Estimating the life-span of oligodendrocytes from clonal data on their development in cell culture

This paper presents a new method to analyze clonal data on oligodendrocyte development in cell culture. The process of oligodendrocyte generation from precursor cells is modelled as a multi-type Bellman-Harris branching process as suggested in an earlier paper [K. Boucher, A. Zorin, A.Y. Yakovlev, M. Mayer-Proschel, M. Noble, An alternative stochastic model of generation of oligodendrocytes in cell culture, J. Math. Biol. 43 (2001) 22]. This model has been extended to allow for death of oligodendrocytes as well as a dissimilar distribution of the first mitotic cycle duration as compared to the subsequent cycles of precursor cells, which lengths are assumed to be independent and identically distributed random variables. Since the time-span of oligodendrocytes is not directly observable in clonal data, plausible parametric assumptions are invoked to make estimation problems tractable. In particular, the time to cell death follows a two-parameter gamma distribution, while the lapse of time between the event of cell death and the event of cell disintegration is assumed to be exponentially distributed. A simulated pseudo maximum likelihood method for estimation of model parameters has been developed using simulation-based approximations of the expected numbers and variance-covariance matrices for different types of cells. Finite sample properties of the estimation procedure are studied by computer simulations. The proposed method is illustrated with an analysis of the clonal development of O-2A progenitor cells isolated from the rat optic nerve and the corpus callosum.     

Approximations for expected generation number

A deterministic formula is commonly used to approximate the expected generation number of a population of growing cells. However, this can give misleading results because it does not allow for natural variation in the times that individual cells take to reproduce. Here we present more accurate approximations for both symmetric and asymmetric cell division. Based on the first two moments of the generation time distribution, these approximations are also robust. We illustrate the improved approximations using data that arise from monitoring individual yeast cells under a microscope and also demonstrate how the approximations can be used when such detailed data are not available.     

A model for hepatocarcinogenesis with clonal expansion of three successive phenotypes of preneoplastic cells

The two-stage model with clonal expansion of intermediate cells has often been used to describe the carcinogenesis process. The model hypothesizes that cells have to undergo two mutations on their way from the normal to the malignant stage. Biological experiments indicate the existence of three types of preneoplastic cells in hepatocarcinogenesis representing three successive intermediate stages in the development of malignant cells from normal cells. This finding suggests that hepatocarcinogenesis should be described by a multi-stage model with three intermediate stages, leading to a four-stage mutation model with clonal expansion of all types of intermediate cells. This model is presented and mathematical approximations for the number and size of nonextinct premalignant clones of the different cell types are derived. The model is applied to focal lesion data from a rat hepatocarcinogenesis experiment.     

Consistency of estimators of the population-scaled recombination rate

We consider (approximate) likelihood methods for estimating the population-scaled recombination rate from population genetic data. We show that the dependence between the data from two regions of a chromosome decays inversely with the amount of recombination between the two regions. We use this result to show that the maximum likelihood estimator (mle) for the recombination rate, based on the composite likelihood of Fearnhead and Donnelly, is consistent. We also consider inference based on the pairwise likelihood of Hudson. We consider two approximations to this likelihood, and prove that the mle based on one of these approximations is consistent, while the mle based on the other approximation (which is used by McVean, Awadalla and Fearnhead) is not.     

A random walk model of oligodendrocyte generation in vitro and associated estimation problems.

A branching stochastic process proposed earlier to model oligodendrocyte generation by O-2A progenitor cells under in vitro conditions does not allow invoking the maximum likelihood techniques for estimation purposes. To overcome this difficulty, we propose a partial likelihood function based on an embedded random walk model of clonal growth and differentiation of O-2A progenitor cells. Under certain conditions, the partial likelihood function yields consistent estimates of model parameters. The usefulness of this approach is illustrated with computer simulations and data analyses.     

A stochastic model to analyze clonal data on multi-type cell populations

This article presents a stochastic model designed to analyze experimental data on the development of cell clones composed of two (or more) distinct types of cells. The proposed model is an extension of the traditional multi-type Bellman-Harris branching stochastic process allowing for nonidentical time-to-transformation distributions defined for different cell types. A simulated pseudo likelihood method has been developed for the parametric statistical inference from experimental data on cell clones under the proposed model. The method uses simulation-based approximations of the means and the variance-covariance matrices of cell counts. The proposed estimator for the vector of unknown parameters is strongly consistent and asymptotically normal under mild regularity conditions, while its variance-covariance matrix is estimated by the parametric bootstrap. A Monte Carlo Wald test is proposed for the test of hypotheses. Finite sample properties of the estimator have been studied by computer simulations. The model and associated methods of parametric inference have been applied to the analysis of proliferation and differentiation of cultured O-2A progenitor cells that play a key role in the development of the central nervous system. It follows from this analysis that the time to division of the progenitor cell and the time to its differentiation (into an oligodendrocyte) are not identically distributed. This biological finding suggests that a molecular event determining the type of cell transformation is more likely to occur at the start rather than at the end of the mitotic cycle.     

Epigenetic cues modulating the generation of cell‐type diversity in the cerebral cortex

The cerebral cortex is composed of a large variety of distinct cell‐types including projection neurons, interneurons, and glial cells which emerge from distinct neural stem cell lineages. The vast majority of cortical projection neurons and certain classes of glial cells are generated by radial glial progenitor cells in a highly orchestrated manner. Recent studies employing single cell analysis and clonal lineage tracing suggest that neural stem cell and radial glial progenitor lineage progression are regulated in a profound deterministic manner. In this review we focus on recent advances based mainly on correlative phenotypic data emerging from functional genetic studies in mice. We establish hypotheses to test in future research and outline a conceptual framework how epigenetic cues modulate the generation of cell‐type diversity during cortical development.     

Models for growth of clones in hexagonal cell arrangements: Applications in Drosophila wing disc epithelia and plant epidermal tissues

Epithelia are commonly two-dimensional sheets of cells that are approximately hexagonally arranged. Reproduction of these hexagonal arrays is further constrained in planet epidermal tissues and in Drosophila imaginal discs by the condition that cells related by common descent form spatially contiguous clones. Two models are presented for reproduction of hexagonal arrays of cells under the clonal constraint. The row-shifting mechanism allows cell movement although it tends to split clonal neighbors. The neighborhood preserving model insures clonal integrity by requiring rigid control over direction of cell division. Parallel rewriting rules for generation of graphs are given for continuing growth of hexagonal arrays. These rules are found to be consistent with observations of cell arrangement in certain plant epidermal tissues. Analysis of clonal tetrad configurations in Drosophila wings show that the row-shifting model is best suited in this case and implicates further, specifically biological means for insuring clonal integrity.     

Modeling continuous auxiliary covariate data in generalized linear mixed models using the kernel smoother

Auxiliary covariate data are often collected in biomedical studies when the primary exposure variable is only assessed on a subset of the study subjects. In this study, we investigate a semiparametric‐estimated likelihood estimation for the generalized linear mixed models (GLMM) in the presence of a continuous auxiliary variable. We use a kernel smoother to handle continuous auxiliary data. The method can be used to deal with missing or mismeasured covariate data problems in a variety of applications when an auxiliary variable is available and cluster sizes are not too small. Simulation study results show that the proposed method performs better than that which ignores the random effects in GLMM and that which only uses data in the validation data set. We illustrate the proposed method with a real data set from a recent environmental epidemiology study on the maternal serum 1,1‐dichloro‐2,2‐bis(p‐chlorophenyl) ethylene level in relationship to preterm births.     

Fitting distributions to microbial contamination data collected with an unequal probability sampling design

Aims

The fitting of statistical distributions to microbial sampling data is a common application in quantitative microbiology and risk assessment applications. An underlying assumption of most fitting techniques is that data are collected with simple random sampling, which is often times not the case. This study develops a weighted maximum likelihood estimation framework that is appropriate for microbiological samples that are collected with unequal probabilities of selection.

Methods and Results

A weighted maximum likelihood estimation framework is proposed for microbiological samples that are collected with unequal probabilities of selection. Two examples, based on the collection of food samples during processing, are provided to demonstrate the method and highlight the magnitude of biases in the maximum likelihood estimator when data are inappropriately treated as a simple random sample.

Conclusions

Failure to properly weight samples to account for how data are collected can introduce substantial biases into inferences drawn from the data.

Significance and Impact of the Study

The proposed methodology will reduce or eliminate an important source of bias in inferences drawn from the analysis of microbial data. This will also make comparisons between studies and the combination of results from different studies more reliable, which is important for risk assessment applications.     

Effect of growth and differentiation stimuli on the development of antigen-responsive B cells in fetal liver

The development of the B cell immune repertoire was studied using an in vitro fetal organ culture system. In order to analyze the mechanism by which B cell precursors clonally expand and diversify, fetal lymphoid tissues were incubated in the presence of several factors known to influence B cell differentiation: IL-1, IL-2, WEHI-3 culture supernatant containing IL-3, and a factor from a cyclic neutropenia patient (CNF). By analyzing the effect of exogenous factors on the frequency of antigen-responsive B cells, the ability of the factor to either inhibit or enhance clonal expansion was determined. It was found that the addition of IL-1, WEHI-3 supernatant, or CNF increased the frequency of DNP-responsive B cells suggesting an enhancement of clonal expansion. IL-2, on the other hand, did not alter the frequency of antigen-responsive B cells. The effect of added factors on the kinetics of appearance of phosphorylcholine (PC)-responsive B cells, which are known to be acquired in ontogeny about 2 weeks later than DNP-responsive B cells, was also analyzed. The data indicate that CNF, unlike IL-1, IL-2, and WEHI-3 culture supernatant, results in an earlier appearance of PC-responsive B cells. These results suggest that soluble factors may play a role in the generation of the B cell repertoire.     

Clones of B lymphocytes: their natural selection and expansion.

The operation of clonal selection for cells of the B-lymphocyte line is discussed with regard to: 1) The clonal repertoire determined by antigen binding to B lymphocytes, which is much larger than that determined by limiting dilution cloning assays. This quantitative difference is interpreted in terms of the multiple shared specificities of each antibody molecule. 2) Multiclonal responses and initial selection by antigen of particular clones (preferential primary selection). 3) Clonal dominance. During an immune response one clone (or a small number of clones) of B cells is preferentially selected and proliferated, apparently at random, from a heterogeneous population of cells capable of responding to the given antigen. Co-dominance of two or more clones simultaneously can be obtained by mixing selected clones. Secreted antibody is seen as playing a role in the establishment of clonal dominance. A model for clonal expansion is presented. The model attempts to explain the generation of memory and antibody secreting cells within each clonal expansion in terms of the ratio of two signals, one for proliferation and one for differentiation. The delivery of these signals is proposed to involve the receptor antibody-antigen interaction for proliferation and a self-recognition site interaction for differentiation.     

Fast approximations of the rotational diffusion tensor and their application to structural assembly of molecular complexes

We present and evaluate a rigid-body, deterministic, molecular docking method, called ELMDOCK, that relies solely on the three-dimensional structure of the individual components and the overall rotational diffusion tensor of the complex, obtained from nuclear spin-relaxation measurements. We also introduce a docking method, called ELMPATIDOCK, derived from ELMDOCK and based on the new concept of combining the shape-related restraints from rotational diffusion with those from residual dipolar couplings, along with ambiguous contact/interface-related restraints obtained from chemical shift perturbations. ELMDOCK and ELMPATIDOCK use two novel approximations of the molecular rotational diffusion tensor that allow computationally efficient docking. We show that these approximations are accurate enough to properly dock the two components of a complex without the need to recompute the diffusion tensor at each iteration step. We analyze the accuracy, robustness, and efficiency of these methods using synthetic relaxation data for a large variety of protein-protein complexes. We also test our method on three protein systems for which the structure of the complex and experimental relaxation data are available, and analyze the effect of flexible unstructured tails on the outcome of docking. Additionally, we describe a method for integrating the new approximation methods into the existing docking approaches that use the rotational diffusion tensor as a restraint. The results show that the proposed docking method is robust against experimental errors in the relaxation data or structural rearrangements upon complex formation and is computationally more efficient than current methods. The developed approximations are accurate enough to be used in structure refinement protocols.     

Effects of parental light environment on growth and morphological responses of clonal offspring

• Environments experienced by parent ramets of clonal plants can potentially influence fitness of clonal offspring ramets. Such clonal parental effects may result from heritable epigenetic changes, such as DNA methylation, which can be removed by application of DNA de‐methylation agents such as 5‐azacytidine.
• To test whether parental shading effects occur via clonal generation and whether DNA methylation plays a role in such effects, parent plants of the clonal herb Alternanthera philoxeroides were first subjected to two levels of light intensity (high versus low) crossed with two levels of DNA de‐methylation (no or with de‐methylation by application of 5‐azacytidine), and then clonal offspring taken from each of these four types of parent plant were subjected to the same two light levels.
• Parental shading effects transmitted via clonal generation decreased growth and modified morphology of clonal offspring. Offspring responses were also influenced by DNA methylation level of parent plants. For clonal offspring growing under low light, parental shading effects on growth and morphology were always negative, irrespective of the parental de‐methylation treatment. For clonal offspring growing under high light, parental shading effects on offspring growth and morphology were negative when the parents were not treated with 5‐azacytidine, but neutral when they were treated with 5‐azacytidine.
• Overall, parental shading effects on clonal offspring performance of A. philoxeroides were found, and DNA methylation is likely to be involved in such effects. However, parental shading effects contributed little to the tolerance of clonal offspring to shading.

     

Clonal Variation In Proliferation Rate of Cultures of Gpk Cells

Pedigrees of twenty-six clones of a line of keratocytes derived from guinea-pig ear epidermis (GPK cells) were analysed from time-lapse film. the mean interdivision time (IDT) for the culture was 1143 φ 215 (SD) min. the mean generation rates (mean reciprocal interdivision times) of clones varied over a range of 3.93–10.2 × 10^-4/min and the standard deviation of the clonal mean generation rates was 16.8% of the average value. Transient intraclonal variations in IDT due to mitoses in a plane perpendicular to the substratum were observed. the data were also analysed on the basis of cell location in sixteen equal zones (quadrats) of the filmed area. the mean generation rate of quadrats was 8.73 x 10^-4/min (SD = 4.9%). the spatial distribution showed some clustering of cells. the mean local density of the clones (2.25 φ 0.62 cells/10^-4 cm²) was significantly higher than the quadrat density (1.76 φ 0.8 cells/10^-4 cm²). There was no significant correlation between clonal density and mean generation rates, whereas for quadrats a significant negative correlation was found (P= 2.7%). the results support the proposition that cell lineage is the major determinant of the proliferation rate of subconfluent cultures.     

Copula‐based semiparametric models for spatiotemporal data

The joint analysis of spatial and temporal processes poses computational challenges due to the data's high dimensionality. Furthermore, such data are commonly non‐Gaussian. In this paper, we introduce a copula‐based spatiotemporal model for analyzing spatiotemporal data and propose a semiparametric estimator. The proposed algorithm is computationally simple, since it models the marginal distribution and the spatiotemporal dependence separately. Instead of assuming a parametric distribution, the proposed method models the marginal distributions nonparametrically and thus offers more flexibility. The method also provides a convenient way to construct both point and interval predictions at new times and locations, based on the estimated conditional quantiles. Through a simulation study and an analysis of wind speeds observed along the border between Oregon and Washington, we show that our method produces more accurate point and interval predictions for skewed data than those based on normality assumptions.     

Model selection in the weighted generalized estimating equations for longitudinal data with dropout

We propose criteria for variable selection in the mean model and for the selection of a working correlation structure in longitudinal data with dropout missingness using weighted generalized estimating equations. The proposed criteria are based on a weighted quasi‐likelihood function and a penalty term. Our simulation results show that the proposed criteria frequently select the correct model in candidate mean models. The proposed criteria also have good performance in selecting the working correlation structure for binary and normal outcomes. We illustrate our approaches using two empirical examples. In the first example, we use data from a randomized double‐blind study to test the cancer‐preventing effects of beta carotene. In the second example, we use longitudinal CD4 count data from a randomized double‐blind study.     

Cellular isoform of the prion protein PrPc in human intestinal cell lines: genetic polymorphism at codon 129, mRNA quantification and protein detection in lipid rafts

The cellular isoform of the normal prion protein PrP(c), encoded by the PRNP gene, is expressed in human intestinal epithelial cells where it may represent a potential target for infectious prions. We have sequenced the PRNP gene in Caco-2 and HT-29 parental and clonal cell lines, and found that these cells have a distinct polymorphism at codon 129. HT-29 cells are homozygous Met/Met, whereas Caco-2 cells are heterozygous Met/Val. The 129Val variant was also detected in Caco-2 mRNAs. Real-time PCR quantifications revealed that PrP(c) mRNAs were more expressed in HT-29 cells than in Caco-2 cells. These data were confirmed by studying the expression of PrP(c) in plasma membranes and lipid rafts prepared from these cells. Overall, these results may be important in view of using human intestinal cell lines Caco-2 and HT-29 as cellular in vitro models to study the initial steps of prion propagation after oral inoculation.     

Multivariate multiple test procedures based on nonparametric copula estimation

Multivariate multiple test procedures have received growing attention recently. This is due to the fact that data generated by modern applications typically are high‐dimensional, but possess pronounced dependencies due to the technical mechanisms involved in the experiments. Hence, it is possible and often necessary to exploit these dependencies in order to achieve reasonable power. In the present paper, we express dependency structures in the most general manner, namely, by means of copula functions. One class of nonparametric copula estimators is constituted by Bernstein copulae. We extend previous statistical results regarding bivariate Bernstein copulae to the multivariate case and study their impact on multiple tests. In particular, we utilize them to derive asymptotic confidence regions for the family‐wise error rate (FWER) of multiple test procedures that are empirically calibrated by making use of Bernstein copulae approximations of the dependency structure among the test statistics. This extends a similar approach by Stange et al. (2015) in the parametric case. A simulation study quantifies the gain in FWER level exhaustion and, consequently, power that can be achieved by exploiting the dependencies, in comparison with common threshold calibrations like the Bonferroni or ?idák corrections. Finally, we demonstrate an application of the proposed methodology to real‐life data from insurance.