ) , revealing the critical role of these lipids in promoting snf7 polymerization . the periphery of the patches showed dimmer snf7 fluorescence than the center : fluorescence decayed radially at the rim over the outer 4  m . this gradient of fluorescence was the same as the patch grew in radius ( figure  1d ) and independent on bulk concentration of snf7 ( figure  1e ) . we postulated that the patch could be made of two parts : a central part where snf7 entirely covers the membrane and can not further assemble , and a rim , representing a growing front . to study whether snf7 was assembled only in the front region , we generated patches with a solution of snf7-alexa488 , which we then replaced with snf7-atto647n ( figure  1f and movie s4 ) . as a result , and because the fluorescence gradient was independent from snf7 concentration , fluorescence intensity curves with time at a given point ( figure  s1e ) could be merged into a single one by rescaling time with snf7 concentration ( figure  s1f ) . the amount of negatively charged lipids also affected the front speed ( figure  s1d ) . in summary , the growth of the snf7 patches reflected a nucleation / growth process , with a nucleation rate of less than 1 seed.m.hour and a radial growth speed of 760  nm.min.m . since snf7 filaments can curl into circles or spirals ( hanson et  al . , 2008 , henne et  al . , 2012 , shen et  al . , 2014 ) , we reasoned that one patch could be made of a single spiral filament growing from its tips at constant rate . in this case , however , the radial growth speed of the patch should slow down as the square root of time , and a dimmer fluorescence at the periphery of the patches would not be expected . to resolve this apparent contradiction , we studied the molecular structure of the snf7 patches with atomic force microscopy ( afm ) and electron microscopy ( em ) . guvs composed of 60% dopc and 40% dops were burst on a mica support ( figure  s2a ) . after a four hours incubation of snf7 at 1  m , afm images revealed that the micron - sized snf7 patches consisted of packed arrays of snf7 circular assemblies ( figure  2a ; figure  s2b ) . each assembly was formed by concentric circle - like structures . however , in these packed conditions , rather than being perfectly circular , each assembly was deformed into polygons with six neighbors on average ( figure  2b ) . the average external radius was 123  35  nm ( in the following , values are mean  sd unless otherwise noted ; n  = 295 ) ( figure  2c ) , and the innermost circle had an average radius of 18  3  nm ( n  = 120 ) ( figure  2d ) . the average distance between successive circles was b=173 nm ( n  = 80 ) ( figure  2e ) . to study the structure of these snf7 assemblies , we performed negative stain electron microscopy ( em ) of large unilamellar vesicles ( luvs ) coated with snf7 upon incubation for 15  min in a 1  m snf7 solution . luvs coated with circular structures were observed , consistent with afm images ( figure  2f ) . the fine structure of the filaments remained difficult to see because the two hemispheres of the luv are projected onto the same em image . however , in many cases , luvs that had adhered on the grid were flushed during staining , leaving snf7 assemblies attached to the grid surface . two kinds of structures were then observed : small rings ( 27  4  nm average radius ; n  = 61 ; figure  2 g ) and large circular assemblies ( r  = 110  40  nm ; n  = 46 ; figure  2h ) . small rings are composed of filaments with two different thicknesses ( figure  2 g and figure  s2c ) . the thinner ones appeared single stranded with an approximate thickness of 4.5  0.3  nm ( n  = 10 ) in agreement with previous data ( pires et  al . , 2009 , shen et  al . , 2014 the thicker ones were double - stranded , with approximately twice the thickness ( 10.7  0.7  nm ; n  = 7 ) . the larger circular assemblies had an average radius of 110  40  nm ( n  = 46 ) . following the path of the innermost filament in these assemblies revealed that they were made of a single filament , self - organized into a spiral ( figure  2h ; figure  s2d ) . within the spiral , we observed that the filament could associate laterally with itself , forming double - stranded filaments . these images showed that the spiraling nature of snf7 filaments previously observed in solution ( shen et  al . , 2014 ) it also suggests that previously reported circular assemblies could also be spirals : in  vitro , a snf7 mutant protein that polymerizes spontaneously onto membranes ( henne et  al . , 2012 ) or , in fibroblasts , the circular structures found upon overexpression of chmp4a and chmp4b ( hanson et  al . , 2008 ) . the formation of rings suggests that snf7 filaments grow with a preferred curvature and the formation of spiral suggests that snf7 filaments can depart from this preferred curvature with some flexibility . the afm images also revealed that filaments could split within the disk assemblies ( figure  2i ) : thick filaments that appeared as concentric circles are actually interconnected by thinner filaments ( figure  2j , arrows ) . this is consistent with the spiral structure seen by em : double - stranded parts are combined with single - stranded connections ( figure  2h ) . the thinner filaments had an average thickness of 4.9  nm  1.5  nm ( n  = 25 ) , probably corresponding to single strands , whereas thicker ones had a thickness of 10.6  1.2  nm ( n  = 25 ) , consistent with double - strands . the afm and em analysis suggested a structure of the snf7 assemblies , where a single spiral filament interacted laterally with itself to form double - stranded filaments . occasionally , spirals were directly observed by afm ( figure  2i , subpanel 6 ) . patch nucleation could , for instance , start from a single closed ring , like those seen by em . it is conceivable that such rings could be prone to break open , thus freeing filament tips that could further grow into a spiral . a possible scenario consists of a two - step growth mechanism ( figure  3a ) . first , new spirals are nucleated in the vicinity of existing spirals ( termed below spiral nucleation ) . second , these spirals would grow independently through the addition of monomers at their filament tips . this scenario accounts for the observed growth dynamics of snf7 patches : the constant speed of the radial growth of the patches implies that the density of growing filament tips at their rim stays constant . the formation of new spirals generates new tips , maintaining a constant density of growing tips . to explore quantitatively the implications of such scenario , we developed a mathematical description of the dynamics of surface coverage by growing snf7 spirals ( figure  3b and figure  s3 ) . in the model , snf7 spirals are represented by hard disks deposited on a surface representing a small ( micron - sized ) piece of membrane . as initial conditions , a few disks with radius r0 are present , corresponding to events of initial patch nucleation . patch nucleation is then neglected ( set to zero ) during the rest of the dynamics . disks growth corresponds to an area gain w per unit time ( in  nm.s ) , as expected if the snf7 filaments are elongating from their tips at a constant speed w / b ( in nm.s , where b  = 17  nm is the distance between snf7 filaments in a single spiral ) . as the snf7 spiral grows , its perimeter increases , offering an increasing number of potential spiral nucleation sites . we model this by stochastic nucleation of new disks with radius r0 at a rate p , where p denotes the total perimeter of the existing disks , and  a constant spiral nucleation rate ( expressed in number of nucleation events per second per micrometer ) . in the model , nucleation is prevented if the new disk location is already occupied by an existing disk . in addition , both nucleation and polymerization stop when the surface is completely covered with disks ( figure  3c ) . solving the model in a mean - field approximation using the value obtained experimentally for r0 gives a final distribution of disk sizes with one unknown parameter ( w/ ) ( supplemental information , supplemental mathematical modeling part 1 ) . fitting ( w/)=9.81.5103 m , we find the distribution in excellent agreement with the experimental size distribution ( figure  3d ) . we then tested experimentally whether three key features of our theoretical model are indeed fulfilled during the generation of snf7 assemblies . first , both the existence of initial single rings and the growth into spirals imply that snf7 filaments have a preferred high curvature . since the average radius of rings is in the range 2530  nm , this might correspond to the preferred curvature . second , the proposal of secondary nucleation of spirals implies that new spirals can form from existing ones . finally , we also sought to determine independently the parameters w and  , whose ratio ( w/ ) had been estimated from the fit of the size distribution of spirals ( figure  3d ) . to address all this , we studied the molecular dynamics of spiral growth by total internal reflection fluorescence microscopy ( tirfm ) and by dynamic high - speed afm ( hs - afm ) imaging ( casuso et  al . , 2012 ) . to characterize the initial events leading to patch formation , we first studied the early steps of snf7 patch nucleation by tirfm , which allowed us to quantify the approximate number of snf7 molecules in diffraction limited spots from their fluorescence intensity ( see experimental procedures for quantification ) . patch nucleation started with the appearance of a fluorescent diffraction limited spot ( nucleus , figure  4a ) containing 50  20 monomers ( n  = 9 ) . at a snf7 concentration of 300  nm , the intensity of the nuclei remained constant for several minutes until these nuclei started to grow ( figure  4a ) . under these conditions , the number of nuclei is very low ( figure  1c ) . to increase the number of nuclei and to obtain more robust statistics , we nucleated snf7 assemblies by adding 1  m escrt - ii and 1  m vps20 to a 75  nm snf7 solution . under these conditions , many snf7 nuclei appeared on the membrane surface ( figure  4b and figure  s4a ) and remained stable for several tens of minutes , consistent with our observations with snf7 alone ( see figure  4a ) . the snf7 nuclei have an average number of molecules of 60    46 ( mean  sd ; n  = 1856 , figure  4c ) . if arranged in a closed  ring , it would generate a circle of about 30  nm radius , considering a distance of 3.2  nm between snf7 monomers in  the filaments ( shen et  al . , 2014 ) ( radius  = perimeter / ( 2 )  = ( 60  3.2)/(2  3.14 ) 32  nm ) . this radius corresponds to those observed in rings seen by em ( see figure  2 g ) , implying that the arrested nuclei observed by tirf could be closed rings . this supports that snf7 patch nucleation starts by the appearance of a single , highly curved snf7 ring that would break to form a spiral . to further confirm this hypothesis , we further showed through photobleaching experiments that breakage of the nuclei induces patch formation ( figures s4b and s4c ) . the formation of highly curved nucleation rings suggests that snf7 filaments have a preferred radius of curvature in the 2530  nm range . indeed , we measured radii of a 27  nm radius by em and estimated a 32  nm radius by tirf , in line with other studies ( 21  nm ( shen et  al . , 2014 ) and 32  nm ( henne et  al . , 2012 ) ) . in spirals , this preference should not be satisfied , as outer turns are under - curved ( 123  nm radius , figure  2c ) and inner turns are over - curved ( 18  nm radius , figure  2d ) . these forced suboptimal radii of curvature may induce significant mechanical stresses in the snf7 filaments , which might in turn underlie snf7 biological function in membrane deformation . to explore the existence of such internal stresses , we used the hs - afm tip as a nanodissector ( scheuring et  al . , 2003 ) , briefly applying strong forces to partially break a densely packed array of snf7 spirals . after breakage , 8 large disks were transformed into 29 small circles ( figure  4d ) , with a radius of 17  5  nm ( see size distribution figure  s4d ) . this is consistent with a scenario where snf7 filaments were excised by rupture from the outer circles and curled back to a radius closer to their preferred radius . the nanodissector experiment indicated that even if polymerized at low radius of curvature , snf7 filaments kept their ability to curl into smaller rings . the radius of these broken filaments ( 17  nm ) is smaller than the one of the initial ring ( 27  nm ) , but very close to the size of the inner turns in large spirals ( 18  nm ; see figure  2d ) . alternatively , the nanodissector - induced rings experienced the lateral pressure of the neighbors , forcing them to a smaller radius . to discriminate these two hypotheses , we studied the nucleation of new spirals from pre - existing snf7 assemblies at molecular resolution by hs - afm . we focused on areas where snf7 spirals were already packed , but free membrane was still available ( figures 4e and f ; movies s5 and s6 ) . our image sequences showed that newly formed spirals were mainly initiated from filaments protruding from pre - existing spirals ( figure  4e ) , revealing the mechanism by which spiral nucleation occurs . the outer radius of these spirals grew with time while forming new turns ( figures 4f and 4 g ) . while growing , bundled filaments can transiently separate and interact laterally with the neighboring bundles ( figure  4h ) . strikingly , when increasing from 2 to 3 concentric circles , the radius of the innermost circle was reduced from 22  nm to 14  nm ( figure  4 g ) . these observations strongly support our hypothesis that the preferred radius of curvature of snf7 oligomers is about 25  nm , but that lateral pressure can induce higher curvatures . the radial growth of free spirals was initially rapid , but then slowed down ( figure  4i ) , roughly following a dependence on the square root of time as expected from our model . from these data , we measured an area growth rate w of 80  36  nm.s ( n  =  5 ; see experimental procedures for quantification ) at 1  m . we estimated from w a growth rate of approximately 3 subunits.s.m ( supplemental information , supplemental mathematical modeling ) . the estimated filament growth rate is in the range of other filament rates : actin and tubulin are in the range of 510 subunits.s.m . using our previous estimate ( w/)=9.8103 m and this experimental value for w , we obtained the spiral nucleation rate as   = 8.2 103 spiral.m.s at [ snf7 ]  = 1  m . this secondary spiral nucleation rate is 500 times larger than the initial patch nucleation rate ( supplemental information , supplemental mathematical modeling ) . it validated our assumption that the patch nucleation was negligible in our theoretical model . in summary , these observations indicated ( 1 ) a preferred high curvature of the snf7 filaments and ( 2 ) the mechanism of spiral nucleation from existing spirals . we then set up to study the third feature of our model , whether lateral contacts between spirals can inhibit their growth . afm images of packed arrays of spirals showed that filaments at the contact zone between spirals were flattened , resulting in spirals acquiring a polygonal shape that was more pronounced for longer incubation times ( figure  5a ) . moreover , the central area of some of these polygons was pushed toward the substrate , as seen in the height profile of afm images ( figure  5b ) . also , the centers of these spirals were often found to be stiffer as seen in afm mechanical maps ( figure  5b ) . we reasoned that this deformation reflected lateral compression of the spirals as the membrane became covered with snf7 . to study the correlation between polymerization rate and lateral compression of the snf7 assemblies , we ought to measure them simultaneously . we started by reconstituting snf7 polymerization on guvs adhered to a glass surface , to avoid any displacement during time - lapse imaging ( figure  s5a ) and followed the increase of snf7 fluorescence on the vesicle with time . in supported bilayers , which have smaller lipid mobility than free bilayers , in contrast , snf7 assemblies had a higher diffusion on guvs explaining that fluorescence showed a homogeneous distribution ( figure  5c ) . the dynamics of saturation of snf7 polymerization over the entire guv ( figure  5c , bottom ) was similar to the dynamics of coverage at a single point in the supported bilayer experiments ( figure  s5b ) : after an approximately exponential increase of the fluorescence , the dynamics of coverage saturated through a progressive slow down phase . if polymerization rate is independent of lateral compression , as it is in our theoretical model , an abrupt arrest of growth is expected ( figure  s5c ) . conversely , a polymerization rate dependent on lateral compression would cause a progressive slow down until reaching saturation . as an indication of lateral compression , we noticed that coated guvs underwent dramatic morphological changes upon several hours of snf7 polymerization : guvs were not spherical anymore and instead showed extreme irregular shapes , similar to rigid punched table tennis balls ( figure  5d ) . upon aspiration into a micropipette , they deformed plastically ( figure  5e and figure  s5d ) , showing that the snf7 solidifies the membrane . these observations are consistent with a scenario where a rigid snf7 coat generates pressure on the guvs , stretching their membrane . we reasoned that the accumulation of lateral compression in the snf7 coat would stretch the underlying membrane , increasing its tension ( figure  5f ) . in order to follow the dynamics of accumulation of lateral compression within the snf7 layer , we directly measured membrane tension generation during snf7 polymerization . using optical tweezers , we pulled a thin tether from a guv held in an aspiration pipette , that allows to monitor membrane tension through the measurement of the force f exerted on the optical tweezers bead ( cuvelier et  al . , 2005 ) we then flowed a 500  nm solution of snf7 using an injection pipette , which triggered protein assembly onto the membrane ( figure  5h ) . monitoring snf7 fluorescence , we found that its membrane binding dynamics was identical to that measured previously , reaching the saturation value after 1020  min ( figure  5i , top ) . concomitant with this saturation , we observed an increase in the force exerted by the tube , indicating an increase of membrane tension ( figure  5i , bottom ) . these data show that snf7 polymerization occurs at a slower rate as compression increases within the snf7 layer , suggesting a coupling between polymerization and compression . the dependence of the polymerization energy  ( polymerization energy per unit surface ) on the changes in tube force is captured by the expression ( supplemental information , supplemental mathematical modeling part  4.3):(1)=ff2fi282where fi=8pn and ff=35pn are the tube forces before and after snf7 polymerization and =4.81020 j , is the membrane bending rigidity ( figure  s5e ) . these values yield =3.1104 j.m , which is a fairly high polymerization energy , twice that of clathrin ( saleem et  al . , 2015 ) , which by itself is able to cause membrane deformation during endocytosis . these data are therefore compatible with a scenario where snf7 spirals act as 2d springs that load themselves through polymerization . constrained by their neighbors , snf7 spirals would deform significantly during polymerization , from a disk - like to a polygonal shape , until deformation and polymerization force are balanced . to test quantitatively whether the polymerization force is sufficient to deform snf7 spirals , we established a theoretical elastic model of spiral compression . in the model , the snf7 layer is approximated to a hexagonal lattice of individual spirals . each spiral is composed of a collection of concentric filaments spaced by a distance b=17 nm up to a typical radius r=130 nm similar to the experimental data shown in figure  2c . the filaments are circular in the absence of lateral compression , but may deform into hexagons with rounded vertices , to accommodate tighter packing , as illustrated in figures 5a and 5f . the amount of energy required to deform circular filaments into more polygonal shapes depend on the stiffness of the snf7 filaments , which is characterized by its persistence length p . we estimated this persistence length from the amplitude of the thermal fluctuations of isolated snf7 filaments on a supported bilayer observed by hs - afm . we obtained p=260  nm ( supplemental information , supplemental mathematical modeling part 2 ) . this is in order - of - magnitude agreement with an estimate from a numerical model of snf7 flexion ( p800 nm ) ( shen et  al . , 2014 ) . this value is higher than for dna ( p=50 nm ) , but smaller than for cytoskeletal filaments ( p=15 m for actin and p=6 mm for microtubules ) ( howard , 2001 ) , implying that they are intrinsically soft enough to be deformed by moderate forces . in our theoretical 2d spring model , / r2b)log(r / b ) ( where kb is the boltzmann constant and t the temperature , see supplemental information , supplemental mathematical modeling part 3 ) . our experimental estimates for r ( 130  nm ) , b ( 17  nm ) and p ( 260  nm ) implied =4.0105jm2 , 8 times smaller than the measured experimental . it indicates that the snf7 polymerization energy , even if underestimated , is sufficient to induce strong deformations . our data show that the snf7 spirals can deform as spiral springs , and can self - load through a mechanism where deformation is mostly generated by growth of a filament . having established that the snf7 spirals can deform to store significant elastic energy , we wondered if they could release this energy to deform the membrane . after several hours of snf7 incubation , holes ( called  pores  in the following ) spontaneously appeared in a few guvs , releasing membrane tension . surprisingly , instead of bursting , the guv membrane shrunk from the rim of the pore toward the opposite side of the guv ( movie s7 ) . occasionally , this process stopped before the vesicle had fully collapsed , and stable vesicles with open pores were observed ( figure  6a ; movie s8 ) . in this case , a stronger fluorescence signal is seen at the rim . to understand the stronger signal of the membrane marker at the rim , we imaged these opened guvs by thin - section em : the membrane at the rim of the pore was rolled toward the interior of the vesicle ( figure  6b ) . this process is known as curling , and has previously been observed in a number of situations , including polymersomes ( mabrouk et  al . , 2009 ) and during the bursting of red blood cells ( callan - jones et  al . , 2012 ) . it occurs when an area difference appears between the two sides of a bi - layered surface . we hypothesized that curling could be driven by the expansion of the previously compressed snf7 layer following pore formation . to quantitatively study the plausibility of such scenario , we used our theoretical model to compute the ratio of the surface occupied by a compressed spiral ( acompressed ) to that of the a relaxed state ( arelaxed ) ( see supplemental information , supplemental mathematical modeling part 3 ) as(2)acompressedarelaxed=[23+(123)]2=94% the value of this ratio implies that , during stress release , the  snf7 layer would expand by 6% relative to the underlying , almost inextensible lipid bilayer ( figure  6c ) . as a result , the membrane of the guv would curl inward ( figure  6d ) , consistently with our  observations in fluorescence and electron microscopy . the  preferred curvature of the curl can be estimated as  rc=(d/2)(arelaxed+acompressed)/(arelaxedacompressed ) , where 2d is the total thickness of the lipid - snf7 sandwich . using afm to measure the thickness of the snf7 coated membranes , we estimated 2d  = 9  nm ( 5  nm for the membrane plus 4  nm for the snf7 coat ) . with this value , we can estimate rc=37 nm . considering previous studies ( callan - jones et  al . , 2012 ) , rc corresponds to the curvature of the innermost roll observed ( figure  6d ) . experimentally , we find a mean radius of rc=396 nm ( n  = 9 ) . therefore curling in the opened vesicles can be explained by the expansion of the snf7 spiral springs . during this expansion , we wondered how much energy was stored in a single spiral , as compared to the energy required for budding of a vesicle . our elastic model implies that the lateral compression of a single snf7 spiral corresponds to the accumulation of an elastic energy e=170kbt=7.01019j , which is bigger than the bending energy 4=160kbt required to form a spherical membrane bud ( see supplemental information , supplemental mathematical modeling ) . thus , a single spiral can accumulate enough elastic energy to form a spherical bud when released . in summary , we show here that snf7 filaments display the ability to act as spiral springs that load through polymerization . the release of the compression stress accumulated during the deformation of the snf7 spiral is sufficient to drive membrane deformation . in this study , we first showed that lipid membranes trigger the formation of wild - type snf7 assemblies at their surface through a process of nucleation - growth . the patch nucleation rate is low ( less than 1 seed.m.hour ) which explains the necessity of a polymerization - activated mutant to observe the same assemblies by em in previous studies ( henne et  al . , 2012 ) . we found that the circular arrays formed by snf7 on these membranes are spirals made of a single filament looping and interacting onto itself . this confirms that the interaction with membrane in  vitro retains the spiral structure recently observed in solution ( shen et  al . , 2014 ) or in  vivo ( cashikar et  al . , 2014 , hanson et  al . , 2008 we also find that snf7 filaments can bundle into double - stranded filaments , probably through parallel lateral interactions . in our assay , spirals become tightly packed into polygonal lattice at the surface of the supported bilayers . the packing of these spirals is correlated with the increase of lateral compression within the snf7 coat . these data implies that escrt - iii spirals , because of the relatively high flexibility of the snf7 filament can be deformed by lateral compression . moreover , we show that the expansion of compressed spirals can lead to membrane deformation if confinement is released ( figure  6 ) . these observations imply that snf7 can work as a two - dimensional spring , being able to compress and expand . in the following , we discuss how this spring - like activity highlighted by our study is relevant for the in  vivo situation . in  vivo , it is unlikely that a densely packed array of escrt - iii spirals is present at the surface of membranes , which may question the physiological relevance of the spiral compression observed in large patches of escrt - iii . but the confinement required for such lateral compression might come from other membrane proteins , which may provide walls into which single spirals could be confined . in the membrane of mvbs , lamp1 and 2 are particularly enriched ( bissig and gruenberg , 2014 ) and may provide a scaffold onto which escrt - iii spirals could be compressed . of course , compression being isotropic in this in  vivo case , compressed spirals would stay circular , instead of polygonal . but another source of lateral compression is intrinsic to the spiral structure , and is present in single snf7 spiral even in the absence of any external confining structures . we show that the  filaments curl spontaneously at 2030  nm , implying that if they grow at a different radius , they are under mechanical stress . indeed , when spirals are broken , all the pieces of filaments further curl to a smaller radius . thus , in the spiral structure , filaments with a radius larger than 25  nm are stretched , compressing the inner filaments . accordingly , we find that even for non - laterally constrained spirals , the inner turn of the spirals tightens when the number of turns in the spirals goes above three . whatever the source of compression is , our observations show the ability of snf7 spirals to deform elastically and accumulate potential energy that can be used for membrane deformation . but how would such energy drive membrane budding ? it was previously proposed that the polymerization of escrt - iii could enclose a patch of membrane and then , by reduction of the length of the snf7 rim , the membrane would be folded into a bud in the middle of the snf7 polymer . the escrt - iii rim reduction has been proposed to be mediated by depolymerization of the snf7 spiral ( lasso model , ( saksena et  al . , 2009 ) ) or by further inward polymerization of the snf7 spiral ( cashikar et  al . , 2014 ) . our data suggests that snf7 spiral spring could mediate the rim reduction by its elastic compression down to a 14  nm radius . however in this scenario , because the membrane is fluid , it is difficult to picture how the force of the spiral spring would be transmitted to the membrane . we propose that cargoes play an essential role for the force transmission ( figure  7,left ) : the rim reduction would lead to compaction of enclosed membrane cargoes . theoretical ( derganc et  al . , 2013 ) and experimental studies ( stachowiak et  al . , 2012 ) indicate that highly dense cargoes could mediate budding by asymmetric crowding . this is consistent with a recent in  vivo study ( mageswaran et  al . , 2015 ) where ilvs budding was critically dependent on accumulation of cargoes within escrt - iii assemblies . another possibility is that the out - of - plane buckling of the spring itself might drive the invagination of the membrane ( figure  7 , right ) ( lenz et  al . , 2009 ) , which could explain the formation of membrane tubules by overexpression of the human homolog of snf7 ( hanson et  al . , 2008 this model implies that the flat membrane could be a metastable state of this elastic system : the stored elastic energy could be suddenly released upon external activation . our observation that the spirals adopt a curved inverted dome shape ( figure  5b ) is consistent with this model , and an estimate of the energy stored in one spiral further confirm that this energy is sufficient to bud the membrane into a sphere . the spring - like properties of snf7 filaments also nourish our understanding of escrt - iii role in membrane fission . because of their high flexibility , snf7 filaments can grow at radii different from their preferred radius of curvature if steric or mechanical constraints force them to do so . this feature explains how snf7 filaments could adapt to the wide range of radii observed in the various escrt - iii mediated fission reactions : from microns in abscission and hundreds of nanometer in virus budding , down to tens of nanometers in ilv formation and membrane repair ( jimenez et  al . , 2014 ) . however , the smallest size of the inner turn is on average 18  nm radius , which is far from the 1.4  nm observed with dynamin to finalize fission ( sundborger et  al . this raises questions regarding the mechanism necessary to provide fission and pore closure and supports the role of other escrt - iii proteins and lipids in these reactions . 21490 ) were purified as previously described ( hierro et  al . , 2004 , snf7 stock solution was 2.5  m in 20  mm hepes , 100  mm nacl ( ph 8) . escrt - ii ( 20  m stock solution in 50  mm tris , 150  mm nacl , 5  mm -mercaptoethanol [ ph 7.5 ] ) and vps20 ( 10  m stock solution in 20  mm hepes 100  mm nacl [ ph 7.5 ] ) were kept unlabeled . guvs were prepared by electroformation using dopc and dops mixtures , purchased from avanti polar lipids ( alabaster , usa ) . when necessary , 0.1% fluorescent lipids ( 1,2-dioleoyl - sn - glycero-3-phosphoethanolamine - n-(lissamine rhodamine b sulfonyl ) ) ( rhodamine - pe ) were added . luvs were prepared by evaporating in a round - bottom glass tube , a volume of lipid mix ( dopc : dops , 6:4 , mol : mol ) containing 1 mg of total lipids . after addition of 200  l of buffer , the tube was vortexed and freeze - thaw 3 times . this solution is kept at 20c until use . unless otherwise noted , the buffer used for all experiments is composed of 20  mm tris hcl ( ph 6.8 ) , 200  mm nacl , 1  mm mgcl2 . for confocal and tirf imaging , a coverslip is cleaned with water and ethanol , and then plasma - cleaned for 2  min ( pdc-32 g , harrick plasma , ny , usa ) . the coverslip is assembled to a flow chamber ( sticky - slide vi 0.4 , ibidi , munich , germany ) , with one entry connected to a syringe pump ( aladdin , world precision instruments , sarasota , fl , usa ) , and the other left open for sequential introduction of other solutions . 5  l of guvs are flushed in the flow chamber ( see extended experimental procedures for methods to get supported membranes or partially adhered vesicles ) . imaging is performed using an inverted microscope assembled by 3i ( intelligent imaging innovation , denver , usa ) and nikon ( eclipse c1 , nikon , tokyo , japan ) . for sdc imaging , a 2-m - thick volume stack ( 1  m above and below the supported membrane ) is acquired then rendered to 2d by maximum intensity projection . the number of molecules within snf7 oligomers is estimated by calibrating the microscope with commercially available fluorescent dna origamis ( gatta - brightness 9r and 18r , gattaquant , braunschweig , germany ) ( figure  s6 ) . a modified version of a published setup ( morlot et  al . , 2012 ) allows simultaneous brightfield imaging , sdc microscopy , and optical tweezing on an inverted nikon eclipse ti microscope . a guv is aspirated within a micropipette connected to a motorized micromanipulator ( mp-285 , sutter instrument , novato , ca , usa ) and a pressure control system ( mfcs - vac 69 mbar , fluigent , villejuif , france ) that sets the aspiration pressure p . a membrane nanotube is then pulled out from the guv through a streptavidin - coated bead ( 3.05  m diameter , spherotec , lake forest , il , usa ) held in a fixed optical trap . the optical trap was custom - made with a continuous 5  w 1064  nm fiber laser ( ml5-cw - p - tks - ots , manlight , lannion , france ) focused through a 100x 1.3 na oil immersion objective . the force f exerted on the bead was calculated from the hooke s law : f  = k.x , where k is the stiffness of the trap ( k  = 60 pn.m ) and x the displacement of the bead from its equilibrium position . snf7 was injected close to the nanotube with a second micropipette connected to another channel of the fluigent pressure control system . for negative stain em observations , luvs were incubated with snf7 in suspension , spun down ( 4  min at 4,000 g ) , washed and then adsorbed onto glow - discharged formvar coated em grids . the samples were negatively stained for 30  s with 2% uranyl acetate before visualization . ultrathin sectioning of snf7 bound luvs fixed in epon was performed using a microtome ( leica ultracut ) at a cutting angle of 6. sections were put on glow - discharged carbon - coated formvar grids and imaged with a tecnai g2 sphera ( fei ) electron microscope . for both pf - qnm afm and hs - afm , guvs , prepared as described above , were adsorbed to the mica support followed by protein addition . for pf - qnm afm experiments 5  l of the guvs and for hs - afm experiments 0.5  l of guvs were deposited onto freshly cleaved mica supports pre - incubated with adsorption buffer ( 220  mm nacl , 10  mm hepes , 2  mm mgcl2 , [ ph 7.4 ] ) . supported lipid bilayers were first imaged to assess the quality of the lipid bilayer preparation before injecting snf7 into the fluid cell to a concentration of 500  nm .
summaryescrt - iii is required for lipid membrane remodeling in many cellular processes , from abscission to viral budding and multi - vesicular body biogenesis . however , how escrt - iii polymerization generates membrane curvature remains debated . 
 here , we show that snf7 , the main component of escrt - iii , polymerizes into spirals at the surface of lipid bilayers . when covering the entire membrane surface , these spirals stopped growing when densely packed : they had a polygonal shape , suggesting that lateral compression could deform them . 
 we reasoned that snf7 spirals could function as spiral springs . by measuring the polymerization energy and the rigidity of snf7 filaments 
 , we showed that they were deformed while growing in a confined area . 
 furthermore , we observed that the elastic expansion of compressed snf7 spirals generated an area difference between the two sides of the membrane and thus curvature . 
 this spring - like activity underlies the driving force by which escrt - iii could mediate membrane deformation and fission .