Architecture of the AP2:clathrin coat on the membranes of clathrin-coated vesicles

Clathrin-mediated endocytosis (CME) is crucial for modulating the protein composition of a cell’s plasma membrane. Clathrin forms a cage-like, polyhedral outer scaffold around a vesicle, to which cargo-selecting clathrin adaptors are attached. AP2 is the key adaptor in CME. Crystallography has shown AP2 to adopt a range of conformations. Here we used cryo-electron microscopy, tomography and subtomogram averaging to determine structures, interactions and arrangements of clathrin and AP2 at the key steps of coat assembly, from AP2 in solution to membrane-assembled clathrin-coated vesicles (CCVs). AP2 binds cargo and PtdIns(4,5)P2-containing membranes via multiple interfaces, undergoing conformational rearrangement from its cytosolic state. The binding mode of AP2 β2-appendage into the clathrin lattice in CCVs and buds implies how the adaptor structurally modulates coat curvature and coat disassembly.


Introduction
CME is a vital multistep process in all eukaryotes in which plasma membrane cargo proteins are first concentrated into a patch by clathrin adaptors, which are themselves clustered by interaction with a polymeric clathrin scaffold. The patch of membrane is deformed towards the cytoplasm and undergoes scission from the parent membrane to form a clathrin-coated vesicle (CCV), which subsequently delivers its cargo into the endocytic system (reviewed in Kirchhausen et al., 2014;Mettlen et al., 2018;Mettlen and Danuser, 2014;Schmid et al., 2014;Taylor et al., 2011).
AP2 is one of the first proteins to arrive at a forming CCV (Taylor et al., 2011) and is also important in initiating clathrin polymerisation (Cocucci et al., 2012;Motley et al., 2003). The favoured although unproven model for AP2 and clathrin in CME suggests that cytosolic AP2 is closed and unable to bind cargo and that membrane-bound AP2 adopts a more open conformation in which cargo binding sites are accessible (Hollopeter et al., 2014;Jackson et al., 2010). A closed conformation has been seen under non-physiological conditions in crystals (Collins et al., 2002). A number of different possible structures for membrane-bound, cargo-binding 'open' forms of AP2 complexes have been determined in the absence of membrane (Jackson et al., 2010;Wrobel et al., 2019). Similarly, the highest-resolution structures of clathrin have been determined in the absence of a membrane and/or a characterised complement of folded adaptors. It therefore remains unclear how AP2 and clathrin interact with one another and the membrane to form CCVs. Here we present the structures, and relative arrangements of AP2 and clathrin under physiological buffer conditions and in membrane-associated vesicle coats.

AP2 structures
We assessed the conformation(s) adopted by recombinant AP2 cores in solution under physiological buffer conditions using single-particle cryo-electron microscopy (Fig. S2A). The bulk of AP2 (~80%) adopted a closed conformation, the structure of which we determined to 3.8 Å. The remaining particles (~20%) did not refine to a reliable structure (i.e. no alternative 'open' conformer was identified). The structure is similar to that seen under high-salt, high-pH conditions in the crystal structure containing inositol hexakis-phosphate (Collins et al., 2002): the C-terminal domain of µ2 (Cµ2) is located in the spatially complementary bowl created by the other subunits, while the YxxΦ and [ED]xxxL[LI] cargo motif binding sites are blocked by portions of the β2 subunit (Fig. 1A, S3) (Jackson et al., 2010).
Recombinant AP2 FLAP (AP2 lacking the hinge and appendage of α; Fig. S1) (Kelly et al., 2014) was recruited onto phospholipid membranes containing PtdIns(4,5)P2 and TGN38 YxxΦ-cargo in the same physiological buffer conditions and imaged by cryo-electron tomography. AP2 coated existing liposomes but did not generate small buds or vesicles -AP2 alone does not drive membrane curvature/budding (Fig. S2B). We applied subtomogram averaging to determine the structure of AP2 to ~9 Å resolution (Fig. 1A, S3). The structure is most similar to the previously-determined crystal structure of the open conformation (Jackson et al., 2010), although Cµ2 and the N-terminal portion of β2 are positioned approximately 5 Å further away from α (Fig. S3C). Compared to the closed form, Cµ2 has moved to form a planar membrane-binding surface (Fig. 1B), and its movement with respect to the β2 N-terminus has freed up the YxxΦ-cargo binding pocket, which has density consistent with bound cargo peptide. The [ED]xxxL[LI] cargo motif binding site on σ2 is accessible to membraneembedded cargo due to a movement of the N-terminus of β2 relative to σ2. In the open form crystal structure (Jackson et al., 2010), the [ED]xxxL [LI] site is occupied by the Myc-tag of a neighbouring AP2. Our structure of AP2 on the membrane shows that the open conformation did not result from this or other crystal packing artefacts.
We observed three sites at which the AP2 electron density contacts the membrane: the proposed PtdIns(4,5)P2 binding site on the α subunit whose mutation abolishes AP2 membrane binding (Gaidarov et al., 1996;Honing et al., 2005;Jackson et al., 2010) and two putative PtdIns(4,5)P2 binding sites on Cµ2 (Fig. 1A), simultaneous mutation of which inhibits membrane binding and reduces CCV nucleation (Jackson et al., 2010;Kadlecova et al., 2017). The first Cµ2 site corresponds to a basic loop including K167, Y168, R169, R170 following the µ2 linker helix, which undergoes an extended to helical transition between closed and open AP2 (Jackson et al., 2010). This location suggests a direct physical connection between membrane binding and stabilisation of the open AP2 conformation and points to interference with this linkage being the explanation for why an R170W mutation impairs CME and causes neurological defects (Helbig et al., 2019). The second Cµ2 contact appears to be mediated   by residues K350, K367, R368 within a basic patch also containing K330, K334, K352, K354, K356 and K365. We do not observe a membrane contact at the proposed β2 N-terminal PtdIns(4,5)P2-binding site (Honing et al., 2005;Jackson et al., 2010;Kadlecova et al., 2017).
We assembled both AP2 and clathrin onto YxxΦ cargo/PtdIns(4,5)P2-containing membranes. In contrast to the sample lacking clathrin, buds and vesicles were now formed with both AP2 and clathrin coating their membranes (Fig. S2) indicating a role for clathrin scaffold recruitment in membrane curvature. The AP2 structure was identical up to the determined resolution (12 Å) to that seen in the absence of clathrin (Fig. 1C). Inclusion of an additional 'dileucine' [ED]xxxL[LI]-containing cargo resulted in tilting of α, and movement of β2 away from σ2 to further expose its [ED]xxxL[LI] binding site. Helices 2 and 5 in σ2 are poorly resolved, and the proposed β2 N-terminal PdIns(4,5)P2 binding site now contacts the membrane as does a region in the vicinity of helices 2 and 3 of µ2 (Fig. 1C).
When combined with published information, our data suggest a model whereby AP2 initially contacts the membrane in the closed conformation via PtdIns(4,5)P2 binding sites on α and β2. Liganding of the two Cµ2 PtdIns(4,5)P2-binding sites will shift the equilibrium to the 'open' state in which the cargo binding sites become unblocked. In vivo this may be aided by the binding of FCHO1/FCHO2/sgip (Hollopeter et al., 2014;Umasankar et al., 2014). AP2 can then 'scan' the local membrane for cargo and its binding would then further stabilise an open form on the membrane. The binding of PtdIns(4,5)P2 and cargo are thus allosterically linked.
The transitions from cytosolic to single-cargo membrane-bound AP2, and from single-to double-cargo membrane-bound AP2, involve conformational flexing of the α and β2 solenoids. We did not observe previously described open+ (Wrobel et al., 2019), AP1-like hyper-open (Jia et al., 2014) or splayed, COPI-like (Dodonova et al., 2015) forms (Fig. S3), suggesting that the open form is the lowest energy conformer for membrane associated, non-phosphorylated AP2.

AP2 distribution on membranes
We found the distribution of AP2 on the surface of membranes to be largely irregular, lacking longrange organization. On YxxΦ-only containing membranes, ~20% of AP2s are dimerised (Fig. S4), their β2 N-terminal helices having apparently moved to participate in the interface (Fig. S4B). The dimerisation interface is not similar to those proposed for AP1 multimerisation via the small GTPase Arf1 (Morris et al., 2018). The AP2 distribution was unchanged by addition of clathrin and hence by the formation of buds and vesicles. In vesicles and buds with both [ED]xxxL [LI] and YxxΦ cargoes, the dimeric form of AP2 is absent, likely because the N-terminal helix of β2 has moved to contact the membrane and can no longer contribute to dimerization interface. It has been speculated on the basis of crystal packing and single-particle electron microscopy (Ren et al., 2013;Shen et al., 2015) that AP1 and by analogy AP2 would adopt a regular lattice that would be stabilised/triggered by the presence of clathrin. There is, however, no AP2 lattice present in our assembled vesicles, excluding AP2 oligomerisation as a factor in membrane curvature generation.

Clathrin structure
We determined the structure of clathrin above AP2 in both the YxxΦ and YxxΦ/[ED]xxxL[LI] cargocontaining liposomes by subtomogram averaging: the structures were the same (Materials and Methods), so were combined for further analysis. The clathrin legs were sorted into two classes according to whether the leg bounds a hexagonal or pentagonal cage face (Fig. S5A,B). Each class was averaged separately to generate structures at ~7.7 Å resolution (Fig. 2, S5C,D). The CLC region that contacts CHC is well resolved, as are most of the leg and the helical hub of CHC. The resolution is lower towards the NTDs of CHC that extend downwards towards the membrane, reflecting mobility of these domains, but is sufficient to position the full NTD. Our structures are generally consistent with those previously described from purified clathrin in solution in the absence of membranes (Fotin et al., 2004b;Morris et al., 2019), but by now resolving the NTDs we were able to derive the positions of peptide binding within the clathrin cage (Fig. 4, S5C).

Clathrin/AP2 relationship
In YxxΦ cargo-containing coated buds, the clathrin NTDs are positioned at a higher radius than AP2, and there are no preferential positions or orientations of AP2 relative to clathrin (Fig. 3, S6). Inclusion of [ED]xxxL[LI] cargo, or transition of the buds to vesicles, both cause clathrin to move towards the membrane by 10-15 Å, after which the NTDs are at a lower radius than the top of AP2 (Fig. S6). In these cases AP2 is preferentially located in the gaps between the NTDs, though with no preferred rotational orientation. This suggests that the preferred localization is due to steric clashing rather than specific interaction. It is not clear to us what causes the movement of clathrin towards the membrane.

AP2 β2-appendage
Between the clathrin NTDs and the undersides of the triskelia, we observed a 'bean-shaped' density that is not part of clathrin (Fig. 2). We applied principal component analysis to sort the datasets according to the presence or absence of this additional density (Fig. S7A), and averaged positions where it was present within a hexagon, obtaining a structure corresponding to the AP2 β2-appendage (Materials and Methods) (Fig. 4A, S7). The β2-hinge is not visible at this resolution. When comparing the density and occupancy of the β2-appendage between sites oriented towards the centres of either hexagons or pentagons, we found preferential binding in hexagonal faces (more than double the apparent occupancy at pentagonal faces, Fig. S7A).
β2-appendages link CHC repeat 1 in one clathrin molecule, CHC repeat 2 in a second clathrin molecule (both in the ankle region), and the NTD of a third clathrin molecule (Fig. 4A). This positions the β2appendage such that its C-terminal platform subdomain is freely accessible to the Fxx[FL]xxxR helical motifs on the unstructured portions of secondary adaptors such as ARH, arrestins and epsins (Edeling et al., 2006) (Fig. 4B) rather than being blocked as speculated (Schmid et al., 2006). Another motifbinding site, recognised by regulatory/accessory proteins including Eps15, is located on the β2appendage sandwich domain close to the point of interaction with CHC repeat 2 (Fig. 4B).
The β2-appendage is dispensable for clathrin polymerisation in vitro (Fig. S8). Binding of the β2appendage to the clathrin scaffold therefore likely reflects roles in regulating membrane curvature, assembly and/or disassembly in vivo. The β2-appendage clathrin binding site we can now see is directly adjacent to the proposed binding site of the DNAJ domain of auxilin ( Fig. 4C). Auxilin can induce coat disassembly by recruiting HSC70 (Smith et al., 2004;Xing et al., 2010), which also could indirectly modulate levels of cargo incorporation by AP2 . We now see that auxilin would occupy a cavity bounded by the β2-appendage, an NTD and clathrin ankles. On binding, an auxilin DNAJ domain would overlap with the binding site for Eps15 on the β2-appendage, and would be able to interact with the NTD (consistent with (Schmid et al., 2006) by contacting the 'Royle' box binding groove (Willox and Royle, 2012) (Fig. 4B,C). Interactions between clathrin, auxilin, the β2-appendage and Eps15 at this regulatory nexus could be competitive or synergistic, coupling the concentration of adaptors (and therefore cargo) to dynamic rearrangement of the clathrin lattice. β2-appendage preferentially binds to hexagons, while bending of the clathrin lattice requires increasing the fraction of pentagons: hence expulsion of β2-appendage from its location in the coat and increasing lattice curvature will favour each other. Together these observations suggest that cargo binding, coat curvature, and dynamic assembly and disassembly of the coat, could be connected and controlled by reconfiguring low affinity, high avidity interactions between clathrin, adaptors and auxilin at a single site on the clathrin scaffold.

Acknowledgements
This study made use of electron microscopes at EMBL, the MRC-LMB EM Facility and the Cryo-EM facility, University of Cambridge, Department of Biochemistry, as well as the high-performance computing resources at EMBL and LMB. We thank Wim Hagen, Dustin Morado, Dimitri Chirgadze and Steve Hardwick, and the staff of the facilities for support; Dustin Morado, William Wan and Aaron Tan for sharing and providing support with data processing scripts; Svetlana Dodonova for assistance in initial stages of sample optimisation and data processing; Frank Thommen, Andres Lindau, Michael Wahlers, Jake Grimmett and Toby Darling for supporting computational resources.

Funding
The

Preparation of reagents
To produce recombinant AP2 proteins, bacterial expression and purification, clathrin purification from porcine brain, liposome pelleting, lipopeptide coupling and liposome preparation were done as in Jackson et al., 2010 andKelly et al., 2014. AP2 FLAP lacks the α subunit hinge and appendage (Fig. S1). Δβ2-appendage FLAP additionally lacks the β2-appendage, but is extended beyond the hinge region with an inert, unstructured region comprising 106 residues taken from the Enterobacteria phage f1 attachment protein G3P (residues 220-326, UniProtKB P69169), followed by a decahistidine tag. This extension facilitates purification of a fully intact β2 hinge region, which is otherwise cleaved.
For clathrin pulldown experiments, Glutathone S-transferase (GST)-tagged adaptors (for capture on glutathione sepharose beads) were constructed in pGEX-4T2 by genetically fusing fragments of β2 to GST. GST-β2hingeapp comprises the hinge and appendage regions of β2 fused to GST, as described previously (Kelly et al., 2014). GST-β2hinge comprises the extended β2 hinge as described above for the "Δβ2-appendage FLAP" construct, fused to GST. As a non-clathrin-binding control, the green fluorescent protein (GFP) was fused to GST. Fusion proteins were expressed and purified by standard techniques, using overnight expression at 22°C in BL21(DE3)pLysS cells.
All lipids were purchased from Avanti Polar lipids. The YxxΦ cargo signal was derived from TGN38 protein with sequence CKVTRRPKASDYQRL, and the [ED]xxxL[LI] signal was derived from phosphorylated CD4 with sequence CHRRRQAERM(SPhos)QIKRLLSEK. N-terminal cysteines were used for lipid coupling to maleimide lipids.

Glutathione sepharose pulldown assays
Clathrin (0.8 µM) and adaptor (1.5 µM) were mixed in HKM buffer (25 mM Hepes pH 7.2, 125 mM potassium acetate, 5 mM magnesium acetate), total volume 100 µl, and incubated at 21°C for 30 minutes. 50 µl aliquots of glutathione sepharose beads (GE Healthcare) were washed four times in HKM/T buffer (HKM buffer supplemented with 0.05% Tween-20) before resuspension in the reaction mixtures. After a further 30 minutes of incubation at 21°C, with continuous gentle inversion to prevent settling, the beads were pelleted by centrifugation, supernatants were removed and retained for gel analysis, and the beads were washed four times in HKM/T before resuspension in 100 µl of HKM buffer. The pellet ('p') and supernatant ('s') samples were supplemented with 33µl 4x SDS gel loading buffer, heated to 37°C for 30 minutes with occasional vortexing, and finally heated to 95°C for 5 minutes before analysis by SDS-PAGE (Fig. S8B).

Single particle cryo-electron microscopy and model building
Purified AP2 core was reconstituted into physiological buffer HKM2 (10 mM Hepes KOH pH7.2, 120 mM KOAc, 2 mM MgCl2) with 0.5 mM DTT and applied to Quantifoil grids (R1.2/1.3, 300 Cu mesh). Grids were glow-discharged for 60 s at 25 mAmp using a Pelco EasiGlow before application of 3.5 µL of sample (0.4 mg/mL) and plunge-freezing using a Vitrobot Mark IV (FEI Company) operated at 4°C and 95% humidity. Data collection was carried out on a Titan Krios transmission electron microscope (FEI/Thermo Fisher) operated at 300 keV, equipped with a Falcon 3EC direct detector (FEI/Thermo Fisher) in counting mode. Automated data acquisition was performed using FEI/Thermo Fisher EPU software at a nominal magnification of 75,000, which corresponds to a pixel size of 1.065 Å per pixel. Dose-fractionated movies were acquired using 60 second exposures and 60 fractions at a dose of 0.54 e -/Å 2 /s with a defocus range of -1.9 to -3.1 µm (summarised in Table S1).
Data quality assessment, movie frame alignment, estimation of contrast-transfer function parameters, particle picking and extraction were carried out using Warp (Tegunov and Cramer, 2019). 120,000 particle images were extracted with a box size of 240 pixels and imported into CryoSPARC (Punjani et al., 2017) for 2D classification and ab initio model building. 3D refinement, filtering and sharpening (B factor -200) was carried out using the Homogeneous Refinement utility in CryoSPARC, including Fourier shell correlation (FSC) mask auto-tightening, followed by Local Resolution calculation by gold-standard FSC threshold (0.143 threshold) using the refined mask and an adaptive window factor of 25 (Fig. S3A,B).
The previously-determined 'closed' conformation of the AP2 core complex (PDB ID 2vgl) was fitted into the final cryo-electron microscopy volume using UCSF Chimera (Pettersen et al., 2004)  The structure was refined using phenix.real_space_refine and found to have an overall RMSD = 1.147 versus the 2vgl coordinates with no major structural rearrangement (Fig. S3B, Table S1).

Cryo-electron tomography sample preparation and data acquisition
To reconstitute AP2 membrane recruitment and Clathrin/AP2 membrane budding, purified AP2 FLAP and clathrin were incubated with synthetic liposomes. The liposomes contained 10% brain PtdIns(4,5)P2 and 10% DOPS in a POPC/POPE (3:2) mixture, with 3% content of each cargo lipopeptide. In vitro budding reactions contained 1.4 µM of AP2, 0.7 µM clathrin and 0.5 mg/ml of 400 nm extruded liposomes in HKM2 buffer with 5 mM b-mercaptoethanol. AP2 and liposomes were incubated for 5 minutes at room temperature, clathrin was then added and the reaction was incubated for a further 15 minutes at room temperature followed by 10 minutes incubation at 37° C. For the reaction without clathrin, liposomes were prepared by extrusion through 200 nm filter, and the clathrin addition was omitted. 10 nm gold fiducial markers in HKM2 buffer was added to the reaction (1:10 fiducials to the reaction volume ratio), and 3 µl of this mixture was back side blotted for 3 seconds at relative humidity 98% and temperature 18° C on a glow-discharged holey carbon grid (CF-2/1-3C, Protochips), before plunge-freezing in liquid ethane (Leica EM GP2 automatic plunger). Dosesymmetrical tilt series acquisition (Hagen et al., 2017) was performed on an FEI Titan Krios electron microscope operated at 300 kV a Gatan Quantum energy filter with a slit width of 20eV and a K2 direct detector operated in counting mode. The total exposure of ~130 e -/A 2 was equally distributed between 41 tilts. 10 frame movies were acquired for each tilt. The details of data collection are given in Table   S2.

Raw image processing and tomogram reconstruction
The raw movies were corrected for detector gain and pixel defects, aligned and integrated using alignframes from the IMOD package (Kremer et al., 1996). A few tilt series with tracking errors or large beam-induced sample movements were discarded. In addition, a small number of defective hightilt images (identified by blur, tracking error, large objects like grid bar or contaminations coming in the field of view) were discarded. Tilt-series were low pass filtered according to the cumulative radiation dose (Grant and Grigorieff, 2015) and aligned using fiducial markers in the IMOD package.

Subtomogram alignment
Subtomogram alignment and averaging was performed using MATLAB (MathWorks) functions adapted from the TOM , AV3 (Nickell et al., 2005), and Dynamo packages (Castano-Diez et al., 2012) essentially as described previously, using a modified wedge mask representing the amplitudes of the determined CTF and applied exposure filters at each tilt (Schur et al., 2016;Wan et al., 2017). Table S3 summarises data processing parameters.

Tracing decorated membrane and initial subtomogram positions
To define initial positions of subtomograms, centres and radii of coated vesicles, buds and tubules were manually marked in bin4 tomograms using a Chimera plug-in (Qu et al., 2018). These measurements were used to define geometrical shapes: flexible tubes (for coated tubules) and spheres (for coated buds and vesicles). Subtomogram positions then were defined on the surface of these shapes (for AP2) or 120 Å above it (for clathrin) with uniform sampling at every ~45 Å or ~110 Å for AP2 and clathrin respectively. Initial subtomogram orientations were calculated to be normal to the shapes' surfaces with random in-plane rotation.

Ab initio reference generation
Subtomograms were extracted at the initial positions from bin8 tomograms and averaged according to their initial orientations. Subtomograms were then aligned to this average in the direction perpendicular to the membrane and averaged to generate a reference in which density layers corresponding to the lipid bilayer, adaptor and clathrin layers were visible.
A subset of the data (three tomograms) was then aligned against this reference. For AP2, a gaussian-blurred sphere 80 Å in diameter was first added to the adaptor layer to assist the convergence of alignment and a cylindrical mask was applied passing the AP2 layer and the membrane. Three iterations of alignment were performed with a 10° angular search increment and a 35 Å low pass filter.
For clathrin a cylindrical mask was applied passing the clathrin layer and excluding the membrane layer.
Four iterations of alignment were performed with a 5° angular search increment and a 47 Å low pass filter. The resulting average was shifted, rotated and 3-fold symmetrised to place the clathrin triskelia in the centre of the box. In this manner separate starting references were generated for AP2 and clathrin.

Subtomogram alignment
These references were then used to align the complete data sets with the same alignment parameters. Upon alignment convergence, oversampling was removed by selecting a single subtomogram with the highest cross-correlation score within a distance threshold of 71 Å or 100 Å for AP2 and clathrin respectively.
Subtomograms were then sorted into identically sized odd and even subsets of coated structures.
Subtomograms were extracted from bin4 tomograms and subsequent alignment was performed independently on the odd and even subsets. The search space and increments for angular and spatial parameters were gradually decreased, and the low pass-filter was gradually moved towards higher resolution. Upon convergence of subtomograms from bin4 tomograms, alignment was continued using bin2 and finally bin1 tomograms. Visibly misaligned subtomograms were removed using a crosscorrelation cut-off threshold manually selected for each tomogram. Resolution was monitored by FSC.
The final maps were sharpened with empirically determined B factor with local low-pass filtering using relion_postprocess from the Relion 3.0 package (Zivanov et al., 2018).
For AP2 alone, after convergence, focussed alignment was performed by local masking of either α, β2/µ2 or the C-termini of α and β2. The focussed maps were multiplied by their alignment mask, summed, and divided by the sum of all three local masks to obtain the final EM map. Focussed alignment was not performed for AP2 in clathrin coats due to insufficient signal. Final maps were multiplied by a soft cylindrical mask to remove diffuse density from neighbouring AP2 molecules.
For clathrin, prior to alignment in bin2 tomograms, we performed symmetry expansion using dynamo_table_subbox from the Dynamo package (Castano-Diez et al., 2012) to generate subtomograms centered at individual clathrin legs and further alignment iterations were performed on individual legs.

Classification of subtomograms
We applied principal component analysis (PCA) to sort subtomograms by β2-appendage occupancy. The PCA was performed on wedge-masked difference maps (Heumann et al., 2011) with calculations implemented in MATLAB using code adapted from PEET and Dynamo packages (Castano-Diez et al., 2012;Heumann et al., 2011). The first eigencomponent of this PCA analysis correlated with the β2-appendage density in the subtomograms and could be used to sort the data according to β2-appendage occupancy. We sorted subtomograms bounding pentagons or hexagons of the clathrin lattice based on the positions of their neighbours (Fig. S5A).
To produce a β2-appendage-enriched subtomogram class, hexagon-and pentagon-bounding subtomograms were split into 10 equally-sized classes according to β2-appendage occupancy (Fig.   S6A). The four classes of hexagon-facing legs with highest β2-appendage occupancy were combined together and the combined class was used for further alignment to derive the EM map resolving the β2appendage density in the clathrin cage.

All EM maps generated from the two clathrin datasets (with YxxΦ and YxxΦ/[ED]xxxL[LI]
cargoes) were essentially identical. Both clathrin datasets were therefore combined for further alignment in bin2 and bin1.

Spatial distributions of AP2 and Clathrin
Plots showing the distribution of proteins relative to their neighbors were created as in (Kovtun et al., 2018). Plots of the distribution of AP2 relative to AP2 (Fig S6), relate the centers of AP2 complexes. These plots were used to identify AP2 dimers in the dataset of AP2 on YxxΦ cargocontaining membrane which appear as a peak in the distribution containing ~20 % of total AP2 (marked by arrow in Fig. S4A). To derive a structure of the dimer, subtomograms containing dimers were aligned in bin4 without symmetrisation then in bin2 with 2-fold symmetrisation until convergence.
Plots of the distribution of clathrin relative to clathrin (Fig. S6), relate the CHCR3 regions of distal clathrin segments. These plots were used to separate clathrin legs that bound hexagons and pentagons in the clathrin cage (Fig. S6).
Plots of the distribution of AP2 relative to clathrin, relate the center of AP2 and the tripod region of the clathrin leg. Plots of the distribution of clathrin relative to AP2 relate the center of AP2 and the membrane-facing edge of clathrin NTDs. These plots were used to analyse spatial relationships between the adaptor and clathrin components of the coat (Fig. S6).
Linear profiles of the radial distribution of AP2 relative to the clathrin tripod were derived by integrating the AP2 distribution plot along the axis of a cylindrical mask with a radius of 54 Å. The mean and standard deviation of the linear profiles were calculated by gaussian fitting (Python, Matplotlib).

Model building in EM maps determined by subtomogram averaging
Rigid-body docking was performed using the Chimera package (Pettersen et al., 2004). Flexible fitting was performed using molecular dynamics flexible fitting (MDFF) in the NAMD package (Trabuco et al., 2008), constraining secondary structure elements. For AP2, fitting was performed using the crystal structure of the open form (PDB ID 2xa7) (Jackson et al., 2010). For clathrin light chain fitting was performed using (PDB ID 6sct) (Morris et al., 2019). For clathrin heavy chain, fitting was performed using (PDB ID 1xa4) (Fotin et al., 2004b). PDB ID 1xa4 is a C-alpha trace model based upon EMDB entry EMD-5119, and to allow MDFF, side chains were added to the model using PD2 ca2main online server (Moore et al., 2013). The separate fragments in PDB ID 1xa4 (1-834, 840-1135, 1078-1278, 1281-1630 were fitted as rigid bodies into the map of a clathrin leg bounding a hexagon, joined using Modeller (Sali and Blundell, 1993), and combined with the rigid-body fitted light chain to make a composite model of CHC and CLC, that was further refined by flexible fitting with MDFF. The resulting refined model was subsequently flexibly fitted into a map of leg bounding a hexagon enriched in the β2-appendage, constraining NTDs as a single domain in addition to the secondary structure constraints used above. This was done to refine the positions of the clathrin NTD-ankle regions, that are better resolved in the β2-appendage-enriched map compared to the map representing all hexagon bounding legs. The β2-appendage (PDB ID 1e42, (Owen et al., 2000) was fit as a rigid body using Chimera. To display the position of the DNAJ domain of Auxilin, the model of NTD/DNAJ taken from PDB ID 1xi5 (Fotin et al., 2004a) was overlaid with the clathrin NTD from our pseudoatomic model.   The β2-appendage makes contact with sites on three CHC: two in the ankle segment (CHC repeats 1 and 2 ) and one in the NTD. B. Close-up of NTD and β2-appendage region indicating the binding sites of Low Density Lipoprotein Receptor adaptor ARH and Eps15. ARH and Eps15 peptides are pink, positioned as in PDB 2g30 (Edeling et al., 2006) and 2iv9 (Schmid et al., 2006), together with a simulated 15 Å resolution isosurface (transparent pink). Binding sites for clathrin boxes in the NTD are marked. C. As in B. showing the binding position of DNAJ Auxilin domain in blue, as described in PDB 1xi5 (Fotin et al., 2004a).    (Collins et al., 2002) and open (2xa7, (Jackson et al., 2010) forms. Panels in the right column show close up views of the N-terminal region of β2. The β2 position is essentially the same in the cytosolic and closed crystal form of AP2, but appears more open in membrane-bound AP2 than in the "open" crystal form.   A. Neighbor plots showing the distribution of the center of AP2 relative to the clathrin tripod or the distribution of clathrin NTDs relative to the center of AP2 molecules. Plots are visualized as in Fig S4A, integrating 90 Åthick slabs (for AP2 relative to clathrin) or 82 Å-thick slabs (for clathrin relative to AP2). Also shown are distributions of the radial distance between AP2 and clathrin calculated from the "AP2 relative to clathrin" neighbor plots (blue lines, see supplementary methods). Mean +/-standard deviation determined by fitting with a Gaussian distribution (red lines) and the number of AP2 subtomograms considered is marked. The distance between clathrin and AP2 is shorter in YxxΦ/[ED]xxxL[LI] cargo-containing coats than in YxxΦ cargocontaining coats, and is shorter in vesicles than in buds. AP2 begins to occupy preferred positions between clathrin NTDs at a distance between AP2 and clathrin shorter than ~220 Å, and this preference becomes pronounced at a distance of ~203 Å as seen in YxxΦ /[ED]xxxL[LI] coated vesicles. Corresponding changes are seen in the distribution of clathrin relative to AP2, with clathrin NTD being excluded from positions directly above AP2 molecules (see also panel B). B-D. Selected neighbor plots from A are additionally illustrated as isosurfaces (the beige isosurface encloses 8% of relative subtomogram positions, the transparent outline encloses 40%), relative to the protein structures (grey surface). B. Clathrin NTDs are preferentially excluded from regions directly above AP2 in vesicles where the distance between AP2 and clathrin is short enough for them to sterically exclude one another. C. Clathrin NTDs are randomly distributed in buds where the distance between AP2 and clathrin is large enough to avoid any steric exclusion. D. The preferred positions of AP2 coincide with the spaces between the clathrin NTDs -each space provides enough room to accommodate the tip of a single AP2. A. Slices through EM maps of clathrin legs bounding hexagons and pentagons. The β2-appendage density (arrowheads) is stronger in the hexagon-bounding leg than in the pentagon-bounding leg. The pixel density was integrated within an ellipsoidal mask placed on the β2-appendage, clathrin, or background, revealing higher occupancy if the β2-appendage on legs bounding hexagons than bounding pentagons. We estimate that the occupancy is approximately 50% and 20% in legs bounding hexagons and pentagons, respectively. B.
Subtomograms classified based on β2-appendage occupancy. Panels are arranged in rows by the polygon and coat types as in A. The datasets were split into ten equally-sized classes by the score of the principal component that A. Cryo-EM screening images showing budding reactions on YxxΦ cargo-containing liposomes using AP2 FLAP and AP2 FLAP lacking the β2-appendage (Δβ2-appendage). Arrows indicate clathrin-coated buds formed in the budding reactions. B. Coomassie stained SDS-PAGE of glutathione sepharose pulldowns using GST-GFP (as a negative control for clathrin binding), GST-β2hinge or GST-β2hingeapp. Supernatant ('s') and pellet ('p'). GST-β2hinge and GST-β2hingeapp bind clathrin to a similar extent, suggesting that deletion of the β2-appendage does not affect clathrin recruitment in this system.