Article No. jmb.1998.2361 available online at http://www.idealibrary.com on
J. Mol. Biol. (1999) 285, 1053±1065
Compartmentalization of Interphase Chromosomes
Observed in Simulation and Experiment
Christian MuÈnkel1,2, Roland Eils2, Steffen Dietzel3, Daniele Zink3
Carsten Mehring1,2, Gero Wedemann1,2, Thomas Cremer3
and JoÈrg Langowski1,2*
1
Division Biophysics of
Macromolecules, Deutsches
Krebsforschungszentrum
(DKFZ), Im Neuenheimer Feld
280, D-69120 Heidelberg
Germany
2
Interdisciplinary Center of
Scienti®c Computing
Ruprecht-Karls-University
Im Neuenheimer Feld 368
D-69120 Heidelberg Germany
3
Institute of Human Genetics
Ruprechts-Karls-University
Im Neuenheimer Feld 328
D-69120 Heidelberg, Germany
Human interphase chromosomes were simulated as a ¯exible ®ber with
excluded volume interaction, which represents the chromatin ®ber of
each chromosome. For the higher-order structures, we assumed a folding
into 120 kb loops and an arrangement of these loops into rosette-like
subcompartments. Chromosomes consist of subcompartments connected
by small fragments of chromatin. Number and size of subcompartments
correspond with chromosome bands in early prophase. We observed
essentially separated chromosome arms in both our model calculations
and confocal laser scanning microscopy, and measured the same overlap
in simulation and experiment. Overlap, number and size of chromosome
15 subcompartments of our model chromosomes agree with subchromosomal foci composed of either early or late replicating chromatin, which
were observed at all stages of the cell cycle and possibly provide a functionally relevant unit of chromosome territory compartmentalization.
Computed distances of chromosome speci®c markers both on Mb and
10-100 Mb scale agree with ¯uorescent in situ hybridization measurements under different preparation conditions.
# 1999 Academic Press
*Corresponding author
Keywords: interphase chromosomes; higher order chromatin structure;
nuclear organization; Monte Carlo; polymers
Introduction
Structure and dynamics of chromatin play an
important role in establishing and maintaining a
stable pattern of gene expression in eukaryotic
cells (Felsenfeld, 1996). However, despite improved
understanding at the chromatin level and the rapid
progress in physical mapping of the human genome, evidence for the three-dimensional (3D)
organization of chromosomes in the cell nucleus
has only emerged recently and is still controversial
Present address: S. Dietzel, Institute of Anthropology
and Human Genetics Ludwig-Maximillian University,
Richard Wagner Str., 10/1, D.80333 MuÈnchen, Germany.
Abbreviations used: 3D, three-dimensional; MLSmodel, multi-loop subcompartment model; RW/GL
model, random walk/giant loop model; SF,
subchromosomal foci; MLS, multi-loop
subcompartment; MLC, multi-loop cluster; ICD,
interchromosomal domain; FFT, fast Fourier
transformation; FISH, ¯uorescent in situ hybridization.
E-mail address of the corresponding author:
[email protected]
0022-2836/99/031053±13 $30.00/0
(Cremer et al., 1993, 1995; Sachs et al., 1995; Zink &
Cremer, 1998, and references cited therein).
Moreover, the implications for the regulation of
transcription, DNA replication and the formation
of chromosome aberrations are only beginning to
be understood (Cremer et al., 1996; Lamond &
Earnshaw, 1998; van Driel et al., 1995).
While a territorial organization of interphase
chromosomes, where each chromosome occupies a
mutually exclusive subvolume of the cell nucleus,
has already been postulated by early cytologists
(for a review see, Cremer, 1985), electron
microscopy studies in the 1960s and 1970s (see
Comings, 1980) were interpreted such that chromatin was thought to be dispersed within the nucleus
(see Comings, 1968; Vogel & Schroeder, 1974).
Starting at the end of the 1970s microbeam UV
irradiation (Cremer et al., 1982; Zorn et al., 1976,
1979) and a modi®ed Giemsa-banding technique
(Stack et al., 1977) again found indications for a
territorial organization of chromosomes. The ®rst
unambiguous visualization of chromosome territories was performed by in situ hybridization in
mammalian and plant cells (Cremer et al., 1988;
# 1999 Academic Press
1054
Leitch et al., 1990; Lichter et al., 1988; Manuelidis,
1990; Pinkel et al., 1988; Schardin et al., 1985;
Schwarzak et al., 1989).
During the last few years the spatial organization of chromatin within a chromosome territory,
including the 3D distribution of genes, has become
a matter of active research (Kurz et al., 1996; van
den Engh et al., 1992). Other recent studies have
suggested the stable compartmentalizaton of
chromosome territories into replication foci, which
can be visualized by the detection of biotinylated
or halogenated thymidin analogs in ®xed cell
nuclei (Nakayasu & Berezney, 1989; Visser et al.,
1998), as well as after microinjection of ¯uorochrome-labeled analogs in living cell nuclei (Zink
et al., 1998a). These foci apparently persist throughout the cell cycle (Berezney et al., 1995; Sparvoli
et al., 1994) and may form a basic functional structure beyond the aggregation of replicon clusters
(Jackson & Pombo, 1998; Zink & Cremer, 1998;
Zink et al., 1998a,b). However, the relationships
between chromatin structures observed at the light
and electron microscopic level have remained
obscure. In the 70th higher-order, structures like
rosettes of chromatin loops were reported (Okada
& Comings, 1979), but the strongly denaturing
preparation conditions did not permit a decision
whether these were in vivo structures or preparation artifacts. Recently, an electron tomography
study demonstrated higher order chromatin structures but no rosettes (Bermont & Bruce, 1994).
Proposed models for interphase chromosome
architecture range from intermingled chromatin
®bers and loops (Comings, 1968; Hahnfeldt et al.,
1993; Ostashevsky & Lange, 1994; Sachs et al.,
1995; van den Engh et al., 1992), to models which
result in considerably more de®ned chromatin
compartmentalization (Cook, 1995; Manuelidis,
1990; Okada & Comings, 1979; Robinett et al.,
1996). Several models have focused on possible
structure-function relationships of higher order
chromatin structures, chromosome territory and
nuclear architecture (Blobel, 1985; Cremer et al.,
1995; Kurz et al., 1996; Manuelidis, 1990;
Manuelidis & Chen, 1990; Zachar et al., 1993; Zink
et al., 1998a,b; Zirbel et al., 1993). These different
models can be evaluated by a comparison of experimental data with computer simulations based on
polymer models, which link sequence information
to the observed higher order 3D organization of
chromosomes. Recently, we have described the
implementation of a ``multi-loop subcompartment''
model (MLS-model) of chromosome territory
organisation (MuÈnkel & Langowski, 1998). Here,
we present an application of this model which
yields quantitative and experimentally testable predictions through computer simulations. In agreement with the experimental data cited above, the
model provides structural ¯exibility together with
a high degree of compartmentalization of chromosome territories.
Compartmentalization of Interphase Chromosomes
Results
Simulated and experimental confocal images
of interphase chromosomes
In the MLS-model chromatin of each subcompartment is arranged into several 120 kb sized
loops (Figure 1(a)). Different subcompartments are
connected by small chromatin fragments of about
the same length as one loop, and do not overlap to
a large extent (see Figure 2(a)). A locally altered
structure was modeled by a giant-loop domain
that is formed by several adjacent bands
(Figure 1(b)). While in the presence of giant-loop
Figure 1. Schematic drawings of the simulated
models. (a) and (d) Multi-loop subcompartment model
(MLS) with subcompartments consisting of 120 kb sized
loops (ca. 1.2 mm contour length), which are formed by
stiff springs between the loop bases. The springs are
enlarged for clarity. About ten loops form a subcompartment (ca 1.2 Mb). Subcompartments are connected
by small chromatin fragments of about 120 kb. (b) and
(e) Altered chromosome structure with alternating giant
loop domains (about 5 Mb) and multi-loop subcompartments as in (a). (c) and (f) A random walk/giant loop
model (RW/GL) chromosome (Sachs et al., 1995) consists of giant loop domains only (ca. 5 Mb each), separated by 200 kb chromatin fragments. In this model, the
chromatin ®bers can intersect without any energy barrier. The structures represented in (d) to (f) are the same
as those in (a) to (c), except that they are more properly
scaled for a comparison with the simulated structures in
Figure 2.
1055
Compartmentalization of Interphase Chromosomes
are separated in Figure 2(a) and (b) overlap largely
in (c).
The different organizations are visible more
clearly in the simulated confocal sections
(Figure 2(d)-(f)), which were generated by our ``virtual confocal microscope'' (see Simulation and
Experimental Methods). Without excluded volume,
large yellow regions of intermingled ®bers become
visible, which is typical for random walk structures
(Figure 2(f)). The simulated confocal sections are
well suited for direct comparison with experimental observations, and were used extensively for the
computation of chromosome arm and subcompartment overlap. Moreover, we computed reconstructions (Figure 2(g)-(i)), which show the different 3D
organization of the chromosomes more clearly.
Without excluded volume interaction, chromosome
arms overlap often (Figure 2(i)).
For human amniotic ¯uid cells, we have stained
the p and q arms of chromosome 6 red and green,
respectively. Very little overlap is visible in the
confocal sections, which represent both chromosomes 6 in the same nucleus (Figure 2(k)) and in
the corresponding 3D reconstructions (Figure 2(j)
and (l)). The overlap coef®cient was smaller than
10 %. The same was observed for chromosome 3
(data not shown). We found similar structures in
our set of simulated con®gurations.
Figure 2. Structure of simulated and observed
chromosomes with q-arms painted in red, p-arms in
green. The top row shows the folding of the chromatin
®ber according to (a) the MLS-model with subcompartments consisting of several 120 kbp sized loops (for
comparison with Figure 1, a single subcompartment is
indicated by a white circle); (b) the MLS-model with
giant loops domains (several Mb each); and (c) the RW/
GL-model. Only a small part of one giant loop (open
arrow) can be distinguished on the right of the chromosome in (c), because the loops are highly intermingled.
MLS-model chromosomes ((a) and (b)) were simulated
with excluded volume interaction, RW/GL-model
chromosomes (c) without. Chromosome 4 is shown in
column (a), chromosome 3 in (b) and (c). Sections of
these chromosome con®gurations were computed by the
virtual confocal microscope ((d)-(f)) and used to prepare
the volume visualizations ((g)-(i)). The simulated resolution was 250 nm (lateral) and 750 nm (axial, i.e. viewing direction). For comparison, confocal sections of both
observed chromosomes 6 within a single nucleus (k)
and their 3D reconstructions ((j) and (l)) are shown
using a Voronoi tesselation.
domains and excluded volume interactions, the
size and shape of the territory in Figure 2(b) looks
similar to the MLS-model chromosome in
Figure 2(a), but they differ in their small scale
structure. Caused by the presence of giant, randomly folded chromatin loops, the territory in
Figure 2(b) appears more diffuse. For giant-loops
without excluded volume interactions of the chromatin ®ber, the structure of the entire territory is
changed (random walk/giant-loop model (RW/
GL:-model) in Figure 2(c)). Chromosome arms that
Interphase distances and
chromatin distribution
Chromosome 4 was simulated for 106 MonteCarlo steps. Projected interphase distances computed for pairs of markers within the region 4p16.3
(Figure 3(a)) are in agreement with the experimental data from van den Engh et al. (1992). Observed
distances between markers on chromosome 5
(Warrington & Bengtsson, 1994) and X (Lawrence
et al., 1990) are equally well predicted in the presence of Mb-sized loops (data not shown). Under
conditions which better preserve the 3D nuclear
structure, considerably smaller distances were
reported (Yokota et al., 1995a). These smaller distances (shown as ®lled circles in Figure 3(a)) are
not compatible with the presence of giant loops,
but ®t with the MLS-model prediction (broken
lines in Figure 3(a)). Similar 3D distances are
obtained for a doubled loop size of 240 kb (eight
segments; dotted line in Figure 3(a)), which is still
much smaller than the size of the subcompartments in the Mb range.
Although the variants of the MLS-model shown
in Figure 1(a) and (b) result in different distances
on the Mb level (Figure 3(a)), both predict similar
distances in the 200 Mb range in agreement with
the experimental data of both preparations, which
also coincide on these length scales (Figure 3(b)).
Hence, the agreement of distances measured at this
scale with the RW/GL-model (Sachs et al., 1995)
does not allow a discrimination between these
models regarding the scatter of the experimental
data. However, the MLS-model predicts interphase
1056
Compartmentalization of Interphase Chromosomes
Figure 3. (a) Mean-squared projected interphase distances of markers in terminal 4 Mb region 4p16.3 of chromosome 4. The result of the MLS-model including a giant-loop domain for that region (continuous line) agrees well with
data of hypotonically swollen nuclei (open circles; van den Engh et al., 1992). Predictions of our model with multiloop subcompartments only (broken lines 120 kb loops, dotted line 240 kb loops) agree well with non-hypotonically
swollen nuclei (®lled circles; Yokota et al., 1995a). (b) Results for the larger marker distances on chromosome 4 (open
circles hypotonically swollen, ®lled circles non-hypotonically swollen nuclei Yokota et al., 1995a) are independent of
preparation, in agreement with our model simulations including giant-loop domains (continuous line) and without
(broken line). (c) A log-log plot indicates that interphase distances of both preparations increase like a random ¯ight
polymer (exponent 0.5) below 50 Mb. The RW/GL-model explains this by a folding of the chromatin ®ber itself
(open circles), the MLS-model by the folding of the chain into subcompartments (®lled circles). Data at larger dis1
tances indicate a globule state with an d3 increase, which is predicted by the MLS-model.
chromosomes to be in a condensed globule state,
where distances
between markers scale as (geno1
mic distance)3 (de Gennes, 1979), while the RW/
GL-model results in an exponent of 12. A double
logarithmic plot of the experimental data from
Yokota et al. (1995a) in Figure 3(c) yields an exponent 13, in agreement with the MLS-model. The globule state is also characterized by an
approximately uniform average chromatin concentration inside the territory, which we found by
analyzing our simulated MLS-model chromosomes. The simulated random walk chromosomes
without excluded volume interactions between
chromatin ®bers showed a higher central density
and a decrease to the periphery. Experimentally,
no such concentration pro®le has ever been
observed (compare e.g. Figure 7(d)).
leads to clearly separated chromosome arms.
Only an insigni®cant overlap at their surface is
observed, supposedly an effect of limited optical
resolution (the overlap decreases with increasing
resolution). The separation is not an artifact of
our initial straight chromosome con®guration
which could be preserved by the excluded
volume interaction. The barrier for ®ber crossing,
i.e. topoisomerase II activity, was small enough
to allow frequent crossings of ®ber segments.
Large structural reorganizations were observed
during the simulation, but the arms always
remained essentially separated (Figure 4). However, the vanishing barrier of the RW/GL-model
leads to a majority of con®gurations, where larger parts of both arms are intermingled. This
Overlap of chromosome arms
Besides distance measurements, a more de®nite
determination of chromosome organization can
be achieved by computing the overlap of subchromosomal structures. We computed the overlap of chromosome p and q-arms for 400
different chromosome 3 con®gurations chosen
from a total set of 5 105 Monte Carlo steps. To
this aim, we developed a simulation technique
for chromosome painting and subsequent confocal imaging, the ``virtual confocal microscope''
(see Simulations and Experimental Methods).
Central sections of simulated con®gurations of
green and red painted arms are shown in
Figure 2(d) for the MLS-model, the modi®ed
MLS-model with giant loops (Figure 2(e)), and
our
simulations
of
the
RW/GL-model
(Figure 2(f)). The presence of excluded volume
interactions between all segments of the chromatin ®ber for the MLS-models (Figure 2(d) and (e))
Figure 4. Structural changes during the simulation of
chromosome 4 with q-arms painted in red, p-arms in.
green. The initial con®guration is shown in (a). (b) to (d)
The chromosome structure after 20,000, 340,000 and
950,000 Monte Carlo steps.
Compartmentalization of Interphase Chromosomes
Figure 5. (a) Overlap of chromosome arms. Open circles indicate the overlap predicted by the MLS-model
for chromosome 3, ®lled circles those of the RW/GLmodel. The observed overlap (chromosome 3, triangles;
chromosome 6, inverted triangles; Dietzel et al., 1997) is
comparable with the MLS-model data. (b) Overlap of R
and G-subcompartments for the MLS-model (open circles) and the RW/GL-model (®lled circles). The experimentally observed early and late replicating domains
result in an overlap of about 4 % (arrow).
intermingling is visible as the large yellow region
in Figure 2(f).
Figure 5(a) shows the distributions of the relative overlaps obtained for the MLS-model, the
RW/GL-model and the observed overlap of
chromosome 3 and 6 arm domains (Dietzel et al.,
1997). Good agreement is found between the prediction of the MLS-model and the observed overlap. One can expect a slightly larger relative
overlap for chromosome 6, because it is smaller
than chromosome 3, while the resolution used for
the computation was the same. Additionally, we
cannot exclude some overlap of the arm probes
used. All computed overlaps are smaller than
about 50 % because a complete overlap would
require arms with identical size and shape which
is very unlikely.
Overlap of chromosome band domains
The notion of a compartmentalized chromosome
territory structure as predicted by the MLS-model
and veri®ed by chromosome 3 and 6 arm experimental data is valid even on the smaller scale subcompartments. Only little inter-subcompartment
overlap is visible in Figure 6(a) and (b) for a
chromosome 15 territory simulated according to
the MLS-model. A simulated confocal section
through an RW/GL-model chromosome 15 shows
a large central region of overlap (Figure 6(c)),
which is caused by the higher, central concentration of intermingled ®bers in the RW/GLmodel.
1057
Figure 6. Simulated and observed chromosomes 15.
R-band and early replicating domains are shown in red,
G-band and? late replicating domains in green. An
example for the MLS-model is shown as a volume rendering (a) and the central confocal section (b). A substantial overlap is visible in the section of a RW/GLmodel chromosome (c). An observed confocal section of
chromosome 15 is most similar to the MLS-model (d).
For comparison, Figure 6(d) shows a representative chromosome 15 territory (confocal mid-section) from a diploid human dermal ®broblast
nucleus with differentially labeled early and late
replicating subchromosomal foci (SF) with diameters of some 400-800 nm. These SF likely correspond with the relatively gene-dense R and genepoor G-band domains, respectively (Zink et al.,
1998a,b). Such sections compare favorably with the
MLS-model sections (see Figure 6(b)). Further support for a subcompartmentalization of chromosome arms into distinct band domains was
provided by FISH (¯uorescent in situ hybridization) experiments with band speci®c microdissection probes (Dietzel et al., 1997).
Using simulated chromosome 15 territories at
250 nm resolution, the mean relative overlap of R
and G-band subcompartments is 6 % of the
chromosome volume for the MLS-model and 2 %
for the RW/GL-model. If the computation is
restricted to the central part of the chromosome
(half the linear size), the overlap increases to about
10 % and 34 %, respectively. Hence, the average
overlap of band domains computed for the RW/
GL-model is about three times higher than for the
MLS-model (Figure 5(b)), re¯ecting the entirely
different internal structure of chromosome territories predicted by the two models, which has
been found for the overlap of chromosome arms
and their density pro®les. The experimentally
observed overlap of early and late replicating
domains of chromosomes 15 territories was found
1058
to be 5-10 % (Zink et al., 1998b), in agreement with
our MLS-model data.
Besides the overlap, the computed volumes of R
and G-bands differ strongly for the models simulated. The modi®ed MLS-model with giant-loop
domains (Figure 1(b)) resulted in R-subcompartment volumes, which are about 2.5-fold larger than
those of the MLS-model (Figure 1(a)). For the RW/
GL-model, we found 2.5-fold larger volumes for
both R and G-subcompartments. Early and late
replicating chromosome 15 subdomains occupy
volumes of 4(1)mm3 and 3(1)mm3, respectively
(H. Born¯eth, unpublished data; Zink et al., 1998b).
H. Born¯eth also analyzed 27 of our simulated
MLS-model chromosomes with the same algorithm, and computed a mean R-subcompartment
volume of 3.0(0.7)mm3 and a mean G-subcompartment volume of 2.5(0.8)mm3, which agree
with the experimental data within the error bars.
The observed mean number of early and late
domains agree with our assumption for R and Gbands, which we derived from the early prophase
band pattern.
Discussion
A functional organization of chromosomes in
interphase nuclei needs speci®c 3D structures. On
the lowest level, speci®c sequences such as the
TATA-box are well-de®ned structures with a
speci®c function in gene regulation. Chromatin, as
the next higher folding pattern, plays an important
role in establishing and maintaining a stable pattern of gene expression in eukaryotic cells
(Felsenfeld, 1996). In agreement with other models
(Manuelidis & Chen, 1990; Zink et al., 1998a) the
multi-loop subcompartment (MLS) model presented here predicts essentially separated chromosome band domains (about 1 Mb) and arm
domains (about 10-120 Mb in the human chromosome complement) in interphase nuclei. Although
modeling was only performed for G1 chromosomes, we anticipate that the results will hold also
for the modeling of G2 chromosomes. The amount
of overlap, as well as the number and size of subcompartments, agrees well with our experimental
data for chromosome 3 and 6 arm domains and SF
of chromosome 15 territories. The presence of these
structures suggests a functional organization on
the Mb scale.
Besides the prediction of Mb-sized separated
structures, our model results in interphase distances between markers on chromosome 4 which
agree with the experimental data (van den Engh
et al., 1992; Yokota et al., 1995a). These experiments
were interpreted as an indication for randomly
folded giant loops (Sachs et al., 1995). While the
occurrence of giant loops is a valid possibility, the
possibility should also be considered that they may
be induced by unfavorable experimental conditions. We note that some experimental distance
measurements were performed on hypotonically
Compartmentalization of Interphase Chromosomes
swollen nuclei which were ®xed with 3:1 methanol
:acetic acid and air dried. Furthermore, the use of
alkaline borate buffer enlarged ®broblast nuclei
about ®vefold and likely disrupted chromosome
structure to a very large extent (Yokota et al.,
1995b). Since this procedure led to extensive ¯attening of the nuclear shape, Yokota et al. (1995a)
performed distance measurements for markers in
the same region in formalin ®xed nuclei under conditions which better preserved their three-dimensional nuclear structure. In these nuclei they
measured considerably smaller distances. These
smaller distances, shown as ®lled circles in
Figure 3(a), are not compatible with the presence
of giant loops, but ®t very well with the MLSmodel prediction (broken lines in Figure 3(a)). It
should be re-emphasized that the 120 kb loop size
(four segments of the polymer model) was motivated by the literature and not selected to ®t these
experimental interphase distances.
Hypotonic conditions (Yokota et al., 1995a)
apparently favor the formation of Mb-sized giantloop domains, but may still preserve relative
arrangements of higher order structures above
about 10 Mb to a considerable extent. Although it is
still not clear whether available protocols are suf®cient to preserve 3D chromatin structures down to
the single Mb level (Popp et al., 1990), it is encouraging to note that a comparison of FISH and in vivo
preparations shows small scale modi®cations only
(Robinett et al., 1996). A condensation of the loops
in a subcompartment preferentially parallel with
the linker chromatin between the subcompartments
can lead to a higher order structure with 100150 nm diameter (Belmont & Bruce, 1994). It has
not been demonstrated unequivocally so far
whether such ®bers occur in vivo or result from ®xation artifacts. Presumably the in vivo condensation
state of SF changes dynamically, suggesting a possible relevance for transcriptional activity (Zink et al.,
1998a). The time evolution of gene activity in the
70 kb b-globulin locus, for instance, can be most
easily explained by a loop in the 100 kb range
(Milot et al., l996), and the inhibition of RNA polymerase II leads to dramatic changes in chromosome
structure (Haaf & Ward, 1996).
In our modeling experiments, changes of the
local organization (51 Mb) may have little effects
on structures above the Mb-scale. For example, an
increase of the loop length by a factor of 2 did not
change the computed mean distances essentially
(Figure 2(a)). Instead of a single loop length, one
can use a distribution of loop lengths as found in
digestion experiments (Cook, 1995; Wolffe, 1995).
Therefore, we also used a Gaussian distribution
with a variance of 50 % mean for simulations of
giant-loop chromosomes without excluded volume
interactions. Computed mean distances for markers agreed for both kinds of simulations within
the small statistical uncertainty. Therefore, even a
dynamically changing local structure, e.g. a temporal and position dependent loop size variation
Compartmentalization of Interphase Chromosomes
(Heng et al., 1996), results in similar mean distances
on larger length scales.
The MLS-model assumes that the chain of subsequent band domains is folded quite randomly in
interphase. Present data, however, do not exclude
the possibility that an individual subcompartment
formed by a multi-loop cluster (MLC) is organized
in a highly non-random manner and that preferential positions of genes related to functional aspects
may occur in MLCs of living cell nuclei (see below
for a possible relationship of MLCs with SF
observed in living cell nuclei). A functionally
important higher order organization of MLCs
resulting in a non-random positioning of regulatory and coding sequences is dif®cult to detect by
measuring mean distances between markers
belonging to a given MLC due to the small scale.
Furthermore, such an organization may be largely
destroyed when cells are ®xed and subjected to
FISH.
A number of studies indicate a non-random
chromatin organization within chromosome territories. For instance, different average positions of
coding and non-coding sequences relative to the
chromosome territory were reported. Several
active and inactive genes were preferentially
observed in the periphery of chromosome territories in contrast with a non-coding sequence
(Kurz et al., 1996). In a recent study, we have
observed that the position of ANT2, a gene subject of X-inactivation, was generally more interior
in the inactive X-territory of human female
amniotic ¯uid cell nuclei than its transcriptionally
active homolog in the active X-territory. In contrast, ANT3, which is located in the pseudoautosomal region and escapes X-inactivation, consistently showed a more peripheral position in
both X-territories (C.M., R.E., S.D., D.Z., C.M.,
G.W., T.C. & J.L., unpublished data; Dietz et al.,
1997). Visser et al. (1998) noted the distribution of
early replicating, gene dense chromatin clusters
throughout the space occupied by human
chromosome 8 territories, indicating that the
localization of genes is not restricted to the territory periphery. These authors also noted the preferential clustering of early replicating chromatin
in the periphery of human Xi-territories but not
in Xa-territories. The emerging picture indicates
complex patterns of chromosome territory organization and suprachromosomal arrangements in
the cell nucleus (Ferreira et al., 1997). The functional implications of these ®ndings will become
the focus of future studies. In a ®rst attempt to
test the effects of such a preferential positioning,
we added an additional attractive force between
G-band chromatin domains to the MLS-model.
This results in a clustering of G-band domains in
our simulations, but the mean distances between
markers up to about 20 Mb distance did not
change substantially.
All these results demand a clari®cation of the
terms ``interior'' and ``exterior'' of a chromosome
territory. On the scale of whole chromosome ter-
1059
ritories, one can de®ne the surface with a precision of some 100 nm, for example, by a
Voronoi tessellation (Eils et al., 1996). But on the
scale of chromatin ®bers (about 30 nm diameter),
a surface can only be de®ned by a mean density
gradient because of the Brownian motion of the
®bers. Moreover, the de®nition of interior and
exterior depends also on the size of the probes.
While small proteins like individual transcription
factors are found ``within'' territories (de Jong
et al., 1996), this nuclear domain is nearly free of
larger structures like coiled bodies, PML bodies
and large speckles (Bridger et al., 1998; Zirbel
et al., 1993). It was also recently shown that
vimentin translocated into the nucleus forms
®bers that are excluded from chromosome territories (Brigder et al., 1998).
Using the 3D-Voronoi tessellation (Eils et al.,
1996) or the Cavalieri approach (Rinke et al., 1995;
Dietzel et al., 1997), an enveloping surface of a
chromosome territory can be de®ned with a precision of some 100 nm. However, these procedures
provide an image of the territory periphery, which
may obscure its true functional complexity predicted by the interchromosomal domain (ICD)
model. According to this model an ICD-space
exists which harbors the macromolecular domains
involved in transcription and splicing, and allows
for a channeled diffusion of factors involved in
these nuclear functions, as well as the channeled
export of spliced RNA. This hypothetical space
starts at the nuclear pores, extends between
chromosome territories (Zirbel et al., 1993) and
further expands into the territory interior due to
invaginations/channels, which connect the interterritory with the intraterritory ICD-space (Cremer
et al., l996; Cremer et al., 1995). Recent in vivo studies have demonstrated the presence of SF within
chromosome territories (Zink & Cremer, 1998; Zink
et al., 1998a). SF observed in vivo apparently correspond with clusters of either early or late replicating chromatin with diameters of some 400-800 nm
previously observed in studies of ®xed cell nuclei
(Berezney et al., 1995; Jackson & Pombo, 1998; Zink
et al., 1998a).
The MLS-model was developed with the
assumption that MLSCs correspond to highly
resolved chromosome band domains with the
size of some 1 Mb. Notably, the size of an SF is
in the same order, and experimental evidence
suggests that SF represent chromosome band and
subband domains in the interphase nucleus (Zink
et al., 1998a). Therefore, the MLS-model provides
an explanation for the formation of SF. However,
it should be emphasized that numerous possibilities exist which could yield the focal chromatin
organization revealed by the experimental observation of SF. Furthermore, the model does not
intend to make predictions on the possible extent
of a cell cycle and cell type-speci®c 3D organization of SF.
The detailed shape of a given territory likely
depends not only on its internal structure but on
1060
interactions with other chromosome territories and
other nuclear compartments (MuÈnkel et al., 1995)
and probably even on structures outside the
nucleus (Maniotis et al., 1997). While geometrical
constraints that result from the compartmentalization of chromosome territories into SF affect intrachromosomal rearrangements, interchromosomal
rearrangements may depend on surface interactions between adjacent chromosome territories
(Cremer et al., 1996). In addition to these implications for chromosome aberration formation, we
expect functional implications from mutual interactions between SF and the RNA processing
machinery (Misteli et al., 1997), as well as other
nuclear compartments found in nuclear matrix
preparations (Berezney et al., 1995; van Driel et al.,
1995). The potential dynamics of these interactions
are still not well understood. Understanding of a
functional chromosome territory architecture
requires an answer to the question whether SF are
more or less randomly arranged or highly organized structures, which undergo dynamic changes
during cell cycle and cell differentiation. A possible
role of SF in the context of the ICD model needs to
be explored in future experiments. Obviously, we
need to know more about the organization of subchromosomal foci and their topological relationships with the formation of nascent RNA and
macromolecular domains involved in transcription
and splicing. While answers to these questions cannot yet be given, the general aspects of chromosome organization in G1 interphase can be
explained by a polymer model of the chromatin
®ber and its folding.
Simulation and Experimental Methods
Compartmentalization of Interphase Chromosomes
interaction between the segments leads to a slightly
higher exponent (N2v, v 0.59). Regarding the uncertain
data on chromatin structure (density) in vivo, this difference can be neglected. For comparison with experiments,
marker separations x have to be expressed in base-pairs
instead of segments N. This can be achieved by introducing the density d in base-pairs per nanometer contour
length of the chromatin ®ber. The separation x can be
computed by the length of each segment in base-pairs db
multiplied by the number of segments N between the
markers:
1
b
hR2 i ˆ b d bN ˆ
x
d
d
For a phantom ®ber a similar expression holds for projected two-dimensional distances (e.g. from a standard
microscope; Doi & Edwards, 1986):
2 b
2
hR i ˆ
x
3 d
Measured projected distances below l Mb of van den
Engh et al. (1992) show an initial slope
2 b
x 2:5…0:5† mm2 =Mb
3 d
A chromatin density d of 6 nucleosomes/
11 nm (d 105 bp/nm; Wolffe, 1995) results in b ˆ 260
(70) nm, in agreement with earlier estimates between
200 and 359 nm (Ostashevsky & Lange, 1994). Because
of the uncertainty regarding the in vivo chromatin structure, we used a Kuhn segment length b of 300 nm (about
30 kb) in our simulations.
An excluded volume interaction energy
r4 ÿ 2D2 r2
E ˆ Emax 1 ‡
D4
between all segments separated by a distance r in the
Polymer model
Our chromosome model is based on two basic
assumptions: a chromosome in interphase (G1) is
formed by a single chromatin ®ber and the folding of
the ®ber is related to the characteristic chromosome
band pattern. Within each band the chromatin is
arranged into several 120 kb sized loops (Figure 1(a)
and Figure 2(a),(d) and (g)). Different subcompartments
are connected by small chromatin fragments of the
same length as one loop.
The detailed structure of chromatin in interphase
nuclei is still under discussion (van Holde & Zlatanova,
1995; Woodcock & Horowitz, 1995). The structural and
dynamical properties of a chromatin ®ber can be
described approximately by a chain of cylinders called
segments. The length of these segments determines the
rigidity against bending of the model ®ber. For a certain
length, which is called the Kuhn length b, the bending
rigidity of the model ®ber and other structural properties
agree with those of the chromatin ®ber. Therefore, b can
be derived from observed structural properties of the
chromatin ®ber. For instance, the mean squared 3D distance hR2i between two markers on the model ®ber separated by N segments is related to the Kuhn length b by
hR2i ˆ b2N approximately (Doi & Edwards, 1986). This
relation is valid exactly for a phantom ®ber, where segments are allowed to intersect. An excluded volume
Figure 7. Excluded volume interaction of the chromatin ®ber. The interaction energy and forces vanish for
separations larger than the ®ber diameter (d ˆ 30 nm).
The height of the barrier (here 1 kBT at r ˆ 0) can be
adjusted to model ®ber crossing, e.g. mediated by topoisomerase II. A barrier larger than 1 kBT surpresses ®ber
crossing almost completely. The resulting force (absolute
value shown as broken line) vanishes at r ˆ d and r ˆ 0
and discontinuous jumps of the ®ber are avoided.
Compartmentalization of Interphase Chromosomes
range [0; D] favors a spatial separation of all segments of
the chromatin ®ber especially for Emax much larger than
l kBT (Figure 7). A ®ber diameter D ˆ 30 nm was used,
which agrees suf®ciently well with the published data of
chromatin ®bers (van Holde & Zlatanova, 1995;
Woodcock & Horowitz, 1995). Because of the electrostatic shielding by the ions in the solution, no long-range
interactions are taken into account, i.e. E ˆ 0 for r > D.
This interaction energy function is the simplest polynomial, which represents a repulsion and a ®nite barrier
without jumps of the ®rst derivative, i.e. the force. By
decreasing the barrier height Emax below about 1 kBT we
can model ®ber crossing, e.g. mediated by topoisomerase
II. Most of the simulations were performed with a barrier
Emax ˆ 0.1 kBT (Boltzmann constant kB, temperature
T ˆ 300 K). Similar equilibrium properties were observed
for higher barriers (e.g. 1.0 kBT).
Without further constraints a chromatin ®ber exceeds
the size of 3D-reconstructed chromosome territories (Eils
et al., 1996) and even that of the nucleus. The mean size
can be estimated by the end-to-end distance of a phantom ®ber:
s
 s
p
b
260 nm
hR2 i ˆ
x
25 108 bp 25 mm
d
105 bp=nm
Therefore, additional topological constraints are
required to explain the size of observed chromosome
territories. Such constraints have been proposed by a
rigid (spherical) territory boundary (Hahnfeldt et al.,
1993) or intra-®ber connections resulting in loops
(Ostashevsky & Lange, 1994). However, there is no
experimental evidence for the proposed rigid, static territory boundary, which con®nes a chromosome within
a territory. In contrast, the observed chromosome territory structure in Figure 2(j)-(l) differs strongly from a
sphere, and the structure and shape of territories
change substantially during in vivo observations
(Robinett et al., 1996; Travis, 1997). Chromatin loops
were reported several times in the past, e.g. in the context of spreaded metaphase chromosomes (Bickmore &
Oghene, 1996; Okada & Comings, 1979; Saitoh &
Laemmli, 1994), nuclear matrix preparations (Pienta &
Coffey, 1984) and biochemical experiments (for references see, Cook, 1995). Based on observed mean interphase distances between markers, the size of these
loops was estimated from the RW/GL-model to be in
the Mb range (Sachs et al., 1995). However, all other
experiments suggest a much smaller loop size of about
100 kb. We therefore used a loop size of four segments
(12 kb) for our simulations. Loops are formed by loop
bases, which have very small or vanishing spatial separations. For technical reasons we introduced stiff
springs between the loop bases, which suppress separations larger than about 50 nm. As long as no elementary ``move'' of the simulation changes the distance
between the loop bases, the springs are not required,
but they ensure that rounding errors do not add up
and ®nally separate the loop bases. A study of the
dynamics will require e.g. Brownian dynamics simulations, where the chromatin ®ber moves according to
the systematic (e.g. from the springs) and random
forces. In this case, springs are required, to ensure the
small spatial separation of the loop bases. Presently, no
experimental data for the detailed arrangement of loop
bases is available. Hence, most of the simulations were
conducted with two consecutive springs attached to
the loop base of the previous spring (``V''-shape
appearance in Figure 1(a)). Within statistics the same
1061
results were found for another spring connectivity
tested, where all loop bases of each subcompartment
are located at a single point in space. In general, the
same results can be expected as long as the mean
extension of the springs (smaller than 50 nm in this
work) is much smaller than the subcompartment extension (about 500 nm diameter). The loop bases were not
attached to additional structures (e.g. the nuclear lamina, matrix etc.) but can diffuse and rotate freely.
About ten such loops form a subcompartment (for
clarity six loops are shown in Figure 1(a) only). The
exact number was derived from the band pattern. For
lack of suf®cient experimental data we extrapolated the
band pattern of the standard human 850 band ideogram
(Francke, 1994) to the earliest stage of human prophase
(about 3000 bands; Yunis, 1981) by subdividing each of
the 850 bands into three equally sized parts. This results
in a mean band size of ca. 1 Mb. The number of loops in
each subcompartment was computed by assuming that
the amount of DNA in each band is proportional to the
band's size in the ideogram and subdividing this number by the size of the loops (120 kb).
Adjacent chromosomes or other nuclear structures
(e.g. nucleoli, nuclear envelope), which occupy essentially separated nuclear subvolumes (Cremer et al.,
1995; van Driel et al., 1995), limit the available space of
each chromosome territory. The simulation of these
other domains results in simulation times which are
two orders of magnitude larger at least. This overhead
can be avoided by focusing on the territory boundary
(which can only be de®ned meaningfully on the length
scale of a whole territory) between a chromosome territory and its neighborhood. In general, observed
chromosome territories have a non-spherical and rough
surface (Eils et al., 1996), but the volume appears to be
constant and proportional to the DNA content approximately. Unfortunately, the simulation of the boundary
as a ¯exible bag with constant volume requires huge
computation times. We therefore approximated the
limitation to a certain territory volume by a spherical
``boundary'' with an energy barrier Emax/2 for each
segment which leaves this sphere. The territory volume
is estimated by the nuclear volume times the ratio of
chromosome DNA content and genome size. The center of the sphere is always placed at the chromosome
center of mass during the simulation. This additional
(and arti®cial) constraint is different from the rigid
boundary used in the analytical computation of Hahnfeldt et al. (1993), which con®nes the chromatin into
the sphere perfectly. Because the barrier Emax/2 is onehalf of the segment interaction barrier only, the chromatin ®ber was not limited to that sphere strictly, but
¯uctuated to the outside sometimes and the shape of
the territories is non-spherical in general as visible in
Figure 2(a). While the agreement with the experimental
data (see below) validates this approximation, the
detailed comparison with simulations including all
chromosomes and other nuclear domains requires a
further, even more elaborated study. The use of a
spherical territory barrier will be obsolete then.
Besides the MLS-model in Figure 1(a) and (d) and
Figure 2(a), (d) and (g), we used a modi®cation of the
MLS-model (Figure 1(b) and (e); Figure 2(b), (e) and (h)),
where several successive bands form a single giant loop
domain in the Mbp range. Each two giant loops were
separated by a subcompartment consisting of small
loops according to the MLS-model. Both variants were
simulated in the presence of excluded volume interactions between all segments of the chromatin ®ber.
1062
Contrary to the analytical RWGL-model (Sachs et al.,
1995), where the number or size of the loops was
adapted to ®t measured interphase distances, we did not
adjust the parameters noted above to ®t the experimental
data and no additional ``backbone'' polymer is assumed.
We also simulated chromosomes according to the analytical RW/GL-model (Sachs et al., 1995; Figure 1(c) and
(f); Figure 2(c), (f) and (i)), which does not include an
excluded volume interaction between segments of the
chromatin ®ber (i.e. Emax ˆ 0). Hence, giant loops can
intersect with other ones without any barrier. Each intersection results in nucleosomes occupying the same
space, which is completely unrealistic. However, this
model can be regarded as an approximation to a
chromosome structure consisting of highly intermingled
®bers and was used to explain measured distances
between markers (see Results).
Monte Carlo simulations
Because of the many collisions with solvent molecules
or other apparently random interactions, macromolecules in a solvent move in a stochastic way instead of
the Newtonian dynamics. Monte Carlo simulations represent a well-established tool for the exploration of such
stochastic dynamics and their equilibrium properties
(Binder & Herrmann, 1992). A ®ber con®guration is
altered by ``random moves'' during the simulation, e.g.
an end of a ®ber segment is displaced by a random
amount and direction (see below). A certain move is
accepted if the internal energy E of the system is lowered
or the increase E results in a Boltzmann factor eÿE
smaller than a random number x 2 [0; 1]. Using this
Metropolis algorithm and moves ful®lling detailed balance (e.g. without a bias in one direction etc.) all relevant
®ber con®gurations are sampled according to the equilibrium distribution at constant temperature. Additionally,
these arti®cial dynamics can be mapped to the Brownian
dynamics (diffusion) of the ®ber (Binder & Herrmann,
1992).
For the initialization of the chromosome structure, a
radial loop model of metaphase chromosomes was used
(MuÈnkel & Langowski, 1998). For the decondensation
and equilibrium dynamics a parallel Monte Carlo algorithm with local and global moves was used (MuÈnkel &
Heermann, 1995). Global changes were achieved by
Pivot moves (Madras & Sokal, 1988). A certain segment
of a chromosome and a unit vector attached to that segment are chosen randomly. Subsequently all segments
below (or above) this segment are rotated by a random
angle f 2 [ ÿ fmax; fmax] around this vector. In general,
fmax is about some degrees to achieve a suitable acceptance rate, but it can be as large as p in the absence of
excluded volume interactions. Hence, global bending
moves of the whole chromosome are speeded up. Local
updates are necessary for the fast stochastic movements
on small length scales. A chosen end of a segment is
rotated around the axis constructed by its left and right
neighbor by a random angle. The range of this angle is
adjusted according to the acceptance rate, typically of
the order of some degrees in the presence of excluded
volume interactions. Up to 100 randomly chosen segment ends are updated concurrently. The update of adjacent segment ends is avoided, because this would violate
the detailed balance condition. Both kind of moves preserve segment lengths. Hence, we are not limited by the
fast vibrations of the segments, which usually limits the
steps size in molecular dynamics simulations. The simulations required about 600 days single CPU time on a
Compartmentalization of Interphase Chromosomes
Parsytec PowerXplorer with 4 and a PowerGC with 192
PowerPC 601 processors. Good parallel ef®ciency was
achieved with up to 16 processors (parallel run time of
about 40 days).
Virtual confocal microscope
Point-like light sources (i.e. ¯uorescent markers) were
positioned on the simulated chromatin ®ber with a separation of 30 nm. Their light emission was convoluted
by an approximated point-spread-function of a confocal
microscope and sampled on a 2003 grid made by (3550 nm)3 sized volume elements (Figure 2(d)-(f)). A lateral
resolution of 250 nm and an axial resolution of 700 nm
was used for the visualizations and measurements
throughout this work, which is similar to that of the
microscope used in the experiments. Using the cube of
2003 voxels we rendered 3D reconstructions. Our rendering software is based on the public domain volume rendering library VolPack (Lacroute & Levoy, 1994). The
reconstructed chromosomes 6 from a human amniotic
¯uid cell nucleus shown in Figure 2(j) and (l) were computed by a 3D Voronoi tesselation of the entire stack of
confocal images recorded from this nucleus (Eils et al.,
1996).
Computation of domain overlap
The overlap of chromosome arms and subcompartments was computed by comparing the intensities of
both color channels for all pixels. As we show in the following, the overlap of background signals can be separated from the chromosome overlap using their different
properties under pixel shifts of one color channel against
the other. Our method is based on an algorithm by van
Steensel et al. (1996), which was used to study the colocalization of receptors. For an in®nite, one-dimensional
image (coordinate x) the correlation (i.e. the overlap) of
the red channel r(x) and the green channel g(x), for
example, is de®ned as
1
…
Corr…r; g† r…x ‡ s†g…x†ds
ÿ1
According to the correlation theorem the same result can
be achieved by multiplying the Fourier transform R of
r(x) with the complex conjugate G* of the Fourier transform of g(x). In the case of a 3D image set, a direct computation of Corr(r, g) for all shifts d3x leads to a
computational complexity of (linear size)6. Using a 3D
fast Fourier transformation (FFT) the evaluation of RG*
and a subsequent back-transformation into real space
has a complexity of (linear size)3 only. Hence, for an
image size of 1283 pixels the later method is faster by
about six orders of magnitude. Random background
intensities result in a constant correlation independent of
the shift distance. For two non-overlapping structures
we expect an increase of the correlation for small shift
distances. In the presence of an overlap region the correlation signal will decrease initially.
In agreement with the size of the yellow overlap
regions in Figure 2(d)-(f), the MLS-model results in an
initial increase (small overlap) and the RW/GL-model in
a decrease (large overlap). Both chromosome 3 and 6
arm-speci®c hybridizations (Dietzel et al., 1997) showed
the same background correlation, which was removed
by setting the threshold to about 10 % of the maximum
Compartmentalization of Interphase Chromosomes
intensity value. This threshold was used for the analysis
of both the observed and the simulated images.
The relative overlap O was computed as the fraction
O ˆ Vboth colors/Vterritory. The Vboth colors value is the sum
of all volume elements, which are painted in both colors,
Vterritory is the sum of all volume elements painted in any
color with an intensity larger than the threshold.
FISH of chromosome arms and replication labeling
Microdissected chromosome 3 and 6 arm-speci®c
probes were used for ¯uorescent in situ hybridization
(FISH) with primary human amniotic ¯uid cells with
normal female karyotype (for details see, Dietzel et al.,
1997). To maintain the 3D nuclear topography, air drying was carefully avoided during ®xation, in situ hybridization and the detection procedure. Biotinylated DNA
probes (3p) were detected using avidin conjugated to
FITC or Cy5. Digoxigenin-labeled DNA probes (3q) were
detected using mouse anti-digoxigenin antibodies and
Cy3 conjugated sheep anti-mouse IgG. Series of light
optical sections of nuclei were recorded with a Leica TCS
4D three channel confocal laser scanning microscope
equipped with a Plan Apo 63x/1.32 oil objective.
In addition, we studied the organization of early and
late replicating chromatin domains in individual
chromosome 15 territories through a combination of
replication labeling and chromosome painting (Zink et al.,
1998a). Brie¯y, non-synchronized human female diploid
®broblasts were pulse-labeled for two hours each with
the thymidine-analogs iododeoxyurdine (IdU) and
chlorodeoxyurdine (CldU; Aten et al., 1992). The ®rst
pulse was performed with IdU, the second pulse four
hours later with CldU. This labeling scheme yielded a
fraction of cells with DNA labeled in the ®rst part of Sphase with IdU and in the second part of S-phase with
CldU. Cells were allowed to grow for some 7-12 cell
cycles before they were ®xed with 4 % (v/v) buffered
paraformaldehyde. This additional growth period
yielded cells with nuclei containing few randomly segregated, replication-labeled chromatids. For a detailed 3D
study of IdU and CIdU replication labeled chromosome
15 territories, we identi®ed a subset of nuclei with the
respective territories by their colocalization with a
chromosome 15q microdissection probe (Zink et al.,
1998b).
Acknowledgments
This work was supported by BMBF grant 01 KW 9620
(German Human Genome Project) and a grant from the
Deutsche Forschungsgemeinschaft (Cr 59/18-1). We
thank M. Tewes for suggesting overlap computations by
FFT and correlation functions, and H. Born¯eth for computing subcompartment volumes with his image analysis
software for a subset of our simulated chromosome 15
images.
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Edited by T. Richmond
(Received 7 September 1998; accepted 12 October 1998)