The nanoscale organization of reticulon 4 shapes local endoplasmic reticulum structure in situ

Fuentes and Marin et al. show that Rtn4 forms linear-shaped oligomers containing an average of five Rtn4 proteins that localize to the sides of elliptical tubules with orientations parallel to the tubule axis. These oligomers increase local curvature in the ER membrane by increasing local Rtn4 density.


Introduction
The endoplasmic reticulum (ER) is the site of several critical cellular functions. These include the morphological regulation of other organelles by ER tubules (Abrisch et al., 2020;Friedman et al., 2011;Hoyer et al., 2018;Zheng et al., 2022), protein translation on rough ER sheets (Jan et al., 2014;Shibata et al., 2010;West et al., 2011), and lipid biogenesis in the tubule-rich ER-Golgi intermediate compartment (Glick and Nakano, 2009). The ER morphology adapts to the needs of different cell types, displaying expansive sheets for enhanced protein expression and secretion or highly tubular ER in the case of androgen production (Lee et al., 2005;Zirkin and Papadopoulos, 2018). This critical link between the ER structure and function has been made clear as disrupting the specialized processes of the ER in these cells consistently leads to perturbed ER structure (Lee et al., 2005;Zirkin and Papadopoulos, 2018). Recently, ER structure has been strongly linked to disease markers for obesity and diabetes in liver tissues by the remarkable discovery that these markers can be rescued to levels of non-diseased tissues by manipulation of ER structure alone (Parlakgül et al., 2022).
Investigations of ER morphology are, however, complicated by the fact that the sizes of typical ER features are below the diffraction limit of standard light microscopes. Studies making use of super-resolution microscopy (Nixon-Abell et al., 2016;Schroeder et al., 2019;Wang et al., 2022) or electron microscopy (Puhka et al., 2012;Terasaki et al., 2013;Zamponi et al., 2022) methods have highlighted the fact that the ER structure is more complex than once thought, as structural details of the ER were not fully appreciated when visualized with conventional light microscopy methods. For example, what were once thought to be continuous ER sheets have been revealed to often be intricate tubular matrices (Nixon-Abell et al., 2016) and sheets containing dynamic nanoholes (Schroeder et al., 2019).
The reticulon (Rtn) and REEPs/DP1/Yop1p protein families are known to be responsible for stabilizing curvature in the ER membrane (Voeltz et al., 2006;Hu et al., 2008). Both protein families possess reticulon homology domains (RHD) with hairpin topologies that do not completely pass through the membrane bilayer (Voeltz et al., 2006;Zurek et al., 2011). This results in the proteins forming wedges in the ER membrane that displace more phospholipids in the cytosolic leaflet than the luminal leaflet. This wedging mechanism is likely a major contributor to the membrane-curving function of these proteins. REEPs/DP1/Yop1p have been shown to form dimers that may organize into a splayed conformation to promote membrane curvature (Wang et al., 2021). However, reticulons and REEPs/DP1/Yop1p have also been shown to form higher-order homo-oligomers in vitro, and it was proposed that these oligomers form arches in the membrane to scaffold it into a curved topology Hu et al., 2008). Due to the difficulty of visualizing such structures at the size scale of tens of nanometers, neither model has been confirmed yet by direct visualization of these complexes.
Reticulon 4 (Rtn4) is one of the best-studied proteins among the reticulon and REEPs/DP1/Yop1p families of proteins. In addition to its well-known partitioning to tubules and sheet edges (Shibata et al., 2010;Voeltz et al., 2006), Rtn4 generally localizes to areas of higher membrane curvature (Kiseleva et al., 2007) and nanoholes within ER sheets (Schroeder et al., 2019). In wider tubules, it also displays two parallel lines along their sides (Wang et al., 2022). Rtn4's several isoforms all possess a C-terminal RHD (Oertle and Schwab, 2003;Yang and Strittmatter, 2007;Schroeder et al., 2019) that is important for its localization as well as Rtn4's ability to curve membranes, which suggests all RHD-containing proteins share a general mechanism for shaping membranes , though the exact mechanism remains unclear.
In this study, we set out to understand how Rtn4 proteins are organized at the nanoscale in situ to enable their membranecurving function and how that organization affects the local ER structure. We make use of a suite of recently developed software tools (Barentine et al., 2018;Thevathasan et al., 2019;Marin et al., 2021Marin et al., , 2023 and super-resolution methods (Zhang et al., 2020;Chung et al., 2022) to accomplish this. Our results lead us to propose a refined model for Rtn4 localization, organization, and its effect on tubule shape.

Results and discussion
Rtn4 density determines local ER membrane curvature We first set out to understand how Rtn4's distribution and local abundance can affect ER structure. Using live-cell stimulated emission depletion (STED) microscopy, we imaged Rtn4 endogenously tagged with HaloTag at its C-terminus, which is shared by all Rtn4 isoforms, via CRISPR Cas9 gene editing (Fig.  S1, A-C). We additionally overexpressed Sec61β, an ER membrane protein, tagged with SNAP-tag to provide information about the underlying ER structure. Analysis of the difference in Rtn4 pixel intensities along tubules revealed that Rtn4 is significantly more abundant in tubules at the outer periphery of the cell than in those that are closer to the nucleus (Fig. 1, A and B), whereas a similar analysis of Sec61β pixel intensities in U-2 OS cells overexpressing Sec61β showed the opposite distribution ( Fig. S1 G). We asked if this discrepancy in the abundance of Rtn4 in different regions of the ER is correlated with differences in the underlying structures. Specifically, we hypothesized that more Rtn4 present in a tubule leads to a smaller tubule diameter. From our live-cell STED images, we measured the diameters of peripheral ER tubules and compared them with the diameters of perinuclear tubules using our previously developed NEP-Fitting tool (Barentine et al., 2018). The peripheral (Rtn4-enriched) tubules displayed significantly smaller diameters on average (Fig. 1, C and D), consistent with our hypothesis and the observed distribution of Sec61β (Fig. S1 G). However, to ensure that this difference in tubule diameters was due to varying amounts of Rtn4 alone, we imaged overexpressed Sec61β tagged with HaloTag in both live U-2 OS and live U-2 OS Rtn4 knock-out cells (Schroeder et al., 2019) and compared the diameters of their ER tubules ( Fig. 1, E-G). Our analysis showed a significant difference between them with U-2 OS and U-2 OS Rtn4 knock-out cells possessing 94-and 119-nm diameter tubules on average, respectively. Emerging studies suggest that Rtn4's effect on tubule size has a direct impact on the ER's ability to deliver Ca 2+ and thus axonogenesis (Konno et al., 2021 Preprint). Altogether, these results strongly suggest that higher Rtn4 abundance leads to thinner tubule diameters, consistent with earlier findings of in vitro studies .
We next investigated how the density of Rtn4 affects ER nanostructure locally by imaging endogenous Rtn4 and overexpressed mCherry-Sec61β in U-2 OS cells using 3D singlemolecule localization microscopy (3D-SMLM; Huang et al., 2016;Zhang et al., 2020). We generated accurate 3D surfaces (Marin et al., 2023) based on the Sec61β point cloud to serve as a proxy for the ER membrane ( Fig. 2 A and Video 1) and calculated the mean surface curvature (Fig. 2 B) and Rtn4 density within 50 nm of each vertex on the surface (Fig. 2 C and Fig. S2). Locations of high Rtn4 density consistently correlate with locations of high mean curvature (Fig. 2,B and C;blue arrowheads). To support this observation quantitatively, we examined Rtn4 density as a function of the local curvature on the 3D surface (the maximal principal curvature at each vertex on a tubule). We normalized the Rtn4 density by the frequency of the maximal principal curvatures on nearby surface vertices. This analysis revealed that as the maximal principal curvature increases, so does the Rtn4 density (Fig. 2 D). The Rtn4 density peaks at a curvature of 0.073 nm −1 , which translates to a tubule diameter of ∼27 nm. These results suggest that the local density of Rtn4 has a significant role in determining the local membrane curvature.
ER tubules have elliptical cross-sections, and Rtn4 localizes to their sides In our 3D data, Rtn4 also appeared to prefer the sides of tubules, in the x-y plane of the sample, over the tops and bottoms of them ( Fig. 2 A), supporting a recently reported observation (Wang et al., 2022). Most ER models depict tubules with circular cross-sections (Goyal and Blackstone, 2013;Georgiades et al., 2017;Shibata et al., 2010;Wang and Rapoport, 2019;Chen et al., 2013;Lin et al., 2012;Shemesh et al., 2014;Obara et al., 2022;Hu et al., 2008), and one would expect a random distribution of Rtn4 around such tubules. However, as recently suggested (Wang et al., 2022), tubules with elliptical cross-sections, where Rtn4 preferentially locates to the regions of higher membrane curvature, could explain our observation. To investigate this in more detail, we considered four possible models (Fig. 3 A). To test which of these models is consistent with our data, we used 3D-SMLM to investigate the spatial distribution of Rtn4, Sec61β, and KDEL in tubule cross-sections. Each sample was labeled with a nanobody, whose localizations were used to generate 3D surfaces, and primary and secondary antibodies, whose localizations were used to analyze the proteins' spatial distribution. The 3D surfaces were subsequently used to create "skeletons" of the ER networks by applying mean curvature flow (Tagliasacchi et al., 2012;Fig. S2 E; see Materials and methods). These skeletons provide critical information about the center and major axis of each tubule in the datasets (Fig. 3, B-D). Using this information, we calculated the angular position of each protein in tubule cross-sections relative to the z-axis of the sample (normal to the coverslip). We refer to these angles as the cross-sectional angles φ (Fig. 3 A; model [i]). We compared the distributions of φ for the three proteins to that of simulated points randomly distributed in a circle around the skeletons (Fig. 3, E-G and Fig. S2 F). We found that Rtn4, Sec61β, and KDEL are all enriched around ±90°from the z-direction of the crosssections when compared with simulated random distributions. To show that these results are not an artifact caused by the large size of primary and secondary antibodies, we repeated the φ analysis on the nanobody localizations of Sec61β and KDEL and observed similar results (Fig. S3, B and C). Since KDEL is localized to the ER lumen and no preference of Sec61β for specific membrane topology has been reported, we conclude from this observation that ER tubules are on average elliptical in  shape, ruling out the first two models. Additionally, the three φ distributions are significantly different from each other with Rtn4 being the most enriched at the sides, followed by Sec61β and then KDEL ( Fig. S3 A). The only model that is consistent with these observations is model (iv; Fig. 3 A), i.e., tubules with elliptical cross-sections and Rtn4 localized to the sides where the local curvature is highest. Indeed, visualizing cross-sections of tubules in our two-color 3D-SMLM data of Rtn4 and Sec61β revealed cross-sections with elliptical shapes and distributions of these two proteins, consistent with model (iv; Fig. 3, H-N).
Rtn4 oligomers contain an average of five copies A visual comparison of Sec61β and Rtn4 point clouds from our 3D SMLM data of ER tubules clearly shows Rtn4 being clustered while Sec61β appears diffusely localized (Fig. S4), supporting earlier reports of Rtn4 oligomerization . To gain insight into the organization of individual Rtn4 oligomers, we determined how many copies are in a typical oligomer using the powerful SMLM variant of fluorogenic DNA-PAINT (Chung et al., 2022) and single-molecule counting. Following an established procedure (Thevathasan et al., 2019), we used nucleoporin Nup96 as a standard to resolve the complications of single molecule counting . We mixed a U-2 OS Nup96-mEGFP cell line (   and confirms that Rtn4 also forms oligomers around this size in situ.

Rtn4 forms linear-shaped clusters enriched at orientations near parallel to the tubule axis
We next sought to understand how Rtn4 oligomers are organized in the ER membrane. We used DBSCAN on the 3D Rtn4 point clouds to segment the localizations into clusters ( Fig. 5 A and Video 2). Analysis of φ for the centers of each cluster (Fig. 5  B) showed a similar result to the angular distribution of the Rtn4 localizations directly (Fig. 3 E). We next used principal component analysis (PCA; Jollife and Cadima, 2016) to determine the principal axis of each cluster with the highest eigenvalue, which we refer to as the major axis. PCA also allowed us to analyze the shape of Rtn4 clusters by comparing the anisotropy of observed clusters to simulated clusters that were circular-or linearshaped (Fig. 5,C and D; and Videos 3 and 4). The observed clusters had anisotropy distributions much more similar to the linear-shaped simulated clusters than the circular-shaped ones (Fig. 5 E). This suggests that the Rtn4 oligomers are organized linearly with discernable major axes. The clusters clearly did not consistently appear as arches oriented orthogonal to the tubule axis Hu et al., 2008), which led us to ask if the clusters' major axes adopted consistent orientations relative to the tubule axes. To help answer this question, we simulated clusters with randomly oriented major axes that are tangential to the ER surface (Fig. 5 F and Video 5). We further projected the vectors of the major axes of the observed clusters onto a plane approximately tangential to the 3D surface (Fig. 5 G;red vector) and calculated the angles ψ between them and vectors in the same plane but perpendicular to the tubule axis (Fig. 5 G; blue vector). Comparing the distributions of ψ for the observed and simulated clusters shows that the observed clusters are strongly enriched at orientations close to parallel with the tubule axis (±90°) and depleted at orientations close to orthogonal to the tubule axis (Fig. 5 H). This orientation preference of the observed clusters only disappears when limiting the analysis to the smallest clusters where the cluster orientations cannot be resolved by our microscope (Fig. S5 A). Plotting φ against ψ, we also see that the orientation of the clusters does not depend on where the clusters are located on the tubules (Fig. S5 B). Our findings in this study culminate in a refined model of Rtn4 organization, localization, and the resulting shape of ER tubules (Fig. 5 I).
With elliptical tubules, the line between what is a tubule and what is a sheet becomes blurred. Recent studies of ER structure have made it clear that this differentiation is not as binary as once thought. Instead, the ER displays a spectrum of morphologies (Nixon-Abell et al., 2016;Schroeder et al., 2019;Puhka et al., 2012). Thus, it may be more appropriate to think of the ER as being composed of a spectrum of sheets including continuous sheets, fenestrated sheets, and now (structurally speaking) very narrow sheets, referred to as ribbon-like ER sheets by Wang et al. (2022), that have traditionally been thought of as tubules.
We consistently observed the major axes of elliptical tubule cross-sections lying in the x-y plane. We do not believe this to be universally true, but rather a side effect of focusing our imaging efforts in the lamellipodia of very flat cells restricting the tubules.
It was recently suggested that ER tubules exist in two distinct forms with consistent diameters of ∼105 and ∼50 nm, with U-2 OS cells' tubules existing predominantly in the ∼105-nm form (Wang et al., 2022). However, our diameter measurements here and in previous analyses (Barentine et al., 2018;Schroeder et al., 2019) do not show consistent narrowly distributed tubule measurements with peaks around these values. Instead, they show broad ranges that include tubules with ∼105 and ∼50 nm amongst many other sizes. However, this may be explained by differing methods. Our approach used Sec61β as an ER membrane proxy since it is a better general ER membrane marker than Rtn4 and an established tool to measure the tubule diameters (Barentine et al., 2018).
We have also shown that Rtn4 organizes into oligomers of around five copies of the protein. However, it is not strictly a pentamer. As our results show, there is a distribution of sizes. To get a sense of how monomers of Rtn4 are organized within an oligomer, we simulated point clouds of Rtn4 oligomers possessing specific distances between monomers positioned in a line (see Materials and methods) and compared their anisotropies to those of observed Rtn4 oligomers (Fig. S6). We calculated the theoretical diameter of Rtn4b molecules to be ∼4.5 nm (see Materials and methods), assuming they are roughly spherical. Using this value as the intermonomer distance in the simulation resulted in remarkably similar distributions between the observed and simulated clusters' anisotropies ( Fig. S6 C), while simulations for half or double that distance showed strong discrepancies (Fig. S6, A and D). Decreasing the intermonomer distance to 3.75 nm resulted in a nearly perfect overlap between simulation and experimental results (Fig. S6 B). This simple simulation supports the idea that Rtn4 oligomers are composed of monomers that roughly organize in a linear fashion. Additionally, using this theoretical ∼4.5 nm diameter and the surface area of our 3D surfaces, we estimate that Rtn4 proteins occupy about 4% of the ER membrane surface area (see Materials and methods). Until now, it was attractive to think that Rtn4 oligomers formed arches around tubules and sheet edges to scaffold the membrane into a curvature Hu et al., 2008). However, we have seen the majority of oligomers at  orientations near parallel to tubule axes, which is the opposite of what one would expect for arching oligomeric scaffolds. Our results are also inconsistent with the possibility of Rtn4 forming splayed dimers (Wang et al., 2021). We, therefore, believe that the oligomerization of Rtn4 in and of itself does not contribute to membrane curvature and instead serves as a mechanism to increase local Rtn4 concentration, which our results show correlates with higher curvature. This further supports a model in which the membrane curvature is primarily induced by a hairpin wedging mechanism Voeltz et al., 2006). This explains both the importance of Rtn4's oligomerization and the lack of its oligomers orienting in a way that would be amenable to a scaffolding mechanism. Consistent with this idea, long transmembrane domain mutants of Rtn4's RHD have been reported to still form oligomers while lacking the ability to curve the ER membrane . We assume that the membrane curvature generated by Rtn4 monomers is in a single direction and that they are oriented in a specific direction within oligomers. Considering that oligomers preferentially orient parallel to the tubule axis, this model suggests that Rtn4 monomers generate curvature in the direction perpendicular to the major axis of oligomers. Given Rtn4's shared characteristics with other known ER membrane-curving proteins Voeltz et al., 2006;Shibata et al., 2008;Hu et al., 2008), it is reasonable to think that this model could be generalized to all RHD-containing proteins as they seem to have some functional redundancy. However, this still needs to be confirmed experimentally and is an interesting future direction.

CRISPR gene editing
The U-2 OS Rtn4-Halo cell line was developed using Cas9 gene editing. Though we expect U-2 OS cells to have high expression of Rtn4b and little to no expression of the other isoforms (Oertle and Schwab, 2003; Uniprot Q9NQC3), we approached the CRISPR gene-editing in a way that would tag all isoforms. Since all Rtn4 isoforms share the same C-terminus, we opted to add the HaloTag to the C-terminus. This ensures that all Rtn4 isoforms expressed in U-2 OS cells will possess the appropriate tag. A gRNA described previously to generate a U-2 OS Rtn4-SNAP cell line was used in the generation of this cell line as well (59-AAACGCCCAAAATAATTAGTAGG-39; the PAM site is underlined; Schroeder et al., 2019). The homology-dependent repair (HDR) template, containing ∼1 kb homology arms from that study, was modified to replace the SNAP-tag sequence with the HaloTag sequence. This was accomplished by using a two-fragment Gibson Assembly using a NEBuilder reaction (E5520S; New England Biolabs). The fragments were amplified using PCR with the following primers (uppercase indicates Gibson overlapping bases): Halo-Forward: 59-GTCGCCACCATGGCAGAAATCGGTACTGG-39 Halo-Reverse: 59-GCTTTAGCCGGAAATCTCGAGCGTC-39 Vector-Forward: 59-CGAGATTTCCGGCTAAAGCGGCCGCGACTC TAGATC-39 Vector-Reverse: 59-ATTTCTGCCATGGTGGCGACCGGTGGATC-39. U-2 OS (HTB-96; Lot #70008732; ATCC) were transfected with the gRNA, HaloTag HDR template, and pSpCas9 (48137; Addgene) via Lipofectamine 2000 in the well of a six-well plate. Transfected cells were expanded for 1 wk before selection with G418 began. After 9 d of selection, cells were labeled with SiRchloroalkane for 1 h followed by 3× washes with warm media and a 1-h recovery at 37°C. The cells were immediately sorted using FACS to obtain monoclonal cell lines. Cells were first screened visually for fluorescence consistent with Rtn4 localization. Then the success and zygosity of gene editing were assessed by Western blotting.
The U-2 OS Rtn4-mEGFP cell line was developed using Cas9 nickase D10A to increase the chances of developing a homozygously tagged cell line (Koch et al., 2018). For the reasons U-2 OS (HTB-96; Lot #70008732; ATCC) were transfected with the pX335-U6-Chimeric-sense-gRNA, pX335-U6-Chimericantisense-gRNA, and mEGFP HDR template plasmids using Jet-Prime (114-07; Polyplus transfection). Cells were expanded for 6 d before sorting with FACS to obtain monoclonal cell lines. Cells were expanded after FACS for 3 wk before visually screening for fluorescence consistent with Rtn4 localization. The success and zygosity of gene editing were assessed by Western blotting.
Western blotting U-2 OS, U-2 OS Rtn4-Halo, U-2 OS Rtn4-mEGFP, and U-2 OS Rtn4-Knockout (KO) cells were seeded into the wells of six-well plates (∼350,000 cells per well) and were allowed to adhere to the wells overnight at 37°C. The following day, media was aspirated from the wells of the 6-well plate, and a buffer containing 900 μl of 4× Laemmli Sample Buffer (1610747; Bio-Rad) and 100 μl of β-mercaptoethanol was added to each well (100 μl per well). Cells were then scraped off the bottom of the well using a cell scraper (353086; Falcon) and pipetted into unique tubes. Samples were run on NuPAGE 4-12% Bis-Tris Gels (NP0335BOX; Invitrogen) in MES SDS buffer for 1 h at 120 V. Proteins were then transferred to a PVDF membrane at 30 V for 1 h at 4°C in 1× transfer buffer (25 mM Tris base, 19 mM glycine, and 20% methanol). Membranes were blocked in block buffer (5% [w/v] milk in PBS-T) for 1 h at room temperature. Then, membranes were incubated with primary antibodies diluted in block buffer (rabbit anti-Rtn4 at 1:1,000: ab47085; Abcam; rabbit anti-Halo at 1:100: G928A; Promega; Rabbit anti-GFP at 1:100: A11122; Invitrogen; mouse anti-alphatubulin at 1:3,000: ab89984; Sigma-Aldrich) overnight at 4°C. The following day, membranes were washed 3× for 5 min each with PBS-T followed by incubation with secondary antibodies diluted in block buffer (goat anti-rabbit-HRP at 1:2,000: 7074S; Cell Signaling Technology; horse anti-mouse-HRP at 1:2,000: 7076S; Cell Signaling Technology) for 1 h at room temperature. Membranes were washed again 3× for 5 min each. Clarity Western ECL Substrate (Bio-Rad) was added onto the membranes which were imaged using an ImageQuant LAS 4000 with chemiluminescence and 10-s to 1-min exposures.

Preparation for STED imaging
For live cell STED imaging of U-2 OS Rtn4-Halo cells transiently overexpressing SNAP-Sec61β, cells were live labeled with 1 µM ATTO 590-chloroalkane and 1 µM of SNAP-Cell 647-SiR (S9102S; New England Biolabs; final concentrations) diluted in warm media for 1 h at 37°C. For the live cell STED imaging, U-2 OS and U-2 OS Rtn4-knockout cells both transiently overexpressing Halo-Sec61β were live-labeled with 1 µM ATTO 590-chloroalkane diluted in warm media for 1 h at 37°C. All live cell STED samples were rinsed three times with warm media and allowed to recover for 1 h at 37°C following incubation with diluted dyes. The media was replaced with Live Cell Imaging Solution (A14291DJ; Gibco) supplemented with 15 mM glucose (G5767; Sigma-Aldrich). Cells were then imaged immediately while being maintained at 37°C with 5% CO 2 .
Preparation for single-molecule counting U-2 OS Rtn4-mEGFP and U-2 OS Nup96-mEGFP cells were removed from flasks using trypsin, mixed together, and seeded into the lanes of a plasma cleaned ibidi slide. The next day, cells were fixed and labeled as described above for immunofluorescence. The samples were labeled with a custom-ordered anti-GFP nanobody conjugated to a single docking site for fluorogenic DNA PAINT imaging (Chung et al., 2022;Massive Photonics). After washing out excess nanobody from the overnight labeling, samples were imaged immediately using 50 nM of Cy3B imager B in a PBS-based buffer (1× PBS, 500 mM NaCl, 1 mM Trolox, 20 mM sodium sulfite, pH 7.3-7.5). Trolox was stored in 1 M aliquots at −20°C in DMSO.

Preparation for 4Pi-SMS imaging
The following samples were labeled sequentially starting with the nanobody overnight at 4°C, then the primary antibody overnight at 4°C, and finally the secondary antibody for 1 h at room temperature. U-2 OS transiently overexpressing mCherry-Sec61β were prepared for immunofluorescence as described above using a rabbit anti-Rtn4 primary (ab47085; Abcam) with a goat anti-rabbit secondary conjugated to Alexa Fluor 647 (A21245; Life Technologies) and a custom ordered FluoTag X4 anti-RFP nanobody conjugated to CF660C (N0404; NanoTag). U-2 OS transiently overexpressing GFP-KDEL or mEmerald-Sec61β were both prepared for immunofluorescence as described above using a rabbit anti-GFP primary (A-11122; Invitrogen) with a goat anti-Rabbit secondary conjugated to CF660C (20812; Biotium), and a FluoTag X4 anti-GFP nanobody conjugated to Alexa Fluor 647 (N0304; NanoTag). To enable microscope alignment, 100-nm crimson Fluospheres (F8816; Thermo Fisher Scientific) were added on top of all samples.
Mounting the samples was performed as reported previously (Zhang et al., 2020). Briefly, STORM imaging buffer was prepared fresh just before imaging (143 mM β-mercaptoethanol, 50 mM Tris pH 8.0, 50 mM NaCl, 10% glucose, 135 U/μl catalase, and 1 U/μl glucose oxidase). Samples were mounted onto a custom-made sample holder facing up. Crimson Fluospheres (F8806; Thermo Fisher Scientific) were added onto the coverslip and were allowed to settle for approximately 5 min before removing the excess buffer. Then, 100 μl of STORM buffer was added to the coverslip, and a second coverslip was added on top of it. Excess STORM buffer was removed using Kimwipes, and the coverslips were sealed with two-component glue (Picodent Twinsil, Picodent) which was allowed to solidify for ∼20 min.
Microscopy STED imaging was performed using a Leica SP8 STED 3× using a pulsed white light laser for excitation (SuperK Extreme EXW-12; NKT Photonics) and a pulsed 775 nm laser for depletion (Onefive Katana-08HP). A 100 × 1.40 NA-high contrast Plan Apochromat oil CS2 objective was used for all image acquisition using the Application Suite X Software (LAS X; Leica Microsystems). ATTO 590-chloroalkane and SNAP-Cell 647-SiR present in the same sample were imaged using excitation wavelengths of 592 nm (∼26 μW) and 650 nm (∼11 μW), respectively, and 775 nm (∼28 mW) depletion wavelength. HyD hybrid detectors with 0.3-6.0 ns gating were used to record fluorescence ranging from 600-630 nm for ATTO 590 and 650-750 nm for SNAP-Cell 647-SiR. Images were acquired sequentially between lines starting with SNAP-Cell 647-SiR using eight line-average and 8,000 Hz resonant scanning. One-color imaging of ATTO 590 in live cells was performed using 592 nm excitation at 24 µW, 775 nm depletion at 49 mW, 604-700 nm detection using a HyD hybrid detector with 0.3-6.0 ns gating, 8 line-average, and 8,000 Hz scanning. Cells in all samples were maintained at 37°C and 5% CO 2 . For figures, STED images were convolved with a Gaussian blur with a Sigma-Aldrich of 1 pixel using ImageJ software. All analyses performed on STED images were done on the raw images. 4Pi-SMLM samples labeled with CF660C and Alexa Fluor 647 were imaged with a ratiometric approach using salvaged fluorescence on a 4Pi-SMLM microscope. The localization analysis and drift correction were executed in custom MATLAB scripts. All of this was performed as described previously (Zhang et al., 2020;Huang et al., 2016). The 4Pi-SMLM microscope possesses opposing silicon oil immersion objectives (100× 1.35 NA; Olympus). A 642-nm laser was used for excitation (2RU-VFL-P-2000-642-B1R; MPB Communications) and a 405-nm laser was used for activation (OBIS 405 LX,50 mW;Coherent). The conventional fluorescence was recorded on a sCMOS camera (ORCA-Flash 4.0v2; Hamamatsu). The salvaged fluorescence was recorded by an EMCCD camera (128 × 128 pixels, iXon DU860; Andor). The microscope hardware was controlled by customwritten LabVIEW software (International Instruments). Samples were imaged at room temperature in STORM buffer (described above).
Single-molecule counting samples were imaged using Fluorogenic DNA PAINT on a Nikon Eclipse Ti2 microscope (Nikon Instruments) with an attached Andor Dragonfly 500 unit (Andor, Oxford Instruments). Cy3B conjugated to fluorogenic imager probe B (Chung et al., 2022) at a working concentration of 50 nM was excited using a 561-nm laser with an 8.2 × 8.2 mm illumination aperture and a P2 power density filter resulting in a laser intensity of ∼1 mW/cm 2 . Fluorescence was filtered through a TR-DFLy-F600-050 emission filter before being collected using a 1.49 NA 60× oil TIRF objective and captured on a Sona 4BV6X sCMOS camera (Andor Technologies) on 512 × 512 pixels with an effective pixel size of 108 nm at 20 Hz. The microscope was controlled using Fusion Software (Andor). Samples were imaged at room temperature.

Skeleton generation and tubule major axis determination
To generate skeletons from a surface, we implemented a mean curvature skeletonization (Tagliasacchi et al., 2012) approach in PYMEVisualize (Marin et al., 2021). We used a weighting of 20 and 0.01 for the velocity and medial axis terms, respectively, to create the initial mesoskeleton. Then, the position of each point on the skeleton was changed to the average position of all points within 50 nm of that point. We applied an upper threshold of 200 to the density of skeleton points within 50 nm of any given skeleton point. Points exceeding this threshold were removed from the skeleton. This served to remove parts of the skeletons found within ER sheets, so analyses were restricted to tubules only. The major axis of the tubule at any given skeleton point was determined by calculating vectors pointing from each skeleton point to the nearest skeleton point that was a minimum of 10 nm away.

Rtn4 pixel intensity
The average Rtn4 intensity per pixel along tubules was analyzed using ImageJ by creating 10-pixel-wide regions of interest (ROI) along tubules. The Rtn4 pixel intensities were summed across the width of the line plots and those sums were averaged along the length of the ROI. The two populations of Rtn4 pixel values were tested for a statistically significant difference by computing the Wilcoxon rank-sum statistic.

Tubule diameter comparison
Tubule diameters were measured using 10-pixel wide line plots in Python Microscopy Environment (PYME) with the NEP fitting plug-in (Barentine et al., 2018). NEP fitting uses ensemble model-based fitting to extract accurate diameters and resolutions for STED-imaged ER tubules, amongst other structures.
The "STEDTubule_SurfaceSNAP" model was used for all tubule diameter measurements. Pairs of tubule diameters populations were tested for statistically significant differences by computing the Wilcoxon rank-sum statistic.
Mean curvature and Rtn4 density analysis 3D surfaces of the ER were created in PYMEVisualize using the NanoWrap algorithm, which uses the localization precisions of SMLM data to extract surfaces from them (Marin et al., 2023), and the surfaces' mean curvatures were calculated (Taubin, 1995) as implemented in PYMEVisualize (Marin et al., 2021).
To determine the Rtn4 density near certain surface curvatures, the maximal principal curvatures along the surface were divided into 50 bins. The Rtn4 density was calculated as the number of Rtn4 localizations within 50 nm of a surface vertex (see Fig. S2 for vertex description and visual) and binned according to that vertex's maximal principal curvature. "Rtn4 density/Frequency" was calculated by dividing the bin counts for Rtn4 density by the bin counts for the maximal principal curvature. Images were created using PYMEVisualize (Marin et al., 2021) and custom Python scripts.
φ Calculation and simulated random data The φ angles of Rtn4, Sec61β, and KDEL localizations in tubule cross-sections were calculated using a custom Python script. In PYMEVisualize, small ROIs of ER tubules were created from larger datasets. The 3D surfaces for each ROI were generated based on the localizations from the nanobody labeling in each sample and the skeletons were generated from those 3D surfaces. Vectors pointing from the skeleton of the tubule to each localization from the secondary antibody labeling in each sample were calculated. The angles between these vectors and the z-axis (vector normal to the coverslip) were calculated using Eq. 1. We used the skeletons from each dataset to simulate data randomly distributed around them in circular rings to show what the φ distribution would be for such data (Fig. S2 F). The distributions of angles for simulated, Rtn4, Sec61β, and KDEL points were tested for significant differences by calculating the Wilcoxon rank-sum statistic.

Single-molecule counting analysis
Single-molecule counting datasets using fluorogenic DNA PAINT probes were localized in PYME. For each dataset, separate ROIs of Nup96 and Rtn4 were created. The Nup96 ROI was fed into super-resolution microscopy platform (SMAP; Thevathasan et al., 2019;Ries, 2020 ψ Calculation DBSCAN was used to segment 3D point clouds of Rtn4 localizations into unique clusters using a search radius of 12 nm and a minimum clump size of 5. Clusters were analyzed using the "MeasureClusters3D" module within PYMEVisualize (Marin et al., 2021). Specifically, principal component analysis was used to determine the principal axis of the clusters with the highest eigenvalue, which we refer to as the major axis. Vectors (N . ) pointing from each cluster's center to the closest point on the skeleton were calculated. Each cluster's major axis was projected onto a plane orthogonal to its N . . The ψ angles were calculated by using Eq. 1 with the projected major axes of the clusters and vectors orthogonal to the tubule axes and tangent to the projected plane as input vectors. Only clusters containing >10 localizations and <50 localizations were used for this analysis. This removed background clusters and clusters that were too close together to segment, respectively. The relative distribution of different-sized clusters is shown in Fig. S5 A.
Rtn4 3D cluster anisotropy analysis and simulated linear and circular clusters Circular and linear clusters were simulated to compare to observed Rtn4 clusters. The simulated clusters possessed the same center points, radii of gyration (Rg), and localization counts as the observed Rtn4 clusters. To simulate circular clusters, each point in the cluster was assigned a uniform random angle from 0 to 2π, and the uniform random radius (distance from the cluster center) varied as ffiffi ffi x √ * Rg, where x ranged from 0 to 1 and Rg was copied from the observed cluster each individual simulated cluster was based on. To simulate linear clusters, each point in the cluster was assigned the same angle, initially pulled from a uniform random distribution from 0 to 2π, and a uniform random radius from 0 to the radius of gyration. All points in both types of simulated clusters had some uncertainty incorporated into their positions. This was done by adding random numbers from a Gaussian distribution (with μ = 0 and σ = 5.26; the average localization precision of the real data) to each component of their coordinates. The anisotropies of the simulated clusters and the observed Rtn4 clusters were calculated and compared. Clusters were filtered as 10 < localizations < 50 to avoid background clusters and clusters that were too close together to segment.
angle cos −1 xy |x||y| , where x and y are vectors and |x| and |y| are their magnitudes. The Rg calculated from the observed clusters and used in the simulations are likely overestimates since they are effectively the true Rg convolved by the localization precision. Thus, our linear-shaped simulated clusters will appear slightly more anisotropic than they would if the true Rg was used. Indeed, if we multiply the calculated Rg by a factor of 0.925, the anisotropy distributions for the linear-shaped simulated data shift left and more closely align with the observed cluster data (Fig. S6 E).

Simulating clusters with explicit intermonomer distances
The frequency of different oligomer sizes was taken from the DNA-PAINT counting data (Fig. 4). We determined a factor (3.23) that could transform the distribution of localizations per cluster of the 3D data to one that looked identical to that of the distribution of proteins per cluster from the counting data. This factor is roughly how many localizations we identify per protein. This was used as the λ for a Poisson distribution that was drawn from to determine the number of localizations per monomer in our simulated clusters. We added some localization precision to each simulated localization by adding some uncertainty drawn from a Gaussian distribution with μ = 0 nm and σ = 5.26 nm, which is the average localization precision of our real data. The intermonomer distances tested were based on the theoretical calculation of Rtn4b molecules possessing a diameter of ∼4.5 nm, assuming they are roughly spherical. The following website was used to calculate the volume of Rtn4b based on its sequence: http://biotools.nubic.northwestern.edu/proteincalc. html.
Estimating the percent area that Rtn4 proteins occupy in the ER membrane We assume that each Rtn4b protein has a diameter of ∼4.5 nm based on the calculation in the section above. We calculated the area that each Rtn4b protein would occupy in the membrane as π * r 2 . We used the same factor of 3.23 (described above) to roughly convert our 3D localizations of Rtn4 to the number of Rtn4 proteins. We then calculated the percent area that Rtn4 proteins occupy in the membrane using Eq. 2: # of Rtn4 proteins ( ) * Area of Rtn4 protein ( ) Surface area of 3D surface * 100. (2)

Statistics
All statistical tests were performed using the SciPy (Virtanen et al., 2020) library of Python functions.
Online supplemental material Fig. S1 shows the Western blots of the U-2 OS Rtn4-Halo and U-2 OS Rtn4-mEGFP CRISPR cell lines. Fig. S2 shows examples of point cloud surface fitting, surface vertices, skeletons, and data simulated randomly in a circle around skeletons. Fig. S3 contains nanobody controls for φ angle analyses and a plot comparing the three distributions of Rtn4, Sec61β, and KDEL. Fig. S4 compares the localization distributions of Rtn4 and Sec61β. Fig. S5 shows the orientation preference of Rtn4 clusters of varying size cutoffs and a 2D histogram of φ vs. ψ. Fig. S6 contains the anisotropy distributions of different oligomer simulations. Video 1 shows an overview and scan of the data shown in Fig. 2. Videos 2, 3, 4, and 5 show a tubule with the observed oligomers or the various simulated oligomers on it.