ETUDE DE L'EQUATION HARMONIQUE DANS UN OUVERT AVEC DES CONDITIONS NONLINEAIRES DE FLUX AU BORD.

The main aim of this thesis is divided into two parts. The first part is devoted to the study of the problem,\begin{equation} \label{Equ.1.resume.anglais}\left\{\begin{aligned}-\Delta u \, + u &= 0 ~~ \text{in} ~~ \Omega, \\ \frac{\partial u}{\partial n} \,+ \, g(u) &= \mu ~~ \text{on} ~~ \partial \Omega,\end{aligned}\right .\end{equation}where $\Omega$ is a bounded regular domain of $\mathbb{R}^N$, $g(\cdot)$ is a continuous function that satisfies the sign condition $s \cdot g(s) \geq 0,$ in some model case we will assume that $g(\cdot)$ is increassing, and finally $\mu$ is a bounded measure on $\partial \Omega.$ Some of our results remain true when $\Omega:=\mathbb{R}^N_+.$We will start by proving the existence of a solution when $\mu$ is an $L^1(\partial \Omega)$ function, and this independently of the nonlinearity $g(\cdot)$ that satisfies the previous hypothesis. Then, we will study the case when $\mu$ is a Radon measure on $\partial \Omega$. In such a context, some new conditions appear on $g(\cdot)$ and $\mu$ that assure the existence of a solution. We will prove the existence of a solution when $g(\cdot)$ is a sub-critical nonlinearity in dimension $N$ larger or equal to three, and when $g$ satisfies the weak singularity assumption on the boundary in case $N$ equals two. When $\Omega:=\mathbb{R}^2_+$ and $\mu:=c \, \delta_0$, our result states that the problem admits a solution if and only if $$\frac{\pi}{a_-(g)} \leq c \leq \frac{\pi}{a_+(g)},$$where $a_-(g)$ and $a_+(g)$ denote the exponential order of growth of the function $g(\cdot)$, respectively at minus and plus infinity.Finally, we fix $g(u):= |u|^{p-1} \, u$, where $p>1$, so we will prove that the problem admits a solution if the measure $\mu$ is diffuse with respect to the capacity $C_{1,p^{'}}$. After, if $\mu$ is a positive measure for which this problem admits a solution, then necessarily this measure must be diffuse with respect to the capacity $C_{1,p^{'}}.$ This allows us to deduce that if $c\in \mathbb{R}^*$ and $a\in \partial \Omega$, then the problem with data $\mu=c \, \delta_0$ does not have a solution when$$p\geq\frac{N-1}{N-2}.$$ The second part of this thesis is devoted to study the singularities of the problem, \begin{equation}\label{Equ.2.resume.ang} \left\{\begin{aligned}&- \Delta u = 0 ~~ \text{in} ~~ \Omega, \\ &\frac{\partial u}{\partial n} \,+ \, |u|^{p-1}\, u = 0 ~~ \text{on} ~~ \partial \Omega \backslash \{a\},\end{aligned}\right .\end{equation}where $\Omega$ is a bounded regular domain of $\mathbb{R}^N$ such that $a\in \partial \Omega$, $p>1$ and the function $u$ is smooth enough in $\overline{\Omega}\setminus\{a\}.$ Without loss of generality we fix $a$ to be the origin $0$.We will see that the nature of the singularity depends on the critical parameter $$p_c:=\frac{N-1}{N-2}.$$We will prove that the singularity is removable in the case $p\geq p_c$. In the second case when $1 1$, alors on montrera que le problème admet une solution si la mesure $\mu$ est absolument continue par rapport à la capacité $C_{1,p^{'}}$. Puis, dans le cas où le problème admet une solution pour une mesure de Radon positive $\mu$, alors nécessairement cette mesure est absolument continue par rapport à la capacité $C_{1,p^{'}}$. Ceci permet de déduire que si $c\in \mathbb{R}^*$ et $a\in \partial \Omega$ alors le problème à donnée $\mu = c \, \delta_a$ n'admet pas de solution lorsque : $$p\geq \frac{N-1}{N-2}.$$ La deuxième partie de cette thèse est consacrée à l'étude de singularités du problème,\begin{equation}\label{Equ.2.resume} \left\{\begin{aligned}&- \Delta u = 0 ~~ \text{dans} ~~ \Omega, \\ &\frac{\partial u}{\partial n} \,+ \, |u|^{p-1}\, u = 0 ~~ \text{sur} ~~ \partial \Omega \backslash \{a\},\end{aligned}\right .\end{equation}où $\Omega$ est un ouvert régulier borné de $\mathbb{R}^N$ tel que $a\in \partial \Omega$, $p>1$ et la fonction $u$ est suffisamment régulière dans $\overline{\Omega}\setminus\{a\}$. Sans perte de généralité on fixe $a$ comme étant l'origine $0$.On verra que la nature de singularité dépend du paramètre critique : $$\displaystyle p_c:=\frac{N-1}{N-2}.$$ On montrera que la singularité est éliminable lorsque $p\geq p_c$. Lorsque $1 < p < p_c$, en considérant les coordonnées sphériques, on obtiendra que $r^{\frac{1}{p-1}} u (r, \sigma)$ converge quand $r \to 0$ vers une composante compacte et connexe d'un certain ensemble $\mathcal{E}$. Maintenant, si $1/(p-1) \notin \mathbb{N}$, et si l'une de conditions suivantes a lieu :i) si $N=2,$ ii) si $u(x) \, |x|^\frac{1}{p-1} \to 0,$ quand $|x| \to 0$, iii)si $u$ est positive et $\displaystyle \frac{N}{(N-1)} < p < p_c,$alors, on déduit une classification précise des singularités de l'équation. Ces résultats seront énoncer respectivement dans Théorème 4.13, Théorème 4.12 et Théorème 4.11

Loss of endothelial membrane KIT ligand affects systemic KIT ligand levels but not bone marrow hematopoietic stem cells

A critical regulatory role of hematopoietic stem cell (HSC) vascular niches in the bone marrow has been implicated to occur through endothelial niche cell expression of KIT ligand. However, endothelial-derived KIT ligand is expressed in both a soluble and membrane-bound form and not unique to bone marrow niches, and it is also systemically distributed through the circulatory system. Here, we confirm that upon deletion of both the soluble and membrane-bound forms of endothelial-derived KIT ligand, HSCs are reduced in mouse bone marrow. However, the deletion of endothelial-derived KIT ligand was also accompanied by reduced soluble KIT ligand levels in the blood, precluding any conclusion as to whether the reduction in HSC numbers reflects reduced endothelial expression of KIT ligand within HSC niches, elsewhere in the bone marrow, and/or systemic soluble KIT ligand produced by endothelial cells outside of the bone marrow. Notably, endothelial deletion, specifically of the membrane-bound form of KIT ligand, also reduced systemic levels of soluble KIT ligand, although with no effect on stem cell numbers, implicating an HSC regulatory role primarily of soluble rather than membrane KIT ligand expression in endothelial cells. In support of a role of systemic rather than local niche expression of soluble KIT ligand, HSCs were unaffected in KIT ligand deleted bones implanted into mice with normal systemic levels of soluble KIT ligand. Our findings highlight the need for more specific tools to unravel niche-specific roles of regulatory cues expressed in hematopoietic niche cells in the bone marrow

Characterisation of Genome-Wide PLZF/RARA Target Genes

The PLZF/RARA fusion protein generated by the t(11;17)(q23;q21) translocation in acute promyelocytic leukaemia (APL) is believed to act as an oncogenic transcriptional regulator recruiting epigenetic factors to genes important for its transforming potential. However, molecular mechanisms associated with PLZF/RARA-dependent leukaemogenesis still remain unclear

The earliest thymic T cell progenitors sustain B cell and myeloid lineage potential

The stepwise commitment from hematopoietic stem cells in the bone marrow to T lymphocyte-restricted progenitors in the thymus represents a paradigm for understanding the requirement for distinct extrinsic cues during different stages of lineage restriction from multipotent to lineage-restricted progenitors. However, the commitment stage at which progenitors migrate from the bone marrow to the thymus remains unclear. Here we provide functional and molecular evidence at the single-cell level that the earliest progenitors in the neonatal thymus had combined granulocyte-monocyte, T lymphocyte and B lymphocyte lineage potential but not megakaryocyte-erythroid lineage potential. These potentials were identical to those of candidate thymus-seeding progenitors in the bone marrow, which were closely related at the molecular level. Our findings establish the distinct lineage-restriction stage at which the T cell lineage-commitment process transits from the bone marrow to the remote thymus. © 2012 Nature America, Inc. All rights reserved

Ezh2 and Runx1 Mutations Collaborate to Initiate Lympho-Myeloid Leukemia in Early Thymic Progenitors.

Lympho-myeloid restricted early thymic progenitors (ETPs) are postulated to be the cell of origin for ETP leukemias, a therapy-resistant leukemia associated with frequent co-occurrence of EZH2 and RUNX1 inactivating mutations, and constitutively activating signaling pathway mutations. In a mouse model, we demonstrate that Ezh2 and Runx1 inactivation targeted to early lymphoid progenitors causes a marked expansion of pre-leukemic ETPs, showing transcriptional signatures characteristic of ETP leukemia. Addition of a RAS-signaling pathway mutation (Flt3-ITD) results in an aggressive leukemia co-expressing myeloid and lymphoid genes, which can be established and propagated in vivo by the expanded ETPs. Both mouse and human ETP leukemias show sensitivity to BET inhibition in vitro and in vivo, which reverses aberrant gene expression induced by Ezh2 inactivation

Initial seeding of the embryonic thymus by immune-restricted lympho-myeloid progenitors

The final stages of restriction to the T cell lineage occur in the thymus after the entry of thymus-seeding progenitors (TSPs). The identity and lineage potential of TSPs remains unclear. Because the first embryonic TSPs enter a non-vascularized thymic rudiment, we were able to directly image and establish the functional and molecular properties of embryonic thymopoiesis-initiating progenitors (T-IPs) before their entry into the thymus and activation of Notch signaling. T-IPs did not include multipotent stem cells or molecular evidence of T cell-restricted progenitors. Instead, single-cell molecular and functional analysis demonstrated that most fetal T-IPs expressed genes of and had the potential to develop into lymphoid as well as myeloid components of the immune system. Moreover, studies of embryos deficient in the transcriptional regulator RBPJ demonstrated that canonical Notch signaling was not involved in pre-thymic restriction to the T cell lineage or the migration of T-IPs

Study of the harmonic equation in an open with nonlinear flux boundary conditions

L’objectif principal de cette thèse est divisée en deux parties. La première partie est consacrée à l’étude du problème, { −Δu + u = 0 dans Ω, ∂u/∂n + g(u) = μ sur ∂Ω, (0.1) où Ω est un ouvert régulier borné de ℝᴺ, g(·) est une fonction continue qui vérifie la condition du signe s · g(s) ≥ 0, dans certains modèles on ajoute l’hypothèse g(·) croissante, et finalement μ est une mesure bornée sur ∂Ω. Certains de nos résultats sont valables lorsque Ω := ℝᴺ+ . On commencera par montrer l’existence de solution de (0.1) lorsque μ est une fonction de L1(∂Ω), et cela sans ajouter une hypothèse supplémentaire sur g(·). Puis, on étudiera (0.1) lorsque μ est une mesure de Radon sur ∂Ω, dans ce contexte, le problème (0.1) pourra ne pas admettre une solution, et des conditions apparaissent sur g(·) et sur μ pour assurer l’existence d’une solution. On montrera l’existence de solutions lorsque, g(·) est une non-linéarité sous-critique en dimension N supérieure ou égale à trois, et lorsque g(·) satisfait l’hypothèse de singularité faible sur le bord en dimension N égale à deux (voir Chapitre 2 pour définitions).The main aim of this thesis is divided into two parts. The first part is devoted to the study of the problem, { −Δu + u = 0 in Ω, ∂u/∂n + g(u) = μ on ∂Ω, (0.3) where Ω is a bounded regular domain of ℝᴺ, g(·) is a continuous function that satisfies the sign condition s · g(s) ≥ 0, in some model case we will assume that g(·) is increassing, and finally μ is a bounded measure on ∂Ω. Some of our results remain true when Ω := ℝᴺ+ . We will start by proving the existence of a solution of (0.3) when μ is an L1(∂Ω) function, and this independently of the nonlinearity g(·) that satisfies the previous hypothesis. Then, we will study (0.3) when μ is a Radon measure on ∂Ω. In such a context, some new conditions appear on g(·) and μ that assure the existence of a solution. We will prove the existence of a solution when g(·) is a sub-critical nonlinearity in dimension N larger or equal to three, and when g satisfies the weak singularity assumption on the boundary in case N equals two (see Chapter 2 for the definitions)

Nonlinear boundary value problems relative to harmonic functions

International audienceWe study the problem of finding a function u verifying −∆u = 0 in Ω under the boundary condition ∂u ∂n + g(u) = µ on ∂Ω where Ω ⊂ R N is a smooth domain, n the normal unit outward vector to Ω, µ is a measure on ∂Ω and g a continuous nondecreasing function. We give sufficient condition on g for this problem to be solvable for any measure. When g(r) = |r| p−1 r, p > 1, we give conditions in order an isolated singularity on ∂Ω be removable. We also give capacitary conditions on a measure µ in order the problem with g(r) = |r| p−1 r to be solvable for some µ. We also study the isolated singularities of functions satisfying −∆u = 0 in Ω and ∂u ∂n + g(u) = 0 on ∂Ω \ {0}

Rôle des protéines du groupe polycomb dans la leucémie aiguë promyélocytaire associée à PLZF/RARA

Les leucémies aiguës promyélocytaires (APLs) sont caractérisées par un blocage de la différenciation des granulocytes au stade promyélocytaire et par une augmentation de la prolifération des cellules leucémiques dans la moelle osseuse. Ce phénotype est induit par des translocations chromosomiques spécifiques qui impliquent dans tous les cas le gène RARA générant ainsi des protéines de fusions X/RARAs. L expression de ces dernières induit le blocage de la transcription des gènes cibles du RARA qui sont importants pour la différenciation granulocytaire. Les APLs associées à PML/RARA répondent d une façon favorable à la thérapie différenciatrice de l acide rétinoïque (AR) alors que les APLs associées à PLZF/RARA se révèlent résistantes à ce traitement. Cette différence de réponse a été expliquée par un modèle décrivant un recrutement de corépresseurs insensible au traitement par l AR au niveau de PLZF/RARA. Cependant, l existence de mutants de PLZF/RARA avoir perdu leurs propriétés oncogéniques sans pour autant perdu leur capacité à recruter ces complexes corépresseurs questionne ce modèle. De plus, l observation que le traitement à l acide rétinoïque dégrade la protéine PLZF/RARA explique mal l absence de réponse et suggère l intervention d autres facteurs probablement de nature épigénétique capables de maintenir la répression induite par PLZF/RARA même après sa dégradation. Comme des résultats antérieurs suggéraient une interaction fonctionnelle entre PLZF et Bmi1, un membre du complexe PRC1 du groupe Polycomb, nous avons recherché à établir un lien entre les activités répressives des protéines PRC1 et les propriétés oncogéniques de PLZF/RARA. Dans cette optique, nous avons tout d abord validé l interaction entre PLZF/RARA et Bmi1 dans différents modèles cellulaires in vitro comme in vivo. De plus, nous avons montré que PLZF/RARA était capable de former un complexe stable avec les protéines du complexe PRC1 et de les recruter au niveau de ses gènes cibles in vitro comme in vivo. Le recrutement de ce nouveau complexe répresseur est spécifique à PLZF/RARA par rapport au RARA ou PML/RARA et n est pas sensible au traitement AR. Finalement, nous avons testé l importance de ce gain de fonction sur les propriétés de transformation de PLZF/RARA et nous avons montré que l absence de Bmi1 réduit les propriétés oncogéniques de PLZF/RARA. L ensemble de nos résultats montre l implication directe du complexe PRC1 dans la transformation induite par PLZF/RARA et probablement le phénomène de la résistance qui l accompagne. Mettre en évidence de nouveaux partenaires aide à mieux cerner les mécanismes impliqués dans la pathogenèse de cette leucémie et à améliorer les stratégiesthérapeutiques.Acute promyelocytic leukemia (APL) is characterized by a differentiation block of granulocytes at the promyelocytic stage and an increase self renewal capacity by leukemic cells in the bone marrow. This phenotype is induced by specific chromosomal translocation always involving the RARA gene and leading to the generation of X/RARAs fusion proteins with gain of function and dominant negative effects on the original proteins. The expression of these fusions is sufficient to block the transcription of RARA s target genes and induce leukemic phenotype in mice similar to those observed in human cases. PML/RARA-APL responds well to retinoic acid treatment and chemotherapy, whereas PLZF/RARA-APL responds poorly to both treatments, thus defining a resistant APL. The model that has been proposed to explain the distinct response describes a retinoic acidresistant binding site in PLZF/RARA for co-repressor recruitment. However, this model has been challenged with the description of PLZF/RARA s mutants, which loose their oncogenic properties, but still interact with the co-repressors. Furthermore, PLZF/RARA s degradation induced by retinoic acid treatment does not explain the lack of response and suggests the implication of others mechanisms mostly epigenetic, which maintain the repression induced by PLZF/RARA even after its degradation. As previous studies showed a functional interaction between PLZF and Bmi1, a member of the PRC1 Polycomb group, we wanted to assess the link between PRC1 repressive activities and PLZF/RARA oncogenic properties. For this purpose, we first validated the interaction between PLZF/RARA and Bmi1 in several cellular models in vitro and in vivo. Then, we showed that PLZF/RARA is able to form a stable complex with others PRC1 components and to recruit them to RARA s target genes in vitro and in vivo. This recruitment was specific to PLZF/RARA when compared to RARA or PML/RARA and was unaffected after retinoic acid treatment. Finally, we attempted to evaluate the importance of this gain of function on the transformation mediated by PLZF/RARA. The loss of the leukemic phenotype from hematopoietic progenitors transformed with PLZF/RARA ex vivo led us to conclude that Bmi1 is necessary for this transformation. Thus, our findings demonstrate the involvement of an epigenetic mechanism in the PLZF/RARA mediated transformation and this could provide an interpretation of its related resistance phenomenon. The evidence presented here could help in better understanding of the mechanisms implicated in the pathogenesis of this type of leukemia and improve therapeutic strategies to overcome the disease.AIX-MARSEILLE2-BU Sci.Luminy (130552106) / SudocSudocFranceF