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.     

Replicative and differentiative behavior in daughter pairs of myogenic stem cells

Time-lapse microcinematography was used to trace the migration and subsequent fate of daughter pairs from single myogenic stem cells. The generation times of siblings which divide are closely correlated (r, 0.73) compared with randomly selected cells (r, 0.059), suggesting the more or less equal partition of stem cell components. The commitment to differentiative expression, however, is not inherited and must occur following stem cell division. Within the combined group in which at least one sibling fused, the ratio of pairs in which both fuse to pairs in which one divides and one fuses is 21:18. X2 for this ratio (compared with 1:1) is 0.103 indicating that it is just as likely that one daughter fuses and the other divides as that both fuse. We see no evidence of an intrinsic mitotic clock. If there were, one would expect that both or neither daughter would differentiate, depending on whether or not the 'clock' had run out for a particular stem cell.     

Myogenic stem cell commitment probability remains constant as a function of organismal and mitotic age

Chicken myogenic stem cells can undergo symmetric and asymmetric cell divisions. Symmetric divisions produce two stem cells or two cells committed to terminal muscle differentiation. Asymmetric divisions produce one stem cell and one committed cell. Committed cells undergo four divisions, and their progeny differentiate into postmitotic, biochemically distinct muscle cells, which can be identified immunocytochemically. The control of stem cell commitment was investigated in vitro by means of cell cloning and subcloning experiments, and computer modeling. We found that stem cell commitment is a process which can be modeled as a stochastic event, with a central tendency or probability of 0.2 +/- 0.1. This value is independent of organismal or mitotic age of the stem cells, cell density, or growth in a mitogen-poor environment. Myogenic stem cells stop dividing after approximately 30 divisions in vitro. Since the probability of commitment to terminal differentiation remains below 0.5, clonal senescence and terminal differentiation are separate processes in this system.     

Interstitial stem cells in Hydra: multipotency and decision-making

Interstitial stem cells in Hydra constitute a population of multipotent cells, which continuously give rise to differentiated products during the growth and budding of Hydra polyps. They also give rise to germ cells in animals undergoing sexual differentiation. Cloning experiments have shown that interstitial stem cells are multipotent. In vivo tracing of stem cell lineages has revealed that stem cells divide symmetrically to yield two stem cells or asymmetrically to yield one stem cell daughter and one daughter cell which initiates nerve or nematocyte differentiation. Following commitment, some nerve cell precursors migrate from the body column into the head or foot region, thus giving rise to the high density of nerve cells observed in these regions. Stem cell proliferation is regulated by changes in the self-renewal probability and is controlled by stem cell density. Nerve cell commitment is controlled by several peptides including the Head Activator. Factors affecting nematocyte commitment are not known, but wnt and notch signaling are both required for differentiation of committed precursors.     

Commitment to erythroid differentiation by friend erythroleukemia cells: a stochastic analysis

A method for the clonal analysis of murine erythroleukemia cells has been developed which allows the precise characterization of the number of progeny produced by each cell and the degree of differentiation of each progeny cell. The potential of almost every cell in the culture can be monitored because a plating efficiency close to 100% has been achieved. The effects of treatment with an inducer of differentiation (DMSO) on the proliferative capacity of the treated cells have been studied with this technique. Cells from a mass culture treated with inducer give rise to colonies of differentiated progeny when subsequently cloned in the absence of inducer. Colonies exhibiting this phenotype represent the progeny of cells committed to the differentiation pathway by treatment with inducer. We observe that the commitment decision limits the subsequent proliferative capacity of the cell to four additional cell divisions. A quantitative analysis suggests that the commitment decision for each cell is made in a stochastic manner. Irreversible commitment to the expression of differentiated functions occurs with discrete probability per cell generation for many cell generations. The value for this probability is a function of the concentration of inducer (DMSO). A correlative biochemical study suggests that an irreversible commitment decision by a significant proportion of the population precedes or accompanies increases in cytoplasmic globin mRNA levels, one of the earliest detectable biochemical markers for erythroid differentiation in this system.A specific kinetic model based on these considerations has been developed to predict clonal phenotypes as a function of time and probability of commitment. Quantitative predictions based on this model are in excellent agreement with experimental observations. The effectiveness of a stochastic model in predicting the behavior of this system is discussed in relation to the stochastic behavior of normal hematopoiesis and the biochemical mechanisms which control these differentiation programs.     

Analytic formulas for discrete stochastic models of cell populations with both differentiation and de-differentiation

Cell differentiation often appears to be a stochastic process particularly in the hemopoietic system. One of the earliest stochastic models for the growth of stem cell populations was proposed by Till et al. in 1964. In this model there are just two cell types: stem cells and specialized cells. At each time step there is a fixed probability that a stem cell differentiates into a specialized cell and a fixed probability that it undergoes mitosis to produce two stem cells. Even though this model is conceptually simple the myriad of possible outcomes has made it difficult to analyse. We present original closed-form expressions for the probability functions and a fast algorithm for computing them. Renewed interest in stem cells has raised questions about the effect de-differentiation has on stem cell populations. We have extended the stochastic model to include de-differentiation and show that even a small amount of de-differentiation can have a large effect on stem cell population growth.     

The kinetics of hematopoietic stem cells during and after hypoxia. A model analysis

A previously described mathematical model of the hematopoietic stem cell system has been extended to permit a detailed understanding of the data during and after hypoxia. The model includes stem cells, erythroid and granuloid progenitors and precursors. Concerning the intramedullary feedback mechanisms two basic assumptions are made: 1) The fraction "a" of CFU-S in active cell cycle is regulated. Reduced cell densities of CFU-S, progenitors or precursors lead to an accelerated stem cell cycling. Enlarged cell densities suppress cycling. 2) The self renewal probability "p" of CFU-S is also regulated. The normal steady state is described by p = 0.5, indicating that on statistical average each dividing mother stem cell is replaced by one daughter stem cell, while the second differentiates. Diminished cell densities of CFU-S or enlarged densities of progenitors and precursors induce a more intensive self renewal (p greater than 0.5), such that the stem cell number increases. The self renewal probability declines (p less than 0.5) if too many CFU-S or too few progenitors and precursors are present. The model reproduces bone marrow data for CFU-S, BFU-E, CFU-C, CFU-E, 59 Fe-uptake and nucleated cells in hypoxia and posthypoxia. Although the ratio of differentiation into the erythroid and granuloid cell lines is kept constant in the model, a changing ratio of CFU-E and CFU-C results. The model suggests that stem cells and progenitor cells are regulated by a regulatory interference of erythropoiesis and granulopoiesis.     

Multi-potent progenitors in freshly isolated and cultured human mesenchymal stem cells: a comparison between adipose and dermal tissue

Mesenchymal stem cells (MSCs) from human adult adipose tissue (A-MSCs) have a better differentiative ability than MSCs derived from the derma (D-MSCs). To test whether this difference is associated with differences in the content of multi-potent progenitors in A-MSCs, the number and the differentiative properties of multi-potent progenitors have been analyzed in various preparations of A-MSCs and D-MSCs. Adipogenic and osteogenic differentiation performed on colony-forming units have revealed that adipogenic and osteogenic progenitors are similar in the two populations, with only a slighty better performance of A-MSCs over D-MSCs from passages p0 to p15. An analysis of the presence of tri-, bi-, uni- and nulli-potent progenitors isolated immediately after isolation from tissues (p0) has shown comparable numbers of tri-potent and bi-potent progenitors in MSCs from the two tissues, whereas a higher content in uni-potent cells committed to adipocytes and a lower content in nulli-potent cells has been observed in A-MSCs. Furthermore, we have characterized the progenitors present in A-MSCs after six passages in vitro to verify the way in which in vitro culture can affect content in progenitor cells. We have observed that the percentage of tri-potent cells in A-MSCs at p6 remains similar to that observed at p0, although bi-potent and uni-potent progenitors committed to osteogenic differentiation increase at p6, whereas nulli-potent cells decrease at p6. These data indicate that the greater differentiative ability of A-MSC populations does not correlate directly with the number of multi-potent progenitors, suggesting that other factors influence the differentiation of bulk populations of A-MSCs.     

Extrathymic hemopoietic progenitors committed to T cell differentiation in the adult mouse

The role of the thymus in T cell commitment of hemopoietic precursor is yet controversial. We previously identified a major T cell progenitor activity in precursor cells isolated from bone marrow-derived spleen colonies. In this study, we characterize the properties of these pre-T cells. We demonstrate that they have unique phenotype and can be generated in a total absence of any thymic influence. Indeed, even when studied at the single-cell level, extrathymic T cell-committed precursors express T cell-specific genes. Moreover, these cells are not committed to a particular T cell differentiation pathway because they can generate both extrathymic CD8alphaalpha+ intraepithelial lymphocytes and thymus-derived conventional thymocytes. We also compared these pre-T cells with fully T cell-committed thymic progenitors. When tested in vitro or by direct intrathymic transfer, these cells have a low clonogenic activity. However, after i.v. transfer, thymus repopulation is efficient and these precursors generate very high numbers of peripheral T cells. These results suggest the existence of extra steps of pre-T cell maturation that improve thymus reconstitution capacity and that can be delivered even after full T cell commitment. Consequently, our studies identify a source of extrathymic progenitors that will be helpful in defining the role of the thymus in the earliest steps of T cell differentiation.     

Lineage development of hematopoietic stem and progenitor cells

Hematopoietic stem cells have the potential to develop into multipotent and different lineage-restricted progenitor cells that subsequently generate all mature blood cell types. The classical model of hematopoietic lineage commitment proposes a first restriction point at which all multipotent hematopoietic progenitor cells become committed either to the lymphoid or to the myeloid development, respectively. Recently, this model has been challenged by the identification of murine as well as human hematopoietic progenitor cells with lymphoid differentiation capabilities that give rise to a restricted subset of the myeloid lineages. As the classical model does not include cells with such capacities, these findings suggest the existence of alternative developmental pathways that demand the existence of additional branches in the classical hematopoietic tree. Together with some phenotypic criteria that characterize different subsets of multipotent and lineage-restricted progenitor cells, we summarize these recent findings here.     

Clonal Attenuation In Chick Embryo Fibroblasts Experimental Data, A Model and Computer Simulations

When cells from mass cultures of chick embryo fibroblasts are grown at very low density, some cells yield large clones while others produce smaller clones, and some cells fail to divide at all. the distribution of clone sizes is related to the number of population doublings which the donor mass culture has undergone: the more doublings which have occurred, the smaller the average clone size. In this report we describe a model which analyses this phenomenon, referred to as ‘clonal attenuation’, in detail. The model is based on the concept that a cell with hypothetically unlimited replicative potential—i.e. a ‘stem’ cell—can become ‘committed’ to a programme of limited replicative potential. This event is assumed to be stochastic and to have a fixed probability per stem cell division. the parameters of the model are: P_c, the probability of commitment; N, the number of differentiative divisions; and T_c, the cell-cycle times. By computer simulation, it is shown that P_c increases roughly exponentially at each successive stem cell division. According to the model, when the daughter of a stem cell becomes committed, its progeny proceed through N obligatory divisions before becoming terminally differentiated (post-mitotic). the best-fit value of N was found to be seven. The simulations also reveal that the absolute number of stem cells in the total population increases for most of the lifespan of the culture. When P_c becomes much greater than 0.5, the number of stem cells declines rapidly to zero, and the culture nears senescence. Sensitivity analysis shows that P_c can assume only a limited range of values at each stem-cell division.     

Binding, internalization and degradation of radio-iodinated interleukin 3 and granulocyte-macrophage colony stimulating factor by various hemopoietic cells

The proliferation and differentiation of hemopoietic committed progenitor cells depend on colony stimulating factors (CSF). However, isolated mouse granulocyte-macrophage progenitor cells can still undergo limited proliferation in serum-free cultures after CSF deprivation. To test whether this is due to an accumulated pool of internalized factor, we examined the binding, internalization and degradation of radiolabelled interleukin 3 (IL-3) and granulocyte-macrophage colony stimulating factor (GM-CSF) in various hemopoietic cells. We found 20,000 high affinity IL-3 receptors on cells of two IL-3-dependent hemopoietic cell lines, FDC-P1 and FDC-P2 (Kd = 85 and 129 pM). FDC-P1 cells, which also respond to GM-CSF, possess 600 high-affinity GM-CSF receptors (Kd = 64 pM). Cells of both lines internalize IL-3, but only FDC-P1 cells release degraded IL-3 at a rapid rate. Both cell lines have similar dose-response curves for IL-3 and survival kinetics after factor removal. All other cells tested behave like FDC-P1, suggesting that the metabolism of IL-3 by FDC-P2 is exceptional. Our study indicates that transient proliferation of committed progenitor cells in the absence of added factors is apparently not due to a stable pool of internalized CSF but merely represents an intrinsic capability of these cells.     

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.     

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     

Postnatal liver hemopoiesis in mice: generation of pre-B cells, granulocytes, and erythrocytes in discrete colonies

Morphologic analysis of hemopoietic tissue in mouse liver reveals the persistence of erythropoietic, granulopoietic, and lymphopoietic activity for approximately 2 wk after birth. Near the end of the first postnatal week, we noted a remarkable reorganization of the hemopoietic cells that was characterized by a transition from a diffuse distribution of mixed erythroid, myeloid, and lymphoid elements to a focal pattern of discrete hemopoietic colonies scattered among the cords of hepatic parenchymal cells. Each hemopoietic focus contained cells progressing along a single differentiation pathway (i.e., erythroid, myeloid, or lymphoid cells). Megakaryocytes were seen as solitary cells surrounded by hepatocytes. This pattern of colonization was observed in all strains of mice examined. In the livers of mice with known hemopoietic defects, however, differences were found in the duration of postnatal hemopoiesis. Accessory cells with macrophage-like features were consistently observed in erythropoietic foci, but were rarely seen in lymphoid foci. The latter were formed by pre-B cells identifiable by the presence of cytoplasmic mu-heavy chains and the absence of light chain expression. The occurrence of discrete colonies of erythroid, myeloid, and pre-B lymphoid cells in the postnatal liver suggests that each is derived from a single, committed precursor cell. This anatomical compartmentalization according to cell type offers a useful model system for analysis of hemopoietic differentiation and of the generation of clonal diversity among B lineage cells.     

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.