Systematic Nanoscale Analysis of Endocytosis Links Efficient Vesicle Formation to Patterned Actin Nucleation

1Clathrin-mediated endocytosis (CME) is critical for many biological processes such as signaling, nutrient uptake, and pathogen entry and involves the internalization of cargo molecules from the cell surface into small membrane vesicles. CME follows a stereotypic order of events: first, a protein coat assembles on the membrane, which then invaginates to form a vesicle with cargo molecules inside. This vesicle is pinched off the plasma membrane and rapidly uncoats allowing fusion with endosomes. CME is performed by a machinery that comprises more than 50 different proteins and is conserved from yeast to humans. Much of our knowledge of the mechanism of CME comes from research in cultured mammalian cells, and yeast. In the budding yeast Saccharomyces cerevisiae, genetic and imaging screens have led to a near-complete parts list. In addition, live-cell imaging has revealed the order of assembly of components and categorized them into modules based on their dynamics. This modular organization is remarkably conserved in metazoans.

2In yeast, CME can be divided into an early phase, when endocytic proteins are recruited to a flat membrane, and a late phase during which invagination occurs. The early phase is characterized by the recruitment of various endocytic adaptor and coat proteins, including clathrin, and is long and variable in duration. The following highly regular late phase begins with the arrival of late coat proteins, followed by actin regulatory proteins including WASP and type I myosins. A burst of actin polymerization starts membrane invagination, and with the arrival of amphiphysin proteins, vesicle scission occurs.

3Although the recruitment timing of proteins during endocytosis is well understood, their spatial organization at endocytic sites is largely unknown. This is due to the complexity, dynamics, and small size of the endocytic machinery, which is below the resolution of conventional light microscopy. Live-cell fluorescence microscopy revealed the average positions of endocytic proteins along the membrane invagination and the shape of the invagination was determined by correlative light and electron microscopy (CLEM). Furthermore, immuno-electron microscopy (EM) reported the approximate location of some endocytic proteins in the late stages of endocytosis. However, systematic information about the location of the different endocytic proteins is currently lacking, particularly during the initial phase before membrane bending. Thus, the molecular architecture of this complex supramolecular machine, and how it can drive endocytosis so efficiently to generate precisely shaped and sized membrane vesicles, remains unknown.

4To address this fundamental gap in our knowledge, we developed a high-throughput superresolution microscopy pipeline to study the nanoscale organization of proteins in the endocytic machinery over the entire endocytic time line. By automating image acquisition and analysis, we could process superresolution images of thousands of cells. We used budding yeast to enable systematic fluorescent tagging of endocytic proteins at their genomic loci to ensure high labeling efficiency, while retaining native expression and biological function. This approach allowed us to analyze the structural organization of 23 different endocytic proteins sampled throughout the endocytic process at, in total, over 100,000 endocytic sites in more than 20,000 fixed yeast cells.

5We found that assembly of the machinery initiates stochastically from irregular structures. Thereafter, an intricate self-organization emerges where endocytic proteins are radially ordered according to their function. WASP family proteins formed a ring-shaped nanoscale template on the flat membrane to pattern the nucleation of actin filaments. Brownian dynamics simulations of actin polymerization showed that this geometry enables the formation of a scaffold of actin filaments producing sufficient force for membrane invagination, and centering provides a mechanism for the high efficiency and robustness of vesicle budding.

6Here, we used single-molecule localization microscopy (SMLM, also called “(f)PALM” or “STORM”) to image sites of clathrin-mediated endocytosis in budding yeast strains with single endocytic proteins endogenously tagged at their C termini with a photoswitchable fluorescent protein. We fixed the cells with formaldehyde, and then placed the focal plane on their underside, where endocytic invaginations are oriented perpendicularly to the focal plane (Figure 1A). Thereby we obtained two-dimensional (2D) projections of endocytic structures, which reveal the lateral distribution of proteins at endocytic sites. In these images, the distribution of endocytic proteins appeared as patches, rings, or irregular shapes (Figures S1, S2, and S3).

7Because endocytosis was arrested by fixation, the individual images provide snapshots of different endocytic time points. To sample the entire endocytic timeline with high statistical power, we automatically acquired and segmented superresolution images of many thousands of endocytic sites (Figures 1B–1D), quantitatively analyzed individual structures (Figures 1E and 1F), spatially aligned them by translation, and averaged them. We thereby generated density profiles of how each protein is on average distributed around the center of the endocytic site (Figure 1G), representing the average structural organization of endocytic proteins over their lifetime. Additionally, we determined how the distribution of four key endocytic proteins evolves during endocytosis.

8We determined the structural organization of 23 endocytic proteins from all functional modules of the machinery (Figures 2A, S1, S2, and S3, mammalian homologs in parentheses): the early proteins Ede1 (Eps15) and Syp1 (an F-BAR protein, FCHo), which initiate endocytic sites; the seven coat proteins Clc1 and Chc1 (clathrin light and heavy chain), Sla2 (Hip1R), Ent1 (epsin), Sla1, End3, and Pan1 (all intersectin), which interact with membrane, cargo, and actin; six WASP/Myo module proteins including the actin nucleation promoting factor Las17 (WASP), Vrp1 (verprolin), the F-BAR protein Bzz1 (syndapin), the type-I myosins Myo3 and Myo5 (both Myo1-E), and Bbc1 (fungi only); seven components of the endocytic actin network including the Arp2/3 complex subunit Arc18 (ArpC3), capping proteins Cap1 and Cap2 (Capping protein), actin binding protein Abp1 (ABP1), actin crosslinker Sac6 (fimbrin), actin turnover factors Twf1 (twinfilin) and Crn1 (coronin); and, finally, the N-BAR protein Rvs167 (amphiphysin). For each of these proteins, we acquired superresolution images of ∼1,000–10,000 endocytic sites (except Rvs167, where n = 413) (Table S1).

9These images revealed how proteins are arranged at endocytic sites: Some proteins, including the coat proteins, formed mostly small patches (Figures S1, S2, and S3). Others, like WASP/Myo proteins, formed mostly ring-like structures with empty centers (Figures S1, S2, and S3). For all proteins, except Ede1 and Syp1, these structures were characteristic in size and in shape, indicating an intricate sub-organization of different components within the endocytic machinery.

10Next, we quantitatively analyzed the individual superresolution images of all structures using a geometric model (Figures 1E and 1F) to extract their shape, size, and position, derived each protein’s average distribution and radial density profile (Figures 2D–2G, S1, S2, and S3), and classified the shape of the average protein distribution as a patch, ring or dome (Table S1). We found the average distribution of a protein (Figure 2A) to be representative of the individual structures (Figures S1, S2, and S3), but note that specific angular distributions or structural asymmetry that are visible in individual images are not represented in the averages. By design, the radial density profiles (Figures 2D–2G) represent the average probability of an endocytic protein to be found at a certain distance from the center of the endocytic site and are intended to quantitatively compare the distribution of different proteins.

11These data showed that endocytic proteins assemble into nanoscale structures of different sizes and geometries, as evident both in images of individual sites (Figures S1, S2, and S3) and in the averages (Figure 2). Proteins within the same functional endocytic module had similar radial profiles and sizes, indicating that structural organization and function are linked. Coat proteins formed the smallest structures, which were mostly patches with mean outer radii of ∼25–50 nm. Proteins of the WASP/Myo module formed larger, ring-like structures with outer radii of ∼60–100 nm, and actin module proteins formed the largest structures with outer radii of ∼80–100 nm. The amphiphysin Rvs167 of the scission module formed small structures with an outer radius of ∼40 nm. Together, our results reveal that endocytic proteins are functionally organized in distinct radial zones at endocytic sites.

12As we relied on formaldehyde fixation to ensure high spatial resolution and localization density in the superresolution images, we next characterized how well fixation preserved endocytic structures. For this, we directly compared the distribution of Ede1, Pan1, and Las17, each from a different functional endocytic module, in living and fixed cells. To achieve optimal resolution in living cells, we treated cells with Latrunculin A (LatA), which arrests endocytosis prior to membrane ingression and thereby allowed us to image defined, stationary structures. In all cases, the observed structures were very similar between living LatA-treated and fixed LatA-treated cells (Figures 2H and S4). Thus, we concluded that chemical fixation preserved yeast endocytic structures well enough for us to take advantage of the excellent image quality of fixed-cell superresolution imaging.

13For most endocytic proteins, the individual images resembled their average distribution, hinting toward a fairly constant structural organization during endocytosis. However, the fact that proteins get recruited and disassembled gradually suggests some structural rearrangements over time. Particularly, the early proteins Ede1 and Syp1 that initiate endocytic sites with variable timing on the order of minutes formed highly variable structures, including rings, patches, crescents, lines, and more irregular shapes (Figures S1, S2, and S3), with average outer radii of ∼66 nm (Figures 2C and 2D).

14To test whether this heterogeneity corresponded to structural changes over time, we combined superresolution imaging of the early protein Ede1 with diffraction-limited imaging of the GFP-tagged coat protein Sla2, whose abundance increases over time until Ede1 is disassembled, thus providing a reference to sort endocytic sites in time (Figure 3A). We found that the distribution of Ede1 continuously grows in size from an average outer radius of 60.8 ± 0.4 nm (mean ± SEM; n = 2,514; SD = 20.9 nm) up to 69.9 ± 0.4 nm (mean ± SEM; n = 2,634; SD = 22.4 nm) (Figures 3B–3D and S5A).

15To further investigate this structural remodeling, we imaged Ede1 and the coat protein Sla2 using dual-color superresolution microscopy. This revealed that Ede1 was arranged either around Sla2 or side by side with it (Figure 3E), but the two proteins rarely overlapped. On average, Ede1 was peripherally organized around Sla2 (Figure 3F).

16Together, the growing size of Ede1 structures and the arrangement around Sla2 suggest that the endocytic machinery is initiated with variable structures, which are then remodeled during coat recruitment, potentially by a mechanism where coat proteins form a stable patch occupying the center, and thereby force early proteins to arrange more peripherally.

17Besides Sla2, a variety of other coat proteins are recruited. These include clathrin (Clc1, Chc1), Ent1, Sla1, Sla2, Pan1, and End3, which on average formed patch-like structures with sizes in a range between 25–50 nm (Figures 2C and 2E). Clathrin, which arrives first, formed the smallest structures, followed by End3, Ent1, and Sla2, and then by the late coat proteins Sla1 and Pan1. Although the averages of all coat proteins were patch-like, part of the individual sites showed ring-like distributions (Figure S1, Figure S2, Figure S3), which agrees with our previous findings that Sla1 can form small rings at endocytic sites.

18We then analyzed how Pan1, which formed the largest structures of the coat, changed over time by imaging Pan1 alongside Abp1-GFP as marker for the actin network (Figures 3G and 3H). Pan1 structures had an average outer radius of 41.8 ± 0.9 nm (mean ± SEM; n = 494; SD = 19.7 nm) before actin polymerization (Figures 3I and S5), which increased to 50.1 ± 1.6 nm (mean ± SEM; n = 98; SD = 16.2 nm) at endocytic sites where actin polymerization had begun, which corresponds to maximum Pan1 recruitment. This indicates that Pan1 structures expand during the continuous recruitment to endocytic sites.

19Taken together, our data suggest that the progressive assembly of endocytic coat proteins translates into a radially expanding architecture: the early coat proteins clathrin, Sla2 and Ent1, form the core of the coat, whereas the late coat proteins, Sla1 and Pan1, extend to its periphery.

20As the coat is assembling, members of the WASP/Myo module, which regulate actin nucleation start to arrive at endocytic sites, where they formed rings of different sizes visible in their individual images and averages (Figures 2F, S1, S2, and S3). The group of Las17 (yeast WASP), Bzz1, and Vrp1 on average formed rings with indistinguishable radii of ∼70 nm, in agreement with their reported interactions and functional cooperation to promote actin nucleation. By contrast, the rings of the type-I myosins Myo3 and Myo5 were significantly larger with radii of ∼90 nm (Figure 2C). This difference was confirmed in dual-color superresolution images of Myo5 and Las17 at individual endocytic sites, where Myo5 was peripherally arranged around a Las17 ring (Figure 4A).

21The discrepancy of ∼20 nm between Vrp1 and Myo5 radii was surprising, as Vrp1 is required to recruit Myo3/5 to endocytic sites. Thus, we hypothesized that Myo5 could assume an extended conformation. Indeed, when we endogenously tagged Myo5 with mMaple at its N terminus, we found its N terminus to be on average ∼14 nm further inside than the C terminus (Figure 4B). This indicates a preferential radial orientation of Myo5, where its motor domain points inward toward the center of the endocytic site. Whether this arrangement facilitates an interaction with the more centrally located Vrp1—and what it implies for myosins’ mode of action during endocytosis—should be the subject of future studies.

22The WASP protein Las17 arrives at endocytic sites together with the most peripheral coat protein Pan1 around 20 s before actin polymerization begins. Las17 is therefore the first protein to form clear ring-like structures. Thus, we asked whether Las17 is pre-patterned as a ring already on the flat plasma membrane or whether its ring-like distribution is caused by the invaginating membrane. When we arrested endocytosis at a flat membrane using LatA, Las17 still formed rings with a slightly larger outer radius of 74.2 ± 0.7 nm (mean ± SEM; n = 2,179; SD = 31.6 nm) (Figure 2H), demonstrating that ring structures of nucleation promoting factors can form on the flat membrane in the absence of polymerized actin. Next, we analyzed whether Las17 rings changed in size during membrane ingression by imaging Las17 alongside Abp1-GFP as a temporal reference for actin polymerization (Figures 3J and 3K). We found that Las17 clearly formed rings prior to membrane bending that barely increased in size from 67.1 ± 0.5 nm (mean ± SEM; n = 2,550; SD = 23.1 nm) to 70.2 ± 0.7 nm (mean ± SEM; n = 1,595; SD = 27.4 nm) (Figures 3L and S5C) during actin polymerization. We conclude that Las17 forms robust ring structures with a radius of ∼70 nm early on the flat plasma membrane before actin polymerization begins.

23Why then does Las17 form a ring, when the previously assembled coat proteins form patches and actin polymerization has not started to invaginate the membrane? The core coat proteins clathrin, Sla2 and Ent1 form a tight molecular lattice in vitro, and might prevent later arriving proteins from accessing the center of the endocytic site, thus determining the minimal size of the ring they form. Consistent with this hypothesis, dual-color superresolution imaging of Las17 and the coat protein Sla2 showed that Sla2 was located inside the Las17 rings (Figure 4C). Taken together, our data revealed that actin nucleation is pre-patterned, already on a flat membrane, by a ring of Las17 molecules around the endocytic coat in its center. Actin monomers are therefore added to filaments close to this nucleation zone. This induces an upward push of the actin network, which is attached to the membrane in the center by Sla2 and Ent1/2 molecules, explaining how polymerizing actin can pull the plasma membrane inward (Figure 4D).

24Interestingly, coat proteins may not only set the physical inner limit of actin nucleation by Las17, but may also ensure this boundary biochemically, as the peripheral coat protein Sla1 is a WASP inhibitor. Thus, we asked whether there is also an outer limit of actin nucleation. Bbc1, another WASP inhibitor, formed the largest rings of the WASP/Myo module with a radius of ∼98 nm. This arrangement could indicate that the ring of Las17 is regulated on its inside by a patch of Sla1 and its outside by a ring of Bbc1, thereby controlling Las17 activity for actin nucleation in its radial zone at ∼70 nm (Figure 4E).

25To test whether this distinct organization of Las17 and its inhibitors is functionally important, we perturbed it by deleting BBC1. We then analyzed the distribution of Las17 over time using Abp1-GFP as timing marker for actin polymerization. In cells lacking Bbc1, Las17 initially formed the same sized rings like in wild-type cells. However, once actin polymerization began, Las17 significantly expanded from the outer radii of 67.1 ± 0.6 (mean ± SEM; n = 1,237; SD = 21.6 nm) to 82.0 ± 1.4 nm (mean ± SEM; n = 503; SD = 30.8 nm) and became more irregular and fragmented (Figures 4F and 4G). Thus, upon actin polymerization, Bbc1 does not merely act as biochemical inhibitor of Las17, but rather regulates the localization of Las17.

26We also imaged Las17 in sla1Δ cells, which have a much stronger phenotype than bbc1Δ cells,. There, Las17 almost always formed large irregular clusters associated with large actin patches (Figure S6A). At the remaining small subset of sites (215 sites out of ∼5,000 cells), Las17 was distributed similar to wild-type (Figures 4F, S6B, and S6C). Likewise, Las17 formed rings in sla2Δ cells (Figure S6D), suggesting that no single coat protein alone defines the inner boundary of Las17 rings.

27Taken together, we have discovered that the major WASP family actin nucleation promoting factor Las17 forms a precisely controlled template for actin nucleation from a ring of ∼70 nm in radius. During actin polymerization, Bbc1 is important to maintain Las17 ring size. This molecular architecture is established on the flat plasma membrane before actin polymerization, and enables the growing actin network to exert a pulling force and create an invagination.

28During the late phase of endocytosis, the plasma membrane is invaginated by polymerizing actin. Here, we determined the average radial distribution of the actin network components Abp1, Arc18, Cap1, Cap2, Crn1, Sac6, and Twf1, all of which formed similar large structures corresponding to the big endocytic actin network (Figures 2A–2C and 2G). Using the amphiphysin Rvs167-GFP as timing marker, we then showed that Abp1 structures were biggest (outer radius 87.9 ± 0.8 nm; mean ± SEM; n = 568; SD = 19.7 nm) and had a pronounced minimum in their center at the time point of vesicle scission (Figures 5A–5D and S5D). This matches the expected distribution resulting from a dome-like actin network encompassing the invagination. Moreover, the size differences of the other actin module proteins revealed that barbed ends of filaments are on average oriented outward further than the pointed ends (Figure S7), agreeing with a previous model.

29Next, we directly visualized the Las17 nucleation zone and the resultant actin network using dual-color superresolution microscopy of Las17 and Abp1 in a side-view configuration (Figure 5E). Whereas Las17 always localized close to the base of the plasma membrane, Abp1 formed structures of different shapes and sizes corresponding to different stages of actin network formation. To infer the endocytic time of our snapshots, we used previously reported live-cell findings that the center of mass of Abp1 is continuously moving inward during endocytosis. Thus, we ordered our snapshots in time by sorting them by increasing distance between the Abp1 centroid and Las17 at the base. The resultant temporal reconstruction revealed that the actin network emanates directly above Las17 and progressively grows into the cytoplasm (Figures 5F and 5G). The average structures were ∼200 nm wide in all but the first time point and increased in height from ∼70 nm to ∼240 nm. This agrees well with previous measurements using CLEM on high-pressure frozen cells (Figure 5G), thus validating our approach and confirming good structural preservation in our chemically fixed samples.

30In summary, ordering our snapshot data in time directly shows how the Las17 nano-template guides actin polymerization.

31During endocytosis, the turgor pressure opposes membrane invagination with forces exceeding 1000 pN, which is much higher than the polymerization stall force of single actin filaments of 1–10 pN. Nevertheless, endocytic vesicles are formed with high efficiency and uniform size. We thus speculated that nanoscale patterning of actin nucleation could be important for the actin network to generate the force required to form vesicles. To test this, we simulated the mechanics of the dynamic endocytic actin network using the open-source modeling framework Cytosim.

32We modeled the actin network with a minimal set of components and experimentally measured parameters. Based on our findings, we implemented a ring-shaped nucleation zone (Figure 6A) where activated Arp2/3 complex continuously appears and creates new filaments from existing ones at a 70° angle (Figure 6B). A single filament acts as first nucleation site, consistent with a “sever, diffuse, and trigger” model where short filaments from fragmenting actin patches activate Arp2/3 complex at new endocytic sites. Filaments grow with Brownian ratchet dynamics and a stall force of 9 pN up to a length of 60 nm, which is in between estimates of filament lengths at endocytic sites in budding and fission yeast. Crosslinkers are modeled as 10 nm-long elastic linkers with a 10 pN unbinding force (Figure 6B). Actin is strongly bound to the tip of the invagination, mimicking the function of Sla2 and Ent1/2 (Figure 6A). The required force is 200 pN at first and then increases up to 1,000 pN at a depth of 60 nm. There, the invagination reaches a previously proposed “snap-through” transition, and endocytosis is regarded as successful.

33In these simulations, actin filaments formed a branched network that reliably produced forces beyond 1000 pN and thus overcame turgor pressure (Figure 6C; Video S1). Around 60 actin filaments were necessary to complete endocytosis, similar to previous reports, and the average filament orientation agreed between simulations and superresolution data, where barbed ends were further outside than the pointed ends bound by Arp2/3 and crosslinkers were in between (Figure S7).

34With this computational model, we next tested whether a ring-shaped nucleation zone is advantageous for the efficiency of vesicle budding. A key advantage of a ring-shaped nucleation zone could be that membrane invagination occurs in its center, with actin polymerizing symmetrically around it, preventing lateral displacement or tilting of the invagination.

35To test this, we simulated endocytosis with two different geometries, either where actin nucleation occurred symmetrically all around the invagination (Figure 6D, Video S1) or where filaments could be nucleated asymmetrically with respect to the invagination, which we simulated by not constraining the invagination to the center of the nucleation zone (Figure 6E, Video S2).

36When we calculated endocytic success rates, we indeed found that endocytic events were far more successful when actin nucleation occurred all around the central invagination (Figure 6F), consistent with the arrangement of Las17 around Sla2 that we observed in our images (Figures 4C and 4D). Moreover, the further actin nucleation activity and invagination were apart, the less likely endocytosis was to succeed (Figure 6F) and the slower it proceeded (Figure 6G, Video S3). These results indicate that actin-driven pulling on the membrane is much more efficient in creating invaginations when they are formed in the center. When actin nucleation was asymmetric, invaginations often moved sideways in our simulations, because the actin network exerted a lateral force on the invagination, rather than pulling it inward. Thus, more time (Figure 6G) and more actin filaments (Figure S7F) were required to reach any invagination depth than when actin nucleation was symmetric around the invagination.

37We conclude that the ring-like actin nucleation nano-template ensures high efficiency of vesicle budding by confining the membrane invagination at its center, triggering actin polymerization all around it and thereby creating a force perpendicular to the plasma membrane.

38Here, we showed that proteins are organized in distinct nanoscale radial zones that correlate with function. The early proteins Ede1 and Syp1 were distributed similarly, which is expected as they directly interact and Syp1 recruitment requires Ede1. The variable structures of Ede1 are remodeled and become preferentially organized around the growing coat (Figures 3B–3F), potentially because Ede1 competes with late coat proteins like Pan1 for binding to the early coat proteins Ent1/2 via their EH domains. We propose that the structural remodeling of early proteins upon coat formation represents a structural switch from the variable initiation phase into the late phase of endocytosis that leads to vesicle budding with highly stereotypic timing.

39In the central coat, Sla2 and Ent1/2 bind the membrane and clathrin, forming a lattice, while Pan1 and Sla1 extend the patch in size, consistent with the recently reported organization of their homolog Intersectin within the endocytic coat in mammalian cells. The coat is likely stable, as its components exchange very slowly at least in LatA treated cells.

40Subsequently, WASP/Myo module proteins are recruited in distinct ring-shaped zones. Arrival time and size are again correlated: Las17, Vrp1, and Bzz1 all directly interact and form rings of similar size around the coat. When actin polymerization begins, Myo3 and Myo5 are recruited and form larger rings, and Bbc1 forms the largest rings around the coat.

41Taken together, our results reveal different stages by which the endocytic machinery is collectively assembled on a flat plasma membrane (Figure 7). After initiation, the coat forms, and newly arriving proteins are recruited to its periphery into distinct radial zones, which are determined by a variety of interactions with proteins that are already present at the endocytic site.

42In yeast, actin polymerization provides the necessary force to bend the plasma membrane, which is much higher than in mammalian cells because yeast have a turgor pressure. We found that actin nucleation, which is rate-limiting for actin polymerization, is patterned by a ring of Las17 around the coat at the plasma membrane, and visualized how an actin network is formed from this nucleation nano-template. Using simulations of actin polymerization at endocytic sites, we could show that this ring-shaped nucleation zone is crucial for fast and efficient vesicle formation.

43In light of the inherent stochasticity of macromolecular machineries, the robustness and efficiency of endocytosis in yeast is remarkable. Endocytosis is virtually always productive and occurs with high spatio-temporal regularity. Interestingly, to pull in the membrane, high forces are already required shortly after membrane ingression begins, when the invaginations are still shallow. Pre-patterning actin nucleation around the center, where membrane and actin are physically linked by Sla2 and Ent1/2 (Figures 4C and 4D), allows rapid filament nucleation from the start, centers the membrane tethers, lends directional stability to the actin machinery, and thereby ensures the endocytic machinery produces enough force during its most crucial phase at the beginning of invagination.

44The mechanistic relevance of this nucleation zone is highlighted in bbc1Δ cells, where Las17 initially formed rings like in wild-type cells, but with the onset of actin polymerization became larger and less regular. It was previously shown that in bbc1Δ cells, the coat protein Sla1 moves in further than in wild-type cells and that more actin is assembled, resulting in a wider actin network. A larger Las17 nucleation zone explains this phenotype, where a bigger, wider actin network can propel the forming vesicle further into the cytoplasm.

45Moreover, it was recently shown that Las17 at endocytic sites is activated when a threshold concentration is reached, indicating that precise control of its nanoscale localization is important to maintain the correct regulation of Las17.

46The type I myosins Myo3/5 were arranged in rings around Las17 (Figure 4A), with their N-terminal motors preferentially oriented inward (Figure 4B). Interestingly, an opposite radial orientation of Myo3/5 has been hypothesized previously, where N-terminal motor domains were proposed to capture peripheral actin filaments, and tether them to the plasma membrane. The arrangement found here rather suggests a mode of action where motors bind to actin filaments closer to the center, and possibly exert a power stroke to translocate filaments to assist endocytosis.

47Our findings of a ring-shaped Las17 nucleation zone with Myo3/5 around it are particularly interesting in light of a recent study that visualized several components of endocytic actin patches in fission yeast (S. pombe) using live-cell superresolution microscopy. Using a side-view perspective (equivalent to Figure 5E), the study reported that Wsp1p and Myo5p (S. pombe homologs of Las17 and Myo3/5) first localized to the membrane base. Wsp1p then moved inward, while Myo1p remained at the membrane, creating two distinct actin networks which push against each other to mediate vesicle scission.

48Here, we have found that in S. cerevisiae Las17 and Myo3/5 are spatially separated in radial zones at the base of the membrane, and we anticipate this organization is present in S. pombe as well. In contrast to Wsp1p in S. pombe, we have shown that in S. cerevisiae Las17 remains close to the base of the membrane (Figures 5F and 5G), in line with previous reports using fluorescence microscopy. Whether the functional consequences of the spatial organization of Las17 and Myo5 are related to the proposed mechanism of S. pombe Wsp1p and Myo1p remains unknown.

49The machinery of clathrin-mediated endocytosis is highly conserved from yeast to humans, with actin, Arp2/3 complex, WASP, and other actin regulators being present, but not at all sites and in variable amounts. Like in yeast, actin is essential when high forces are needed for membrane deformation, examples of which involve endocytosis at cellular adhesions, of large cargo particles, and when membrane tension is high. In these cases, branched actin networks are formed at the base of clathrin-coated pits, which indicates that actin nucleation by the Arp2/3 complex could be patterned there by WASP similar to what we have shown here.

50Actin polymerization is essential for membrane remodeling in various other cellular processes. During cell migration, WASP activates Arp2/3-mediated filament nucleation at the leading edge to push forward the membrane. Recently, WASP was shown to act as distributive polymerase on the membrane, where it dramatically accelerates growth of actin filaments. A nano-template of concentrated WASP molecules might thus assist nearby filaments to grow faster than surrounding ones, which for instance is a requirement for filopodia formation in dynamic lamellipodia.

51In summary, the data presented in this work substantially improve our understanding how the complex and dynamic endocytic machinery produces vesicles with high precision and efficiency. We believe our data will be useful for further mechanistic modeling of the endocytic machinery and anticipate that the combination of our and other complementary approaches, including live-cell fluorescence and superresolution imaging and EM, will continue to be fruitful for future studies of endocytosis.

52Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Jonas Ries (jonas.ries@embl.de).

53All yeast strains used in this study were derivatives of S. cerevisiae MKY0100 or MKY0102 (Kaksonen lab). Construction of the strains is described below and a complete list of the strains used in this study is given in Table S3. Yeast cells were inoculated from single colonies on plates into 4 mL YPAD in a glass tube, and grown overnight at 30°C with shaking. The next morning, the culture was rediluted into 10 mL YPAD in a glass flask to OD600 of 0.25, and grown for 3-4 more hours at 30°C for sample preparation, typically reaching OD600 of 0.6-1.0. SLA1 and SLA2 deletion strains were incubated at 25°C and grown for longer times to reach the desired OD600, but otherwise prepared identically. For imaging of Latrunculin A arrested endocytic sites, cells were grown overnight in YPAD but diluted the next morning in SC-Trp to reduce the autofluorescent background for live cell experiments.

54Yeast strains expressing endocytic proteins tagged with mMaple or SNAPftag at their C-termini were generated by homologous recombination using the PCR cassette system in the parental strains MKY0100, MKY0102, MKY0122, MKY1596 and MKY2832. Sla2 was tagged with GFP in a parental strain expressing Ede1-mMaple. Correct integration of the tag was validated by colony PCR and fluorescence microscopy. Tagging plasmids containing the coding sequences of mMaple or SNAPftag were created by replacing the coding sequence of GFP in either pFA6a-EGFP-HIS3MX6 (for histidine auxotrophy as selectable marker) or pFA6a-GFP-hphNT1 (for hygromycin resistance as selectable marker) between the SalI and BamHI restriction sites. The plasmid pMaM173-mMaple for N-terminal tagging was derived in a similar way from pMaM173 by replacing the parts specific for sfGFP using the SalI, NcoI, PacI and BamHI restriction sites. Las17-mMaple was mated with MKY0764 to obtain the SLA2 deletion with Las17-mMaple (JRY0040). JRY0038 was mated with MKY3247 to obtain the BBC1 deletion in Las17-mMaple (JRY0076). The SLA1 deletion with Las17-mMaple and Abp1-GFP (JRY0084) was generated by mating JRY0041 with MKY1596. For N-terminal tagging of Myo5, the protocol for seamless tagging was used. Here, a DNA cassette containing the first 180 bp of mMaple, a selectable marker for the synthesis of uracil surrounded by two I-SceI restriction sites and full-length mMaple is inserted into MKY1743 using homologous recombination. After correct integration of this cassette, the expression of I-SceI is induced by cultivation on plates containing galactose. This leads to an excision of the selectable marker and repair of the resulting double strand break using the fragment of mMaple and full-length mMaple as templates. Successful removal of the cassette is tested by negative selection against the URA3 marker using a 5-FOA plate.

5524 mm round glass coverslips were cleaned overnight in methanol/hydrochloric acid (50/50) while stirring. They were then rinsed repeatedly with water until the pH of the washing solution remained neutral. Subsequently, they were plasma cleaned for 5-10 min. A drop of 20 μL ConA solution (4 mg/mL in PBS) was added to each coverslip, and let incubate for 30 min in a sealed, humidified atmosphere to avoid evaporation. Then, the remaining liquid was removed and the coverslips were dried overnight at 37°C.

56Prior to the day of imaging, yeast cells were inoculated from single colonies on plates into 4 mL YPAD in a glass tube, and grown overnight at 30°C with shaking. The next morning, the culture was rediluted into 10 mL YPAD in a glass flask to OD600 of 0.25, and grown for 3-4 more hours at 30°C for sample preparation, typically reaching OD600 of 0.6-1.0. SLA1 and SLA2 deletion strains were incubated at 25°C and grown for longer times to reach the desired OD600, but otherwise prepared identically.

57Because endocytosis proceeds considerably faster than typical image acquisition times in SMLM, we chemically fixed the cells in order to obtain images with the highest possible spatial resolution. For this, 2 mL of the culture were collected by centrifugation at 500 rcf. for 2.5 min, resuspended in 100 μL YPAD and pipetted on a ConA coated coverslip, which has been briefly rinsed with water. The cells were allowed to settle for 15 min in a humidified atmosphere to prevent evaporation, and protected from light. After settling, the coverslip was directly transferred into the freshly prepared fixation solution containing 4% (w/v) formaldehyde, 2% (w/v) sucrose in PBS. Fixation was allowed to proceed for 15 min at gentle orbital shaking. The coverslip was then incubated for 15 min in 100 mM NH4Cl in PBS to quench remaining aldehyde groups. Quenching was repeated once more, before the coverslip was washed 3 times 5 min in PBS. At this point, the sample was ready for single color superresolution imaging.

58For simultaneous dual-color imaging using mMaple and SNAPftag (Figures 4A, 4C, and 5F), samples were processed further. 300 μL of permeabilization solution (0.25% (v/v) Triton X-100, 50% (v/v) ImageIT FX, in PBS) were added to the coverslip with cells facing up, and the coverslip was slowly agitated on an orbital shaker. The gentle shaking dissociated loosely bound cells from the coverslip, reducing the background. Permeabilization and blocking was allowed to proceed for 30 min, before the coverslip was washed 3 times 5 min in PBS. The coverslip was then transferred face down on a drop of 100 μL staining solution (1 μM SNAP Surface Alexa Fluor 647, 1% (w/v) BSA, 1 mM DTT, 0.25% (v/v) Triton X-100, in PBS) on parafilm. After staining for 2h, the sample was washed 3 times 5 min in PBS.

59For the dual-color imaging of Ede1 and Sla2 (Figure 3E), GFP-tagged Sla2 was stained with nanobodies that are specific for GFP and are conjugated to Alexa Fluor 647 using sortase tagging. Yeast cells on a coverslip were fixed, permeabilized and blocked as described above. Subsequently, the coverslip was transferred face down on a drop of 100 μL nanobody staining solution (anti-GFP nanobody, 1% (w/v) BSA, 0.25% (v/v) Triton X-100, in PBS) on parafilm and incubated for 2 hr in the dark under a humidified atmosphere. After washing the coverslip 3 times for 5 min in PBS the sample was ready for simultaneous imaging of mMaple and Alexa Fluor 647.

60For imaging of Latrunculin A arrested endocytic sites, cells were grown overnight in YPAD but diluted the next morning in SC-Trp to reduce the autofluorescent background for live cell experiments. For live cell imaging, 200 μL of a log phase culture were mixed with 2 μL of 20 mM LatA in DMSO (f.c. 200 μM) and pipetted onto a ConA coated coverslip. After 15 min of incubation to let the cells settle and LatA take effect, the medium was replaced by 200 μL fresh SC-Trp supplemented with 200 μM LatA to further reduce background fluorescence. The arrested endocytic patches were imaged until they clustered too much to distinguish individual sites, which was typically 45 min. As comparison a sample with fixed LatA arrested cells was prepared. For this, 1 mL from the same culture was spun down, resuspended in 100 μL of SC-Trp, supplemented with 200 μM LatA and pipetted onto a ConA coated coverslip. After 10 min, 100 μL of 8% (w/v) formaldehyde in SC-Trp was added onto the coverslip and incubated for another 10 min. Subsequently, the sample was prepared as described above for single color sample preparation by fixation, quenching, and washing.

61All single-color superresolution images were acquired on a custom-built, fully automated microscope, which was built for stable long-term automated image acquisition, and featured homogeneous high power illumination as described previously. The free-space output of a commercial LightHUB laser box with 405 nm, 488 nm, 561 nm and 638 nm laser lines was collimated, focused on a speckle reducer and coupled into a multimode fiber. The output of the fiber was then imaged into the sample to homogenously illuminate a circular area of ∼1000 μm2. Fluorescence was collected through a 160x NA 1.42 TIRF objective, filtered by a bandpass filter (for GFP: 525/50; for mMaple: 600/60), and focused onto an Evolve512D EMCCD camera. The z focus was optically stabilized by total internally reflecting an additional IR laser off the coverslip onto a quadrant photo diode, which was coupled into an electronic feedback loop with the piezo objective positioner. Z focus stability was typically better than 5 nm/h. All microscope components are controlled by a custom-written plugin for μManager.

62For single-color superresolution imaging, samples were mounted in a D2O-based imaging buffer (50 mM Tris-HCl pH 8 in 95% D2O) to improve brightness. After selection of a region of interest, the back focal plane was imaged to ensure that the immersion oil contained no air bubbles. Then, videos of typically 10,000-100,000 frames were acquired using 561 nm illumination at ∼10 kW/cm2 in the specimen plane at 25 ms exposure times with an EM gain of 200. During the experiment, mMaple was sparsely photoconverted to its red state by 405 nm illumination, making sure that single non-overlapping PSFs were observed. Using an automated feedback loop, 405 nm laser power was adjusted to keep a constant number of localizations per frame throughout the experiment. When no more blinking was observed, the experiment was terminated.

63The sample was mounted in imaging buffer and subsequently sealed airtight using parafilm to prevent evaporation of the buffer. For each sample, we first focused on the midplane of yeast cells, and acquired several fields of view to get a qualitative impression about the number and distribution of endocytic sites in each strain. We then adjusted the focal plane to ∼300 nm above the coverslip in order to image endocytic sites at the bottom of the cells. Because endocytic invaginations grow perpendicular to the plasma membrane in yeast, with a small spread around the right angle, and our depth of field is more than 600 nm as determined from bead stacks, this allowed us to obtain two-dimensional projections of endocytic structures along their axis of invagination into the plane of the plasma membrane.

64Using μManager, a grid of 100-500 positions was defined around the center of the stage, with each position spaced 200 μm away in every direction from the next region of interest to avoid cross-excitation and activation of neighboring positions due to scattered laser light. For each grid position, a set of acquisitions was performed automatically, each with a pre-defined set of settings for laser intensities, lens, and filter positions. First, a blinking video was recorded as described above, which was automatically stopped once the 405 nm intensity reached a threshold value, indicating that all mMaple molecules have been imaged and bleached. Subsequently, an image of the back focal plane was recorded to check for air bubbles in the immersion oil.

65For some experiments, mMaple superresolution imaging was combined with diffraction-limited GFP imaging to obtain an additional, diffraction-limited reference signal. GFP has been previously shown to have no substantial cross-talk into the mMaple channel. For this, z stacks of ± 2 μm were recorded in 50 nm steps around the focal plane in the GFP channel after mMaple superresolution imaging was completed. Once all different types of acquisitions were completed for one grid position, the stage was moved to the next one. In between different positions, a waiting time of 15 s allowed for mechanical equilibration after stage movement. The measurement cycle was repeated until all positions were imaged, or the experiment was terminated manually.

66The dual-color images shown in Figures 4 and 5 were acquired on a custom-built microscope with single-mode fiber-based illumination, where the single-mode output of a commercial iChrome MLE laser box with 405 nm, 488 nm, 561 nm and 638 nm laser lines was collimated, focused on the back focal plane of a 60 x NA 1.49 TIRF objective, and adjusted for epi illumination. Fluorescence emission was laterally constricted by a slit, split using a 640 LP dichroic mirror, separately filtered by 600/60 (mMaple signal) and 676/37 (Alexa Fluor 647 signal) bandpass filters, and imaged on two parts of the camera chip of an Ixon Ultra EMCCD camera. Analogous to the setup described above, the z focus was optically stabilized.

67Samples were mounted in thiol-containing blinking buffer with an enzymatic oxygen scavenger (50 mM Tris pH 8, 10 mM NaCl, 10% (w/v) D-glucose, 35 mM cysteamine, 0.5 mg/mL glucose oxidase, 40 μg/mL catalase, in ∼90% D2O). After selection of a region of interest, the back focal plane was imaged to ensure that the immersion oil contained no air bubbles. Then, the sample was illuminated both with 561 nm and 640 nm light, and videos of typically 10,000-100,000 frames were acquired at 30 ms exposure times with an EM gain of 200. During the experiment, 405 nm laser intensity was automatically adjusted to keep a constant number of non-overlapping PSFs as described above. When no more blinking was observed, the experiment was terminated.

68Dual-color images shown in Figure 3E were acquired on the microscope described under Single-color superresolution imaging with the following modifications: The signal of the 2 fluorophores was split using a 640 LP dichroic mirror, separately filtered by 600/60 and 676/37 bandpass filters, and imaged on two parts of the camera chip.

69All data analysis was performed using a custom comprehensive analysis software framework, SMAP (“Superresolution Microscopy Analysis Platform”, unpublished data), which was developed in MATLAB.

70For localization, peaks were detected in the raw images by smoothing, background subtraction using a wavelet filter, and non-maximum suppression. Peaks with intensities above a dynamically determined threshold were then localized by fitting a pixelated Gaussian function with a homogeneous photon background. Fitting of individual PSFs was highly parallelized by using a GPU-based algorithm of a maximum-likelihood estimator for data that is Poisson distributed.

71All experiments were automatically fitted online during the acquisition. During automatic acquisitions, new experiments were automatically detected and subjected to localization.

72All image reconstruction was done in SMAP. Localizations that were found in consecutive frames (a gap of 1 frame was allowed) within a circular range of 75 nm radius were grouped into a single localization.

73Localizations with a localization precision worse than 30 nm and a fitted PSF standard deviation larger than 175 nm were discarded. These cutoffs are loose, and retained the majority of localizations, but efficiently removed dim localizations resulting from autofluorescent background and out-of-focus events.

74All filtered localizations were plotted at their coordinates as normalized Gaussians with a standard deviation proportional to their localization precision. To increase visibility of very precisely localized events, a minimum Gaussian standard deviation of 6 nm was used. To equalize pixels with very high brightness, the contrast was adjusted to saturate 0.01%–0.1% of the brightest intensity values.

75To correct for sample drift during the image acquisition, localizations were sorted according to the frame in which they were detected and binned in ten time windows, for which individual superresolution images were calculated. Then, the pairwise image cross-correlation of all intermediate images with all others was calculated, and spline interpolation was used to calculate the lateral drift trajectory, which was then corrected for. Typically, we observed a lateral drift of 20-100 nm/h. Drift correction was not applied for very short experiments with less than 5000 frames or when the detected lateral drift was below 10 nm.

76In our dual-color imaging, the signals from mMaple and Alexa Fluor 647 were imaged on two separate parts of the camera chip. To overlay both channels, we experimentally determined a transformation function using a calibration bead sample. For the bead sample, we diluted TetraSpeck beads 1:200 in 100 mM MgCl2 on a glass coverslip. We imaged at least 1,000 beads in both channels, localized them, and calculated a projective transformation from their positions. The accuracy of this transformation was better than 10 nm, as judged by the standard deviation of individual bead positions. This transformation was subsequently used to transform the mMaple channel onto the Alexa Fluor 647 channel.

77Datasets that were generated by automatic superresolution imaging typically consisted of 100 to 500 fields of view, and were first subjected to quality control. All individual back focal plane (BFP) images were inspected for air bubbles. If single BFPs showed bubbles, the corresponding fields of view were discarded. If multiple BFPs showed bubbles, the entire dataset was discarded.

78Subsequently, statistics from the individual superresolved images were compared. We analyzed the median localization precision, median fitted photon background, total number of localizations and number of frames for each experiment. If any of those parameters did not remain approximately constant over time, this indicated changes in the sample or imaging conditions, e.g., a change in salt concentration or pH due to buffer evaporation. In this case, the experiment was either entirely discarded, or only the first adequate fields of view were used.

79Cells were segmented in the superresolved images by filtering the image with a large Gaussian blur, and detecting peaks above a user-defined threshold, which was adjusted so that all cells were segmented properly.

80To segment endocytic sites, the superresolved image of the cell was rendered with a pixel size of 200 nm and masked using a user-defined threshold, which was adjusted once for each endocytic protein corresponding to their different abundances. This mask roughly represented the boundary of the cell. Then, a convex hull was drawn around all localizations within this mask, and subsequently constricted by iteratively removing the points on the hull 3 times. The resulting convex hull faithfully enveloped the cellular signal. The convex hull was then shrunk by at least 30% to define the center bottom of the cell, where endocytic sites were then segmented as follows.

81To segment endocytic sites, the superresolved image was rendered with a pixel size of 100 nm. In the filtered image, peaks above a user-defined threshold were picked. This cutoff was adjusted once for each endocytic protein. To avoid closely juxtaposed sites an upper size limit was empirically set, and visually confirmed to not be too restrictive and to only exclude clear double-sites, and no big individual sites. The size range was adjusted once for each protein.

82For clathrin (Clc1 and Chc1), site segmentation was complicated by the fact that in yeast a major fraction of clathrin molecules are found at intracellular membrane compartments, which are often close to the plasma membrane. Thus, we cannot rule out that a minor part of the segmented structures are not actually endocytic sites, but comparably small intracellular compartments, which might confound the structural analysis.

83Endocytic sites in SLA1 and SLA2 deletion strains, in LatA arrested live cell experiments as well as in dual color experiments were picked manually.

84Superresolved images of individual endocytic sites were rendered with a pixel size of 3 nm, and fitted with a geometric model that describes the shape either as ring or as patch, where rings have a hole in their center, around which there is a rim of a certain thickness. Patches do not have holes. Both rings and patches are described by their outer radius rout and the rim thickness dr. Because of their central holes, rings have rout > dr, whereas patches have rout ≤ dr. The model is illustrated below and formally described in Equations 1 and 2, where I(X, Y) is the pixelated image, x0, y0 are the coordinates of the center, rout is the outer radius, dr is the rim thickness, and A is a scaling factor. To account for the expected localization precision, a Gaussian blur with σ = 15 nm is introduced.Least-squares fitting was then performed numerically as shown in Equation 3. We then calculated the radial distribution of the localizations around the fitted center coordinates to obtain the radial profile of individual endocytic sites.

85As we used a low threshold during automatic site segmentation to avoid biases from overly stringent segmentation, the dataset contained a comparably small set of structures with a low number of localizations and a small size on the order of the resolution. Because these structures were too small to obtain geometric information, we excluded structures with outer radii below 30 nm and below 30 localizations, i.e., with less than approximately 10 mMaple proteins, from the analysis. Because structures in the coat and scission modules (Clc1, Chc1, End3, Ent1, Pan1, Rvs167, Sla1, Sla2) mostly formed small structures, we only excluded structures with less than 30 localizations, and did not apply a size threshold. We then aligned the superresolution images and radial profiles of all endocytic sites by their center coordinates, and calculated the average images and radial profiles.

86Proteins of the actin module (Abp1, Arc18, Cap1, Cap2, Crn1, Sac6, Twf1) on average assembled into large structures (outer radius > 80 nm) with a slight minimum in the center of their radial profiles (density at the center is more than 80% of the maximum intensity). Because our images acquired in the equatorial plane (Figure 5) show that the actin network occupies a large, hemispherical volume around the endocytic site, which agrees with previous reports using electron microscopy, we classified these structures as dome-shaped.

87For dual-color bottom-view images (Figures 3 and 4), both colors were analyzed analogously. In the geometric fit, both structures were fitted with common center coordinates (Figure 4), or aligned by the fitted center coordinates of Sla2 (Figure 3).

88To quantify GFP intensity corresponding to superresolved endocytic sites (Figures 3, 4, and 5), we first calculated a maximum intensity projection of the 7 z stack slices around the focal plane. The projected images were corrected for chromatic aberrations between the GFP and mMaple channels using a transformation that was pre-determined using TetraSpeck beads, as described above. The background was calculated using a wavelet filter of level 3, and subtracted from the transformed images. For each endocytic site, the corresponding GFP intensity was determined by fitting the GFP image with three Gaussians: a first one fixed at the center coordinate of the superresolved site, and a second and third one with variable centers at least 350 nm away from the first one and each other to account for potential partial overlap of the diffraction-limited signals from proximal sites, which occurred frequently. If a site was entirely isolated, the amplitude of the second and third Gaussians were negligibly low. To avoid artificially high fitted GFP intensities that result from overlapping GFP signals from more than 2 sites, as was the case mostly in small buds, we excluded endocytic sites from the analysis where the fitted GFP intensity typically was more than 1.5 times the 80th percentile of GFP intensities, which we empirically determined to faithfully exclude the highest GFP intensities. Eventually, we binned sites by their corresponding normalized GFP intensities into a bin with “no GFP” containing all sites with a normalized intensity < 0.1 times the 80th percentile of GFP intensities, and three same-sized bins “low GFP,” “medium GFP” and “high GFP” containing equal share of the remaining sites sorted by GFP intensity.

89Endocytic sites were segmented and rotated manually so that the direction of endocytosis is oriented upward. Then, the structures from both channels were segmented by thresholding and masking. For both channels, localizations were projected on the axis of endocytosis, and centroid and quantiles of the distribution along this axis were calculated. Endocytic sites were then aligned at the bottom by the 5th percentile of the Las17 localizations, laterally aligned manually, and sorted by increasing Abp1 centroid position. The dual color images were rendered, and running window averages were calculated in Fiji using the Running Z-Projector plugin using ‘Average intensity’ and ‘window size 7’. We then compared the resulting averages to time-resolved outer boundaries of the actin network, that were determined as ribosome exclusion zones by CLEM. Using the centroid distances from, we determined that the first of the running window averages corresponds approximately to −7 s, and that the last average corresponds to approximately 1 s. We assumed that the remaining frames are equally spaced in between, and manually overlaid the respective exclusion zone shapes from Figure 7 of, using the bottom of Las17 to align the membrane.

90In brief, the Brownian dynamics simulation contains actin filaments assembled into a 3D network producing forces on the membrane. Filaments are nucleated by Arp2/3 complexes and connected by crosslinkers. The membrane invagination is represented by a movable object of constant shape, to which some actin filaments are bound via connectors mimicking Sla2/Ent1 proteins. All objects diffuse within a cylindrical volume built around an active patch on the plasma membrane, and may associate stochastically upon collision. The mechanical equilibrium of the network is simulated using overdamped Langevin dynamics, thus including Brownian motion and elasticity of the network. Chemical association/dissociations between the components, and filament assembly, are simulated stochastically following a modified Gillespie algorithm, which includes the effect that forces may have on the reaction rates. We describe the elements and methods of simulations in more details below.

91Actin is modeled as slender elastic beams of rigidity κ, hence with a persistence length lp = κ / kB T, where kB T is the thermal energy, κ = 0.08 pNμm2 and thus lp ≈20 μm. The filaments are represented as strings of points separated by a distance s = 5.5 nm, and bending rigidity promotes the alignment of these points. For simplicity, actin filaments are not helical, i.e., they are cylindrical with complete rotational symmetry around their central axis, although they are displayed as helices on the figures for increased realism.

92The model includes steric interaction between actin filaments: two filaments located at a distance d repel each other if d<h, with a force ks(d-h), where h = 8 nm and ks = 20,000 pN/μm. This repulsive force is soft, and extends slightly further than the atomic radius of F-actin of 4.5 nm, as it is meant to represent the electrostatic interactions between filaments, as well as between proteins bound to the filaments, rather than solely the physical radius of actin itself.

93Filaments in Cytosim are confined inside a volume V by adding a force kc (p-x) to every model point x located outside V, where p is the projection of x on the edge of V. By convention in this work, the cell wall (and the membrane before invagination) is located at z = 0, and we used therefore V = { (x,y,z) | z ≥ 0 }. A filament pushing on the cell wall must have some of its model points with z<0, and these points receive a force f = -kc z directed upward. We used a stiffness kc = 50,000 pN/μm, to match the mechanical characteristics of the cell wall in yeast cells, with a published Young Modulus Y ∼120 MPa. The simulation volume was big enough that actin was unconstrained laterally and at the top.

94We assumed that actin filaments assemble only at the barbed end, and implemented a Brownian ratchet model as previously described. Assuming a concentration A1 of free actin monomers, the polymerization rate k+ and depolymerization rate k- for a free actin end is:such that koff /kon = A1∗ is the critical G-actin concentration.

95The Brownian ratchet model predicts the effect of a force f ≥ 0 opposing actin assembly:in which δ ≈2.8 nm is the extension provided by the addition of one monomer. From there, we can define f0 = kB T log(A1/A1∗) / δ as the stall force of actin assembly. Using kon = 400 s-1, koff = 1.4 s-1 and the free actin concentration measured in vivo in fission yeast A1 = 40 μM, one finds f0 ∼9 pN.

96This force is greater than the force measured in vitro, but much lower concentrations of G-actin were used in these experiments, and indeed the stall force depends critically on the concentration of free monomers (A1) such that higher forces are possible in vivo.

97Actin filaments reaching a length of 60 nm are capped, cease growing and remain at this length.

98In yeast endocytosis, the core nucleation activity of Arp2/3 is activated by Las17. In the simulation, we simplified this process by assuming that Arp2/3 is rapidly activated by Las17, and rapidly inactivated once Las17 is released. With these assumptions, Arp2/3 is effectively active only in the “nucleation zone” defined by the localization of Las17. This nucleation zone on the plasma membrane (z = 0) is represented in the simulation as a ring (Ri2 < x2 + y2 < Ro2 ). We used Ri = 10 nm and Ro = 55 nm, slightly smaller than the measured outer radius of Las17 of ∼70 nm. This compensates for the current limitation of Cytosim that prevented us from implementing the true radial density profile of Las17, but restricted us to implementing a simple ring shape where Las17 is homogenously distributed.

99We modeled the gradual build-up of active Arp2/3 after in vivo data: after an initial phase of slow Arp2/3 accumulation (ka0 = 5 s-1), the rate of Arp2/3 addition increases eightfold (ka1 = 40 s-1). For simplicity, we did not include the biochemical feedbacks that could underlie this simple constant accumulation of Arp2/3.

100Arp2/3 is modeled as a complex including a binder and a nucleator. The binder may bind to any filament at any location, and never detaches from this filament. The nucleator is only active if the binder is attached, and in this case creates filaments with a rate knuc.

101The nucleator stays attached to a new actin filament that it nucleated, and remains inactive henceforth. The number of filaments therefore cannot exceed the number of nucleators.

102Mechanically, Arp2/3 entities that are bound to two filaments behave as stiff corner brace with a resting angle of 70 degrees, and angular stiffness of kθ = 1 pN μm/rad and a linear stiffness of 20,000 pN/μm.

103Because this is the only mode of nucleation in the simulation, the network that forms is a single connected “tree,” and with this value of kθ, branch angles are close to 70 degrees.

104Crosslinkers in the endocytic machinery are bivalent complexes composed of two identical passive actin binders. Binders may attach with a rate kon = 10/sec to any filament located within 18 nm, at the closest position, and crosslinkers may thus connect parallel and antiparallel filaments equally. Binders remain at fixed positions and can unbind stochastically following Kramer’s law:Here fu is the unbinding force, koff the unbinding rate in the absence of force, and ku the effective unbinding rate. We used koff = 0.025 s-1 and fu = 10 pN.

105Mechanically, a crosslinker bound to two filaments behaves as a spring of resting length lc = 10 nm and stiffness kx = 5,000 pN/μm.

106In yeast cells, the endocytic actin network is connected to the membrane via a large number of Sla2 proteins, but their biochemical properties are unknown.

107For this model, it appeared sufficient to use a simple approach in which actin is connected to the vesicle by a tether constituted of only three permanent binders, but the stiffness of these binder was set appropriately high kv = 200,000 pN/μm to represent multiple molecular connections. For simplicity, their resting length is zero and they never detach. As the simulation starts, these binders are unattached.

108The remodeling of the membrane by endocytosis involves the interplay between mechanical properties of the coated membrane and the forces generated by the actin cytoskeleton. We have previously studied the mechanics of the membrane while simplifying the actin cytoskeleton to the bare force that it is able to generate. We proceed inversely here, and simplify the membrane mechanics to focus on the actin cytoskeleton. The invagination is represented by an undeformable “cylinder” starting below the plasma membrane, with just three actin-connectors at its tip protruding inside the cell, representing the activity of the Sla2 patch.

109To pull the invagination inward, actin has to overcome turgor pressure and membrane rigidity. Based on our previous estimate, we approximate the force by which the invagination resists, as a function of L, the length of the invagination (with L = 0 corresponding to a flat membrane):This simplified dependence keeps the most important features of the force profile identified previously: a non-zero force f0 is needed to initially lift the membrane; the force increases steadily until a length L0, and vanishes above. This is characteristic of the “snap-through” transition identified in yeast endocytosis. Based on the values obtained by fitting the experimental invagination profiles, we used here f0 = 200 pN, L0 = 60 nm and kΠ such that the force peaks at f0 + kΠ L0 = 1000 pN.

110Endocytosis was considered successful if the invagination reached the distance L0 at which the snap-through transition occurs.

111To obtain the simulated radial distribution of proteins, we monitored the position of simulation elements in 382 centered simulations. When mentioned, we simulated localization precision by adding a normally-distributed random term on the x and y position, with a deviation of 15 nm per axis, i.e., an overall spread of 21.2 nm.

112For the different superresolution experiments at least two biological replicates were performed, in each of which typically images of 1,000-10,000 cells were acquired. In the individual experiments single fields of view were excluded as described in Quality control of automated superresolution imaging or entire experiments were repeated if quality standards were not met.

113To statistically analyze the differences between the outer radii of two datasets, the null hypothesis of equal medians was tested using a Mann-Whitney U test (Wilcoxon rank-sum test, MATLAB function ranksum), which is non-parametric and does not rely on the data following any specific distribution. The definition of the different levels of significance is stated in the figure legends. n denotes the number of analyzed individual endocytic sites and can be found in the figures, the figure legends, the main text or Table S1.

114Hundreds of simulations with the same parameters were run and analyzed, N denotes the numbers of simulations and is indicated in the figures. Their outcomes differ because most events in the simulation are stochastic (only the seed of the random number generator is changed).

115The collection of MATLAB scripts used to reconstruct the superresolution images and to analyze the endocytic sites are available online (https://github.com/jries/SMAP).