Computational analysis of lamin isoform interactions with nuclear pore complexes

Nuclear lamin isoforms form fibrous meshworks associated with nuclear pore complexes (NPCs). Using data sets prepared from sub-pixel and segmentation analyses of 3D-Structured Illumination Microscopy images of WT and lamin isoform knockout mouse embryo fibroblasts, we determined with high precision the spatial association of NPCs with specific lamin isoform fibers. These relationships are retained in the enlarged lamin meshworks of Lmna-/- and Lmnb1-/- fibroblast nuclei. Cryo-ET observations reveal that the lamin filaments composing the fibers contact the nucleoplasmic ring of NPCs. Knockdown of the ring-associated nucleoporin ELYS induces NPC clusters that exclude lamin A/C fibers, but include LB1 and LB2 fibers. Knockdown of the nucleoporins TPR or NUP153 alter the arrangement of lamin fibers and NPCs. Evidence that the number of NPCs is regulated by specific lamin isoforms is presented. Overall the results demonstrate that lamin isoforms and nucleoporins act together to maintain the normal organization of lamin meshworks and NPCs within the nuclear envelope.


Introduction
The nuclear envelope (NE) is a complex multicomponent structure separating the nuclear genome from the cytoplasm.It has evolved as a highly compartmentalized multifunctional organelle with a wide range of functions.The NE structure includes the nuclear lamina (NL), a double membrane bilayer forming a lumen continuous with the endoplasmic reticulum and nuclear pore complexes (NPCs).However, details of the structural and spatial relationships among the components of the NE have been difficult to define.This lack of information is largely attributable to the dense packing and close spatial relationships of the structures comprising the NE (Aebi et al.,86;Fisher et al.,86;Goldman et al.,86;McKeon et al.,86).To better understand the structural relationships within the NE, we have combined super-resolution light microscopy with recently developed computer vision techniques.This approach has allowed us to quantitatively analyze the structural organization of the lamins and NPCs in the NE by making highly precise measurements of lamin structures and NPC localization over large areas of the NE.Our goal is to test the utility of large data sets to provide new insights into the interactions between these two major components of the NE.
The four major lamin isoforms in somatic cells are lamin A (LA), lamin C (LC), lamin B (LB ), and lamin B (LB ).These type V intermediate filament proteins are closely apposed to the inner nuclear membrane where they assemble into discrete fibrous

NPCs are structurally linked to lamin fibers
We used D-SIM and image reconstruction to determine the structural relationships among immunolabeled lamin fiber meshworks and NPCs in MEFs.NPCs in WT MEFs were distributed all across the NL region, but did not show an obvious co-localization with any of the lamin meshworks, as indicated by the very few white areas in merged overlays (Figure A).This was remarkable because some co-localization of lamins and NPCs would be expected by chance given the densely packed environment of the NL.This lack of co-localization between lamins and NPCs suggested the existence of a bona fide spatial relationship.We took advantage of our previous finding that the spaces or "faces" delineated by lamin fibers comprising the meshworks increase in size in Lmna -/-and Lmnb -/-MEF nuclei (Shimi et al., ).This allowed us to examine the association between NPCs and specific lamin isoforms in WT, Lmna -/-, and Lmnb -/-MEFs.Importantly, NPCs remained in close proximity to the LA and LB fibers in the expanded meshworks of Lmna -/-and Lmnb -/-MEF nuclei and were absent in the meshwork faces (Figure B).These results strongly suggest that LA and LB 86 are required for the normal distribution of NPCs.Although these images provide qualitative evidence that there is an association between lamin isoform fibers and NPCs, it is important to verify such associations using a quantitative approach to ascertain the 88 extent of the relationships between each lamin isoform fiber and NPCs.

Image analysis reveals enrichment of NPCs within to nm of LA fibers in WT and Lmnb -/-MEFs
We developed quantitative image analysis tools to precisely determine the spatial relationships between lamin isoform fibers and NPCs, and to localize both structures with sub-pixel precision in dense and sparse lamin meshworks (Figure A; details of analysis tools in Materials and Methods).We reasoned that by measuring the distances between the centers of lamin fibers and the center of lamin meshwork faces to the centers of NPCs (Figure S ), we could quantitatively assess the association of NPCs with individual lamin isoforms.To evaluate the frequency of observing distances between the lamin fibers or face centers and NPCs by chance, we compared our observed distance measurements to the expected distances under a null hypothesis, which assumes the NPCs and lamin meshworks have no relationship and are thus independently distributed.For example, we measured the LA fiber center to NPC center distance in WT cells as compared to the expected distances assuming no relationship (Figure B compare the measured data in the blue violin plot on top vs the expected distances in the red violin plots on bottom).By examining the difference in the observed from the expected distributions (Figure C), we could see a paucity (green) or excess (purple) of NPCs at certain distances from the centers of LA fibers.For example, in a single WT nucleus we observed fewer NPCs within nm of the fibers and an excess of NPCs between and nm relative to the null hypothesis (green area; Figure C WT).In order to validate this approach, we performed the same analysis of the LA fiber to NPC distance in a single Lmnb -/-MEF nucleus (Figure B).As in the WT nucleus, we saw an excess of NPCs between and nm in the Lmnb -/-nucleus (Figure C).This agreed with the qualitative observation that the of

LA and LB fibers have a more pronounced relationship with NPCs than LC and LB fibers in WT MEFs
We previously found that the four main lamin isoforms (LA, LC, LB , and LB ) form independent meshworks (Shimi et al., ), and we sought to see if each isoform had a distinct relationship with NPCs.Having established our approach to analyzing lamin-NPC associations, we measured the distances between the center of individual NPCs and the center of the nearest lamin fiber across the surface of the nucleus closest to the coverslip of WT nuclei for each lamin isoform.Overall, the data obtained supports the lack of direct colocalization between NPCs and lamin fibers, which we observed qualitatively and quantitatively in single nuclei (Figures , ).
The median distances from the centers of NPCs to the centers of LA fibers ( .nm; p < . ; Table A S C).The expected distribution represents the distances between NPCs and lamins that we would expect under the null hypothesis that there is no relationship between the position of NPCs and lamins.It was calculated by a Monte Carlo simulation randomly placing a NPC within the segmented area of the nucleus.The median distance between NPCs and the center of faces in the LA meshworks was similar ( .nm; -. nm vs expected; p < .; Table B) to LB ( 8. nm; -.8 nm vs expected; p < .; Table B) and both median distances were less than expected if the lamins and NPCs were not associated (Figure C; Table B).These data show that NPCs and LA or LB fibers are not directly colocalized, but have a proximal lateral relationship.These findings suggest that NPCs and LA or LB fibers are structurally linked within the NL.
In contrast to the relationships between the NPCs and LA or LB , the median distance from LC fibers to NPC centers did not differ significantly from expected ( .8 nm observed, + .nm vs expected; p= .; Table A, A and B leads to an alpha level of 0.05∕12 ≈ 0.004.However, the median distance determined for the NPC center to LC face center differed from the expected distribution ( .nm observed, -. nm vs expected; p < . ; Table B, Figure C).While these measurements followed a pattern similar to that detected for LA and LB , the magnitude of the differences were much smaller for LC (Figure C, D, Table B).Overall, these data suggested that the offset between NPCs and LC fibers is closer (median: .8nm) than between NPCs and LA or LB fibers (medians: nm).However, given the small differences in the LC fiber to NPC center measurements relative to expected, we cannot completely reject the null hypothesis for the LC fiber to NPC distances.
The relationship between LB fibers and NPCs in WT MEFs differed from the other lamin isoforms.We observed a statistically significant difference in medians from expected distributions between the centers of LB fibers and NPCs ( .6 nm observed; -.6 nm vs expected; p < .
; Table A , Figure A, Figure S D).However, the shift was an order of magnitude less and in the opposite direction than observed for LA and LB fibers.The median distance from NPCs to LB face centers ( 6. nm observed; -.6 nm vs expected; Table A, Figure C) was not significantly different from expected.These findings suggest that there is no obvious 66 relationship between the distribution of LB fibers and NPCs, or if there is, it cannot be discerned in our analyses.We analyzed the spatial relationships between LA fibers and NPCs in Lmnb -/-nuclei using the same quantitative methods applied to our studies of WT nuclei.In Lmnb -/-nuclei, there was a greater median distance between LA fiber centers and NPC centers than expected ( .nm observed; + .nm vs expected; Table A, Figure A, Figure S A), however, this shift in medians was not statistically significant (p = ., Table A).Interestingly a statistical test comparing the standard deviations showed that the distributions are significantly different ( 8.6 nm observed; -68.nm vs expected; p < .

Knocking out
; Table A, Figure A, B).This reflects the long tail of the expected distributions, since under the null hypothesis some NPCs may appear in the middle of the faces of the enlarged LA meshworks, that is, farther away from the lamin fibers.The median distance of NPCs from the LA face centers was less than expected by a large magnitude ( .nm; -. nm vs expected; p < .; Table B; Figure C, D).This difference is due to the distribution of the offsets of the NPCs from the lamin fibers, which is larger than the expected offset distributions where more NPCs were closer to the lamin fibers.The observed distance distributions of WT and Lmnb -/-MEFs (Figure A) both differ from the expected distributions under the null hypothesis in a similar manner (Figure B).This indicates that, in Lmnb -/-nuclei, the proximal lateral relationship between LA fibers and NPCs remains although the median distance between LA fibers and NPCs increased by nm.Overall, this suggests that the distance between the centers of LA fibers and NPCs does not depend strongly on the presence of 86 LB fibers.
The results showed a relationship similar to LA fibers in WT MEFs for distances less than nm where NPCs occurred less frequently than expected (green area; Figure B) and more frequently than expected around -nm (purple area; Figure B).This differed from the analysis of the single nucleus which consisted mostly of enlarged faces (Figure A), whereas most nuclei typically had a mix of small and large faces (Figure B).Interestingly, the median distances between the centers of LB fibers and NPCs in Lmna -/-MEFs matched the expected distribution ( .nm observed; -.8 vs expected; p < .
; Table A Recall that in contrast, the LB fiber to NPC median distances in WT MEFs were slightly larger and differed from the expected ( 8. nm; p < . ; Table A, Figure A).Additionally, the difference between the frequencies of the observed and expected distributions were smaller in magnitude in Lmna -/-MEFs compared to WT MEFs along with a small positive peak suggesting some colocalization (Figure B).The standard deviation of LB fiber to NPC medians in Lmna -/-MEFs did differ significantly from expected ( .nm observed; -6 .nm vs expected; p < .; Table A    In order to further investigate the relationship between lamin filaments and NPCs, we carried out cryo-ET of WT MEFs coupled with immunogold labeling of both LA and LB .We hypothesized that this may shed additional insights on the lamin-NPC interaction and could reflect the relative abundance of LA and LB filaments contacting the NPC.We extracted nm x nm x nm subtomograms around the nucleoplasmic ring of NPCs (  B).We observed more LA/C filaments than LB filaments in these regions (Figure C).These results also demonstrate that both LA and LB fibers are closely associated with the nucleoplasmic ring.

Organizational changes in LA meshworks and NPCs differ in response to silencing the expression of ELYS, TPR and NUP
The cryo-ET observations, taken together with the demonstration that there was a proximal lateral association between NPCs and both LA and LB fibers suggested that there are attachments of lamin filaments to nucleoplasmic components of NPCs.We next explored the potential roles of individual nucleoporins in attaching lamin fibers to the NPCs.For these studies we focused on ELYS,

NUP
and TPR, all components of the nucleoplasmic NPC structures that are in close proximity to the lamina (Roux et al., ).The nucleoporin ELYS is a component of the nucleoplasmic ring of NPCs and is required for post-mitotic NPC assembly where it binds to the chromosomes and recruits the Nup -6 complex of the nucleoplasmic ring (Franz et al., ).TPR and Nup are both components of the nuclear basket structure of the NPC tht associates with the nucleoplasmic ring (Duheron et al., ; Krull et al., ).We employed siRNA knockdown of each nucleoporin to determine their potential roles in linking the NPC to lamin fibers (Figure S6).We evaluated the efficacy of the knockdown by Western blot of whole cell lysates resulting in reductions of amount of each protein by %, %, or % for NUP , ELYS, or TPR, respectively (Figure S ).Knockdown of either ELYS or TPR led to significant changes in NPC distribution and structural relationship to the LA fibers.The most dramatic effect was the reorganization of NPCs into clusters after ELYS knockdown (Figure A).Individual fluorescent puncta could still be resolved within each cluster indicating that some NPC structure was likely retained.In contrast, siRNA knockdown of NUP or TPR did not cause NPC clustering in WT MEFs  S6).These data suggested that LA fibers were being excluded from the ELYS depleted NPC clusters such that these clusters became located in large faces within the LA meshwork.Interestingly, the size of faces contained within the LA meshwork also appeared to increase upon ELYS knockdown (Figure A, F).As a measure of lamin face size, we summed the NPC to fiber distances and the NPC to face center distances, since, for a perfectly circular face in the meshwork, this quantity would be the radius of the circle with respect to each NPC.The face radius of the LA fiber meshwork ( 6 .nm; Table C) significantly increased versus the scrambled siRNA control ( 6 .nm; p < . ; Table C) upon ELYS knockdown indicating that the LA meshwork expanded when ELYS was depleted.
While there did not appear to be NPC clustering upon TPR depletion, the NPCs appeared to be less associated with the LA fibers and more centered within the faces of a dense LA meshwork (Figure A).The median distance between the centers of NPCs and LA fibers with TPR knockdown ( .nm; Table A S6) increased versus a scrambled siRNA control, though to a lesser magnitude than for ELYS knockdown (+8.nm TPR KD vs + .nm ELYS KD; p < .
; Table A, Figure B,C).The median distance between NPCs and LA face centers ( .nm; Table B, Figure D) was reduced with TPR knockdown (-6.nm; p < .; Table B, Figure D, E).The face radius of the LA fiber meshwork ( .nm; p < .; Table C) was decreased upon TPR depletion (-.nm; p < . ; Table C).These data suggested that the NPCs were less closely associated with LA fibers following TPR knockdown.Additionally, the reduced face size suggested that the LA meshwork faces were reduced in size (e.g., compacted) upon TPR knockdown forcing NPCs into more confined spaces than in WT LA meshworks.
In contrast to ELYS and TPR knockdowns, NUP knockdown only slightly reduced the median distance between NPCs and LA fibers (-.8 nm; p < .; Table A , Figure B, C).This reduction was an order of magnitude smaller than observed for the knockdown of either ELYS or TPR.The distance between LA face centers and NPCs was reduced (-6.nm; p < . ; Table B, Figure D, E, Figure S6) and the face radius for the LA meshwork was reduced (-.nm; p < .; Table C).The faces in the LA meshwork appeared smaller and more compact compared to controls which was similar to the effect seen with TPR knockdown.Thus, upon NUP knockdown, the faces in the LA meshwork became smaller compared to the scramble control, modestly decreasing both the LA fiber-NPC and LA face-NPC distances.The effect of NUP knockdown is similar to that of TPR knockdown but reduced in

Changes in LC meshworks are similar to LA meshworks but of lesser magnitude following silencing of ELYS, TPR and NUP
Our analysis of LC fibers and NPCs suggested that LC fibers do not have a definable relationship with NPCs in WT MEFs (see

Figure )
. However, the co-distribution of LC fibers and NPCs was significantly modified by knockdown of either ELYS or TPR.ELYS knockdown resulted in an increase in the median distance between NPCs and LC fibers (6 .nm; + .nm vs scrambled; p < .; Table A, Figure 6 A,B,C, Figure S ) and the LC face center to NPC center distances decreased ( 6. nm; -. nm vs scrambled; p < .; Table B, Figure 6 D,E,F).The knockdown of ELYS also increased the effective face radius ( 6 .nm; + .nm vs scrambled; p < . ; Table C) indicating that ELYS knockdown results in expanded LC meshworks as it did for LA meshworks.These results suggest that the NPC clusters induced by ELYS depletion exclude LC fibers as well as LA fibers.
siRNA knockdown of TPR resulted in an increase in the median distance between NPCs and LC fibers (+ .nm vs scramble; p < . ; Table A C).While these decreases are consistent with the change seen in the distances between NPCs and LA fibers, the magnitude of the change is much less than for depletion of ELYS or TPR.Overall, the observed changes in the NPC distribution relative to LC fibers upon ELYS, TPR, and NUP knockdown were similar to those observed for LA fibers.
; Table A, Figure A, B, Figure S8) relative to scrambled siRNA controls.The small magnitude of these changes suggests that depletion of these nucleoporins had a minimal impact on the relationship between LB and NPCs compared to the changes seen in the distances between NPCs and LA/C fibers (Figure C).In contrast, the changes in median distance between LB face centers and NPCs were larger in magnitude upon knockdown of TPR, NUP , or ELYS (-.nm, -. nm, and -. nm, respectively; Obs.-Scram.; p < .; Table B, Figure D, E, F, Figure S8) ; and face radii decreased (-.nm, -. nm, -.6 nm; Obs.-Scram.; p < . ; Table C).Knocking down TPR or ELYS decreased the distances between NPCs and LB face centers as well as the LB face radii, while knocking down NUP had less impact.
Visual inspection of the accompanying images reveals denser LB meshworks upon TPR and NUP depletion relative to scrambled siRNA controls as the numerical analysis suggests, but also enlarged faces upon ELYS knockdown in contrast with the quantitative measurements.Closer inspection of the images upon ELYS depletion reveals LB fibers protruding into the enlarged faces (Figure ).This is not seen in the enlarged faces of LA/C meshworks (Figure A and 6A).The interdigitation of LB fibers within the NPC clusters explains why an increase in LB fiber to NPC distances is not seen quantitatively. 86

Depletion of ELYS, TPR, or Nup has a minor impact on the independence between LB fibers and NPCs
As described in previous sections, we could not detect a relationship between LB fibers and NPCs in WT MEFs (see Figure ).
88 Upon knockdown of TPR, NUP , or ELYS, the observed distances between LB fibers and NPCs differed by a few nanometers from expected (-.nm, -6.6 nm, and + .nm, respectively; Obs.-Exp., p < .; Table A, Figure 8A,B, Figure S ) and from the scramble control (-.nm, -. nm, and + .nm, respectively; Obs.-Scram; p < .; Table A, Figure 8A,B,C).Although the changes in association between the NPCs and LB fibers were minimal, the differences were statistically significant with NUP knockdown having the greatest effect.In contrast, LB face center to NPC center distances (-.6 nm, + .nm, and -8.nm vs scrambled; Obs.-Scram.; p < .; Table B; Figure 8D,E,F) and the face radii decreased significantly (-6.nm, -. nm, -.8 nm vs scrambled; Obs.-Scram; p < .; Table C, , Figure S ), following knockdown of TPR, NUP , or ELYS, respectively.Thus, the main effect of the TPR and ELYS knockdown was to decrease the LB face radii and the distance to the LB face centers relative to the NPC distribution.In contrast, the LB fiber to NPC center distances were not perturbed to the same extent when compared to the other lamin fibers.

Discussion
Ever since the first descriptions of the NE as a distinct structure in eukaryotic cells, the relationships between the components of the structure have been the subject of intense scrutiny.However, due to multiple factors, including its dense composition, relative insolubility and thin structure sandwiched between the chromatin and the cytoplasm, determination of its fine structure has been elusive.Several lines of evidence support the consensus that NPCs are anchored to the lamina during interphase.).Extracting information about fibrous lamin structures from SMLM data would require additional analysis not directly realizable from SMLM localizations or their graphs (Peters et al.,8;Kittisopikul et al.,).Our analysis of lamin fibers as employed here has been purpose built and validated for use in dense structures such as lamin meshworks with complex junctions (Kittisopikul et al., ).Electron microscopy as well as the meshwork altering perturbations produced here suggest the fibrous nature of lamins exists even in the dense wild-type lamina.To evaluate the relationship between lamin fibers and NPCs to high precision, we have exploited the continuous nature of the imaging data set afforded by Nyquist sampling to localize structures by mathematical optimization as described in the Appendix.The combination of super-resolution microscopy and computational analysis as a data set will allow researchers to pursue further questions about the relationship of lamin fibers and NPCs as we have demonstrated here.
Which of the lamin isoforms interact with the NPCs has been a relevant question, since the four major lamin isoforms, LA, LC, LB , and LB are not all expressed throughout development and each may not be expressed in all cell types (Burke and Stewart, ).With the aid of super resolution microscopy techniques, it is now established that each of the lamin isoforms assembles into a distinct network in the NE (Shimi et al ).These blebs are also deficient in NPCs.Together these studies suggest that B-type lamins may be more important than LA/C for the normal distribution of NPCs in the NE.This conclusion makes sense intuitively since stem cells and some differentiated cells express very little or no LA/C, yet have what appears to be a regular distribution of NPCs Burke and Stewart ( ).However, other studies have suggested that lamin isoforms can function redundantly to ensure normal NPC distribution (Guo of Preprint et al., ).Our findings presented here support the notion that both LA and LB have clear spatial relationships with NPCs and these relationships are preserved when either LA/C or LB is absent.Although the proximal lateral relationship between NPCs and LA and LB fibers is retained in both types of lamin null cells, the quantitative data suggest that the presence of LA fibers may be more important to the LB -NPC relationship than the presence of LB fibers are to the LA-NPC relationship.Using cryo-ET, we were able to demonstrate that both LA and LB fibers lie in close proximity to the NPC, and in several cases can be seen in intimate association with the nucleoplasmic ring structure of the NPC.This finding supports our super resolution results that indicate a close physical relationship for both LA and LB with NPCs over the entire nucleus.Measurement of LC interactions with NPCs followed a similar trend to those of LA and LB in our analyses, although we could not draw firm conclusions on the LC-NPC interaction due to the small magnitude of the observed values relative to expected.Surprisingly, we did not find an obvious relationship between LB and NPCs in our analysis.
Xie and coworkers have previously carried out super resolution microscopy studies of the relationships between lamins and NPCs in mouse adult fibroblasts (MAFs) (Xie et al.,6).By re-expressing mEOS-tagged LA or LC in Lmna-/-cells, they found NPCs concentrated in the spaces between LA fibers, and a close association of NPCs with the LC networks.These findings are directly the opposite of those we report here.There are several possible explanations for these discrepancies including: ) possible differences between adult fibroblasts and embryonic fibroblasts, ) possible differences in an ectopically expressed lamin network versus the endogenous networks, and ) over-expression of LA only or LC only versus cells expressing all four lamin isoforms in the natural ratio.
Further studies will be necessary to address these differences in results.
Our results also provide new and important insights into lamin-NPC interaction by knocking down specific nucleoporin levels using siRNA for ELYS, TPR, or NUP .Each knockdown had unique effects on both NPC distribution and lamin meshwork structure.).These two processes differ in the order that nucleoporins assemble and the enzymatic requirements for assembly.The postmitotic phase involves the recruitment of the NUP -6 subcomplex to the chromatin surface by the binding of one component of the complex, ELYS/MEL-8 to nucleosomes (Rasala et al.,6;Galy et al.,6;6).While we have not demonstrated a direct interaction between ELYS and the lamins, it is clear that the presence of ELYS is required to maintain lamin-NPC interactions.The clustering of NPCs after ELYS knockdown is likely due to the failure of NPCs to correctly assembly on chromatin following mitosis suggesting that, at least for NPCs formed at NE reformation, their association with lamins occurs at that time.ELYS  ).However, these previous studies did not find clustering of NPCs or changes in lamin meshwork structure.

ELYS knockdown caused dramatic changes in NPC distribution attributable to
TPR is a nucleoporin located in the nuclear basket structure of the NPC and could act as a negative regulator of NPC number (McCloskey et al.,8).In contrast two other studies found that siRNA reduction of TPR reduced NPC number (Funasaka et al., ; Fišerová et al., ).In our experiments, we also observed a small, but statistically significant increase in NPC numbers after TPR knockdown in WT cells.When we depleted TPR in Lmna -/-and Lmnb -/-cells, a similar small increase in NPCs was observed suggesting that neither lamin isoform alone is involved in regulating NPC numbers.As with ELYS knockdown, TPR knockdown resulted in displacement of the NPCs away from the lamin fibers, with the exception of LB fibers, which were slightly closer to the NPCs when TPR was depleted.NUP depletion had the most consistent effects on the lamin fiber-NPC relationship with a decrease in lamin fiber to NPC distance and a compaction of the lamin meshworks, although these changes were more modest than those of the other nucleoporin knockdowns.Surprisingly, knockdown of NUP in Lmna-/-and Lmnb -/-cells led to clustering of NPCs in the lamin meshwork faces.This suggests that an interaction of NUP with both lamin isoforms is required for normal NPC distribution.The results presented here suggest that the lamina structure and NPCs are co-dependent, that is, changing one of the structures has an effect on the other's distribution.In addition to the NPC clustering in lamin meshwork faces after ELYS reduction, the lamin meshworks became larger for LA and LC, but became smaller for LB and LB .In contrast, knockdown of either TPR or NUP caused each of the lamin meshwork faces to decrease in size.Based on these results, it is tempting to speculate that the number of NPCs helps to determine lamin meshwork structure.Our results show that each of the lamin isoforms appears to interact differently with the three nucleoporins.It should be noted that while ELYS is required for post-mitotic NPC assembly (Franz et al., ) ) and all three nucleoporins are known to affect chromatin modification states (Kuhn and Capelson, ).The lamins are also closely associated with chromatin at the nuclear periphery and it is likely that peripheral chromatin is also playing a role in the association of lamins and NPCs and their distribution in the NE.
Overall, the extensive SIM imaging and quantitative analysis performed here provides important biological insight as to how NPCs and lamin fibers are arranged in the mammalian nucleus.In perturbing the cells and their nuclei by either knocking out lamin isoforms, LA/C or LB , or knocking down nucleoporins, our data set provides knowledge about interactions mediated by those specific lamin isoform and nucleoporins.In particular, it is clear from this data set that knocking down lamin isoforms results in a change in the spatial distribution of NPCs.Additionally, knocking down nucleoporins has an effect on the spatial distribution of the lamin fiber meshwork.Therefore, the lamins and NPCs play a role in organizing each other at the nuclear periphery.

Sample size estimation
The initial light microscopy images of WT, lamin knockout cells, and the cryo-ET data were acquired before the design of the study and before the computational analysis was developed.Hierarchical power analysis was performed for the siRNA knockdown series of experiments based upon the effect sizes observed in the initial light microscopy images.We sought to evaluate changes in distance between lamin and NPCs as well as changes in NPC number.The limiting factor was the number of cells that needed to be observed in order to detect a ±20% change in number of NPCs per cell with a power of .8 at an alpha of .with the Mann-Whitney U test.The wmwpower package (Mollan et al., ) in R (R Core Team, 6) was used.Using the estimation methods in that package it was determined that imaging cells would exceed those requirements.Based on thousands of distances being measured per cell, it was determined that the power of the lamin-NPC distance studies would also exceed the requirements.

Replicates
Each experiment was performed in duplicate as technical replicates.Each technical replicate was performed at a distinct time and included all steps from cell culture to fixation and staining.Additionally, for each technical replicate two sets of coverslips were produced.In Tables A and B, cells were evaluated per row.In Tables A, B, and C, cells were evaluated per row.The cells were distributed across the four coverslips produced.Outliers were not excluded from the data.Microscopy as described below was done on fixed samples in blocks of time using coverslips from multiple technical replicates.Experimental samples and their controls were conducted within the same microscopy session.

Statistical reporting
Statistical analysis was done in MATLAB (Mathworks, Natick, MA) other than the power calculation down in R as noted above.
The frequency of the simulated distances was compared to the observed distances using the Mann-Whitney U test, also known as the Wilcoxon rank sum test.A non-parametric test was used since the Kolmogorov-Smirnov test rejected the null hypothesis that the distributions were normal.
The Mann-Whitney U test evaluated the null hypothesis that the two sets of samples (observed vs expected, ELYS siRNA versus scrambled siRNA, etc) were drawn from the same distribution.If the Mann-Whitney U test failed to reject the null hypothesis for the distance measurements, the Ansari-Bradley test was applied to examine the null hypothesis that the dispersion (i.e. the standard deviation) of the distributions were the same.Bonferroni corrections were applied to the alpha value to compensate for multiple comparisons by dividing an alpha value of .by the number of comparisons in the table or figure.

Super resolution microscopy
D-SIM was carried out as previously described (Shimi et al., ).Briefly, a Nikon Structured Illumination Super-resolution Microscope System (Nikon N-SIM; Nikon, Tokyo, Japan) was built on an ECLIPSE Ti-E (Nikon) equipped with a sCMOS camera ORCA-Flash .(Hamamatsu Photonics Co., Hamamatsu, Japan) and an oil immersion objective lens CFI SR (Apochromat TIRF ×, of Preprint NA= ., Oil, WD= .; Nikon).N-SIM was operated with NIS-Elements AR (Nikon).For image acquisition, optical sections including a region of the lamina were taken at -nm intervals.For image reconstruction from the raw data, illumination modulation contrast, high-resolution noise suppression, and out-of-focus blur suppression were set with fixed values of , ., and ., respectively.For presentation, images were adjusted for brightness and contrast.

Indirect immunofluorescence
Samples for indirect immunofluorescence were processed as previously described (Shimi et al
Scrambled sequence for control siRNAs; . .(J--) '-CAACAAACAUUCAUCGGUA-' .(J--) '-CGUGACAUGUACCGAAUUU-' × EFs were plated into each well of 6-well plates h before transfection.pmol of siRNA oligos was transfected onto the cells in each well with Lipofectamine RNAiMAX transfection reagents (Thermo Fisher Scientific), following the manufacturer's instructions.8h after incubation at °C, the transfected cells were trypsinizedand replated at × ells/well into each well of 6-well plates and transfected with pmol of the siRNA.8h after incubation at °C, the transfected cells were trypsinized and replated on coverslips for indirect immunofluorescence or plated into a 6 mm dish for western blotting.
Quantitative blotting of anti-nucleoporin antibodies.
The linearity of antibodies to nucleoporins was determined by immunoblotting of whole cell lysates of WT MEFs.Five samples of MEF lysates containing between .× o × ells were separated in duplicate lanes of a .% SDS-polyacrylamide gel (SDS-PAGE) and transferred to nitrocellulose for immunoblotting.After transfer, the membrane was briefly rinsed in dH O and stained with Revert Protein Stain (LI-COR) and imaged in an Odyssey Fc (LI-COR Biosciences, Lincoln NB) at nm.The membrane was then washed with Tris-buffered saline (TBS) and blocked in % non-fat dry milk (NFM) in TBS for hr at room temperature and then in the same solution containing .% Tween for minutes.For incubation with antibodies, the appropriate antibody was diluted in blocking solution with Tween at the indicated concentration (See Table Below) and incubated overnight at °C with gentle agitation.
The blots were washed times for mins each with TBS containing .% Tween .For detection, the appropriate secondary antibodies (Licor IRDye 8 CW) were diluted : in % NFM containing .% Tween and incubated with the membrane for hr at room temperature with gentle agitation.The membranes were washed X mins each with TBS containing .% Tween and 88 allowed to dry.The dried membranes were imaged in an Odyssey Fc at 8 nm.Images of the total protein stain and specific antibody labeling were analyzed using Empiria Studio Software (LI-COR Biosciences, Lincoln NB).The intensity of the specific antibody labeling in each lane was corrected for protein load using the software and the linearity of the antibody response was determined by the software.
The degree of knockdown for each nucleoporin was determined by SDS-PAGE by loading duplicate samples of each knockdown cell lysate such that the antibody response should be in a linear range, based on the analysis of WT lysates.For quantitation of knockdown, a dilution series of WT lysate was run on the same gel at concentrations that were expected to be in the linear range of the antibody response.After electrophoresis and transfer, the membranes were treated identically to the conditions for determining antibody linearity, imaged in the Odyssey Fc and the images analyzed using Empiria software.

NPC-lamin rendered view
Cryo-electron tomograms that were acquired previously (Turgay et al., ) were further analyzed.The central coordinates of NPCs within cryo-tomograms of NE were determined manually and sub-tomograms ( nm x nm x nm) were reconstructed in MATLAB, using the TOM toolbox (Nickell et al., ).The lamin filaments and NPCs in selected sub-volumes were segmented manually and rendered, using the Amira software package (Thermo Fisher Scientific).
Fawcett DW.On the occurrence of a fibrous lamina on the inner aspect of the nuclear envelope in certain cells of vertebrates.), 1 and 2 may differ since the orientation resolution used for orientation detection may differ from the orientation resolution used to localize the detection in space.

Localization of Lamin Meshwork Face Centers
To understand the relationship of NPCs to the lamin structure, we also measured the distance of the NPCs from their "centers" which we defined as the points furthest away from the lamins within a local neighborhood.
Face centers were localized by identifying local maxima of the distance transform relative to the lamin fibers.A D disc with a five pixel radius ( nm) was used as a structuring element with morphological dilation.This identified the maximum distance within a disc centered at each pixel.The local maxima were detected at the points when the maximum distance within the disc coincided with an identical distance assigned to that pixel via the distance transform.If a connected region with points equidistant from the lamin fibers were found, the centroid of that region was selected as the face center.
Because faces are not always convex or there maybe lamin fibers protruding into faces, multiple distinct centers may be detected.In this case, the distance from the NPC is measured to the nearest face center. of

Figure .
Figure .NPCs are arranged along LA and LB fibers in enlarged lamin meshworks .Colabeling of lamins and nuclear pore complexes in WT and lamin KO MEF nuclei using indirect immunofluorescence with a pair of specific antibodies against each lamin isoform (LA, LB , LB or LC) and the FXFG-repeat nucleoporins.A) WT MEF nuclei colabeled with the indicated lamin isoform and FXFG-repeated nucleoporins.B) Nuclei of Lmna -/-(left pair) and Lmnb -/-(right pair) MEFs.The indicated areas with white squares are enlarged approximately eight-fold along each edge and displayed on the right side of each pair of images.Scale bar = .

Figure 2
Figure 2 Computational Image Analysis of Lamin A and NPCs in Individual NucleiA) Immunofluoresence images labeling LA (green) and NPCs (magenta) of wt and Lmnb1 -/-MEF nuclei as in Figure1were subjected to computational image analysis.White boxes in the top row are magnified ~8 times along each edge.The centers of LA fibers (yellow dots), NPCs (cyan dots), and faces (white Xs) were segmented to subpixel precision.Scale bar is 5 μm.B) Paired violin and box plots of NPC to LA fiber distances for the nuclei in (A).The violin (blue) and box plots on top represent the observed distance distributions.The violin (red) and box plots on bottom represent the expected distance distributions under the null hypothesis.The white circle indicates the median.The thick black bar indicates the interquartile range (IQR).The black whiskers indicate 1.5 times the IQR.C) Frequency difference plot of observed minus expected LA fiber to NPC distances.The green portion below the line indicates where the observed frequency is less than expected.The purple portion above the line indicates where the observed frequency is greater than expected.D) NPC to LA face center distances displayed as in (B), rotated 90 degrees counter clockwise.E) Frequency difference plot of NPC to LA face center distances, displayed as in (C), rotated 90 degrees counter clockwise.

Figure .
Figure .Computational image analysis reveals that NPCS are closely associated with LA fibers A) Immunofluoresence images labeling LA (green) and NPCs (magenta) of WT and Lmnb -/-MEF nuclei as in Figure were subjected to computational image analysis.White boxes in the top row are magnified 8 times along each edge.The centers of LA fibers (yellow dots), NPCs (cyan dots), and faces (white Xs) were segmented to subpixel precision (Kittisopikul et al. ( ); Appendix ).Scale bar is .B) Paired violin and box plots of NPC to LA fiber distances for the nuclei in (A).The violin (blue) and box plots on top represent the observed distance distributions.The violin (red) and box plots on bottom represent the expected distance distributions under the null hypothesis.The white circle indicates the median.The thick black bar indicates the interquartile range (IQR).The black whiskers indicate .times the IQR.C) Frequency difference plot of observed minus expected LA fiber to NPC distances.The green portion below the line indicates where the observed frequency is less than expected.The purple portion above the line indicates where the observed frequency is greater than expected.D) NPC to LA face center distances displayed as in (B), rotated degrees counterclockwise.E) Frequency difference plot of NPC to LA face center distances, displayed as in (C), rotated degrees counterclockwise.
Lmna affects the LB -NPC relationship more than knocking out Lmnb affects the LA-NPC relationship 68 The results presented in the previous section showed a clear spatial relationship between both LA and LB fibers and NPCs in the dense meshworks of WT MEF nuclei.The removal of either LA/C or LB by gene knockout in MEFs leads to dramatic changes in the remaining lamin meshwork characteristics, most notably an increase in the lamin mesh size (Figure B and Shimi et al).Because the lamin fibers have close structural relationships with NPCs, we next wanted to determine if these relationships are altered when the lamin meshwork structure changes.

Figure .
Figure .Quantitative analysis of Lamin-NPC distances over many nuclei reveals NPCs are offset from the center of LA and LB fibers in WT, Lmna -/-, and Lmnb -/-MEFs by -nm A) Paired violin and box plots of NPC to lamin fiber distances.The violin (blue) and box plots on top represent the observed distance distributions.The violin (red) and box plots on bottom represent the expected distance distributions under the null hypothesis.The white circles indicate the medians.The thick black bar indicates the interquartile range (IQR).The black whiskers indicate .times the IQR.B) Frequency difference plots of observed minus expected lamin fiber to NPC distances.The green portion below the line indicates where the observed frequency is less than expected.The purple portion above the line indicates where the observed frequency is greater than expected.C) NPC to lamin face center distances displayed as in (A), rotated degrees counterclockwise.D) Frequency difference plot of NPC to lamin face center distances, displayed as in (C), rotated degrees counterclockwise.
Figure A; Turgay et al. ( )) and counted the number of LA/C or LB filaments (Figure Figure .Cryo-electron tomography showing LA/C and LB filament contacts with the nucleoplasmic ring.A) Lamin filaments (yellow) interact with NPCs (red) as seen by surface rendering representations of cryo-sub-tomograms.B) Gold labelling of lamin filaments observed by cryo-ET.The position of Lamin A/C labels (green) and Lamin B labels (red) are indicated.Double labeling (left) or labeling of individual lamin isoforms were analyzed and presented as histograms.The unmarked gold particles (B-middle, right) are fiducial markers.C) A total number of Lamin A/C labels and Lamin B labels were detected around nucleoplasmic rings.

Figure 5 Figure 6 .Figure 8 .
Figure 5 Co-distribution of Lamin A and NPCs after siRNA Transfection showing NPC clustering in enlarged LA faces upon ELYS knockdown Figure .Co-distribution of LA and NPC components after siRNA transfection show enlarged LA meshworks filled with NPC clusters upon ELYS knockdown.A) Immunofluorescence images of LA (green) and NPCs (magenta) following knockdowns (KD) of TPR , NUP , ELYS and scramble control.Note the clustering of NPCs in the ELYS KD.Area of white box (left) is shown merged (center) and just lamin (right).White arrows indicate areas of NPC clustering.Scale bar = .B) Paired violin and box plots of NPC center to LA fiber center distances.The violin (blue) and box plots represent the observed distance distributions.The violin (red) and box plots on bottom represent the expected distance distributions under the null hypothesis.The white circle indicates the median.The thick black bar indicates the interquartile range (IQR).The black whiskers indicate .times the IQR.C) Frequency difference plots of observed minus expected LA fiber to NPC distances for the knockdown series.The green portion below the line indicates where the observed frequency is less than expected.The purple portion above the line indicates where the observed frequency is greater than expected.D) NPC center to LA face center distances displayed as in (B), rotated degrees counterclockwise.E) Frequency difference plot of NPC to LA face center distances, displayed as in (C), rotated degrees counterclockwise.F) 2 areas around NPC clusters formed after scramble treatment or ELYS KD indicated by white arrows in (A) shown merged (left) and just lamin (right).
Studies of the dynamics of both lamins and NPCs in interphase cells show that neither has appreciable lateral mobility in the NE (Moir et al., ; Daigle et al., ).Biochemical fractionation of the NE as well as electron microscopy studies of both somatic cells and amphibian eggs demonstrated that lamins and NPCs are intimately associated (Dwyer and Blobel, 6; Gerace et al., 8 ; Scheer et al., 6).Our D-SIM imaging and quantitative analysis of the MEF nuclei constitute a data set that reveals important insights into the structural relationship between the lamin fibers and NPCs.The image analysis focuses on localizing structures, lamin fibers, and NPCs, to high precision and then performing statistical analysis on the aggregate data set.This is distinct from localizing individual fluorophores through single molecule localization microscopy (SMLM), the Delaunay triangulation (DT) of those fluorophore localizations, or subgraphs of the DT such as the Euclidean Minimum Spanning Tree(Xie et al.,  6; Kittisopikul et al., NPCs clustering within the open faces formed by all of 66 the lamin meshworks and a reduction in NPC number.Depletion of ELYS also led to an increase in the lamin fiber to NPC distance for LA, LC and LB , but a decrease in the LB to NPC distance.NPCs form in a biphasic pattern; at the end of mitosis as the NE 68 reforms and then during interphase (Doucet et al., bind to both LA and LB (Al-Haboubi et al., ).
Figure S .Bivariate histograms of LA fiber-NPC and face center-NPC distances in single nuclei.illustration of distances.A) Observed bivariate histogram of NPC to LA face center distances versus NPC to lamin A fiber distances of a single WT MEF Lamin A nucleus shown in panel A of the Figure .B) Expected bivariate histogram of NPC to lamin A face center distances versus NPC to lamin A fiber distances of a single WT MEF Lamin A nucleus under the null hypothesis.C) Difference between the observed and expected distance distributions with purple indicating where the observed exceeds the expected frequency and green showing when the observed frequency is less than the expected frequency.D-F) Same as A-C except for the single Lmnb -/-nucleus shown in panel A of the Figure .Marginal violin plots and box plots of the distances correspond with the half-violin plot counterparts of the same orientation and color as in Panel B of the Figure .G) Zoomed in plot showing the NPC to lamin A fiber (red) and NPC to lamin A face center distances (blued) measured.Other colors correspond with those as in panel B of Figure .
, Figure A, Figure S A) and to the centers of LB fibers ( 8. nm; p < .; Table A, Figure A) were similar.The observed median distances were 6 nm greater than the expected distribution (+6.nm LA; +6.nm LB ; Table A, Figure A, B; Figure

Table B ,
, Figure6B, C, Figure S), a decrease in median distances between NPCs and LC face centers (-.nm; p < .;Figure6D,E)and a decrease in the effective face radius (-6.nm;TableC; p < .).These results indicate that the LC meshwork face size decreased after TPR knockdown, similar to LA.
66NUPknockdown resulted in a decrease (-.nm; p < .;TableA, Figure 6 B, C, Figure S ) in the median distance between NPCs and LC fibers.Decreases in LC face to NPC center distances (-.nm; p < . .; Table B, Figure 6 D,E) and face radius were 68 also detected (-. nm; p < .; Table the formation of the lamina(Smythe et al.,  ).TPR is also required to maintain the heterochromatin exclusion zones found at the NPCs(Krull et al., , NUP is required for interphase NPC assembly (Vollmer et al., ; Franz et al., ), whereas TPR is required only for formation of the nuclear basket (Duheron et al., ).In cell-free extracts of Xenopus eggs that recapitulate nuclear assembly, the recruitment of Nup to the NE is Preprint dependent on San Diego, CA).The secondary antibodies used were donkey anti-mouse immunoglobulin G (IgG)-Alexa Fluor 88, donkey anti-mouse IgG-Alexa Fluor 68, donkey anti-rabbit IgG-Alexa Fluor 88, donkey anti-rabbit IgG-Alexa Fluor 68, donkey anti-goat IgG-Alexa Fluor 88, and donkey anti-goat IgG-Alexa Fluor 68 (all :; Thermo Fisher Scientific).Processed coverslips were mounted with ProLong Diamond antifade reagent (Thermo Fisher Scientific).
Maninová M, Sieger T, Uhlířová J, Šebestová L, Efenberková M, Čapek M, Fišer K, Hozák P. Nuclear pore protein TPR associates with lamin B and affects nuclear lamina organization and nuclear pore distribution.Cellular and Molecular Life Sciences.Kim Y, Shimi T, Goldman RD, Zheng Y. Concentration-dependent lamin assembly and its roles in the localization of other nuclear proteins.Schibler AC, Wesley CC, Pegoraro G, Misteli T, Levy DL.The nucleoporin ELYS regulates nuclear size by controlling NPC number and nuclear Meuleman W, Pagie L, Bruggeman SWM, Solovei I, Brugman W, Gräf S, Flicek P, Kerkhoven RM, van Lohuizen M, Reinders M, Wessels 6 L, van Steensel B. Molecular Maps of the Reorganization of Genome-Nuclear Lamina Interactions during Differentiation.Molecular Cell.⃗ is a vector normal to the structure being localized.As explained inKittisopikul et al. ( Fisher DZ, Chaudhary N, Blobel G. cDNA sequencing of nuclear lamins A and C reveals primary and secondary structural homology to intermediate filament proteins.Proceedings of the National Academy of Sciences.Franz C, Walczak R, Yavuz S, Santarella R, Gentzel M, Askjaer P, Galy V, Hetzer M, Mattaj IW, Antonin W. MEL-8/ELYS is required for the recruitment of nucleoporins to chromatin and postmitotic nuclear pore complex assembly.EMBO reports.6Jevtić P,

Table 1B : Face -NPC center to center distance distributions for WT
Median and standard deviation of the observed and expected lamin fiber to NPC center to center distances, the difference between them, p-values (see Methods), and number of NPCs.The data in each row was collected from 10 cells.The Mann Whitney U test and Ansari-Bradley test were used as in described in the Materials and Methods.P-values in red were above the Bonferroni corrected alpha value of 0.05/8 tests = 0.006.Median and standard deviation of the observed and expected lamin face to NPC distances, the difference between them, pvalues (see Methods), and number of NPCs.The data in each row was collected from 10 cells.The Mann Whitney U test and Ansari-Bradley test were used as in described in the Materials and Methods.P-values in red were above the Bonferroni corrected alpha value of 0.05/7 tests = 0.007.

Table 2B : Lamin face to NPC center to center distance distributions of WT MEFs with TPR, NUP153, and ELYS knockdown siRNA Lamin Obs. -Scram. P vs Scram. Num. of NPCs Knockdown Labeled Median St. Dev. Median St. Dev. Median St. Dev. Median St. Dev. Median (nm)
Median and standard deviation of the observed and expected lamin fiber to NPC center to center distances, the difference between them, pvalues (see Methods), and number of NPCs.The distributions were also comapared to scrambled siRNA control.The data in each row was collected from 20 cells.The Mann Whitney U test and Ansari-Bradley test were used as in described in the Materials and Methods.Median and standard deviation of the observed and expected lamin face to NPC distances, the difference between them, p-values (see Methods), and number of NPCs.The distributions were also comapared to scrambled siRNA control.The data in each row was collected from 20 cells.The Mann Whitney U test and Ansari-Bradley test were used as in described in the Materials and Methods.

Table 2C : Face radii distributions (fiber to NPC + face to NPC) of WT MEFs with TPR, NUP153, and ELYS knockdown siRNA Lamin Obs. -Scram. P vs Scram. Num. of NPCs Knockdown Labeled Median St. Dev. Median St. Dev. Median St. Dev. Median St. Dev. Median (nm)
Median and standard deviation of the observed and expected sum of lamin fiber and lamin face to NPC distances, the difference between them, p-values (see Methods), and number of NPCs.The distributions were also comapared to scrambled siRNA control.The data in each row was collected from 20 cells.p-values less than the Bonferroni corrected alpha value are in red.The Mann Whitney U test and Ansari-Bradley test were used as in described in the Materials and Methods.