Diameter dependence of transport through nuclear pore complex mimics studied using optical nanopores

The nuclear pore complex (NPC) regulates the selective transport of large biomolecules through the nuclear envelope. As a model system for nuclear transport, we construct NPC mimics by functionalizing the pore walls of freestanding palladium zero-mode waveguides with the FG-nucleoporin Nsp1. This approach enables the measurement of single-molecule translocations through individual pores using optical detection. We probe the selectivity of Nsp1-coated pores by quantitatively comparing the translocation rates of the nuclear transport receptor Kap95 to the inert probe BSA over a wide range of pore sizes from 35 nm to 160 nm. Pores below 55 ± 5 nm show significant selectivity that gradually decreases for larger pores. This finding is corroborated by coarse-grained molecular dynamics simulations of the Nsp1 mesh within the pore, which suggest that leakage of BSA occurs by diffusion through transient openings within the dynamic mesh. Furthermore, we experimentally observe a modulation of the BSA permeation when varying the concentration of Kap95. The results demonstrate the potential of single-molecule fluorescence measurements on biomimetic NPCs to elucidate the principles of nuclear transport.


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The nuclear pore complex (NPC) forms the sole connection across the nuclear envelope 29 that regulates all transport between the cytoplasm and nucleus. The central channel  (Kim et al., 2018). 35 Recently, it has been discovered that the inner diameter of the central transporter is    (Figure 1 A, bottom). 154 After functionalization, the palladium membrane was mounted in a flow cell made 155 of polydimethylsiloxan (PDMS) which provides a reservoir on the upper side for the 156 addition of analyte, as well as a flow channel on the lower detection side to which a rates by 5% (Appendix 3-Figure 2). 174 The metal membrane was thick enough to prevent the incident laser light from reaching 175 the other side, which served to suppress the background fluorescence coming from 176 the reservoir side. Additionally, the nanopore acted as a zero-mode waveguide (ZMW), 177 resulting in an evanescent wave within the pore that exponentially decays on a length 178 scale of 10 nm to 20 nm, depending on the pore size (Levene et al., 2003). To (Figure 4). 248 Note that for pores above 80 nm diameter, it was necessary to reduce the fraction of 249 labeled proteins five-fold in order to avoid too high event rates that would lead to non-250 linearity in the event detection due to overlapping events. This dilution is accounted for 251 in the reported normalized event rates. We made sure that all data sets showed the 252 same average molecular brightness (i.e., fluorescence signal per molecule). Data sets with 253 lower average molecular brightness, which could occur due to sub-optimal alignment or 254 trapping of air bubbles in the flow cell, were removed from further analysis (see Data 255 analysis for details).
diffusivity of the probe, . Additionally it scales linearly with the cross-sectional area of 261 the pore, given by = 2 and thus it scales quadratically with the pore radius . Further 262 on, it scales inversely with the length of the pore, . This results in a protein dependent 263 translocation rate, 264 Prot = Δ = 2 Δ . (1) As a guide to the eye and for numerical comparison, we fitted the normalized event rates 265 versus pore radius with such a quadratic function, where Prot is the concentration-normalized event rate, is the pore radius, and Prot is the 267 radius of the protein (Kap95 in this case). Note that this equation accounts for a reduction 268 of the effective cross-sectional pore area due to the fact that a protein has a finite volume 269 and hence its center can not fully reach the rim of the pore. The only free parameter in the 270 model is the multiplicative scaling factor which combines the effects of the pore length, 271 concentration gradient, and protein diffusivity, as well as any experimental factors arising 272 from event detection and protein-pore interaction (see Appendix 6 for further details).

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Note that this simple model does not include the pore diameter-dependent reduction In other words, we observed no significant reduction of the normalized event rate for 279 Nsp1-coated pores compared to open pores (Figure 4 A,C). While this is remarkable, since 280 one might a priori expect a reduction of the rate as an Nsp1-filled pore might obstruct 281 protein transport, this finding signals the optimized properties of the Kap95 that interacts 282 in a highly dynamic way with the FG repeats in Nsp1, which facilitate efficient transport.

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Our finding is in agreement with previous results on pores smaller than 30 nm (Jovanovic- indicates that, on the exit side, Kap95 diffuses closer to the pore walls compared to BSA 291 due to interactions with the Nsp1 mesh.

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For BSA, the normalized event rates for Nsp1-coated pores were, by contrast, signifi-293 cantly reduced, especially at small pore diameters (Figure 4 B,D). More specifically, we observed an approximate 10-fold reduction of the event rate for Nsp1-coated pores with 295 a diameter of 35 nm, whereas only a two-fold reduction was observed for pores with a 296 diameter of 100 nm, which further decreases for larger pores (Appendix 6-Figure 2 E).

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Normalized event rates for open pores were well described by the quadratic function 298 Equation 2. However, the BSA data for Nsp1-coated pores could not be described using 299 the quadratic dependence with a single scaling factor over the whole range of pore diam-300 eters due to the steep increase of the event rate for larger pores (Appendix 6- Figure 2 301 B,D). We hence introduced an additional fit parameter , which shifts the onset of the 302 curve to higher pore diameters: The parameter reduces the effective pore diameter accessible to BSA and can be seen because the relative amount of Nsp1 molecules per pore cross-sectional area is reduced, 323 as will be discussed in more detail below.

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While the event rates were adequately described by the quadratic function, we ob-   ( Figure 4 E), which we estimate to be due to pore-to-pore variations of the grafting density. 330 We note that the variability was not due to chip-to-chip variation as a similar spread is 331 also seen within pores that were measured together on one chip in the same experiment 332 (see Appendix 9- Figure 1). 333 Coarse-grained modeling reveals transition of the Nsp1 mesh 334 To gain a microscopic understanding of the structure and dynamics of the Nsp1 meshwork, BSA through the nanopore channel was a rare event, especially at the smaller-size pores.

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To obtain statistically meaningful estimates of the translocation rates, we applied a void  were then obtained using the Arrhenius relation:  (not shown here), which prompted us to probe much lower grafting densities between   concentration on the translocation rates of Kap95 was observed (Appendix 11-Figure 1). 462 This suggests that the binding of Kap95 to the FG-Nup mesh increased the selectivity of this difference was small for Kap95 concentrations of 0 nM and 100 nM, a considerable 467 reduction to almost the bare pore selectivity was observed for 1000 nM Kap95. After this 468 initial step, we found a gradual decrease of the selectivity with the pore diameter, which 469 is expected because the amount of Nsp1 deposited on the pore wall scales only linearly 470 with the pore diameter while the pores cross-sectional area scales quadratically.

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As suggested by the MD simulations, the loss of selectivity for pores above 60 nm may where the factor was the only fit parameter. The unit of the product is a length

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In this study, we present an assay to measure the selectivity of nanopore-based NPC mim-  one could increase the throughput of our approach by moving towards a camera-based 515 readout which would enable the simultaneous reading of hundreds of pores. Despite the 516 many benefits of our approach, some differences remain when comparing our biomimetic 517 ZMW pores to the NPC, as e.g. the 90 nm long channel used here is approximately three 518 times longer (Kim et al., 2018), and FG-Nups are grafted to the entire metal surface rather 519 than being limited to the pore walls. In spite of these differences, the in vitro biomimetic 520 approaches remain useful to study key elements of nuclear transport.

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To evaluate the performance and sensitivity of our approach, it is relevant to compare   Coarse-grained molecular dynamics simulations allowed us to reproduce the experi-567 mental selectivities for a grafting density of 1/(300 nm 2 ). While this value is lower com-568 pared to previous reports on silcon nitride nanopores (Fragasso et al., 2021), we still 569 achieve similar protein densities at the center of the 90 nm-long channel. Similar to the 570 experimental data, the steepest decrease of the selectivity occurred at small diameters.  This occurred due to the following factors. First, the increased entropic cost of extension 584 for the Nsp1 molecules to interact across the pore. Second, the amount of Nsp1 molecules 585 per pore volume decreases with pore diameter, as the volume increases quadratically 586 while the number of molecules increases linearly. Last, while increasing the diameter, also the curvature decreases which reduces the lateral constraint of neighbouring Nsp1. 588 We found experimentally that the main loss of selectivity falls in a size range between 589 40 nm to 60 nm. Intriguingly, it has recently been reported that the inner ring diameter 590 of the NPC can be significantly larger in situ at 60 nm compared to 40 nm for isolated 591 NPCs (Akey et al., 2022). Furthermore, NPC dilation is modulated in cellulo in response to 592 stress conditions such as energy depletion or osmotic shock (Zimmerli et al., 2021). This 593 suggests that the dilation of the NPC might be a way for the cell to tune the permeability 594 of the NPC under stress to increase the selectivity at the cost of lower transport rate .

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In light of Kap-centric models of nuclear transport (Lim et al., 2015), we also tested the however, showed that the selective area fraction within the pore was significantly reduced 608 at 1 µM Kap95, which we attribute to a compaction of the Nsp1 layer. From our data, we 609 found a 2-fold reduction of the cross-sectional area of the Nsp1 layer inside the pore.  Additionally, we acknowledge that 1 µM of Kap95 is still considerably below physiological 620 Kap95 concentrations of around 4 µM (Kalita et al., 2022), so it is hard to relate the effect  629 but instead form percolating hydrogels at high concentration (Frey et al., 2006). These 630 FxFG-Nups are are predominanantly anchored on the nuclear and cytosolic side of the 631 NPC, with Nsp1 being an exception that is also located in the center (Kim et al., 2018). 632 On the other hand, GLFG-type FG-Nups contain a low amount of charged amino acids  , 2021, 2022). 645 Finally, our approach could be used to study the full systems for protein import or 646 export with all required cofactors, including, for example, the Ran system that provides 647 directionality to molecular transport across the nuclear envelope (Görlich and Kutay, 1999). 648 In particular, by using specific labeling coupled with multicolor detection it will be possible 649 to simultaneously follow different components of the transport machinery, providing  (Guimaraes et al., 2013). Unreacted dyes were removed by size 712 exclusion chromatography on a Superdex S200 column pre-equilibrated with PBS buffer.

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To fully remove free fluorophores, labeled Kap95 was further dialyzed as described above.    (Appendix 3-Figure 2). We ensured 779 that the flow was constant between different experiments such that the relative event    (Klughammer et al., 2023a). In brief, photon bursts were detected  Over the course of the study, several data sets had to be discarded based on the 821 following criteria. First, we discarded a data set for which a lower excitation power was 822 used (8 pores). Next, we discarded the data of 4 pores that showed negligible protein 823 translocations due to clogging. For three full data sets totalling 24 pores, we found a  6-Figure 1). 837 Fluorescence Correlation Spectroscopy (FCS) and lifetime analyses were performed 838 using the PAM software package (Schrimpf et al., 2018). For fitting of the FCS curves, 839 the size of the confocal volume was determined from measurements of the free dyes 840 Alexa647 and Alexa488 by fitting a single-component diffusion model with triplet state.

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Axi-radial density maps were obtained from the equilibrium trajectories using the 867 gmx densmap utility of GROMACS, where a sample was taken every 5000 steps (100 ps).

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The 2D number-density maps created by GROMACS (in nm −3 ) were converted to mass 869 densities (in mg/mL) using the average mass of an Nsp1 residue (∼100 Da). We note 870 that the obtained densities are slightly lower than observed previously for 20 nm-pores (Ananth et al., 2018), as there a simplified average residue mass of 120 Da was used.  To assess the path that BSA proteins take through the Nsp1 mesh, we determined the Three-dimensional FDTD simulations were performed using Lumerical FDTD (ANSYS, Inc., 910 USA). The surrounding medium was modeled as water with a refractive index of 1.33.

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The refractive index of the 100 nm thick palladium membrane was modelled according to 912 (Palik, 1998). For the simulation of the excitation field, the ZMW was illuminated by a pulse 913 from a total-field scattered-field source polarized in the x-direction, set as a plane wave 914 source for widefield excitation and a Gaussian source with a numerical aperture of 1.1 915 for focused excitation. The simulation box size was 1x1x0.8 µm 3 for widefield excitation. In the absence of the ZMW, the decay rate of the excited molecule is given by where 0 and 0 are the radiative and non-radiative decay rates. Note that 0 accounts 935 only for internal processes that lead to non-radiative relaxation to the ground state and 936 was assumed to be unchanged in the presence of the ZMW. The intrinsic quantum yield is 937 defined as Φ 0 = 0 /( 0 + 0 ) and was estimated from the measured fluorescence lifetimes 938 0 for BSA-Alexa488 and Kap95-Alexa647 of 2.30 ns and 1.37 ns, respectively, as: where lit and Φ lit are reference values for the free dyes ( lit = 4.0 ns and Φ lit = 0.80 for Kap95-Alexa647, respectively. Note that the quantum yield of Alexa647 increased slightly 943 due to steric restriction when attached to the protein, an effect known as protein-induced 944 fluorescence enhancement (Stennett et al., 2015). The lower quantum yield for BSA-

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Alexa488 compared to the literature value is most likely a consequence of dye-dye inter-946 actions due the high degree of labeling of ≈ 6 dye molecules per protein, as specified by 947 the manufacturer.

948
In the presence of the nanostructure, the radiative decay rate is modified and an 949 additional non-radiative rate loss is introduced because part of the power emitted by the where 0 and are the radiative rates in the absence and the presence of the ZMW 953 respectively. The absolute decay rates , loss , and 0 cannot be obtained from FDTD where and 0 are the powers radiated by the dipole in the presence and absence of 958 the ZMW, and ff is the power that is radiated into the far-field in the presence of the 959 ZMW. The fluorescence lifetime is given by the inverse of the sum of all de-excitation 960 rates and can be obtained from eq. 8 using the relation = Φ/ as: Here, the intrinsic radiative rate 0 in the numerator was estimated as 0 = Φ lit / lit . The  2-Figure 4. 972 Using the signal profile ( ), we compute the signal-averaged fluorescence lifetime 973 ⟨ ⟩ as: which agrees well with the experimental fluorescence lifetimes measured in the translo-975 cation experiments (Appendix 2-Figure 4). repository at (Klughammer et al., 2023b)). Next, we switched the buffers to 150 mM of KCl in 1xTE and flushed 500 nM of BSA followed by TE buffer and 500 nM of Kap95. After switching back to TE buffer, we found a frequency shift of less than 5 Hz, which was much less than expected for untreated surfaces (Appendix 1-Figure 2). This result indicates that the surface had been passivated against proteins adhering to the surface. While   (Appendix 1-Figure 3). This was comparable to previous experiments on piranha cleaned gold QCM-D chips. Since deducing a grafting density from QCM-D experiments was difficult, this serves more as a qualitative result and the actual test of sufficient grafting needed to be made in the nanopore.  IEI²  IEI²  IEI²   IEI²  IEI²  IEI²   IEI²  IEI²  IEI²   IEI²  IEI²  IEI²   IEI²  IEI²  IEI²   IEI²  IEI²  Signal-to-background ratio 1495 The single-molecule signal obtained in this study offers a significantly higher signal- By quantifying the event-wise signal-to-background ratios for the measurement shown in Figure 3, we estimate an average signal-to-background ratio of 56 ± 41 for BSA and 67 ± 53 for Kap95 ( Figure 3). Using a representative segment of a 1 min- In (Fragasso et al., 2022), individual Kap95 translocations could only be resolved at low concentrations of 119 nM, above which single events were not visible due to an insufficient signal-to-noise ratio, as stated by the authors. Such a limitation does not exist for the ZMW approach, where we could detect single protein translocations also at high occupancy of Kap95 in Nsp1 coated pores. Moreover, as pointed out in the discussion section, the discrepancy between theoretically predicted translocation rates and experimentally measured translocation rates is orders of magnitude better for the ZMW approach compared to the conductance based readout. We hence conclude that the capability to resolve single translocations is markedly improved for the ZMW-based fluorescence readout compared to the conductance based approach.

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To determine the radius of a protein (used in the void analysis and for fitting the event rates), we used the procedure as described in (Winogradoff et al., 2022). We started by computing the protein's moments of inertia, , and , from the all-atom crystal structure. We then matched the moments of inertia of the protein with those of a constant density ellipsoid using = 1 5 ( 2 + 2 ) , = 1 5 ( 2 + 2 ) and = 1 5 ( 2 + 2 ) , where is the total mass of the protein and , and are the respective lengths of the three principal axes of the ellipsoid. To obtain the protein radius, we equated the volume of a sphere to the volume of the ellipsoid, i.e., p = ( ) 1/3 . Using this method we find a probe radius of p = 34 Å for BSA (PDB ID: 4F5S) and p = 40 Å for Kap95 (PDB ID: 3ND2).   Potential of mean force for Nsp1-coated pores 1750 The Nsp1 proteins in our simulations were anchored to the surface in a triangular fashion to achieve a homogeneous grafting density across the entire scaffold. We note that the location of the peaks in the PMF curves align with the -coordinates of the Nsp1 anchor sites. Although the anchor sites clearly contribute to the translocation barrier, it would not be correct to use the maximum PMF as the energy barrier for translocation, as the idealized anchoring of Nsp1 on the scaffold is not a good approximation of the experiments (where Nsp1 is not anchored at discrete -positions). Instead, to obtain a correct estimate of the energy barrier, Δ , we used the average PMF for −25 nm ≤ ≤ 25 nm.     Note that this corresponds to the harmonic mean of the selectivities.

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When considering the structure of the pore, the number of Nsp1 molecules in the pore is determined by the grafting density , the pore's radius and length as = 2 .
If we assume that each Nsp1 molecule renders a certain volume selective, the effectively selective cross-sectional area can be calculated from the selective volume Nsp1 as: Thus, the selective area fraction depends on the pore radius as: Combining both expressions for the selective area fraction, we obtain: where is the only fit parameter that we fit to the selectivities measured in Note that, if each Nsp1 molecule occupies the same volume V, the rim thickness would depend on the pore radius and the ring thickness ℎ can be calculated using Nsp1 = 2 − ( − ℎ) 2 as: which requires < 2 . For flat surfaces, where → ∞ the parameter → ℎ and can be represents the Nsp1 layer height in these cases. In the case of curved surfaces, the layer height needs to be calculated using Equation 26. Notably, the assumption of constant volume that is applied here remains valid for situations where the Nsp1 phase is not localized in the rim, e.g. forming a central plug but is in contrast to previous models that assume a selective area (of whatever shape) similar in size to a ring of constant thickness, such as proposed by Kowalczyk et al.