Clathrin mediates membrane fission and budding by constricting membrane pores

Membrane budding, which underlies fundamental processes like endocytosis, intracellular trafficking, and viral infection, is thought to involve membrane coat-forming proteins, including the most observed clathrin, to form Ω-shape profiles and helix-forming proteins like dynamin to constrict Ω-profiles’ pores and thus mediate fission. Challenging this fundamental concept, we report that polymerized clathrin is required for Ω-profiles’ pore closure and that clathrin around Ω-profiles’ base/pore region mediates pore constriction/closure in neuroendocrine chromaffin cells. Mathematical modeling suggests that clathrin polymerization at Ω-profiles’ base/pore region generates forces from its intrinsically curved shape to constrict/close the pore. This new fission function may exert broader impacts than clathrin’s well-known coat-forming function during clathrin (coat)-dependent endocytosis, because it underlies not only clathrin (coat)-dependent endocytosis, but also diverse endocytic modes, including ultrafast, fast, slow, bulk, and overshoot endocytosis previously considered clathrin (coat)-independent in chromaffin cells. It mediates kiss-and-run fusion (fusion pore closure) previously considered bona fide clathrin-independent, and limits the vesicular content release rate. Furthermore, analogous to results in chromaffin cells, we found that clathrin is essential for fast and slow endocytosis at hippocampal synapses where clathrin was previously considered dispensable, suggesting clathrin in mediating synaptic vesicle endocytosis and fission. These results suggest that clathrin and likely other intrinsically curved coat proteins are a new class of fission proteins underlying vesicle budding and fusion. The half-a-century concept and studies that attribute vesicle-coat contents’ function to Ω-profile formation and classify budding as coat-protein (e.g., clathrin)-dependent or -independent may need to be re-defined and re-examined by considering clathrin’s pivotal role in pore constriction/closure.


Introduction
Membrane budding, which mediates fundamental processes such as endocytosis, intracellular trafficking, membrane-bound organelle formation, and virus infection, involves two membrane transformation steps: (1) the formation of an Ω-shaped membrane profile and (2) the cutting of the Ω-profile at the pore region (fission) [1][2][3] .The Ω-profile formation is accompanied by the coating of membrane proteins, among which clathrin is the most observed 4,5 , and COP I/II and caveolin are sometimes reported 2,3 .Accordingly, membrane buddings are classified as either clathrin-dependent or -independent [4][5][6] .Since clathrin (and other membrane coat proteins) coats Ω-profiles' head, the primary function of clathrin (and other membrane coat proteins) is thought to be involved in Ω-profile formation, although whether and to what extent clathrin coating (and other coat proteins) provides forces to form Ω-profiles remains unsettled 4,5,[7][8][9][10] .
Following Ω-profile formation, proteins that form helices surrounding and constricting the Ω-profile's pore are generally thought to mediate fission.The most commonly observed helix-forming protein for fission is dynamin and its family of proteins 11 .In brief, decades of studies establish the current view that membrane budding may require coat proteins to form Ω-profiles and helixforming proteins to mediate fission 1,[3][4][5]11 .
The present work examined this current view in live neuroendocrine chromaffin cells, where fission of Ωprofiles preformed via the flat-to-Ω-shape transition or formed via vesicle fusion at the plasma membrane can be readily resolved with imaging 12,13 .We found that clathrin polymerization with an intrinsically curved shape around the pore region of the Ω-profile generates elastic forces to constrict and thus close the Ω-profile's pore.This new mechanism is of much more widespread importance than the classical role of clathrin in coating small budding vesicles because it mediates the fission of either budding or fusing vesicles of all sizes regardless of the clathrin coating on vesicles.Consequently, in addition to underlying clathrin-coated vesicle endocytosis, this mechanism underlies diverse endocytic and exocytotic modes previously considered clathrin (coat)-independent.These findings reveal a new design principle for membrane buddingthe primary and universal function of clathrin and likely other protein coats with an intrinsically curved shape is to generate pore-constriction forces to mediate fission and control fusion pore dynamics.Decades of studies that classified vesicle budding and endocytosis into clathrin-dependent or -independent mode based on whether the Ω-profile's head is coated with clathrin may need to be re-examined.Membrane fission machinery should include the intrinsically curved clathrin coat as a new class of fission proteins.
Clathrin is at Ω-profiles' base/pore region for pore constriction and closure The requirement of clathrin for pre-Ω and fs-Ω pore closure implies that clathrin acts at the pore region.The following three sets of data showed that clathrin is at the Ω-profile's base/pore region to mediate pre-Ω and fs-Ω pore closure.
Second, we applied 1 depol 1s per cell to induce pore closure while repeatedly performing the XZ-plane STED imaging at a fixed Y-axis location (near the cell center) every 50-300 ms (XZ/Y fix scanning), which improved time resolution and thus allowed us to observe pore closure in real-time but reduced the chance of seeing Ωprofiles 12,13 .3-color STED XZ/Y fix scanning showed that CLC-mTFP1 puncta were at the base/pore region during pre-Ω nvp pore closure (Fig. 2e, 12 out of 13 events, 13 cells), that pre-Ω vp pore constriction paralleled the decrease of the distance between CLC-mTFP1 puncta flanking pre-Ω vp 's pore (Fig. 2d, n = 3 events, 3 cells), and that depol 1s -induced, PH G /Atto 532-labelled fs-Ω (ref. 12) colocalized with pre-existing CLC-mTFP1 puncta at fs-Ω's pore region (8 out of 8 fs-Ω, 8 cells; Fig. 2g).These results showed in real time that clathrin is at or surrounds the base/pore region to mediate pore closure during pre-Ω and fs-Ω pore closure.
Third, to examine clathrin distribution in pre-Ω's pore region in more detail, we performed minimal photon fluxes (MINFLUX) imaging of CLC attached with a SNAP-surface® Alexa fluor 647 (SNAP-CLC-A647) at a localization precision of ~3 nm 22 .We first performed XZplane confocal imaging of PH-mScarlet (similar to PH G , except mNeonGreen replaced with mScarlet) along Y-axis every ~0.5-1 μm (XZ/Y stack scanning) to identify the pre-Ω's pore region, which appeared mostly as confocally non-visible pore, a PH-mScarlet spot (Fig. 2h II-IV ), but occasionally confocally visible as a ring at the XY-plane A reconstructed trace reflecting pre-close (R fs+pre , a down-step at F 655 dimming onset) is also plotted.F PH , F 655 and F FFN were normalized to the baseline.d, e F PH , F 655 , F FFN , R fs+pre and confocal images showing rapid and slow close-fusion (d), stay-or shrink-fusion (e).R fs+pre : a reconstructed trace reflecting fusion (up-step, at F 655 rising onset) and fusion pore closure (down-step, at F 655 dimming onset).f Left: sampled western blot results of CHC, dynamin 1/2 (Dyn), adaptor protein 2 α subunit (AP2), synaptotagmin 1 (Syt1), syntaxin 1 (Stx1), and actin in chromaffin cell cultures transfected with si-Ctrl or si-CHC.Right: the percentage (mean ± s.e.m., 3 transfections) of the above proteins in cultures transfected with si-CHC (data normalized to the corresponding mean of si-Ctrl).g-i The percentage of pre-spots undergoing pore closure (pre-close%, g), the percentage of closefusion in all fusion events (close-fusion%, h), and FFN511 20%-80% decay time (i) in: ( 1  (Fig. 2h I ) (see also Fig. 2b for STED images).These structures could also be observed confocally at the XZplane (Supplementary Fig. S8, see also Fig. 2a, c for STED images).Next, we performed 2D MINFLUX imaging of SNAP-CLC-A647 at these identified pre-Ω's base/pore region at the XY-plane (Fig. 2h).MINFLUX imaging resolved many individual SNAP-CLC-A647 molecules as clusters of localizations around or at the pre-Ω's pore region (22 pre-Ω, 17 cells, 4 cultures; Fig. 2h).Some SNAP-CLC-A647 molecules were localized close together within a ~10-30 nm distance (Fig. 2h), consistent with clathrin polymerization in these regions 4,5 .
Clathrin polymerization is required for pore closure Three sets of evidence suggest that clathrin polymerization is needed for pore closure.First, pitstop 2, which blocks dynamic clathrin patch formation and disassembly 21 , inhibited pre-Ω/fs-Ω closure (Fig. 1g, h).Second, platinum replica electron microscopy (EM) in si-CHC-transfected cells showed that overexpression of C1573S CHC mutant, which abolishes clathrin trimerization 23 , reduced clathrin lattice density when compared to wildtype CHC overexpression (Fig. 3a, b).Consistently, pre-close and close-fusion percentages in si-CHCtransfected cells overexpressed with C1573S CHC were much lower than those in si-CHC-transfected cells overexpressed with wildtype CHC (Fig. 3c).Evidently, lower clathrin lattice density was associated with lower pre-close and lower close-fusion (Fig. 3d).These results suggest that clathrin polymerization is required for mediating pre-Ω/ fs-Ω pore closure.Third, a top-to-bottom EM view showed that clathrin lattices associated with some apparently oval/round shape membrane invaginations (9.1 ± 1.2%, n = 20 cells; Fig. 3e) reminiscent of STED images of clathrin surrounding pre-Ω's base/pore region (Fig. 2a-c).Invaginations not associated with clathrin lattices could be because: (1) a top-to-down view precludes seeing Ω-profiles' base/pore region, and (2) EM may not recognize non-polymerized clathrin.While most Ω-profiles were apparently oriented in parallel to the topto-down direction, which showed a complete oval/roundshape bright and clear edge (Supplementary Fig. S9a; see also Fig. 3e), some Ω-profiles were apparently tilteda U-or C-shape bright and clear edge plus the remaining non-bright and non-clear edge that appeared to be connected with the plasma membrane (Supplementary Fig. S9b; see also Fig. 3f).In 24% (16 out of 66) of these apparently tilted Ω-profiles (20 cells), we observed clathrin lattices at the non-bright and non-clear edge, the base/pore region of the apparently tilted Ω-profiles (Fig. 3f), supporting that clathrin may polymerize at the Ωprofile's base/pore region.

Modelling: clathrin polymerization generates poreclosure forces
We performed theoretical modeling to determine how clathrin polymerization generates pore-closure forces.Our modeling started with a Ω-bud without clathrin as recently computed 9 ; clathrin was then recruited to the Ωbud's base and gradually polymerized into a coat.The coat was assumed to have an inherent stress-free conformation of an element of the elastic sphere with bending modulus, κ C , and intrinsic radius of curvature, R S (Fig. 3g, h; see Materials and methods).The coat then applied a torque to the Ω-profile's base.Torque value reflected coat polymerization extent, ranging from 0 before polymerization to κ C =R S for complete polymerization, where R S ¼ 70nm, a typical clathrin-coated vesicle's radius 7 , and the reported κ C is approximately equal or significantly the membrane bending modulus κ m % 20k B T ðk B T ¼ 4:110 À21 Joule, product of Boltzmann constant and absolute temperature) 24,25 .
Computation (see Materials and methods) revealed that as κ C =R S (the polymerization extent) increases, Ω-bud's pore gradually constricts from ~110 nm (non-polymerized clathrin) to nanometers (fully polymerized coat, Fig. 3g, h).For κ C ¼ 40k B T (ref. 24) and R S ¼ 70nm (ref. 7), pore radius reached ~1.2 nm (Fig. 3g, h), which (see figure on previous page) Fig. 2 Clathrin at Ω-profile's base/pore region constricts the pore.a Left: clathrin surrounds pre-Ω's visible pore: STED XZ-plane images of PH G and CLC-mTFP1 for a pre-Ω with a visible pore (pre-Ω vp ) along Y-axis every 100 nm as labelled.Right: XY-plane images at two Z-planes (z1, z2) across the pore region.b STED XY-plane images of PH G and SNAP-CLC-SiR (see Materials and methods) showing different sizes of pre-Ω's pore surrounded by clathrin (left: pore visible; middle and right: pore too small to resolve).c Clathrin at pre-Ω's non-visible pore and base region: STED XZ-plane images of PH G , CLC-mTFP1 and A532 for a pre-Ω with a non-visible pore (pre-Ω nvp , permeable to A532).d CLC-mTFP1 puncta flanked and moved with the constricting pore of a pre-Ω vp : F PH , F 532 , CLC-mTFP1 fluorescence (F CLC ), Ω p 's pore diameter (d p ), the distance between two CLC-mTFP1 puncta flanking the pore (d CLC ), and sampled STED XZ-plane images of PH G /CLC-mTFP1/A532 taken at times indicated sticks.Gray circles: < 60 nm (STED resolution); triangle: depol 1s .e CLC-mTFP1 puncta at the base/pore region of a pre-Ω nvp : F PH , F 532 , F CLC and sampled STED XZ-plane images of PH G /CLC-mTFP1/A532.F 532 decay (A532 was strongly excited) reflected pre-Ω pore closure.Triangle: depol 1s .f STED XZ-plane images of PH G , FFN206, and CLC-mTFP1 (merge at the bottom) showing CLC-mTFP1 puncta at vesicle docking sites (triangles, contact between FFN511-labelled vesicles and the PH G -labelled PM).PM and cytosol (Cyto) locations are labelled.g F PH , F 532 , F CLC (F) and sampled XZ/Y fix images of PH G /A532/CLC-mTFP1 showing that PH G /A532-labelled fs-Ω co-localized with pre-existing CLC-mTFP1 puncta at fs-Ω's pore region (8 out of 8 fs-Ω).h Confocal images of PH-mScarlet showing the visible (I) or non-visible pore (II-IV) of 4 Ω-profiles at the XY-plane (upper) and 2D MINFLUX images of CLC-SNAP-A647 at the same XY-plane region (middle, upper and middle images merged at the bottom).may lead to fission 26,27 .For a larger reported κ C (refs. 24,25), the pore radius became even smaller, but beyond the model validity.Thus, the intrinsically curved shape of a rigid clathrin coat covering the Ω-bud base may constrict and close the pore.This conclusion was obtained with the constant area scenario for clathrin coat formation 28 , consistent with the observation of clathrin at the pre-Ω's base/pore region (Fig. 2a-e).A similar conclusion was obtained for the constant curvature scenario 28 (Supplementary Fig. S10).

Clathrin mediates slow, fast, ultrafast and overshoot endocytosis by closing pre-Ω/fs-Ω's pore in chromaffin cells
To recycle exocytosed vesicles, secretory cells use many endocytic modes, including slow (τ > ~6 s), fast (τ < ~6 s), ultrafast (τ < ~0.6 s), and overshoot endocytosis (more endo-than exocytosis).These modes may generate nonclathrin-coated vesicles and are thus considered clathrin (coat)-independent mode of endocytosis [30][31][32] .Given that clathrin closes Ω-profile's pore (Figs. 1, 2), here we determined whether these different modes depended on  c). e Platinum replica EM images from control cells: clathrin lattices are associated with oval-shape membrane structures (top-to-bottom view).f Platinum replica EM images showing clathrin lattices are associated with the apparently tilted oval-shaped membrane structures at the base/pore region.g Evolution of Ω-bud shape (including pore waist).Upper row illustrates the extent of clathrin polymerization at the base; lower row presents the computed shape profiles.Panel I: no clathrin polymerization; panel II: partial clathrin polymerization; panel III: full clathrin polymerization.The degree of clathrin polymerization is quantified by the value of torque, κ C =R S , indicated in panel f by the numbers corresponding to those at the panels.Coat area is kept constant (= 302; 191nm 2 ).Ω-bud's height: 1128 nm; Ω-bud's base boundary width: 282 nm; from typical Ω-buds observed in chromaffin cells 13 .Panel III inset: boxed area showing enlarged pore waist region with a pore radius of 1.2 nm for a fully polymerized coat.h Pore radius plotted versus κ C =R S quantifying the extent of the coat polymerization.Data points I-III correspond to Ω-bud profiles I-III in panel g, respectively.clathrin for pore closure in chromaffin cells containing large (~200-1500 nm), non-clathrin-coated vesicles 15 and in hippocampal synapses containing small (~30-80 nm) vesicles.
Two sets of data suggest that clathrin-mediated pre-Ω/ fs-Ω closure underlies each of these modes, including slow, fast, ultrafast, overshoot, and bulk endocytosis.First, without affecting ICa or ΔCm, si-CHC, sh-CHC or pitstop 2 blocked Decay Cm averaged from all cells (Fig. 5a), or each of the five groups divided based on ICa density, which yielded five endocytic modes in control (Fig. 5b).Second, we reconstructed the exo-endocytosis trace (R fs +pre ) from individual fusion and pre-close by assigning an up-step at fusion onset and a down-step at close-fusion or pre-close (at F 655 dimming onset; e.g., Fig. 1c-e; see Materials and methods), and then summing up-and down-steps within a cell.R fs+pre resembled the corresponding cell's Decay Cm amplitude and time course in five groups (Fig. 5c, d), confirming pre-Ω/fs-Ω closure mediates each detected endocytic mode mentioned above 13 .si-CHC, sh-CHC or pitstop 2 blocked Decay Cm and R fs +pre decay in all groups (Fig. 5d, e), indicating that clathrin underlies each above-mentioned endocytic mode by closing pre-Ω/Fs-Ω.
Rate decay did not decrease substantially at day 2-4 after Cre transfection at which CHC was ~86%-26% of control, but decreased substantially at day 5-6 at which CHC was ~22%-12% of control (Fig. 6e-g).The relation between Rate decay and CHC level (Fig. 6g, right) was much leftshifted compared to that between transferrin uptake and CHC, as obtained at day 2-6 after Cre transfection (Fig. 6d, right).For example, with ~26% CHC left on day 4, Rate decay was reduced negligibly whereas transferrin uptake was reduced substantially (by ~74%); whereas with ~12% CHC left on day 6, both Rate decay and transferrin e STED XY-plane images of SNAP-tag-labelled PHA (SNAP-PHA-SiR, left) or CLC (SNAP-CLC-SiR, right) show rings resembling clathrin-coated pits.The boxed areas are enlarged in the insets.Images were obtained with a higher-spatial-resolution (~30 nm, XY-plane) STED scope equipped with a highpower 775-nm depletion laser (see Material and methods for more detail).f Confocal XY-plane PHA G and CLC-mTFP1 images before (-5 s) and after (+15 s) depol 1s .Dotted circles indicate PHA/CLC puncta pinch off after depol 1s .g Fluorescence (F) of PHA G (F PHA ), CLC-mTFP1 (F CLC ), and A655 (F 655 ) and sampled confocal XY-plane images showing three PHA/CLC puncta pinch off (one with a A655 spot, two without A655 spots).Dotted circles indicate PHA/CLC puncta XY-plane movement after pinching off.h F PHA , F CLC , F 655, and sampled confocal XY-plane images showing an averaged PHA/CLC/A655 spot pinch-off.The images were aligned at the onset of F PHA decay.i F PHA and confocal XZ-plane images showing a PHA G spot (right, dotted) moving from the PM towards cytosol after depol 1s (gray triangle).Another spot (left) did not move, serving as control.j The percentage of PHA G spot pinch-off in the absence (Ctrl, 24 cells) or presence of dynasore (DnS, 80 μM; 30 min, bath; 14 cells), pitstop 2 (PST2, 30 μM, bath, 10-30 min, 16 cells), or si-CHC (12 cells).uptake were greatly reduced (Fig. 6d, right, 6 g, right).Thus, Rate decay is less sensitive to CHC reduction than receptor-mediated transferrin endocytosis.

Reconciling apparent conflicts of clathrin involvement at synapses
Our results are apparently different from previous studies showing that clathrin knockdown insignificantly affects slow or ultrafast endocytosis [36][37][38]44 (but see ref. 39 ) and that pharmacological blockers insignificantly affect fast or ultrafast endocytosis at synapses, particularly hippocampal synapses 45,46 . Whle these studies led to a current view that clathrin is dispensable for synaptic vesicle endocytosis 31,32 , the possibility that much less clathrin at synapses is required to mediate endocytosis than the classical clathrin-dependent receptor-mediated endocytosis has not been excluded. Suporting this possibility, endocytosis inhibition was only evident when clathrin was reduced by > ~74% (Fig. 6e-g).Reducing clathrin by ~70-75% blocked clathrin-dependent transferrin uptake, but marginally affected synaptic vesicle endocytosis at hippocampal synapses in a study, leading to a suggestion that synaptic vesicle endocytosis is clathrindispensable 38 .In contrast, reducing clathrin by ~88% blocked both transferrin uptake and synaptic vesicle endocytosis at hippocampal synapses in another study, leading to a suggestion that clathrin is required for synaptic vesicle endocytosis 39 .These apparently conflicting suggestions can now be reconciled by our finding that the relation between Rate decay and CHC level was much left-shifted compared to that between transferrin uptake and CHC level (Fig. 6g, right, 6d, right).This left-shifted relation indicates that Rate decay is much less sensitive to CHC reduction than transferrin endocytosis, explaining why CHC knockdown, if not sufficient, may block transferrin uptake, but affect marginally the synaptic vesicle endocytosis.

Both clathrin and dynamin are essential for pore closure
Clathrin is crucial for pre-Ω and fs-Ω closure (Fig. 1), clathrin-coated vesicle pinch-off (Fig. 4), and secretory vesicle endocytosis (Figs. 5, 6).Similarly, dynamin is crucial for all these processes shown in many previous studies 5,12,14,47 .On the other hand, filamentous actin, which may generate forces for membrane invagination [48][49][50][51] , is not involved in pre-Ω pore closure 9 .Here we present four sets of evidence showing that clathrin or dynamin alone is insufficient to mediate pore closure and that both are required (Fig. 7a-g).First, si-CHC, sh-CHC or pitstop 2 reduced pre-close by ~75-91% (Figs.1g, 7a).3][14] ).Similarly, a large reduction of close-fusion percentage was observed when clathrin or dynamin was inhibited.The block of most pore closure events by either clathrin or dynamin inhibition (Fig. 7a) suggests that both clathrin and dynamin are required for each single pore-closure event.Second, si-CHC plus Dyn1-K44A inhibited pre-close similar to si-CHC alone (~75%-83%, Fig. 7b).Therefore, Dyn1-K44A could not exert an inhibitory effect when clathrin was knocked down (Fig. 7b), suggesting the requirement of both dynamin and clathrin for pore closure.Third, CHC overexpression in control cells enhanced the pre-close percentage above the control level, whereas CHC overexpression to Dyn1-K44Atransfected cells could not (Fig. 7c), suggesting the requirement of dynamin for clathrin overexpression to enhance pore closure.Likewise, dynamin 2 overexpression in control cells increased the pre-close above  the control level, whereas dynamin 2 overexpression in si-CHC-transfected cells or pitstop 2-treated cells could not (Fig. 7d), suggesting the requirement of clathrin for dynamin overexpression to enhance pore closure.Fourth, three-color STED imaging showed that both dynamin and clathrin were associated with the PH G -labelled pre-Ω's pore/base region (145 out of 148 pores), and they may surround the PH G -labelled visible or non-visible pore/ base region of the Ω-profiles at the XZ-(Fig.7e) or XY-plane (Fig. 7f).Thus, clathrin and dynamin are physically available around the pore region to mediate pore closure (Fig. 7e, f).We concluded that clathrin and dynamin are both required to provide sufficient constriction forces to close the pore (Fig. 7g).
For three reasons, this new function is of a much wider impact than clathrin's well-known universal function in coating and thus likely in forming Ω-profiles.First, clathrin coating of the Ω-profile's head is limited to small ~40-150 nm Ω-profiles, whereas clathrin-mediated pore constriction/closure may apply to all Ω-profiles regardless of their sizes (~40-1500 nm) or their head's coating with clathrin or not (Figs.1-4).Second, clathrin coating of vesicles is limited to clathrin-coated vesicle endocytosis and budding, whereas clathrin-mediated pore closure may apply not only to clathrin-coated vesicle endocytosis (Fig. 4), but also non-clathrin-coated vesicle endocytosis or budding (Figs. 5, 6).We showed that clathrin mediates all kinetically detectable forms of endocytosis, including ultrafast, fast, slow, bulk, and overshoot endocytosis, in chromaffin cells and synapses (Figs. 5, 6).Since these modes of endocytosis are widely reported in neurons, endocrine cells, and non-secretory cells [30][31][32]52 , clathrin may mediate fission of these diverse endocytic modes observed in many different cell types. Thrd, clathrin coats only budding vesicles, whereas clathrin constricts/closes the pore of both budding (pre-Ω) and fusing (fs-Ω) vesicles (Fig. 1).Consequently, clathrin is essential to mediating fusion pore closure (Fig. 1), the widely reported kiss-and-run fusion previously considered the 'bona-fide' clathrin-independent fusion 12,17,30,[53][54][55] .By constricting the fusion pore, clathrin counteracts fusion pore expansion and thus inhibits vesicular content release (Fig. 1).Clathrin may therefore control important secretionrelated functions previously unrecognized, such as synaptic transmission, fight or flight responses, immune responses, and regulation of diabetes-relevant blood glucose levels 30,56 .In brief, the traditional function of clathrin in coating an Ω-profile's head is limited to small budding vesicles, whereas clathrin's pore-constriction/closure function may apply widely to all different sizes of budding and fusing vesicles coated with or without clathrin to control vesicle endocytosis, intracellular trafficking, and exocytosis.
Clathrin coating of vesicles has been used to classify vesicle endocytosis and budding into clathrin-dependent and -independent modes 5,6,57 .Our results suggest a thorough redefining of this half-a-century-old concept, because all clathrin (coat)-independent modes of endocytosis previously classified in secretory cells, such as ultrafast 36,37 , fast 45 , slow 38 , bulk, and overshoot endocytosis, as well as kiss-and-run 30,53 , depend on clathrin for pore closure as demonstrated here (Figs.1-5).We suggest redefining these endocytic modes and kiss-and-run fusion as the clathrin-dependent mode regarding the pore closure.Numerous previous studies interpreting results based on the old concept of the clathrin (coat)-dependent endocytosis or budding may need to be re-examined.The widely held view that clathrin is indispensable for synaptic vesicle endocytosis [36][37][38]44 (but see ref. 39 ) is likely due to insufficient clathrin knockdown or inhibition, as shown here at hippocampal synapses (Fig. 6).
We found that clathrin generates constriction forces by polymerization at the base/pore region, explaining how clathrin constricts and closes the pore of non-clathrincoated Ω-profiles (referring to no clathrin coating at the Ω-profile's head; Figs.1-3).This mechanism may also explain clathrin-coated Ω-profiles' pore closure (Fig. 4), if clathrin also polymerizes at the base/pore region of clathrin-coated Ω-profiles.Alternatively, polymerized clathrin at the head of the Ω-profile may also generate elastic forces to constrict the clathrin-coated Ω-profile's pore, as suggested by an early mathematical modelling study 26 .Taken together, clathrin polymerization at the Ωprofile's base/pore and/or head may generate elastic forces to constrict the Ω-profile's pore, mediating fission of non-clathrin-coated or clathrin-coated vesicles.Clathrin is thus an essential component of the fission machinery.
The extent of clathrin polymerization at the Ω-profile's base/pore region might contribute to explaining the speed of endocytosis.If clathrin is largely polymerized, further polymerization may take much less time and thus contribute to mediating ultrafast or fast endocytosis.On the contrary, if clathrin is much less polymerized, further polymerization towards completion may take a longer time and thus contribute to mediating slow endocytosis.It is unclear how clathrin is recruited to the Ω-profile's base/ pore region.Many mechanisms may contribute to recruiting clathrin, such as the random stochastic collision of endocytic adaptor proteins 58 , the involvement of PI(4,5)P 2 in recruiting adaptors that may bind clathrin, the endocytic cargos that recruit clathrin adaptors to bind clathrin 59,60 , and the curvature that may recruit adaptors and clathrin 61 (see also review in refs. 4,5).It would be of interest to study how clathrin is recruited to the Ω-profile's base/pore region in the future.
While clathrin is crucial for pore closure of pre-Ω, fs-Ω, clathrin-coated pits and synaptic vesicles (Figs.1-6), dynamin is also essential for each of these pore-closure events (Figs. 4, 7) [12][13][14]34,62,[67][68][69][70][71][72] . This findin suggests that neither dynamin nor clathrin alone, but the two together generate constriction forces sufficient to close the Ωprofile's pore in live cells, challenging the long-held concept that dynamin alone provides forces driving fission 11,27 .We suggest modifying this concept to include both dynamin and clathrin in providing constriction forces essential for fission, but with two different mechanisms: the pore-surrounding dynamin helix constriction together with constriction forces generated by clathrin polymerization at the Ω-profile's base/pore and/or head region.This modification may be of widespread application, given that both dynamin and clathrin are ubiquitous proteins involved in intracellular trafficking, endocytosis, membrane-bound organelle generation and exocytosis.Although dynamin alone can mediate fission in vitro 11,27 , in vivo protein and lipid composition, membrane tension, and pore geometry may differ from in vitro conditions, which may explain the need for more forces cooperating to constrict and close the Ω-profile's pore in live cells.
In summary, clathrin polymerization into an intrinsically curved coat produces elastic forces to constrict and close the fission or fusion pores of ~40-1500 nm non-clathrincoated or clathrin-coated Ω-profiles.This mechanism may underlie and/or regulate diverse endocytic modes, kissand-run fusion, vesicular content release, intracellular trafficking, membrane-bound organelle formation, and viral infection in most cells.Therefore, clathrin plays much broader and more important roles than previously recognized in coating small budding vesicles, calling for a thorough redefining of the half-a-century-old concept regarding clathrin-dependent and -independent endocytosis or budding.Clathrin is an essential component of the fission machinery in live cells, calling for modifying the fission-machinery concept, which contains only the helixforming proteins as force-generators, to include membrane protein coats with an intrinsic curvature that may generate pore-constriction/closure forces.

Electroporation and plating for chromaffin cell culture
Cells were transfected by electroporation using Basic Primary Neurons Nucleofector Kit (Lonza), according to the manufacturer's protocol and plated onto glass coverslips with mouse Laminin coating over PDL layer (Neuvitro) 73,74 .The cells were incubated at 37 °C with 9% CO 2 and used within 5 days.

STED imaging for chromaffin cells
We performed STED imaging as described previously 12,13,73 .If not mentioned, STED images were acquired with Leica TCS SP8 STED 3× microscope that is equipped with a 100× 1.4 NA HC PL APO CS2 oil immersion objective and operated with the LAS-X imaging software.Excitation was with a tunable white light laser and emission was detected with hybrid (HyD) detectors.PH G and A532 were sequentially excited at 485 and 540 nm, respectively, with the 592 nm STED depletion beam, and their fluorescence collected at 490-530 nm and 545-587 nm, respectively.
The excitation power for A532 was 10% of the maximum, at which fluorescent A532 can be bleached within a few seconds during repeated XZ-plane imaging (Y-plane fixed) every 26-200 ms.This feature was used to distinguish whether the PH G -labelled Ω-profile's pore is closed or not, because pore closure prevents bleached A532 (caused by strong excitation) from exchange with fluorescent A532 in the bath, resulting in A532 spot fluorescence decay 12,18 .In contrast, an open pore would not cause A532 spot fluorescence decay, because an open pore allows for continuous exchange of bleached A532 in the Ω-profile with fluorescent A532 in the bath 12,18 .
For STED at the XZ-plane with a fixed Y-axis location (e.g., Fig. 2d, e, g), images were acquired at XZ-plane every 26-200 ms at 15 nm per pixel in an XZ area of 15-20 μm × 0.7-2.5 μm, with a fixed Y-axis location at about the cell center (Fig. 1a).The imaging duration was limited to 10-20 s before, and 60 s after depol 1s .We limited to 60 s, because whole-cell endocytosis after depol 1s , measured with capacitance recordings, usually takes place within 60 s (e.g., Fig. 1a) 12,14,18 .Each cell was subjected to only 1 depol 1s to avoid endocytosis rundown 79 .For these time-lapse experiments, we did not scan images in multiple Y-axis locations to obtain a volume scanning, because such a volume scanning may significantly reduce the time resolution and substantially bleach fluorophores.
For one-color STED imaging of SNAP-PHA-SiR or SNAP-CLC-SiR (Fig. 4e), excitation (ex) was with 640 nm laser; STED depletion was conducted with 775 nm depletion beam; emission fluorescence (em) was collected at 650-754 nm.The excitation power for 647-SiR was 1%-5% of the maximum (maximum power: 1 mW) and the 775 nm depletion laser power was set at 5%-10% of the maximum (maximum power: 3 W).

Detection of pore closure with STED imaging
During repeated XZ-plane imaging (Y-plane fixed), A532 was excited at a high laser power so that fluorescent A532 can be bleached with a time constant of 1.5-3.5 s.Pore closure was identified as the gradual dimming of the A532 spot fluorescence to baseline during repeated XZplane PH G /A532 imaging.A532 fluorescence dimming is due to pore closure that prevents bleached A532 (by strong excitation) from exchange with a large reservoir of fluorescent A532 (very small molecule,~1.2nm) in the bath.This is not due to a narrow pore smaller than A532 molecule size, because after spot dimming, bath application of an acid solution cannot quench the pH-sensitive VAMP2-EGFP or VAMP2-pHluorin overexpressed at the same spot, indicating that the spot is impermeable to H + or OH -, the smallest molecules, and thus is closed 14,18 .Furthermore, the closure time course calculated from spot dimming matches approximately with whole-cell endocytosis time course 18 , and inhibition of dynamin by dynamin inhibitors, dynamin dominant-negative mutant dynamin 1-K44A, or dynamin knockdown blocks not only whole-cell endocytosis but also pore closure detected with the spot dimming method 14,18 .These results further confirm that spot dimming under strong excitation reflects pore closure.

Confocal imaging at chromaffin cells
Confocal imaging of pore closure has been described in detail previously 13,73,74 .Imaging of PH G , A655 and FFN511 was performed with an inverted confocal microscope (TCS SP5II, Leica, Germany, 100× oil objective, numerical aperture: 1.4).PH G was excited by a tunable white light laser at 515 nm (laser power set at ~1-4 mW); A655 was excited by an HeNe laser at 633 nm (laser power set at ~12-15 mW); FFN511 was excited by an Argon laser at 458 nm (laser power set at ~2-4 mW); their fluorescence was collected at 520-600 nm, 650-800 nm, and 465-510 nm, respectively.Confocal imaging area was ~70-160 μm 2 at the XY plane with a fixed Z-axis focal plane ~100-200 nm above the cellbottom membrane.Images were collected every 40-80 ms at 40-60 nm per pixel.
Confocal XY-plane imaging of PHA G , CLC-mTFP1 and A655 (Fig. 4a) were performed with prolonged averaging (~64-128 frames) to resolve A655 spots that may fill a tiny Ω-profile.These small spots were not visible in experiments performed for data shown in Figs. 1 and 2 (see Materials and Methods for more detail).PHA G /CLC-mTFP1/A655 spots with a half-maximum-full-width more than 300 nm were not selected, which avoid contamination with large pre-Ω analysed in Fig. 1.

Fusion modes and pre-close detection with confocal microscopy
Fusion-generated Ω may close its pore at ~0.05-30 s later (close-fusion, Fig. 1d), maintain an open pore (stayfusion, Fig. 1e), or shrink to merge with the plasma membrane (shrink-fusion, Fig. 1e) 12,19 .Close-fusion was detected as A655 fluorescence (F 655 , strongly excited) dimming due to pore closure that prevented bath fluorescent A655 from exchanging with bleached A655, while F PH (weakly excited) sustained or decayed with a delay that reflected PtdIns(4,5)P 2 conversion into PtdIns(4)P and/or vesicle pinch off (Fig. 1d); stay-fusion was detected as sustained F 655 and F PH ; shrink-fusion, A655 and PH G spot shrinking with parallel decreases of F 655 and F PH (Fig. 1e) 12,14,19 .Pre-close was detected as A655 fluorescence (F 655 , strongly excited) dimming due to pore closure that prevented bath fluorescent A655 from exchanging with bleached A655, while F PH (weakly excited) sustained or decayed with a delay (Fig. 1c).
Pore closure (close-fusion and pre-close) detected with spot F 655 bleaching by strong excitation is not due to a narrow pore smaller than A655 molecule size, because after spot dimming, bath application of an acid solution cannot quench the pH-sensitive VAMP2-EGFP or VAMP2-pHluorin overexpressed at the same spot, indicating that the spot is impermeable to H + or OH -, the smallest molecules, and thus is closed 13,14,18 .Furthermore, pore closure detected with this method was blocked by dynamin inhibitor dynasore, dynamin dominantnegative mutant dynamin 1-K44A, or dynamin knockdown, suggesting that fusion pore closure is mediated by dynamin 13,14,18 .
For imaging of A655 and CLC-EGFP or imaging of A655 and A488, excitation wavelength was 640 nm and 488 nm, respectively; fluorescence emission was collected at 650-800 nm and 495-600 nm, respectively.Without FFN511, fusion was identified as the sudden appearance of A655 spot, the fluorescence of which reached the peak within 20-200 ms.This method was verified with concurrent confocal or STED imaging of NPY-EGFP release or FFN511 release, and with STED imaging of the sudden appearance of (within single frame: ~26-200 ms) of PH Glabelled Ω containing A532 spot or releasing FFN511 12,18,19 .

Reconstruction of exo-endocytosis from individual vesicle fusion, close-fusion and pre-close
To reconstruct the exo-endocytosis trace from individual fusion, close-fusion, and pre-close events (R fs+pre ), we assigned a 1-unit up-step at each fusion's onset, a 1-unit down-step for each close-fusion's onset (at F 655 dimming onset, e.g., Fig. 1d, e), and a down-step at each pre-close's onset (A655 bleaching onset; e.g., Fig. 1c).The down-step amplitude of the pre-close was calculated as downÀstep size ¼ ðmean preÀclose spot width=mean fusion spot widthÞ 2 where pre-close spots and fusion spots were taken from the same cell (down-step size range: 1.2-2.8,27 cells).This amplitude rescaling was necessary because the prespot size (half width) was on average about 1.38 times as large as the fusion spot 13 .Summing all up and down-steps in each cell yielded the reconstructed R fs+pre , which reflects vesicle fusion, close-fusion, and pre-close observed at the cell bottom (e.g., Fig. 5c-e).

MINFLUX nanoscopy Cell preparation and SNAP labeling
Chromaffin cells transfected with PH-mScarlet and SNAP-CLC were fixed with paraformaldehyde (PFA, 2.4%) and sucrose (2.4%) solution for 30 min.Excess PFA was quenched with 50 mM NH 4 Cl solution for 10 min.and incubated with Image-iT Signal Enhancer solution for 30 min.at room temperature.Subsequently, cells were incubated at room temperature for 50 min with SNAP substrate dye solution containing 1 µM SNAP-Surface ® Alexa Fluor ® 647 (NEB, S9136S), 0.5% bovine serum albumin, and 1 mM DTT, resulting in the attachment of SNAP-surface® Alexa fluor 647 to SNAP-CLC (SNAP-CLC-A647), which was used for MINFLUX imaging.Next, an undiluted dispersion of gold beads (EM.GC150/ 4, BBI Solutions) was incubated for 10 min and rinsed of several times with PBS to remove unbound gold beads.The coverslips containing chromaffin cells were mounted on a depression slide with the MINFLUX imaging buffer containing 50 mM Tris/HCl, 10 mM NaCl, 10% (w/v) glucose, 64 µg/mL catalase, 0.4 mg/mL glucose oxidase, and 15 mM MEA at pH 8.0.The coverslips were sealed with Elite double 22 dental epoxy (Zhermack).

MINFLUX data acquisition
MINFLUX imaging was performed on a commercial 3D MINFLUX microscope that was driven by the Imspector software with MINFLUX drivers (Abberior Instruments) 80 .Generally, fields of view with multiple gold beads were chosen and locked in a 3D set position for active sample stabilization using the near-infrared scattering from gold beads and active feedback correction via the piezo stage.It was ensured that the standard deviation of the sample position relative to the stabilization set point was less than 2 nm in all directions during measurements.Fields of view were chosen close to the coverslip surface at the bottom of the cell expressing both fusion proteins.Before starting the MINFLUX data acquisition, the fluorophores were driven into the dark state using iterative confocal scans with the 640 nm excitation laser and a power between 8%-15% (maximum power at periscope: 1.94 mW).The sample was imaged with the standard MINFLUX imaging sequence provided by the manufacturer using 10% fixed laser power.During the MINFLUX measurement, the 405 nm activation laser power was ramped up slowly from 0% to 50% over several hours (maximum power at periscope: 27 μW).Samples were generally imaged for 12-24 h.

MINFLUX data analysis
The raw final valid molecule position estimates were exported directly from the MINFLUX Imspector interface as a .matfile.Custom MATLAB analysis software was then used to identify and segregate clusters of localizations.The data were filtered to remove traces (group of localizations originating from the same fluorophore emission burst) with a standard deviation of more than 10 nm and less than three localizations per trace 81,82 .

Platinum replica transmission electron microscopy
Chromaffin cells were rinsed in intracellular buffer (70 mM KCl, 30 mM HEPES maintained at pH 7.4 with KOH, 5 mM MgCl 2 , 3 mM EGTA), and manually unroofed with a 19-gauge needle and syringe using 2% paraformaldehyde (Electron Microscopy Sciences, 15710) in the intracellular buffer 7 .After unroofing, the coverslips were transferred to 2% glutaraldehyde (Electron Microscopy Sciences, 16019) at 4 °C until EM sample preparation.For correlative analysis, they were transferred to fresh 2% paraformaldehyde in the intracellular buffer for 20 min.They were washed with phosphate-buffered saline (PBS).Unroofed cells were stained with ~50 nM of Alexa Fluor 647-phalloidin (Life Technologies, A22287) for 15 min.Cells were then rinsed with PBS. 1 mm × 1 mm fluorescent montage images were generated for EGFP and Alexa Fluor 647 using a Nikon Eclipse Ti inverted microscope with a 100× 1.49 NA objective (Nikon, SR HP Apo TIRF) and an Andor iXon Ultra 897 EM-CCD camera under the control of Nikon Elements software.This spatial map was used to locate transfected cells 83 .The imaged area was marked with a circle (4 mm in diameter) around the center of the imaged area using an objective diamond scriber (Leica, 11505059).The immersion oil was carefully removed from the bottom of the glass coverslip.The sample was stored in 2% glutaraldehyde at 4 °C until EM sample preparation.
EM samples were prepared as described previously 84 .Briefly, coverslips were transferred from glutaraldehyde into 0.1% w/v tannic acid for 20 min.They were rinsed 4 times with water and placed in 0.1% w/v uranyl acetate for 20 min.The coverslips were dehydrated, critical point dried with a critical point dryer (Tousimis Samdri, 795), and coated with platinum and carbon with a freeze fracture coating device (Leica, EM ACE 900).The region of interest on the coverslip marked by a diamond scriber was imaged in brightfield with a 20× phase-contrast objective to obtain another map of the region imaged in fluorescence.The replicas were lifted and placed onto formvar/ carbon-coated 75-mesh copper TEM grids (Ted Pella, 01802-F) that were freshly glow-discharged with a PELCO easiGlow 91000.Again, the grid was imaged in brightfield light with a 20× phase-contrast objective to find the same region that was originally imaged in fluorescence.Each cell of interest was located on the grid prior to EM imaging.TEM imaging was performed on a JEOL 1400 equipped with a CMOS camera (NanoSprint43 Mk-II, AMT) at 10,000× or 6000× magnification (0.71 or 1.19 nm per pixel) using SerialEM freeware for montaging 85 .Stitched electron microscopy montages were assembled using IMOD freeware 86 .
Identification of the apparently tilted membrane invagination is described in the main text and in Supplementary Fig. S9 and its legends.
CHC Loxp/Loxp mouse, culture and imaging CHC Loxp/Loxp mouse generation is described in Supplementary Fig. S13 (genotypes determined by PCR).Breeding CHC LoxP/LoxP mice with actin β-Cre or synapsin-Cre mice that express Cre broadly produced no CHC knockout mice (> 30 pups from > 5 litters), likely due to embryonic death.
Cultures were transfected with a plasmid containing SpH (or Synaptobrevin-pHluorin, gift from Dr. Yongling Zhu) alone (control) or with L309 plasmid containing Cre/mCherry.A nuclear localization sequence was tagged at the N-terminal of Cre, and cloned into L309 vector via BamHI and EcoRI sites.Accordingly, mCherry was expressed in the nucleus (Fig. 6a).For CHC rescue, we transected a plasmid (pmCherry-C1-CHC17) containing wildtype CHC and mCherry.pmcherry-C1-CHC17 was generated from pEGFP-C1-CHC17 plasmid by replacing EGFP with mCherry.Without the nuclear localization sequence in the pmCherry-Cl-CHC17 plasmid, mCherry expression was not limited to nucleus (Supplementary Fig. S18a).
For acid quenching, we replaced HEPES in the bath with MES-buffered (25 mM) solution (pH 5.5).For transferrin uptake, cells were incubated with serum-free MEM for 30 min at 37 °C, and then kept in serum-free MEM containing 50 μg/mL Alexa 488 conjugated transferrin for 20 min at 37 °C.Cells were washed twice in 1× PBS and then fixed with 4% paraformaldehyde before mounting for imaging (Leica SP8 confocal microscope).
Except mentioned, SpH (pHluorin) images were acquired at 1-2 Hz with Leica SP8 confocal microscope (Objective: 63×, 1.4 NA).Varicosities (2 × 2 μm) responded to stimulation were analyzed with Leica software.Rate decay after a train of APs at 20-80 Hz was measured as the decay rate in the first 4-10 s after fluorescence increase.Before calculating Rate decay , F SpH trace was normalized with ΔF = 100%.Thus, Rate decay reflects the initial decay of F SpH in the percentage of ΔF per second.
Each data group was obtained from ≥ 3 cultures.For each experiment, 10-30 boutons were used.
To study endocytosis after an AP, we induced an AP at 0.03-0.05Hz, which caused a detectable ΔF at a probability of 0.15 per bouton in control (9 experiments, 73 boutons), consistent with a previous report (21).F SpH increase after an AP was identified if it was > 3 times baseline F SpH s.d.

Virus induction into hippocampal cultures
We modified the vector of adeno-associated virus (AAV)-GFP/Cre (Addgene# 49056) into AAV-mCherry/ Cre, in which mCherry was attached at the C-terminal of Cre, and a nuclear localization sequence was tagged at the N-terminal of Cre.The constructed plasmid were sent to the Vigene Biosciences company for package into AAV-D/J serotype.This virus can be transduced into most (> 95%) cells.

EM
Hippocampal cultures were fixed with 4% glutaraldehyde (freshly prepared, Electron microscopy sciences, Hatfield, PA) in 0.1 N Na-cacodylate buffer solution containing for at least one hour at 22-24 o C, and stored in 4 °C refrigerator overnight.The next day, cultures were washed with 0.1 N cacodylate buffer, and treated with 1% OsO 4 in cacodylate buffer for 1 hr on ice, and 0.25% uranyl acetate in acetate buffer at pH 5.0 overnight at 4 °C, dehydrated with ethanol, and embedded in epoxy resin.Thin sections were counterstained with uranyl acetate and lead citrate then examined in a JEOL200CX TEM.Images were collected with a CCD digital camera system (XR-100 from AMT, Danvers, MA) at a primary magnification of 10,000-20,000×.Synapses were selected based on the structural specialization including synaptic vesicle clustering, synaptic cleft and the postsynaptic density.

Computational model
To determine the equilibrium shapes of Ω-like membrane buds we used an elastic model.The system contains two distinct structural elements, the lipid bilayer and the clathrin coat covering the lipid bilayer at the bud base.The lipid bilayer was modeled as an elastic inextensible film exhibiting properties of a two-dimensional fluid, capable of sustaining a lateral tension, γ, and resisting the deformation of bending as described by Helfrich model 87 .The bilayer elastic energy, F m , was computed according to where J is the local total curvature (twice mean curvature 88 ) of the bilayer surface, A is the bilayer area, κ m ; is the bilayer bending modulus 87,89 .The first contribution to Eq.1 represents the bending energy upon vanishing spontaneous curvature 87 , whereas the second contribution is the thermodynamic work of the membrane area exchange with the surrounding plasma membrane subject to lateral tension, γ.The energy of the bilayer Gaussian curvature 87 is not included in Eq.1 since the considered membrane deformations do not change the topological genus of the bilayer surface.
The clathrin coat is formed through cross-linking of protein complexes (triskelia) 90 .Therefore, in contrast to the lipid bilayer, the coat is not expected to have properties of a two-dimensional fluid and we considered it as a solid layer.In spite of a complex microstructure of the coat, we used a simplified approach and modelled it as a continuous layer of isotropic homogeneous elastic material characterized by Young modulus, E, and Poisson ratio, ν (ref. 91).The layer has an intrinsic stress-free shape of a sphere with radius R S .The bending energy per unit area of such a layer can be written as 92 , where c m and c p are the two principle curvatures of the surface 88 , κ C1 and κ C2 are the bending elastic moduli of the coat, which can be expressed through E and ν, have opposite signs, κ C1 > 0 and κ C2 < 0 and similar absolute values 92 , so that we assumed κ C1 ¼ Àκ C2 ¼ κ C .The elastic energy of the clathrin coat, F C , is obtained by integration of f C (Eq. 2) over the coat area.
To determine the equilibrium shape of an Ω-bud for each extent of the clathrin coat polymerization on its base, we used the following procedure.We computationally created an initial coat-free Ω-bud by application of a localized pulling force to the center of a flat circular region of lipid bilayer upon assumptions that the bilayer is subject to lateral tension, γ, and the boundary of the forming Ω-bud base is set and fixed, as described in refs. 9,13.Then we imposed on the base of the initial Ω -bud a clathrin coat with certain values of κ C and R S describing the desired phase of the coat polymerization.Based on our experimental observations (Fig. 2), the coat area was chosen to cover the whole base of the initial Ω -bud from the boundary to the pore waist, and was assumed constant for all stages of the coat polymerization, hence, corresponding to the constant area scenario of clathrin coat formation 93 .The equilibrium Ω-bud configuration was found by numerical minimization of the total energy, F T ¼ F m þ F C .The computations were performed using Ken Brakke's Surface Evolver 94 .

Data selection
For every cell recorded with a pipette under the wholecell configuration, the data within the first 2 min at the whole-cell configuration were used, which avoided rundown of endocytosis (gradual disappearance of endocytosis) as previously reported under the whole-cell configuration for a long time 18,79 .For reconstructing R fs +pre , cells with less than 5 fusion events were not used, which avoided large fluctuations from individual cells.
STED images were analyzed with ImageJ and LAS X (Leica).Confocal images were analyzed with ImageJ and LAS X (Leica).The fluorescence intensity from an area covering the fluorescence spot was measured at every image frame.The full-width-half-maximum (W H ) was measured from intensity profiles of 1-4 lines across the spot center.

Statistical tests
Data were expressed as mean ± s.e.m.Replicates are indicated in results and figure legends.n represents the number of cells, fusion events or experiments as indicated in results and figure legends.The statistical test used is ttest or ANOVA.Although the statistics were performed based on the number of cells, fusion events and pre-close, each group of data were replicated from at least four primary chromaffin cell cultures.Each culture was from at least two glands from one bovine.

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see figure on previous page) Fig. 4 Clathrin-mediated pore closure underlies clathrin-coated vesicle pinch off.a Confocal XY-plane PHA G , CLC-mTFP1, and A655 images (left) and their merged images (right).Since images were obtained by averaging as much as 128 times, these puncta were not visible in experiments shown in Figs. 1, 2. b The percentage of PHA G puncta colocalized with CLC-mTFP1 or A655 spots (10 cells).c Left: STED XZ-plane PHA G and CLC-mTFP1 images (merged at bottom) showing an oval-(pit) and a flat-shape spot (STED resolution: X: ~60-80 nm; Z: ~150-200 nm).Right: percentage of PHA G spots showing oval/round-or flat-shape (mean + s.e.m., 8 cells).d EM images showing two typical clathrin-coated pits in chromaffin cells.

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see figure on previous page) Fig.6Clathrin is essential for fast and slow endocytosis at hippocampal synapses.a CHC antibody staining, and mCherry fluorescence in neurons at 2, 4, 5, and 6 days after Cre/mCherry transfection to CHC Loxp/Loxp hippocampal culture (confocal images).mCherry fluorescence is shown to distinguish between transfected (arrows) and un-transfected neurons (triangles, control).b CHC labelling intensity at Cre/mCherry-transfected neuronal soma at 2-6 days after Cre/mCherry transfection to CHC Loxp/Loxp culture.Data normalized to the mean of day 0 group taken from untransfected neurons (each group: 45-65 neurons; 4 transfections, 16 mice).c Sampled Alexa 488-conjugated transferrin (TF) uptake in cell bodies of Chc Loxp/Loxp hippocampal neurons at 2, 4 and 6 days after Cre/mcherry transfection.mCherry fluorescence is shown to distinguish between transfected (arrows) and un-transfected neurons (triangles, control).d TF uptake intensity in cell bodies of Chc Loxp/Loxp hippocampal neurons plotted versus the day after Cre/mcherry transfection (left) or the corresponding CHC level (right, CHC level obtained from b).Each data group: 33-59 neurons, 4 transfections, 16 mice.e SpH fluorescence trace (F SpH , mean ± s.e.m., every 5 s) induced by AP 20H/10s in 0 (Ctrl, n = 10 experiments), 2 (n = 6), 4 (n = 5), 5 (n = 6), and 6 days (n = 10) after Cre/mCherry transfection at 22-24 o C. f Traces (s.e.m. not included) in panel e (same color code) re-scaled to the same peak and superimposed for comparison of the decay time course.g Rate decay (mean ± s.e.m.) induced by AP 20H/10s plotted versus the day after Cre transfection (left) or the corresponding CHC level (right, CHC level obtained from b