L’autorenouvellement est une propriété fondatrice du concept de cellule souche. Cependant, malgré l’avancée des connaissances actuelles, les mécanismes moléculaires sous-jacents restent mal compris. Nous nous sommes donc intéressés à cette question, en étudiant l’équilibre entre autorenouvellement et différenciation dans des progéniteurs érythrocytaires primaires. D’une part, grâce à une étude combinant des approches pharmacologiques et de génétique fonctionnelle, nos résultats montrent que le contrôle de la synthèse cellulaire du cholestérol joue un rôle essentiel dans la régulation du basculement de l’autorenouvellement vers la différenciation. D’autre part, nous avons étudié la nature stochastique de l’expression génique au cours du passage de l’autorenouvellement vers la différenciation. En effet, contrairement au caractère déterministe initialement attribué à l’expression des gènes, les données accumulées au cours des dernières années démontrent que cette expression repose sur des processus stochastiques. Nous avons en particulier oeuvré à la conception et à la mise en place d’un dispositif permettant de suivre en temps réel l’expression génique dans des cellules individualisées, afin de pouvoir mesurer et évaluer cette stochasticité. Au final, l’ensemble de ces travaux participent à la compréhension des bases moléculaires de l’autorenouvellement et du contrôle des choix du devenir cellulaire. / Self-renewal is a key property of the stem cell concept. However, despite the recent advances in this field, the underlying molecular bases are not yet properly understood. We tackled this question by studying the balance between self-renewal and differentiation, in primary erythroid progenitors. Our work is twofold. First, by combining pharmacologic approaches and functional genetics, we have shown that the control of cellular cholesterol synthesis plays a central role in the regulation between self-renewal and differentiation. Second, we have studied the stochastic nature of gene expression along the transition from self-renewal to differentiation. Indeed, while gene expression was initially deemed to be deterministic, more and more data tend to show that it relies on stochastic processes. In particular, we participated to the design of an experimental method allowing to mesure gene expression in a single cell, in real-time. All in all, the work presented here brings new elements towards the understanding of molecular bases controlling self-renewal and cell fate choices.

Erythropoiesis maintains stable tissue oxygenation in the basal state, while accelerating red cell production in anemia, blood loss or high altitude. The principal regulator of erythropoiesis is the hormone erythropoietin (Epo). In response to hypoxic stress, Epo can increase a 1000-fold, driving erythropoietic rate by up to 10-fold. It’s been suggested that survival pathways activated by the Epo receptor (EpoR) underlie its regulation of erythropoietic rate. A number of apparently redundant EpoR survival pathways were identified in vitro, raising the possibility of their functional specialization in vivo. Here I assessed the roles of three survival pathways activated by EpoR in erythroblasts in-vivo: the suppression of cell-surface Fas and FasL, the suppression of the pro-apoptotic regulator Bim, and the induction of the anti-apoptotic regulator Bcl-xL. I used the novel CD71/Ter119 flow-cytometric method of identifying erythroblast maturation stages in vivo to measure these apoptotic pathways in fetal liver and adult erythropoietic tissues. I found that these pathways differ markedly in their regulation of erythropoietic rate. Using mouse genetic models, I found that apoptosis mediated by interaction between erythroblasts that co-express cell-surface Fas and FasL plays a key autoregulatory role in stabilizing the size of the erythroblast pool in the basal state. Further, mice mutant for Fas or FasL showed a delayed erythropoietic response to hypoxia or high Epo. This suggests that Fas and FasL accelerate the stress response by providing an apoptotic ‘cell reserve’ that can be rescued by Epo in stress. I also examined the in-vivo behavior of two cell-intrinsic apoptotic regulators, Bcl-xL and Bim, previously unexamined in stress. The induction of Bcl-xL was rapid but transient, whilst the suppression of Bim was slower but persistent. My data suggest that Bcl-xL is a key mediator of EpoR’s anti-apoptotic signal very early in the stress response, before Bim and Fas are suppressed. Bcl-xL adaptation to high Epo occurs through inhibition of Stat5 activation, and resets it for the next acute stress. My findings suggest that in vivo, Epo regulates erythropoietic rate through erythroblast apoptosis, and that various apoptotic regulators play distinct and unique roles in this process. My work provides new molecular insights into erythropoiesis that are relevant to cytokine biology and to clinical approaches of disease treatment.

Ce mémoire concerne la modélisation mathématique de l’érythropoïèse, à savoir le processus de production des érythrocytes (ou globules rouges) et sa régulation par l’érythropoïétine, une hormone de contrôle. Nous proposons une extension d’un modèle d’érythropoïèse tenant compte du vieillissement des cellules matures. D’abord, nous considérons un modèle structuré en maturité avec condition limite mouvante, dont la dynamique est capturée par des équations d’advection. Biologiquement, la condition limite mouvante signifie que la durée de vie maximale varie afin qu’il y ait toujours un flux constant de cellules éliminées. Par la suite, des hypothèses sur la biologie sont introduites pour simplifier ce modèle et le ramener à un système de trois équations différentielles à retard pour la population totale, la concentration d’hormones ainsi que la durée de vie maximale. Un système alternatif composé de deux équations avec deux retards constants est obtenu en supposant que la durée de vie maximale soit fixe. Enfin, un nouveau modèle est introduit, lequel comporte un taux de mortalité augmentant exponentiellement en fonction du niveau de maturité des érythrocytes. Une analyse de stabilité linéaire permet de détecter des bifurcations de Hopf simple et double émergeant des variations du gain dans la boucle de feedback et de paramètres associés à la fonction de survie. Des simulations numériques suggèrent aussi une perte de stabilité causée par des interactions entre deux modes linéaires et l’existence d’un tore de dimension deux dans l’espace de phase autour de la solution stationnaire. / This thesis addresses erythropoiesis mathematical modeling, which is the process of erythrocytes production and its regulation by erythropeitin. We propose an erythropoiesis model extension which includes aging of mature cells. First, we consider an age-structured model with moving boundary condition, whose dynamics are represented by advection equations. Biologically, the moving boundary condition means that the maximal lifespan varies to account for a constant degraded cells flux. Then, hypotheses are introduced to simplify and transform the model into a system of three delay differential equations for the total population, the hormone concentration and the maximal lifespan. An alternative model composed of two equations with two constant delays is obtained by supposing that the maximal lifespan is constant. Finally, a new model is introduced, which includes an exponential death rate depending on erythrocytes maturity level. A linear stability analysis allows to detect simple and double Hopf bifurcations emerging from variations of the gain in the feedback loop and from parameters associated to the survival function. Numerical simulations also suggest a loss of stability caused by interactions between two linear modes and the existence of a two dimensional torus in the phase space close to the stationary solution.

Cette thèse est consacrée à la modélisation mathématique de l'hématopoïèse et des maladies sanguines. Plusieurs modèles traitant d'aspects différents et complémentaires de l'hématopoïèse y sont étudiés.Tout d'abord, un modèle multi-échelle de l'érythropoïèse est analysé, dans lequel sont décrits à la fois le réseau intracellulaire, qui détermine le comportement individuel des cellules, et la dynamique des populations de cellules. En utilisant des données expérimentales sur les souris, nous évaluons les rôles des divers mécanismes de retro-contrôle en réponse aux situations de stress.Ensuite, nous tenons compte de la distribution spatiale des cellules dans la moelle osseuse, question qui n'avait pas été étudiée auparavant. Nous décrivons l'hématopoïèse normale à l'aide d'un système d'équations de réaction-diffusion-convection et nous démontrons l'existence d'une distribution stationnaire des cellules. Puis, nous introduisons dans le modèle les cellules malignes. Pour certaines valeurs des paramètres, la solution "disease-free" devient instable et une autre solution, qui correspond à la leucémie, apparaît. Cela mène à la formation d'une tumeur qui se propage dans la moelle osseuse comme une onde progressive. La vitesse de cette propagation est étudiée analytiquement et numériquement. Les cellules de la moelle osseuse échangent des signaux qui régulent le comportement cellulaire. Nous étudions ensuite une équation integro-différentielle qui décrit la communication cellulaire et nous prouvons l'existence d'une solution du type onde progressive en utilisant la théorie du degré topologique et la méthode de Leray et Schauder. L'approche multi-agent est utilisée afin d'étudier la distribution des différents types de cellules dans la moelle osseuse.Finalement, nous étudions un modèle de type "Physiologically Based Pharmacokinetics-Pharmacodynamics" du traitement de la leucémie par l'AraC. L'AraC agit comme chimiothérapie et induit l'apoptose de toutes les cellules proliférantes, saines et malignes. La pharmacocinétique donne accès à la concentration intracellulaire d'AraC. Cette dernière, à son tour, détermine la dynamique des populations cellulaires et, par conséquent, l'efficacité de différents protocoles de traitement. / This PhD thesis is devoted to mathematical modelling of haematopoiesis and blood diseases. We investigate several models, which deal with different and complementary aspects of haematopoiesis.The first part of the thesis concerns a multi-scale model of erythropoiesis where intracellular regulatory networks, which determine cell choice between self-renewal, differentiation and apoptosis, are coupled with dynamics of cell populations. Using experimental data on anemia in mice, we evaluate the roles of different feedback mechanisms in response to stress situations. At the next stage of modelling, spatial cell distribution in the bone marrow is taken into account, the question which has not been studied before. We describe normal haematopoiesis with a system of reaction-diffusion-convection equations and prove existence of a stationary cell distribution. We then introduce malignant cells into the model. For some parameter values the disease free solution becomes unstable and another one, which corresponds to leukaemia, appears. This leads to the formation of tumour which spreads in the bone marrow as a travelling wave. The speed of its propagation is studied analytically and numerically. Bone marrow cells exchange different signals that regulate cell behaviour. We study, next, an integro-differential equation which describes cell communication and prove the existence of travelling wave solutions using topological degree and the Leray-Schauder method. Individual based approach is used to study distribution of different cell types in the bone marrow. Finally, we investigate a Physiologically Based Pharmacokinetics-Pharmacodynamics model of leukaemia treatment with AraC drug. AraC acts as chemotherapy, inducing apoptosis of all proliferating cells, normal and malignant. Pharmacokinetics provides the evolution of intracellular AraC. This, in turn, determines cell population dynamics and, consequently, efficacy of treatment with different protocols.

Stem cells differentiate through an organized hierarchy of intermediate cell types to terminally differentiated cell types. This process is largely guided by master transcriptional regulators, but it also depends on the expression of many other types of genes. The discrete cell types in the differentiation hierarchy are often identified based on the expression or non-expression of certain marker genes. Historically, these have often been various cell-surface proteins, which are fairly easy to assay biochemically but are not necessarily causative of the cell type, in the sense of being master transcriptional regulators. This raises important questions about how gene expression across the whole genome controls or reflects cell state, and in particular, differentiation hierarchies. Traditional approaches to understanding gene expression patterns across multiple conditions, such as principal components analysis or K-means clustering, can group cell types based on gene expression, but they do so without knowledge of the differentiation hierarchy. Hierarchical clustering and maximization of parsimony can organize the cell types into a tree, but in general this tree is different from the differentiation hierarchy. Using hematopoietic differentiation as an example, we demonstrate how many genes other than marker genes are able to discriminate between different branches of the differentiation tree by proposing two models for detecting genes that are up-regulated or down-regulated in distinct lineages. We then propose a novel approach to solving the following problem: Given the differentiation hierarchy and gene expression data at each node, construct a weighted Euclidean distance metric such that the minimum spanning tree with respect to that metric is precisely the given differentiation hierarchy. We provide a set of linear constraints that are provably sufficient for the desired construction and a linear programming framework to identify sparse sets of weights, effectively identifying genes that are most relevant for discriminating different parts of the tree. We apply our method to microarray gene expression data describing 38 cell types in the hematopoiesis hierarchy, constructing a sparse weighted Euclidean metric that uses just 175 genes. These 175 genes are different than the marker genes that were used to identify the 38 cell types, hence offering a novel alternative way of discriminating different branches of the tree. A DAVID functional annotation analysis shows that the 175 genes reflect major processes and pathways active in different parts of the tree. However, we find that there are many alternative sets of weights that satisfy the linear constraints. Thus, in the style of random-forest training, we also construct metrics based on random subsets of the genes and compare them to the metric of 175 genes. Our results show that the 175 genes frequently appear in the random metrics, implicating their significance from an empirical point of view as well. Finally, we show how our linear programming method is able to identify columns that were selected to build minimum spanning trees on the nodes of random variable-size matrices.