Statistical analysis of 3D images detects regular spatial distributions of centromeres and chromocenters in animal and plant nuclei.

Abstract

In eukaryotes, the interphase nucleus is organized in morphologically and/or functionally distinct nuclear "compartments". Numerous studies highlight functional relationships between the spatial organization of the nucleus and gene regulation. This raises the question of whether nuclear organization principles exist and, if so, whether they are identical in the animal and plant kingdoms. We addressed this issue through the investigation of the three-dimensional distribution of the centromeres and chromocenters. We investigated five very diverse populations of interphase nuclei at different differentiation stages in their physiological environment, belonging to rabbit embryos at the 8-cell and blastocyst stages, differentiated rabbit mammary epithelial cells during lactation, and differentiated cells of Arabidopsis thaliana plantlets. We developed new tools based on the processing of confocal images and a new statistical approach based on G- and F- distance functions used in spatial statistics. Our original computational scheme takes into account both size and shape variability by comparing, for each nucleus, the observed distribution against a reference distribution estimated by Monte-Carlo sampling over the same nucleus. This implicit normalization allowed similar data processing and extraction of rules in the five differentiated nuclei populations of the three studied biological systems, despite differences in chromosome number, genome organization and heterochromatin content. We showed that centromeres/chromocenters form significantly more regularly spaced patterns than expected under a completely random situation, suggesting that repulsive constraints or spatial inhomogeneities underlay the spatial organization of heterochromatic compartments. The proposed technique should be useful for identifying further spatial features in a wide range of cell types.

Full text

Page 1

Statistical Analysis of 3D Images Detects Regular Spatial
Distributions of Centromeres and Chromocenters in
Animal and Plant Nuclei
Philippe Andrey1,2,3,4., Kie ˆn Kie ˆu5., Cle ´mence Kress6., Gae ¨tan Lehmann7,8., Leı ¨la Tirichine9., Zichuan
Liu7,8.¤, Eric Biot1,2,3,9, Pierre-Gae ¨l Adenot7,8, Cathy Hue-Beauvais6, Nicole Houba-He ´rin9, Ve ´ronique
Duranthon7,8, Eve Devinoy6, Nathalie Beaujean7,8, Vale ´rie Gaudin9, Yves Maurin1,2,3, Pascale Debey7,8*
1INRA, UMR1197 Neurobiologie de l’Olfaction et de la Prise Alimentaire, Jouy-en-Josas, France, 2Universite ´ Paris-Sud 11, UMR 1197, Orsay, France, 3IFR144 Neuro-Sud
Paris, France, 4UPMC, Universite ´ Paris 06, France, 5INRA, UR341, Mathe ´matiques et Informatique Applique ´es, Jouy-en-Josas, France, 6INRA, UR1196 Ge ´nomique et
Physiologie de la Lactation, Jouy-en-Josas, France, 7INRA, UMR1198 Biologie du De ´veloppement et Reproduction, Jouy-en-Josas, France, 8ENVA, Maisons Alfort, France,
9INRA, Institut J.-P. Bourgin, UMR1318 INRA-AgroParisTech, Versailles, France
Abstract
In eukaryotes, the interphase nucleus is organized in morphologically and/or functionally distinct nuclear ‘‘compartments’’.
Numerous studies highlight functional relationships between the spatial organization of the nucleus and gene regulation.
This raises the question of whether nuclear organization principles exist and, if so, whether they are identical in the animal
and plant kingdoms. We addressed this issue through the investigation of the three-dimensional distribution of the
centromeres and chromocenters. We investigated five very diverse populations of interphase nuclei at different
differentiation stages in their physiological environment, belonging to rabbit embryos at the 8-cell and blastocyst stages,
differentiated rabbit mammary epithelial cells during lactation, and differentiated cells of Arabidopsis thaliana plantlets. We
developed new tools based on the processing of confocal images and a new statistical approach based on G- and F-
distance functions used in spatial statistics. Our original computational scheme takes into account both size and shape
variability by comparing, for each nucleus, the observed distribution against a reference distribution estimated by Monte-
Carlo sampling over the same nucleus. This implicit normalization allowed similar data processing and extraction of rules in
the five differentiated nuclei populations of the three studied biological systems, despite differences in chromosome
number, genome organization and heterochromatin content. We showed that centromeres/chromocenters form
significantly more regularly spaced patterns than expected under a completely random situation, suggesting that
repulsive constraints or spatial inhomogeneities underlay the spatial organization of heterochromatic compartments. The
proposed technique should be useful for identifying further spatial features in a wide range of cell types.
Citation: Andrey P, Kie ˆu K, Kress C, Lehmann G, Tirichine L, et al. (2010) Statistical Analysis of 3D Images Detects Regular Spatial Distributions of Centromeres and
Chromocenters in Animal and Plant Nuclei. PLoS Comput Biol 6(7): e1000853. doi:10.1371/journal.pcbi.1000853
Editor: Christophe Zimmer, Institut Pasteur, France
Received July 29, 2009; Accepted June 3, 2010; Published July 8, 2010
Copyright: ? 2010 Andrey et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This study has been supported by the AgroBI 2006–2008 INRA program. We thank the Re ´gion Ile-de-France for funding the purchase of a Leica TCS SP2
confocal microscope (INRA Versailles) and the Zeiss AxioObserver imaging Apotome system (INRA, Jouy). LT was funded by an INRA post-doctoral fellowship
(Department of Plant Biology) and LZ was supported by a grant from the French embassy in Beijing and the MRI at INRA. The funders had no role in study design,
data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: debey@mnhn.fr
¤ Current address: SKLRB, Institute of Zoology, CAS, Beijing, China
. These authors contributed equally to this work.
Introduction
In eukaryotes, the interphase nucleus is organized into distinct
nuclear ‘‘compartments’’, defined as macroscopic regions within
the nucleus that are morphologically and/or functionally distinct
from their surrounding [1]. Complex relationships between the
spatial organization of these compartments and the regulation of
genome function have been previously described. Furthermore,
changes in nuclear architecture are among the most significant
features of differentiation, development or malignant processes.
Thus, these findings question whether topological landmarks and/
or nuclear organization principles exist and, if so, whether these
architectural principles are identical in the animal and plant
kingdoms. To investigate nuclear organization principles, multi-
disciplinary approaches are required based on image analysis,
computational biology and spatial statistics.
Spatial distributions of several compartments, which can be
proteinaceous bodies or genomic domains, have been analyzed.
Chromosome territories (CT), areas in which the genetic content
of individual chromosomes are confined [2,3], are usually radially
distributed, with gene-rich chromosomes more centrally located
than gene-poor chromosomes. Some studies report that chromo-
some size could also influence CT location [4–7]. Centromeres
may be close to the nuclear periphery and those located on
chromosomes bearing ribosomal genes are generally tethered to
the nucleolar periphery [4]. Transcription sites, as well as early
PLoS Computational Biology | www.ploscompbiol.org1July 2010 | Volume 6 | Issue 7 | e1000853

Page 2

replicating foci, assumed to correspond to active chromatin, are
morecentrallylocated,whereasinactiveheterochromatintendstobe
at the nuclear periphery. At a finer level, active genes widely
separated in cis or located on different chromosomes can colocalize
toactivetranscriptionsites[8–10],whereasproximitytocentromeric
heterochromatin or to the nuclear periphery is generally associated
with gene silencing [11–14]. Changes in the transcriptional status of
genes have been frequently associated with their repositioning in the
nucleus relative to their CTs, the nuclear periphery or the repressive
centromeric heterochromatin [13,15–20]. Furthermore, large reor-
ganization in nuclear architecture (e.g. CTs, heterochromatic
compartments, centromeres, speckles, nucleoli,..) can accompany
some differentiation, development, malignant processes or natural
variations [21–32].
However, it still remains difficult to extract common rules and
establish comparisons due to various limitations. Indeed, most data
have been gathered on limited sets of nuclear elements in isolated
plant cell nuclei or in nuclei from immortalized animal cell lines
outside their physiological environment, except for circulating
blood cells. Little is known about possible differences in nuclear
organization of cells within their tissue [33]. Some studies
compared nuclear organization in primary cells versus cell lines,
in cell lines versus tissues, and in 2D culture versus 3D cultures;
these studies suggested that tissue architecture is involved in the
control of nuclear organization [34–36]. In addition, data on
nuclear organization in plant cell nuclei in situ are rare [37,38].
Finally, few three-dimensional (3D) studies and quantitative
measures have been performed to investigate spatial nuclear
organization [39–42].
The statistics used to analyze the data were mostly based on
radial patterns of nuclear elements, such as genes, chromosome
territories, and centromeres. Radial positions have been measured
with respect to the nuclear geometric center or the nuclear
envelope [43,44]. Spatial affinity between several elements has
been investigated and spatial correlations have been assessed
through central angles, for example between the radii joining
homologous chromosome territory centers and the nuclear center
[5,45]. Alternative approaches based on distances between
elements have been developed. Distances between a small number
of elements, like two pairs of homologous alleles, were used for
testing spatial attraction or repulsion [39]. Remarkably, spatial
statistics tools, such as distance functions, that have been
developed in ecology or epidemiology for analyzing spatial point
patterns [46] have rarely been applied in nuclear organization
studies. For example, (cross) nearest-neighbor distances have been
used to analyze large numbers of nuclear elements, such as
molecular complexes, PML bodies, or RNA Polymerase II foci
[47,48]. Alternatively, all pairwise inter-distances have been used
to analyze the spatial distribution of chromocenters [49] and
nucleocapsids [50].
In spatial statistics, data are usually collected through a
sampling window over a single realization of a point process.
This point process is generally considered as unbounded and
spatially homogeneous. Such a theoretical framework makes sense
in applications in which the investigated phenomenon extends far
beyond the observed region. By contrast, analyses of nuclear
spatial patterns are based on images of entire nuclei: the whole
domain of interest is observed. Furthermore, one should not
consider observed nuclear patterns as realizations of spatially
homogeneous point processes.
Another difference is that replicated data are available as the
analysis is carried out on a sample of nuclei. Recently, distance
functions have been extended to replicated spatially heterogeneous
point patterns [51,52]. For instance, an extended F-function has
been used for analyzing spatial patterns of transmissible spongi-
form encephalopathy lesions in brain tissue [53]. The extended F-
function takes into account the expected spatial heterogeneity of
the point process intensity. To estimate this intensity, the
replicated patterns are first registered to locate all observed points
in a common coordinate system. However, this type of preliminary
registration is not possible for nuclei due to the lack of identifiable
nuclear landmarks. Hence, further developments are required to
make spatial statistics tools appropriate for nuclear spatial
organization studies.
In this study, we develop an approach to furthering the analysis
of nuclear spatial organization. Spatial distributions of nuclear
compartments were quantified using the cumulative distribution
functions of nearest-neighbor distances (G-function) and of
distances between arbitrary points within the nucleus and their
nearest compartment (F-function). The analysis of G- and F-
functions was designed specifically to cope with patterns observed
in non-registered and variable (both in size and shape) domains.
We applied this new approach to the investigation of the 3D
distribution of centric/pericentric heterochromatin in five inter-
phase nuclei populations belonging to the animal and plant
kingdoms [54]. The centric/pericentric compartment was chosen
due to its dual structural and regulatory functions. Indeed, it
usually behaves as a transcription repressor and is essential for
genome organization and the proper segregation of genetic
information during cell division [55,56]. This compartment often
clusters and forms chromocenters [57–59]. We studied nuclei of
cells at various differentiation stages, in three biological systems:
rabbit embryos at the 8-cell and blastocyst stages, differentiated
rabbit mammary epithelial cells during lactation, and differenti-
ated cells of A. thaliana plantlets.
Wefoundnon-completelyrandomandsignificantlymoreregularly
spaced patterns than expected under complete randomness of the
centric/pericentric heterochromatin compartment in the five differ-
entiated cell populations, suggesting the existence of inter-kingdom
nuclear organizational rules and possible nuclear regularities.
Author Summary
Several reports suggest functional relationships within the
spatial organization of the nucleus, gene regulation and
cell differentiation. However, it still remains difficult to
extract common rules, mostly because i) most data have
been gathered on limited sets of nuclear elements and in
nuclei outside their normal physiological environment, and
ii) few three-dimensional (3D) quantitative measures have
been performed. Thus, we questioned whether common
nuclear organization principles exist in the animal and
plant kingdoms. For that purpose, we investigated the 3D
distribution of centromeres/chromocenters in five popu-
lations of animal and plant nuclei: rabbit embryos at 8-cell
and blastocyst stages, rabbit mammary gland epithelial
cells and Arabidopsis thaliana plantlets. We set up adapted
procedures to segment confocal images and developed a
new analytical methodology based on distances between
positions within the nucleus and centromeres/chromocen-
ters. We showed that in all systems, despite large
differences in chromosome number (44 in rabbit; 10 in A.
thaliana) and genome size (rabbit estimated size 2.77 Gbp;
A. thaliana 125 Mbp), centromeres/chromocenters form
significantly more regularly spaced patterns than expected
under a completely random situation. This suggests that,
whatever their specific features, conserved rules govern
the spatial distribution of genomes in nuclei of differen-
tiated cells.
Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org2July 2010 | Volume 6 | Issue 7 | e1000853

Page 3

Results
Centric/pericentric heterochromatin markers
The most common or comparable markers of the centromeres/
chromocenters were chosen in the three biological systems, rabbit
embryos, rabbit mammary gland and A. thaliana. The non-histone
heterochromatin protein 1 (HP1b) family plays an important role
in chromatin organization and transcriptional regulation of both
heterochromatin and euchromatin compartments [60,61]. Several
HP1 isoforms are usually present in higher eukaryotes with various
specificities and localization [60,62]. The human or mouse HP1b
isoform is usually used as marker for pericentric heterochromatin
regions. However, our preliminary experiments revealed that
immunodetection of HP1b in rabbit embryo, as well as in rabbit
mammary gland nuclei, did not exhibit enough contrast to
delineate the pericentromeric heterochromatin blocks (Figure 1A).
By contrast, immunolabeling of centromeric proteins (CENP)
using sera of patients with autoimmune diseases led to dots with
significant differences in contrast, which allowed the positioning of
the centromeres. HP1b–labeling was retained to label the whole
nucleus in embryos.
In A. thaliana, LHP1, the HP1 homolog, is mainly involved in
gene regulation and does not colocalize with centromeric
heterochromatin [63], and therefore could not be used to follow
heterochromatic centromeres. However, well-defined chromocen-
ters can be revealed by DAPI staining in interphase nuclei, which
mostly include centromeric and pericentromeric heterochromatic
regions [57,58].
Therefore, nuclei of rabbit embryos, mammary gland and A.
thaliana plantlets were labeled with CENP and HP1b, CENP and
DAPI, and DAPI alone, respectively to visualize centromeres/
chromocenters and the nuclear volume (Figures 1 and 2).
Acquisition conditions and resulting image collection
After acquisition and treatment of a first set of images, capture
conditions needed for a proper segmentation and for the best
quality measurements were set up. We paid particular attention to
i) the setup of the minimal (background) and maximal intensity
level, ii) the spacing of the optical planes, and iii) the procedure to
limit squeezing between slides and coverslips, particularly in the
case of whole embryos. The acquisition parameters defined at this
stage remained unchanged for the rest of the project. The resulting
collection of images and the acquisition protocols have been
deposited on the ICOPAN (‘‘A 3D Image Collection of Plant and
Animal Nuclei’’) website (http://amib.jouy.inra.fr/icopan).
Morphometric characterization of nuclei
Five populations of nuclei were analyzed. Nuclei were from
rabbit embryos at the 8-cell and blastocyst stages, and from rabbit
differentiated mammary epithelial cells (DMEC). DMEC nuclei
were easily identified among nuclei of other mammary cell types
based on their relative position within the tissue [64]. The DMEC
flank the lumen of acini and are surrounded by elongated
myoepithelial cells. Both cell types are buried within a stroma
composed of adipocytes, fibroblasts and vascular cells. In A.
thaliana plantlets, two populations of nuclei were analyzed based on
their shapes: rounded or elongated nuclei (Figure 2 A and A9).
The size and shape parameters were determined for the five
populations of nuclei and highlighted both a certain nuclear
diversity between the various systems and homogeneity within
each of them (Table 1, Figures 1 and 2). Shape analysis was
detailed by determining flatness, compactness, and elongation
indexes to characterize the 3D morphology of the studied nuclei.
At the two rabbit embryonic developmental stages, the nuclei
compactness value was rather low due to deep invaginations in the
nuclear volume (Figure 1A). At the 8-cell stage, flatness was high
(1.7, Table 1) and the main direction of flattening was closest to
the Z-axis for almost all nuclei (28/29). The observed flattening
may be due to the embryos being pressed between slides and
coverslips. For blastocyst nuclei, the proportion of nuclei with the
main direction of flattening close to the Z-axis was lower (25/41)
and the flatness parameter for the 16 other nuclei was close to the
overall average (1.36 vs 1.40). This suggested that, although
experimental artifacts were partly responsible of the observed
flattening, blastocyst nuclei were naturally relatively flat.
The observed DMEC nuclei were rather regular and spherical
(high compactness and low flatness values). The main direction of
flattening was closest to the Z-axis for most nuclei (57/79)
suggesting that the low observed flattening may be partly
experimental.
The three rabbit nucleus populations showed unimodal
distributions of volume, compactness and elongation, as expected
in homogeneous populations. In A. thaliana, the nuclear volume
within the population of rounded nuclei exhibited a unimodal
distribution (Figure 3A), as did compactness and elongation (data
not shown). Flatness distribution was also unimodal and was
concentrated in the lower flatness range (Figure 3B). The
distributions of the size and shape parameters thus confirmed
that, though they were not selected based on cellular type, the
rounded nuclei constitute a morphologically homogeneous
population. Similar homogeneous distributions were observed
within the population of elongated nuclei (data not shown). The
main direction of flattening was closest to the Z-axis for 76% (45/
59) of the rounded nuclei and flatness was close to 1 (i.e., no or
moderate flattening) for the remaining nuclei. Similar observations
were made within the population of elongated nuclei, in which
79% (48/58) of nuclei presented flattening oriented along the Z-
axis. Thus, nuclear flatness measurements in the five analyzed
populations suggested some experimental effects and a natural
flatness in rabbit blastocyst nuclei.
Detection of centromeres and chromocenters
Various segmentation procedures were developed to adapt to
the size and contrast of the objects. Centromeres in rabbit embryo
and mammary gland nuclei were revealed by CENP immunola-
beling. In both cases, images were denoised with median and
Gaussian filters, and the background lowered with a top-hat
transform by size. Some of the CENP spots appeared to be outside
of the nucleus mask, because of the elongation caused by the
microscope’s point spread function. To avoid truncating some of
the spots, the nuclear masks were enlarged with a morphological
dilation. Objects smaller than 0.02 mm3were then removed in the
masked CENP image.
In rabbit embryo, centromeres could not be extracted using a
fixed threshold over all nuclei because of the high level of
remaining background signal. Rather, the a priori knowledge of the
number of centromeres (44) was used in searching for a threshold
value that would produce, at most, 44 connected objects, starting
with a threshold of 1 and incrementing by 1.
With this method, mean values of 42.8 and 43.7 centromeres
were counted in rabbit 8-cell and blastocyst nuclei, respectively
(Table 1). To assess the quality of the segmentation, subsamples of
nuclei (6 at the 8-cell stage and 8 at the blastocyst stage) were
checked visually. This revealed that at the 8-cell stage, 2.7% of
segmented regions turned out not to be associated to HP1b
labeling and thus not to be centromeric spots (false positives) and
4.7% of centromeric spots (as assessed by their association with
HP1b labeling) were missed by the segmentation (false negatives).
Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org3July 2010 | Volume 6 | Issue 7 | e1000853

Page 4

Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org4July 2010 | Volume 6 | Issue 7 | e1000853

Page 5

The false positive rate was 4.9% at the blastocyst stage, whereas no
false negatives were identified. Finally, the centromeres were
mapped within the 3D nucleus model (Figure 1F) for subsequent
spatial analyses.
In rabbit mammary gland nuclei, a threshold computed as the
median of the 11 brightest regional maxima divided by 4 was
applied to each image. We identified a mean of about 38
centromeres per nucleus (Table 1). To visually check the result of
the segmentation process, all input images were overlaid with their
segmentations (Figure 1E9). Among 2996 segmented spots, 30
(1.0%) were considered to be false positives on the basis of their
size or position. About 20 centromeres (0.7%) were under the
threshold that had been set for intensity or size and were therefore
not detected during segmentation (false negatives). The total
number of visually detected centromeres was always lower than
44. Centromeres were mapped within the 3D nucleus model
(Figure 1F9) for subsequent spatial analysis.
In A. thaliana, chromocenters could not be accurately detected
via intensity thresholding. We thus developed an alternative
strategy based on the fact that chromocenters have spherical or
ellipsoidal shapes and present a positive contrast relative to their
immediate neighborhood. Using a 3D watershed transform [65],
the nucleus was partitioned into regions (Figure 2B). Each region
was assigned a value given by the average intensity in the
neighborhood of its barycenter. To correct for possible over-
segmentation of chromocenters or nucleoli, region merging was
repeatedly applied until all differences between values of adjacent
regions were above a predefined threshold. The contrast of non-
chromocenter regions adjacent to dark regions, such as the
nucleolus, was reduced using a morphological region closing
(Figure 2C). The contrast of each region was then computed as the
average difference between its value and those of its neighbors,
weighted by their sizes to limit the influence of small regions with
exceptionally high or low values.
The contrast of each region was multiplied by its compactness to
obtain a shape/contrast criterion that enhances chromocenters at
the expense of other regions, even if they display similar intensities
(Figure 2D). Using the ImageJ software [66], a threshold was then
interactively set to a value ensuring the extraction of all
chromocenters (Figure 2E). All segmentations were visually
checked and compared to the original images by an experienced
experimenter. Identified false positives were removed using the
Free-D software [67]. Finally, the chromocenter regions were
mapped within the 3D nucleus model (Figure 2 F and F9) for
subsequent spatial analysis and their sizes quantified by their
equivalent spherical diameters.
A few false negatives, generally corresponding to small and
weakly labeled chromocenters that had been smoothed out when
computing the Gaussian gradient, were also identified during the
visual examination of segmented images. For rounded A. thaliana
nuclei, the algorithm detected 470 chromocenters and the number
of false negatives was 27 (error rate of 5.4%). For the elongated
nuclei, 633 chromocenters were detected and 11 false negatives
were identified (error rate of 1.7%).
The number of detected chromocenters differed between
rounded and elongated nuclei (Table 1). Five to 10 chromocenters
(average 8.061.5) were detected per nucleus in rounded nuclei.
Our results therefore confirmed previously published data
indicating that A. thaliana diploid cells (2n=10) contain 4 to 10
chromocenters, due to a non-random association of homologous
chromocenters or the coalescence of chromocenters containing
rDNA repeats [58,68]. Six to 17 (average 10.962.4) chromocen-
ters were detected in elongated nuclei. Plants contain cell types
with different ploidy levels that may vary from 2C (where 1C is the
haploid genome complement) to 64C [69]. Previous studies
reported a positive correlation between polyploidy and nuclear
volume [38,70]. Our data thus suggested that elongated nuclei,
which on average contained more than 10 chromocenters and
were ,2 times larger than rounded nuclei (Table 1), were
extracted, at least for a certain proportion of them, from
endoreduplicated cells and that this population of nuclei
may represent nuclei from cells that have undergone further
differentiation.
Non-completely random distribution of centromeres/
chromocenters
Following the image processing stage, chromocenters and
centromeres were segmented as regions within nuclei. To analyze
their spatial distribution, all regions were represented by their
centers of gravity, with, in the A. thaliana case, their equivalent
spherical diameters. For the sake of brevity, we refer below to
chromocenters/centromeres to mean their centers of gravity, with,
in the A. thaliana case, their associated diameters.
Our method encompasses four key steps that can be
summarized as follows and will be detailed below:
– The spatial patterns of centromeres/chromocenters within
nuclei were quantified using two distance functions computed
for each imaged nucleus.
– For each centromere/chromocenter pattern, observed distance
functions were compared to the mean distance function
associated with a completely random point pattern conditioned
by the observed pattern size (number of points) and the
observed nuclear space. In such a completely random binomial
point process (CRBPP), points are distributed uniformly and
independently [71]. For chromocenters, a variant of CRBPP
was used involving a hardcore distance.
– Departures of observed distance functions from CRBPP mean
distance functions were scored using p-values. Below, those
scores will be referred to as spatial distribution indexes (SDI).
Clustered patterns yield values close to 0; regular (evenly
spaced) patterns yield values close to 1. The SDI of a CRBPP is
uniformly distributed between 0 and 1. The computation of
spatial indexes involves Monte-Carlo simulations.
– Statistical tests of departure from CRBPP were performed for
each cell population using a goodness-of-fit test on SDI
distributions.
Distance functions are standard tools in the statistical analysis of
spatial point processes [46]. The nearest neighbor distance
function G of a point pattern is the cumulative distribution
Figure 1. Image processing and 3D modeling of rabbit nuclei. (AA9) Single confocal microscopy sections. (A) Rabbit blastocyst nucleus, HP1b
(red) and CENP (green) immunolabeling. (A9) Rabbit nucleus of a mammary gland epithelial cell, CENP (green) immunolabeling and DAPI
counterstaining (blue). (BB9) Gaussian gradient magnitudes of nuclear staining images (HP1b or DAPI). (CC9) Overlay of nuclear contours (white) and
DNA/HP1b staining. Contours were obtained after applying a Gaussian gradient-weighted threshold to nuclear staining images. (DD9) Enhancement
of centromeric spots using top-hat filtering of CENP images. (EE9) Single section overlay of nuclear contours (white), CENP labeling, and centromeres
(color) obtained by thresholding DD9. Note that centromeres are distributed within the whole nucleus, and not confined to the nuclear periphery.
(FF9) Resulting 3D models with centromeres in dark blue. Scale bar: 2 mm.
doi:10.1371/journal.pcbi.1000853.g001
Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org5July 2010 | Volume 6 | Issue 7 | e1000853

Page 6

A’A
F’F
BC
DE
Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org6 July 2010 | Volume 6 | Issue 7 | e1000853

Page 7

function of the distance X between a typical point (i.e., a uniformly
randomly chosen point) of the pattern and its nearest neighbor
(Figure 4):
G x
ð Þ~P Xvx
ðÞ
Computing this function from the point pattern is straightforward.
The F-function is the cumulative distribution function of the
distance Y between a typical position within the nucleus and its
closest point in the pattern:
F y
ð Þ~P Yvy
ðÞ
Thus, F(y) is the nuclear volume fraction that lies at a distance less
than y from a point of the pattern. We are considering the
distribution of centromeres/chromocenters as a finite process
within the bounded nuclear space. To analyze populations of
nuclei, we developed an original strategy, based on F- and G-
functions, which does not require nucleus registration.
A stochastic scheme was adopted to compute the F-function
corresponding to a nuclear point pattern. A number of
independent evaluation points NEwere generated uniformly at
random within the nucleus. For each evaluation point, the distance
to the closest point of the pattern was determined (Figure 4). The
cumulative distribution function F(y) was then estimated by the
proportion of evaluation points for which this distance is below y.
Setting NEto 10000 was sufficient to smooth out the effect of
evaluation point sampling on the F-function.
To determine whether the spatial distribution of centromeres/
chromocenters obeys any organizational rule, the observed distri-
butions were compared against a completely random distribution,
conditioned on the observed numbers of centromeres/chromocen-
ters and, in A. thaliana, on chromocenter sizes. Due to the arbitrary
shape of the nucleus, the expected distance functions under CRBPP
cannot be determined analytically. A Monte-Carlo approach was
therefore adopted, whereby the distance functions were computed
over sets of patterns simulated according to CRBPP. For each
nucleus, random patterns were generated with the same number of
centromeres/chromocenters as detected within the nucleus. In A.
thaliana, each random point was also assigned the radius of one
chromocenter.Thishardcoredistancedefined a sphere withinwhich
no other point was allowed to fall and a minimum distance between
the point and the nuclear envelope. Taking care of rabbit
centromere sizes was not necessary because of their small size. The
CRBPP distance functions were estimated by computing averages
over a number P1=500 of such independent patterns.
Observed and CRBPP mean F-functions obtained for the three
nuclei from Figures 1A, 1A9 and 2A are displayed in Figure 5 (A:
rabbit embryo; B: rabbit mammary gland; C: A. thaliana leaflets). As
illustrated by these examples, the observed F-functions were
frequently located on the left side of the CRBPP ones, and presented
a steeper slope. On average, the observed distance between any
nuclear position and the closest centromere/chromocenter was thus
lower and less variable than expected under CRBPP. This suggests a
non-completely random and regular distribution of centromeres/
chromocenters within the nucleus (see Figure 4). Discerning any
particular trend by visually examining G-functions was much more
difficult (data not shown). This may be due to the fact that i) this
function is potentially less discriminant than the F-function and the
fact that ii) it was estimated from a smaller pool of data (number of
detected centromeres or chromocenters compared with an arbitrary
number of arbitrary positions for F-function).
The next step in our analysis was to test, at the population level,
the statistical significance of the differences between the observed F-
and G-functions and the CRBPP theoretical F- and G- functions.
Due to the arbitrary shape of the nucleus, the fluctuations under
CRBPP of the distance functions around their averages are not
analytically accessible and a Monte-Carlo approach was designed.
To avoid under-estimation of these variations, they were estimated
using a second set of randomly generated P2=500 patterns. For
each simulated pattern, the difference between its distance function
and the CRBPP theoretical function was defined as the signed
difference of maximum amplitude. Taking for example the F-
function, we thus have:
D~F x?
ðÞ{F0x?
ð Þ{F0x
ðÞ with x?such that F x?
ð Þ
ðÞ{F0x?
ðÞ
jj
~ max
x[<zF x
jj
Figure 2. Image processing and 3D modeling of Arabidopsis nuclei. (AA9) Single confocal microscopy section through a rounded (A) and
elongated (A9) nucleus. (B–E) Segmentation of the nuclear envelope and chromocenters. Following an initial partition of the 3D image using the
watershed transform (B), a closing morphological operation was applied to the region adjacency graph (C) and each region was assigned a shape/
contrast index (D). The chromocenters obtained by applying a threshold to the index map are shown in (E) as colored regions superimposed over the
corresponding single section image. The nuclear boundary (white contour) was obtained by applying a threshold to the original 3D image. Note that
chromocenters are distributed within the whole nucleus, and not confined to the nuclear periphery. (FF9) Resulting 3D models for the rounded (F)
and elongated (F9) nuclei. Scale bar: 1 mm.
doi:10.1371/journal.pcbi.1000853.g002
Table 1. Morphometric characterization of nuclei and number of detected centromeres/chromocenters.
TissueCell typenVolume (m mm3)Compactness FlatnessElongation
Centromeres [CM]
Chromocenters [CC]
Rabbit embryo8-cell stage29 1225 (346.1)0.40 (0.11) 1.7 (0.3)1.3 (0.2)42.8 (1.8) [CM]
Blastocyst stage 41 1140 (354.9)0.58 (0.13) 1.4 (0.2)1.2 (0.2) 43.7 (0.6) [CM]
Rabbit mammary gland Epithelium79 255 (28.4)0.84 (0.07)1.3 (0.2)1.2 (0.1) 37.9 (2.4) [CM]
Arabidopsis plantletsRound nuclei 59 83.4 (31.0)0.78 (0.12)1.5 (0.4)1.1 (0.1) 8.0 (1.5) [CC]
Elongated nuclei 58182.7 (62.5) 0.41 (0.08)1.7 (0.4)2.6 (0.6) 10.9 (2.4) [CC]
For each cellular type, the table gives the number of analyzed nuclei (n) and the average size (Volume) and shape parameters (Compactness, flatness, and elongation),
as well as the average numbers of detected centromeres (CM) or chromocenters (CC). Standard errors are given in parenthesis.
doi:10.1371/journal.pcbi.1000853.t001
Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org7July 2010 | Volume 6 | Issue 7 | e1000853

Page 8

where F0is the F-function under CRBPP computed using the
Monte-Carlo approach described above.
We also computed the difference between the observed pattern
distance function and that of the CRBPP; this yielded a total of
P2+1 differences. A p-value (the probability of observing, under
CRBPP, a difference at least as large as that observed) could then
be computed for each nucleus as the proportion of random
patterns with a difference equal to or above that observed. Since it
quantifies a spatial repartition, this p-value was called spatial
distribution index (SDI). For example, low values of the SDI
associated to the F-function indicate regularity in the patterns
(evenly distributed points) while high values correspond to
clustered patterns. Under the hypothesis that centromeres/
chromocenters obey CRBPP, the SDI within a population is
uniformly distributed between 0 and 1. Our test thus consists in
comparing the observed SDI distribution with the uniform
distribution. This was done using the two-sided Kolmogorov-
Smirnov test (a=5%) in the R statistical software package [72].
Within the five groups, the distributions of the SDI based on F-
function were significantly different from the uniform distribution






Figure 3. Distribution of size and shape parameters within the population of Arabidopsis rounded nuclei. (A) Histogram of nuclear
volume. (B) Histogram of nuclear flatness (defined as the length ratio between the intermediate and the shortest nuclear axes). The sample 3D
nuclear models illustrate low (red), moderate (blue), and high (green) flatness values.
doi:10.1371/journal.pcbi.1000853.g003
Figure 4. Spatial point patterns within the nucleus and distance functions. Centromere/chromocenter positions are represented as dots
within nuclear contours. (A) Various types of spatial distribution. Positions can be uniformly and independently distributed (completely random
pattern), or exhibit mutual attraction (aggregated pattern) or mutual repulsion (regular pattern). (B) The G-function is the cumulative distribution
function of the distance between each centromere/chromocenter and its nearest neighbor (orange lines). This distance tends to be small for
aggregated patterns and large for regular patterns. (C) The F-function is the cumulative distribution function of the distance between typical nuclear
positions (blue crosses) and their nearest centromere/chromocenter (orange lines). This distance tends to be large for aggregated patterns and small
for regular patterns.
doi:10.1371/journal.pcbi.1000853.g004
Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org8July 2010 | Volume 6 | Issue 7 | e1000853

Page 9

(Figure 6 and Table 2). Hence, the spatial distributions of
centromeres and chromocenters are different from the completely
random distribution. Besides, the histograms were concentrated in
the lower range of SDI (Figure 6), meaning that the observed F-
functions were generally above the CRBPP ones. This analysis
thus demonstrated that the centromeres or chromocenters tend to
form more regularly spaced patterns than expected under CRBPP.
For G-functions, the distributions of the SDI within the five groups
(data not shown) were also significantly different from the uniform
distribution (Table 2). The SDI histograms were concentrated in
the upper range, meaning that the observed G-functions were
generally below the CRBPP ones and that the nearest centro-









Figure 5. Sample observed and CRBPP estimated mean F-functions. (A) Rabbit blastocyst nucleus (same as in Fig. 1A). (B) Rabbit mammary
gland nucleus (same as in Fig. 1A9). (C) Arabidopsis rounded nucleus (same as in Fig. 2A). In each case, a 3D model of the centromere/chromocenter
positions within the nuclear envelope is displayed above the corresponding observed F-function (blue), the CRBPP mean F-function estimated by
Monte-Carlo simulations (orange), and the 95% envelope (dotted black).
doi:10.1371/journal.pcbi.1000853.g005














Figure 6. Histograms of the F-function-related spatial distribution index, within the five cellular types. For each nucleus, the SDI is the
probability of observing, under a completely random binomial point pattern, a difference at least as large as that observed between the empirical
and the CRBPP mean F-functions.
doi:10.1371/journal.pcbi.1000853.g006
Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org9 July 2010 | Volume 6 | Issue 7 | e1000853

Page 10

mere/chromocenter was on average farther away than expected
under CRBPP. Thus, though departure from complete random-
ness was less pronounced, analysis by G-function was consistent
with the results obtained with F-function.
Lastly, we examined whether the regularity of the spatial
distribution of centromeres or chromocenters could be explained
by the experimental flattening of the nuclei along the Z direction.
A link between flatness and SDI was tested on the nuclei with a Z-
oriented minor axis. As flatness (e.g., Figure 3B) and rank (Figure 6)
distributions largely deviate from normality, a non-parametric test
based on Kendall’s tau rank correlation [73] was applied (a=5%).
In A. thaliana (rounded and elongated nuclei) and blastocyst nuclei,
no correlation was found between flatness and the F-function-
associated SDI (Table 2). In 8-cell embryo and mammary gland
nuclei, correlations between flatness and F-function SDI turned
out to be significant (Table 2). However, the values of tau
remained rather small (about 30%). Therefore, even for those two
latter cell populations, the regularity of centromere patterns
cannot be considered as caused by flattening. Similarly, no relation
was found between nucleus flatness and the SDI associated with
G-function. Consequently, the possibility that flattening along the
Z direction is responsible for the regular spatial distribution of
centromeres/chromocenters was ruled out.
Discussion
The Rabl configuration observed in salamander [74], fission yeast
[75], drosophila embryos [76], as well as in some plants such as
Allium cepia [77], wheat, rye, barley and oats [78,79] but not in A.
thaliananorinmammals,isprobablythemostspectacularexampleof
a non-random organization in interphase nuclei. In this configura-
tion, the centromeres are clustered at one end of the nucleus and
telomeres at the opposite end. Besides this extremely recognizable
organization, detection of any regularity in the complex nuclear
organization is difficult and requires the development of specific 3D
image analysis and statistical tools. Indeed, as nuclei exhibit large
morphological fluctuations both within and between cellular types
[80], spatial normalization is required. However, no nuclear
landmark has yet been identified as a suitable reference to perform
this standardization [40]. In this study, we addressed this issue and
developed original tools adapted to various biological models,
allowing a common treatment of data and extraction of rules.
Building on well-established distance functions from spatial statistics,
we designed a new methodological framework to analyze replicated
samples without explicit nucleus registration.
Spatial statistics distance functions have only rarely been
applied to study nuclear organizations. Nearest neighbor distances
(G-function) have been used to characterize the spatial distribution
of transcription factors [47,48,81], centromeres [49], and other
nuclear compartments [82]. The distribution of all inter-distances
(quantified through the pair correlation function or the K- and L-
functions) has also been considered [49,81]. To our knowledge,
the present study is the first to rely on the F-function (the
cumulative distribution of the distance from arbitrary nuclear
positions to the nearest centromere/chromocenter) to investigate
nuclear architecture. In contrast to the F-function, the G, K and
L-functions and the pair correlation function only depend on the
relative positioning of the points within the pattern, irrespective of
their absolute positioning within the nucleus. For instance, a
translation of a clustered pattern from the nucleus center to its
periphery has no effect on the G-function while it will tend to shift
the F-function towards the left (larger empty nuclear region). Thus,
in the finite and bounded context of nuclear organization studies,
the F-function captures more information about spatial repartition
and therefore represents a potentially more discriminant and
sensitive tool to detect differences between spatial distributions. In
accordance with this, our results showed more pronounced
departure from complete randomness with F-function than with
G-function, be it in individual function plots or SDI distributions.
The J-function, a more recently introduced function [83],
combines the F- and G-functions and has an easy interpretation
for point patterns with random size. However, it needs to be
further elaborated for analyses conditioned on the number of
points.
The completely random patterns that were simulated here
contained a number of points equal to that actually observed in the
patterns and not to the number of chromosomes in the species. In
A. thaliana, it is known that centromeres aggregate into a variable
number of chromocenters. In the rabbit, exactly 44 centromeres
have never been visually observed in interphase nuclei, be it
because of aggregation, limited optical resolution, or labeling
issues. Hence, the number of chromosomes only provides an upper
bound on the expected number of points. For this reason, our
analysis has focused on the spatial distribution of observed patterns.
The F-function was computed using a Monte-Carlo scheme for
sampling the nuclear space. An alternative computational scheme
to estimate the F-function consists in computing the Euclidean
distance map (EDM) [84,85], which gives the distance between
each voxel of the nucleus and the closest voxel containing a
centromere or chromocenter center of gravity; the F-function is
then given by the normalized cumulative histogram of the distance
map. In our preliminary experiments, we have implemented,
tested, and compared the two approaches. We have retained the
estimation of F based on randomly generated points throughout
Table 2. Analysis of the spatial distribution of centromere/chromocenter: results of statistical tests.
F-functionG-function Correlation with flatness
TissueCell typenD p-valueDp-valuetaup-value
Rabbit embryo 8-cell stage290.62 3.0 10210
0.433.7 1025
20.270.04
Blastocyst stage 410.503.4 1029
0.34 1.2 1024
20.10 0.48
Rabbit mammary gland Epithelium 790.74
,2.2 10216
0.422.4 10212
20.240.01
Arabidopsis plantletsRound nuclei590.49 1.0 10212
0.267.2 1024
0.020.88
Elongated nuclei58 0.46 3.9 10211
0.365.8 1027
20.040.69
For F- and G-functions, the table gives the statistic (D) and the p-value of the bilateral Kolmogorov-Smirnov test that was used to assess differences between observed
distributions and completely random patterns. The table also gives the statistic (tau) and the p-value of the Kendall’s rank correlation test that was used to assess a link
between observed centromere/chromocenter spatial distributions and nucleus flatness. n: number of analyzed nuclei.
doi:10.1371/journal.pcbi.1000853.t002
Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org 10July 2010 | Volume 6 | Issue 7 | e1000853

Page 11

the nucleus for essentially two reasons. The first one is that this
approach retains the subpixel precision at which the positions
(centers of mass) of centromeres and chromocenters are computed.
On the contrary, using distance maps introduces a loss of precision
because these positions must be rounded to voxel (integer)
coordinates. This is not critical in our case because the voxel size
is small as compared to the nucleus size. However, this effect could
bias the analysis when processing data extracted from images with
large voxel sizes. The second reason is computational efficiency:
our experience did not reveal any computational advantage of the
EDM approach over the stochastic one.
Standard methods for computing empirical G- and F-functions
usually include boundary corrections [86]. Since point patterns are
traditionally observed within sampling windows, nearest point
distances can indeed be over-estimated due to the exclusion of
some points from the experiment. For the G-function, for
example, the Hanisch correction [87] consists in discarding the
recorded points whose nearest neighbor is farther than the
boundary. Such standard estimation corrections have been applied
in studies on nuclear patterns [49,81]. In this context, however, no
point (here, centromere or chromocenter) is expected outside the
nucleus. Hence, edge-corrections should be all the more avoided.
Indeed they may decrease statistical power by reducing the
number of analyzed points and potentially bias the analysis,
especially if the assumed sampling window is computed from the
pattern itself [49]. To obtain unbiased estimates of G- and F-
functions, we proposed an alternative computational scheme that
takes into account the actual boundary of the nucleus and involves
no edge-correction.
Previous spatial statistical analyses of populations of nuclei have
been conducted based on distance functions either averaged
without normalization [49,81] or pooled after standardization with
respect to the greatest inter-object distance, to account for nuclear
size fluctuations [47]. This left the difficult issue of nuclear shape
normalization unsolved. A first significant contribution of the
approach described here is to take into account both size and
shape variability. This was achieved by comparing, for each
nucleus, the observed distribution against a reference distribution
estimated by Monte-Carlo sampling within the same nucleus. This
implicit normalization (each nucleus being its own reference)
circumvents the unfeasibility of an explicit nucleus registration in
the absence of identified nuclear reference points [40]. A second
significant contribution of the present study is the introduction of a
test for complete randomness at the population level. For each
nucleus, the departure from the completely random spatial
distribution was quantified through a spatial distribution index
(SDI). This SDI could have been used to independently classify
each centromere or chromocenter pattern as completely random
(CRBPP) or not. Then a global conclusion concerning the
population level could have been drawn by a simple proportion
test. However, by such a binarization of the SDIs, one focuses
mainly on extreme patterns (clustered or regular) and may fail to
detect slight deviations from complete randomness. Avoiding
binarization gives more sensitivity to detect spatial structure.
Overall, our methodology therefore allows for sensitive and
unbiased statistical assessment of distribution differences against
reference distributions. Using this approach, we showed that, in
three biological systems belonging to plant and animal kingdoms
and in the five types of interphase nuclei, centromeres/
chromocenters form significantly more regularly spaced patterns
than expected under a complete random situation. Interestingly,
this feature was found in biological systems with extremely
different numbers of chromosomes (44 in rabbit versus 10 in A.
thaliana) and different genome sizes (rabbit estimated size
2.77 Gbp; J. Johnson, Broad Institute, personal communication
[https://www.broadinstitute.org/ftp/pub/assemblies/mammals/
rabbit/oryCun2/Stats.pdf]; A. thaliana last estimated size 125 Mbp
[http://arabidopsis.org/portals/genAnnotation/], [88]). This sug-
geststhat conservedrulesgovernthespatial distributionof genomes,
whatever their specific features.
In A. thaliana, 2D analyses suggested non-uniform distributions
of some nuclear elements, such as telomeres, mostly localized in
the vicinity of the nucleolus [89], as well as the non-random
association of homologous chromocenters or chromocenters that
contain homologous rDNA repeats [58]. More recent studies
based on 3D imaging suggested the existence of a radial
arrangement pattern in A. thaliana interphase nuclei, with
centromeres localized predominantly at the nuclear periphery
[43,90]. Our results are consistent with a non-random distribution
of A. thaliana heterochromatic domains, but further demonstrate
their tendency to form regular patterns. The prevailing hypothesis
about the spatial organization of A. thaliana interphase nuclei is that
of a globally random distribution of chromosome territories under
non-specific constraints and interactions [2,90,91]. According to
this view, the regular distribution of chromocenters we have
observed could merely result from the partitioning of the nucleus
into distinct chromosome territories. Whether more specific
mechanisms of mutual repulsion exist remains to be elucidated,
but in any case, the concomitant aggregation of some centromeres
into chromocenters and the regular distribution of chromocenters
suggest that constraints or control mechanisms are exerted at
multiple scales to determine the positioning of heterochromatic
domains in A. thaliana nuclei.
A priori, a SDI distribution may differ from CRBPP due to
spatial heterogeneity or due to spatial interactions (or both). The
volume occupied by the nucleoli, which can be rather large in
some biological systems (rabbit), are sources of heterogeneity that
have not been taken into account in our analyses since simulated
points could fall anywhere within the nucleus. However, the only
bias that may have resulted from neglecting these excluded nuclear
regions is a bias toward artifact aggregation. Preliminary
calculations, performed on a subset of rabbit nuclei, showed that
taking into account the nucleolus volume accentuated the
deviation from the CRBPP (data not shown). This confirmed that
the observed regular dispersion of centromeres/chromocenters
was not due to nucleoli volume omission. Nevertheless, further
developments will be necessary to integrate the nucleoli into the
3D nuclear modeling and analyses. Other spatial inhomogeneities,
due for example to the size and nuclear position of the
chromosome territories, may also impact on the distribution of
centromeres/chromocenters, especially in species with a large
range of chromosome sizes and shapes (e.g. rabbit) [92]. It would
therefore be interesting to refine the model by taking into account,
whenever possible, the identity of all or most of centromeres/
chromocenters. In rabbit, probes allowing the detection of four
centromeric DNA families are already available [93].
Previous authors have reported clustering of pericentric
heterochromatin during terminal differentiation, e.g. during
myogenenesis [94], in human neutrophils [28], human and mouse
neurons [95,96] and rat myoblasts [97]. In these biological models,
centromeres cluster into chromocenters and comparisons between
undifferentiated and differentiated cell nuclei show that the
number of chromocenters decreases during the differentiation
process. These results may seem contradictory with the regular
patterns revealed by the F-function, especially in A. thaliana in
which chromocenters are also observed. However, our analysis
concerned the spatial distribution of chromocenters instead of
their number. In particular, each given observed pattern of
Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org 11July 2010 | Volume 6 | Issue 7 | e1000853

Page 12

chromocenters was compared with simulated random patterns of
the same size. Results showed that the observed patterns are more
regularly spaced than completely random patterns of the same
size. Therefore, it appears that centromeres in A. thaliana
differentiated cells cluster into chromocenters that are regularly
spaced within the nucleus. In differentiated rabbit cells, centro-
meres do not form chromocenters, but the numbers of detected
centromeres in mammary gland cells indicate that a small fraction
of centromeres may cluster. In the rabbit mammary gland model,
centromeres and a few small clusters of centromeres are more
regularly spaced than completely random patterns.
The approach and the tools we developed could now be applied
to other nuclear compartments and -even more interestingly- to
other differentiation stages, to determine whether this tendency to
form more regularly spaced patterns than expected under
complete randomness might represent a ‘‘signature’’ of the
differentiated states. This methodology can also be generalized
to investigate further the properties of intra-nuclear spatial
distributions. Indeed, our strategy consists in comparing, on the
basis of appropriate distance functions, observed nuclear organi-
zations to patterns simulated from a reference distribution.
Introducing constraints on the simulated point patterns, as for
example interactions with the nuclear envelope or other nuclear
compartments, will allow evaluating further hypotheses beyond
randomness.
Materials and Methods
Ethics statement
All experiments involving animals were carried out according to
European regulations on animal welfare.
Biological materials
All animals were handled following ethical rules for animal welfare
according to the INRA ethics statement. Rabbit embryos were
obtained by natural fertilization of superovulated mature New
Zealand White rabbit females, as already described [98,99].
Superovulation was induced by two 0.25 mg, two 0.65 mg and one
0.25 mg intramuscular injections of follicle-stimulating hormone
(FSH,Stimufol, Me ´rial, Lyon, France) given 12 hours apart. Females
were mated with males 12 hours after the last FSH injection and 30
IU of human chorionic gonadotropin (hCG, Choluron, Intervet,
Angers, France) was injected a few minutes after mating. In rabbit,
fertilization occurred at ,12 hours post coitum (hpc). Two-cell
embryos were collected in the rabbit oviduct at 24 hpc and were
further cultured in vitro in B2 medium supplemented with 2.5% fetal
calf serum (Sigma) in 5% CO2atmosphere at 38.5uC until the 8-cell
(48 hpc) and blastocyst (100 hpc) stages.
Mammary glands were collected from 16-day lactating New
Zealand INRA-1077 rabbits, one hour after suckling. Mammary
gland tissues were cut into small pieces, fixed in 4% paraformal-
dehyde (PFA) in phosphate-buffered saline (PBS) for 30 min at
room temperature (RT), washed three times with PBS and
equilibrated in 40% sucrose before embedding in Cryomount
(Histolab) and snap freezing in liquid nitrogen. Samples were
conservedat280uC.Cryosectionsofabout14 mminthicknesswere
prepared on a Reichert Jung cryo-microtome (Leica, Wetzlar,
Germany), deposited on slides (SuperFrost Plus glass slides, Menzel-
Gla ¨ser J1800AMNZ) and stored at 280uC until use.
A. thaliana plantlets (Col-0 accession) were grown in vitro as
previously described [25]. Three-week-old plantlets were fixed for
30 min in 4% PFA in PBS buffer (PFA-PBS), under vacuum, at
room temperature. The fixative was replaced, and plantlets were
fixed for an additional 30 min in the same conditions. Up to 8 fixed
seedlings were transferred into anEppendorftube and gentlyground
in 500 ml of extraction buffer (10 mM Tris HCl pH 7, 4 mM
spermidine, 1 mM spermine, 5 mM MgCl2, 0.1% triton X-100,
5 mM b-mercaptoethanol). Nuclei suspension was filtered through a
50 mm nylon mesh. After gentle centrifugation (5006g, 3 min), the
pelletwas washed in16PBS,treated with 0.5%triton X-100 inPBS
and washed in PBS. Nuclei were resuspended in 30 ml PBS.
Immunoprocessing and labeling
Rabbit embryos at 8-cell and blastocyst stages were fixed
overnight at 4uC in 4% PFA-PBS, permeabilized 30 min at RT
with 0.5% Triton X-100, and blocked with 3% bovine serum
albumin in PBS (BSA-PBS) for 1 hour [30].
Fixed mammary gland sections were incubated in 50 mM
NH4Cl in PBS for 15 min and washed with PBS. They were then
permeabilized with 0.5% Triton X-100 for 30 min at RT, washed
again with PBS, and blocked with 2% BSA-PBS for 1 hour at RT.
Immunoprocessing was then similar for rabbit embryos and
mammary gland sections. Fixed embryos and slides with fixed
mammary gland sections were incubated with the primary
antibodies overnight at 4uC in 2% BSA-PBS. After three washes
with 0.05% or 0.1% tween-20 in PBS at RT (15 min each),
incubation with the secondary antibodies was performed for
1 hour in 2% BSA-PBS at RT followed by three washes (10 min
each) with 0.1% tween-20 in PBS at RT. For double immuno-
staining, primary antibodies and secondary antibodies were mixed
together at the same final dilutions as for simple immunodetection.
Rabbit embryos were then deposited on slides and mounted in
VECTASHIELD medium (Vector laboratories, Burlingame, CA).
Mammary gland sections were washed once in PBS, counter-
stained with DAPI (1 mg/ml in PBS for 5 min, at RT), washed in
PBS for 5 min at RT and mounted under a coverslip with
ProLong Gold antifade reagent (Invitrogen).
The suspension of A. thaliana nuclei was spotted on a slide and
left to evaporate at 4uC for 20 min, before mounting in
VECTASHIELD medium with 1 mg/ml of DAPI for DNA
counterstaining.
Antibodies
HP1b was detected with a mouse monoclonal anti-HP1b
antibody (clone 1 MOD 1A9, dilution 1:250), and revealed with a
lissamine–rhodamine-conjugated anti-mouse secondary antibody
(Jackson ImmunoResearch, dilution 1:150). Centromeres were
detected in rabbit embryos and in rabbit mammary glands by a
human autoantibody against centromeres (HCT-0100, Immuno-
vision, dilution1:300) followed by FITC-conjugated donkey anti-
human antibody (Jackson ImmunoResearch, dilutions 1:150 in
rabbit embryos and 1:300 in rabbit mammary glands).
Imaging
Embryos were scanned with a Zeiss LSM 510 confocal laser-
scanning microscope equipped with a 663/NA 1.4 oil immersion
objective. Z stack images were acquired at intervals of 0.24 mm
with 488-, 543- and 633-nm wavelengths of the lasers and with an
XY voxel size of 0.04 mm.
Images of mammary gland sections were captured with an
optical sectioning microscope attached to an AxioObserver
imaging Apotome system (Zeiss) (663/NA 1.4 oil immersion
objective). Z stack images were acquired at intervals of 0.24 mm on
two channels (DAPI and FITC), with an XY voxel size of 0.1 mm.
A. thaliana nuclei images were captured on a Leica DM IRE2
SP2 AOBS spectral confocal microscope equipped with a 405 nm
diode (25 mW) using a 663 HCX PL APO objective (NA 1.2). Z
Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org12July 2010 | Volume 6 | Issue 7 | e1000853

Page 13

stack images were acquired at intervals of 0.122 mm, with an XY
voxel size of 0.05 mm.
The anisotropy of voxel sizes in XY-Z was taken into account in
all subsequent image processing and spatial analysis procedures.
Images can be freely retrieved in their native formats together
with detailed acquisition protocols at the ICOPAN Website
(http://amib.jouy.inra.fr/icopan).
Definition of the nuclear periphery from HP1b and DAPI
labeling
Nucleus contours were determined on the HP1b (embryos) and
DAPI (mammary gland and A. thaliana) images.
Images of rabbit nuclei were denoised with a median filter and a
Gaussian filter. They were subsequently segmented through two
different pathways.
HP1b images (embryos), on which several nuclei are present,
were analyzed with the Insight Toolkit (ITK) library. The robust
automatic threshold selection method (RATS) [100] was used to
compute a threshold to ‘binarize’ the HP1b images. The threshold
is computed as the mean of the intensity values in the HP1b image
weighted by their Gaussian gradient magnitude. To avoid the high
gradient values in the nucleus caused by non-homogeneous
content, the small bright and dark zones were removed with a
3D area opening and a grayscale fill hole transformation before
computing the gradient. The joined masks of nuclei were
separated using a watershed transform on the distance map.
Truncated nuclei at the image border as well as objects smaller
than 200 mm3were removed.
A semi-automated procedure was developed to segment
mammary gland nuclei from the DAPI image. DAPI signal was
denoised with a median and a Gaussian filter, and manually
thresholded to produce partial nuclear masks. The DAPI signal
was mostly present on the border of the nuclei. As a result,
thresholding this signal results in an incomplete nucleus, in which
the center is not filled and the border is not continuous. The
nuclear borders were thus closed with a morphological closing
transform with a large round kernel, and content of the nuclei was
filled with a binary hole filling transform. The masks of the
different nuclei were then separated by a watershed transform on
the distance map, and the nuclei from the cell types of interest
were manually selected.
Confocal image stacks of A. thaliana nuclei were processed and
analyzed with programs developed using the Free-D software
libraries [67]. Each image stack contained a single nucleus. Images
were automatically cropped to limit processing to a bounding box
surrounding the nucleus. To separate the nucleus from the
background, a preliminary intensity threshold was then computed
using the isodata algorithm [101]. This algorithm is sensitive to the
relative size of the nucleus within the image. As a result, the
threshold was generally too high because of the larger background
size. To correct for this bias, the intensity average m and standard-
deviation s were computed over the nucleus region defined by the
preliminary threshold and the actual threshold was set to m-2s.
The resulting binary image generally contained holes, correspond-
ing in particular to the nucleolus, and presented boundary
irregularities due to noise. In addition, bumps were also observed
on some nuclei at their basal and apical faces, because of blur from
chromocenters [39]. Hole filling, opening and closing binary
morphological operators [65] were therefore applied to regularize
the binary image. The subsequent processing and analyses were
confined to this final nucleus mask. A surface model of the nuclear
envelope was generated by applying the marching cubes algorithm
[102] to the binary mask.
Morphometric analysis of nuclei
Nuclear size was quantified by nuclear volume. Nuclear shape
was quantified using the compactness parameter, which is given
by:
Compactness~36pVolume2
Surface area3
This parameter takes its maximum value 1.0 for a sphere and
decreases toward 0.0 as the shape surface becomes less regular.
Visual image examination revealed that some nuclei were
flattened along the Z-axis; thus, a flatness parameter was defined,
based on the lengths of the principal axes of the nuclear surface:
Flatness~Length of intermediate axis
Length of shortest axis
Symmetrically, an elongation parameter was also defined:
Elongation~
Length of longest axis
Length of intermediate axis
The main direction of flattening (resp. elongation) was defined by
the coordinate frame axis that was the closest to the shortest (resp.
the longest) principal axis of the nucleus.
Acknowledgments
We are grateful to Olivier Grandjean and Lionel Gissot, to the PCIV
platform (INRA Versailles), as well as the RIO MIMA2 platform (INRA
Jouy-en-Josas) for technical support in confocal imaging. We thank Jasmine
Burguet (NOPA, INRA) for fruitful discussions and for comments on the
manuscript. We are also thankful to the anonymous reviewers for their
close examination of our work and their useful comments on the initial
version of the manuscript.
Author Contributions
Conceived and designed the experiments: PA KK ED NB VG YM PD.
Performed the experiments: CK LT ZL. Analyzed the data: PA KK CK
GL EB PGA ED NB VG YM PD. Contributed reagents/materials/
analysis tools: CHB NHH VD. Wrote the paper: PA KK CK GL ED NB
VG PD.
References
1. Misteli T (2005) Concepts in nuclear architecture. Bioessays 27: 477–487.
2. Pecinka A, Schubert V, Meister A, Kreth G, Klatte M, et al. (2004)
Chromosome territory arrangement and homologous pairing in nuclei of
Arabidopsis thaliana are predominantly random except for NOR-bearing
chromosomes. Chromosoma 113: 258–269.
3. Cremer T, Cremer M, Dietzel S, Muller S, Solovei I, et al. (2006) Chromosome
territories–a functional nuclear landscape. Curr Opin Cell Biol 18: 307–
316.
4. Mayer R, Brero A, von Hase J, Schroeder T, Cremer T, et al. (2005) Common
themes and cell type specific variations of higher order chromatin arrange-
ments in the mouse. BMC Cell Biol 6: 44.
5. Bolzer A, Kreth G, Solovei I, Koehler D, Saracoglu K, et al. (2005) Three-
dimensional maps of all chromosomes in human male fibroblast nuclei and
prometaphase rosettes. PLoS Biol 3: e157.
6. Croft JA, Bridger JM, Boyle S, Perry P, Teague P, et al. (1999) Differences in
the localization and morphology of chromosomes in the human nucleus. J Cell
Biol 145: 1119–1131.
7. Cremer M, von Hase J, Volm T, Brero A, Kreth G, et al. (2001) Non-random
radial higher-order chromatin arrangements in nuclei of diploid human cells.
Chromosome Res 9: 541–567.
8. Hu Q, Kwon YS, Nunez E, Cardamone MD, Hutt KR, et al. (2008)
Enhancing nuclear receptor-induced transcription requires nuclear motor and
Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org 13July 2010 | Volume 6 | Issue 7 | e1000853

Page 14

LSD1-dependent gene networking in interchromatin granules. Proc Natl Acad
Sci U S A 105: 19199–19204.
9. Faro-Trindade I, Cook PR (2006) Transcription factories: structures conserved
during differentiation and evolution. Biochem Soc Trans 34: 1133–1137.
10. Osborne CS, Chakalova L, Mitchell JA, Horton A, Wood AL, et al. (2007) Myc
dynamically and preferentially relocates to a transcription factory occupied by
Igh. PLoS Biol 5: e192.
11. Zink D, Amaral MD, Englmann A, Lang S, Clarke LA, et al. (2004)
Transcription-dependent spatial arrangements of CFTR and adjacent genes in
human cell nuclei. J Cell Biol 166: 815–825.
12. Dietzel S, Zolghadr K, Hepperger C, Belmont AS (2004) Differential large-
scale chromatin compaction and intranuclear positioning of transcribed versus
non-transcribed transgene arrays containing beta-globin regulatory sequences.
J Cell Sci 117: 4603–4614.
13. Francastel C, Walters MC, Groudine M, Martin DI (1999) A functional
enhancer suppresses silencing of a transgene and prevents its localization close
to centrometric heterochromatin. Cell 99: 259–269.
14. Brown KE, Guest SS, Smale ST, Hahm K, Merkenschlager M, et al. (1997)
Association of transcriptionally silent genes with Ikaros complexes at
centromeric heterochromatin. Cell 91: 845–854.
15. Brown JM, Leach J, Reittie JE, Atzberger A, Lee-Prudhoe J, et al. (2006)
Coregulated human globin genes are frequently in spatial proximity when
active. J Cell Biol 172: 177–187.
16. Merkenschlager M, Amoils S, Roldan E, Rahemtulla A, O’Connor E, et al.
(2004) Centromeric repositioning of coreceptor loci predicts their stable
silencing and the CD4/CD8 lineage choice. J Exp Med 200: 1437–1444.
17. Kim SH, McQueen PG, Lichtman MK, Shevach EM, Parada LA, et al. (2004)
Spatial genome organization during T-cell differentiation. Cytogenet Genome
Res 105: 292–301.
18. Chambeyron S, Bickmore WA (2004) Chromatin decondensation and nuclear
reorganization of the HoxB locus upon induction of transcription. Genes Dev
18: 1119–1130.
19. Cammas F, Oulad-Abdelghani M, Vonesch JL, Huss-Garcia Y, Chambon P,
et al. (2002) Cell differentiation induces TIF1beta association with centromeric
heterochromatin via an HP1 interaction. J Cell Sci 115: 3439–3448.
20. Bartova E, Kozubek S, Jirsova P, Kozubek M, Gajova H, et al. (2002) Nuclear
structure and gene activity in human differentiated cells. J Struct Biol 139:
76–89.
21. Koehler D, Zakhartchenko V, Froenicke L, Stone G, Stanyon R, et al. (2009)
Changes of higher order chromatin arrangements during major genome
activation in bovine preimplantation embryos. Exp Cell Res 315: 2053–2063.
22. Bartova E, Krejci J, Harnicarova A, Kozubek S (2008) Differentiation of
human embryonic stem cells induces condensation of chromosome territories
and formation of heterochromatin protein 1 foci. Differentiation 76: 24–32.
23. Merico V, Barbieri J, Zuccotti M, Joffe B, Cremer T, et al. (2007) Epigenomic
differentiation in mouse preimplantation nuclei of biparental, parthenote and
cloned embryos. Chromosome Res 15: 341–360.
24. Meshorer E, Misteli T (2006) Chromatin in pluripotent embryonic stem cells
and differentiation. Nat Rev Mol Cell Biol 7: 540–546.
25. Tessadori F, Chupeau MC, Chupeau Y, Knip M, Germann S, et al. (2007)
Large-scale dissociation and sequential reassembly of pericentric heterochro-
matin in dedifferentiated Arabidopsis cells. J Cell Sci 120: 1200–1208.
26. Terranova R, Sauer S, Merkenschlager M, Fisher AG (2005) The reorganisa-
tion of constitutive heterochromatin in differentiating muscle requires HDAC
activity. Exp Cell Res 310: 344–356.
27. Stadler S, Schnapp V, Mayer R, Stein S, Cremer C, et al. (2004) The
architecture of chicken chromosome territories changes during differentiation.
BMC Cell Biol 5: 44.
28. Beil M, Durschmied D, Paschke S, Schreiner B, Nolte U, et al. (2002) Spatial
distribution patterns of interphase centromeres during retinoic acid-induced
differentiation of promyelocytic leukemia cells. Cytometry 47: 217–225.
29. Zink D, Fischer AH, Nickerson JA (2004) Nuclear structure in cancer cells. Nat
Rev Cancer 4: 677–687.
30. Martin C, Beaujean N, Brochard V, Audouard C, Zink D, et al. (2006)
Genome restructuring in mouse embryos during reprogramming and early
development. Dev Biol 292: 317–332.
31. Tessadori F, Schulkes RK, van Driel R, Fransz P (2007) Light-regulated large-
scale reorganization of chromatin during the floral transition in Arabidopsis.
Plant J 50: 848–857.
32. Tessadori F, van Zanten M, Pavlova P, Clifton R, Pontvianne F, et al. (2009)
Phytochrome B and histone deacetylase 6 control light-induced chromatin
compaction in Arabidopsis thaliana. PLoS Genet 5: e1000638.
33. Mateos-Langerak J, Goetze S, Leonhardt H, Cremer T, van Driel R, et al.
(2007) Nuclear architecture: Is it important for genome function and can we
prove it? J Cell Biochem 102: 1067–1075.
34. Kaminker P, Plachot C, Kim SH, Chung P, Crippen D, et al. (2005) Higher-
order nuclear organization in growth arrest of human mammary epithelial
cells: a novel role for telomere-associated protein TIN2. J Cell Sci 118:
1321–1330.
35. Meaburn KJ, Misteli T (2008) Locus-specific and activity-independent gene
repositioning during early tumorigenesis. J Cell Biol 180: 39–50.
36. Chandramouly G, Abad PC, Knowles DW, Lelievre SA (2007) The control of
tissue architecture over nuclear organization is crucial for epithelial cell fate.
J Cell Sci 120: 1596–1606.
37. Costa S, Shaw P (2006) Chromatin organization and cell fate switch respond to
positional information in Arabidopsis. Nature 439: 493–496.
38. Baroux C, Pecinka A, Fuchs J, Schubert I, Grossniklaus U (2007) The triploid
endosperm genome of Arabidopsis adopts a peculiar, parental-dosage-
dependent chromatin organization. Plant Cell 19: 1782–1794.
39. Ronneberger O, Baddeley D, Scheipl F, Verveer PJ, Burkhardt H, et al. (2008)
Spatial quantitative analysis of fluorescently labeled nuclear structures:
problems, methods, pitfalls. Chromosome Res 16: 523–562.
40. Shiels C, Adams NM, Islam SA, Stephens DA, Freemont PS (2007)
Quantitative analysis of cell nucleus organisation. PLoS Comput Biol 3: e138.
41. Gue M, Sun JS, Boudier T (2006) Simultaneous localization of MLL, AF4 and
ENL genes in interphase nuclei by 3D-FISH: MLL translocation revisited.
BMC Cancer 6: 20.
42. Mahy NL, Perry PE, Gilchrist S, Baldock RA, Bickmore WA (2002) Spatial
organization of active and inactive genes and noncoding DNA within
chromosome territories. J Cell Biol 157: 579–589.
43. Fang Y, Spector DL (2005) Centromere positioning and dynamics in living
Arabidopsis plants. Mol Biol Cell 16: 5710–5718.
44. Rosin FM, Watanabe N, Cacas JL, Kato N, Arroyo JM, et al. (2008) Genome-
wide transposon tagging reveals location-dependent effects on transcription and
chromatin organization in Arabidopsis. Plant J 55: 514–525.
45. Kozubek S, Lukasova E, Jirsova P, Koutna I, Kozubek M, et al. (2002) 3D
Structure of the human genome: order in randomness. Chromosoma 111:
321–331.
46. Diggle PJ, ed (2003) Statistical Analysis of Spatial Point Patterns. 2nd edition
ed: A Hodder Arnold Publication.
47. McManus KJ, Stephens DA, Adams NM, Islam SA, Freemont PS, et al. (2006)
The transcriptional regulator CBP has defined spatial associations within
interphase nuclei. PLoS Comput Biol 2: e139.
48. Young DW, Zaidi SK, Furcinitti PS, Javed A, van Wijnen AJ, et al. (2004)
Quantitative signature for architectural organization of regulatory factors using
intranuclear informatics. J Cell Sci 117: 4889–4896.
49. Beil M, Fleischer F, Paschke S, Schmidt V (2005) Statistical analysis of the
three-dimensional structure of centromeric heterochromatin in interphase
nuclei. J Microsc 217: 60–68.
50. Buser C, Fleischer F, Mertens T, Michel D, Schmidt V, et al. (2007)
Quantitative investigation of murine cytomegalovirus nucleocapsid interaction.
Journal of Microscopy 228: 78–87.
51. Baddeley A, Gregori P, Mateu J, Stoica R, Stoyan D (2006) Case studies in
spatial point process modeling. Springer-Verlag.
52. Diggle PJ, Mateu J, Clough HE (2000) A comparison between parametric and
non-parametric approaches to the analysis of replicated spatial point pattern.
Advances in Applied Probability 32: 331–343.
53. Webster S, Diggle PJ, Clough HE, Green RB, French NP (2006) Strain-typing
transmissible spongiform encephalopathies using replicated spatial data. In:
Baddeley A, Gregori P, Mateu J, Stoica R, Stoyan D, eds. Springer-Verlag. pp
197–214.
54. Gaudin V, Andrey P, Devinoy E, Kress C, Kieu K, et al. (2009) Modeling the
3D functional architecture of the nucleus in animal and plant kingdoms. CR
Biol 332: 937–946.
55. Guenatri M, Bailly D, Maison C, Almouzni G (2004) Mouse centric and
pericentric satellite repeats form distinct functional heterochromatin. J Cell Biol
166: 493–505.
56. Goncalves Dos Santos Silva A, Sarkar R, Harizanova J, Guffei A, Mowat M,
et al. (2008) Centromeres in cell division, evolution, nuclear organization and
disease. J Cell Biochem 104: 2040–2058.
57. Fransz P, Armstrong S, Alonso-Blanco C, Fischer TC, Torres-Ruiz RA, et al.
(1998) Cytogenetics for the model system Arabidopsis thaliana. Plant J 13:
867–876.
58. Fransz P, De Jong JH, Lysak M, Castiglione MR, Schubert I (2002) Interphase
chromosomes in Arabidopsis are organized as well defined chromocenters from
which euchromatin loops emanate. Proc Natl Acad Sci U S A 99:
14584–14589.
59. Alcobia I, Dilao R, Parreira L (2000) Spatial associations of centromeres in the
nuclei of hematopoietic cells: evidence for cell-type-specific organizational
patterns. Blood 95: 1608–1615.
60. Kwon SH, Workman JL (2008) The heterochromatin protein 1 (HP1) family:
put away a bias toward HP1. Mol Cells 26: 217–227.
61. Hediger F, Gasser SM (2006) Heterochromatin protein 1: don’t judge the book
by its cover! Curr Opin Genet Dev 16: 143–150.
62. Zhang X, Germann S, Blus BJ, Khorasanizadeh S, Gaudin V, et al. (2007) The
Arabidopsis LHP1 protein colocalizes with histone H3 Lys27 trimethylation.
Nat Struct Mol Biol 14: 869–871.
63. Libault M, Tessadori F, Germann S, Snijder B, Fransz P, et al. (2005) The
Arabidopsis LHP1 protein is a component of euchromatin. Planta 222:
910–925.
64. Hue-Beauvais C, Pechoux C, Bouguyon E, Chat S, Truchet S, et al. (2007)
Localisation of caveolin in mammary tissue depends on cell type. Cell Tissue
Res 328: 521–536.
65. Soille P (2003) Morphological Image Analysis: Principles and Applications
Springer-Verlag.
66. Rasband WS (1997–2009) ImageJ. BethesdaMaryland, , USA: U.S. National
Institutes of Health.
Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org14 July 2010 | Volume 6 | Issue 7 | e1000853

Page 15

67. Andrey P, Maurin Y (2005) Free-D: an integrated environment for three-
dimensional reconstruction from serial sections. J Neurosci Methods 145:
233–244.
68. Dittmer TA, Stacey NJ, Sugimoto-Shirasu K, Richards EJ (2007) LITTLE
NUCLEI genes affecting nuclear morphology in Arabidopsis thaliana. Plant
Cell 19: 2793–2803.
69. Melaragno JE, Mehrotra B, Coleman AW (1993) Relationship between
Endopolyploidy and Cell Size in Epidermal Tissue of Arabidopsis. Plant Cell 5:
1661–1668.
70. Jovtchev G, Schubert V, Meister A, Barow M, Schubert I (2006) Nuclear DNA
content and nuclear and cell volume are positively correlated in angiosperms.
Cytogenet Genome Res 114: 77–82.
71. Stoyan D, Kendall WS, Mecke J (1995) Stochastic geometry and its
applications John Wiley & Sons, Chichester, Second Edition.
72. R RDCT (2007) A Language and Environment for Statistical Computing. R
Foundation for Statistical Computing Vienna, Austria, ISBN 3-900051-07-0,
‘‘http://www.R-project.org’’.
73. Kendall M (1938) A new measure of rank correlation. Biometrika 30: 81–89.
74. Rabl C (1885) Ueber Zelltheilung. Morphol Jahrbuch 10: 214–330.
75. Franco A, Meadows JC, Millar JB (2007) The Dam1/DASH complex is
required for the retrieval of unclustered kinetochores in fission yeast. J Cell Sci
120: 3345–3351.
76. Wilkie GS, Shermoen AW, O’Farrell PH, Davis I (1999) Transcribed genes are
localized according to chromosomal position within polarized Drosophila
embryonic nuclei. Curr Biol 9: 1263–1266.
77. Stack SM, Clark CR (1974) Chromosome polarization and nuclear rotation in
Allium cepa roots. Cytologia 39: 553–560.
78. Dong F, Jiang J (1998) Non-Rabl patterns of centromere and telomere
distribution in the interphase nuclei of plant cells. Chromosome Res 6.
79. Santos AP, Shaw P (2004) Interphase chromosomes and the Rabl
configuration: does genome size matter? J Microsc 214: 201–206.
80. Chytilova E, Micas J, Galbraith DW (1999) Green fluorescent protein targeted
to the nucleus, a transgenic phenotype useful for studies in plant biology.
Annals of Botany 83: 645–654.
81. Noordmans HJ, van der Kraan K, van Driel R, Smeulders AW (1998)
Randomness of spatial distributions of two proteins in the cell nucleus involved
in mRNA synthesis and their relationship. Cytometry 33: 297–309.
82. Russell RA, Adams NM, Stephens DA, Batty E, Jensen K, et al. (2009)
Segmentation of fluorescence microscopy images for quantitative analysis of
cell nuclear architecture. Biophys J 96: 3379–3389.
83. van Lieshout MNM, Baddeley AJ (1996) A nonpara-metric measure of spatial
interaction in point patterns. Statistica Neerlandica 3: 344–361.
84. Maurer CRJ, Qi R, Raghavan V (2003) A linear time algorithm for computing
exact euclidean distance transforms of binary images in arbitrary dimensions.
IEEE Transactions on Pattern Analysis and Machine Intelligence 25: 265–270.
85. Mayer J (2004) A time-optimal algorithm for the estimation of contact
distribution functions of random sets. Image Analysis and Stereology 23:
177–183.
86. Reed MG, Howard CV (1997) Edge-corrected estimators of the nearest-
neighbour distance distribution function for three-dimensional point patterns.
Journal of Microscopy 186: 177–184.
87. Hanisch K-H (1984) Some remarks on estimators of the distribution function of
nearest neighbour distance in stationary spatial point processes. pp 409–412.
88. AGI (2000) Analysis of the genome sequence of the flowering plant Arabidopsis
thaliana. Nature 408: 796–815.
89. Roberts NY, Osman K, Armstrong SJ (2009) Telomere distribution and
dynamics in somatic and meiotic nuclei of Arabidopsis thaliana. Cytogenet
Genome Res 124: 193–201.
90. Berr A, Schubert I (2007) Interphase chromosome arrangement in Arabidopsis
thaliana is similar in differentiated and meristematic tissues and shows a
transient mirror symmetry after nuclear division. Genetics 176: 853–863.
91. de Nooijer S, Wellink J, Mulder B, Bisseling T (2009) Non-specific interactions
are sufficient to explain the position of heterochromatic chromocenters and
nucleoli in interphase nuclei. Nucleic Acids Res 37: 3558–3568.
92. Hayes H, Rogel-Gaillard C, Zijlstra C, De Haan NA, Urien C, et al. (2002)
Establishment of an R-banded rabbit karyotype nomenclature by FISH
localization of 23 chromosome-specific genes on both G- and R-banded
chromosomes. Cytogenet Genome Res 98: 199–205.
93. Ekes C, Csonka E, Hadlaczky G, Cserpan I (2004) Isolation, cloning and
characterization of two major satellite DNA families of rabbit (Oryctolagus
cuniculus). Gene 343: 271–279.
94. Brero A, Easwaran HP, Nowak D, Grunewald I, Cremer T, et al. (2005)
Methyl CpG-binding proteins induce large-scale chromatin reorganization
during terminal differentiation. J Cell Biol 169: 733–743.
95. Solovei I, Schermelleh L, During K, Engelhardt A, Stein S, et al. (2004)
Differences in centromere positioning of cycling and postmitotic human cell
types. Chromosoma 112: 410–423.
96. Martou G, De Boni U (2000) Nuclear topology of murine, cerebellar Purkinje
neurons: changes as a function of development. Exp Cell Res 256: 131–139.
97. Chaly N, Munro SB (1996) Centromeres reposition to the nuclear periphery
during L6E9 myogenesis in vitro. Exp Cell Res 223: 274–278.
98. Christians E, Rao VH, Renard JP (1994) Sequential acquisition of
transcriptional control during early embryonic development in the rabbit.
Dev Biol 164: 160–172.
99. Challah-Jacques M, Chesne P, Renard JP (2003) Production of cloned rabbits
by somatic nuclear transfer. Cloning Stem Cells 5: 295–299.
100. Kittler J, Illingworth J, Fo ¨glein J (1985) Threshold selection based on a simple
image statistic. Computer Vision, Graphics and Image Processing 30: 125–147.
101. Ridler TW, Calvard S (1978) Picture thresholding using an iterative selection
method. IEEE Transactions on Systems, Man, and Cybernetics 8: 630–632.
102. Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface
construction algorithm. ACM Computer Graphics 21: 163–169.
Statistical 3D Analysis of Animal and Plant Nuclei
PLoS Computational Biology | www.ploscompbiol.org 15July 2010 | Volume 6 | Issue 7 | e1000853