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.     

Stochastic branching model for hemopoietic progenitor cell differentiation

We present algebraic expressions describing the predictions of a stochastic branching model for differentiation of hemopoietic progenitor cells. The model assumes that there is a fixed probability, p (0 less than or equal to p less than or equal to 1), that commitment to a differentiative event occurs per progenitor cell division for each daughter cell. The model describes properties of in vitro hemopoietic cell differentiation including the population structure at the time the first progenitor cell becomes committed, the number of committed progenitor cells engendered by a single progenitor cell, and the probability of eventual commitment of all daughter cells derived from a single progenitor or stem cell. Application of the model to experimental data obtained from erythroid cultures suggests that the observed data can be explained by the stochastic branching model alone without making the deterministic assumption that there is a differentiative hierarchy in the lineage of the progenitors of erythropoiesis (BFU-E). The qualitative and quantitative aspects of the proposed stochastic model are discussed in conjunction with other analogous stochastic branching models.     

A stochastic model of brain cell differentiation in tissue culture

 The timing of cell differentiation can be controlled both by cell-intrinsic mechanisms and by cell-extrinsic signals. Oligodendrocyte type-2 astrocyte progenitor cells are known to be the precursor cells that give rise to oligodendrocytes. When stimulated to divide by purifed cortical astrocytes or by platelet-derived growth factor, these progenitor cells generate oligodendrocytes in vitro with a timing like that observed in vivo. The most widely accepted model of this process assumes a cell-intrinsic biological clock that resides in the progenitor cell. The intrinsic clock model originally proposed in 1986 remains as the dominant theoretical concept for the analysis of timed differentiation in this cell lineage. However, the results of a recent experimental study (Ibarrola et al., Developmental Biology, vol. 180, 1–21, 1996) are most consistent with the hypothesis that the propensity of a clone of dividing O-2A progenitor cells initially to generate at least one oligodendrocyte may be regulated by cell-intrinsic mechanisms, but that environmental signals regulate the extent of further oligodendrocyte generation. We propose a stochastic model of cell differentiation in culture to accommodate the most recent experimental findings. Our model is an age-dependent branching stochastic process with two types of cells. The model makes it possible to derive analytical expressions for the expected number of progenitor cells and of oligodendrocytes as functions of time. The model parameters were estimated by fitting these functions through data on the average (sample mean) number of both types of cells per colony at different time intervals from start of experiment. Using this method we provide a biologically meaningful interpretation of the observed pattern of oligodendrocyte generation in vitro and its modification in the presence of thyroid hormone. Received: 18 April 1997 / Revised version: 30 November 1997     

Estimation problems associated with stochastic modeling of proliferation and differentiation of O-2A progenitor cells in vitro

Our previous research effort has resulted in a stochastic model that provides an excellent fit to our experimental data on proliferation and differentiation of oligodendrocyte type-2 astrocyte progenitor cells at the clonal level. However, methods for estimation of model parameters and their statistical properties still remain far away from complete exploration. The main technical difficulty is that no explicit analytic expression for the joint distribution of the number of progenitor cells and oligodendrocytes, and consequently for the corresponding likelihood function, is available. In the present paper, we overcome this difficulty by using computer-intensive simulation techniques for estimation of the likelihood function. Since the output of our simulation model is essentially random, stochastic optimization methods are necessary to maximize the estimated likelihood function. We use the Kiefer-Wolfowitz procedure for this purpose. Given sufficient computing resources, the proposed estimation techniques significantly extend the spectrum of problems that become approachable. In particular, these techniques can be applied to more complex branching models of multi-type cell systems with dependent evolutions of different types of cells.     

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.     

The development of cell lineages: A sequential model

Abstract. The concept of cell lineage and the empirical characterization of specific lineages provide valuable insight into the problems of developmental biology. Of central interest is the decision-making process that results in the diversification of cell lines. Studies of the haemopoietic system, in which stem cells can be committed to one of at least six pathways of differentiation, have suggested that the restriction of differentiation potentials is a progressive and stochastic process. We have recently proposed an alternative model which hypothesizes that lineage potentials during haemopoiesis are expressed individually and in a predetermined sequence as progenitor cells mature. The model first arises from experimental studies which show that both normal myeloid progenitor cells and a human promyeloid cell line, which are able to differentiate towards either neutrophils or monocytes, express these potentials sequentially in culture. The close linear relationship between other haemopoietic progenitor cells is inferred from collective data from studies of bipotent progenitor cells and of haemopoietic proliferative disorders. If the development of haemopoietic cell lineages shows a tendency to follow a particular program, such a mechanism is likely to operate throughout development. In this paper we consider the evidence in favour of programmed events within progenitor cells implementing diversification, and the implications of predetermined and restricted pathways of embryonic development.     

Reconstruction of rat retinal progenitor cell lineages in vitro reveals a surprising degree of stochasticity in cell fate decisions

In vivo cell lineage-tracing studies in the vertebrate retina have revealed that the sizes and cellular compositions of retinal clones are highly variable. It has been challenging to ascertain whether this variability reflects distinct but reproducible lineages among many different retinal progenitor cells (RPCs) or is the product of stochastic fate decisions operating within a population of more equivalent RPCs. To begin to distinguish these possibilities, we developed a method for long-term videomicroscopy to follow the lineages of rat perinatal RPCs cultured at clonal density. In such cultures, cell-cell interactions between two different clones are eliminated and the extracellular environment is kept constant, allowing us to study the cell-intrinsic potential of a given RPC. Quantitative analysis of the reconstructed lineages showed that the mode of division of RPCs is strikingly consistent with a simple stochastic pattern of behavior in which the decision to multiply or differentiate is set by fixed probabilities. The variability seen in the composition and order of cell type genesis within clones is well described by assuming that each of the four different retinal cell types generated at this stage is chosen stochastically by differentiating neurons, with relative probabilities of each type set by their abundance in the mature retina. Although a few of the many possible combinations of cell types within clones occur at frequencies that are incompatible with a fully stochastic model, our results support the notion that stochasticity has a major role during retinal development and therefore possibly in other parts of the central nervous system.     

Semi-parametric ROC regression analysis with placement values

Advances in technology provide new diagnostic tests for early detection of disease. Frequently, these tests have continuous outcomes. One popular method to summarize the accuracy of such a test is the Receiver Operating Characteristic (ROC) curve. Methods for estimating ROC curves have long been available. To examine covariate effects, Pepe (1997, 2000) and Alonzo and Pepe (2002) proposed distribution-free approaches based on a parametric regression model for the ROC curve. Cai and Pepe (2002) extended the parametric ROC regression model by allowing an arbitrary non-parametric baseline function. In this paper, while we follow the same semi-parametric setting as in that paper, we highlight a new estimator that offers several improvements over the earlier work: superior efficiency, the ability to estimate the covariate effects without estimating the non-parametric baseline function and easy implementation with standard software. The methodology is applied to a case control dataset where we evaluate the accuracy of the prostate-specific antigen as a biomarker for early detection of prostate cancer. Simulation studies suggest that the new estimator under the semi-parametric model, while always being more robust, has efficiency that is comparable to or better than the Alonzo and Pepe (2002) estimator from the parametric model.     

Stochastic model for multipotent hemopoietic progenitor differentiation

In this study, the authors propose a stochastic model for multipotent hemopoietic progenitor differentiation, which assumes that there is a fixed probability (P) that a progenitor with a potential for differentiation along a particular lineage maintains the potential in each cell division in each daughter cell, and this differentiation process of each lineage proceeds independently. To examine the applicability of this model, a sequential micromanipulation of paired progenitors was carried out and followed by cytological examination of the cells contained in the colonies derived from these progenitors; then calculation was made of the ratio of the number of paired colonies containing cell(s) with a particular lineage to the number of paired colonies in which only one colony contained cell(s) with the lineage at the first and second cell division. The ratios were similar at the first and second cell division within each lineage. Furthermore, the frequences of each lineage in multilineage hemopoietic colonies were calculated using the P values obtained from these micromanipulation experiments. The expected frequencies were similar to those in the actual experiments. These results suggested that the stochastic model was applicable to multipotent hemopoietic progenitor differentiation.     

A novel simulation model for stem cells differentiation

A novel mathematical model to simulate mesenchymal stem cells differentiation into specialized cells is proposed. The model is based upon material balances for extracellular matrix compounds, growth factors and nutrients coupled with a mass-structured population balance describing cell growth, proliferation and differentiation. The proposed model is written in a general form and it may be used to simulate a generic cell differentiation pathway occurring in vivo or during in vitro cultivation when specific growth factors are used. Literature experimental data concerning the differentiation of mesenchymal stem cells into chondrocytes in terms of total DNA and glycosaminoglycan content are successfully compared with model results, thus demonstrating the validity of the proposed model as well as its predictive capability. A further test of the model capability is performed for the case of in vivo fracture healing during which mesenchymal stem cells differentiate into chondrocytes and osteoblasts. Considerations about the extension of the proposed model to different pathologies beside fracture healing are reported. Finally, sensitivity analysis of model parameters is also performed in order to clarify what mechanisms most strongly influence differentiation and the distribution of cell types.     

Clonal analysis of the differentiation potential of human adipose-derived adult stem cells

Pools of human adipose-derived adult stem (hADAS) cells can exhibit multiple differentiated phenotypes under appropriate in vitro culture conditions. Because adipose tissue is abundant and easily accessible, hADAS cells offer a promising source of cells for tissue engineering and other cell-based therapies. However, it is unclear whether individual hADAS cells can give rise to multiple differentiated phenotypes or whether each phenotype arises from a subset of committed progenitor cells that exists within a heterogeneous population. The goal of this study was to test the hypothesis that single hADAS are multipotent at a clonal level. hADAS cells were isolated from liposuction waste, and ring cloning was performed to select cells derived from a single progenitor cell. Forty-five clones were expanded through four passages and then induced for adipogenesis, osteogenesis, chondrogenesis, and neurogenesis using lineage-specific differentiation media. Quantitative differentiation criteria for each lineage were determined using histological and biochemical analyses. Eighty one percent of the hADAS cell clones differentiated into at least one of the lineages. In addition, 52% of the hADAS cell clones differentiated into two or more of the lineages. More clones expressed phenotypes of osteoblasts (48%), chondrocytes (43%), and neuron-like cells (52%) than of adipocytes (12%), possibly due to the loss of adipogenic ability after repeated subcultures. The findings are consistent with the hypothesis that hADAS cells are a type of multipotent adult stem cell and not solely a mixed population of unipotent progenitor cells. However, it is important to exercise caution in interpreting these results until they are validated using functional in vivo assays.     

A pedagogical walkthrough of computational modeling and simulation of Wnt signaling pathway using static causal models in MATLAB

The discrete coefficient of determination (CoD) measures the nonlinear interaction between discrete predictor and target variables and has had far-reaching applications in Genomic Signal Processing. Previous work has addressed the inference of the discrete CoD using classical parametric and nonparametric approaches. In this paper, we introduce a Bayesian framework for the inference of the discrete CoD. We derive analytically the optimal minimum mean-square error (MMSE) CoD estimator, as well as a CoD estimator based on the Optimal Bayesian Predictor (OBP). For the latter estimator, exact expressions for its bias, variance, and root-mean-square (RMS) are given. The accuracy of both Bayesian CoD estimators with non-informative and informative priors, under fixed or random parameters, is studied via analytical and numerical approaches. We also demonstrate the application of the proposed Bayesian approach in the inference of gene regulatory networks, using gene-expression data from a previously published study on metastatic melanoma.     

Endocrine differentiation by a human rectal adenocarcinoma cell line (HRA-19)

Colorectal epithelium is composed of a variety of cell types, including absorptive, mucous and endocrine cells. All of these cell types are thought to arise from stem cells located at the base of the crypt. However, the factors which control these differentiation pathways are poorly understood. In attempts to establish differentiated in vitro systems, one approach has been to grow primary human colorectal adenocarcinomas as cell lines. Some of these cell lines retain a sufficient number of the differentiated features of their tissue of origin to make them useful experimental systems for studying differentiation. This study describes the characterisation of such a cell line, the HRA-19 line. HRA-19 cells were derived from a primary human rectal adenocarcinoma. The cells grew as monolayers in vitro on tissue-culture plastic and remained pleomorphic even after 150 passages in vitro. Some colonies of cells expressed alkaline phosphatase activity, an enzyme normally expressed in vivo by absorptive cells of the upper crypt and surface epithelium. No evidence of differentiation into goblet or endocrine cells was obtained in monolayer cultures of HRA-19 cells. Xenografts of this cell line contained cells with the ultrastructural characteristics of absorptive and endocrine cells. These endocrine cells exhibited Grimelius silver staining, displayed formaldehyde-induced fluorescence and contained many basally located, electron-dense granules. When grown as monolayers, clones of this cell line retained the heterogeneity with respect to morphology and alkaline phosphatase expression of the parent cell line. It is proposed that this cell line is derived from malignant progenitor cells which retain the ability to differentiate.(ABSTRACT TRUNCATED AT 250 WORDS)     

Endocrine differentiation by a human rectal adenocarcinoma cell line (HRA-19)

Abstract. Colorectal epithelium is composed of a variety of cell types, including absorptive. mucous and endocrine cells. All of these cell types are thought to arise from stem cells located at the base of the crypt. However, the factors which control these differentiation pathways are poorly understood. In attempts to establish differentiated in vitro systems, one approach has been to grow primary human colorectal adenocarcinomas as cell lines. Some of these cell lines retain a sufficient number of the differentiated features of their tissue of origin to make them useful experimental systems for studying differentiation. This study describes the characterisation of such a cell line, the HRA-19 line. HRA-19 cells were derived from a primary human rectal adenocarcinoma. The cells grew as monolayers in vitro on tissue-culture plastic and remained pleomorphic even after 150 passages in vitro. Some colonies of cells expressed alkaline phosphatase activity, an enzyme normally expressed in vivo by absorptive cells of the upper crypt and surface epithelium. No evidence of differentiation into goblet or endocrine cells was obtained in monolayer cultures of HRA-19 cells. Xenografts of this cell line contained cells with the ultrastructural characteristics of absorptive and endocrine cells. These endocrine cells exhibited Grimelius silver staining, displayed formaldehyde-induced fluorescence and contained many basally located, electron-dense granules. When grown as monolayers, clones of this cell line retained the heterogeneity with respect to morphology and alkaline phosphatase expression of the parent cell line. It is proposed that this cell line is derived from malignant progenitor cells which retain the ability to differentiate. This cell line has properties not previously reported for a human colorectal adenocarcinoma cell line and will be useful for studying the control of differentiation in colorectal epithelial cells.     

Additive partial linear models with measurement errors

We consider statistical inference for additive partial linearmodels when the linear covariate is measured with error. Wepropose attenuation-to-correction and simulation-extrapolation,simex, estimators of the parameter of interest. It is shownthat the first resulting estimator is asymptotically normaland requires no undersmoothing. This is an advantage of ourestimator over existing backfitting-based estimators for semiparametricadditive models which require undersmoothing of the nonparametriccomponent in order for the estimator of the parametric componentto be root-n consistent. This feature stems from a decreaseof the bias of the resulting estimator, which is appropriatelyderived using a profile procedure. A similar characteristicin semiparametric partially linear models was obtained by Wanget al. (2005). We also discuss the asymptotics of the proposedsimex approach. Finite-sample performance of the proposed estimatorsis assessed by simulation experiments. The proposed methodsare applied to a dataset from a semen study.     

Bayesian Inference in Semiparametric Mixed Models for Longitudinal Data

Summary .  We consider Bayesian inference in semiparametric mixed models (SPMMs) for longitudinal data. SPMMs are a class of models that use a nonparametric function to model a time effect, a parametric function to model other covariate effects, and parametric or nonparametric random effects to account for the within-subject correlation. We model the nonparametric function using a Bayesian formulation of a cubic smoothing spline, and the random effect distribution using a normal distribution and alternatively a nonparametric Dirichlet process (DP) prior. When the random effect distribution is assumed to be normal, we propose a uniform shrinkage prior (USP) for the variance components and the smoothing parameter. When the random effect distribution is modeled nonparametrically, we use a DP prior with a normal base measure and propose a USP for the hyperparameters of the DP base measure. We argue that the commonly assumed DP prior implies a nonzero mean of the random effect distribution, even when a base measure with mean zero is specified. This implies weak identifiability for the fixed effects, and can therefore lead to biased estimators and poor inference for the regression coefficients and the spline estimator of the nonparametric function. We propose an adjustment using a postprocessing technique. We show that under mild conditions the posterior is proper under the proposed USP, a flat prior for the fixed effect parameters, and an improper prior for the residual variance. We illustrate the proposed approach using a longitudinal hormone dataset, and carry out extensive simulation studies to compare its finite sample performance with existing methods.     

Elucidating the Sources of β-Catenin Dynamics in Human Neural Progenitor Cells

Human neural progenitor cells (hNPCs) form a new prospect for replacement therapies in the context of neurodegenerative diseases. The Wnt/[Formula: see text]-catenin signaling pathway is known to be involved in the differentiation process of hNPCs. RVM cells form a common cell model of hNPCs for in vitro investigation. Previous observations in RVM cells raise the question of whether observed kinetics of the Wnt/[Formula: see text]-catenin pathway in later differentiation phases are subject to self-induced signaling. However, a concern when investigating RVM cells is that experimental results are possibly biased by the asynchrony of cells w.r.t. the cell cycle. In this paper, we present, based on experimental data, a computational modeling study on the Wnt/[Formula: see text]-catenin signaling pathway in RVM cell populations asynchronously distributed w.r.t. to their cell cycle phases. Therefore, we derive a stochastic model of the pathway in single cells from the reference model in literature and extend it by means of cell populations and cell cycle asynchrony. Based on this, we show that the impact of the cell cycle asynchrony on wet-lab results that average over cell populations is negligible. We then further extend our model and the thus-obtained simulation results provide additional evidence that self-induced Wnt signaling occurs in RVM cells. We further report on significant stochastic effects that directly result from model parameters provided in literature and contradict experimental observations.     

Systems Mapping for Hematopoietic Progenitor Cell Heterogeneity

Cells with the same genotype growing under the same conditions can show different phenotypes, which is known as “population heterogeneity”. The heterogeneity of hematopoietic progenitor cells has an effect on their differentiation potential and lineage choices. However, the genetic mechanisms governing population heterogeneity remain unclear. Here, we present a statistical model for mapping the quantitative trait locus (QTL) that affects hematopoietic cell heterogeneity. This strategy, termed systems mapping, integrates a system of differential equations into the framework for systems mapping, allowing hypotheses regarding the interplay between genetic actions and cell heterogeneity to be tested. A simulation approach based on cell heterogeneity dynamics has been designed to test the statistical properties of the model. This model not only considers the traditional QTLs, but also indicates the methylated QTLs that can illustrate non-genetic individual differences. It has significant implications for probing the molecular, genetic and epigenetic mechanisms of hematopoietic progenitor cell heterogeneity.     

Estimated quadratic inference function for correlated failure time data

An estimated quadratic inference function method is proposed for correlated failure time data with auxiliary covariates. The proposed method makes efficient use of the auxiliary information for the incomplete exposure covariates and preserves the property of the quadratic inference function method that requires the covariates to be completely observed. It can improve the estimation efficiency and easily deal with the situation when the cluster size is large. The proposed estimator which minimizes the estimated quadratic inference function is shown to be consistent and asymptotically normal. A chi-squared test based on the estimated quadratic inference function is proposed to test hypotheses about the regression parameters. The small-sample performance of the proposed method is investigated through extensive simulation studies. The proposed method is then applied to analyze the Study of Left Ventricular Dysfunction (SOLVD) data as an illustration.