Elevated TRIB2 with NOTCH1 activation in paediatric/adult T-ALL

TRIB2 is a potent oncogene, elevated in a subset of human acute myeloid leukaemias (AML) with a mixed myeloid/lymphoid phenotype and NOTCH1 mutations. Although rare in AML, activating NOTCH1 mutations occur in 50% of all T cell acute lymphoblastic leukaemias (T-ALL). TRIB2 is a NOTCH1 target gene that functions in the degradation of key proteins and modulation of MAPK signalling pathways, implicated in haematopoietic cell survival and proliferation. This study showed that TRIB2 expression level is highest in the lymphoid compartment of normal haematopoietic cells, specifically in T cells. Analysis of TRIB2 expression across 16 different subtypes of human leukaemia demonstrated that TRIB2 expression was higher in ALL phenotypes versus all other phenotypes including AML, chronic lymphocytic leukaemia (CLL), myelodysplastic syndrome (MDS) and chronic myeloid leukaemia (CML). A T cell profile was distinguished by high TRIB2 expression in normal and malignant haematopoiesis. High TRIB2 expression was seen in T-ALL with normal karyotype and correlated with NOTCH signalling pathways. High TRIB2 expression correlated with NOTCH1/FBXW7 mutations in a paediatric T-ALL cohort, strongly linking NOTCH1 activation and high TRIB2 expression in paediatric T-ALL. The relationship between TRIB2 and T cell signalling pathways uniquely identifies leukaemia subtypes and will be useful in the advancement of our understanding of T cell and ALL biology.

Activation of the ACE2/Angiotensin-(1-7)/Mas Receptor Axis Enhances the Reparative Function of Dysfunctional Diabetic Endothelial Progenitors

We tested the hypothesis that activation of the protective arm of the renin angiotensin system, the angiotensin-converting enzyme 2 (ACE2)/angiotensin-(1-7) [Ang-(1-7)]/Mas receptor axis, corrects the vasoreparative dysfunction typically seen in the CD34(+) cells isolated from diabetic individuals. Peripheral blood CD34(+) cells from patients with diabetes were compared with those of nondiabetic controls. Ang-(1-7) restored impaired migration and nitric oxide bioavailability/cGMP in response to stromal cell-derived factor and resulted in a decrease in NADPH oxidase activity. The survival and proliferation of CD34(+) cells from diabetic individuals were enhanced by Ang-(1-7) in a Mas/phosphatidylinositol 3-kinase (PI3K)/Akt-dependent manner. ACE2 expression was lower, and ACE2 activators xanthenone and diminazine aceturate were less effective in inducing the migration in cells from patients with diabetes compared with controls. Ang-(1-7) overexpression by lentiviral gene modification restored both the in vitro vasoreparative functions of diabetic cells and the in vivo homing efficiency to areas of ischemia. A cohort of patients who remained free of microvascular complications despite having a history of longstanding inadequate glycemic control had higher expression of ACE2/Mas mRNA than patients with diabetes with microvascular complications matched for age, sex, and glycemic control. Thus, ACE2/Ang-(1-7)\Mas pathway activation corrects existing diabetes-induced CD34(+) cell dysfunction and also confers protection from development of this dysfunction.

Topoisomerase IIα promotes activation of RNA polymerase I transcription by facilitating pre-initiation complex formation

Type II DNA topoisomerases catalyse DNA double-strand cleavage, passage and re-ligation to effect topological changes. There is considerable interest in elucidating topoisomerase II roles, particularly as these proteins are targets for anti-cancer drugs. Here we uncover a role for topoisomerase IIa in RNA polymerase I-directed ribosomal RNA gene transcription, which drives cell growth and proliferation and is upregulated in cancer cells. Our data suggest that topoisomerase IIa is a component of the initiation-competent RNA polymerase Iß complex and interacts directly with RNA polymerase I-associated transcription factor RRN3, which targets the polymerase to promoter-bound SL1 in pre-initiation complex formation. In cells, activation of rDNA transcription is reduced by inhibition or depletion of topoisomerase II, and this is accompanied by reduced transient double-strand DNA cleavage in the rDNA-promoter region and reduced pre-initiation complex formation. We propose that topoisomerase IIa functions in RNA polymerase I transcription to produce topological changes at the rDNA promoter that facilitate efficient de novo pre-initiation complex formation.

Nuclear translocation and functions of growth factor receptors

Cellular signal transduction in response to environmental signals involves a relay of precisely regulated signal amplifying and damping events. A prototypical signaling relay involves ligands binding to cell surface receptors and triggering the activation of downstream enzymes to ultimately affect the subcellular distribution and activity of DNA-binding proteins that regulate gene expression. These so-called signal transduction cascades have dominated our view of signaling for decades. More recently evidence has accumulated that components of these cascades can be multifunctional, in effect playing a conventional role for example as a cell surface receptor for a ligand whilst also having alternative functions for example as transcriptional regulators in the nucleus. This raises new challenges for researchers. What are the cues/triggers that determine which role such proteins play? What are the trafficking pathways which regulate the spatial distribution of such proteins so that they can perform nuclear functions and under what circumstances are these alternative functions most relevant?

TNF alpha-Induced p38MAPK Activation Regulates TRPA1 and TRPV4 Activity in Odontoblast-Like Cells

The transient receptor potential (TRP) channels are unique cellular sensors that are widely expressed in many neuronal and nonneuronal cells. Among the TRP family members, TRPA1 and TRPV4 are emerging as candidate mechanosensitive channels that play a pivotal role in inflammatory pain and mechanical hyperalgesia. Odontoblasts are nonneuronal cells that possess many of the features of mechanosensitive cells and mediate important defense and sensory functions. However, the effect of inflammation on the activity of the odontoblast's mechanosensitive channels remains unknown. By using immunohistochemistry and calcium microfluorimetry, we showed that odontoblast-like cells express TRPA1 and TRPV4 and that these channels were activated by hypotonicity-induced membrane stretch. Short treatment of odontoblast-like cells with tumor necrosis factor (TNF)-α enhanced TRPA1 and TRPV4 responses to their chemical agonists and membrane stretch. This enhanced channel activity was accompanied by phospho-p38 mitogen-activated protein kinase (MAPK) expression. Treatment of cells with the p38 inhibitor SB202190 reduced TNF-α effects, suggesting modulation of channel activity via p38 MAPK. In addition, TNF-α treatment also resulted in an up-regulation of TRPA1 expression but down-regulation of TRPV4. Unlike TRPV4, enhanced TRPA1 expression was also evident in dental pulp of carious compared with noncarious teeth. SB202190 treatment significantly reduced TNF-α-induced TRPA1 expression, suggesting a role for p38 MAPK signaling in modulating both the transcriptional and non-transcriptional regulation of TRP channels in odontoblasts.

Regulatory interactions between the metabolic sensors SIRT1 and AMPK in modulating PPARα linked functions, in obesity-dependent type 2 diabetes mellitus

Tese de doutoramento, Ciências Biomédicas (Ciências Funcionais), Universidade de Lisboa, Faculdade de Medicina, 2014

Activity-Dependent Neurorehabilitation Beyond Physical Trainings: "Mental Exercise" Through Mirror Neuron Activation

The activity dependent brain repair mechanism has been widely adopted in many types of neurorehabilitation. The activity leads to target specific and non-specific beneficial effects in different brain regions, such as the releasing of neurotrophic factors, modulation of the cytokines and generation of new neurons in adult hood. However physical exercise program clinically are limited to some of the patients with preserved motor functions; while many patients suffered from paralysis cannot make such efforts. Here the authors proposed the employment of mirror neurons system in promoting brain rehabilitation by "observation based stimulation". Mirror neuron system has been considered as an important basis for action understanding and learning by mimicking others. During the action observation, mirror neuron system mediated the direct activation of the same group of motor neurons that are responsible for the observed action. The effect is clear, direct, specific and evolutionarily conserved. Moreover, recent evidences hinted for the beneficial effects on stroke patients after mirror neuron system activation therapy. Finally some music-relevant therapies were proposed to be related with mirror neuron system.

IB1/JIP-1 controls JNK activation and increased during prostatic LNCaP cells neuroendocrine differentiation.

The scaffold protein Islet-Brain1/c-Jun amino-terminal kinase Interacting Protein-1 (IB1/JIP-1) is a modulator of the c-Jun N-terminal kinase (JNK) activity, which has been implicated in pleiotrophic cellular functions including cell differentiation, division, and death. In this study, we described the presence of IB1/JIP-1 in epithelium of the rat prostate as well as in the human prostatic LNCaP cells. We investigated the functional role of IB1/JIP-1 in LNCaP cells exposed to the proapoptotic agent N-(4-hydroxyphenyl)retinamide (4-HPR) which induced a reduction of IB1/JIP-1 content and a concomittant increase in JNK activity. Conversely, IB1/JIP-1 overexpression using a viral gene transfer prevented the JNK activation and the 4-HPR-induced apoptosis was blunted. In prostatic adenocarcinoma cells, the neuroendocrine (NE) phenotype acquisition is associated with tumor progression and androgen independence. During NE transdifferentiation of LNCaP cells, IB1/JIP-1 levels were increased. This regulated expression of IB1/JIP-1 is secondary to a loss of the neuronal transcriptional repressor neuron restrictive silencing factor (NRSF/REST) function which is known to repress IB1/JIP-1. Together, these results indicated that IB1/JIP-1 participates to the neuronal phenotype of the human LNCaP cells and is a regulator of JNK signaling pathway.

The roles of ERK1/2 and PI3K in abnormal vascular functions in angiotensin II-infused hypertensive rats

Background: Ang II plays a major role in cardiovascular regulation. Recently, it has become apparent that vascular superoxide anion may play an important role in hypertension development. Treatment with antisense NAD(P)H oxidase or SOD decreased BP in Ang II-infused rats. Wang et al recently reported mice which lack one of the subunits of NAD(P)H oxidase developed hypertension at a much lower extent when compared to the wild type animals infused with Ang II, indicating that superoxide anion contributes to elevation in BP in the Ang II-infused hypertensive model. In the Ang II-infused hypertensive model, altered reactivity of blood vessels is often associated with the elevation of systolic blood pressure. We have observed abnormal tension development and impaired endothelium-dependent relaxation in the isolated aorta of Ang II-infused and DOCA-salt hypertensive rats. Recently, several other cellular signal molecules, including ERK1I2 and PI3K, have been determined to play important roles in the regulation of smooth muscle contraction and relaxation. ERKl/2 and PI3K pathways are also reported to contribute to Ang II induced cell growth, hypertrophy, remodeling and contraction. Moreover, these signaling pathways have shown ROS-sensitive properties. Therefore, the aim of the present study is to investigate the roles of ERKl12 and PI3K in vascular oxidative stress, spontaneous tone and impaired endothelium relaxation in Ang II-infused hypertensive model. Hypothesis: We hypothesize that the activation of ERKl12 and PI3K are elevated in response to an Ang II infusion for 6 days. The elevated activation of phospho-ERKl/2 and PI3K mediated the increased level of vascular superoxide anion, the abnormal vascular contraction and impaired endothelium-dependent vascular relaxation in Ang II-infused hypertensive rats. Methods: Vascular superoxide anion level is measured by lucigenin chemiluminescence. Spontaneous tone and ACh-induced endothelium-dependent relaxation was measured by isometric tension recording in organ chamber. The activity of ERK pathway will be measured by its Western blot of phosphorylation of ERK. PI3K activity was evaluated indirectly by Western blot of the phosphorylation of PDKl, a downstream protein of PI3K signaling pathway. The role of each pathway was also addressed via comparing the responses to the specific inhibitors. Results: Superoxide anion was markedly increased in the isolated thoracic aorta from Ang II-infused rats. There was spontaneous tone developed in rings from Ang II-induced hypertensive but not sham-operated normotensive rats. ACh-induced endothelium-dependent relaxation function is impaired in Ang II-infused hypertensive rats. Superoxide dismutase and NAD(P)H oxidase inhibitor, apocynin, inhibited the abnormal spontaneous tone and ameliorated impaired endothelium-dependent relaxation. The expression of phopho-ERKII2 was enhanced in Ang II-infused rats, indicating the activity of ERK1I2 could be increased. MEK1I2 inhibitors, PD98059 and U126, but not their inactive analogues, SB203580 and U124, significantly reduced the vascular superoxide anion in aortas from Ang II-infused rats. The MEK1I2 inhibitors reduced the spontaneous tone and improved the impaired endothelium-dependent relaxation in aorta of hypertension. These findings supported the role of ERKII2 signaling pathway in vascular oxidative stress, spontaneous tone and impaired endothelium-dependent relaxation in Ang II-infused hypertensive rats. The amount of phospho-PDK, a downstream protein of PI3K was increased in Ang II rats indicating the activity of PI3K activity was elevated. Strikingly, PI3K significantly inhibited the increase of superoxide anion level, abnormal spontaneous tone and restored endothelium-dependent relaxation in Ang II-infused hypertensive rats. These findings indicated the important role of PI3K in Ang II-infused hypertensive rats. Conclusion: ERKII2 and PI3K signaling pathways are sustained activated in Ang II-infused hypertensive rats. The activated ERKII2 and PI3K mediate the increase of vascular superoxide anion level, vascular abnormal spontaneous tone and impaired endothelium-dependent relaxation.

Hot cognition and activation of the medial prefrontal cortex: Self-regulating in contexts involving motivational pressures

The medial prefrontal cortex (mPFC) is involved in performance-monitoring and has been implicated in the generation of several electrocortical responses associated with self-regulation. The error-related negativity (ERN), the inhibitory Nogo N2 (N2), and the feedback-related negativity (FRN) are event-related potential (ERP) components which reflect mPFC activity associated with feedback to behavioural (ERN, N2) and environmental (FRN) consequences. Our main goal was to determine whether or not rnPFC activation varies as a function of motivational context (e.g., those involving performance-related incentives) or the use of internally versus externally generated feedback signals (i.e., errors). Additionally, we assessed medial prefrontal activity in relation to individual differences in personality and temperament. Participants completed a combination of tasks in which performance-related incentives were associated with task performance and feedback generated from internal versus external responses. MPFC activity was indexed using both ERP scalp voltage peaks and intracerebral current source density (CSD) of dorsal and ventral regions. Additionally, participants completed several questionnaires assessing personality and temperament styles. Given previous studies have shown that enhanced mPFC activity to loss (or negative) feedback, we expected that activity in the mPFC would generally be greater during the Loss condition relative to the Win condition for both the ERN and N2. Also, due to the evidence that the (vmPFC) is engaged in arousing contexts, we hypothesized that activity in the ventromedial prefrontal cortex (vmPFC) would be greater than activity in the dorsomedial prefrontal cortex (dmPFC), especially in the Loss condition of the GoNogo task (ERN). Similarly, loss feedback in the BART (FRN) was expected to engage the vmPFC more than the dmPFC. Finally, we predicted that persons rating themselves as more willing to engage in approach-related behaviours or to exhibit rigid cognitive styles would show reduced activity of the mPFC. Overall, our results emphasize the role of affective evaluations of behavioural and environmental consequences when self-regulating. Although there were no effects of context on brain activity, our data indicate that, during the time of the ERN and N2 on the MW Go-Nogo task and the FRN on the BART, the vrnPFC was more active compared to the dmPFC. Moreover, regional recruitment in the mPFC was similar across internally (ERN) and externally (FRN) generated errors signals associated with loss feedback, as reflected by relatively greater activity in the vmPFC than the dmPFC. Our data also suggest that greater activity in the mPFC is associated with better inhibitory control, as reflected by both scalp and CSD measures. Additionally, deactivation of the subgenual anterior cingulate cortex (sgACC) and lower levels of self-reported positive affect were both related to increased voluntary risk-taking on the BART. Finally, persons reporting higher levels of approach-related behaviour or cognitive rigidity showed reduced activity of the mPFC. These results are in line with previous research emphasizing that affect/motivation is central to the processes reflected by mediofrontal negativities (MFNs), that the vmPFC is involved in regulating demands on motivational/affective systems, and that the underlying mechanisms driving these functions vary across both individuals and contexts.

Mécanismes d'activation de la voie lysosomale durant l'apoptose chimio-induite

L’apoptose est une forme de mort cellulaire essentielle au développement et au maintien de l’homéostase chez les animaux multicellulaires. La machinerie apoptotiq ue requiert la participation des caspases, des protéases conservées dans l’évolution et celle des organelles cytoplasmiques. Les lysosomes subissent des ruptures partielles, labilisation de la membrane lysosomale (LML), qui entraînent l’activation des cathepsines dans le cytoplasme de cellules cancéreuses humaines en apoptose induite par la camptothecin (CPT), incluant les histiocytes humains U-937. Ces modifications lysosomales se manifestent tôt durant l’activation de l’apoptose, concomitamment avec la perméabilisation de la mitochondrie et l’activation des caspases. Une étude protéomique quantitative et comparative a permis d’identifier des changements précoces dans l’expression/localisation de protéines lysosomales de cellules U-937 en apoptose. Lors de deux expériences indépendantes, sur plus de 538 protéines lysosomales identifiées et quantifiées grâce au marquage isobarique iTRAQ et LC-ESIMS/ MS, 18 protéines augmentent et 9 diminuent dans les lysosomes purifiés de cellules en cours d’apoptose comparativement aux cellules contrôles. Les candidats validés par immuno-buvardage et microscopie confocale incluent le stérol-4-alpha-carboxylate 3- déhydrogénase, le prosaposin et la protéine kinase C delta (PKC-d). Des expériences fonctionnelles ont démontrées que la translocation de PKC-d aux lysosomes est requise pour la LML puisque la réduction de son expression par ARN interférents ou l’inhibition de son activité à l’aide du rottlerin empêche la LML lors de l’apoptose induite par la CPT. La translocation de PKC-d aux lysosomes conduit à la phosphorylation et l’activation de la sphingomyelinase acide lysosomale (ASM), et à l’accroissement subséquent du contenu en céramide (CER) à la membrane lysosomale. Cette accumulation de CER endogène aux lysosomes est un évènement critique pour la LML induite par la CPT car l’inhibition de l’activité de PKC-d ou de ASM diminue la formation de CER et la LML.Ces résultats révèlent un nouveau mécanisme par lequel la PKC-d active l’ASM qui conduit à son tour à l’accumulation de CER à la membrane lysosomale et déclenche la LML et l’activation de la voie lysosomale de l’apoptose induite par la CPT. En somme, ce mécanisme confirme l’importance du métabolisme des sphingolipides dans l’activation de la voie lysosomale de l’apoptose.

Caractérisation de la MAP kinase atypique Erk4 : activation et fonction physiologique

Les MAP kinases sont des enzymes essentielles impliquées dans 7 voies de signalisation distinctes qui permettent à la cellule de répondre de manière adéquate aux stimuli extra-cellulaires. Chez les mammifères, les MAP kinases les mieux caractérisées sont Erk1/2, Jnk, p38 et Erk5. Ces enzymes jouent un rôle important dans l’embryogenèse, la prolifération et la différenciation cellulaire ainsi que dans la réponse au stress. Erk4 est un membre atypique de la famille MAP kinase. D’une part, la boucle d’activation de Erk4 possède un motif SEG au lieu du motif TXY, très conservé chez les MAP kinases. D’autre part, Erk4 possède une extension en C-terminal du domaine kinase qui n’est pas présente chez les MAP kinases classiques. Jusqu’à présent aucune fonction n’a été attribuée à Erk4. De plus, la voie de signalisation ainsi que le mode de régulation conduisant à l’activation de Erk4 ne sont pas connus. Le seul substrat de Erk4 identifié jusqu’à maintenant est la MAPKAP kinase MK5. L’impact fonctionnel de cette interaction n’est également pas connu. Afin d’en apprendre davantage sur la MAP kinase atypique Erk4, nous avons étudié le mécanisme d’activation de cette kinase ainsi que sa fonction physiologique par une approche de délétion génique chez la souris. En ce qui concerne l’activation de Erk4, nous avons montré que la boucle d’activation de Erk4 (S186EG) est constitutivement phosphorylée in vivo et que cette phosphorylation n’est pas modulée par les stimuli classiques des MAP kinases dont le sérum et le sorbitol. Cependant, nous avons observé que la phosphorylation de la S186 augmente en présence de MK5 et que cette augmentation est indépendante de l’activité kinase de l’une ou l’autre de ces kinases. De plus, nous avons établi que la phosphorylation de la boucle d’activation de Erk4 est requise pour l’interaction stable entre Erk4 et MK5 ainsi que pour l’activation, et la relocalisation cytoplasmique de MK5. Ainsi, notre étude a permis de révéler que Erk4 est régulée de manière différente des MAP kinases classiques et que la phosphorylation de la boucle d’activation de Erk4 joue un rôle essentiel dans la régulation de l’activité de MK5. Parallèlement, nos résultats mettent en évidence l’existence d’une “Erk4 kinase”, dont le recrutement et/ou l’activation semble être facilité par MK5. Afin identifier la fonction physiologique de Erk4, nous avons généré des souris Erk4-déficientes. L’inactivation génique de Erk4 est viable et les souris ne présentent aucune anomalie apparente. Dans le but d’expliquer l’absence de phénotype, nous avons regardé si l’expression de Erk3, le paralogue de Erk4, pouvait compenser la perte de Erk4. Notre analyse a révélé que l’expression de Erk3 dans les souris Erk4-/- n’augmente pas au cours du développement embryonnaire ou dans les tissus adultes afin de compenser pour la perte de Erk4. Par la suite, nous avons adressé la question de redondance entre Erk4 et Erk3. Dans notre laboratoire, les souris Erk3-déficientes ont également été générées et le phénotype de ces souris a récemment été analysé. Cette étude a révélé que l’inactivation génique de Erk3 entraîne un retard de croissance intra-utérin, un défaut de maturation pulmonaire et la mort néo-natale des souriceaux. Nous avons donc regardé la contribution de Erk4 dans ces phénotypes. L’analyse des souris Erk4-/- a révélé que l’inactivation de Erk4 n’entraîne pas de retard de croissance ou de maturation du poumon. De plus, nous avons montré que l’inactivation additionnelle de Erk4 dans les souris Erk3-/- n’accentue pas le phénotype des souris Erk3-déficientes. Ainsi, notre étude a révélé que contrairement à Erk3, Erk4 n’est pas essentielle au développement murin dans des conditions physiologiques. Parallèlement, nous avons montré que Erk4 et Erk3 possèdent des fonctions non-redondantes in vivo.

Special functions of Weyl groups and their continuous and discrete orthogonality

Cette thèse s'intéresse à l'étude des propriétés et applications de quatre familles des fonctions spéciales associées aux groupes de Weyl et dénotées $C$, $S$, $S^s$ et $S^l$. Ces fonctions peuvent être vues comme des généralisations des polynômes de Tchebyshev. Elles sont en lien avec des polynômes orthogonaux à plusieurs variables associés aux algèbres de Lie simples, par exemple les polynômes de Jacobi et de Macdonald. Elles ont plusieurs propriétés remarquables, dont l'orthogonalité continue et discrète. En particulier, il est prouvé dans la présente thèse que les fonctions $S^s$ et $S^l$ caractérisées par certains paramètres sont mutuellement orthogonales par rapport à une mesure discrète. Leur orthogonalité discrète permet de déduire deux types de transformées discrètes analogues aux transformées de Fourier pour chaque algèbre de Lie simple avec racines des longueurs différentes. Comme les polynômes de Tchebyshev, ces quatre familles des fonctions ont des applications en analyse numérique. On obtient dans cette thèse quelques formules de <>, pour des fonctions de plusieurs variables, en liaison avec les fonctions $C$, $S^s$ et $S^l$. On fournit également une description complète des transformées en cosinus discrètes de types V--VIII à $n$ dimensions en employant les fonctions spéciales associées aux algèbres de Lie simples $B_n$ et $C_n$, appelées cosinus antisymétriques et symétriques. Enfin, on étudie quatre familles de polynômes orthogonaux à plusieurs variables, analogues aux polynômes de Tchebyshev, introduits en utilisant les cosinus (anti)symétriques.

Régulation de la kinase Ste20 Slik de Drosophila par phosphorylation de la boucle d'activation

Les kinases constituent une famille majeure de protéines qui régulent divers processus par la phosphorylation de leurs substrats, mais aussi par leur activité non- catalytique. Ce rôle indépendant de l’activité kinase a été observé chez quelques protéines dont des membres de la famille Sterile-20. La kinase Ste20 Slik de Drosophila aide au maintien de l’intégrité des tissus épithéliaux en phosphorylant l’ERM Moesin et peut aussi induire une prolifération cellulaire non-autonome indépendamment de son activité catalytique. La méthode de régulation de ces deux rôles était jusqu’ici inconnue. Nous avons identifié 19 sites de phosphorylation chez Slik par spectrométrie de masse. À l’aide de mutants, nous démontrons que les deux fonctions de Slik sont régulées par la phosphorylation d’au moins 2 résidus conservés de son segment d’activation par un mécanisme d’auto- et/ou trans-phosphorylation. Cette étude amène une meilleure compréhension de la régulation de l’intégrité épithéliale et de la croissance, deux processus clés qui sont souvent déréglés dans le cancer et certaines maladies génétiques.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.