Statistical analysis of the three-dimensional structure of centromeric heterochromatin in interphase nuclei

Spatial modeling of biological patterns shows multiscale organization of Arabidopsis thaliana heterochromatin

The spatial organization in the cell nucleus is tightly linked to genome functions such as gene regulation. Similarly, specific spatial arrangements of biological components such as macromolecular complexes, organelles and cells are involved in many biological functions. Spatial interactions among elementary components of biological systems define their relative positioning and are key determinants of spatial patterns. However, biological variability and the lack of appropriate spatial statistical methods and models limit our current ability to analyze these interactions. Here, we developed a framework to dissect spatial interactions and organization principles by combining unbiased statistical tests, multiple spatial descriptors and new spatial models. We used plant constitutive heterochromatin as a model system to demonstrate the potential of our framework. Our results challenge the common view of a peripheral organization of chromocenters, showing that chromocenters are arranged along both radial and lateral directions in the nuclear space and obey a multiscale organization with scale-dependent antagonistic effects. The proposed generic framework will be useful to identify determinants of spatial organizations and to question their interplay with biological functions.

Characterization of squamous cell carcinomas of the head and neck using methods of spatial statistics

In the present study, 53 cases of squamous cell carcinomas of the head and neck were characterized by a quantitative histological texture analysis based on principles of spatial statistics. A planar tessellation of the epithelial tumour component was generated by a skeletonization algorithm. The size distribution of the virtual cells of this planar tessellation, and the size distribution of the profiles of the tumour cell nuclei were estimated in terms of area and boundary length. The intensity, the reduced second moment function (K-function) and the pair correlation function of the point process of the centroids of the profiles of the tumour cell nuclei were also estimated. For both purposes, it is necessary to correct for edge effects, which we consider in this paper in some detail. Specifically, the point patterns of the tumour cell nuclei were considered as realizations of a point process, where the points exist only in the epithelial tumour component (the permitted phase) and not in the stroma (the forbidden phase). The methods allow to characterize each individual tumour by a series of summary statistics. The total set of cases was then partitioned into two groups: 19 cases without lymph node metastases (pN0), and 34 nodal positive cases (pN1 or pN2). Statistical analysis showed no significant differences between the intensities, the mean K-functions and the mean pair correlation functions of the tumour cell nucleus profiles of the two groups. However, there were some significant differences between the sizes of the virtual cells and of the nucleus profiles of the nodal negative cases as compared to the nodal positive cases. In a logistic regression analysis, one of the quantitative nuclear size variables (mean nuclear area) was found to be a significant predictor of lymph node metastasis, in addition to tumour stage. The study shows the potential of methods of spatial statistics for objective quantitative grading of squamous cell carcinomas of the head and neck, and provides an example for modelling histological point patterns as realizations of planar point processes occupying a reference phase which is only a partial component of the total tissue.

Nuclear architecture and chromatin dynamics in interphase nuclei of Arabidopsis thaliana

The interphase cell nucleus is extraordinarily complex, ordered, and dynamic. In the last decade, remarkable progress has been made in deciphering the functional organisation of the cell nucleus, and intricate relationships between genome functions (transcription, DNA repair, or replication) and various nuclear compartments have been revealed. In this review, we describe the architecture of the Arabidopsis thaliana interphase cell nucleus and discuss the dynamic nature of its organisation. We underline the need for further developments in quantitative and modelling approaches to nuclear organization.

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

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.

Spatial Point Pattern Analysis of Neurons Using Ripley's K-Function in 3D

The aim of this paper is to apply a non-parametric statistical tool, Ripley's K-function, to analyze the 3-dimensional distribution of pyramidal neurons. Ripley's K-function is a widely used tool in spatial point pattern analysis. There are several approaches in 2D domains in which this function is executed and analyzed. Drawing consistent inferences on the underlying 3D point pattern distributions in various applications is of great importance as the acquisition of 3D biological data now poses lesser of a challenge due to technological progress. As of now, most of the applications of Ripley's K-function in 3D domains do not focus on the phenomenon of edge correction, which is discussed thoroughly in this paper. The main goal is to extend the theoretical and practical utilization of Ripley's K-function and corresponding tests based on bootstrap resampling from 2D to 3D domains.

Centromeres in cell division, evolution, nuclear organization and disease

As the spindle fiber attachment region of the chromosome, the centromere has been investigated in a variety of contexts. Here, we will review current knowledge about this unique chromosomal region and its relevance for proper cell division, speciation, and disease. Understanding the three-dimensional organization of centromeres in normal and tumor cells is just beginning to emerge. Multidisciplinary research will allow for new insights into its normal and aberrant nuclear organization and may allow for new therapeutic interventions that target events linked to centromere function and cell division.

Spatial quantitative analysis of fluorescently labeled nuclear structures: problems, methods, pitfalls

The vast majority of microscopic data in biology of the cell nucleus is currently collected using fluorescence microscopy, and most of these data are subsequently subjected to quantitative analysis. The analysis process unites a number of steps, from image acquisition to statistics, and at each of these steps decisions must be made that may crucially affect the conclusions of the whole study. This often presents a really serious problem because the researcher is typically a biologist, while the decisions to be taken require expertise in the fields of physics, computer image analysis, and statistics. The researcher has to choose between multiple options for data collection, numerous programs for preprocessing and processing of images, and a number of statistical approaches. Written for biologists, this article discusses some of the typical problems and errors that should be avoided. The article was prepared by a team uniting expertise in biology, microscopy, image analysis, and statistics. It considers the options a researcher has at the stages of data acquisition (choice of the microscope and acquisition settings), preprocessing (filtering, intensity normalization, deconvolution), image processing (radial distribution, clustering, co-localization, shape and orientation of objects), and statistical analysis.

Quantitative investigation of murine cytomegalovirus nucleocapsid interaction

In this study, we quantitatively investigate the role of the M97 protein for viral morphogenesis in murine cytomegalovirus (MCMV)-infected fibroblast cells. For this purpose, a statistical analysis is performed for the spatial distribution of nuclear B-capsids (devoid of DNA, containing the scaffold) and C-capsids (filled with DNA). Cell nuclei infected with either wild-type or an M97 deletion mutant were compared. Univariate and multivariate point process characteristics (like Ripley's K-function, the L-function and the nearest neighbour distance distribution function) are investigated in order to describe and quantify the effects that the deletion of M97 causes to the process of DNA packaging into nucleocapsids. The estimation of the function L(r) -r reveals that with respect to the wild type there is an increased frequency of point pairs at a very short distance (less than approximately 100 nm) for both the B-capsids as well as for the C-capsids. For the M97 deletion mutant type this is no longer true. Here only the C-capsids show such a clustering behaviour, whereas for B-capsids it is almost nonexistant. Estimations of functionals such as the nearest neighbour distance distribution function confirmed these results. Thereby, a quantification is provided for the effect that the deletion of M97 leads to a loss of typical nucleocapsid clustering in MCMV-infected nuclei.

Spatial arrangement of microglia in the mouse hippocampus: a stereological study in comparison with astrocytes

Microglia are classically considered to be immune cells in the brain, but have now been proven to be involved in neuronal activity as well. Here we stereologically analyzed the spatial arrangement of microglia in the mouse hippocampus. First, we estimated the numerical densities (NDs) of microglia identified by ionized calcium-binding adaptor molecule 1 (Iba1). Despite that microglia appeared to be evenly distributed throughout the hippocampal area, the NDs demonstrated significant dorsoventral, interregional, and interlaminar differences. Briefly, the NDs in the ventral hippocampus were significantly lower in the CA3 region than in the CA1 region and dentate gyrus, although no interregional differences were detectable in the dorsal hippocampus. Both in the CA1 and CA3 regions, the NDs were significantly higher in the stratum lacunosum-moleculare than in the remaining layers. Next, we investigated the spatial patterns of distribution of Iba1-labeled microglia and S100beta-labeled astrocytes. So far as we examined, the somato-somatic contacts were not seen among microglia or among astrocytes, whereas the close apposition between microglia and astrocytes were occasionally detected. The 3D point process analysis showed that the spatial distribution of microglia was significantly repulsive. Because the statistical territory of single microglia was larger than that estimated from process tracing, they are not likely to touch each other with their processes. Astrocytes were distributed slightly repulsively with overlapping areas. The 3D point process analysis also revealed a significant spatial attraction between microglia and astrocytes. The present findings provide a novel anatomical basis for glial research.

Quantitative analysis of cell nucleus organisation

There are almost 1,300 entries for higher eukaryotes in the Nuclear Protein Database. The proteins' subcellular distribution patterns within interphase nuclei can be complex, ranging from diffuse to punctate or microspeckled, yet they all work together in a coordinated and controlled manner within the three-dimensional confines of the nuclear volume. In this review we describe recent advances in the use of quantitative methods to understand nuclear spatial organisation and discuss some of the practical applications resulting from this work.

Cell-type specific proximity of centromeric domains of one homologue each of chromosomes 2 and 11 in nuclei of cerebellar Purkinje neurons

In Purkinje neurons of the mouse cerebellum, the centromeres of several chromosomes are placed in close proximity to form a distinct pattern of clusters and exhibit reproducible spatial redistributions during development. In granule neurons, an adjacent cell type in the cerebellum, the pattern, size, and number of centromeric aggregations are different from those of Purkinje neurons. The present work was undertaken to test the hypothesis that the same chromosomes form part of one aggregate in a cell-type-specific manner. Fluorescence in situ hybridization (FISH) with chromosome-specific paracentromeric probes was used to identify centromeric regions of individual chromosomes in cerebellar Purkinje and granule neurons of the adult mouse. When pairs of centromeric probes were used in two-color FISH, one homologue each of chromosomes 2 and 11 were routinely found close to each other in Purkinje neurons but not in granule neurons. This finding of specific proximity was limited to the pair 2 and 11, out of the ten chromosome pairs that were randomly selected and studied. Our results indicate that, in adult Purkinje neurons, a cell-type-specific spatial proximity is present between centromeric domains of one homologue each of chromosomes 2 and 11.

Quantitative analysis of keratin filament networks in scanning electron microscopy images of cancer cells

The keratin filament network is an important part of the cytoskeleton. It is involved in the regulation of shape and viscoelasticity of epithelial cells. The morphology of keratin networks depends on post-translational modifications of keratin monomers. In-vitro studies indicated that network characteristics, such as filament crosslink density, determines the biophysical properties of the filament network. This report presents a quantitative method for the morphological analysis of keratin filament networks. Visualization of filaments was based on prefixation extraction of epithelial cells and scanning electron microscopy (SEM). SEM images were processed by a skeletonization algorithm to obtain a graph structure that represents individual filaments as well as their connections. This method was applied to investigate the effects of transforming growth factor alpha (TGFalpha) on the morphology of keratin networks in pancreatic cancer cells. TGFalpha contributes to pancreatic cancer progression and activates signalling pathways phosphorylating keratin monomers. Using this new method, a significant alteration to the keratin network morphology could be detected in response to TGFalpha.