Nuclear Envelope Reconstructions
We created 3D reconstructions of entire nuclei from electron micrographs of serial thin sections to determine the number, surface density, and distribution of NPCs throughout the cell cycle of the budding yeast S. cerevisiae
. As shown in an earlier study (Winey et al., 1995
), fixation of the cells by high-pressure freezing followed by freeze substitution resulted in good morphological preservation of the cells. Critical for this study, the nuclear envelope exhibited smooth round profiles in cross-section, the membranes of the nuclear envelope were evenly spaced, and NPCs were clearly observed as dense bodies spanning the envelope (Figure A). To avoid any artificial perturbation of the cell cycle, samples were prepared from logarithmically growing cultures. Serial electron micrographs of the selected nuclei were digitized and models were constructed with the aid of the IMOD program (Kremer et al., 1996
; see also MATERIALS AND METHODS for special features developed for this analysis). The models (Figure ) have three components; nuclear envelope, NPCs, and SPBs. Tracings of the outer envelope in each section (Figure B) generated the lines that define the nuclear surface in the wire-basket style models (Figure , C, E, and G). The position of each NPC was marked by a sphere of appropriate size inserted into the model. As expected, individual NPCs spanned more than one section, because their 97-nm diameter (Rout and Blobel, 1993
) exceeds the thickness of our sections (53 or 60 nm, MATERIALS AND METHODS). Detection of stained material in adjacent sections was one of the criteria used to confirm that the densely staining material was a NPC. The sphere used to mark the position of the NPC was displayed as a large circle on the section where the bulk of the NPC was found (Figure B) and as a smaller circle on adjacent sections. This feature, in combination with precise alignment of adjacent sections, allowed us to visualize the position of NPCs in adjacent sections and to avoid duplicate modeling of the same NPC. Finally, SPBs, which can be difficult to detect in cells prepared by the methods used herein, were unambiguously identified by their laminar morphology and/or the association of microtubules and mapped in 14 of the 32 nuclei modeled (Table ).
Figure 1 Model building of nuclear envelopes is carried out by using digitized electron micrographs of serially sectioned nuclei (A) on which the outer nuclear envelope and the position of the NPCs are manually indicated (B, outer nuclear envelope is green and (more ...)
NPC Number and Nuclear Dimensions for Individual Reconstructed Nuclei
Nuclei from 32 cells at different points of the cell cycle were reconstructed and modeled. A critical aspect of the analysis was to define the stage of the cell cycle for each cell whose nucleus was modeled. Several criteria were used during examination of cells in the electron microscope to discriminate between four stages of the cell cycle, G1
, S, early mitosis, and late anaphase, that could be determined entirely by morphological criteria. The “G1
group” was composed of mother–bud pairs that had completed cytokinesis but were still joined at the new septum. In these cells, the nuclei were spherical. We did not distinguish between mother and bud in the analysis. A representative model of a G1
cell is shown in Figure C, and 10 such cells were modeled (Table ). The “S-phase” group consisted of cells with minimal size buds. These very small buds are filled with the characteristic darkly stained vesicles described previously (Byers and Goetsch, 1975
). As with the G1
cells, the nuclei in these cells were spherical (Table , n = 8). A third class of cells in early mitosis forming the “early mitotic” group of eight models (Table ) were identified as cells with the nucleus elongated through the bud neck (e.g., Figure , D and E). The nuclei included in the early mitotic group were just ballooning out slightly on the bud side of the neck. Both SPBs were identified in three of these nuclei, and the pole-to-pole distances were 1.96, 2.69, and 3.14 μm (taken to be spindle length; Table , models 26, 19, and 24, respectively), indicating that these cells are indeed in mitosis (Winey et al., 1995
). Finally, the fourth class of cells were those in late anaphase, where extensive separation of the SPBs (anaphase B) has occurred such that there is a spherical nuclear body in both the mother cell and the bud (not distinguished) joined by the thin tube of envelope and spindle remnants (e.g., Figure G). Six such nuclei were modeled (Table ) with spindle lengths of 3.94–6.16 μm, consistent with late anaphase (Winey et al., 1995
The IMOD program was used to extract various parameters from the 32 models of yeast nuclei. These values include the number of NPCs per nucleus, as well as the volume and surface area of each nucleus (Table ). Surface area was determined from a mesh of triangles over the surface of the nuclear models (Figure , see MATERIALS AND METHODS). By using the surface area and NPC values for each nucleus, an average NPC density (NPC/μm2 of nuclear envelope) was derived (Table ). The number of NPCs observed in models of individual nuclei ranged from 65 in a G1 cell (Table , model 1) to 182 NPCs in a late anaphase cell (Table , model 32). The surface area of the nuclei ranged from 5.5 μm2 in a G1 cell to 16.9 μm2 in a late anaphase cell (Table , models 5 and 30, respectively). The volume of the nuclei ranged from 1.3 μm3 in a S-phase cell to 4.0 μm3 in a mitotic cell (Table , models 12 and 24, respectively). The trend toward increasing numbers in later stages of the cell cycle is reversed for average NPC density per μm2 of nuclear envelope, which ranged from 8.2 NPCs/μm2 in a late anaphase cell to 18 NPCs/μm2 in a S-phase cell (Table , models 27 and 15, respectively). Finally, the overall average number of NPCs/nucleus for this data set is 117 (SD = 29.7), with an average nuclear volume of 2.39 μm3 (SD = 0.78), average surface area of 10.1 μm2 (SD = 3.08), and an average NPC density of 12.0 NPCs/μm2 (SD = 2.66).
Another technique that has been used in a variety of cell types to examine NPC structure, number, and distribution is freeze–fracture analysis. Because membrane systems are frequent sites of fracture, this has been a popular technique to examine complexes embedded in membranes, such as NPCs. This technique has the advantage of sampling large regions of the nuclear envelope and of possibly showing fine structure of the organelle being examined (Figure ). The disadvantage of freeze–fracture analysis for the type of analysis described herein is that it is usually difficult to determine the cell cycle stage of the cell whose nucleus is exposed, and it is difficult to estimate the size of the entire nucleus from the image of the fracture through part of the nuclear envelope. Nonetheless, we estimated the NPC density in fragments of 36 nuclei imaged by freeze fracture, as shown in Figure (see MATERIALS AND METHODS). These cells were from all stages of the cell cycle and yielded an average NPC density of 9.4 NPCs/μm2
of nuclear envelope (SD = 2.6 NPCs/μm2
), which is similar to previously reported numbers (Moor and Mühlethaler, 1963
). Because the sampling technique is so different, these results are not directly comparable to those from the 3D reconstructions of entire nuclei. Nonetheless, the number of 9.4 NPCs/μm2
compares favorably with the average NPC density of 12.0 NPCs/μm2
for the entire data set of 3D models. Furthermore, the NPC densities observed in the segments of the 36 nuclear envelopes imaged by freeze–fracture analysis corresponded to the range of NPC densities that were observed in areas of 32 nuclei modeled in 3D (Table ). This result suggests that the NPC numbers presented herein are reliable because they can be derived by two independent techniques, indicating that we probably did not miss significant numbers of NPCs, if any, in the serial reconstructions.
Freeze–fracture images of the nuclear envelope (see MATERIALS AND METHODS) from two different (A and B) cells, where B appears to be a mitotic nucleus. The position of a few NPCs is indicated by arrows. Bars, 0.2 μm.
Cell Cycle Trends
The selection of the 32 cells for modeling on the basis of their stage in the cell cycle allows us to derive average values for the different parameters described above at each of the cell cycle stages. Roughly equivalent numbers of nuclei were modeled for each of the four cell cycle stages (G1, n = 10; S, n = 8; early mitosis, n = 8; late anaphase, n = 6). The values for the parameters were averaged within each cell cycle group, and the standard deviations were derived (Table ). To complete the cell cycle by comparing results between late anaphase and G1 nuclei, we have divided the anaphase numbers by two (anaphase/2) for some analyses. Because these late anaphase nuclei will give rise to two G1 nuclei by karyokinesis, the anaphase/2 bin may approximate the lowest values that might be expected in G1 cells.
Figure consists, in part, of graphs of these averages versus cell cycle stage. Figure A shows the change in average NPC number in the four cell cycle classes plus the anaphase/2 numbers. As expected, the G1 class clearly has the lowest number of NPCs. The anaphase/2 numbers show that there is some increase in NPC number from late anaphase to G1, which could occur during late anaphase, early G1, or both. The average number of NPCs is higher in S-phase and even higher in early mitotic cells (G1 versus S, p < 0.001; S versus early mitosis, p < 0.01; one-tailed t test), but the number of NPCs is approximately the same in the early mitotic and late anaphase cells. Interestingly, the volume of the nucleus follows a similar trend (Figure D), with a steady increase from anaphase/2 to early mitotic nuclei but no increase from the mitotic to late anaphase nuclei. However, the largest change in volume occurs from the S-phase group to the early mitotic group (anaphase/2 versus G1, p = 0.09; G1 versus S, p = 0.09; S versus early mitosis, p = 0.006; one-tailed t tests). The early mitotic and late anaphase nuclei are nearly twice the volume of the G1 nuclei and are about the same as each other despite the contortions of the envelope during mitosis (see Figure for examples). The nuclear envelope surface area increases throughout the cell cycle, but unlike the NPC number, the greatest increase is between the S and early mitotic classes of cells, and smaller increases are observed between the G1 and S classes and the early mitotic and late anaphase classes (Figure B). The different trends in NPC number and envelope surface area combine to make for very interesting behavior of NPC density (Figure C), which is highest in the S-phase class cells (G1 versus S, p = 0.03; S versus early mitosis, p = 0.01; two-tailed t test). This trend could be inferred by seeing that the NPC numbers rises steadily from G1- to S-phase nuclei (Figure A), whereas the nuclear envelope surface area increases mainly between the S and early mitotic groups (Figure B).
Figure 4 Graphs of mean NPC number (A), nuclear surface area (B), NPC density (C), and nuclear volume (D) versus cell cycle stage. The stages G1, S, early mitotic (EM), and late anaphase (LA) are defined in the text. The category LA/2 is defined by dividing the (more ...)
The observations that the numbers of NPCs in late anaphase cells were similar to those in early mitotic cells and that late anaphase cells exhibited relatively low NPC density led us to examine whether undercounting of NPCs in the narrow connecting region of the late anaphase nuclei could account for both of these results. In fact, this region of the late anaphase nuclei has the very low mean density of 5.4 NPCs/μm2
(compare to Table ). It seemed possible that the number of NPCs was underestimated because of difficulty in detecting NPCs in the longitudinal view of the narrow portion of the nuclear envelope connecting the separating nuclear masses (see Figure , F and G). However, three such late anaphase cells analyzed in another study (Winey et al., 1995
) had been cross-sectioned through the entire neck and the determination of NPC number was unambiguous when these cells were examined. The cells were found to contain 4, 6, and 9 NPCs in this region, whereas the six anaphase cells collected for this study have 2, 2, 3, 7, 11, and 12 NPCs in this region. The means of these two groups of cells match quite well (6.3 versus 6.2). Therefore, we consider the number of NPCs in the sample set collected from the longitudinally sectioned cells presented herein to be accurate.
Another possible explanation for the similarity between the NPC numbers in the early mitotic and late anaphase nuclei could be that these two cell cycle stages are not separated by much time in the cell cycle, so that we would not expect to see much change in the NPC number. The relative progression through the cell cycle between the bins that we have defined cannot be determined directly from our electron micrographs. However, we have correlated the stages of the cell cycle we examined with the kinetics of the cell cycle as determined by the examination of living cells with time-lapse and digital- and video-enhanced differential interference contrast microscopy. In this study the cell cycle time was an average of 125 min (±9 min), and our early mitotic nuclei correlate to stage IV and our late anaphase nuclei correlate to stage Va, which are only separated by approximately 12 min (Yeh et al., 1995
; K. Bloom, personal communication). Although the distinction between G1
- and S-phase in Yeh et al. (1995)
is not as clearly defined as the mitotic stages, our attempt to fit our data to the cell cycle clock defined by Yeh et al. (1995)
is shown in Figure , E–H. A line indicating the doubling of the given value at a constant rate during the cell cycle has been placed on these graphs and shows a good fit for the increase in NPC number (Figure E) and nuclear volume (Figure H) but not for nuclear surface area (Figure F), which contributes to the behavior of the NPC density (Figure G). In conclusion, the lack of increase in NPC number and nuclear volume from the early mitotic to late anaphase stages appears to be a consequence of the close temporal proximity of these two stages and is consistent with a uniform increase of these parameters through the cell cycle.
NPC Distribution over the Nuclear Envelope
The high-resolution 3D models of nuclei and their NPCs proved useful not only for the analysis of general trends in NPC numbers and nuclear envelope accumulation during the cell cycle but also for the examination of the distribution of NPCs over the surface of the nuclear envelope. We first wished to determine whether NPCs were evenly dispersed over the surface of the nuclear envelope. To do this, an algorithm (see MATERIALS AND METHODS) was developed to determine a smoothed relative surface density of NPCs. These relative densities can be displayed in false color on the surface of the nuclear envelope model as shown in Figure , H and I. The mitotic nucleus shown in Figure has a wide range of smoothed densities from 1.3 NPC/μm2 to 26.7 NPC/μm2. All nuclei showed similarly irregular distributions with at least a fourfold range of smoothed densities (Table ). Thus, NPCs are not evenly distributed or regularly spaced apart from one another over the surface of the nuclear envelope.
SDs of smoothed density in modeled nuclei compared to SDs in 500 randomizations of each model
Because NPCs are not spread over the surface of the nucleus equidistant from one another, we endeavored to determine whether the organization of the NPCs was random or not. To do this, we used the SD of the smoothed density over the whole surface as a measure of the irregularity of the NPC distribution. For each model, the SD of the smoothed density was compared with a similar number derived from randomized data. The placement of NPCs was randomized in each of the models 500 times as described in the MATERIALS AND METHODS, and the SD of the smoothed density for each randomization was compared with the SD derived from the real data. Table lists the percent of randomly generated data sets that had an SD greater than the SD of the real data set. Each of these percents estimates the probability that the actual data are equivalent to a sample from a random distribution, or in other words, the percentage is a measure of the statistical significance of nonrandomness of NPC distribution for each nucleus. The majority (n = 19) of nuclei were significantly nonrandom, having fewer than 4% of the random data sets being more irregular than the actual distribution. Another 8 nuclei had from 5.2 to 11.8% of the SDs of randomized data greater than the SD for real data, so their nonrandomness might be considered marginally significant. Only 3 nuclei showed no evidence of being more irregular than a random distribution (SDrandom > SDreal, 30%, 66%, and 99%, see Table ). The degree of nonrandomness is most striking for mitotic and late anaphase nuclei, wherein the 500 randomizations for each of 9 of 14 nuclei in these classes did not produce any single randomized model with an SD greater than that of the actual data. Although NPCs are not equidistant from one another, this analysis shows that they are also not randomly dispersed over the surface of the nuclear envelope.
Two kinds of nonrandom NPC arrangements that could contribute to the observed nonrandom, yet nonequidistant, arrangement are a preferred nearest neighbor distance and longer range clustering. In fact, such clustering is suggested by the high density of NPCs in the red regions of Figure , H and I. To explore NPC distribution over the nuclear envelope in more detail, SDA was developed (Figure , see MATERIALS AND METHODS). In SDA, ever larger concentric rings of defined radii (to the inner and outer circles that define the ring) are drawn around each NPC in a given nuclear envelope model. The NPC density found in each ring of given minimal and maximal radii is recorded, and these values are averaged over every NPC in the model (Figure ). The data can be displayed as a graph of NPC density versus distance from the NPC (ring radii), as shown in Figure . The SDAs for two mitotic nuclei, model 23 and 26 (Table ), are displayed in Figure , A and B, respectively. These SDAs are for a total of 136 NPCs in Figure A and 176 NPCs in Figure B.
Three trends are recognizable in these histograms. One is a region close to NPCs, up to 120 nm, that has very few NPCs, suggesting that few if any NPCs are touching each other or are very close to each other. This is easily verified by viewing the models (Figure ). Next is a small peak of density around 240 nm, which is most obvious in Figure A. This small peak is suggestive of some preferred NPC nearest neighbor spacing. The SDA for another mitotic nucleus is shown to demonstrate that this feature is not necessarily evident in every model (Figure B). However, note that in both cases the density out to 600 nm is elevated above the dashed line that shows the average density from 600 to 920 nm. This is the third feature, a slight decline in density with distance. When an average SDA is formulated for all eight mitotic nuclei (Table , models 19–26), all three trends are apparent in this population (Figure C). This averaging makes it clear that density is elevated out to about 600 nm, which implies that NPCs occur in clusters approximately 0.5–1.0 μm across. A randomization control is shown in Figure D. SDAs were derived for one randomization of each of the eight mitotic nuclei and averaged. After performing 40 such averaged randomizations, the mean and SD of the density in each bin was computed. Figure D shows the mean SDA and the mean plus or minus two standard deviations (thin lines). In this analysis the most closely spaced NPCs were excluded so that the rising phase of the graph would match the same region of the graph of the actual data (thick lines). The SDAs derived from randomized data are basically flat from 200 nm to 1.0 μm, so the elevation of the graph from actual data out to 600 nm is clearly significant. Also, the small peak of actual density at about 200 nm is not simply an overshoot from the low density at short distances, because the randomizations have similarly low initial density without such a peak. Average SDAs for the 18 G1- and S-phase nuclei and for the six late anaphase nuclei are presented in Figure , E and F, respectively. Both graphs show some elevation in density above the baseline level out to 400–600 nm, but the clustering effect is not as strong as it is for the mitotic nuclei. Randomization controls showed that these elevations, although small, were significant at a confidence level of at least 98%.
Finally, we examined the distribution of NPCs relative to the SPB, the other nuclear-envelope–embedded organelle. For this analysis, 19 SPBs were identified unambiguously in 13 cells. By using these SPBs, an SDA of NPC density around each SPB in all the models was performed (Figure ). Like NPC SDAs, there is a small zone of exclusion around the SPB that does not contain NPCs, but then a high density of NPCs is observed just outside of that region (Figure , peaks in graphs). Again, mitotic cells showed the strongest effects, with two separate components (Figure B). The single high bin from 100 to 200 nm reflects that there are 3.3 NPCs within 200 nm of the SPB, whereas only 0.9 is expected based on the average density. In addition to this small local cluster, the elevated density out to 1.0 μm implies a more extended cluster of NPCs within that distance of the SPB. The late anaphase cells show both effects (Figure C), but less strongly than the mitotic nuclei, whereas the G1 and S nuclei show only the local clustering (Figure A). To visualize this result, the location of the SPBs was examined on nuclear envelope models that had been pseudocolored to display relative NPC density as shown in Figure , H and I. As illustrated in Figure , H and I, all the SPBs identified in mitotic cells (n = 8) were found to be in or adjacent to a region of highest NPC density, whereas this relationship appeared for 4 of 7 SPBs in late anaphase and only 1 of 4 SPBs in G1- or S-phase cells. The extended elevation in density seen in the SDA graphs of Figure thus reflects the degree of colocalization of SPBs and regions of peak NPC density. This result suggests that nuclei in early mitotic cells may have some higher-order organization involving NPCs and SPBs.
Figure 7 SDA of NPCs relative to SPBs as the center. The axes are as in Figure , but the scale on the Y-axis is different. The SDAs presented are cumulative for the G1- and S-phase nuclei (A, n = 4 SPBs), the early mitotic nuclei (B, n = 8 SPBs), (more ...)