A quantitative map of nuclear pore assembly reveals two distinct mechanisms – Nature

Cell culture

Wild-type HeLa Kyoto cells (RRID: CVCL_1922) were a gift from S. Narumiya; their genome was sequenced previously³⁹. Cells were grown in high glucose Dulbecco’s Modified Eagle’s Medium (DMEM) containing 4.5 g l⁻¹ d-glucose (Sigma Aldrich) supplemented with 10% fetal calf serum (FCS), 2 mM l-glutamine, 1 mM sodium pyruvate and 100 μg ml⁻¹ penicillin and streptomycin at 37 °C and 5% CO₂. Cells tested negative for mycoplasma contamination by PCR every 2 or 3 months.

Genome editing

Monomeric enhanced GFP (mEGFP) and mCherry were inserted into the genome using zinc finger nucleases, CRISPR–Cas9 nickases, or Alt-R S.p. HiFi Cas9 Nuclease V3. The following six cell lines had been generated and published previously: Nup62–mEGFP¹⁸, mEGFP–Nup107¹², mEGFP–Nup205¹¹, mEGFP–Nup214, mEGFP–Nup358 (also called RanBP2) and Tpr–mEGFP¹⁷. The following five cell lines were generated in this study: mEGFP–Seh1, Nup93–mEGFP, mEGFP–Nup153, Nup188–mEGFP and Pom121–mCherry. The guide RNA (gRNA) sequences used to generate these cell lines are summarized in Supplementary Table 2. For the Nup93–mEGFP cell line, CRISPR–Cas9 nickases and the donor plasmid were transfected by electroporation (Neon Transfection System, Thermo Fisher Scientific) instead of a polymer-mediated transfection reagent.

Western blot

Cells were lysed on ice in RIPA buffer (50 mM Tris-HCl, 150 mM NaCl, 1.0% Triton X-100, 1% sodium deoxycholate, 0.1% SDS, 2 mM EDTA, pH 7.5), supplemented with complete EDTA-free protease inhibitor cocktail (Sigma Aldrich), PhosSTOP (Sigma Aldrich), and 0.1 mM phenylmethylsulfonyl fluoride (Sigma Aldrich). The cell lysates were snap-frozen in liquid nitrogen and quickly thawed at 37 °C two times. The lysates were then centrifuged at 16,000g at 4 °C for 10 min and the supernatant was used for immunoblot analysis. Protein concentration was quantitated using the Pierce BCA Protein Assay Kit (Thermo Fisher Scientific). For Nup188 (Extended Data Fig. 10b), the cell lysates were run on NuPAGE 4–12% Bis-Tris Gels (Novex Life Technologies) and transferred onto PVDF membrane using the Bio-Rad transfer system. After blocking with 4% milk solution (nonfat milk powder in PBS + 0.05% Tween 20), the proteins were labelled with anti-Nup188 (A302–322A, Bethyl Laboratories, 1:5,000) and anti-γ-tubulin (T5192, Sigma Aldrich, 1:1,000) antibodies. Subsequently anti-rabbit IgG horseradish peroxidase (HRP)-conjugated secondary antibody (W4011, Promega) was used to detect the protein of interest with chemiluminescence reaction. For Nup205 and Nup358 (Extended Data Fig. 2), lysates were run on NuPAGE 3–8% Tris-acetate gels (Novex Life Technologies), and anti-Nup205 (ab157090, Abcam, 1:1,000), anti-Nup358 (HPA023960, The Human Protein Atlas, 1:1,000), and anti-vinculin (ab219649, Abcam, 1:1,500) antibodies were used to detect the proteins. Simple western assays were also performed in a Jess instrument (ProteinSimple) using 66–440 kDa capillary cartridges in accordance with the provider’s instructions. The anti-Nup205, Nu358, and γ-tubulin antibodies were used at 1:50 dilution. For Nup205, mouse anti-γ-tubulin antibody (T5326, Sigma) was used instead of the rabbit anti-γ-tubulin antibody to adjust the signal intensity. The secondary antibodies used were the ones provided by the company at a ready-to-use dilution (goat anti-mouse HPR-conjugated secondary antibody, 040-655, Bio-Techne; goat anti-rabbit HPR-conjugated secondary antibody, 040-656, Bio-Techne).

FCS-calibrated live-cell imaging and estimation of Nup copy numbers per NPC

Live-cell imaging was performed using wild-type cells, wild-type cells transfected with mEGFP using Fugene6 (Promega), mEGFP–Nup107 genome-edited cells, or cells of another mEGFP–Nup genome-edited cell line. Cells were seeded in 8-well Lab-Tek Chambered Coverglass (Thermo Fisher Scientific). On the day of live-cell imaging, DMEM was replaced with imaging medium: CO₂-independent medium without phenol red (Invitrogen) containing 20% FCS, 2 mM l-glutamine, and 100 μg ml⁻¹ penicillin and streptomycin. The imaging medium was supplemented with 50 nM SiR (Hoechst) to stain DNA²⁴. Cells were incubated inside the microscope-body-enclosing incubator at 37 °C for at least 30 min before imaging. For Nup188–mEGFP genome-edited cells, the following medium was also used instead of the imaging medium: 30 mM HEPES pH 7.4 containing 9.3 g l⁻¹ minimum essential medium Eagle (Sigma Aldrich), 10% FCS, 1% MEM non-essential amino acids (Thermo Fisher Scientific, Gibco), and 100 μg ml⁻¹ penicillin and streptomycin.

Calibrated imaging using FCS was carried out as described²², using Fluctuation Analyzer 4G 150223 (https://www-ellenberg.embl.de/resources/data-analysis), FCSFitM v0.8 (https://git.embl.de/grp-ellenberg/FCSAnalyze), FCSCalibration v0.4.2 (https://git.embl.de/grp-ellenberg/FCSAnalyze), RStudio 1.1.383, R 3.4.1, and Python v3.6.8. In brief, the confocal volume was determined by performing FCS using a dye with known diffusion coefficient and concentration (Alexa Fluor 488 NHS ester; Thermo Fisher Scientific for mEGFP). To convert fluorescence intensity to the concentration, FCS was performed in cells that transiently express mEGFP alone, and a calibration curve was obtained by plotting the fluorescence intensity against concentration. The background fluorescence signal was measured in cells not expressing fluorescent proteins and subtracted.

To measure the concentration of Nups, mEGFP–Nup genome-edited cells in interphase were imaged in 3D using a confocal microscope (LSM780; Carl Zeiss, Oberkochen, Germany) and a 40× 1.2 NA C-Apochromat water immersion objective (Carl Zeiss) at 37 °C in a microscope-body-enclosing incubator, under the following conditions: 21 optical sections, section thickness of 2.0 μm, z-stacks every 1.0 μm, and xy pixel size of 0.25 μm. When the nuclear envelope is not perpendicular to the confocal plane of the 3D stacks, the fluorescence intensity at the nuclear envelope is non-isotropic in the point-spread function (PSF), which results in underestimation of the signal. To avoid such underestimation, a single plane was selected that contains the largest nuclear area in which the nuclear envelope is perpendicular to the imaging plane and thus isotropic in the PSF. The fluorescence intensity of Nups was quantified on this single plane using the nuclear envelope mask with the width of three pixels (0.75 μm) that was generated from a SiR–DNA channel. Background fluorescence intensity was measured in wild-type cells without expressing any fluorescent proteins and subtracted. The Nup fluorescence intensity on the nuclear envelope was converted to the concentration using the calibration curve generated by FCS above. The number of Nups per μm² was calculated from the concentration and then divided by the NPC density per μm² measured by STED microscopy. This absolute quantification of Nup copy number with FCS calibration was done using 47 mEGFP–Nup107 genome-edited cells in interphase. For other mEGFP-Nups genome-edited cells, their Nup fluorescent intensities on the nuclear envelope were directly compared with the ones of mEGFP–Nup107 genome-edited cells on the same 8-well Lab-Tek Chambered Coverglass, and then their concentrations were determined using the intensity ratios to the mean intensity of mEGFP–Nup107 without using a FCS calibration curve. For Pom121–mCherry, the copy number was quantified independently by performing FCS using Alexa Fluor 568 NHS ester (Thermo Fisher Scientific) to measure the confocal volume and using the cells that transiently express mCherry alone to convert fluorescence intensity to the concentration.

Measurement of nuclear pore density by STED microscopy

Cells were fixed with 2.4% formaldehyde (Electron Microscopy Sciences) in PBS for 10 min, extracted with 0.4% Triton X-100 (Sigma Aldrich) in PBS for 5 min, and blocked with 5% normal goat serum (Life Technologies) in PBS for 10 min at room temperature. Subsequently, the cells were incubated overnight at 4 °C with a mouse anti-Nup62 (610497; BD Biosciences, 1.25 μg ml⁻¹) antibody, and then with an Abberior Star Red-conjugated anti-mouse IgG (Abberior, 0.5 μg ml⁻¹) for 30 min at room temperature. For Extended Data Fig. 4b, anti-GFP (Roche, 1:200) and anti-Elys (The Human Protein Atlas, 0.5 μg ml⁻¹) antibodies, Star Red-conjugated anti-rabbit IgG (Abberior, 0.5 μg ml⁻¹) and Star 580-conjugated anti-mouse IgG (Abberior, 0.5 μg ml⁻¹) were used. After multiple washes in PBS, cells were mounted in Vectashield (H-1500, Vector Laboratories). Super-resolution imaging was performed on a Leica SP8 3X STED microscope as described¹². Images were taken with a final optical pixel size of 20 nm, z-stacks of every 250 nm, and optical section thickness of 550 nm. Images were filtered with a Gaussian filter (kernel size: 0.5 × 0.5 pixels) for presentation purposes. The shrinkage of the nucleus caused by formaldehyde fixation and/or Vectashield mounting was quantified by comparing the volume of the nuclei of live cells with the ones of fixed cells. The shrinkage was 9.1 ± 2.6% (mean ± s.e.m., n = 36 cells). The NPC density was corrected for the nuclear shrinkage for the calculation of Nup copy number per NPC in Fig. 1d.

To quantify NPC density, the raw STED data were processed in ImageJ⁴⁰ with a mean filter (kernel size: 2 × 2 pixels) and a sliding paraboloid (radius: 5 pixels) for background subtraction. Detection of central peak positions for individual NPCs was carried out with the plugin TrackMate⁴¹, using DoG detector and adjusting the detection threshold as the spot diameter size. The resulting 3D NPC coordinates were used to visualize and determine flat and curved regions of the nucleus. Using this map, circular and ellipsoidal regions of interest (ROIs) could then be selected in the flatter parts containing central NPC positions within the z-depth of approx. 500 nm, which corresponds to 2–3 microscopic slices in the images. The remaining signal outside the ROIs, as in curved regions or cytoplasmic structures were discarded from further analysis. NPC densities were calculated for each cell separately by dividing the number of NPCs within the selected ROIs by the corresponding ROI areas. For each cell line, the values were combined to calculate the mean and median NPC density values.

3D STED microscopy for visualizing single nuclear pore assembly intermediates

Cells were coated on 18 × 18 mm no. 1.5 square coverslips and synchronized by double thymidine arrest. After 10 h release from the second thymidine treatment, cells were fixed with 2.4% formaldehyde in PBS for 15 min, extracted with 0.25% Triton X-100 (Sigma Aldrich) in PBS for 15 min, and blocked with 2% bovine serum albumin (A2153; Sigma Aldrich) in PBS for 30 min at room temperature. Subsequently, the cells were incubated overnight at 4 °C with rabbit anti-Tpr (HPA019661; The Human Protein Atlas, 1:100) and a GFP nanobody (FluoTag-X4 anti-GFP nanobody Abberior Star 635P; N0304-Ab635P-L; NanoTag Biotechnologies, 1:50), and then with an Alexa Fluor 594 goat anti-rabbit IgG (A-11037; Life Technologies, 1:250) for 30 min at room temperature. After multiple washes in PBS, cells were mounted in ProLong Gold Antifade Mountant (P10144; Invitrogen). Super-resolution imaging was performed on an Abberior STED/RESOLFT Expert Line microscope. Samples were imaged with an UPlan-S Apochromat 100× 1.4 NA oil-immersion objective on an IX83 stand (Olympus). Stimulated depletion was performed using a 775 nm pulsed laser (40 MHz) in combination with 594 and 640 nm pulsed excitation lasers in line switching mode. Fluorescence signal was detected using two separate Avalanche photo diodes with bandpass filters of 605–625 and 650–720 nm. The images were taken with a final optical pixel size of 35 nm, z-stacks of every 200 nm, and optical section thickness of 1,000 nm. For presentation purposes, images were filtered with PureDenoise plugin⁴² in ImageJ, and lines with width of 175 nm were drawn along the nuclear envelope, flattened and shown in the figures.

Quantification of Nup copy number in the cytoplasm and the nucleoplasm and in non-core and core regions of the nuclear envelope

Mitotic cells were imaged and monitored from anaphase onset for 2 h in 3D by confocal microscopy. The microscopy setup and the imaging conditions are described above. Time-lapse imaging for mEGFP-tagged Nups was performed every 30 s. Photobleaching was negligible and thus not corrected. Time-lapse imaging for Pom121–mCherry was carried out every 60 s, and photobleaching was corrected by measuring a fluorescence signal decay in a neighbouring cell in the same field of view. Visualization of the chromosome surface in 3D was done in the Amira software package⁴³.

To measure Nup accumulation on the nuclear envelope, single planes were selected that contain the largest nuclear area at individual time points to avoid underestimation of the signal as mentioned earlier. The Nup intensity was quantified on the nuclear envelope mask with the width of 0.75 μm that was generated from a SiR–DNA signal at each time point. Except for Nup107 and Seh1, the Nup signal in the cytoplasm and nucleoplasm was measured and used as background. For Nup107 and Seh1, only the cytoplasmic signal was used as background because of their localization at kinetochores. These background values were quantified at individual time points and subtracted from the Nup intensities on the nuclear envelope. The measured Nup intensity was converted into the concentration and then multiplied with nuclear surface area to calculate the total number of the Nups on the nuclear envelope. For Nup153 and Pom121, we did not convert the fluorescence intensity to the concentration as the cell lines were not fully validated to be homozygously tagged.

The Nup copy number was also calculated in the cytoplasm and the nucleoplasm during the first 2 h after anaphase onset. The cytoplasm mask was created by subtracting a mask of the nucleus generated from a SiR–DNA signal from a mask of the whole cell generated from a mEGFP–Nup signal. The mask for the nucleoplasm was created by eroding three pixels of the nuclear mask generated from a SiR–DNA signal. The Nup fluorescence intensity was quantified on these cytoplasmic and nucleoplasmic masks over time and then converted into the concentration. To calculate the total number of Nups in the cytoplasm and the nucleoplasm, the measured concentration was multiplied by the volume of the respective compartments. Cytosol volume at metaphase was quantified using the cytosolic signal of the Nups. The cytosolic GFP signal of some of the Nups (for example, Nup205, Nup214, Tpr and Nup358) were too low to precisely segment the cytosol in the z-slices close to the glass surface due to the relatively high background fluorescence signal. Therefore, we measured the cell volume using the brightest Nup62–mEGFP cell line (4,900 ± 330 μm³ (mean ± s.d. from 8 cells)), and for the other Nup cell lines, we measured the cytosol area on a middle z-slice plane and calculated the ratios to the area for the Nup62 cell line (the ratios were 0.97, 0.97, 1.09, 1.14, 1.03, 1.07 and 1.02 for Nup107, Seh1, Nup205, Nup93, Nup214 and Nup358, respectively). From the measured volume of the Nup62 cell and the ratios of cytosol area to the Nup62 cell, we estimated the volume for the other cell lines (4,670, 4,660, 5,550, 6,030, 5,110, 5,420 and 5,080 μm³ for Nup107, Seh1, Nup205, Nup93, Nup214 and Nup358 lines, respectively). For the cytoplasm volume after anaphase, we used the data that were measured previously in histone H2b–mCherry-expressing HeLa cells using fluorescently labelled dextran¹⁷. Assuming that the cell volume changes in the same degree during mitosis exit as the H2b–mCherry cell, we calculated the cytoplasmic volume of the Nup cell lines using the ratio to the volume at metaphase (5,300 μm³ for the H2b–mCherry cell¹⁷). The nucleoplasmic volume was quantified in each mEGFP–Nup knock-in cell line using a SiR–DNA signal at every time points as described previously¹².

Core regions were predicted on the nuclear envelope based on a previously described protocol using the core marker Lap-2α¹². In brief, nuclear volume was segmented using SiR–DNA fluorescence signals that were processed with a 3D Gaussian filter and a multi-level thresholding. Nuclear volume was then divided into inner and outer volumes using the cutting plane that was constructed from the largest eigenvector and the second one orthogonal to the first vector of the pixel coordinates of the nuclear volume. Surface area of each nucleus was calculated and utilized to adjust the size of the inner and outer-core regions at individual time points. The previously defined criteria for being core and non-core regions¹² was applied. The position of inner and outer core was determined with respect to the intersection point of the largest eigenvector on the nuclear surface. The core region prediction was done in MATLAB (MathWorks).

Mathematical modelling for the nuclear pore assembly kinetics

Previous EM data showed that within 2 h after the onset of anaphase, postmitotic assembly is the dominant process in the non-core region, whereas slower interphase assembly predominates in the core region¹². Assuming that this relation is also reflected in the live-cell Nup dynamics, we derived a mathematical model. We assumed that the observed total fluorescence intensity in the non-core, n(t), and core region, c(t), at time t after anaphase onset is a linear combination of the postmitotic, pm(t), and interphase assembly, ip(t), according to

The fraction of postmitotic assembly in the non-core and core regions are denoted f_n and f_c, respectively. To test this assumption and obtain an estimate of the fractions, we used a model that accounts for the observed sigmoid-like kinetics

and ({rm{pm}}left(t < {d}_{n/c}right)={rm{ip}}left(t < {d}_{n/c}right)=0.) The parameters n_p, K_p and n_i, K_i characterize the postmitotic and interphase kinetics, respectively. The parameter ({d}_{n/c}) accounts for an additional delay in NPC initiation. In the non-core region we assumed d_n = 0; in the core region due to the presence of kinetochore microtubule fibres²⁶, d_c > 0. The model is used to derive the underlying postmitotic and interphase assembly kinetics. Using equations (1 and 2), we obtain

Parameter estimation

For each Nup, there are two parameters that define the interphase (n_i, K_i) and postomitic (n_p, K_p) assembly, respectively. The fractions f_n and f_c and the delay d_c in the core region were estimated globally for all Nups. In total, we have 43 parameter, 4 × 10 = 40 parameters describing the assembly kinetics and 3 global parameters, fitted to 4,446 data points.

In detail, to find the model parameters we minimized the mean squared distance between data and model for all the time points M

(Nleft({t}_{j}right)) and (Cleft({t}_{j}right)) are the mean background-subtracted and normalized fluorescence intensities in the non-core and core region with standard deviation ({sigma }_{N}left({t}_{j}right)) and ({sigma }_{C}left({t}_{j}right)), respectively, at time point t = t_j. We subtracted a background computed from the average of the first 3 time points. The data were normalized with the average value between 100 and 120 min after anaphase. In a first step, for each protein and cell line, we estimated the postmitotic fractions in the core and non-core region and the kinetic parameters. Overall, we computed 61 parameters (6 parameters per protein plus one delay parameter). For the postmitotic fractions, we obtained on average f_n = 0.857 [0.76, 0.95] and f_c = 0.295 [0.17, 0.4], where the number in brackets indicates the 95% confidence interval estimated using the profile likelihood method⁴⁴. Importantly, the obtained postmitotic fractions are well in agreement with the previously reported estimates obtained from EM data¹². The delay in pore formation between core and non-core region was estimated by systematically varying d_c from 0 to 6 min in steps of 1 min. A value of d_c = 2 min, gave optimal result. In a second step, we used the previously estimated average postmitotic fractions, f_n and f_c, and d_c and recomputed the kinetics parameters for each protein. The model with reduced parameters well agrees with the data (Extended Data Figs. 5 and 6, R² > 0.99). To verify if the choice of common postmitotic fractions for all Nups is valid, we computed the Baysian information criterion (BIC)⁴⁵. The difference in BIC between the model with reduced parameters, 43 parameters, compared to the full model, 61 parameters, was −7, indicating that the model with reduced parameters is justified. The obtained parameter values are listed in Supplementary Table 3.

Median assembly time and duration of assembly

One can think of an assembly curve as a cumulative distribution function and its derivative as the corresponding probability density function (PDF) for binding events. The median assembly time, i.e. the time where 50% of binding events have occurred, is K_i and K_p, for the interphase and postmitotic assembly respectively. We consider the time intrinsic to the assembly mechanism and independent of the initiation delay d_c. We further define the duration of assembly as the time interval where 80% of binding events occur, i.e. from a fraction of α₁ = 0.1 up to α₂ = 0.9, one obtains (see also Extended Data Fig. 7a)

The duration of assembly quantifies the width of the binding events PDF.

In Extended Data Fig. 7c we see a strong positive correlation between median assembly time and duration of assembly for the postmitotic assembly. This suggests a sequential assembly mechanism. The rationale is that for a strict sequential pathway, the binding events PDF for subsequent Nup is a convolution of all previous binding events PDF and so will broaden for later binding proteins. For example, if an early protein has an assembly duration of 1 h, within this time window binding sites for the subsequent protein will continue to appear. Therefore, the subsequent protein in the sequence will also accumulate for at least 1 h.

For the simplified case of irreversible sequential assembly and linear rate constants, a positive correlation can be demonstrated. This correlation is independent on whether the initiation is synchronous or spread within a time-period. For simplicity reasons, we omit the fact that each Nup binds in multiple copies to the NPC. A Nup _Pi binds with rate constant κ_i to a NPC intermediate X_i−1 according to the reaction scheme in Supplementary Fig. 2.

The corresponding system of ordinary differential equations is

with X_i(0) = 0, ({k}_{i}={kappa }_{i}{P}_{i}^{text{free}}), and an excess of free Nup ({P}_{i}^{text{free}}approx {rm{constant}}). The function g accounts for the appearance of NPC initiation sites after anaphase. We assume that NPC initiation is completed within a finite time after anaphase and neglect the slowly and continuous appearance of pores in G1—that is, ({int }_{0}^{infty }gleft(tright){rm{d}}t={rm{constant}}). The amount of ith Nup bound to a complex is ({P}_{i}=mathop{sum }limits_{j=i}^{n}{X}_{i}) and its time derivative ({f}_{i}left(tright)=frac{{rm{d}}{P}_{i}}{{rm{d}}t}={k}_{i}{X}_{i-1}) is proportional to the binding events PDF. We can quantify the assembly time τ_i and assembly duration θ_i by the mean and standard deviation of the binding events PDF, respectively⁴⁶,

and

After integration by parts, one obtains

and

Where ({tau }_{g}=frac{{int }_{0}^{infty }tg(t){rm{d}}t}{{int }_{0}^{infty }g(t){rm{d}}t}) and ({theta }_{g}=sqrt{frac{{int }_{0}^{infty }{t}^{2}g(t){rm{d}}t}{{int }_{0}^{infty }g(t){rm{d}}t}-{tau }_{g}^{2}}) are the mean and standard deviation of the initiation function, respectively. From equations (10 and 11), it is clear that ({tau }_{i+1} > {tau }_{i}) and ({theta }_{i+1} > {theta }_{i}) for any parameter combinations and independently on how synchronous the initiation of pores is. This shows that for a strictly sequential pathway a linear correlation between assembly time and duration is expected.

Integrative modelling of the NPC assembly pathway

A model of the assembly pathway is defined by a series of static structures, including a static structure at each sampled time point along the assembly process. Therefore, we model the NPC assembly by first modelling static structures at each time point, independently from each other. We then enumerate alternative assembly pathways and rank them based on the static structure scores and plausibility of transitions between successive static structures.

Integrative modelling of static structures at each time point

The static structures are modelled by standard integrative structure modelling³⁰ as follows.

Representing a static structure model

The time points correspond to times with available electron tomography protein densities¹¹: 5 min, 6 min, 8 min, 10 min and 15 min after anaphase onset. We divide the mature NPC structure (PDB: 5A9Q and 5IJO) into eight spokes and further divide each spoke into a set of rigid subcomplexes, including the Y-complex, the inner-ring Nup205–Nup155–Nup93 subcomplex, the inner-ring Nup93–Nup188–Nup155 subcomplex, and the central channel Nup62–Nup58–Nup54 subcomplex. For each domain, we coarse-grained the structure by grouping ten consecutive amino acid residues into a single bead at the centre of mass of those residues. Each subcomplex is represented as a rigid body. The nuclear envelope is represented as a fixed toroid surface embedded in two parallel planes. Thus, the variables of the model include the Euclidean coordinates of the Nup subcomplexes and the copy number of each Nup subcomplex.

We set the inner pore diameter and minor radius of the pore at each time point to the mean of previously determined nuclear envelope cross sections¹¹ with a pore diameter of 51.5 nm, 58.4 nm, 72.7 nm, 84.6 nm, 79.8 nm and 87 nm; and minor radius of 21.4 nm, 21.2 nm, 21.5, 20.3 nm, 17.1 nm and 15 nm for time points at 5 min, 6 min, 8 min, 10 min, 15 min and the mature pore, respectively.

Scoring a static structure model

The copy numbers of the NPC subcomplexes at each time point were restrained by a Gaussian function with mean and variance determined by the single-cell traces presented in this study. The relative likelihood of a set of copy numbers is proportional to the product of individual Gaussian likelihoods.

Distances between pairs of Nups that are in contact with each other in the native NPC structure^27,28 were restrained by a harmonic Gō-like model⁴⁷. Inter-subcomplex contacts within 5 nm in the mature structure were restrained by a harmonic function (strength 0.01 kcal mol⁻¹ Å). Each Gō-like scoring term was scaled at each time point, from zero at the first time point to full strength at the mature pore time point. Distances between all pairs of Nups were also restrained by a harmonic excluded volume restraint (strength 0.01 kcal mol⁻¹ Å⁻¹). Proximity between Nup domains containing a membrane interacting ALPS-motif and the nuclear envelope was restrained by a harmonic term (strength 0.1 kcal mol⁻¹ Å⁻¹), based on their sequences. Overlap between the Nups and nuclear envelope surface was avoided by imposing a harmonic repulsion between the Nups and nuclear envelope surface (strength of 0.01 kcal mol⁻¹ Å⁻¹).

The shape of a static structure was restrained by a correlation coefficient between the model and electron tomography protein density¹¹. The forward model density was represented by fitting each Nup subcomplex with a Gaussian mixture model of two components per subcomplex copy using the gmconvert utility⁴⁸. Similarly, the electron tomography protein densities at each time point were represented with a Gaussian mixture model with 150 components fit to the experimental density.

Sampling static structure models

A state of the NPC at any given time point is defined by the copy numbers and coordinates of its components. Only copy number assignments and structures consistent with the C-8 symmetries were sampled. The assumption that the subcomplexes preform with 8-fold multiplicity before assembling into the NPC is supported by our previous electron microscopy analysis¹¹. The averaged electron tomograms of the intermediates demonstrated 8-fold symmetry of the outer-ring complex at 5, 6, 8, 10, and 15 min after anaphase onset and 8-fold symmetry of the inner-ring complex at 10 and 15 min after anaphase onset¹¹, indicating that the majority of intermediates have approximate 8-fold symmetry for the outer- and inner rings. However, there are likely to be variations in the copy numbers at the single pore level. We only sampled structures for the top 20-scoring Nup copy number combinations. Each sampling started with the mature pore structure, followed by applying 10⁶ Monte Carlo moves. These moves included rotational and translational perturbations to each Nup subcomplex, drawn from a uniform distribution in the range from −0.04 to +0.04 radians and from −4 to +4 Å, respectively.

Modelling the assembly pathway

With the static structure models in hand, we connect them into complete alternative assembly pathways, as follows.

Each pathway is represented by a static structure at each sampled time point, starting with t = 5 min and culminating in the native structure; we do not model the completely disassembled NPC. The score of a pathway is the sum of the scores for the static structures on the pathway (defined above) and transitions between them. A transition score is uniform for all allowed transitions. A transition between two successive static structures is allowed if the subcomplexes in the first structure are included in the second structure. All possible pathways were enumerated, scored, and ranked. The best-scoring pathways were extracted for further analysis (Fig. 5). Molecular visualization was performed with UCSF ChimeraX⁴⁹.

Immunofluorescence for visualizing Nup155 during assembly

Cells were treated, fixed and blocked as described in the previous section (STED microscopy for visualizing single nuclear pore assembly intermediates). Afterwards, cells were incubated overnight at 4 °C with rabbit anti-Nup155 (HPA037775; The Human Protein Atlas, 1:100), and then with an Abberior Star 635P goat anti-rabbit IgG (ST635P-1002-500UG, Abberior GmbH, 1:250) for 30 min at room temperature. After multiple washes in PBS, cells were mounted in ProLong Gold Antifade Mountant with DAPI (P36941, Invitrogen). Imaging was performed in 3D using a confocal microscope (LSM780; Carl Zeiss) and a 63× 1.4 NA Plan-Apochromat objective (Carl Zeiss) under the following conditions: 31 optical sections, section thickness of 0.7 µm, z-stacks of every 0.39 µm, and xy pixel size of 0.13 µm.

Sample size determination and statistical analysis

For quantitative imaging in Fig. 1a,d, the data were from 4, 4, 4, 2, 3, 2, 3 and 2 independent experiments for Nup107, Seh1, Nup205, Nup93, Nup62, Nup214, Tpr and Nup358, respectively. STED imaging in Fig. 4a and Extended Data Fig. 4a and live imaging in Extended Data Fig. 10 were from two independent experiments. For dynamic quantitative imaging in Fig. 3, the data were from 4, 4, 4, 2, 3, 4, 3, 2, 2 and 4 independent experiments for Nup107, Seh1, Nup205, Nup93, Nup62, Nup214, Tpr, Nup358, Nup153 and Pom121, respectively. STED imaging in Figs. 1b,c and  4b, Southern blotting in Extended Data Fig. 1 and immunofluorescence microscopy in Extended Data Fig. 9 are from single experiments. Statistical analyses were performed only after all the data were taken. Sample sizes for each experiment are indicated in figure legends. Sample sizes were based on pilot experiments to determine the number of cells required to observe stable population averages with high Pearson’s correlation between replicates. No blinding and randomization was done, as this study does not involve animals or human participants. Samples were organized into groups based on cell lines. Cells were imaged in randomly chosen fields of view per experiment. All imaged cells were further analyzed. Videos of dividing cells with rotating nuclei are removed from the analysis, because we cannot properly assign the non-core and core regions.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.