Overlapping nuclear import and export paths unveiled by two-colour MINFLUX

Abstract

The nuclear pore complex (NPC) mediates nucleocytoplasmic exchange, catalysing a massive flux of protein and nucleic acid material in both directions¹. Distinct trafficking pathways for import and export would be an elegant solution to avoid unproductive collisions and opposing movements. However, the three-dimensional (3D) nanoscale spatiotemporal dynamics of macromolecules traversing the NPC remains challenging to visualize on the timescale of millisecond-scale transport events. Here we used 3D MINFLUX² to identify the nuclear pore scaffold and then to simultaneously monitor both nuclear import and nuclear export, thereby establishing that both transport processes occur in overlapping regions of the central pore. Whereas translocation-arrested import complexes bound at the pore periphery, tracks of translocating complexes within the central pore region revealed a preference for an approximately 40- to 50-nm diameter annulus with minimal circumferential movement, indicating activity-dependent confinement within the permeability barrier. Movement within the pore was approximately 1,000-fold slower than in solution and was interspersed with pauses, indicating a highly restricted environment with structural constraints and/or transient binding events during transport. These results demonstrate that high spatiotemporal precision with reduced photobleaching is a major advantage of MINFLUX tracking, and that the NPC permeability barrier is divided into annular rings with distinct functional properties.

Main

The NPC embedded within the nuclear envelope of eukaryotic cells mediates the bidirectional transport of both small and large protein and nucleic acid cargos^1,3. An intrinsically disordered polypeptide network generates the permeability barrier and provides binding sites for the cargo-carrying nuclear transport receptors (NTRs)^4,5. This complex milieu occupies the approximately 50- to 70-nm diameter pore⁶ where the transiting cargos are confined to specific regions during their millisecond-scale migration through the barrier^7,8,9,10. Physically separate trafficking pathways for import and export would provide an elegant solution to alleviate congestion and prevent unproductive collisions between complexes moving in opposite directions^8,9,10,11,12. Simultaneously monitoring both import and export with nanometre-scale precision would provide a rigorous test of this model. Although directly monitoring actively diffusing molecules with high spatiotemporal precision in cellular contexts is feasible with single-molecule fluorescence and super-resolution methods, the illumination intensities typically required result in rapid photobleaching, thus reducing sample observation time^13,14. Consequently, although real-time transport trajectories obtained thus far have directly visualized transport through the NPC, the number of localizations within the pore itself have been low (typically less than three)^7,9,15, making experimental characterization of the permeability barrier properties largely inaccessible. The substantially higher illumination intensities needed by diffraction-limited approaches to increase time resolution¹³ raise serious concerns about sample integrity and have not yielded substantially longer trajectories⁹.

MINFLUX (minimal emission flux) is a powerful recently developed strategy to achieve exceptional spatiotemporal resolution on single molecules. It thus has the potential for delivering incredible new breakthroughs in biological imaging and cellular dynamics; nonetheless, its substantial promise for high-precision tracking of moving molecules remains at an early stage. Single-particle localization with MINFLUX is extremely photon efficient compared with diffraction-limited approaches, thus requiring substantially lower illumination intensities to achieve a similar precision^2,16. MINFLUX localizes fluorophores with high precision and a low photon count by scanning an excitation donut in a pattern around a fluorophore and calculating the position of the molecule on the basis of the number of photons collected at the various positions¹⁷. For nanometre-scale tracking, the assumption is that diffusional steps are approximately less than 100–200 nm (depending on acquisition parameters), and therefore, that the scan pattern for each subsequent localization can be initiated where the molecule was last found¹⁶. For free diffusion in low-viscosity solutions, this assumption cannot currently be met due to diffusional steps in excess of multiple hundreds of nanometres per millisecond-scale timestep. However, in a diffusionally restricted environment, such as the NPC permeability barrier, MINFLUX tracking is feasible. We now demonstrate high-precision tracking of cargos moving in both directions through NPCs, whose position and orientation were directly imaged within the same experiment.

Imaging transport-active NPCs

NPCs have been a key biological structure for developing and demonstrating the resolving power of super-resolution approaches as they are structurally well characterized and have suitable dimensions, symmetry and physiological numbers for illustrating advanced imaging capabilities^2,18,19,20. Although NPCs are well resolved by 3D MINFLUX, most studies have utilized fixed cells and GLOX buffer (deoxygenation + thiol) to induce blinking for dSTORM-type imaging^2,17,18, conditions that preclude real-time nucleocytoplasmic transport measurements. Although fixation ensures structural stability, we recently demonstrated high spatial stability (less than 10-nm fluctuations) of NPCs in an unfixed permeabilized cell system⁷. In this previous work, NPCs were localized using 3D astigmatism imaging with the spontaneous blinking dye HMSiR affixed via an anti-GFP nanobody to NUP96–monomeric enhanced GFP (mEGFP), which yielded individual xyz localization precisions of 7–12 nm. The identical conditions were used here to image NPCs on the bottom of U2OS cell nuclei using 3D MINFLUX with up to 3.3-ms time resolution per HMSiR dye localization (Extended Data Fig. 1a,b and Supplementary Table 1). Within 15 min, more than 100 localizations per NPC were typically obtained, thereby identifying the locations of 30–50 NPCs per field. Gold beads near the cell surface were used to correct any translational fluctuations of the sample with less than 2-nm precision in xyz (Fig. 1a–e). Confocal imaging of eGFP fluorescence at the beginning and end of the MINFLUX acquisition revealed that the NPCs at the centre of the semi-flat nuclear envelope were the most positionally stable, which was quantitatively confirmed by splitting the MINFLUX dataset to generate early and late images (Extended Data Fig. 2). Recognizable single-pore images were obtained from HMSiR localizations (Fig. 1f and Extended Data Fig. 3a). A composite NPC image exhibited the expected double-ring structure and eightfold rotational symmetry (Fig. 1f,g and Extended Data Fig. 3). Measurement of the spacing between the cytoplasmic and nucleoplasmic rings by astigmatism imaging was used to calibrate the z scale in MINFLUX images (see Methods; Extended Data Fig. 4 and Supplementary Table 2). These data confirmed the positional stability of the NPCs in unfixed permeabilized cells under MINFLUX imaging conditions.

Fig. 1: MINFLUX imaging of transport-active nuclear pores.

a, Equal distribution of 32 NUP96 molecules between the cytoplasmic (maroon) and nucleoplasmic (orange) rings of human NPCs. Adapted from the electron microscopy density map EMD-2444 (refs. ^28,40, Springer Nature, and ref. ⁴¹, Cell Press). b–e, MINFLUX imaging of NPCs in permeabilized U2OS cells containing NUP96–mEGFP. The confocal image of eGFP fluorescence identifies the outline of a cell nucleus and a gold bead (100 nm) used for image stabilization (lower left corner, b). A section of the bottom of the nucleus in b (c), and 3D MINFLUX imaging of NPCs (d,e) are also shown. Anti-GFP nanobodies (Nb^GFP)⁴² modified with the HMSiR blinking dye⁴³ were used to visualize the NPCs within the region shown in c via the stochastic blinking of the dye. In d, the curvature of the nuclear envelope is apparent from the layers defined by the cytoplasmic and nucleoplasmic rings of the NPCs (see a). In e, all NPCs identified by confocal imaging in c were detected. Coloration shows the z scale. During data collection, the cytoplasm was on the bottom, but images throughout this article were flipped to place the cytoplasm on top for consistency with convention. f, MINFLUX images of single NPCs (more examples in Extended Data Fig. 3a). g,h, Composite 2D histogram images of an averaged NPC obtained by aligning individual pores on the basis of their centroids and rotated on the basis of their expected eightfold rotational symmetry (see Methods and Extended Data Fig. 3; 37 cells, 541 NPCs, n = 82,331 localizations). The scale is percent of maximum. i, Localization precision determined from centroid deviations within HMSiR ‘trajectories’ (20 points or more per trajectory, 37 cells, 269 clusters; n = 32,184 localizations; σ_x = 6.5 ± 0.1 nm (black), σ_y = 7.0 ± 0.1 nm (red) and σ_z = 4.2 ± 0.1 nm (blue)). The values σ_x/σ_y = 0.93 and σ_x/σ_z = 1.55 were assumed throughout this article. j, Jump step histogram analysis of localization precision. The predicted distribution assuming the localization precision values determined in i (blue curve) fits the experimental data (black) poorly, thus indicating that the method in i overestimates the localization precision. A simulation model assuming diffusional drift (red; n = 96,000 jump steps, 25 localizations per trajectory; σ_x = 4.1 nm = 0.93σ_y = 1.55σ_z; D_x, D_y and D_z = 0.00072, 0.00083 and 0.0003 µm² s⁻¹, respectively) agrees with the data and yields the same centroid deviations as determined in i (see Extended Data Fig. 5i). See Methods and Extended Data Fig. 5 for a description of the analytical approach and a fit with no diffusional drift.

Source Data

As the HMSiR fluorophores were bound to an NPC scaffold during imaging, successive localizations could therefore be used to estimate localization precision. On the basis of centroid deviations, localization precisions of σ_x = 6.5 nm, σ_y = 7.0 nm and σ_z = 4.2 nm were obtained, yielding σ_x/σ_y = 0.93 and σ_x/σ_z = 1.55 (Fig. 1i). Jump step analysis revealed, however, that these precision values were too large (Fig. 1j, blue curve). The explanation is that the movement of particle centroids during the measurements broadened the observed distributions of repeated localizations. Whereas sample drift or multiple semi-stable dye positions around the attachment point can produce significant deviations of the average centroid from the instantaneous centroid during acquisition of a localization, jump step analysis only includes distances between successive pairs of points and thus is much less sensitive to centroid error. The jump step data were well fit by a simulation model that included diffusional drift and 37% lower localization precisions (Fig. 1j, red curve); these simulated data yielded centroid deviations that matched the experimentally determined values (Extended Data Fig. 5i). The ‘diffusional drift’ required to fit the data is not expected to be sample drift that would generate large displacements over the total imaging time, as this would make it impossible to assemble the NPC scaffolds from localizations collected over a 20-min period. Rather, the diffusional drift models the confined movement of the dye centroid on the NPC scaffold during the measurement period, for example, to favourable positions enabled by linkage error, or conformational shifts or jiggles of the NPC scaffold. Considering that the nanobody-bound HMSiR fluorophore is potentially up to 6 nm away from the NUP96 attachment point of the eGFP tag⁷, a low nanometre-scale zone in which the dye maintains distinct preferential positions is reasonable.

Bidirectional transport of importin α

We next sought to track import and export complexes migrating through the super-resolved NPCs (Fig. 2a,b). This required that the MINFLUX excitation donut was at the right place at the right time for the expected approximately 10-ms duration translocation events²¹. As is typical for MINFLUX, we scanned a region of interest (for example, Fig. 1c), and then, once a fluorescent molecule was found, a series of reduced-size scan patterns were implemented for increased localization precision (see Methods and Supplementary Table 3). Thus, a fluorophore had to be first detected through the scanning approach, and then continuously tracked with the anticipation that the molecule might go through an NPC (Fig. 2b), which turned out to be a rare event (less than 1% of the time). We first identified the NPC positions and then implemented the tracking routine.

Fig. 2: MINFLUX tracking of the bidirectional transport of Imp α.

a, Schematic of the concurrent import and export of Imp α labelled with JF549. The NPC structure was adapted from refs. ^44,45, AAAS. b, Target coordinate pattern. The MINFLUX 3D donut was scanned in a seven-point octahedral pattern (black dots) for the Imp α–JF549 tracking algorithm, yielding successive localizations (gold stars). The NPC structure was adapted from ref. ²⁸, Springer Nature, ref. ⁴⁶, AAAS and the RCSB Protein Data Bank⁴⁷. c,d, Unfiltered two-colour MINFLUX localization data obtained in the presence of transport mix. NPC localizations (blue; Nb^GFP–HMSiR; see Fig. 1) were collected for 20 min, and these were followed by tracking localizations (coloured z scale, Imp α–JF549) collected for 20 min. Views from the cytoplasm (c; xy) and the side (d; xz) for two different cells are shown. e, Tracks (magenta) that satisfied MINFLUX filtering criteria (see Methods and Extended Data Fig. 6) overlaid onto four NPC scaffolds (blue).

Importin α (Imp α) binds to a protein cargo via a nuclear localization signal (NLS) and it simultaneously binds to importin β1 (Imp β1), an NTR that mediates interactions with the NPC¹. After cargo release in the nucleoplasm, Imp α is then returned to the cytoplasmic compartment by CAS in combination with RanGTP for another round of cargo import²² (Fig. 2a). Fluorescent Imp α was added to permeabilized cells under conditions where both import (cargo translocation) and export (Imp α recycling) occur. We positioned the nuclear envelope near the focal plane, which yielded an effective observation window of approximately ±400 nm in z when scanning in xy. Despite this range, most tracking localizations were within approximately 150 nm of the nuclear envelope, and some were near NPCs (Fig. 2c,d). Multiple filtration criteria were used to identify tracks as bona fide translocation events (Fig. 2e and Extended Data Fig. 6). Although the low cellular background yielded some false-positive tracks, these were largely eliminated with a low detector channel ratio filter (Extended Data Fig. 6c,d). From a total of 12,384 filtered tracks of 5 or more consecutive localizations from 37 cells (541 NPCs), 2,678 tracks had at least one localization within a 400-nm cube centred on an NPC. Of these, 225 tracks were deemed to have been caught transiting a pore (at least one point 25 nm or less from the midplane of an NPC) and were further analysed. With a maximal time resolution of 0.5–0.6 ms (Extended Data Fig. 1c,d), the median track length for those that entered the 400-nm NPC-centred cube was 18 points (longest = 238 points; data summary in Supplementary Table 4). Although this time resolution is somewhat better than most previous studies, which utilized multiple fluorophores for increased brightness^7,15,23,24, the average number of points per trajectory was approximately fivefold larger than previously observed⁷, yet required only a single fluorophore. This suggests that earlier results were significantly influenced by photobleaching and/or a high illumination flux. Of note, a median of 6 points for a single trajectory within the central pore was observed (Supplementary Table 4), compared with approximately 1 point per trajectory previously⁷, allowing for the characterization of transport behaviour within the NPC transport channel, which was previously impossible.

The 3D transport trajectories identified by MINFLUX in the context of the double-ring structure of the NPC scaffold (Fig. 3) revealed multiple novel findings. Lengthy, confined interactions with the NPC permeability barrier (Fig. 3a,b, Extended Data Figs. 8 and 9 and Supplementary Video 1) suggest that transport is a discontinuous process. Slow movements both in and around the pore indicate a fairly large, highly restricted diffusional environment (Fig. 3c,d, Extended Data Figs. 8 and 9 and Supplementary Video 2). Both import and export trajectories were observed near the pore periphery, and neither were observed near the central axis of the pore, suggesting that the opposing traffic pathways overlap (Fig. 3e–l). Within the central region of the pore (|z| ≤ 25 nm), both import and export trajectories were largely confined to an octant defined by the NPC scaffold, suggesting constraints that restrict angular movement (Fig. 3g,h,k,l). Such behaviour is consistent with defined translocation routes. Abortive import and abortive export trajectories virtually never crossed the midplane (z = 0), suggesting that this was the ‘point of no return’ (Fig. 3m,n and Supplementary Videos 3 and 4), a conclusion also reported earlier⁷.

Fig. 3: Import and export trajectories.

Imp α–JF549 trajectories were overlaid on a composite NPC image (from Fig. 1g,h). The blue curved lines approximate the nuclear envelope. See Supplementary Table 4 for data summary and Extended Data Figs. 7 and 8 for additional trajectories. a,b, Representative import track observed from the cytoplasm and the side (see Supplementary Video 1). c,d, Representative export track observed from the cytoplasm and the side (see Supplementary Video 2). e–h, Import trajectories (n = 13 for e,f). The polar plot in g (20 tracks, |z| ≤ 25 nm) reveals that the translocation paths are peripheral and largely confined to one of the eight lobes of the NPC scaffold, which is supported by the distribution of angular differences within the channel (h; Gaussian width = 19°). i–l, Export trajectories (n = 17 for i,j). The polar plot in k (20 tracks, |z| ≤ 25 nm) reveals that the export paths are also peripheral and largely confined to one of the eight lobes of the NPC scaffold, which is supported by the distribution of angular differences within the channel (l; Gaussian width = 17°). m, Abortive import trajectories (n = 32). n, Abortive export trajectories (n = 35). o,p, Localization error and diffusional behaviour from jump step and R²/t analysis of all 225 tracks that interacted with an NPC. The simplest simulation model (blue) assuming diffusive movement of a single species (D = 0.049 µm² s⁻¹; σ_x = 4.45 nm = 0.93σ_y = 1.55σ_z) does not simultaneously fit both representations of the experimental data (black) well. A three-species model (red; 7%, 56% and 37% of total, respectively) in which only species 3 undergoes diffusive movement (D = 0.055 µm² s⁻¹) fits the data much better (σ_x = 4.1 nm = 0.93σ_y = 1.55σ_z for species 1, and σ_x = 8.2 nm = 0.93σ_y = 1.55σ_z for species 2 and 3). Although species 1 and 2 do not have any prescribed diffusive movement, the large error for species 2 may subsume confined movements (see Extended Data Fig. 5j,k for additional models).

Source Data

Jump step analysis revealed that all movements of Imp α are consistent with a simulated model that includes a single diffusion coefficient (D = 0.049 µm² s⁻¹) and σ_x = 4.45 nm = 0.93σ_y = 1.55σ_z (Fig. 3o, blue curve), which is an unexpectedly good precision for molecules moving with more than 20-nm average steps. Such parameters are inconsistent with the experimental data, however, when replotted as an R²/t histogram (Fig. 3p, blue curve). A good fit to both jump step and R²/t histograms could not be obtained when assuming a two-species model (Extended Data Fig. 5j,k). Instead, a three-species model was required to simultaneously obtain a good fit to both the jump step and the R²/t histograms (Fig. 3o,p, red curves). This model assumes that approximately 7% of molecules are tightly bound (the dye is highly immobilized), approximately 56% of molecules are highly confined (no diffusion coefficient) and yet poorly localized (probably due to localized translational movements and/or rotations of the complexes, conditions that can lead to dye displacements on the order of approximately 10 nm), and 37% of the molecules are moving with a diffusion coefficient of 0.055 µm² s⁻¹ (Fig. 3o,p). This model is consistent with visual inspection of the trajectories, where binding behaviour is seemingly observed as a series of localized small steps interspersed with movements that generated larger displacements (for example, Fig. 3b,d). This behaviour is consistent with a model in which NPC transport is mediated by a series of weak interactions between NTRs and the disordered polypeptides of the permeability barrier, but, in addition, translocation pauses occasionally occur, which may reflect staging sites for functionally important biochemical reactions (such as permeability barrier constraints, higher-affinity interactions, or transport complex assembly and disassembly reactions). Considering the relatively low number of trajectories recovered thus far, additional work is needed to establish and characterize translocation pause sites more thoroughly. The major findings of the jump step analysis are a direct estimate of the average diffusion coefficient, the localization precision for the moving particles (see Extended Data Fig. 5j,k for additional models) and the identification of multiple molecular species. The localization precision of approximately 7.2–8.2 nm during tracking (Fig. 3o,p and Extended Data Fig. 5j,k) was substantially worse than the approximately 4-nm precision obtained for the NPC scaffold dye (Fig. 1h), which is consistent with the worse localization precision expected due to movement.

The vacant centre

The absence of localizations near the central transport axis (Fig. 3g,k) is consistent with our previous work⁷. To more firmly demonstrate the absence of MINFLUX localizations within the pore centre, a volume-corrected radial density map was constructed from all localizations in the vicinity of an NPC (Fig. 4a). One potential concern is that the experimental strategy might have missed fast events going through the central region of the pore. However, the fact that molecules were first localized outside the pore and then continuously tracked for tens of localizations going through the pore without crossing through the pore centre laterally suggests a barrier to access the NPC centre. To further probe accessibility, Imp β1 was tagged with the photoactivatable fluorescent protein mEosEM²⁵. NPCs were saturated with Imp β1–mEosEM, and then single photoactivated mEosEM molecules were localized using 3D astigmatism microscopy at 70 ms per frame (Fig. 4b,c, Extended Data Fig. 9c,d and Supplementary Video 5). These conditions ensured that the imaged Imp β1–mEosEM was tightly bound and that it did not undergo movement within or through NPCs during imaging. Here too we observed a clear absence of molecules near the central transport axis within the pore scaffold region (Fig. 4c). Translocation-arrested import complexes were also preferentially localized to the periphery of the NPC (Fig. 4d). Both Imp β1 and import complexes were redistributed by RanGTPase activity, but still did not occupy the pore centre (Extended Data Fig. 9l,p). Cytoplasmic localizations of Imp β1 and import complexes up to approximately 200 nm away from the pore centre (Fig. 4c,d) indicate the presence of high-affinity binding sites, possibly on disordered FG-containing polypeptides of the permeability barrier that extend for long distances⁵. Lower-affinity binding sites are probably responsible for the migration observed in both import and export trajectories during movements to, from and through the pore. Although bound Imp β1 and translocation-arrested import complexes localized to the extreme periphery of the pore, active transport occurred at a radius of approximately 23 nm (current work) to approximately 30 nm (previous work⁷) from the central axis (Fig. 4e and Extended Data Fig. 9g,h). These data are consistent with a model in which the permeability barrier is divided into three distinct annular zones with respect to the binding behaviour of Imp β1: a non-binding zone (the centre), a transport active zone (approximately 50-nm diameter annulus) and a peripheral zone (strong binding of empty and cargo-loaded Imp β1; Fig. 4f).

Fig. 4: Peripheral binding and translocation.

a, Volume-corrected radial density map for all MINFLUX localizations of Imp α–JF549 (2,678 tracks, n = 48,603 localizations). b, Confocal image of a permeabilized U2OS cell nuclear envelope decorated with Imp β1–mEosEM (excitation = 478 nm). The punctate pattern indicates localization to NPCs. Typical result from n = 41 cells. c, Volume-corrected radial density map of Imp β1–mEosEM showing peripheral binding within the pore. Reference NPC scaffolds were identified as described earlier⁷, and mEosEM was localized by astigmatism imaging (excitation = 561 nm) after photoactivation (excitation = 408 nm; n = 5,500 localizations, 48 cells, 412 NPCs; see Extended Data Fig. 9c,d and Supplementary Video 5). d, Volume-corrected radial density map for translocation-arrested import complexes (Imp β1/Imp α/NLS–BFP–mEosEM). Binding within the pore was largely at the periphery, yielding a largely vacant centre (n = 4,361 localizations, 39 cells, 391 NPCs), similar to Imp β1 alone (c). The white curved lines in a,c,d approximate the locations of the nuclear envelope. The image in a is scaled from 0 (black) to maximum density (yellow); c,d are scaled to 70% and 60% of maximum, respectively, due to the hotspots at approximately 100 nm and approximately 170 nm above the pore centres (see Extended Data Fig. 9e,f for full scale). Average localization densities from a,c,d were calculated for |z | ≤ 15 nm. e, Localization densities for bound Imp β1, translocation-arrested import complexes and actively transiting Imp α. f, Annular zone model. Three distinct binding behaviours for Imp β1 were observed: (I) an empty centre (no binding); (II) a transport active zone (low-affinity binding of import complexes); and (III) a high-affinity binding zone for Impβ1 and import complexes. INM, inner nuclear membrane; ONM, outer nuclear membrane. The NPC structure was adapted from ref. ⁴⁸, Cell Press.

Source Data

Discussion

This study illustrates the power of MINFLUX for high spatiotemporal precision 3D tracking of diffusing molecules in the context of a spatially resolved structure. Although millisecond-scale tracking of nuclear transport complexes has been previously described^{7,9,23,24,26,27}, the approximately fivefold longer trajectories reported here in 3D allowed us to uncover multiple critical properties of the NPC permeability barrier. First, transport complexes containing Imp α utilize the same or overlapping translocation conduits for both import and export, and this transport occurs in an annulus with a notable exclusion zone in the pore centre. Second, both import and export were largely confined to an octant within the pore scaffold, probably due to structural constraints established by the rotational symmetry of the NPC^20,28,29. Third, transient pauses were observed; these may reflect staging sites for functionally important biochemical reactions, such as transport complex assembly and disassembly. Last, an apparent diffusion coefficient of approximately 0.055 µm² s⁻¹ (Fig. 3o,p) was obtained, which is over 40× slower than previously reported⁷ and approximately 1,000× slower than free diffusion in buffer (Extended Data Fig. 10). Thus, movements within the NPC permeability barrier are comparable with those in an environment with an effective viscosity similar to glycerol³⁰. Such an environment provides an effective diffusion barrier whose permeability is enhanced by selective access. The power of MINFLUX is evident by comparison with our previous work in which the same import complexes were tracked in 3D via astigmatism imaging using Imp α labelled with four dye molecules at 2-ms resolution. In this previous work, generally only one localization was observed within the NPC scaffold⁷. By contrast, the current study reports trajectories for the same import complex that have a median of seven localizations within this same region, corresponding to a median pore residence time of approximately 14 ms during import (Supplementary Table 4). One explanation is that the high illumination intensities and the greater number of dye molecules in the previous work created local photophysical effects (for example, heating, chemical modifications, among others) that influenced the transport properties of the pore. Alternatively, and more likely, is that rapid photobleaching artificially selected those molecules that transported faster, and local binding events were rejected.

An interesting feature of NPCs is their ability to conduct a massive flux of macromolecules in both directions³¹, traffic that seemingly occurs simultaneously¹¹. Distinct trafficking pathways for import and export would be an elegant solution to avoid unproductive collisions and opposing movements^8,9,10,11,12. Two-dimensional data have been unclear in this regard^8,10,24. The current work, however, argues against this model, as both import and export occurred in an approximately 46-nm diameter annulus, and, surprisingly, both import and export trajectories were largely confined to a single lobe of the octagonal structure, which complicates resolving encounters between traffic moving in opposing directions. Simulations indicate, however, that self-regulating mechanisms can influence binding interactions, and distributions of proteins within the permeability barrier can mitigate anticipated complications due to competition and crowding³². On the basis of structural propensities, it was postulated over a decade ago that regions of different FG-polypeptide densities exist within the pore³³, which could differentiate high-probability regions for translocation (for example, channels). More recently, such conduits were detected in an electron microscopy reconstruction of the permeability barrier³⁴. However, we cannot rule out whether confinement during transport is influenced by direct interactions with the NPC scaffold. The Kap-centric model predicted distinct binding regions for strongly bound (translocation arrested) and weakly bound (transiting) NTRs^35,36, which is supported by the reported data (Fig. 4), although we find that transport occurs in an annulus rather than through the centre of the pore. Of note, a recent cryo-electron microscopy study has found that large preribosomal subunits are exported near the NPC periphery³⁷, which undoubtedly must overlap with the transport pathways characterized here. The absence of any identified transport in this work near the central axis of the NPC remains an intriguing mystery as colloidal gold-labelled import and export cargos have been previously found to be centrally localized^11,12. Although it is possible that the central region is used primarily for mRNA export^8,11, an alternate explanation is that a central plug^29,38 generally restricts access. Thus, the central permeability barrier is subdivided into at least three zones with respect to Imp β1: a central non-binding zone, a transport annulus (r = 23–30 nm from the centre) and a strongly bound annulus (pore periphery). Of note, the lamin-B receptor seemingly migrates around the pore during transport³⁹, suggesting a lack of confinement for membrane proteins and, hence, different structural constraints. Future studies are expected to resolve whether the permeability barrier exhibits different functional properties towards other transport receptors and transport pathways.

Methods

mEosEM fusion proteins

New plasmids were submitted to Addgene, and their construction is described in the history of the linked SnapGene files. Plasmid pET28a–Imp β1–mEosEM encoding Imp β1–mEosEM with a C-terminal 6×His tag was created by attaching mEosEM to the C terminus of human Imp β1. The gene encoding Imp β1 was from pQE9-β1 (ref. ⁴⁹) and the gene encoding mEosEM was from pRSET-mEosEM²⁵. Plasmid pTrcHisA–NLS–BFP–mEosEM encoding NLS–BFP–mEosEM with a C-terminal 6×His tag was created by replacing the C-terminal blue fluorescent protein (BFP) domain in the import cargo NLS–2×BFP⁷ with mEosEM²⁵. Coding sequences were verified by DNA sequencing.

Protein overproduction and purification

Protein overproduction and purification protocols are provided in the following sections or the indicated references. When used, antibiotics were 50 µg ml⁻¹ for ampicillin (Amp) and 30 µg ml⁻¹ for kanamycin (Kan). All purified proteins were aliquoted and stored at −80 °C until use.

LaG-9(S151C), Imp α, Imp β, NLS–2×BFP, RanGDP and NTF2

These proteins were overproduced in Escherichia coli and purified as previously described⁷. Plasmids pET21b–LaG9(S151C) and pNLS–2×BFP are available from Addgene (ID#172490 and ID#176151, respectively).

GST–CAS

The plasmid pGEX4T3–CAS⁵⁰ encodes GST fused to the N terminus of CAS (GST–CAS). JM109 cells⁵¹ transformed with pGEX4T3–CAS were inoculated into 5 ml Luria-Bertani (LB) medium⁵² + Amp, and then were incubated overnight at 30 °C. The following day, the starter culture was transferred to 0.5 l LB + 1% glucose + Amp and incubated at 30 °C. At an optical density at 600 nm (OD₆₀₀) of approximately 2, 2 mM isopropyl-β-d-1-thiogalactopyranoside (IPTG) was added, and the culture was incubated for another 2 h at 30 °C. The cells were harvested by centrifugation (at 5,000g for 10 min at 4 °C). The cell pellet was resuspended in 1.5 ml of 10× PBS (1.37 M NaCl, 27 mM KCl, 100 mM Na₂HPO₄ and 18 mM KH₂PO₄) and 13.5 ml of H₂O, and then 5 mM dithiothreitol, 5 mM phenylmethane sulfonyl fluoride (PMSF) and 1 mg ml⁻¹ lysozyme were added. Cells were lysed by French Press (three times at 16,000 psi). The lysate was centrifuged (at 10,000g for 15 min at 4 °C) and the supernatant was mixed with 0.6 ml of glutathione Sepharose beads (#GE17-0756-01, Millipore Sigma) that had been equilibrated with ice cold PBS. After rotary incubation (for 3 h at 4 °C), the suspension was transferred to a gravity column, and the resin was washed with 10 ml of PBS + 0.1 mM PMSF, 10 ml of PBS + 600 mM NaCl, and then 10 ml of PBS + 0.1 mM PMSF. The protein was eluted (1-ml fractions) with ice-cold 100 mM Tris-Cl, 120 mM NaCl and 20 mM reduced glutathione, pH 8.

RanGAP and RanBP1

Plasmids pQE60–RanGAP and pQE60–RanBP1 (gifts from D. Görlich)⁴⁹ were used to overproduce Schizosaccharomyces pombe RanGAP and mouse RanBP1, respectively, in JM109. The proteins had a C-terminal 6×His-tag and were purified identically. Cells were inoculated into 5 ml LB + Amp, and then were incubated overnight at 37 °C. The following day, the starter culture was transferred to 1 l LB + Amp and incubated at 37 °C. At an OD₆₀₀ of approximately 0.8, 1 mM IPTG was added, and the culture was incubated overnight at 25 °C. The cells were harvested by centrifugation (at 5,000g for 20 min at 4 °C). The cell pellet was resuspended in 20 ml of 5 mM Tris, 200 mM NaCl, 5 mM MgCl₂, 10 mM imidazole, 4 mM β-mercaptoethanol (βME), pH 7.0, + protease inhibitors (1 mM PMSF, 100 µg ml⁻¹ trypsin inhibitor, 20 µg ml⁻¹ leupeptin and 100 µg ml⁻¹ pepstatin A), and then lysed by French Press (three times at 16,000 psi). The lysate was centrifuged (15,000g for 20 min at 4 °C), and the supernatant was mixed with 0.5 ml Ni-NTA resin (rotated for 30 min at 4 °C). The suspension was transferred to a gravity column, and the resin was washed with 20 ml of 5 mM Tris, 500 mM NaCl, 5 mM MgCl₂, 0.1% Triton X-100, pH 8.0, + protease inhibitor and then 20 ml of 5 mM Tris, 50 mM NaCl, 5 mM MgCl₂, 20 mM imidazole, pH 8. The protein was eluted (1-ml fractions) with 5 mM Tris, 50 mM NaCl, 5 mM MgCl₂ and 250 mM imidazole, pH 8. The protein in the highest concentration fraction was purified by Enrich SEC 650 (7801650, Bio-Rad) size-exclusion chromatography using 20 mM HEPES, 110 mM potassium acetate (KOAc), 5 mM sodium acetate (NaOAc), 2 mM magnesium acetate (MgOAc₂) and 2 mM dithiothreitol, pH 7.4.

Imp β1–mEosEM

BL21(DE3) cells⁵³ transformed with plasmid pET28a–Imp β1–mEosEM were inoculated into 5 ml LB supplemented with 2% glucose + Kan, and then were incubated overnight at 37 °C. The following day, the starter culture was transferred to 1 l of LB medium with 2% glucose and Kan and incubated at 37 °C. At an OD of approximately 0.8, 0.7 mM IPTG was added, and the culture was incubated for another 3 h at 37 °C. The cells were harvested by centrifugation (at 5,000g for 10 min at 4 °C). The cell pellet was resuspended in 6 ml of 5 mM Tris, 500 mM NaCl, 5 mM MgSO₄, 10 mM imidazole, 4 mM βME, pH 8.0, + protease inhibitors and then lysed by French Press (three times at 16,000 psi). The lysate was centrifuged (at 15,000g for 20 min at 4 °C), and the supernatant was mixed with 0.5 ml Ni-NTA resin (rotated for 30 min at 4 °C). The suspension was transferred to a gravity column, and the resin was washed with 20 ml of 5 mM Tris, 500 mM NaCl, 5 mM MgSO₄, 10 mM imidazole, 4 mM βME, 0.1% Triton X-100, pH 8.0, + protease inhibitors and then 20 ml of 5 mM Tris, 100 mM NaCl and 10 mM imidazole, pH 8. The protein was eluted (500-µl fractions) using 5 mM Tris, 100 mM NaCl and 250 mM imidazole, pH 8.0. The highest concentration fractions were combined, and the protein was purified by Enrich SEC 300 size-exclusion chromatography using 20 mM HEPES, 110 mM KOAc, 5 mM NaOAc, 2 mM MgOAc₂ and 2 mM dithiothreitol, pH 7.4.

NLS–BFP–mEosEM

JM109 cells⁵¹ transformed with plasmid pTrcHisA–NLS–BFP–mEosEM–6×His were inoculated into 5 ml LB + Amp, and then were incubated overnight at 37 °C. The following day, the starter culture was transferred to 1 l LB + Amp and incubated at 37 °C. At an OD of approximately 0.8, 0.7 mM IPTG was added, and the culture was incubated for 14 h at 25 °C. The remainder of the protein purification protocol was identical to that for Imp β1–mEosEM.

Protein labelling

The spontaneously blinking dye HMSiR maleimide (SaraFluor 650B-maleimide; A209-01, Goryo Chemical) was attached to the C-terminal cysteine on the anti-GFP nanobody LaG-9(S151C) by incubating with a 15-fold molar excess at room temperature for 15 min to yield Nb^GFP–HMSiR. Imp α was under labelled with JF549 maleimide (Janelia Fluor 549 maleimide; 6500, Tocris) by incubating with a 10-fold molar excess at room temperature for 15 min in 20 mM HEPES, 150 mM NaCl, pH 7.4 (maximum reaction volume of 1 ml) to yield Imp α–JF549. On the basis of the concentration-dependent labelling efficiency, this molar excess produced approximately 25% labelling saturation (approximately 1 cysteine labelled, on average, out of the 4 available reactive cysteines). The reactions were quenched with 10 mM βME. Excess dye was removed by adding the dye–protein mixture to 0.1 ml Ni-NTA resin (30-min incubation), washing the resin-bound protein with 50 ml of 20 mM HEPES, 500 mM NaCl, 0.1% Triton X-100, pH 7.3, and 20 mM HEPES and 150 mM NaCl, pH 7.3, and then eluting the labelled proteins with 20 mM HEPES, 150 mM NaCl and 250 mM imidazole, pH 7.3.

Protein concentrations and labelling purity

Protein concentrations were determined by densitometry using SDS–PAGE gels stained with Coomassie Blue R-250 with bovine serum albumin as a standard and a ChemiDoc MP imaging system (Bio-Rad Laboratories). The purity of dye-labelled proteins was more than 95%, as determined by in‐gel fluorescence imaging using the same ChemiDoc imaging system.

Cell culture

For MINFLUX imaging, U2OS-CRISPR–NUP96–mEGFP clone #195 (300174, CLS GmbH) cells were grown in Dulbecco’s modified eagle medium (11880028, Thermo Fisher Scientific) supplemented with 1× MEM non-essential amino acids solution (11140050, Thermo Fisher Scientific), 1× GlutaMAX solution (35050061, Thermo Fisher Scientific), 1× ZellShield (13-0050, Minerva Biolabs) and 10% (v/v) fetal bovine serum (F7524, Sigma) in 5% (v/v) CO₂ enriched air at 37 °C. Cells were typically grown to approximately 80% confluency and split using TrypLE Express (12604013, Thermo Fisher Scientific) without phenol red.

For 3D astigmatism and Luminosa confocal imaging, U2OS-CRISPR–NUP96–mEGFP clone #195 and U2OS (300364, CLS GmbH) cells were grown in McCoy’s 5A (modified) media (16600082, Thermo Fisher Scientific) supplemented with 100 U ml⁻¹ penicillin–streptomycin (15140148, Thermo Fisher Scientific), 1 mM sodium pyruvate (11360070, Thermo Fisher Scientific), 1× MEM non-essential amino acids solution (11140050, Thermo Fisher Scientific) and 10% (v/v) fetal bovine serum (A3160401, Thermo Fisher Scientific) in 5% (v/v) CO₂ enriched air at 37 °C. Cells were typically grown to approximately 95% confluency and were split using Accutase (A1110501, Thermo Fisher Scientific). Cells were grown from fresh stocks and used within 1 month; they were not tested for mycoplasma contamination or authenticated.

3D MINFLUX imaging

Microscope system

A MINFLUX 3D microscope (Abberior Instruments) was used for all MINFLUX localization and tracking experiments. A 100× oil immersion objective lens (UPL SAPO100XO/1.4, Olympus) and 488-nm, 561-nm and 642-nm CW excitation lasers were used for mEGFP confocal imaging, cargo tracking and NPC scaffold localization, respectively. Four avalanche photodiodes (SPCM-AQRH-13, Excelitas Technologies) with detection ranges of 500–550 nm, 580–630 nm, 650–685 nm and 685–760 nm were used with a pinhole size corresponding to 0.78 airy units. All hardware was controlled by Abberior Imspector software (v16.3.13924-m2112). Drift during tracking was minimized using the built-in stabilization system with typical drifts less than 1 nm in xyz. Scattering from 200 nm gold nanoparticles (A11−200-CIT-DIH-1-10, Nanopartz) pre-deposited on the coverslip surface and at a similar z height to the bottom of the nucleus were used as a positional reference for the sample stabilization and two-colour alignment registration.

Sample preparation

Six channel μ-Slide VI 0.5 glass bottom slides (80607, Ibidi) were pre-treated with 200 nm gold nanoparticles (used as a positional references) and poly-l-lysine (which reduced cell-detachment after permeabilization). Undiluted 200 nm gold nanoparticles (A11-200-CIT-DIH-1-10, Nanopartz) were added to each channel, and 15 min later were washed away with 1× PBS. Then, 50 µl of 0.01% poly-l-lysine (P4832, Sigma) was added to each lane. After 5 min, the lanes were washed with cell culture media (3 × 100 µl). Freshly split U2OS NUP96–mEGFP cells (to less than 60% confluence) were grown overnight on the pre-treated coverslips. The next day, the cells were washed with 50 µl of import buffer (20 mM HEPES, 110 mM KOAc, 5 mM NaOAc, 2 mM MgOAc₂ and 1 mM EGTA, pH 7.3) and then permeabilized by the addition of 2 × 50 µl of 40 µg ml⁻¹ digitonin in import buffer for 3 min. Permeabilized cells were washed once with 50 µl import buffer–polyvinylpyrrolidone (IB–PVP; import buffer containing 1.2% (w/v) PVP (360,000 g mol⁻¹; P5288, Sigma)). This permeabilization method was slightly modified from Yang et al.²⁶ to accommodate the different cell line and growth conditions. Nb^GFP–HMSiR in IB–PVP (40 µl, 150 nM) was incubated with the permeabilized cells for 6 min. The cells were washed twice (2 × 40 µl IB–PVP). ‘Transport mix’ (40 µl), consisting of 1.5 µM RanGDP, 1.5 µM NTF2, 1.0 µM RanGAP, 1.0 µM RanBP1, 1 mM GTP, 0.5 µM Imp β1, 0.5 µM NLS–2×BFP, 2 µM GST–CAS and 1 nM Imp α–JF549 in IB–PVP was added to the permeabilized nanobody-tagged cells, and MINFLUX imaging begun approximately 1 min after addition.

Imaging and tracking

A diagonal scanning approach with a grid spacing of 300 nm was used to find both fluorophores, and then an iterative strategy within z = 0 ± 400 nm was used to localize HMSiR on the NPC scaffold or to track Imp α–JF549 in 3D. Non-default measurement parameters for the individual MINFLUX scan iterations are summarized in Supplementary Tables 1 and 3. The pooled results reported here were acquired using slightly different measurement parameters to optimize signal acquisition over background contributions. The data obtained via these distinct imaging conditions are identified as datasets 1 and 2 (see Supplementary Tables 1 and 3). Approximately 15–20 min was used for Nb^GFP–HMSiR localizations, and approximately 15–20 min was used for tracking cargo transport. Confocal images of the mEGFP fluorescence (excitation = 488 nm) from NUP96–mEGFP in the region of interest were obtained at the beginning and end of MINFLUX imaging.

Channel alignment

Coordinates were transformed from the JF549 emission channel to the HMSiR emission channel, which was the reference. The xyz coordinates from the same 8–10 gold nanoparticles (200 nm) on each cell were measured every few seconds during the two independently recorded MINFLUX datasets (HMSiR imaging and cargo tracking). During post-processing, the gold nanoparticle coordinates from the two datasets were used to derive an xy alignment matrix incorporating rotational and translational corrections, as described earlier⁷, which was used to transform the JF549 coordinates to the HMSiR coordinate system with a precision of approximately 2 nm. A correction factor of 0.67 as determined in Extended Data Fig. 4 was applied to all z values. The mean z position for the gold nanoparticles associated with each cell differed by 5–14 nm between the two channels, and the z coordinate was corrected by simple subtraction of this mean z deviation.

Data filtering parameters

Multiple parameters providing information about the photons collected in the MINFLUX scan patterns were used for data filtering. These are reported as frequencies (in kHz) or ratios. The frequencies are discrete variables, as they were obtained by dividing the number of photons collected (that is, a quantized variable) during a collection period:

Effective frequency at centre

The effective frequency at centre (EFC) is the emission frequency measured at the centre of the MINFLUX scan pattern.

Effective frequency at offset

The effective frequency at offset (EFO) is the averaged emission frequency measured over all points in the xy plane of the MINFLUX scan pattern except for the centre.

Centre frequency ratio

The centre frequency ratio (CFR) is the ratio of the EFC and EFO, that is, CFR = EFC/EFO. The CFR is a measure of the quality of a localization. As the fewest photons are collected when the centre of the excitation donut coincides with the fluorophore position, a high CFR can indicate that the centre of the scan pattern is not well localized to the position of the fluorophore or that a second fluorophore is close by. Thus, lower CFR values indicate good localizations.

Detector channel ratio

The detector channel ratio (DCR) is the fractional component of photons collected in one of two channels. It is used to distinguish fluorophores with different emission spectra present within the same sample, and it can be effective for eliminating some background signals. For example, if detector channel 1 collects an emission frequency in the 650- to 685-nm range (EF1), and detector channel 2 collects an emission frequency in the 580- to 630-nm range (EF2), the detector channel ratio = EF1/(EF1 + EF2).

Identifying NPC scaffolds from HMSiR localizations

3D HMSiR localizations were obtained using an eight iteration MINFLUX sequence (Supplementary Table 1). Iterations 1–6 were used first to locate the molecule and then for progressively increased localization precision. The final output coordinates came from iteration 7 (xy) and iteration 8 (z). The CFR upper limit was set to 0.8 (see Extended Data Fig. 6a) and was checked within iteration 7. This CFR check occurred at the level of data acquisition to help eliminate acquisitions where two nearby HMSiR molecules were simultaneously in the ‘on’ state. Successive localizations occurred by cycling between iterations 7 and 8 until the CFR check failed, or the fluorophore switched off for longer than 3 ms. To distinguish HMSiR localizations from background noise, an EFO lower limit of 25 kHz or 50 kHz (for datasets 1 and 2, respectively) was used during acquisition. An upper EFO threshold of 60 kHz or 100 kHz (for datasets 1 and 2, respectively) was used post-acquisition to eliminate signals from multiple dye molecules that were not eliminated by the CFR check during acquisition (see Extended Data Fig. 6b). HMSiR localizations were exported using ‘MINFLUX-BASE Imspector 16.3.15620’ and Paraview 5.8.1 software.

Individual NPCs were identified, and averaged NPC scaffolds were generated essentially as done previously using localizations from astigmatism imaging⁷. This approach is briefly outlined here and in Extended Data Fig. 3. The localizations in each of the individual NPC localization clusters were fit to a double-circle model, which reflected the double-ring structure of NUP96 within the NPC (Fig. 1a). Owing to the relatively flat nuclear envelope, we assumed that the two circles were both parallel to the xy plane with their centres defining an axis parallel to the z axis. Although the nuclear envelope was not perfectly flat (for example, Fig. 1d), the angular tilt of the NPCs used was less than 10°, consistent with our previous analysis⁷. The angles of the individual localizations relative to the centroid obtained from the double-circle fit for each NPC were binned (0–45°), assuming an eightfold periodicity, and fit to a sinusoidal function with a 45° period and a variable phase. The individual localization clusters were rotated in the xy plane about their xyz centroids using the determined phase angle, and then these clusters were aligned on the basis of their xyz centroids to yield averaged NPC scaffolds (for example, Fig. 1g,h and Extended Data Fig. 3e). All the fitting routines were performed using MATLAB scripts available on GitHub (https://github.com/npctat2021/MINFLUX_NPC_Tracking.git).

Measuring the z-scaling factor

The z-axis data in 3D MINFLUX imaging required a correction to account for spherical aberrations caused by the difference in refractive index of the sample (approximately 1.33) and that of the immersion medium (1.51) used with the objective. The z-scaling factor of 0.7 recommended by the manufacturer of the MINFLUX microscope was calculated on the basis of simulations⁵⁴. This z-scaling factor has been applied previously to 3D MINFLUX data^2,16,17 and has been directly measured as 0.69 (ref. ⁵⁵). The z-scaling factor used here was estimated from independent measurements of NPC scaffold structures as determined by HMSiR astigmatism imaging (see the ‘3D astigmatism imaging’ section). The advantage of this approach is that both MINFLUX and astigmatism measurements were made under identical conditions (the same buffer and added reagents, cell type, nanobodies, HMSiR labelling conditions and range of z heights above the surface) and the astigmatism measurements were independently calibrated for each day’s experiments by imaging beads while z stepping a nanostage⁷. As the z spacing between the two rings of the NPCs at the bottom of cell nuclei can be assumed to be identical for both imaging strategies, the astigmatism ring spacing of 51.5 ± 1.1 nm was used to correct the raw MINFLUX data, where the ring spacing was determined as 76.8 ± 0.8 nm (see Supplementary Table 2 and Extended Data Fig. 4). The z-scaling factor was therefore calculated as 51.5 nm/76.8 nm = 0.67. This value was used for all MINFLUX z-axis scalings. A direct comparison of the MINFLUX and astigmatism NPC images and the corresponding data is shown in Extended Data Fig. 4, and a summary of the associated parameters is given in Supplementary Table 2.

Identifying Imp α trajectories from JF549 localizations

After collecting the NPC scaffold data, the scanning and localization protocol for JF549 was implemented and continued for approximately 15–20 min. For tracking Imp α–JF549, the five iteration MINFLUX sequence was designed to be as fast as possible with an octahedral scan pattern in the last iteration, which yielded an xyz localization within a single step (Supplementary Table 3). The fifth iteration was repeated if insufficient photons were collected (20 or 25 minimum; see Supplementary Table 3) or to yield the next localization within the trajectory until the particle was lost. Unlike for HMSiR localizations in which the CFR check during imaging was set to a low value to select for high-quality localizations at the time of acquisition, for tracking, the CFR ratio was set to a large cut-off (more than 2.0) to avoid rejecting tracks that were temporarily interrupted. Instead, the CFR was checked during data analysis of the localization data. All detected tracks within the acquisition volume (z = 0 ± 400 nm) were identified with Abberior Imspector 16.3.15620 and Paraview 5.8.1 software and exported to MATLAB format. Imp α–JF549 trajectories were converted into red channel (HMSiR) coordinates via the alignment procedure discussed earlier. The data were curated by eliminating those tracks that did not have any localizations within a 400-nm cube centred on an NPC. Each trajectory was then rotated by the same angle as the NPC that it was linked to. The alignment routine was performed using MATLAB scripts available on GitHub (https://github.com/npctat2021/MINFLUX_NPC_Tracking.git). For trajectories that entered an NPC scaffold (|z| ≤ 25 nm), the tracks were verified as authentic using the criteria summarized in Extended Data Fig. 6c–f. Although there was some background fluorescence and leakage from HMSiR fluorescence within the permeabilized cells, tracks that resulted from this background were effectively eliminated with a DCR filter (Extended Data Fig. 6c,d). On the basis of the earlier results⁵⁶, we used a CFR of less than 0.8 (Extended Data Fig. 6e). The EFO was used to eliminate background signals, but it also indicated that approximately 10–15% of transport trajectories had two JF549 dyes on Imp α instead of one (Extended Data Fig. 6f). This was an expected consequence of the under-labelling strategy. The reference angle in Fig. 3h,l was the localization nearest the pore midplane (z = 0), except for three cases of poor localization precision.

3D astigmatism imaging

Microscope system

The 3D astigmatism microscope system was described earlier⁷ and was used here without modification except that a ×2 magnifying lens was removed⁵⁷ and either a Prime 95B or Kinetix22 CMOS camera (both from Teledyne Photometrics) was used for imaging, which yielded square pixels of 120 nm and 138 nm at camera plane, respectively. A TIRF-lock system provided a z stability for the coverslip of less than 3 nm for the duration of the experiment. The astigmatism was set to 60-nm root mean square (rms) deviation using a deformable mirror to generate the z-dependent spot ellipticity needed for 3D information. Orange (mEosEM) and red (HMSiR) fluorescence emission were collected with a quad-bandpass filter set (ZT405/488/561/640/rpcv2-UF2, Chroma). Data collection on this Zeiss 200M microscope was acquired using Micro-Manager 2.0 (ref. ⁵⁸). The Mirao 52-e deformable mirror system (Imagine Optic) used for wavefront correction and to create astigmatism utilized CasAO 1.0 and MiCAO 1.3. The Nano-LPS200 piezo nano-positioning stage controlling a TIRF-lock stabilization system (Mad City Labs) was controlled by LabVIEW 2015. Image J (Fiji 1.52P), Origin 8.5, Kaleidagraph 5.01 and Microsoft Excel 16.76 (23081101) were used for data analysis, data presentation and simulations.

Sample preparation

Freshly split U2OS NUP96–mEGFP cells were grown overnight at less than 60% confluence on #1.5 coverslips (24 × 60 mm; 16004-312, VWR), which were pretreated with 0.01% poly-l-lysine (P4832, Sigma) for 10 min at room temperature and air-dried overnight. The next day, flow chambers (approximately 10 µl) were constructed by inverting a small coverslip (10.5 × 35 mm; 72191-35, Electron Microscopy Sciences) with beads of high-vacuum grease parallel to its short edges over the cells⁵⁹. Cells within the flow chambers were permeabilized by incubating with digitonin (40 µg ml⁻¹) in import buffer for 3 min. Permeabilized cells were washed once with 10 µl IB–PVP. Then, 10 µl of 150 nM Nb^GFP–HMSiR in IB–PVP was flowed onto the permeabilized cells and incubated for 3 min. The cells were washed (2 × 10 µl IB–PVP) and then Imp β1–mEosEM (0.5 µM) or a mixture of Imp β1 (0.5 µM), Imp α (0.5 µM) and NLS–BFP–mEosEM (0.5 µM) was added. After 10 min, the permeabilized cells were washed twice (2 × 10 µl IB–PVP) to remove unbound proteins. For Extended Data Fig. 9j–l, cells with bound Imp β1–mEosEM were incubated with ‘Ran mix’ (2 × 10 µl; 1.5 µM RanGDP, 1.5 µM NTF2, 1 mM GTP, 1 µM RanBP1 and 1 µM RanGAP in IB–PVP) for 10 min, and then washed (2 × 10 µl IB–PVP). For Extended Data Fig. 9n–p, cells with bound Imp NLS–BFP–mEosEM (cargo complexes) were incubated with ‘transport mix–high-α’ (2 × 10 µl; 1.5 µM RanGDP, 1.5 µM NTF2, 1.0 µM RanGAP, 1.0 µM RanBP1, 1 mM GTP, 0.5 µM Imp β1, 0.5 µM Imp α, 0.5 µM NLS–2×BFP and 2 µM GST–CAS in IB–PVP) for 10 min, and then washed (2 × 10 µl IB–PVP). Note that ‘transport mix–high-α’ is the same composition of proteins used in the simultaneous import–export MINFLUX experiments (‘transport mix’), except with a higher concentration of Imp α (non-fluorescent).

3D localizations

HMSiR localizations were acquired first (excitation = 641 nm; 50 ms per frame, twenty 500-frame videos with a 5-s gap between videos), and then the photoactivatable mEosEM was imaged (excitation = 561 nm; 70 ms per frame, thirty 1,000-frame videos with a 5-s gap between videos) in the presence of constant UV illumination (activation laser, 408 nm). Data analysis to identify and align NPC scaffolds and to then align mEosEM localizations with these scaffolds was performed as described earlier⁷. With minimum photon counts of 3,000 and 1,000 for HMSiR and mEosEM, respectively, the average precisions were 4.2–5.4 nm and 6–8.3 in xy, and 8.7–9.9 nm and 14.6–15.2 nm in z, determined as previously described^7,57. Note that the precisions varied slightly for the two cameras used⁵⁷.

Channel alignment

The two channels were aligned by imaging five 0.1-µm TetraSpeck microspheres (T7279, Thermo Fisher Scientific) embedded in 2% agarose, as previously described⁷, with a precision of 1–2 nm (xy) and 3–7 nm (z).

Confocal imaging and fluorescence correlation spectroscopy

Confocal imaging and fluorescence correlation spectroscopy (FCS) measurements were performed with a Luminosa single-photon counting confocal microscope (Picoquant). For confocal imaging of NPCs in U2OS cells decorated with mEosEM fusion proteins, samples were prepared as for astigmatism imaging, except that the final wash step before adding Nb^GFP–HMSiR and the mEosEM protein was 3 × 10 µl IB–PVP. Imaging of mEosEM was performed using 478-nm excitation in continuous-wave mode. FCS experiments of purified proteins were performed in buffers as indicated in Extended Data Fig. 10 using the FCS measurement function of the Luminosa system software (Luminosa 1.0.0.4067).

Error estimation and dye movement analysis

Jump histograms

Jump probability histograms summarize the measured distances between two successive localizations, either for static particles (for example, on the NPC scaffold) or for moving particles (for example, cargo movement around and through the NPC). The following jump probability distributions (equations (1)–(4)) were summarized earlier⁷ and are provided here for completeness. These distributions assume anisotropic translational movement described by a diffusion coefficient, D. All distributions are normalized (that is, the sum of all probabilities = 1):

One dimension:

$$p(x\,;D,t){\rm{d}}x=\frac{2b}{\sqrt{4\pi Dt}}\exp \left(-\frac{{x}^{2}}{4Dt}\right){\rm{d}}x$$

(1)

where t is the time between successive localizations, b is the bin size of the jump distances, and x is the measurement axis for the displacements. This is a Gaussian (normal) distribution, except that we have assumed that all the jump distances are positive for easier comparison with the 2D and 3D cases, which necessitates the factor of 2.

Two dimensions:

$$p(r\,;D,t){\rm{d}}r=\frac{br}{2Dt}\exp \left(-\frac{{r}^{2}}{4Dt}\right){\rm{d}}r$$

(2)

where r² = x² + y².

Three dimensions:

$$p(R\,;D,t){\rm{d}}R=\frac{{bR}^{2}}{\sqrt{4\pi }{(Dt)}^{\frac{3}{2}}}\exp \left(-\frac{{R}^{2}}{4Dt}\right){\rm{d}}R$$

(3)

where R² = x² + y² + z². If there are distinct molecular populations with different diffusion coefficients, a weighted sum can be generated. For example, for two species in 3D:

$$p(R\,;{D}_{1},{D}_{2},A,t){\rm{d}}R=[Ap(R\,;{D}_{1},t)+(1-A)p(R\,;{D}_{2},t)]{\rm{d}}R$$

or,

$$p(R\,;{D}_{1},{D}_{2},A,t){\rm{d}}R=\frac{{bR}^{2}}{\sqrt{4\pi }}\left[\frac{A}{({D}_{1}t{)}^{\frac{3}{2}}}\exp \left(-\frac{R}{4{D}_{1}t}\right)+\frac{1-A}{({D}_{2}t{)}^{\frac{3}{2}}}\exp \left(-\frac{R}{4{D}_{2}t}\right)\right]{\rm{d}}R$$

(4)

where A is a weighting factor for the two distributions. In this case, there are three fitting parameters, D₁, D₂ and A for a fixed time step t.

Time-independent histograms

The jump probability histograms described by equations (1)–(4) are valid for equal time steps (t = constant). For larger t, the distributions become broader, a consequence of larger average jump distances. MINFLUX localizations are typically rejected unless a minimum number of photons are collected; this is typically rectified by repeating the localization process until the minimum photon limit is met, leading to unequal timesteps (see Extended Data Fig. 1). To correct for unequal timesteps, the probability distributions for isotropic diffusion can be converted to time-independent expressions with a change of variables. For completeness, this is demonstrated here for all three cases, although only the approach of the 3D case was used to analyse data (for example, Fig. 3p and Extended Data Fig. 5).

One dimensions:

Assume, $u=\frac{{x}^{2}}{t}$

Then: ${\rm{d}}u=\frac{2x}{t}{\rm{d}}x$ and $\sqrt{u}=\frac{x}{\sqrt{t}}$

From equation (1),

$$\begin{array}{l}p(x\,;D,t){\rm{d}}x\,=\,\frac{2b}{\sqrt{4\pi Dt}}\exp \left(-\frac{{x}^{2}}{4Dt}\right){\rm{d}}x=\,\frac{2b}{\sqrt{4\pi Dt}}\frac{t}{2x}\exp \left(-\frac{{x}^{2}}{4Dt}\right)\frac{2x}{t}{\rm{d}}x\\ \,\,\,\,=\,\frac{b}{\sqrt{4\pi D}}\frac{\sqrt{t}}{x}\exp \left(-\frac{{x}^{2}}{4Dt}\right)\frac{2x}{t}{\rm{d}}x\end{array}$$

or,

$$p(u\,;D){\rm{d}}u=\frac{b}{\sqrt{4\pi Du}}\exp \left(-\frac{u}{4D}\right){\rm{d}}u$$

(5)

Two dimensions:

Assume, $u=\frac{{r}^{2}}{t}$

Then: ${\rm{d}}u=\frac{2r}{t}{\rm{d}}r$

From equation (2),

$$p(r\,;D,t){\rm{d}}r=\frac{br}{2Dt}\exp \left(-\frac{{r}^{2}}{4Dt}\right){\rm{d}}r=\,\frac{b}{4D}\exp \left(-\frac{{r}^{2}}{4Dt}\right)\frac{2r}{t}{\rm{d}}r$$

or,

$$p(u\,;D){\rm{d}}u=\frac{b}{4D}\exp \left(-\frac{u}{4D}\right){\rm{d}}u$$

(6)

Three dimensions:

Assume, $u=\frac{{R}^{2}}{t}$

Then: ${\rm{d}}u=\frac{2R}{t}{\rm{d}}R$ and $\sqrt{u}=\frac{R}{\sqrt{t}}$

From equation (3),

$$p(R\,;D,t){\rm{d}}R=\frac{b{R}^{2}}{\sqrt{4\pi }{(Dt)}^{\frac{3}{2}}}\exp \left(-\frac{{R}^{2}}{4Dt}\right){\rm{d}}R=\frac{b}{2\sqrt{4\pi }{(D)}^{\frac{3}{2}}}\left(\frac{R}{\sqrt{t}}\right)\exp \left(-\frac{{R}^{2}}{4Dt}\right)\frac{2R}{t}{\rm{d}}R$$

or,

$$p(u\,;D){\rm{d}}u=\frac{b\sqrt{u}}{4\sqrt{\pi }{(D)}^{\frac{3}{2}}}\exp \left(-\frac{u}{4D}\right){\rm{d}}u$$

(7)

If there are distinct molecular populations with different diffusion coefficients, a weighted sum can be generated. For two species in 3D:

$$p(u\,;{D}_{1},{D}_{2},A){\rm{d}}u=[Ap(u\,;{D}_{1})+(1-A)p(u\,;{D}_{2})]{\rm{d}}u$$

or,

$$p(u\,;{D}_{1},{D}_{2},A){\rm{d}}u=\,\frac{b\sqrt{u}}{4\sqrt{\pi }}\left[\frac{A}{{({D}_{1})}^{\frac{3}{2}}}\exp \left(-\frac{u}{4{D}_{1}}\right)+\frac{1-A}{{({D}_{2})}^{\frac{3}{2}}}\exp \left(-\frac{u}{4{D}_{2}}\right)\right]{\rm{d}}u$$

(8)

where A is a weighting factor for the two distributions. In this case, there are three fitting parameters, D₁, D₂, and A.

Simulations

Simulations were performed using the Jump Step Histogram Simulator⁶⁰ to demonstrate the time independence of equation (7). Three-dimensional translational steps were randomly selected from a normal distribution centred around the starting position with a step variance (Var) of Var(R) = 6Dt [with Var(x) = 2D_xt, Var(y) = 2D_yt, and Var(z) = 2D_zt]. The simulations yielded diffusional trajectories unconstrained by boundary conditions (such as the NPC scaffold) with a defined number of localizations per trajectory. In the case of Nb^GFP–HMSiR localizations, diffusional trajectories correspond to sample drift. For the Imp α–JF549 localizations, the diffusional trajectories approximate the jump steps of the protein interacting with the NPC. The simulation program allows for the inclusion of both sample drift and particle movement simultaneously, modelled identically. When the jump (R) histograms shown in Extended Data Fig. 5a were replotted as R²/t histograms, the time dependence vanished (Extended Data Fig. 5b), as predicted by equation (7). The Jump Step Histogram Simulator program⁶⁰ includes additional features to approximate potentially relevant motions of the dye. To approximate a ‘jiggle’, that is, dye movement around a central location, the position of the dye was selected from a normal distribution around a centroid with σ = jiggle. Jiggle was used to approximate the movement of the HMSiR dye around its attachment point to the NPC scaffold, that is, the linkage error, or the localized, constrained movement of Imp α–JF549 within the NPC permeability barrier network. Particle movement was modelled on the basis of its centroid. Hence, rotational error (similar to the linkage error) results from the distance between the dye on the surface of the protein and the particle centroid, for example, rotation of the import and export complexes within the NPC permeability barrier. This rotational error (sphere rotation) was modelled by randomly selecting a position on the surface of a sphere with a defined radius. Both jiggle and rotational error were assumed to equilibrate rapidly such that randomization occurred between timesteps, but nonetheless that distinct positions were populated during measurements.

The probability distributions in equations (1)–(8) do not account for the precision of the measurements. This precision was included in the simulation program (Jump Step Histogram Simulator⁶⁰) by assuming a normally distributed measurement precision (σ) for all localizations. For MINFLUX, σ_z is typically less than σ_x ≈ σ_y (refs. ^2,17), so these were independently adjustable in the simulations; nonetheless, on the basis of Fig. 1i, σ_x/σ_y = 0.93 and σ_x/σ_z = 1.55 were assumed for all simulations. The effects of localization precision on the jump and R²/t histograms are shown in Extended Data Fig. 5c,d. Of note, in the presence of localization precision, the R²/t histograms were no longer independent of t (Extended Data Fig. 5d). This finding led to a wider conclusion that illustrates an important feature of R²/t histograms, namely, that R²/t histograms have different sensitivities to parameters influencing jump step histograms. The magnitude of jump steps squared (R²) for sample drift or particle movements depends on t and, hence, dividing by t makes the values time independent (Extended Data Fig. 4b). However, localization precision, jiggle (linkage error) and rotational error do not depend on time (as modelled here): they yield similar effects on the measurements of R irrespective of the length of the time step. Consequently, they yield effects on R²/t histograms that, as a group, are distinct from the effects of D. This dichotomy is dramatically illustrated in Fig. 3o,p. Although jump histograms could be fit with multiple combinations of parameters, R²/t histograms were substantially more difficult to fit. Consequently, reproducing both histograms with the same parameters significantly increased confidence in the goodness of fit. Critically, the time steps and precision must be accounted for when using simulations to approximate the experimental data.

Simulations that include localization precision, diffusional drift and variable time steps were used to approximate the data in Fig. 1j. As the MINFLUX measurements yielded variable timesteps, the simulations included timesteps distributed according to the observed experimental frequencies (Extended Data Fig. 1). As these data in Fig. 1j reflect the distances between successive localizations of HMSiR fluorophores affixed to or tethered to static objects (NPCs), inclusion of a non-zero diffusion coefficient to improve the fit was not expected but turned out to be the most straightforward way to fit the data. We expect that this ‘diffusional drift’ is not sample drift that would generate large displacements over the total imaging time, as this would make the assembly of the NPC scaffold from the data impossible. Rather, the diffusional drift is confined and models the movement of the dye centroid on the NPC scaffold, for example, to favourable positions enabled by linkage error, or conformational shifts or jiggles of the NPC scaffold. This diffusional drift was instrumental to reproduce the experimental centroid deviations from simulated data (Fig. 1i and Extended Data Fig. 5i).

The data in Fig. 3o,p were fit using simulations that included localization precision, a diffusion coefficient and variable time steps. The localization precisions were independently adjustable for the three distinct molecular species, to account for the fact that the precision of static and moving particles are expected to be different. The effect of localization precision is clearly identified in an R²/t histogram (Extended Data Fig. 5d), and this was the primary initial clue that suggested to us that the precision estimates obtained from centroid deviations were too high. The Imp α–JF549 tracking data revealed that R and t were largely independent (Extended Data Fig. 5l), indicating that the jump histogram (Fig. 3o) largely reflected localization error rather than diffusive motion. This interpretation was borne out by the more complex model used to fit the data and reproduce the R²/t histogram (Fig. 3p).

Reporting summary

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