Kiên Kiêu

The efficiency of systematic sampling in stereology — reconsidered

In the present paper, we summarize and further develop recent research in the estimation of the variance of stereological estimators based on systematic sampling. In particular, it is emphasized that the relevant estimation procedure depends on the sampling density. The validity of the variance estimation is examined in a collection of data sets, obtained by systematic sampling. Practical recommendations are also provided in a separate section.

Cellular Parameters of the Shoot Apical Meristem in Arabidopsis

The shoot apical meristem (SAM) is a small group of dividing cells that generate all of the aerial parts of the plant. With the goal of providing a framework for the analysis of Arabidopsis meristems at the cellular level, we performed a detailed morphometric study of actively growing inflorescence apices of the Landsberg erecta and Wassilewskija ecotypes. For this purpose, cell size, spatial distribution of mitotic cells, and the mitotic index were determined in a series of optical sections made with a confocal laser scanning microscope. The results allowed us to identify zones within the inflorescence SAM with different cell proliferation rates. In particular, we were able to define a central area that was four to six cells wide and had a low mitotic index. We used this technique to compare the meristem of the wild type with the enlarged meristems of two mutants, clavata3-1 (clv3-1) and mgoun2 (mgo2). One of the proposed functions of the CLV genes is to limit cell division rates in the center of the meristem. Our data allowed us to reject this hypothesis, because the mitotic index was reduced in the inflorescence meristem of the clv3-1 mutant. We also observed a large zone of slowly dividing cells in meristems of clv3-1 seedlings. This zone was not detectable in the wild type. These results suggest that the central area is increased in size in the mutant meristem, which is in line with the hypothesis that the CLV3 gene is necessary for the transition of cells from the central to the peripheral zone. Genetic and microscopic analyses suggest that mgo2 is impaired in the production of primordia, and we previously proposed that the increased size of the mgo2 meristem could be due to an accumulation of cells at the periphery. Our morphometric analysis showed that mgo2 meristems, in contrast to those of clv3-1, have an enlarged periphery with high cell proliferation rates. This confirms that clv3-1 and mgo2 lead to meristem overgrowth by affecting different aspects of meristem function.

Precision of systematic sampling and transitive methods

The use of the transitive methods for assessing the precision of systematic sampling is discussed. A key point of the transitive methods is the choice of a local model for the covariogram near the origin. The relationship between the regularity of the measurements and the regularity of their covariogram is given. This result is useful for choosing the appropriate covariogram model. A method for estimating the measurement regularity from discrete data is proposed for cases where it cannot be assessed a priori. Stereological applications where sampling is based on geometric probes such as serial sections, point or line grids are also discussed.

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.

Dynamic changes in the subcellular distribution of the tobacco ROS-producing enzyme RBOHD in response to the oomycete elicitor cryptogein

Highlight text The oomycete elicitor cryptogein triggers the relocation of RBOHD from intracellular compartments to the plasma membrane in tobacco cells. This suggests that intracellular trafficking is a potential determinant of RBOHD activity.

Computation of the integrated flow of particles between polygons

To quantify the flow of particles over a heterogeneous area, some models require the integration of a pointwise dispersal function over source and target polygons. This calculation is a non-trivial task and may require a great deal of computing time. In this paper, an efficient and accurate algorithm is presented to integrate general individual dispersal functions between pairs of convex or non-convex polygons. Geometric calculations are performed using standard tools from computational geometry. Numerical integration is then performed either by a grid method or by an adaptive cubature method. The procedure is illustrated with a case study. It is shown that the cubature method is much more efficient than the grid method and that its error estimates are accurate. The algorithm is implemented in a C++ program, Califlopp.

The nuclear localization of WAP and CSN genes is modified by lactogenic hormones in HC11 cells

Whey acidic protein (WAP) and casein (CSN) genes are among the most highly expressed milk protein genes in the mammary gland of the lactating mouse. Their tissue‐specific regulation depends on the activation and recruitment of transcription factors, and chromatin modifications in response to hormonal stimulation. We have investigated if another mechanism, such as specific positioning of the genes in the nucleus, could be involved in their functional regulation. Fluorescent in situ hybridization was used to study the nuclear localization of WAP and CSN genes in mouse mammary epithelial cells (HC11) cultured in the absence and presence of lactogenic hormones. Automatic 3D image processing and analysis tools were developed to score gene positions. In the absence of lactogenic hormones, both genes are distributed non‐uniformly within the nucleus: the CSN locus was located close to the nuclear periphery and the WAP gene tended to be central. Stimulation by lactogenic hormones induced a statistically significant change to their distance from the periphery, which has been described as a repressive compartment. The detection of genes in combination with the corresponding chromosome‐specific probe revealed that the CSN locus is relocated outside its chromosome territory following hormonal stimulation, whereas the WAP gene, which is already sited more frequently outside its chromosome territory in the absence of hormones, is not affected. We conclude that milk protein genes are subject to nuclear repositioning when activated, in agreement with a role for nuclear architecture in gene regulation, but that they behave differently as a function of their chromosomal context. J. Cell. Biochem. 105: 262–270, 2008.

Pathogen population dynamics in agricultural landscapes: the Ddal modelling framework.

Modelling processes that occur at the landscape scale is gaining more and more attention from theoretical ecologists to agricultural managers. Most of the approaches found in the literature lack applicability for managers or, on the opposite, lack a sound theoretical basis. Based on the metapopulation concept, we propose here a modelling approach for landscape epidemiology that takes advantage of theoretical results developed in the metapopulation context while considering realistic landscapes structures. A landscape simulator makes it possible to represent both the field pattern and the spatial distribution of crops. The pathogen population dynamics are then described through a matrix population model both stage- and space-structured. In addition to a classical invasion analysis we present a stochastic simulation experiment and provide a complete framework for performing a sensitivity analysis integrating the landscape as an input factor. We illustrate our approach using an example to evaluate whether the agricultural landscape composition and structure may prevent and mitigate the development of an epidemic. Although designed for a fungal foliar disease, our modelling approach is easily adaptable to other organisms.

Stereological estimation based on isotropic slices through fixed points

Stereological estimators of length and surface area based on measurements in an isotropic slice through a fixed point are described. Measurements of three‐dimensional angles are not needed. The estimators depend only on distance measurements. The variance of the length estimator is studied in some detail. Applications to particle analysis and second‐order stereology are discussed.

Precision of stereological planar area predictors

Total planar area can be estimated based on sampling by a lattice of figures (e.g. point patterns, line segments, quadrats). General formulae are provided for the approximation of mean squared errors. The approximation formulae are products of the boundary length and of a parameter that depends only on the sampling scheme. An R package is provided by the authors for the numerical computation of the mean squared error formulae. The speed of convergence of the mean squared error approximation is assessed on the basis of several simulations. Several sampling schemes are compared in view of the approximated mean squared errors.