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 6 (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 8 (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 For correspondence: r-goldman@northwestern.edu † These authors contributed equally to this work. ‡ Present Address: Janelia Research Campus, Howard Hughes Medical Institute, Helix Dr, Ashburn, VA § Present Address: IIR Advanced Research Center for Cell Biology, Tokyo Institute of Technology, Yokohama, Kanagawa, Japan 6-8 of meshworks. In mouse embryo fibroblast nuclei, the NL is a . nm thick layer composed of . nm diameter filaments (Turgay 6 et al., ). Using three-dimensional structured illumination microscopy ( D-SIM) combined with computer vision analysis, we demonstrated that bundles of these filaments, termed fibers in the light microscope, are non-randomly organized into complex 8 interwoven meshworks within the NL (Shimi et al., ; Turgay et al., ). Notably, each lamin isoform assembles into distinct meshworks with similar structural organization (Shimi et al., ). Previous studies on Lmna -/- MEFs (Sullivan et al., ) showed that loss of lamin A/C caused dramatic changes in nuclear morphology with some NPC clustering. Subsequently, we showed that the meshworks formed by individual lamin isoform fibers are significantly expanded in size in Lmna or Lmnb knockout (KO) MEF nuclei compared to the lamin meshworks in WT or Lmnb KO MEF nuclei demonstrating that LA/C and LB interactions are required for normal lamin fiber meshwork structure in WT MEFs (Shimi et al., ). The NPCs penetrate the NE forming transport passageways delineated by the fusion of the inner and outer nuclear membranes, thereby allowing for bidirectional transport across the NE. They are composed of multiple copies of proteins known as nucleoporins 6 (Beck and Hurt, 6). For many years, it has been apparent that there are structural interactions between the NL and NPCs of vertebrate nuclei. The earliest studies on identification of components of the NE identified a cell free NPC-NL fraction that could be 8 isolated under fairly stringent conditions suggesting their strong physical association (Kay et al.,;Dwyer and Blobel,6;Scheer et al.,6;Aebi et al.,86). In addition, both lamins and the NPCs are relatively immobile in the plane of the NE indicating that both are anchored in some fashion (Broers et al., ; Moir et al., ; Rabut et al., ). Both the nuclear lamins and NPC structures are closely associated with chromatin at the nuclear periphery (Guelen et al.,8;;Ibarra and Hetzer,) with the NPCs located in spaces where both the lamina and heterochromatin appear to be discontinuous (Fawcett,66;Ou et al., ). Super-resolution microscopy analysis of lamins and NPCs in Lmna -/fibroblasts also found NPCs closely associated with exogenously expressed LA and LC in Xie et al. ( 6). Some clustering of NPCs within the remaining LB networks has also been reported in Lmna -/fibroblasts (Xie et al.,6). Our previous study by cryo-ET also supports the close association of lamin filaments 6 with the NPCs (Turgay et al.,;Tatli and Medalia,8). Biochemical analyses of lamin-NPC interactions have shown connections between lamins and a subset of specific nucleoporins expectation that NPCs would be near the LA fibers and away from the faces by chance in a broad distribution. However, the NPCs were offset from the LA fibers in a narrower than expected distribution (Figure S A-F). In the WT MEFs, the negative correlation between the distances was also apparent, which is expected since the NPCs that are farther from the lamin fibers tend to be closer to the face centers ( Figure S A-B). However, the two-dimensional histograms of single nuclei were sparse and noisy indicating that additional distance measurements were needed for evaluation.
The localizations of both lamin fibers and NPCs were based on finding local maxima within the continuous reconstruction of the fluorescence intensity from critically sampled D-SIM images and was not dependent on rounding to the nearest pixel (See Methods and Supplement; Kittisopikul et al. ( )). Here we focused on localizing lamin fibers and NPCs resolved by D-SIM, 6 and not their specific molecular components consisting of individual . nm lamin filaments Turgay et al. ( ) and/or specific nucleoporins. Furthermore, we measured the distance between structures localized within two channels separated by their chromatic 8 properties, and thus these distance measurements were not limited by resolution (Stelzer,8). The main limitations to the precision of the localization and distance measurements are the inaccuracy of indirect immunofluoresence labeling, signal-to-noise ratio, and structured illumination microscopy reconstruction artifacts. This was mitigated by examining the distribution of tens of thousands of distance measurements. These analyses permitted us to express the magnitude of differences in the co-distributions, or the lack thereof, in terms of nanometers with high statistical power (see Appendix ).

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 6 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 8 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 ; 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 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 6 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 8 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

Computational Image Analysis of Lamin A and NPCs in Individual Nuclei
A) Immunofluoresence images labeling LA (green) and NPCs (magenta) of wt and Lmnb1 -/-MEF nuclei as in Figure 1 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. 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 .
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. of the pairs of distributions compared in Tables 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 < 6 .
; 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 8 fibers is closer (median: .8 nm) 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 6 distances. 6 The relationship between LB fibers and NPCs in WT MEFs differed from the other lamin isoforms. We observed a statistically 6 significant difference in medians from expected distributions between the centers of LB fibers and NPCs ( .6 nm observed; -.6 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 6 direction than observed for LA and LB fibers. The median distance from NPCs to LB face centers ( 6. nm observed; -.6 nm 6 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.

6
Knocking out 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 6 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.
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 6 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 < .
; Table A, Figure A, B). This reflects 8 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 8 than expected by a large magnitude ( . nm; -. nm vs expected; p < . ; Table B; Figure Figure B). This indicates that, in Lmnb -/nuclei, the proximal 8 lateral relationship between LA fibers and NPCs remains although the median distance between LA fibers and NPCs increased by 8 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. 8 The results showed a relationship similar to LA fibers in WT MEFs for distances less than nm where NPCs occurred less 88 frequently than expected (green area; Figure B) and more frequently than expected around -nm (purple area; Figure B). This 8 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, Figure A,B, Figure S B). 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 6 NPC medians in Lmna -/-MEFs did differ significantly from expected ( . nm observed; -6 . nm vs expected; p < . ; Table A, Figure A  Observed > Expected Observed < Expected 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.
of Cryo-electron tomography (Cryo-ET) and immunogold labeling show LA/C and LB filaments contacting the nucleoplasmic ring of NPCs In order to further investigate the relationship between lamin filaments and NPCs, we carried out cryo-ET of WT MEFs coupled with 6 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 8 around the nucleoplasmic ring of NPCs ( Figure A; Turgay et al. ( )) and counted the number of LA/C or LB filaments ( Figure 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, ; 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 6 ( Figure A). The median distance between the centers of NPCs and LA fibers in ELYS depleted cells ( .8 nm; + nm vs scrambled; p < .
; Table A, Figure A, B, Figure S6) increased compared to scrambled siRNA controls ( . nm; p < . ; Table A, Figure A, 8 B, Figure S6). Additionally, the median distance between face centers of the LA fiber meshwork and the NPCs was reduced (8 . nm; Table B; Figure C) compared to scrambled siRNA ( 6. nm; p < . ; Table B, Figure C, Figure 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. 6 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 8 LA fibers with TPR knockdown ( . nm; Table A, Figure B,C, Figure 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 6 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, 8 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 6 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 < . ; 8 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 C) indicating that ELYS knockdown results in expanded LC meshworks as it did for LA meshworks. These results 6 suggest that the NPC clusters induced by ELYS depletion exclude LC fibers as well as LA fibers. 6 siRNA knockdown of TPR resulted in an increase in the median distance between NPCs and LC fibers (+ . nm vs scramble; p < 6 . ; Table A, Figure 6B, C, Figure S ), a decrease in median distances between NPCs and LC face centers (-. nm; p < . ; 6 Table B, Figure 6 D,E) and a decrease in the effective face radius (-6. nm;  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 C). While these decreases are consistent with the change seen in the distances between 6 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.

Depletion of TPR or NUP results in denser LB meshworks, while LB fibers protrude into NPC clusters upon ELYS knockdown
Depletion of TPR, NUP , or ELYS altered the median center-to-center distance between LB fibers and NPCs (+ . nm, -. nm, and -. nm, respectively, Obs. -Scram; p < .
; 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 6 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, 8 -. 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 8 face centers as well as the LB face radii, while knocking down NUP had less impact. 8 Visual inspection of the accompanying images reveals denser LB meshworks upon TPR and NUP depletion relative to 8 scrambled siRNA controls as the numerical analysis suggests, but also enlarged faces upon ELYS knockdown in contrast with the 8 quantitative measurements. Closer inspection of the images upon ELYS depletion reveals LB fibers protruding into the enlarged 8 faces ( Figure ). This is not seen in the enlarged faces of LA/C meshworks ( Figure A and 6A). The interdigitation of LB fibers within 8 the NPC clusters explains why an increase in LB fiber to NPC distances is not seen quantitatively.

8
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 8 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 6 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. Studies of the . Electron microscopy as well as the meshwork altering perturbations produced here suggest the fibrous nature of lamins exists even 8 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 ). 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 6 of 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 8 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. 6 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 8 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 6 between adult fibroblasts and embryonic fibroblasts, ) possible differences in an ectopically expressed lamin network versus the 6 endogenous networks, and ) over-expression of LA only or LC only versus cells expressing all four lamin isoforms in the natural ratio.
6 Further studies will be necessary to address these differences in results. 6 Our results also provide new and important insights into lamin-NPC interaction by knocking down specific nucleoporin levels 6 using siRNA for ELYS, TPR, or NUP . Each knockdown had unique effects on both NPC distribution and lamin meshwork structure. ). However, these previous studies did not find clustering of NPCs or changes in lamin meshwork structure. 8 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 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 ( ) 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 6 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 6 determined that the power of the lamin-NPC distance studies would also exceed the requirements.

8
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. 6 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 8 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.

Cell culture
Immortalized WT, Lmna -/-, Lmnb -/-, and Lmnb -/-MEFs were cultured as previously described (Shimi et al., ). Briefly, cells 6 were cultured in modified DMEM (Thermo Fisher Scientific, Waltham, MA, USA) supplemented with % fetal calf serum, U/ml penicillin G, /ml streptomycin sulfate (Thermo Fisher Scientific) at °C in a humidified CO incubator. . 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. 6

Indirect immunofluorescence
Samples for indirect immunofluorescence were processed as previously described (  . × 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 6 replated on coverslips for indirect immunofluorescence or plated into a 6 mm dish for western blotting. 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 6 antibody linearity, imaged in the Odyssey Fc and the images analyzed using Empiria software.

NPC-lamin rendered view
8 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).

Immunogold labelling image processing
Sub-tomograms of gold labeled lamins (Turgay et al., ) were reconstructed as described above ( sub-tomograms). The subvolumes containing NPCs (in top-view orientation), were projected along the Z axis, to produce a D image. The coordinates of the gold clusters (6 nm and nm) were identified manually and counted. The respective histograms were drawn in Excel (Microsoft). 6

Computational image analysis
Computational image analysis was done using MATLAB (Mathworks, Natick, MA) using custom software developed in the 8 Jaqaman Lab. Nikon ND files containing image and meta data were loaded into MATLAB using Bioformats (Open Microscopy Environment, Linkert et al. ( )). Nuclear pore complexes were detected and localized using an adapted point Source Detector routine from the lab of Gaudenz Danuser which involved two-dimensional local maxima detection, Gaussian fitting, and Gaussian mixture modeling. Lamin fibers were segmented using multi-orientation analysis as described in Kittisopikul et al. ( ) to accurately segment a meshwork structure with many junctions. Lamin fibers were further localized as in Appendix . The source is available on Github at https://github.com/mkitti/LaminNpcAnalysis Computation was conducted on Northwestern University's high performance computing environment, Quest. Files were stored on Northwestern University Research Data Storage Service FSMRESFILES. Globus.org and Box.com were used to transfer files between 6 storage and computational environments. of Expected distribution of NPCs 8 In this study, the null hypothesis is that there is no relationship between the position of the lamin fibers and NPCs within the nucleus. To determine if a relationship or an association between lamin fibers and NPCs exists, we used statistical methods to see if the observed distances between lamin fibers and NPCs were significantly different than what would expect under this null hypothesis.
To calculate the expected distribution of NPCs relative to the lamin fibers for each nucleus under that null hypothesis we used a Monte Carlo simulation to randomly place NPCs within the nucleus. 6 , psuedorandom pairs of numbers representing XY locations of NPCs were selected within the image. If they were not within the mask of the nucleus represented by a complex hull, then the XY locations were rejected. The distance between the remaining XY locations were measured to the nearest lamin fiber location as in Appendix . The initial number of pairs was selected empirically such that the distance frequencies would not fluctuate more 6 than % for nm bins.   Stelzer. Contrast, resolution, pixelation, dynamic range and signal-to-noise ratio: fundamental limits to resolution in fluorescence light microscopy. Here we extend the procedure by using the orientations to localize lines, the lamin fibers, to sub-pixel precision by also treating the spatial dimensions as continuous. Given sufficient signal-to-noise ratios and sampling in excess of that required by the Nyquist-Shannon-Whittaker-Kotelnikov sampling theorem, the spatial dimension could also be treated continuously through interpolation. In particular, we use spline interpolation (Unser, ). In that case, we can state the localization problem as solving a system of partial differential equations where ( , , ; ) is the steerable filter response at some location ( , ) at orientation at the orientation-resolution .

Image Data Repository
For ⃗ = (cos( ), sin( )), we want all ( , , ) such that ⃗ is a vector normal to the structure being localized. As explained in Kittisopikul et al. ( ), 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.       . D) Fourth row shows the same with siRNA knockdown of Elys. First column represents the observed bivariate distribution. Second column represents the expected bivariate distribution. Third column represents the difference between expected and observed. 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. Marginal violin plots and box plots of the distances correspond with the half-violin plot counterparts of the same orientation and color as in Panels B-E of Figure 6.