| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |


* Kirchhoff Institute for Physics, and
Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, Heidelberg, Germany; and
Department Biology II, University of Munich and Institute of Human Genetics, Technical University, Munich, Germany
Correspondence: Address reprint requests to G. Kreth, Kirchhoff Institute for Physics, INF 227, D-69120 Heidelberg, Germany. E-mail: gkreth{at}kip.uni-heidelberg.de.
| ABSTRACT |
|---|
|
|
|---|
| INTRODUCTION |
|---|
|
|
|---|
10 µm (Cremer et al., 2001
However, the different positioning of a gene density-related radial dependence of chromatin obviously does not apply for all human cell types. In nuclei of human diploid fibroblasts, the CTs of small CTs were found in the nuclear center irrespective of the gene density, while large chromosomes were positioned toward the nuclear periphery, arguing for a chromosome size rather than a gene density-correlated radial arrangement (Cremer et al., 2003
; A. Bolzer et al., unpublished results). In contrast to the size-correlated positioning found for chromosomes in these flat nuclei with a thickness of 34 µm, model calculations assuming a linear correlation between DNA content and CT volume revealed an inverse distribution of small and large chromosomes with small chromosomes in the nuclear periphery and large chromosomes in the nuclear center in flat ellipsoid nuclei (Habermann et al., 2001
). Similarly, in simulated spherical nuclei, the same behavior for small and large chromosomes was predicted (Cremer et al., 2001
).
This indicates that the applied geometrical constraints alone are not sufficient to explain the observed radial arrangements. In this contribution, model calculations based on the existing "spherical 1 Mbp chromatin domain (SCD)" model were extended to estimate the influence of gene density (number of genes per Mbp) as an additional geometrical constraint in the initial distribution of "mitotic-like" chromosomes. In this model, each chromosome was described as a linear chain of elastic spherical 1 Mbp-sized domains that are linked together by entropic spring potentials. Starting from such mitotic-like chromosome configurations, assumed to exist shortly after cell division, Metropolis Monte Carlo relaxation runs were applied to calculate relaxed interphase configurations for all the chromosome territories simultaneously. This relaxation process made it possible that during the decondensation, the dynamical spreading of CTs can change their positions and thus is not fixed by the initial distribution. In the case of spheres, for example, this latter case is realized by the modeling procedure performed in Holley et al. (2002)
.
The 3D mapping of CTs Nos. 18 and 19 described in Cremer et al. (2001)
and of CTs Nos. 12 and 20 performed in Weierich et al. (2003)
was used as an experimental basis for the comparison with the radial arrangements of simulated CTs.
| MATERIAL AND METHODS |
|---|
|
|
|---|
10 µm. CTs of chromosomes Nos. 18, 19, 20, and 12 were visualized after chromosome painting with labeled fluorochromes. In these experiments, the CTs of No. 18 and No. 19 were visualized simultaneously by painting these territories with differently labeled fluorochromes. The CTs No. 12 and No. 20 were hybridized in two different experiments. The shape of the nucleus was visualized using a DNA counterstain in all experiments. For details see Cremer et al. (2001)
A detailed description of the quantitative radial 3D evaluation of light optical serial sections by a voxel- (volume element) based algorithm was published elsewhere (Cremer et al., 2001
). Briefly, as a first step, the geometrical center and the border of the nucleus were determined using the 3D data set of the DNA-counterstain fluorescence. For segmentation, we defined all voxels not belonging to the nuclear interior as image background. For comparison of nuclei with different shape and size, the distance between the nuclear center and each point located on the segmented nuclear border was given as the relative radius (r0 = 100). A decline of the curve for the nuclear counterstain in the most peripheral shells observed by this approach results in part from the Gaussian filtering of the data and in part from irregularities of the nuclear border. In the second step, segmentation of CTs was performed in each 3D stack representing the color channels for painted CTs. All voxel intensities below an automatically set threshold were set to zero. Using an iterative procedure, a threshold value was estimated for each 3D data set for CT thresholding. The segmented nuclear space was divided into 25 equidistant shells with a thickness of
r = 1/25 r0. For each voxel located in the nuclear interior, the relative distance r from the nuclear center was calculated as a fraction of r0. A shell at a given r contains all nuclear voxels with a distance between r
r/2 and r +
r/2. For each shell, all voxels assigned to a given CT were identified and the fluorescence intensities derived from the respective emission spectrum were summed up. This procedure yielded the individual relative DNA content (differential DNA content) within each shell for painted CTs as well as the overall DNA content as reflected by the DNA counterstain. The sum of the voxel intensities measured in each nucleus was set to 100% for each fluorochrome. Using this normalization, the differential DNA content within a nuclear shell as a function of the relative distance r from the 3D center in the entire set of evaluated nuclei was plotted as a graph.
Virtual microscopy of simulated CTs
To allow a comparison between the experimentally observed and the simulated distributions of CTs inside the nuclear volume, the influence of the limited light optical resolution was simulated by "virtual microscopy". For this purpose, from the simulated nuclear configurations, virtual image data stacks were calculated. This virtual microscopy approach consisted of a digitization of the spherical domains with diameters of 500 nm by a grid of 39 x 39 x 156 nm voxel spacing and a convolution of the digitized stacks with a measured confocal point spread function (with a full width at half-maximum (FWHM): FWHMx = 279 nm, FWHMy = 254 nm, FWHMz = 642 nm). By this procedure, the mapping of simulated nuclei can be made in the same way as for the experimental one (see method described above).
Simulation of human cell nuclei
For a simulation of the overall structure of CTs in human cell nuclei, the SCD model was applied (Kreth et al., 2001
; Cremer et al., 2000
). According to this model, each chromosome of the diploid human genome is approximated by a linear chain of spherical 1 Mbp-sized chromatin domains (with a diameter of 500 nm each). The number of 1 Mbp domains is given directly by the DNA content of a given chromosome (according to National Center for Biotechnology Information (NCBI) data, http://www.ncbi.nlm.nih.gov/genome/guide/human/; September 2003). To relate these domains in a linear sequence, adjacent domains are linked together by entropic spring potentials (Fig. 1), which describe the rigidity of "real" 120 kbp linker connections. These latter are assumed to connect adjacent rosettes (of
10 120 kbp loops) according to the multi-loop subcompartment model (Münkel and Langowski, 1998
). For a description of the stiffness of flexible polymers, usually the worm-like chain model is used that correlates the mean-squared distance
R2
with the persistence length LP and the contour length LC to:
![]() | (1) |
![]() | (2) |
![]() | (3) |
1200 nm. This corresponds to the limit case mentioned above where the linker flexibility can be described by an ideal Gaussian chain (random walk). The connection between adjacent domains in the SCD model is therefore described by the potential energy (entropic spring energy) of such a chain:
![]() | (4) |
![]() | (5) |
![]() | (6) |
![]() | (7) |
|
Relaxation process
To obtain thermodynamic equilibrium configurations with respect to the energies, the Metropolis Monte Carlo method was applied. For this purpose, in a first-start configuration, the spherical domains of each simulated chromosome were placed side by side in a "mitosis-like" arrangement ("start cylinders", compare Fig. 2 a) with a distance of 14 nm from each other. Random displacements of the domains resulted in relaxed interphase-like configurations using the Metropolis Monte Carlo procedure. According to this procedure, consecutive states in the relaxation process were generated by a Markov process (see, e.g., Binder and Heermann, 1997
). This process implicates the principle of the "microscopic reversibility"; this means that the relation between the transition probabilities from an old to a new state and vice versa depend only on the energy difference of the two states. In this way, the procedure can be performed by the following: beginning from an arbitrary state, a new state (generated by a random displacement of a domain) is accepted when the potential energy difference between the new and the old state is
H
0. When the energy difference
H is larger than zero, the new state is accepted with the probability exp(
H/kBT). In this way, the energies of the states are distributed according to a Boltzmann distribution in the equilibrium.
|
400,000 Monte Carlo steps (in one Monte Carlo step for each CT a randomly chosen domain was displaced) were used (Fig. 2 b). The achievement of an equilibrium state was controlled by the calculation of different geometrical modes during the relaxation process, like the gyration radius (the slowest increasing mode for this system). When this mode showed no further increase, the equilibrium state was assumed to be reached (
200,000 Monte Carlo steps). Further 200,000 Monte Carlo steps were then executed; these end configurations were used for the quantitative evaluations. | RESULTS |
|---|
|
|
|---|
|
|
For the probabilistic initial case (Fig. 3 b), after the incorporation of the two nucleoli, the CTs were put into the nuclear volume in the same order according to gene density as realized for the deterministic initial case. Here, however, in contrast to the deterministic case, the initial CT spheres were not located on discrete shells, but the distance from the center of the initial spheres to the nuclear center was weighted with an exponential probability density function that depends on the gene density of a given chromosome i and the distance d of the initial sphere to the nuclear center in units of the nuclear radius (equal to d = 1.0):
![]() | (8) |
P(d)i, according to the Monte Carlo procedure. This means: a given initial sphere for a CT (i) = A (e.g., No. 22) was first placed into a nonoverlapping position into the nucleus, according to the rules described above. Then the distance d to the nuclear center was determined for this special position, and P(d)A was calculated using Eq. 8, with the gene density of CT A (e.g., No. 22). Then the calculated P(d)A value (e.g., P(d)A = 0.37) was compared with a random number between zero and 1. If the random number turned out to be equal to or larger than the calculated P(d)A value, then the position of the initial (CT A) sphere was accepted. If the random number turned out to be smaller than the calculated P(d)A value, then again a new randomly chosen position for CT A was tested for nonoverlap; the d value of the new nonoverlapping position was again inserted in Eq. 8 and tested as described above. The procedure was continued until a nonoverlap position was obtained with a random number equal to or larger than the P(d)A value tested. Besides a reduction of the volumes (v = 0.22; Eq. 7) of the initial CT spheres, an acceptance factor
is required (Eq. 8) to ensure the loop criteria (see above) for this procedure. With
= 0.774, typically 3 min on the personal computer used were needed.
After the start configuration with the initial spheres of the diploid human chromosome set (22, X, Y) and the two nucleoli had been created as described above, the midpoints of the start cylinders were placed in these spheres (in all three simulation cases the distance of adjacent domains in the start cylinders was the same). To create relaxed interphase configurations, in the next step, the start cylinders were relaxed into an equilibrium state (this can be interpreted as the dynamic spreading out early in G1); the initial spheres were then discarded and played no further role in the relaxation process. For all three cases, 50 nuclei each were calculated. The relaxation of one simulated nucleus took
1 day of computing time on the personal computer (1 GHZ Intel Pentium III) used.
To investigate the differences in the localization of CTs between the initial start arrangement and after the relaxation process, in Fig. 4 the radial distances (distances to the nuclear center) of the gravity centers are plotted for all CTs in the order of the gene density for the three simulation cases. The error bars denote the standard deviations determined by averaging over the 50 simulated nuclei and the both homologous CTs for each case.
|
For comparison of the experimentally observed and the simulated radial arrangements of the reconstructed CTs Nos. 12, 18, 19, and 20, the simulated nuclear genome configurations were virtually labeled using the virtual microscopy approach (see Material and Methods). Fig. 5 visualizes 3D reconstructions of painted CTs No. 18 and No. 19 in a nucleus of a human lymphocyte (Fig. 5 d) as well as for the three simulated model assumptions (Fig. 5, ac). The quantitative 3D evaluation of the nuclear positions of the (virtually) painted territories was made by the assessment of the 3D relative radial distribution of each voxel assigned to the respective territory (Material and Methods). Fig. 6 shows the voxel distributions (differential DNA content) for the respective painted CTs plotted against the relative radius in lymphocyte nuclei (Fig. 6, g and h, experimental data described in Cremer et al. (2001)
and Weierich et al. (2003)
) and in simulated nuclei (Fig. 6, af), where Fig. 6, a and b, represents the quantitative distribution of the statistical, Fig. 6, c and d, of the probabilistic and Fig. 6, e and f, of the deterministic model assumptions. For each given relative radius, the respective differential DNA content was determined as the mean over the single distribution curves for each nucleus for this radius. The error bars represent the standard deviations of the mean. In Table 2, the mean differential DNA contents for all relative radii averaged over all nuclei with the respective standard deviations are given.
|
|
|
76% of the relative radius. A small shift of the larger CTs Nos. 12 and 18 toward the interior results here from the larger DNA amount (volume) of the CTs Nos. 12 and 18 in comparison to the CTs Nos. 20 and 19, which enforces larger distances to the nuclear envelope (compare Cremer et al., 2001For the probabilistic simulation case, the distribution patterns (Fig. 6, c and d) are in good agreement with the experimentally obtained data (Fig. 6, g and h) for CTs Nos. 18, 19, and 12: Here, the CTs No. 19 with the highest gene density are localized in the interior whereas the gene-poor No. 18 CTs are arranged close to the nuclear envelope; CTs No. 12 shows an intermediate position. For the CTs No. 20, the slight movement of a homologous CT in some model nuclei (data not shown) revealed a quite broad distribution compatible with the experimentally observed distribution. Here also a broad distribution was observed. Furthermore, the mean relative radii of the radial distribution values (given in Table 2) also agreed fairly well with the experimental data.
| DISCUSSION |
|---|
|
|
|---|
For the deterministic simulation case, initial CT spheres (representing a certain start volume of the CTs according to their DNA content) were located on discrete shells in the nuclear volume in the order of their gene densities; for the probabilistic simulation case, the distances of the initial CT spheres to the center of the nuclear volume were weighted with the respective gene densities (derived from the latest sequence data). This weighting was executed in a probabilistic way using a Monte Carlo procedure. In the case of the statistical simulation case, the initial CT spheres were located randomly in the nuclear volume. After the location of the initial CT spheres, Metropolis Monte Carlo relaxation runs were performed to calculate relaxed interphase genome configurations. Using the same quantitative 3D mapping algorithm for experimental and simulated data, the evaluated radial distributions of single CTs Nos. 12, 18, 19, and 20 in experiment and simulation were compared.
In the statistical simulation case, large differences between predicted and experimental values were found for the mean relative radii for CTs No. 19. The radial distributions were fairly different for all evaluated CTs. In the probabilistic simulation case, the evaluated more interior arrangement (in the nuclear volume) of the CTs No. 19, the more peripheral arrangement of the CTs No. 18, the intermediate arrangement of the CTs No. 12, and the quite broad intermediate arrangement of the CTs No. 20 fitted quite well the experimental data (with respect to the broadness, the mean values (Table 2), and the height of the radial distribution curves); for CT No. 20 in some simulated nuclei, a slight movement of one of the homologous CTs to a more peripheral position was predicted during the relaxation process, which caused the determined broad distribution. This may be also a reason for the experimentally observed broad distribution. In the deterministic simulation case, the mean relative radii (Table 2) for all CTs evaluated were in quite good agreement with the experimental values. For the CTs Nos. 19 and 20, however, quite large movements from the interior of the nucleus to a peripheral position was predicted during the relaxation process. At least for CT No. 19, this was not compatible with the experimental values. The reason here is the quite dense packaging of the CTs on discrete shells in the initial start configuration.
Recent experimental investigations indicated that global chromosome positions may be maintained through the cell cycle in mammalian cells (Gerlich et al., 2003
; Walter et al., 2003
). This may suggest that chromosomal localization might be controlled by a global chromosome positioning code. However, precise radial (e.g., Tanabe et al., 2002
) or relative positioning is not found in all cells in a population, and relatively large variations in the positioning of a chromosome can be observed when single cells are compared (A. Bolzer et al., unpublished results). E.g., when analyzing the radial positioning of all human CTs, statistically significant patterns are evident, although every CT can be found at variable radial positions in a cell population. These findings are also in good agreement with the study of Cornforth et al. (2002)
: here, frequencies between all possible heterologous pairs of CTs with 24-color whole-chromosome painting after damage to interphase lymphocytes by sparsely ionizing radiation in vitro were performed to test the influence of nonrandom CT-CT associations on aberration frequencies between specific CTs. It was found that only a group of five chromosomes (Nos. 1, 16, 17, 19, and 22), previously observed to be preferentially located close to the center of the nucleus (suggested by Boyle et al., 2001
), showed a statistically significant deviation of a random CT-CT association. According to Cornforth et al. (2002)
, these findings suggest a predominantly random location of CTs with respect to each other in interphase lymphocyte cells.
The results obtained in this report by computer simulations using the SCD model indicated that the idea of an appropriately designed global chromosome positioning code is compatible with such experimentally observed variations if an uncertainty condition is introduced in the initial distribution of CTs.
The computer simulations of nuclear genome structure presented here allowed first quantitative predictions about the possible influence of sequence length and gene density of a chromosome on its spatial positioning in the nuclear volume of lymphocyte cells. Besides some general constants and procedural rules, only linear sequence-derived data (chromosomal DNA content and gene density) were included as first parameters in the model. However, other constraints (not yet realized) also have to be regarded, like the arrangement of specific CTs around the nucleoli, the specific R-/G- band pattern, and other still unknown factors, e.g., specific attachment sites. The simulations presented here may help to determine the influence of such constraints on the arrangement of CTs in the nucleus and may provide a quantitatively testable model system for further experimental investigations. As a biophysically important application of such simulations, effects of ionizing irradiation and other clastogenic agents on specific chromosomal rearrangements (e.g., relative frequencies of translocations, dicentrics, deletions, and inversions) can be predicted.
| ACKNOWLEDGEMENTS |
|---|
|
|
|---|
These studies were supported financially from the Deutsche Forschungsgemeinschaft (grant CR 60/19-1) and the European Commission (grant FIGH-CT1999-00011).
Submitted on August 1, 2003; accepted for publication January 20, 2004.
| REFERENCES |
|---|
|
|
|---|
Boyle, S., S. Gilchrist, J. M. Bridger, N. L. Mahy, J. A. Ellis, and W. A. Bickmore. 2001. The spatial organization of human chromosomes within the nuclei of normal and emerin-mutant cells. Hum. Mol. Genet. 10:211219.
Cornforth, M. N., K. M. Greulich-Bode, B. D. Loucas, J. Arsuaga, M. Vazquez, R. K. Sachs, M. Brückner, M. Molls, P. Hahnfeldt, L. Hlatky, and D. J. Brenner. 2002. Chromosomes are predominantly located randomly with respect to each other in interphase human cells. J. Cell Biol. 159:237244.
Cremer, T., and C. Cremer. 2001. Chromosome territories, nuclear architecture and gene regulation in mammalian cells. Nat. Rev. Genet. 2:292301.[Medline]
Cremer, T., G. Kreth, H. Koester, R. H. A. Fink, R. Heintzmann, M. Cremer, I. Solovei, D. Zink, and C. Cremer. 2000. Chromosome territories, interchromatin domain compartment and nuclear matrix: an integrated view of the functional nuclear architecture. Crit. Rev. Eukaryot. Gene Expr. 10:179212.[Medline]
Cremer, M., K. Küpper, B. Wagler, L. Wizelmann, J. von Hase, Y. Weiland, L. Kreja, J. Diebold, M. R. Speicher, and T. Cremer. 2003. Inheritance of gene density-related higher order chromatin arrangements in normal and tumor cell nuclei. J. Cell Biol. 162:809820.
Cremer, M., J. von Hase, T. Volm, A. Brero, G. Kreth, J. Walter, C. Fischer, I. Solovei, C. Cremer, and T. Cremer. 2001. Non-random radial higher-order chromatin arrangements in nuclei of diploid human cells. Chromosome. Res. 9:541567.[Medline]
Croft, J. A., J. M. Bridger, S. Boyle, P. Perry, P. Teague, and W. A. Bickmore. 1999. Differences in the localization and morphology of chromosomes in the human nucleus. J. Cell Biol. 145:11191131.
Dimitrova, D. S., and R. Berezney. 2002. The spatio-temporal organization of DNA replication sites is identical in primary, immortalized and transformed mammalian cells. J. Cell Sci. 115:40374051.
Dundr, M., and T. Misteli. 2001. Functional architecture in the cell nucleus. Biochem. J. 356:297310.[Medline]
Gerlich, D., J. Beaudouin, B. Kalbfuss, N. Daigle, R. Eils, and J. Ellenberg. 2003. Global chromosome positions are transmitted through mitosis in mammalian cells. Cell. 112:751764.[Medline]
Habermann, F. A., M. Cremer, J. Walter, G. Kreth, J. von Hase, K. Bauer, J. Wienberg, C. Cremer, T. Cremer, and I. Solovei. 2001. Arrangements of macro- and microchromosomes in chicken cells. Chromosome Res. 9:569584.[Medline]
Holley, W. R., I. S. Mian, S. J. Park, B. Rydberg, and A. Chatterjee. 2002. A model for interphase chromosomes and evaluation of radiation-induced aberrations. Radiat. Res. 158:568580.[Medline]
Kreth, G., P. Edelmann, and C. Cremer. 2001. Towards a dynamical approach for the simulation of large scale, cancer correlated chromatin structures. Ital. J. Anat. Embryol. 106(Suppl.):2130.
Münkel, C., and J. Langowski. 1998. Chromosome structure predicted by a polymer model. Phys. Rev. E. 57:58885896.
O'Brien, T. P., C. J. Bult, C. Cremer, M. Grunze, B. B. Knowles, J. Langowski, J. McNally, T. Pederson, J. C. Politz, A. Pombo, G. Schmahl, J. P. Spatz, and R. van Driel. 2003. Genome function and nuclear architecture: from gene expression to nanoscience. Genome Res. 13:10291041.
Parada, L., and T. Misteli. 2002. Chromosome positioning in the interphase nucleus. Trends Cell Biol. 12:425432.[Medline]
Tanabe, H., S. Müller, M. Neusser, J. von Hase, E. Calcagno, M. Cremer, I. Solovei, C. Cremer, and T. Cremer. 2002. Evolutionary conservation of chromosome territory arrangements in cell nuclei from higher primates. Proc. Natl. Acad. Sci. USA. 99:44244429.
Visser, A. E., R. Eils, A. Jauch, G. Little, P. J. M. Bakker, T. Cremer, and J. A. Aten. 1998. Spatial distribution of early and late replicating chromatin in interphase chromosome territories. Exp. Cell Res. 243:398407.[Medline]
Walter, J., L. Schermelleh, M. Cremer, S. Tashiro, and T. Cremer. 2003. Chromosome order in HeLa cells changes during mitosis and early G1, but is stably maintained during subsequent interphase stages. J. Cell Biol. 160:685697.
Weierich, C., A. Brero, S. Stein, J. von Hase, C. Cremer, T. Cremer, and I. Solovei. 2003. Three-dimensional arrangements of centromeres and telomeres in nuclei of human and murine lymphocytes. Chromosome Res. 11:485502.[Medline]
Zink, D., H. Bornfleth, A. E. Visser, C. Cremer, and T. Cremer. 1999. Organization of early and late replicating DNA in human chromosome territories. Exp. Cell Res. 247:176188.[Medline]
This article has been cited by other articles:
![]() |
L. S. Shopland, C. R. Lynch, K. A. Peterson, K. Thornton, N. Kepper, J. v. Hase, S. Stein, S. Vincent, K. R. Molloy, G. Kreth, et al. Folding and organization of a contiguous chromosome region according to the gene distribution pattern in primary genomic sequence J. Cell Biol., July 3, 2006; 174(1): 27 - 38. [Abstract] [Full Text] [PDF] |
||||
![]() |
O. Mudrak, N. Tomilin, and A. Zalensky Chromosome architecture in the decondensing human sperm nucleus J. Cell Sci., October 1, 2005; 118(19): 4541 - 4550. [Abstract] [Full Text] [PDF] |
||||
![]() |
J. Diblik, M. Macek Sr, M.-C. Magli, R. Krejci, and L. Gianaroli Topology of Chromosomes 18 and X in Human Blastomeres from 3- to 4-Day-old Embryos J. Histochem. Cytochem., March 1, 2005; 53(3): 273 - 276. [Abstract] [Full Text] [PDF] |
||||
![]() |
S. Monajembashi, A. Rapp, E. Schmitt, H. Dittmar, K.-O. Greulich, and M. Hausmann Spatial Association of Homologous Pericentric Regions in Human Lymphocyte Nuclei during Repair Biophys. J., March 1, 2005; 88(3): 2309 - 2322. [Abstract] [Full Text] [PDF] |
||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |