Chapter 5 Localization of Single Nuclear Pore Complexes by Confocal Laser Scanning Microscopy and Analysis of Their Distribution

CHAPTER 5

Localization of Single Nuclear Pore Complexes by Confocal Laser Scanning Microscopy and Analysis of Their Distribution Ulrich Kubitscheck and Reiner Peters Instittit Hir Mrdizitiische l'hysik i ~ n dIhphytik Westfali,clie WilI~rlms-Ut~ivt.rcitat 4X 140 Mutistrr, <;rmiany

I . Introduction I I . Test and Optimization of Single-Particle Localization Using a Model System A. Specimen Preparation U. Iniagng by High-liesolutioii Confocal Fluorescence Microscopy C . Imaging by Electron Microscopy I). Single-Particle Localization I I I . Visualization and Localization of Single Nuclear Pore Complexes A. Cell Culture and Permeabilization U. Fluorescent Labeling of the Nuclear Pore Complex C. Iniagng by High-Resolution Confocal Fluoresccnce Microscopy I). Localization of the Nuclear Pore Complex IV. Statistical Analysis of Particle I h t r i b u t i o n s A. Nearest-Neighbor Distribution Function and Pair Correlation Function U. Cluster AnalysiF V. Discussion Iieferences

I. Introduction The nuclear pore complex (NPC) undoubtedly assumes a central role in the communication between nucleus and cytoplasm. It controls both the export of 79

Ulrich Kubitscheck and Reiner Peters

mature nuclei acids from the nucleus and the import of large proteins, such as transcription factors, into the nucleus. Transport activities of the NPC and their molecular determinants are currently intensively studied and progress is made rapidly (for review, see Pant6 and Aebi, 1994; Melchior and Gerace, 1995; Gorlich and Mattaj, 1996). However, in addition to nucleocytoplasmic transport the NPC may have another, equally important but less obvious function: the induction and maintenance of the three-dimensional architecture of the genome. Chromosomes occupy defined territories in the interphase nucleus (Agard and Sedat, 1983). Chromosomal territories are probably separated by interchromatin channels serving as pathways for the transport of mRNA and gene regulatory proteins between genetic loci and the nuclear periphery (Cremer et al., 1993). Possibly, the genome as a whole has a three-dimensional (3D) structure characteristic and specific for the cell type as well as cell cycle phase and developmental stage (Blobel, 1985). Among structural elements that may affect the 3D architecture of genome, the nuclear matrix and the nuclear envelope (NE) have to be considered in the first place (cf. Georgatos, 1994). Despite considerable progress (compiled in Berezney and Jeon, 1995), the debate on the molecular composition and physiological relevance of the nuclear matrix continues, whereas the structure, molecular composition, and function of the NE have been clarified to a certain extent. On the ultrastructural level a large fraction of chromatin appears to be coaligned with the NE (Paddy et al., 1990), which raises the possibility that chromosomes are specifically attached to the inner surface of the nuclear envelope. In fact, a study by Marshall et al. (1996) reported that in Drosophila embryos there are approximately 15 NE-chromosome contacts per chromosome arm. These contacts are thought to organize the genome such that each genetic locus occupies a highly determined position within the nucleus. The nature of NE-chromosome contacts is still unresolved. One possibility is that the nuclear lamina provides contacts via lamin B, the lamin B receptor, and lamina-associated proteins (Worman et al., 1988; Sirnos and Georgatos, 1992; Glass et al., 1993). Another possibility is that the NPC harbors contact sites. The filaments radiating from the internal face of the NPC into the karyoplasm and connecting in the fashion of a basket or fishtrap (Ris, 1991; Jarnik and Aebi, 1991) seem to suit that purpose. In accordance with this contention the gene gating hypothesis (Blobel, 1985) assumes that the NPC is the major factor determining the 3D architecture of the genome. Each NPC is actually thought to graft a specific genetic locus and to channel its transcripts to the cytoplasm. If the hypothesis applies, the distribution of NPCs in the NE would directly reflect the 3D organization of the genome and its changes during cell cycle and ontogenesis. In addition to the potentially important but speculative role of the NPC in nuclear morphogenesis, there are many other reasons for studying the distribution of the NPC in the NE. During interphase the surface area of the NE approximately doubles while the area density of the NPCs remains approximately constant. This implies that new NPCs are synthesized and inserted into the NE in large numbers. How and where this occurs is perfectly obscure. During mitosis

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the NE disappears, together with the NPCs. All components of the NE, however, seem to be preserved and equally distributed among daughter cells to rebuild the NEs within them. Almost nothing is known about the mechanisms and sites for these processes. For these and other reasons the manner in which the NPC is distributed in the NE has been a point of interest for many years. The freeze-fracture technique provided the possibility to expose parts of the nuclear envelope and to visualize the NPC distribution by electron microscopy. The outcome of such studies has been summarized by Maul (1977), who eventually concluded that a “random distribution (of the NPC) has never been proved, and all investigated cases seem to have non-random distribution.” We may add that the number of investigated cases is small and that the claims of nonrandom distributions are not always convincing. New access to the study of the NPC distribution was provided by Davis and Blobel (1986), who discovered that NPC-specific antibodies would label the NE in a punctuate pattern. The pattern can be observed most easily by confocal fluorescence microscopy and meanwhile is widely applied as a necessary criterion for the specificity of anti-NPC antibodies. However, because the NPC, an approximately cylindrical structure 120 nm in diameter and 70 nm long, has submicroscopic dimensions the nature of the punctuate pattern remained unresolved for some time. Kubitscheck et uf. (1996) showed by refined experimental and theoretical methods that the punctuate pattern can be resolved into single NPCs, at least under carefully controlled and favorable conditions. The fact that single NPCs can be visualized by light microscopic methods opens new avenues to study NPC distribution as well as to elucidate its composition, biosynthesis, disassembly, and recycling. Thus, light microscopic methods, in conjunction with in vivo fluorescent labeling methods-such as the green fluorescent protein technique-have the potential to be applied to the living cell. It may become possible to monitor directly the distribution of the NPC during cell cycle and differentiation and to correlate it with the 3D organization of the genome. Furthermore, because light microscopic detection of single NPCs is based on fluorescence methods, it can be used to monitor two or more NPC components simultaneously. This could be used, for instance, to study a question that has remained perfectly unresolved so far, namely, whether all NPCs are alike or whether, on the contrary, different NPC types exist, possibly serving different functions, such as nuclear import and export. Finally, it may be noted that the same methods employed for visualizing single NPCs might be extended to observe the transport of single particles and even molecules through single NPCs. In this chapter we consider in some detail the methods for visualizing single NPCs and for analyzing their distribution. The approach comprises several distinct steps: (1) the specific fluorescent labeling of the NPC by the indirect antibody method, (2) the acquisition of high-resolution optical sections by confocal fluoresccnce microscopy, (3) the evaluation of stacks of confocal images for the 3D coordinates of single NPCs, and (4) the analysis of the NPC distribution by

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statistical methods. Each step will be considered separately. However, because we are dealing with a submicroscopic structure and thus are actually working right at the limit of optical microscopy, it is absolutely indispensable to test and characterize all methods by means of a simple and well-defined model system before dealing with the NPC. Such a model system and its use will be described in Section 11. Subsequently (Section 111) the visualization and localization of single NPCs in cultured cells will be discussed. After that, a discourse on the statistical analysis of particle distributions follows (Section IV). This is not an easy topic and will be discussed only as much as necessary for a meaningful and productive application. In order to make the described methods more concrete, their application to a particular cell type is given in Section V. Eventually (Section VI) some limitations and potential artifacts of the methods as well as their extension to transport studies will be discussed.

11. Test and Optimization of Single-Particle Localization

Using a Model System

The model system essentially consists of small fluorescent beads. A large variety of such beads is commercially available. Their size, surface properties, and fluorescence spectra can be chosen within wide limits. The beads are deposited on coated electron microscopic grids in the form of small drops. After drying, individual droplets are first visualized by confocal fluorescence microscopy and subsequently by standard transmission electron microscopy. Thus, the model system permits one to compare directly confocal with electron microscopic results. This is demonstrated in Fig. 1 (see color plate). Also, the size and average area density of the beads can be matched to those of the NPC. The model system is also well suited for optimizing imaging conditions and quantitating resolution in terms of the point spread function. A. Specimen Preparation

1. Electron microscopic copper grids are covered with pioloform membranes essentially according to standard procedures (Robards and Wilson, 1993). However, a 10-fold concentrated pioloform solution [5% (w/v) in chloroform] is employed to produce particularly resistant membranes approximately 100-200 nm thick. An increased resistance is necessary because of the immersion, washing, and drying procedures described below. 2. Grids are deposited on pieces of Parafilm and placed approximately 5 mm in front of a sprayer head (Micro-Spray, AGAR AIDS, Stansted, GB). The sprayer is filled with a suspension of fluorescent microbeads (Fluoresbrite beads, Polysciences, Eppelheim, Germany). 3. The sprayer button is pushed 7-10 times, by which means a sufficient number of small droplets is deposited on the grids. The average density of the

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beads in the dried droplets can be adjusted by variation of the bead concentration in the suspension. We found that a 0.25% (v/v) bead suspension yields an average density of approximately 5 beads/pm’, which corresponds well to the average density of NPCs in the NE of 3T3 and many other cultured cells. B. Imaging by High-Resolution Confocal Fluorescence Microscopy

For confocal microscopy a grid is placed on a glass slide with the pioloform layer carrying the beads on top, embedded in glycerol, and topped with a cover slip. 1 . Optimization of Ini~gingConditions The goal is to obtain a complete stack of optical sections at highest possiblc resolution and signal-to-noise ratio. It is therefore necessary, even when dealing with such an “easy” object as fluorescent microbeads, to optimize the imaging conditions carefully. In general, photobleaching will inevitably occur to a certain extent and has to be monitored and corrected for whenever possible. How the imaging conditions of a confocal laser scanning microscope are optimized has been discussed extensively in the literature, in particular in the “Handbook of Biological Confocal Microscopy” (Pawley, 1995), and therefore will be only briefly outlined: 1. Chose an objective lens for fluorescence microscopy that has a large numerical apperture (NA 1.3 or 1.4). 2. Adjust the confocal pinhole to a value between 2 and 4 optical units for an optimal signal-to-noise ratio and spatial resolution. 3. Reduce excitation laser power as far as possible. 4. Choose the size of the imaged area such that a sufficient resolution is obtained (-40-60 nm/pixel) while leaving photobleaching at an acceptably low level. 5. Check for optimum averaging conditions: line or frame averaging fourto eightfold. 6 . Adjust the axial step size to 0.2-0.3 p m for a NA of 1.3-1.4. 7. Take care not to saturate the photomultiplier tube (PMT), and use the 8bit dynamic range optimally: when obtaining an image with neither frame nor line averaging, a dark image should have a mean intensity close to zero, and an image of objects with maximum intensity should comprise only a few pixels with the maximum value of 255. 8. After acquisition of the data, set the axial step size to zero, and acquire a final series of images to monitor the extent of photobleaching per image. For a particular confocal microscope, model TCS of Leica, optimum imaging conditions are achieved in our experience by employing the following components and instrument settings:

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1. 2. 3. 4. 5. 6. 7.

63X, NA 1.4, or lOOX, NA 1.3, oil immersion objectives Pinhole size of 50, corresponding to -2 optical units Laser power set at minimum Object field size 20 X 20 pm2, corresponding to -40 nm/pixel Eightfold line averaging Axial steps of 0.2 p m PMT voltage of 640 V

2. Approximate Determination of the Point Spread Function The image of a point object, as generated by a confocal or by any microscope, has a complex 3D intensity distribution referred to as the point spread function (PSF). The PSF determines the spatial resolution that can be achieved by the employed microscope and therefore is a limiting parameter in single-particle localization. The PSF can be estimated on theoretical grounds. However, because the PSF depends on many parameters, some of which are difficult to assess, an experimental determination of the PSF is much more reliable. The PSF is experimentally determined by imaging a very small object and measuring the 3D intensity distribution of the image. An example is given in Fig. 2 (see color plate), which shows an xz image of a 170-nm fluorescent bead. Although the measured 3D intensity distribution is complex and its simulation by computing the exact equations is time consuming, it can be well approximated by a simpler function, namely the following 3D Gaussian:

That Eq. (1) well approximates the experimentally determined PSF is demonstrated in Fig. 2b. Showing the absolute differences between the measured and computed intensity distribution, Fig. 2c reveals even more clearly that the center region of the PSF is very closely approximated, in contrast to the side lobes. This implies that the accuracy of localizing the center of a particle by the Gaussian approximation is very high, amounting to a few nanometers, as we have determined. The limit at which two particles can be recognized as separate entities is approximately equal to the full-width half-maximum (FWHM) of the PSF. For the instrumental conditions given in Section II,B,l, we found by the Gaussian approximation the FWHM to be 0.27 p m in the lateral direction and 0.49 p m in the axial direction.

3. Image Correction and Snioothing Prior to further analysis the image stacks have to be corrected for a small amount of photobleaching that inevitably occurs during data acquisition (this

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should be 51% per image). To determine the correction factor for the nth image of a series, c(n),the mean intensity of some bright image features of the control image series (see Section II,B,l, step 8) is plotted as function of the image number, 11, and fitted by an exponential according to I ( n ) = I. exp( - k n ) . Then, c ( n ) is given as c ( n ) = exp(kn). Finally the image stacks are smoothed with a 3 X 3 X 3 Gaussian filter in order to reduce the inherent photon noise. The later localization procedures will work more reliably with images whose noise is as low as possible. The width of the smoothing matrix must be small compared to the width of the point spread function. Otherwise, the intensity peaks due to single particles will be artificially smeared out, increasing the problem of differentiating closely neighboring particles. C. Imaging by Electron Microscopy

After confocal imaging a surplus of glycerol is added to the specimen to carefully lift and remove the cover slip. Thus, the electron microscopic grid is exposed and can be grasped with forceps. The grid is carefully washed in distilled water and dried in air. After insertion of the grid into a transmission electron microscope, the beads can be directly visualized, without any processing or staining. Because the dried droplets have characteristic shapes it is easy to relocate that droplet and to image exactly those beads that had been imaged previously by confocal fluorescence microscopy. D. Single-Particle Localization

The stacks of confocal images are used to determine the 3D coordinates of the center of each imaged particle. For that purpose we have developed an interactive image-processing computer program by which small 3D cubes can be selected within image stacks. The cubes define a region of interest (ROI) and thus reduce computation time requirements. Particle center localization is straightforward in the case of isolated particles, but more complex with particle aggregates. Therefore the localization procedure is performed in three steps: 1. Consider only those spots that are well separated from other spots and clearly represent single, isolated beads. For these spots the 3D intensity distribution is fitted to a single 3D Gaussian, Eq. (l),by minimizing the X2 function with a numerical Levenberg-Marquardt routine (Press ef af.,1992) to determine the axial and lateral standard deviations (axyand a,) and additional offset levels due to background light and electronic offset. These parameters are individually determined for each image stack, because they depend on acquisition conditions such as depth in the sample and background level. 2. Select now those ROIs containing single spots; the centers and amplitudes of the respective spots can be automatically determined by a fit to a 3D

Ulrich Kubitscheck and Reinet Peters

Gaussian utilizing the determined SDs and offset level. This results not only in a coordinate list of the spot centers, but also in minimum and maximum values for single spot intensities. These values are used as restrictions in the subsequent analysis. 3. Intensity distributions presumably representing clusters of two or more beads are evaluated individually. The analysis ROI is selected, and the putative centers of the beads are selected interactively by clicking with the mouse onto respective ROI voxels. The position and intensity values of these voxels serve as starting values for the fitting procedure that simultaneously uses up to six 3D Gaussians to reproduce the ROI intensity distribution optimally, and thus to locate the centers of the beads. After convergence of the Levenberg-Marquardt routine, the analysis program inverts the voxel values nearest to the centers such that three-dimensional crosses indicating the detected bead centers are created in the image stack. In this way the fitting results can be displayed without losing the original data. After each fitting process the results are checked by inspecting an image stack composed of the original data, the fitted intensities, and the absolute residuals. In the case of an unsatisfactory fitting result, the voxel values of the marker crosses are inverted once more to reproduce the original intensity data, and the process is started once more after selection of new start values. The procedure eventually results in a list of x, y , and hundreds of beads.

z coordinates of several

111. Visualization and Localization of Single Nuclear

Pore Complexes For the visualization and localization of single NPC cells are grown in monolayer culture. Cells are permeabilized such that the plasma membrane becomes permeable to antibodies while the nuclear envelope and the NPC remains intact. The NPC is labeled with a primary antibody that is specific for an NPC protein. This is followed by reaction with a second fluorescently labeled antibody. Thc subsequent acquisition of stacks of high-resolution confocal images as well as the localization of single NPCs closely follows the procedure described for the model system. The final result of the procedure is illustrated in Fig. 3a (see color plate). A. Cell Culture and Permeabilization

When an established cell line is studied the cells can be cultured at standard conditions and plated on cover slips. Cells are permeabilized in situ by either of two methods. Both methods are suited to make the plasma membrane permeable to antibodies while leaving the NE and the NPC intact.

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1 . l~c.rmcabilizatio~i by Treatment with Iligtonin 1. A stock solution is prepared by dissolving digitonin (Calbiochem, Bad Soden. Germany) in DMSO at a concentration of 20 mg/ml. The stock solution is divided into small aliquots and stored at -20°C. 2. The stock solution of digitonin is diluted in transport buffer [50 m M HEPES/ KOH, pH 7.3, 110 mM potassium acetate, 5 mM sodium acetate, 2 m M magnesium acetate, 1 mM EGTA, 2 mM DTI', transport buffer (TB)] to yield a final concentration of 50 pg digitonidml. 3. A cover slip carrying a cell monolayer is washed three times with ice-cold transport buffer. 4. The cover slip is incubated with 1 ml of the digitonin solution for 5 min on ice. 5. Cells are washed carefully with TB. This is the method of Adam et af. (1990). The quoted concentrations and times apply to 3T3 monolayers grown for 24-48 hr. It is recommended to optimize concentrations and times when using different cells. 2. Mechnniccil Pernie'ibiliz'ition 1. A cover slip (15 X 15 mm) carrying a cell monolayer is removed from the culture medium, placed in a petri dish containing 2 ml phosphate-buffered saline (PBS). and gently shaken for about 60 sec. 2. PBS is removed, and the cover slip washed again twice with fresh Ca2+/ Mg"-free PBS. 3. The cover slip is removed from the petri dish and the cell monolayer is drained by touching an edge of the cover slip with a piece of common dry laboratory tissue (Kleenex, Kimberly-Clark, Code 7108). 4. The drained cell monolayer is moistened with 3 pI of intracellular buffer (50 mM HEPEYKOH, pH 7.3,llO mM potassium acetate, 5 mM sodium acetate, 2 mM magnesium acetate, 1 mM EGTA, 2 mM DTT, 1 pg/ml aprotinin, 1 pg/ ml pepstatin, and lpglml leupeptin). 5. A 15 X 15-mm piecc of the laboratory tissue is separated with forceps into it5 layers and the cell monolayer is blotted with one of the tissue layers. 6. After a very short time (-2 sec), the piece of laboratory tissue is peeled of the cell monolayer. 7. Finally, the cover slip is washed once with PBS. This is the method of Walaschewski et af. (1995). Blotting of the cell monolayer with the laboratory tissue is the critical step. Its success and reproducibility may requirc some practice. B. Fluorescent Labeling of the Nuclear Pore Complex

1. An anti-NPC antibody ( e g , mAb414) is appropriately diluted in TB supplemented with 1% bovine serum albumin (BSA).

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2. A cover slip carrying a permeabilized cell monolayer is deposited in a wet chamber and covered with 40 p1 of antibody solution. 3. After incubation for 40 min, cells are washed three times in TB-BSA. 4. Add to the cell monolayer 40 pI of a solution of a fluorescent secondary antibody, e.g., a fluorescein-labeled sheep antimouse polyclonal antibody (F3008, SIGMA-ALDRICH) diluted 1 : 100 in TB-BSA; incubate for 40 min. 5. Cells are carefully washed in TB-BSA. 6. During the incubation time a microchamber is created by attaching to a slide a piece of double-sided tape (Scotch 3M, obtainable, e.g., from Plano, Marburg, Germany) into which a hole 5.0-mm in diameter has been punched. The microchamber is loaded with 5 pl of the mounting buffer, which is made up from threefold concentrated TB-BSA (33.3 vol%), glycerol (66.6 vol%), and the antifading compound DABCO [SIGMA-ALDRICH, 2% (w/v)]. 7. The cover slip with labeled cells is mounted upside down onto the microchamber. All incubations are done at 4°C. The monoclonal antibody mAb 414 can be obtained from Berkeley Antibody Company (Richmond, CA). It is specific for a class of NPC proteins containing the XFXFG motif, of which p62 is a typical example. C. Imaging by High-Resolution Confocal Fluorescence Microscopy

Imaging by confocal fluorescence microscope and correcting for photobleaching and the smoothing are essentially done as described for the model system (Section 11,B). Usually the imaging of a particular nucleus is restricted to its upper sperical shell. From 11 to 16 xy images, separated in the z direction by 0.2 pm, are acquired, thus covering a total volume of 20 p m X 20 p m X 2-3 pm. D. Localization of the Nuclear Pore Complex

Single-particle localization is performed in three steps, as described for the model system (Section 11,D). The analysis eventually results in a list containing the x, y, and z coordinates of 300-500 individual fluorescent spots assumed to represent single NPCs. These coordinates represent a warped surface, namely, that of the NE. This curved surface may be approximated by a sphere surface. Thus, the x, y , and z coordinates of the NPCs must be converted to spherical coordinates, and then can be projected to the best fitting sphere surface. The unambiguous distance between a pair of coordinates is finally given by the arc length between the projected points on this sphere surface.

IV. Statistical Analysis of Particle Distributions The methods described so far yield maps displaying the centers of many particles, be it microbeads or NPCs. The question then arises whether the particles

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are distributed randomly or in any type of order. The human visual system is not a good referec for deciding that question, because it tends to recognize order in any distribution. Therefore objective criteria are required. Here we shortly summarize three approaches-the nearest-neighbor distribution function (NNDF). the pair correlation function (PCF), and the cluster analysis; these are frequently used for analyzing deviations from randomness in particle populations. To yield correct conclusions concerning distributional features, it is required to combine several statistical analysis methods (for further details, see Diggle, 1983; Konig et al., 1990; Karlsson and Liljeborg, 1994). Figure 4 displays a few computed distributions together with their NNDF and PCF to give a first intuitive understanding of the approach. A. Nearest-Neighbor Distribution Function and Pair Correlation Function

1 . Nearest-Neighbor Distribution Function The NNDF is computed for a given sample of particles by determining the distance between a particle and its nearest neighbor for each of the particles. From the table of nearest neighbor distances the probability of finding the nearest neighbor within a distance r is calculated and plotted versus r. Explicitly, the nearest-neighbor distribution function d ( r ) is given by

44

= P (distance from a typical object to the nearest object is at most r ) ,

(2)

where P is the accumulated probability. For a completely random distribution of point objects in a plane (which is generated by the so-called two-dimensional stationary Poisson point process), d ( r ) can be derived analytically as

dpc,l(r)= 1 -

e-nr'p,

(3)

where p denotes the average surface density of objects. By comparison of the nearest-neighbor distribution function of a given sample with a random distribution (Poisson reference model) having the same average particle density, it can be decided whether particles are aggregated (relative excess of small nearestneighbor distances) or repelled from each other (relative deficiency of nearestneighbor distances). The situation is complicated by the fact that each experimental data set is only a limited and random representation of the true distribution. Therefore, from an experimcntal data set the true distribution can never be derived but only approximated. This approximation is referred to as the estimator. Particular obstacles in deriving estimators from experimental data sets are presented by edge effects (Diggle, 1983; Karlsson and Liljeborg, 1994). For an object set a,,, that is confined to a region W, the edge-corrected estimator & r ) for the nearestneighbor distribution function is calculated as:

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5. Laser Scanning Microscopy of Nuclear Pore Complexes

&r) =

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Here, d designates the distance from an arbitrarily chosen object to its next neighbor, and R is the distance to the next point on the edge of region W. In other words, only objects whose next-neighbor distance is smaller than the minimum distance to the region edge are considered.

2. Pair Correlation Function The PCF is computed for a given sample of particles by determining the mean number of particles n(r) d r found in a shell of radii r and r + dr around an average particle. The pair correlation function g ( r ) (McQuarrie, 1976) is then given by g ( r ) = n(r) d r l p 2 ~ dr. r

(5) In other words, the pair correlation function describes the deviation of the local density from the average density. For a random distribution of points (Poisson process), gpoi( r ) = 1 for r > 0,

(6)

because there are no deviations between local and global density on the average. The correction of g(r) for edge effects is not trivial. A relatively straightforward approach makes use of the K function. K ( r ) is the expectation value of the number of objects that are positioned within a given distance r from an arbitrary object (that itself is not counted) divided by the object density. For the Poisson point process,

KPoi(r)= T?. (7) The correction of K ( r ) for edge effects depends on the geometry of the sample region W. For a circular area W of radius a, the corrected estimator is given by (Diggle, 1983): Fig. 4 Model object distributions and the corresponding estimators for the nearest-neighbor distribution and pair correlation functions d(r) and g(r). (a) Random point set, (b) random hard disk set, (c) predominantly regular hard disk set, and (d) clustered hard disk set. The diameter of the hard disks was d = 2. The middle and right columns show the corresponding NNDF and PCF estimators, respectively. The functions of the random points were calculated according to Eqs. (3) and ( 6 ) ;the estimators were calculated using Eqs. (4) and (10). Each of the qualitatively different object sets shows very specific distribution functions. For the random points, d ( r ) > 0 for r > 0, and g(r) = 1 for r > 0. However, for all hard disk sets, d ( r ) = g(r) = 0 for r 5 d. For the regularly distributed hard disks, d ( r ) rises significantly less steeply in the beginning, whereas for the clustered hard disks d ( r ) rises extremely steeper compared to the randomly distributed hard disks for r just larger than d. For random hard disks of relatively low density, g(r) = 1 for r > d. For the regular disks, g(r) peaks at distances that correspond to multiples of the mean interparticle distance, and for the clustered disks g ( r ) S 1 for r just larger than d.

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Ulrich Kubitscheck and Reiner Peters

where n designates the total number of objects in W and d, is the distance between the objects i and j , and the function t, (d,) is defined as Ir(dij)

=

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(9)

After computation of kwo(r) for a set of discrete distances m Ar, m = 1 , 2 . . . , an edge-corrected estimator gw,(r) for the pair correlation can be calculated as gw,,(m AT) =

k,,[(m

+ 1) Ar] - k w o [ ( m- 1) Ar] 4nr Ar

(10)

3. Numerical Computation of Estimators The preceding work shows that it is not always trivial to obtain corrected reference curves for the NNDF and PCF, even in the comparatively simple case of point objects. To render the statistical analysis more realistic and thus applicable to the distribution of the NPC, one would have at least to consider disks instead of points. In the theoretical description, disks are characterized by a hard-core potential, implying that the center-to-center particle distance cannot be smaller than the particle diameter. More complicated interaction potentials can be thought of to account for any type of attraction or repulsion between particles. Although theoretical methods for calculating the distribution functions for particles with arbitrary interaction potentials do exist (McQuarrie, 1976), explicit solutions cannot always be obtained. However, as a substitute for the complicated analytical methods, numerical methods can be applied. In that approach, Monte Carlo methods are used to generate particle coordinates at random while taking their interaction potential into account (Kubitscheck et al., 1993). For the case of disks (hard-core potential), for instance, coordinates of an object are generated at random. Following that, it is checked whether the distance between the new object and all other objects is greater than the particle diameter. If that is not the case the object is removed and a different set of coordinates generated. Because every numerical simulation is only a special case, the simulation is repeated 500-1000 times. The estimators for the distribution functions for the single simulations are then averaged and standard deviations calculated. Eventually, the thus produced reference curve can be compared with the experimentally determined estimator.

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4. Application to the Model System and the NPC Estimators of the NNDF and the PCF are given in Figs. 5 (model system) and 6 (NPC of 3T3 cells). Figure 5 contains data for 105-nm beads (Fig. 5, a and b) and 170-nm beads (c and d). Moreover, in all cases the NNDF and PCF estimators were calculated from both confocal data (solid symbols) and electron microscopic data (open symbols) from the same specimen, which allows a direct comparison.

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Fig. 5 Estimators of the distribution functions d ( r ) and g ( r ) of microbead model systems. (a) NNDF estimators were calculated from the bead positions that were determined from the CLSM (solid symbols) and TEM (open symbols) images for beads with a diameter of 105 nm. (b) PCF estimators for beads with a diameter of 105 nm. The full lines in a and b correspond to the averaged NNDF and PCF estimators of simulated random disks ( d = 105 nm). The large deviations from the randomly distributed hard-core disks indicate a strong particle aggregation. (c) NNDF and (d) PCF estimators for beads with a diamctcr of 170 nm from CLSM (solid symbols) and TEM data (open symbols). (Reproduced from Kubitscheck ef al., 1996, with permission.)

Ulrich Kubitscheck and Reiner Peters

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0.0

0.0

0.1

0.2

0.3 0.4 0.5 0.6

r [vml

Fig. 6 (a) Estimator for the nearest-neighbor distribution function of NPCs of a single 3T3 ccll nucleus. The data are shown together with the averaged estimators of randomly distributed hardcore particles (dashed line) with the corresponding SD. For the hard-core particles, NNDF and PCF estimators were calculated for 1000 individually simulated random distributions of particles (d = 145 nm) with area densities corresponding t o that of the NPC data set. (b) Corresponding pair correlation function estimator. The PCF estimator is shown with the averaged outcome of simulated random distributions of hard core as above (dashed line; bars corresponding to SDs). The PCF for point objects is unity for r > 0. The PCF estimator values of the NPCs is significantly smaller than unity for distances bclow 145 nm, thus not complying with randomly distributed point objects. (Reproduced from Kubitscheck rt al., 1996, with permission.)

Figure 5a, displaying the NNDF estimator of 105-nm beads, shows that there are no nearest-neighbor distances <90 nm. This is not surprising for the electron microscopic data because of the high resolution. Remarkably, however, the confocal data yielded the same value, although the lateral resolution was -270 nm, as mentioned in Section II,B,2. Figure 5c shows the same analysis for 170-nm particles. Again, the diameter of the particles determined from the confocal images corresponds well with the electron microscopic result. Thus, it is not only possible to locate particles with an accuracy well below the optical resolution limit, but also, by combining numerical image processing with statistical nearest-neighbor analysis, to deduce a particle diameter even if it is well below the resolution limit. The confocal and electron microscopic images of the model system (Fig. 1) suggest that the beads are heavily clustered. This is confirmed by both the estimators of NNDF and PCF. Both deviate from the reference (Fig. 5 , a and b, full lines with error bars) for randomly distributed hard-core particles. The clustering is particularly impressive in the PCF estimator in which the data curves have marked maxima at distances just larger than the particle diameter (Fig. 5 , b and d).

9s

5. Laser Scanning Microscopy of Nuclear Pore Complexes

The analysis of the NPC distribution from a single cell nucleus by the NNDF and PCF estimators is illustrated in Fig. 6. In addition, the reference estimators for disks with a diameter of 145 nm are shown (dotted line with standard deviations). The data correspond very well to the results of the hard-core particle distributions, but do not agree with the functions for point particles (compare to Fig. 4, a and b). As Figure 6 shows, extrapolation of the downward slope of the curves for the hard-core particles pointed to the particle diameter because it represented the lower limit for nearest-neighbor distances, d,,,,. The extrapolation for the NNDF estimator of NPCs from eight different cell nuclei yielded a value of dI,I,.Bvc' = 138 -+ 17 nm. This value is in good agreement with the results of recent electron microscopic and in vivo atomic force microscopic measurements of inter-NPC distances (Akey, 1989; Oberleithner et d.,1994).This particle diameter verified the assumption that the observed diffraction-limited spots indeed represented single NPCs. Only very few NPCs exhibited nearest-neighbor distances below d,l,,d,,, probably due to inaccuracies in the localization process or to errors in estimating the correct numbers of pores in larger NPC patches. B. Cluster Analysis

For the cluster analysis of a given sample of particles, the nearest-neighbor distances are determined for all particles and their mean value and variance (T?, The experimentally determined values are then normalized by their expectation values, E() and E((r2).The expectation values are derived on the assumption that the particles are distributed at random. For randomly distributed point objects (Poisson point processes) the expectation values are given by

E()

=

WV5)

(11)

and

E

(d) = (4 - n)/(4 np).

(12)

For particles with a given interaction potential, e.g., disks characterized by a hard-core potential, E() and E ( d ) must be determined by employing the Monte Carlo methods described above. Again, more than 500 different simulations have to be carried out for each condition in order to obtain meaningful expectation values. For further analysis the ratio values Q = /E(), and R = / E ( < ( r 2 ) are calculated. If the objects of the sample data set are distributed according to the interaction potential that was assumed for calculation of the expectation values, Q and R values are unity (Schwarz and Exner, 1983). Deviations of Q and R from unity indicate clustering (Q < 1) or repulsion respectively ordering ( Q 2 1). The R value furthermore contains information about a possible

Ulrich Kubitscheck and Reiner Peters

“background noise,” i.e., the fluctuation of the actual in comparison with a perfect ordering. These features of Q and R are compiled in Table I.

V. Discussion Light microscopy enables visualization of single NPCs as bright diffractionlimited spots. Combination of image analysis methods and distribution analysis allows assessment and characterization of 3D arrangement on the nuclear envelope. This is made possible by two features of the NPC system: (1) the large diameter of the pore complexes, which nearly approach the lateral optical resolution, and (2) a relatively low pore density on the nuclear envelope surface. This was determined to be 4-5/pm2 for 3T3 cells. Because many cell types have higher NPC densities (up to more than 50/pm2) (Maul, 1977), it is clear, that a detailed analysis of the pore distribution as described here can be applied only in a limited number of systems. Another drawback may be that it is very difficult to automate the described complex particle localization procedure. However, the potential applications of the introduced methods are wide, as discussed below. The great advantage is that several staining methods can be combined to yield information that is not attainable otherwise. Due to the application of highly specific markers, i.e., monoclonal antibodies, the possible experimental artifacts are negligible. One problem when detecting the NPCs in the nuclear envelope are certainly those NPCs that are not yet assembled in the nuclear membrane, but are found, for example, in the annulate lamellae. Due to the high resolution in the axial direction, it will in most cases be possible to differentiate them from the nuclear envelope due to a different z position, but it cannot be excluded that some of the detected NPCs are not located in the nuclear envelope. Finally, it may be noticed that the method described herein also has implications for problems other than the NPC distribution. We have suggested (Kubitscheck et al., 1996) application of the method, in suitably modified form, to analysis of the transport of single particles and even single molecules through

Table I Quantification of Cluster Analysis“ Ordering

Presence of background noise R < l R = l R>1

Q<1 Clustered sets -

Clustered set with background

Adapted from Schwarz and Exner (1983).

Q > I

Q-1

Random set. no background

Regular sets -

-

-

5. Laser Scanning Microscopy of Nuclear Pore Complexes

97

individual NPCs. Current models of nucleocytoplasmic transport assume that both import and export are multistep processes. For instance, protein import seems to proceed in at least six steps (for review, see Melchior and Gerace, 1995): receptor-ligand recognition in the cytoplasm, initial binding of the transport cargo to cytoplasmic filaments of the NPC, transport of the cargo to the cytoplasmic opening of the central channel of the NPC, translocation of the cargo through the central channel, release of the cargo at the karyoplasmic opening of the central channel, and transport of the cargo on the karyoplasmic, fish-trap-like filaments. The distances involved are 50-100 nm for the cytoplasmic filaments, 70 nm for the central channel, and 50-100 nm for the karyoplasmic filaments. The cargo can have a diameter of up to 30 nm. The transition times for the different steps are absolutely unknown, but may well be on the order of 1 sec. Thus, it appears perfectly feasible to follow the transport of large fluorescently labeled particles such as protein-coated microbeads or ribosomal subunits through individual NPCs by the method described in this paper. In particular, if the nuclear envelope is imaged in cross-section, the spatial resolution of the method (<20 nm) and its time resolution (maximal 10 scanshec) are apparently sufficient. Significant progress has been made (Schmidt et af.,1995) in the detection and tracking of single fluorophores. Therefore, it might become possible in the near future to follow not only the transport of single particles but also of singlc molecules through individual NPCs. References Adam, S., Sterne-Marr, R., and Gerace. L. (1990). Nuclear protein import in permeabilized mammalian cells rcquire soluble cytoplasmic factors. ./. Cell Biol. 111, 807-816. Agard. D. A.. and Sedat, J. W. (1983).Three-dimensional architecture of a polytene nucleus. Nairrre (Londotl) 302, 676-681. Akey. C . W. (1989). Interactions and structure of the nuclear pore complex revealed by cryoelectron microscopy. J . Cell Biol. 109, 955-970. Berezney, R.. and Jeon, K. W.. cds. (1995). Structural and functional organization of the nuclear matrix. Irrr. Rev. Cyiol. 162b, 1-460. Blobel. G. (1985). Gene gating, a hypothesis. Proc. Nail. Acad. Sci. U.S.A. 82, 8527-8529. C'remcr. T.. Kurz. A., Zirbcl. R., Dictzcl, S., Rinke, B., Schrock, E., Speicher. M. R., Mathieu. U., Jauch, A.. Emmcrich. P.. Scherthan, H.. Ried, T.. Cremer. C.. and Lichtcr, P. (1993). Rolc of chromosome territories in the functional compartmentalization of the cell nucleus. Cold Spring Hurhor S p p . Qiratri. B i d 58, 777-792. Davis. L.. and Blobel, G. (1986). Identification and characterization of a nuclear pore complex protein. Cell (Cambridge, Mass.) 45, 699-709. Diggle. P. J. ( 1983). "Statistical Analysis of Spatial Point Patterns." Academic Press, London. Georgatos. S. D . (1994). Towards an undcrstanding of nuclear morphogenesis. J . Cell. Biocheni. 55, 69-76, Glass. C. A.. Class. J. R.. Taniura, H.. Hasel. K. W., Blevitt. J. M., and Gerace. L. (1993). The alphahclical rod domain of human lamins A and C contains a chromatin binding site. EMBO J . 12,4412-4424. Gdrlich. D.. and Mattaj, 1. W. (1996). Nucleocytoplasmic transport. Scirrzce 271, 1513-1518. Jarnik, M . . and Aebi. U. (1991). Toward a more complete 3-D structure of the nuclear pore. J. S/rrtcr. Biol. 107, 291-308.

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Karlsson, L. M.. and Liljeborg, A. ( 1 0 4 ) . Second-order stereology for pores in translucent alumina studied by confocal scanning laser microscopy. J . Microsc. ( O x f o r d ) 175, 186-194. Kiinig. D.. Carvajal-Gonzalez, S.. Downs. A . M.. Vassy. J., and Rigaut, J. P. (1990). Modelling and analysis of 3-D arrangements of particles by point processes with examples of application to biological data obtained by confocal scanning light microscopy. J . Microsc. (Oxford ) 161,405-433. Kuhitscheck. U.. Schweitzer-Stenner, R., Arndt-Jovin. D. J.. Jovin. T. M., and Pecht, I . (1993). Distribution of type I Fcs-receptors on the surface of mast cells probed by fluorescence resonance energy transfer. Biophys. J . 64, 110-120. Kubitscheck. U.. Wedekind, P., Zeidler. 0..Grote, M.. and Peters. R. (1996). Single nuclear pores visualized by confocal microscopy and image processing. Biophys. J . 70, 2067-2077. Marshall, W. F.. Dernburg. A. F.. Harmon, B.. Agard. D. A., and Sedat, J. W. (1996). Spccilic interactions of chromatin with the nuclear envelope. positional determination within the nucleus in Drosophila rnelanogaster. Mol. Biol. Cell I, X25-842. Maul, G. G. (1977). The nuclear and the cytoplasmic pore complex. structure. dynamics. distribution, and evolution. lnt. Rev. Cytol., Sicppl. 6, 76-187. McQuarrie, D. A. (1976). “Statistical Mechanics.” HarperCollins, New York. Melchior. F., and Gerace, L. (1995). Mechanisms of nuclear protein import. Cirrr. Opin. Cell Biol. 7, 310-318.

Obcrleithner. H., Brinckmann, E., Schwab, A., and Krohne, G. (1994). Imaging nuclear pores of aldosteronc-sensitive kidney cells by atomic force microscopy. Proc. Natl. Acad. Sci. U.S.A. 91,9784-97XX.

Paddy. M. R.. Bclniont, A. S., Saumweber. H.. Agard. D. A,, and Sedat, J. W. (1990). lntcrphasc nuclear envelope lamins form a discontinuous network that interacts with only a fraction of the chromatin in the nuclear periphery. Cell (Cambridge, Mass.) 62, 89-106. PantC. N., and Aebi. U. (1994). Toward the molecular details of the nuclear pore complex. J . Strrcct. Biol. 113, 179-189. Pawley. J. B.. ed. (1995). “Handbook of Biological Confocal Microscopy.” 2nd ed. Plenum, New York. Press. W.. Teukolsky, S. A,. Vettcrling, W. V., and Flannery. B. P. (1992) “Numerical Recipies in C.“ Cambridge University Press. Cambridge, UK. Ris, H. (1991). The three-dimensional structure of the nuclear pore complex as seen by high voltage electron microscopy and high resolution low voltage scanning electron microscopy. EMSA Bull. 21,54-.56.

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