Frank Fleischer

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 S100β‐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.

Statistical analysis of reduced pair correlation functions of capillaries in the prostate gland

Blood capillaries are thread‐like structures that may be considered as an example of a spatial fibre process in three dimensions. At light microscopy, the capillary profiles appear as a planar point process on sections. It has recently been shown that the observed pair correlation function g(r) of the centres of the fibre profiles on two‐dimensional sections may be used to estimate the reduced pair correlation function of stationary and isotropic fibre processes in three dimensions. In the present study, we explored how this approach may be extended to statistical analysis of reduced g‐functions of capillaries from multiple specimens of different groups and with replicated observations. The methods were applied to normal prostatic tissue compared with prostate cancer. Confidence intervals for the mean reduced g‐functions of groups were estimated for fixed r‐values parametrically using the t‐distribution, and by bootstrap methods. Each estimated reduced g‐function was furthermore characterized in terms of its first maximum and minimum. The mean length of capillaries per unit tissue volume was significantly higher in prostate cancer tissue than in normal prostate tissue. Significant differences between the mean reduced g‐functions of malignant and benign lesions could be demonstrated for two domains of r‐values. In general, bootstrap‐based confidence intervals were slightly wider than parametrically estimated confidence intervals. Falsely negative lower bounds of the intervals, which sometimes arose using the parametric approach, could be avoided by the bootstrap method. Testing of group mean values for significant differences by the bootstrap method yielded more conservative results than multiple t‐tests. The functional value of the first maximum of the reduced g‐function and a global statistical parameter of short‐range ordering was significantly reduced in the carcinoma group. Prostate cancer tissue is more densely supplied with capillaries than normal prostate tissue and the three‐dimensional arrangement of the vessels differs with respect to interaction at various distance ranges. In the local approach used here, bootstrap methods can be used as a robust statistical tool for the computation of confidence intervals and group comparisons of mean reduced g‐functions at specific ranges of interaction.

Fitting of stochastic telecommunication network models via distance measures and Monte---Carlo tests

We explore real telecommunication data describing the spatial geometrical structure of an urban region and we propose a model fitting procedure, where a given choice of different non-iterated and iterated tessellation models is considered and fitted to real data. This model fitting procedure is based on a comparison of distances between characteristics of sample data sets and characteristics of different tessellation models by utilizing a chosen metric. Examples of such characteristics are the mean length of the edge-set or the mean number of vertices per unit area. In particular, after a short review of a stochastic-geometric telecommunication model and a detailed description of the model fitting algorithm, we verify the algorithm by using simulated test data and subsequently apply the procedure to infrastructure data of Paris.

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 α (TGFα) on the morphology of keratin networks in pancreatic cancer cells. TGFα 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 TGFα.

Simulation of typical Cox–Voronoi cells with a special regard to implementation tests

We consider stationary Poisson line processes in the Euclidean plane and analyze properties of Voronoi tessellations induced by Poisson point processes on these lines. In particular, we describe and test an algorithm for the simulation of typical cells of this class of Cox–Voronoi tessellations. Using random testing, we validate our algorithm by comparing theoretical values of functionals of the zero cell to simulated values obtained by our algorithm. Finally, we analyze geometric properties of the typical Cox–Voronoi cell and compare them to properties of the typical cell of other well-known classes of tessellations, especially Poisson–Voronoi tessellations. Our results can be applied to stochastic–geometric modelling of networks in telecommunication and life sciences, for example. The lines can then represent roads in urban road systems, blood arteries or filament structures in biological tissues or cells, while the points can be locations of telecommunication equipment or vesicles, respectively.

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

Translocation of genes into the pericentromeric heterochromatin occurs during cellular differentiation and leads to a long‐term silencing of these genes. Consequently, a structural remodelling of this heterochromatin compartment is observed during differentiation but this remains to be defined from a topological point of view. In a previous study, we analysed the three‐dimensional (3D) distribution patterns of centromere clusters (chromocentres) by confocal scanning laser microscopy and found that differentiation of the promyelocytic leukaemia cell line NB4 along the neutrophil lineage is associated with a progressive clustering of centromeres. This clustering was reflected by a decreased number of detectable chromocentres, i.e. groups of centromeres with a distance below the diffraction‐limited resolution of optical microscopy. The purpose of this study was to perform a statistical analysis of the 3D distribution of chromocentres in NB4 cells. Several point field characteristics (Ripleys K‐function, L‐function, pair correlation function, nearest‐neighbour distribution function) were investigated to describe the topology of chromocentres during differentiation of NB4 cells. The pair correlation function revealed a higher frequency of chromocentre distances between 350 nm and 800 nm in undifferentiated NB4 cells as compared with differentiated cells. The L‐function and the nearest‐neighbour distribution function confirmed these results. These data imply the existence of intranuclear heterochromatin zones formed by functionally related centromeric regions. In view of the observed decrease in the number of detectable chromocentres during differentiation, we hypothesize that these zones with a diameter of 350–800 nm in undifferentiated NB4 cells contract into zones with a diameter below 350 nm in differentiated cells.

Statistical modelling of the geometry of planar sections of prostatic capillaries on the basis of stationary Strauss hard-core processes

In a recent study, the capillarization of normal prostatic tissue and prostatic carcinoma tissue was characterized by means of explorative methods of spatial statistics. In the present paper, an attempt was made to go beyond the explorative approach and to characterize the observed point patterns of the capillary profiles on sections by means of a parametric model. For this purpose, the flexible class of Gibbs processes was considered. Specifically, stationary Strauss hard‐core processes were fitted to the observed point patterns. The goodness of fit achieved by the model was checked by simulations with the Markov chain Monte Carlo method using the Metropolis–Hastings algorithm. Model fitting and simulations were performed with the help of the spatstat package under R. The observed point patterns were in some cases compatible with realizations of stationary Strauss hard‐core processes for all ranges of spatial interaction. However, deviations from the model were found for one or more domains of ranges in other cases. In the tumour tissue, a highly significant decrease of the interaction parameter of the Strauss hard‐core process could be found as compared to the normal prostatic tissue. This finding is discussed in terms of a loss of the normal lobular architecture of the glands in the tumour tissue.

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 Ripleys 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.

Myc Regulates Embryonic Vascular Permeability and Remodeling

Previous work has shown that c-Myc is required for adequate vasculogenesis and angiogenesis. To further investigate the contribution of Myc to these processes, we conditionally expressed c-Myc in embryonic endothelial cells using a tetracycline-regulated system. Endothelial Myc overexpression resulted in severe defects in the embryonic vascular system. Myc-expressing embryos undergo widespread edema formation and multiple hemorrhagic lesions. They die between embryonic days 14.5 and 17.5. The changes in vascular permeability are not caused by deficiencies in vascular basement membrane composition or pericyte coverage. However, the overall turnover of endothelial cells is elevated as is revealed by increased levels of both proliferation and apoptosis. Whole-mount immunohistochemical analysis revealed alterations in the architecture of capillary networks. The dermal vasculature of Myc-expressing embryos is characterized by a reduction in vessel branching, which occurs despite upregulation of the proangiogenic factors vascular endothelial growth factor-A and angiopoietin-2. Thus, the net outcome of an excess of vascular endothelial growth factor-A and angiopoietin-2 in the face of an elevated cellular turnover appears to be a defect in vascular integrity.

Bootstrap methods for statistical inference from stereological estimates of volume fraction

We suggest the use of bootstrap methods for inference from stereological estimates of volume fraction. An informal introduction to stereological estimation of volume fraction and to principles of bootstrap techniques is given. The bootstrap method is a robust computer‐intensive resampling technique, based on independent random sampling from a data set with replacement. Bootstrap methods were used to estimate confidence intervals for volume fractions, and to test for a significant difference between estimated volume fractions from two samples. Two sampling designs are considered: independent replicated samples (visual fields) from a single object, and estimates of volume fraction from multiple independent objects. The methods are presented as worked examples on real data sets obtained from tumour pathology (mammary cancer, pancreatic cancer). The volume fraction of glandular lumina per total volume of the epithelial phase was chosen as target parameter. It indicates the degree of glandular differentiation in adenocarcinomas and is estimated as a ratio‐of‐means statistic with variable denominator within cases. The confidence intervals of the volume fraction estimated by the bootstrap method were slightly narrower than the parametrically calculated confidence intervals for all data sets. The outcomes of significance tests based on the bootstrap technique were unchanged as compared with classical tests based on the assumptions of normality and homoscedasticity of the data. Special attention was paid to the reproducibility of the bootstrap technique in replicated trials on the same data.