Introduction Somatic cells within an organism possess genomes that are, with only a few minor exceptions, identical. However, various cell types may possess different epigenomes including the variation of DNA methylation and histone modification patterns. Epigenome variability accounts for cell-type-specific gene expression and silencing patterns in multicellular organisms. The impact of higher-order nuclear architecture on these patterns is not yet known . Studies of higher-order chromatin arrangements in numerous cell types from different species form an indispensable part of a comprehensive approach to understanding epigenome evolution and cell-type-specific variability. Numerous research groups have attempted to map the large-scale organization and distribution of chromatin in cycling and postmitotic cell types (for reviews see [2,3,4,5,6,7,8]). Reliable topological maps, however, for the three-dimensional (3D) and 4D (3D plus spatiotemporal) arrangements of the two haploid chromosome complements in a diploid somatic cell nucleus have been lacking so far. Such 3D and 4D maps would provide the necessary foundation for studying the effect of higher-order chromatin distribution on nuclear functions, and are needed for different cell types at various stages of the cell cycle and at various stages of terminal differentiation. In addition to their importance for epigenome research, these maps should also help to understand karyotype evolution [9,10,11,12] and the formation of chromosomal rearrangements in irradiated or cancer cells [13,14,15,16,17]. In a 2D analysis of human fibroblast prometaphase rosettes, Nagele et al. [18,19] measured distances and angular separations for a number of chromosomes. These authors concluded that the maternal and paternal chromosome sets were separate, and that the heterologous chromosomes in each set showed highly nonrandom distributions. Subsequent studies further emphasized a highly ordered chromosome territory (CT) pattern for the nuclei of polarized human bronchial epithelial cells  and for nuclei of quiescent (G0) diploid (46, XY) human fibroblasts in culture . Koss  reported that angles between the center of the nucleus and homologous pairs of Chromosome 1, 7, and X CTs were nearly identical in about two-thirds of bronchial epithelial cell nuclei to the angles reported by Nagele et al. for the same chromosome pairs in fibroblast prometaphase rosettes . In contrast, Allison and Nestor  found a relatively random array of chromosomes on the mitotic ring of prometaphase and anaphase cells in cultured human diploid fibroblasts, diploid cells from human lung tissue, and human lymphocytes. The causes of these discrepancies have so far remained elusive. For nuclei of human lymphocytes, phytohemagglutinin-stimulated lymphoblasts, and lymphoblastoid cell lines, several groups have consistently reported a preferential positioning of gene-rich CTs (e.g., Homo sapiens chromosome [HSA] 19) towards the center of the nucleus, and of gene-poor CTs (e.g., HSAs 18 and Y) towards the nuclear periphery [23,24,25,26]. We recently confirmed this gene-density-correlated radial CT positioning for several other normal and malignant human cell types . Bickmore and colleagues [23,27] also reported gene-density-correlated CT arrangements for cycling human fibroblasts. In contrast, Sun et al.  and our group [23,24,25,26] provided support for chromosome-size-correlated radial arrangements in quiescent fibroblasts. Although Sun et al. refer to nuclei studied in the G1-phase of the cell cycle, we believe that most of the cells included in their analysis were in a quiescent state (G0), since fibroblasts were grown on coverslips to 90%–95% confluence. Bridger et al.  reported that Chromosome 18 CTs were significantly closer to the nuclear periphery in S-phase fibroblasts than in quiescent fibroblasts. These findings suggest that cycling and noncycling fibroblasts differ in higher-order chromatin organization. We tested this hypothesis further in the present study. To overcome some of the technical limitations of previous studies, and to explore some of their inconsistencies, we employed 3D fluorescence in situ hybridization (FISH) protocols that allowed the differential coloring of all 24 chromosome types (22 autosomes plus X and Y) simultaneously within a population of human male fibroblasts (46, XY) under conditions preserving the 3D nuclear shape and structure to the highest possible degree [29,30]. In addition, we performed a series of two-color 3D FISH experiments in semi-confluent cultures, and determined the radial 3D positions of a subset of CTs (HSAs 1, 17–20, and Y) in quiescent (G0) and cycling (early S-phase) fibroblasts. Our data demonstrate unequivocally that the 3D arrangements of chromosomes in quiescent and cycling human fibroblasts follow probabilistic rules, and suggest that nuclear functions in human fibroblasts do not require a deterministic neighborhood pattern of homologous and heterologous chromosomes. Throughout, when we use the term “probabilistic chromosome order,” we mean an order that cannot be explained simply as a consequence of geometrical constraints that affect the distribution of chromosomes in mitotic rosettes or of CTs in cell nuclei. Constraints may enforce an arrangement of large and small chromosomes or CTs that deviates significantly from the prediction of a random order of points without any functional implications. Our long-term goal is to contribute to the elucidation of the set of rules (most likely a combination of probabilistic and deterministic) that generate cell-type-specific, functionally relevant higher-order chromatin arrangements. Results Differential Coloring of All 24 Chromosome Types in Nuclei of Human Male Diploid Fibroblasts Early-passage human fibroblast cultures (46, XY) were grown to confluence and maintained at this stage for several days before being fixed with buffered 4% paraformaldehyde. Under these conditions, the overwhelming majority (>99%) of cells were postmitotic (G0), as demonstrated by a lack of both pKi67 staining and incorporation of thymidine analogs (data not shown). Two 3D multiplex FISH (M-FISH) protocols were used for the differential coloring of all 24 human chromosome types (22 autosomes plus X and Y). The first approach was based on 3D M-FISH with 24 chromosome paint probes. Probes were differentially labeled using a combinatorial labeling scheme with seven different haptens/fluorochromes . DAPI was used to stain nuclear DNA. Light-optical serial sections were separately recorded for each fluorochrome using digital wide-field epifluorescence microscopy (Figure 1). A second approach, called ReFISH , achieved differential staining of all 24 human chromosome types in two sequential FISH experiments with triple-labeled probe subsets. Light-optical serial sectioning of the same nuclei with laser confocal microscopy was performed after both the first and the second hybridization. Both approaches provided stringent accuracy for color classification of all CTs, and yielded the same results. Therefore, we combined data from 31 nuclei studied with the first approach and from 23 nuclei studied with the second approach (54 nuclei in total). Following careful correction for chromatic shifts, and image deconvolution in the case of wide-field microscopy (Figure S1), we performed overlays of the corresponding light-optical sections from all channels with voxel accuracy. CT classification was carried out on these overlays by the computer program goldFISH  (Figures 1B and S1C). This program classifies chromosomes by virtue of differences in the combinatorial fluorescent labeling schemes. Figure 1C shows the 3D reconstruction of a nucleus with all CTs viewed from different angles. Although the present experiments were not designed to address the issue of chromatin intermingling from neighboring CTs, it is obvious that goldFISH should have led to numerous misclassifications if there were excessive, widespread intermingling (for further discussion of CT boundaries, see ). For each individual CT the classification achieved by goldFISH was confirmed or rejected by careful visual inspection of light-optical sections. Any CT that could not be classified with certainty was omitted from further consideration. We were thus able to identify 2,030 CTs (82%) from a total of 2,484 CTs present in the 54 diploid fibroblast nuclei. As reference points for all distance and angle measurements reported below, we determined the 3D location of the fluorescence intensity gravity centers (IGCs) of individual painted CTs and the IGC of the nucleus (CN). Unless stated otherwise, when we describe below the position of a CT or prometaphase chromosome (PC) and report distance and angle measurements, we are referring to the 3D position of the CT's or PC's IGC. As a control for the reliability of the CT localizations, we subjected nuclei first studied by 24-color 3D FISH to a sequential five-color FISH experiment with individually labeled paint probes for Chromosomes 1 (Cy5), 3 (Cy3), 10 (FITC), 12 (Cy3.5), and 20 (Cy5.5). We were able to retrieve 11 of the 31 originally studied nuclei and to determine whether 3D positions of CTs first classified in the 24-color 3D FISH experiment could be confirmed after the second hybridization. In 96% of the re-hybridized CTs, the 3D position of the IGC differed by less than 1 μm, the range being between 0.01 and 1.3 μm. Size-Correlated Radial CT Positions in Nuclei of Quiescent (G0) Fibroblasts For every identified CT we measured the 3D radial CN–CT distance (from the CN to the CT's IGC). For a graphic overview of the location of each CT in 2D nuclear projections, the 3D positions of all IGCs obtained for a given CT were normalized and drawn into an ellipse representing the nuclear rim (Figure 2). As representative examples, Figure 2A shows nuclear projections of the normalized 3D IGC locations of CTs of HSAs 1, 7, 11, 18, 19, and Y, while Figure 2B shows cumulative 3D CN–CT graphs for the same CTs. Figures S2 and S4 provide the respective data for the entire chromosome complement. Notably, 3D radial CN–CT distance measurements did not reveal a significant difference between the positions of the gene-poor HSA 18 and the gene-rich HSA 19, although distinctly peripheral and interior locations, respectively, have been found for these two chromosomes in the spherical nuclei of lymphocytes and several other cell types (see Introduction). In summary, our data (Figures 2B, S2, S4, and S7 [left panel]) demonstrate that the territories of all small chromosomes—independent of their gene density—were preferentially found close to the center of the nucleus, while the territories of large chromosomes were preferentially located towards the nuclear rim. Figure 3 displays the positive correlation obtained in quiescent human fibroblasts for the mean normalized radial CN–CT distances and the DNA content of the chromosomes. The broad variability of radial CT positions seen in the set of 54 G0 nuclei indicates that radial CT arrangements in quiescent fibroblasts follow probabilistic, not deterministic, rules. To visualize the relative average positions of the IGCs of all heterologous CTs, we generated multidimensional scaling (MDS) plots [35,36] based on the mean of all normalized 3D CT–CT distances (Figure 4). Consistent with the data shown in Figure 3A, we found CTs from small chromosomes preferentially clustering towards the center of the nucleus, while CTs from large chromosomes were preferentially located towards the periphery. The acrocentric chromosomes (13–15, 21, and 22) carry nucleolar organizer regions (NORs) on their short arms, and active NORs are associated with the nucleoli. Since nucleoli are generally located away from the nuclear envelope in the inner nuclear space, we expected that normalized 3D CN–CT distances for all acrocentric chromosomes should be significantly shorter on average than 3D CN–CT distances for the largest chromosomes. Figure 5 confirms this expectation in the sample of 54 3D evaluated nuclei, emphasizing the sensitivity of the IGC approach. We also found a highly significant difference (p 0.05; Mann-Whitney U-test [U-test]). In contrast, the gene-poor Y territory was slightly more shifted towards the nuclear interior than the gene-rich HSA 17 CTs (Figure 6B and 6E). This shift was significant for cycling fibroblasts (p 0.05; U-test), but located significantly closer to the nuclear center than expected in the case of a uniform radial distribution (p 0.05; one-tailed K-S test of goodness of fit). With few exceptions pairwise comparisons of the mean angular separation between a pair of homologous CTs with the respective mean angle distribution in 60 random point distribution model nuclei did not show a significant difference (p > 0.05; two-tailed K-S test). Significant differences (p 0.05; two-tailed K-S test). (426 KB JPG). Click here for additional data file. Figure S11 Significance Levels for Pairwise Comparisons between Heterologous 3D CT–CN–CT Angles in 54 G0 Fibroblast Nuclei Significance levels were determined by the two-tailed K-S test. Green, not significant, p > 0.05; yellow, p 0.05; two-tailed K-S test). (328 KB JPG). Click here for additional data file. Video S1 Model Nucleus: CT Simulation The video shows the simulation of CT expansion in a fibroblast model nucleus according to the SCD model (compare with Figure 1). (567 KB MPG). Click here for additional data file.