Membrane bending begins at any stage of clathrin-coat assembly and defines endocytic dynamics

Clathrin-mediated endocytosis internalizes membrane from the cell surface by reshaping flat regions of membrane into spherical vesicles(1, 2). The relationship between membrane bending and clathrin coatomer assembly has been inferred from electron microscopy and structural biology, without directly visualization of membrane bending dynamics (3–6). This has resulted in two distinct and opposing models for how clathrin bends membrane (7–10). Here, polarized Total Internal Reflection Fluorescence microscopy was improved and combined with electron microscopy, atomic force microscopy, and super-resolution imaging to measure membrane bending during endogenous clathrin and dynamin assembly in living cells. Surprisingly, and not predicted by either model, the timing of membrane bending was variable relative to clathrin assembly. Approximately half of the time, membrane bending occurs at the start of clathrin assembly, in the other half, the onset of membrane bending lags clathrin arrival, and occasionally completely assembled flat clathrin transitions into a pit. Importantly, once the membrane bends, the process proceeds to scission with similar timing. We conclude that the pathway of coatomer formation is versatile and can bend the membrane during or after the assembly of the clathrin lattice. These results highlight the heterogeneity in this fundamental biological process, and provide a more complete nanoscale view of membrane bending dynamics during endocytosis.

immunofluorescence of clathrin light chain combined with platinum-replica correlative electron microscopy to image the structure of even the smallest clathrin-coated assemblies at the plasma membrane of SK-MEL-2 cells (Fig. 1c). The fluorescence signal increased over flat to domed to highly invaginated clathrin structures indicating that clathrin was added throughout pit formation (Fig. 1d). Additionally, the observed clathrin morphologies were heterogeneous and displayed a range of lateral radii (Fig. 1d, and Extended Data Figures 3,4), raising the possibility that clathrin accommodates multiple modes of membrane bending and the addition of new clathrin subunits at different stages (11,12). Measuring the dynamics of membrane bending during clathrin assembly at single endocytic sites in living cells is required to distinguish the possible modes of membrane bending.
Polarized Total Internal Reflection Fluorescence (pol-TIRF) microscopy generates contrast between vertical and horizontal DiI-C18 labeled plasma membrane in living cells (13)(14)(15). Pol-TIRF has been used to image changes in membrane topography during exocytosis of chromaffin granules, which are much larger than CME sites (16)(17)(18). We improved upon these methods by developing a microscope capable of creating pol-TIRF fields that were parallel (spol, S) or perpendicular (p-pol, P) to the coverslip with improved spatial uniformity by averaging multiple illumination directions (19,20) (Extended Data Figure 2). These P and S fields were used to selectively excite DiI molecules in vertical or horizontal membrane respectively, thereby encoding membrane topography into the ratio of P/S fluorescence images from DiI (Fig. 2a). A computer simulation of pol-TIRF for the formation of 100 nm vesicles by either model (Fig. 1a, b) predicted that the P/S image was sensitive to small changes in membrane bending (Fig. 2c).
Although the simulation predicted small differences between the two CME models, these models can be readily distinguished by comparing P/S with the arrival of clathrin (Fig. 2b, and Extended Data Figure 1). For membrane bending during assembly, clathrin and P/S increase together as the pit forms (Fig. 2b). Conversely, for the model in which flat clathrin is reshaped into a sphere, the clathrin intensity is maximal prior to changes in P/S and then decreases as bending moves the top of the pit deeper in the exponentially decaying TIRF field (Fig. 2b, and Extended Data Figure   1). We considered the possibility that detection of the P/S signal would be less sensitive than detection of fluorescent clathrin arrival, thereby creating an apparent temporal delay between clathrin arrival and membrane bending. However, simulations of P/S and clathrin over a range of signal-to-noise ratios (SNR) indicated that detection of P/S is weakly dependent on the SNR and that the two models are distinguishable over a wide range of SNRs encountered in live-cell imaging (Fig. 2b, and Extended Data Figure 1).
We validated pol-TIRF's sensitivity to membrane bending during CME by correlative light and electron (CLEM) and light and atomic force microscopy (CLAFM). In pol-TIRF-CLEM, endogenous clathrin-Tq2 fluorescence colocalized with the expected clathrin ultrastructure (Fig. 2d), and corresponding P/S signals were observed on individual clathrincoated pits over a range of invagination stages (Fig. 2e). Importantly, P/S increased with pit stage as determined by morphology (Extended Data Figure 3), and with pit heights determined from TEM tomograms (Fig. 2h, ρ = 0.548, p<0.001, and Extended Data Figure 4). Pol-TIRF-CLAFM on wet samples confirmed pol-TIRF's sensitivity for membrane bending, despite the reduced resolution achieved by AFM owing to the softness of biological membranes.
Specifically, the endogenous clathrin-Tq2 and P/S overlaid with peaks in the AFM images ( Fig.   2f, g), and pit height and P/S were positively correlated (Fig. 2h, ρ = 0.351, p<0.001, and Extended Data Figure 4). Variations in CLEM and CLAFM measurements and topographical features near the measured pit were responsible for variability in P/S ratio quantification (Fig. 2h, and Extended Data Figure 4). Therefore, pol-TIRF is sensitive to membrane bending on the scale of CME.
Given that pol-TIRF could reliably detect nanoscale changes in membrane bending, we recorded the dynamics of membrane bending on single endocytic events in SK-MEL-2 cells labeled with DiI that endogenously express clathrin-Tq2 and dynamin2-eGFP (Extended Data Figure 5 and movies S1, S2). Single diffraction-limited endocytic events were tracked(21), filtered to retain only those that contained isolated clathrin, dynamin, and P/S events, and categorized based on detection of membrane bending relative to clathrin arrival (Fig. 3). The reliability of the detection of P/S relative to clathrin arrival can be seen in the example traces (Extended Data . From these cells, approximately 7,100 tracks had clathrin-Tq2 signatures that appeared and disappeared during the time of imaging. Of these tracks, 481 were selected for analysis based on a set of criteria, the most stringent of which were the absence of adjacent membrane curvature in the P/S image and a dynamin signature (Extended Data Figure   6a). In approximately half of the CME events, membrane bending was detected at the moment clathrin arrived and grew in intensity (Fig. 3a, Class 1), consistent with bending during assembly.
In the other half of the events, clathrin accumulated prior to detection of membrane bending (Fig.   3b, c). The delayed bending group was divided into two categories -a small subset in which all of the clathrin accumulated at the endocytic site prior to membrane bending (Fig. 3b, Class 2) and a larger group in which some clathrin accumulated prior to bending, but more clathrin was added during membrane bending (Fig. 3c, Class 3). The relative proportions of these events were Class 1 (43%), Class 2 (14%), and Class 3 (43%) (Fig. 3d). Thus, within the same cell, clathrin assembly and membrane bending occurs with heterogeneous timing with the clathrin coat accommodating several modes of membrane bending.
A population view of membrane bending dynamics during CME revealed a variable delay between clathrin assembly and the onset of membrane bending. We observed that the clathrin lifetimes for Class 1 events were shorter than Class 2 and 3 events (Class 1 (80±42 s), Fig. 4a). Unlike clathrin, the lifetimes of membrane bending and of dynamin showed no statistical differences across classes (Fig. 4a), indicating the dynamics of these processes are identical regardless of class. This suggested Class 2/3 events had a delay in progression that was not present in Class 1 events. Delays of unknown mechanism have been suggested for CME (22) and a checkpoint related to membrane bending has been proposed (21).
In comparison with class 1, class2/3 events lagged behind the start of clathrin assembly with Δt = 25.5 s (Fig. 4b). This same mean delay was also observed when comparing the lag for dynamin between class 1 and class 2/3 (Δt = 24.1s) (Fig. 4b). We observed minimal differences between the dyanimin lag from P/S initiation across the classes (Δt = 0.2 s, Fig. 4b), indicating that the principle difference in lifetime for the two classes arose during the time that clathrin began to assemble and the onset of membrane bending (Fig. 4c).
These results raise the possibility that the initial moments of clathrin association with the plasma membrane determine whether bending will begin immediately or if a flat intermediate state will occur. Correlative dSTORM-platinum replica TEM of clathrin structures containing only a few triskelia revealed both flat and curved morphologies (Fig. 1c), consistent with a bifurcation for entry into either Class 1 or Class 2/3 occurring early in the assembly process.
Factors that influence this bifurcation could include the shape of the membrane at the moment clathrin binds, lateral membrane tension(23), curvature sensing/generating proteins (24), the stabilization of the curved state by additional factors such as AP2 (25), or engagement of the actin cytoskeleton (22). Consistent with a stabilization step being required, we observed many short-lived (<18 sec) flat clathrin associations that did not recruit dynamin (Extended Data Figure 6bd). Close inspection of the CME events did not reveal any examples of P/S signals that preceded clathrin association, suggesting that either initial membrane topography was not a factor in defining the sites at which clathrin assembled or that the scale of membrane bending needed to recruit clathrin was below what could be detected by pol-TIRF. Essentially, all CME structures that acquired P/S, acquired dynamin, indicating that once membrane bending starts, progression to a vesicle is a robust process (Fig. 4b). Thus, within the same cell, clathrin bends membrane through multiple heterogenous pathways in which the initiation of curvature is a key rate limiting step (Fig. 4c).

Reagents
St. Louis, MO) was dissolved in DMSO to prepare a 1 mg/mL stock. Cells were labeled using 1 µg/mL DiI in 2.5% DMSO/dPBS. Imaging buffer was sterile 1x Dulbecco's PBS with calcium and magnesium added (ThermoFisher, Rochester, NY) supplemented with 5mM glucose (Mediatech) and 10 mM Hepes (ThermoFisher). 100 µl DiI solution was added dropwise to 1 ml of imaging buffer and mixed by pipetting for less than 30 seconds and subsequently washed 3 times in imaging buffer and visualized by polarized TIRF immediately for no more than 30 minutes. Cells were imaged if p-polarized excitation intensities were less than 3000 to ensure that dynamics were not altered.  Back-focal plane centering. In order to determine the center of the objective lens' optical axis, a calibration was carried out daily and for each chamber used in data acquisition. This centering calibration ensured that the excitation laser light encountered the glass/cell interface with a single incidence angle and, hence, produced a single TIRF excitation volume. A calibration protocol was used that steered the laser to positive and negative mirror positions, and thus incidence angles, with a small increment (1002 total steps), the intensity of the reflected light from the glass/water interface was read on a commercial quadrant photodiode module.
Intensity values were plotted as a function of mirror position and the half-maximal values were used to adjust the mirror angles to center the optical axis (Extended Data Figure 2).
Fiducial data collection and image registration. Images were registered using calibration images acquired simultaneously on each of the three EMCCD detectors. Briefly, 200 nm green beads (Life Technologies, Carlsbad, CA) immobilized on a glass coverslip were excited using to create a well-sampled grid. Beads were localized in each channel and a polynomial transformation was determined to overlay each of the red and blue camera data onto that of the green detector. Because two excitation mirrors were used during the experiment fine tuning of the registration was completed using clathrin and dynamin spots that nearly correlate following the bead-based registration. Spots were identified, the inverse transformation was applied to obtain the original coordinates of the objects, and the subpixel positions were found by fitting to a 2D Gaussian. These points served as the fiducials for the final rigid affine transformation.

Simulation.
To predict the quantitative relationships between clathrin assembly and membrane bending signals from pol-TIRF, we created a discrete 3D simulation in MATLAB (The MathWorks Inc, Natick, MA) and DIPimage toolbox version 2.8 (Delft University of Technology, Delft, The Netherlands), building on our previous work for 3D microscopy simulations (19,26,27). The plasma membrane was represented as a plane that could either be bent into a sphere via a fixed radius of curvature (Fig. 1a, Extended Data Figure 1) or through progressive bending (Fig. 1b, Extended Data Figure 1), forming a vesicle of diameter = 100 nm.
For membrane bending during assembly, the forming clathrin pit was modeled as a sphere of fixed radius (r=50 nm) intersecting a plane. By shifting the center of the sphere along the zdirection we obtain the topographies outlined in Extended Data Figure 1a. In this case, clathrin is assumed to cover the spherical cap and ultimately the spherical vesicle. In the case of clathrin assembly preceding curvature, the pit is modeled as a circular patch of membrane emanating from the plane of plasma membrane. Here, the circular patch is designated to have uniform lateral clathrin intensity and the sphere is translated vertically over a progression of discrete radii. Thus, the vertical shift was set to z shift = Area/2π/r i , where r i ranged from 25,000 nm (slightly bent) to 50 nm (fully formed sphere). This produced the progression in outlined in Extended Data Figure 1b.
The fluorophores were modeled relative to each discrete element of plasma membrane or clathrin coat. Since 360 TIRF illumination was used for the clathrin images, no orientation dependencies were modeled. Thus, the equation defining the 2-dimensional clathrin image is given by, Where, I c is the 3D (x,y,z) distribution of clathrin during pit stage k, d is the penetration depth of the TIRF field (100 nm), the microscope point spread function was modeled as a Gaussian distribution of with full width half max of 211 nm, typical of a 1.49 NA objective lens.
Detection noise (N) was modeled by drawing intensities from a Poisson distribution.
Simulation of the pol-TIRF signals was achieved using the pol-TIRF fluorophore excitation equations of Axelrod and Anatharam(13) for the relative contributions of a plane and a sphere.
Based on this work, we assume that the depth-dependent detection of emitted polarizations in the near field was approximately constant for a 1.49 NA objective and could therefore be neglected.
Thus, using our discrete model, the polarization for a growing pit could be described as a plane and spherical components excited by either p-pol or s-pol illumination.
Where, spherical coordinates (θ,ϕ) are defined relative to the center of the sphere, β is the angle between the dipole moment of DiI and the plane, I pla and I sph are the intensities/unit membrane in the plane and sphere (assumed equal). Beta was determined by measuring planar regions of the plasma membrane and measuring the regional minimum which was found to be 0.26, which sets β=70°, which is nearly identical to the 69° value measured by Anantharam et al (13).  First, coverslips were rinsed in stabilization buffer (70 mM KCl, 30 mM HEPES brought to pH 7.4 with KOH, 5 mM MgCl2) for 2 minutes and unroofed by sonication in 2% paraformaldehyde (PFA) in stabilization buffer. They were then fixed in 2% PFA for 20 minutes. After rinsing with PBS, cells were placed in blocking buffer (3% bovine serum albumin in PBS) for one hour. They were immunolabeled with 11 nM Alexa Fluor 647 labeled GFP nanotrap (preparation described below) in blocking buffer for 45 minutes, rinsed in PBS, and post-fixed in 2% PFA for 20 minutes. Coverslips were then imaged in a sealed chamber containing blinking buffer (10% w/v glucose, 0.8 mg/mL glucose oxidase, 0.04 mg/mL catalase, 100mM 2-mercaptoethanol made fresh in PBS immediately before imaging). dSTORM was performed on a Nikon NSTORM system with 10 kW/cm 2 647 nm laser in TIRF illumination with 30,000 10 ms frames. A final image was created with Nikon Elements NSTORM analysis software with 5 nm pixel spacing.
After imaging, coverslips were marked with a diamond objective marker (Leica 11505059).
The oil was cleaned off of the coverslip with 80 % ethanol. They were then stored in 2% glutaraldehyde in PBS and processed for EM the following day. EM processing and imaging was performed as described above. The gold nanoparticles that were embedded in the coverslips were visible in both dSTORM and EM and were therefore used as spatial fiducial markers. Three gold nanoparticles were used to map the fluorescence onto the EM image using an affine spatial transformation and nearest neighbor interpolation.
GFP nanotrap was expressed and purified as previously described (29). It was then labeled with Alexa Fluor 647 NHS ester (ThermoFisher 37573) using 2.4 molecules of dye for every one nanobody. These were purified using size exclusion chromatography and concentrated to 11 µM.