Mycobacterium tuberculosis (M.tb), the causative agent of tuberculosis (TB), has remained the largest killer among infectious diseases for over a century. The increasing emergence of drug resistant varieties such as the multidrug resistant (MDR) and extremely drug resistant (XDR) strains are only increasing the global burden of the disease. Available statistics indicate that nearly one-third of the world’s population is infected, where the bacteria remains in the latent state but can reactivate into an actively growing stage to cause disease when the individual is immunocompromised. It is thus immensely important to rethink newer strategies for containing and combating the spread of this disease. Extraction of iron from the host cell is one of the many factors that enable the bacterium to survive in the harsh environments of the host macrophages and promote tuberculosis. Host–pathogen interactions can be interpreted as the battle of two systems, each aiming to overcome the other. From the host’s perspective, iron is essential for diverse processes such as oxygen transport, repression, detoxification and DNA synthesis. Infact, during infection, both the host and the pathogen are known to fight for the available iron, thereby influencing the outcome of the infection. It is of no surprise therefore, that many studies have investigated several components of the iron regulatory machinery of M.tb and the host. However, very few attempts have been made to study the interactions between these components and how such interactions lead to a better adapted phenotype. Such studies require exploration at multiple levels of structural and functional complexity, thereby necessitating the use of a multiscale approach. Systems biology adopts an integrated approach to study and understand the function of biological systems. It involves building large scale models based on individual biochemical interactions, followed by model validation and predictions of the system’s response to perturbations, such as a gene knock-out or exposure to drug. In multiscale modeling, an approach employed in this thesis, a particular biological phenomenon is studied at different spatiotemporal levels. Studying responses at multiple scales provides a broader picture of the communications that occur between a host and pathogen. Moreover, such an analysis also provides valuable insights into how perturbation at a particular level can elicit responses at another level and help in the identification of crucial inter-level communications that can possibly be hindered or activated for a desired physiological outcome. The broad objectives of this thesis was to obtain a comprehensive in silico understanding of mycobacterial iron homeostasis and metabolism, the influence of iron on host-pathogen interactions, identification of key players that mediate such interactions, determination of the molecular consequences of inhibiting the key players and finally the global response of M.tb to altered iron concentration. Perturbation of iron homeostasis holds a strong therapeutic potential, given its essentiality in both the host and the pathogen. Understanding the workings of iron metabolism and regulation in M.tb has been a main objective, so as to ultimately obtain insights about specific therapeutic strategies that capitalize on the criticality of iron concentration. An in-depth study of iron metabolism and regulation is performed at different levels of temporal and spatial scales using diverse methods, each appropriate to investigate biological events associated with the different scales. The specific investigations carried out in the thesis are as follows, a) Reconstruction of a host-pathogen interaction (HPI) model, with focus on iron homeostasis. This study represented the inter-cellular level analysis and was crucial for the identification of key players that mediate communication between the host and pathogen. Additionally, the model also provided a mathematical framework to study the effect of perturbations and gene knock-outs. b) Understanding the influence of iron on IdeR, an iron-responsive transcription factor, also identified as a key player in the HPI model. The study was carried out at the molecular level to identify atomistic details of how IdeR senses iron and the resulting structural modifications, which finally enables IdeR-DNA interaction. The study enabled identification of residues for the functioning of IdeR. c) Genome scale identification of genes that are regulated by IdeR to obtain an overview of the various biological processes affected by changing iron concentrations and IdeR mutation in M.tb. d) To understand the direct and indirect influences of iron and IdeR on the M.tb proteome using large scale protein-protein interaction network. The study enabled identification of highest differentially regulated genes and altered activity of the different biological processes under differing iron concentrations and regulation. e) Systems level analysis of the M.tb metabolome to investigate the metabolic re-adjustments undertaken by M.tb to adapt to altered iron concentration and regulation. The conceptual details and the background of each of the methods used to study the specific aims are provided in the Methodology chapter (Chapter 2). Construction of the host-pathogen interaction (HPI) model and the insights obtained from this study are presented in Chapter 3. A rule based HPI model was built with a focus on the iron regulatory mechanisms in both the host and pathogen. The model consisted of 194 rules, of which 4 rules represented interactions between the host and pathogen. The model not only represented an overview of iron metabolism but also allowed prediction of critical interaction that had the potential to form bottleneck in the system so as to control bacterial proliferation. Infact, model simulation led to the identification of 5 bottlenecks or chokepoints in the system, which if perturbed, could successfully interfere with the host-pathogen dynamics in favour of the host. The model also provided a framework to test perturbation strategies based on the bottlenecks. The study also established the importance of an iron responsive transcription factor, IdeR for regulating iron concentration in the pathogen and mediating host-pathogen interactions. Additionally, the importance of mycobactin and transferrin as key molecular players, involved in host-pathogen dynamics was also determined. The model provided a mathematical framework to test TB pathogenesis and provided significant insights about key molecular players and perturbation strategies that can be used to enhance therapeutic strategies. Given the importance of IdeR in HPI, its molecular mechanism of activation and dimerization was explored in Chapter 4. The main objective of the study was to explore the structural details of IdeR and its iron sensing capacity at the molecular level. A combination of molecular dynamics and protein structure network (PSN) were used to analyse IdeR monomers and dimers in the presence and absence of iron. PSNs used in this thesis are based on non-covalent interactions between sidechain atoms and are quite efficient in identifying iron induced subtle conformational variations. The study distinctly indicated the role of iron in IdeR stability. Further, it was observed that IdeR monomers can take up two major conformations, the ‘open’ and ‘close’ conformation with the iron bound structure preferring the ‘close’ conformation. Major structural changes, such as the N-terminal folding and increased propensity for dimerization were observed upon iron binding. Interestingly, careful analysis of structure suggests a role of these structural modifications towards DNA binding and has been tested in the next chapter. Overall, the results clearly highlight the influence of iron on IdeR activation and dimerization. The predisposition of IdeR to bind to DNA in the presence of metal is clearly visible even when the simulations are performed solely on protein molecules. However, to confirm the conjectures proposed in this chapter and to obtain the atomistic details of IdeR-DNA interactions, the IdeR-DNA complex was investigated. Chapter 5 focuses on the mechanistic details of IdeR-DNA interactions and the influence of iron on the same. IdeR is known to bind to a specific stretch of DNA, known as the ‘iron-box’ motif to form a dimer-of-dimer complex. Molecular dynamics followed by protein-DNA bipartite network analysis was performed on a set of four IdeR-DNA complexes to obtain a molecular level understanding of IdeR-DNA interactions. A striking observation was the dissociation of IdeR-DNA complex in the absence of iron, undoubtedly establishing the importance of iron for IdeR-DNA binding. At the residue level, hydrogen bond and non-covalent interactions clearly established the importance of N-terminal residues for DNA binding, thereby confirming the conjecture put forth in the previous chapter. An important aspect studied in this chapter is the allosteric nature of IdeR-DNA binding. Recent years have witnessed a paradigm shift in the understanding of allostery. Unlike the classical definition of allostery that was based on static structures, the newer definition is based on the conformational ensemble as represented by the shift in the energy landscape of the protein. The allosteric nature of IdeR-DNA complex was probed using simulated trajectories and indeed they suggest iron to be an allosteric regulator of the protein. Finally, based on the known experimental data and observations presented in Chapters 4 and 5, a multi-step model of IdeR activation and DNA binding has been proposed. In chapter 6, a global perspective of IdeR regulation in M.tb was obtained. This was important to gain insights about the influences of iron and its regulation at the M.tb cellular level. A genome scale identification of all possible IdeR targets based on the presence of ‘iron-box’ motif in the promoter region of the genes was carried out. An interesting aspect of this study was the use of energetic information from previous molecular dynamics study as an input for generation of the motif. A total of 255 such IdeR targets were identified and converted into an IdeR target network (IdeRnet). Along with IdeRnet, an unbiased systems level protein-protein interaction network was also generated. To study the response of the pathogen to external perturbations, iron-specific gene expression data was integrated into the network as node weights and edge weights. Analysis of IdeRnet provides interesting associations between fatty acid metabolism and IdeR regulations. Specific genes such as fadD32, DesA3 or lppW have been found to be affected by IdeR mutation. While IdeRnet discusses the direct associations, the global level responses are monitored by analysing pathways for the flow of information in the protein-protein interaction network (PPInet). Comparisons of the PPInets under conditions such as altering iron concentrations and lack of iron homeostasis led to the identification of the ‘top-most’ active paths under the different conditions. The study clearly suggests a halt in the protein synthesis machinery and decreased energy consumption under iron scarcity and an uninhibited consumption of energy when iron homeostasis is perturbed. In the final chapter (Chapter 7), flux balance analyses has been used to investigate the influence of iron on M.tb metabolism. The importance of iron for metabolic enzymes has already been established in the previous chapter. Additionally, M.tb is known to produce siderophores, an important metabolite that requires amino acids as its precursors, for iron extraction. All this, together highlighted the importance of iron and its regulation of M.tb metabolism. Flux balance analysis has been used previously to study the metabolic alterations that occur in an organism under different conditions. For this study, iron specific gene expression data was also incorporated into the model as reaction bounds and the flux values so obtained were compared in different environmental conditions. The study provided valuable insights into the metabolic adjustments taken up by M.tb under iron stress conditions and correlates well with the responses observed from the interactome as well as experimental observations. Most significantly, changes were observed in the energy preferences of the cell. For instance, it was noted that while the wild type strain of M.tb prefers synthesis of ATP via glycolysis, the IdeR mutant strain preferred oxidative phosphorylation. The picture becomes clearer when one accounts for the uncontrolled utilization of energy and rapid activation of protein synthesis machinery in the IdeR mutant strain. Biological systems are inherently multiscale in nature and therefore for a successful drug target regime, analysis of the genome to the phenome, which captures interactions at multiple levels, is essential. In this thesis, a detailed understanding of iron homeostasis and regulation in M.tb at multiple levels has been attempted. More importantly, insights obtained from one level, formed questions in the next level. The study was initiated at the inter-cellular level, where the influence of iron on HPI was modeled and analysed. From this study, IdeR, an iron-responsive transcription factor was identified as a key player that had the potential to alter host-pathogen interactions in the favour of the host. For a complete understanding of how IdeR regulates iron homeostasis, it was imperative to obtain a molecular level insight of its mechanism of action. Finally, the various aspects of IdeR regulation were investigated at the cellular level by analysing direct and indirect influences of IdeR on M.tb proteome and metabolome. The study suggests certain therapeutic interventions, such as 1) reduction in the concentration of free transferrin various, 2) mutations at the N-terminal sites of IdeR, 3) regulation of proteins involved in production of mycolic acids by iron and 4) perturbation of altering energy sources, which capitalize on iron and should be investigated in detail. In summary, the consequences of iron on TB infection were studied by threading different levels. This is based on the belief that most biological functions involve multiple spatio-temporal levels with frequent cross talks between the different levels, thereby making such multiscale approaches very useful.

Les leucémies aigues myéloïdes (LAM) sont des hémopathies malignes de mauvais pronostic dont les thérapies actuelles ne permettent d’obtenir des taux de survie à 5 ans chez les adultes que d’environ 40%. Par conséquent, il est nécessaire d’approfondir nos connaissances concernant les mécanismes d’oncogenèse pour développer de nouvelles approches thérapeutiques. Malgré leur hétérogénéité clinique et biologique, les LAM ont certaines caractéristiques communes comme l’activation de la voie de signalisation mTORCl qui est détectée dans la plupart des échantillons de LAM. MTORCl contrôle la survie, la croissance et la prolifération cellulaire, notamment via le contrôle de la traduction des ARNm et donc de la synthèse protéique. Au cours de ce travail, nous montrons qu’il existe, dans les LAM, une dérégulation de mTORCl qui explique les limites des effets anti-leucémiques observés avec la rapamycine (un inhibiteur allostérique de mTORCl) et qui est médiée en partie par l’activité de la sérine thréonine kinase Pim2, qui contrôle la phosphorylation de la cible de mTORCl, la protéine 4E-BP1. Cependant, cibler directement la traduction produit des effets anti-leucémiques importants, ce que nous avons montré en utilisant une molécule inhibant spécifiquement le complexe d’initiation de la traduction, le 4EGI-l. EIF4E est essentiel à l’initiation de la traduction et nous avons montré sa surexpression au niveau protéique dans la plupart des échantillons de LAM au diagnostic par comparaison à des cellules hématopoïétiques normales CD34+. Bien que son niveau d’expression n’ait pas de valeur pronostique intrinsèque, ce résultat suggère un potentiel important au blocage de la traduction dans la plupart des cas de LAM. Dans la perspective d’inhiber mTORCl, nous avons activé la voie LKBl/AMPK par la metformine, ce qui a induit des effets anti-leucémiques in vitro et in vivo via une modification du métabolisme cellulaire avec en particulier une inhibition de la synthèse de protéines oncogéniques. La metformine n’étant pas un candidat en thérapeutique dans les LAM du fait d’un index thérapeutique trop étroit, de nouvelles molécules modulant la voie LKBl/AMPK sont en cours de développement. Enfin, nous avons étudié le rôle de la sérine thréonine kinase Pim2, qui contrôle la traduction protéique et la survie dans les cellules de LAM Flt3-ITD+. Nous avons de plus montré que la sur-expression de Pim2 constitue un nouveau mécanisme de résistance aux inhibiteurs de Flt3 et représente donc une cible thérapeutique prometteuse dans cette catégorie de LAM. L’étude de la voie mTORCl et de la traduction permet donc d’envisager de multiples perspectives thérapeutiques dans les LAM dont certaines sont déjà en cours de développement clinique. / Acute myeloid leukemia (AML) are hematological malignancies with adverse prognosis in which therapies only gives 40% survival within 5 years in adults. Hence, it is important to increase our knowledge regarding oncogenesis to further develop new therapeutic approaches. Despite their clinical and biological heterogeneity, AML have in common the constitutive activation of mTORC1 signaling which is detected in most AML samples. MTORC1 controls cell survival, growth and proliferation, in particular through control of mRNA translation and protein synthesis. During this work, we show, in AML, that mTORC1 is deregulated which explain the poor effects observed with rapamycin (a mTORC1 allosteric inhibitor) and is partially mediated by the serine/threonine kinase Pim-2 which controls the mTORC1 target 4E-BP1. Nevertheless, directly targeting translation, using a specific translation initiation inhibitor named 4EGI-1, have important anti leukemic effects. EIF4E is described as essential in translation initiation and we show its protein overexpression in most AML samples at diagnosis compared with normal hematopoietic CD34+ cells. Whereas eIF4E level expression has no prognostic impact, this result suggests an important potential for treatment targeting translation initiation in AML. In our purpose of inhibiting mTORC1, we were able to activate LKB1/AMPK signaling pathway with metformin, which induces anti leukemic effects in vitro and in vivo through in particular oncogenic protein translation inhibition. Metformin is not a good AML therapeutic candidate because of a narrow therapeutic index, new compound targeting LKB1/AMPK are in development. Finally, we studied the role of the serine/threonine kinase Pim-2 and show that it controls protein translation and FLT3-ITD+ AML cells survival. Furthermore, we show that Pim-2 overexpression is a new mechanism of Flt3 inhibitors resistance and represent a new promising therapeutic target in this AML subtype. Overall, mTORC1 and protein translation study in AML show multiple therapeutics perspective, some of them are already in clinical development.

Text in Afrikaans, abstract in Afrikaans and English / Different methods of calculation of the loss of support of minor children, are investigated. According to one method (A), one first has to establish that the deceased's income was not all absorbed for his/her own maintenance. Only if there is surplus income available, it can be inferred that the deceased contributed towards the maintenance of the minor children and that the children have suffered a loss. According to another method (B) both parents' income are added and then divided between the family members. The minor child's loss of support is an amount which represent his/her share in the deceased's own income - a child automatically suffers a loss according to this method, in the event of death of a parent. Method B ought to be applied, because it is consistent with the reciprocal duty of support between spouses and the duty of spouses to maintain children. / Verskillende metodes om die verlies aan onderhoud van afhanklike kinders te bereken word ondersoek. Volgens een benadering (A) moet eers vasgestel word of die oorledene se inkomste nie alles geabsorbeer is vir sy /haar eie onderhoud nie. Slegs indien daar surplusinkomste was, kan aanvaar word dat die oorledene bygedra het tot die onderhoud van die minderjarige kinders en dat die kinders 'n verlies ly. Volgens die ander benadering (B) word beide ouers se inkomste bymekaar getel en dan tussen die gesinslede verdeel. Elke minderjarige kind se verlies aan onderhoud is 'n bedrag wat sy/haar aandeel in die oorlede ouer se afsonderlike inkomste verteenwoordig - 'n kind ly outomaties volgens hierdie metode 'n verlies. Metode B behoort meestal aanwending te vind, aangesien dit in ooreenstemming is met die wederkerige onderhoudsplig tussen gades en die plig van ouers om hul kinders te onderhou. / Private Law / LL. M. (Law)

Le travail présenté dans ce manuscrit s’articule en trois axes distincts. Dérivation de modèles mathématiques de phénomènes électrophysiologiques en cardiologie Nous utilisons des méthodes d'analyse asymptotique pour dériver un modèle simplifié à partir d'un modèle de tissu auriculaire tridimensionnel, tout en contrôlant l'erreur d'approximation. Ces méthodes ont permis de dériver un modèle bisurfacique qui permet de simuler des comportements tridimensionnels dans les oreillettes pour un coût numérique bidimensionnel afin d'étudier des phénomènes entrant en jeu lors d'arythmies auriculaires, tels que la dissociation électrique ou des hétérogénéités transmurales. La preuve de la convergence du modèle bisurfacique est apportée, et une stratégie d'optimisation du modèle en dehors du régime asymptotique est formalisée. Une méthode d’homogénéisation est également utilisée pour construire un modèle continu homogénéisé de l'activité des myocytes incluant le comportement non linéaire des gap junctions. Processus déclencheurs d'arythmie Des preuves de concepts de mécanismes arythmogènes sont apportées à l'aide de modèles numériques des veines pulmonaires. Le premier mécanisme repose sur un bloc de conduction unidirectionnel engendré par une discontinuité dans la structure fibreuse. Le second est basé sur une dynamique différente lors de la dépolarisation et de la repolarisation lorsque deux couches de fibres de directions différentes sont superposées. Perpétuation des arythmies auriculaires Un modèle bicouche des oreillettes est construit à partir d'une méthode semi-automatique de construction des fibres que nous avons développées. Nous étudions avec l'influence d'hétérogénéités transmurales de fibrose sur la perpétuation des arythmies. Plusieurs protocoles d'ablation sont ensuite testés. Enfin, une méthode de personnalisation du modèle auriculaire est formalisée. / Three axes are explored.Derivation of mathematical models of electrophysiological phenomena applied to cardiology Asymptotic analysis methods allow to derive simplified models from three-dimensional complex atrial ones, while controlling approximation errors. We construct a bilayer surface model that allows to simulate three-dimensional phenomena for a bi-dimensional computational load, and to investigate 3D atrial patterns involved in atrial arrhythmia such as electrical dissociation or transmural heterogeneities. We prove the convergence of the bilayer model, and an optimization strategy to improve the model outside the asymptotic regime is formalised. Homogeneisation methods are also used to construct a homogenized continuous model of the electrical activity of the myocytes that includes the non linear behavior of gap junctions. Triggers of atrial arrhythmia Proofs of concept of arrhythmogenic mechanisms are given by using numerical models of the pulmonary veins. The first mechanism is based on a unidirectional conduction block triggered by a discontinuity of the fibre distribution. The second one comes from a different propagation pattern during the depolarization and the repolarization when two layer of fibres are superimposed. Atrial arrhythmia perpetuation A bilayer model of the atria is constructed from a semi automatic method that we developed. We investigate the influence of transmural heterogeneities of the distribution of fibrosis on the perpetuation of atrial arrhythmia. Several ablation protocols are assessed. Finally, a method of personalization of the model is given.

Text in Afrikaans, abstract in Afrikaans and English / Different methods of calculation of the loss of support of minor children, are investigated. According to one method (A), one first has to establish that the deceased's income was not all absorbed for his/her own maintenance. Only if there is surplus income available, it can be inferred that the deceased contributed towards the maintenance of the minor children and that the children have suffered a loss. According to another method (B) both parents' income are added and then divided between the family members. The minor child's loss of support is an amount which represent his/her share in the deceased's own income - a child automatically suffers a loss according to this method, in the event of death of a parent. Method B ought to be applied, because it is consistent with the reciprocal duty of support between spouses and the duty of spouses to maintain children. / Verskillende metodes om die verlies aan onderhoud van afhanklike kinders te bereken word ondersoek. Volgens een benadering (A) moet eers vasgestel word of die oorledene se inkomste nie alles geabsorbeer is vir sy /haar eie onderhoud nie. Slegs indien daar surplusinkomste was, kan aanvaar word dat die oorledene bygedra het tot die onderhoud van die minderjarige kinders en dat die kinders 'n verlies ly. Volgens die ander benadering (B) word beide ouers se inkomste bymekaar getel en dan tussen die gesinslede verdeel. Elke minderjarige kind se verlies aan onderhoud is 'n bedrag wat sy/haar aandeel in die oorlede ouer se afsonderlike inkomste verteenwoordig - 'n kind ly outomaties volgens hierdie metode 'n verlies. Metode B behoort meestal aanwending te vind, aangesien dit in ooreenstemming is met die wederkerige onderhoudsplig tussen gades en die plig van ouers om hul kinders te onderhou. / Private Law / LL. M. (Law)

Les problèmes abordés et les résultats obtenus dans cette thèse se divisent en deux parties. La première concerne l'étude de la valeur asymptotique de jeux dépendant de la fréquence (jeux-FD). Nous introduisons un jeu différentiel associé au jeu-FD dont la valeur se ramène à une équation de Hamilton-Jacobi-Bellman-lsaacs. En affrontant un problème d'irrégularité à l'origine, nous prouvons l’existence de la valeur du jeu différentiel sur [0.1 ] et ceci nous permet de prouver que la valeur du jeu FD converge vers la valeur du jeu continu qui débute à l'état initial 0. Dans la deuxième partie, l'objectif fondamental est la décomposition de l'espace des jeux finis en sous espaces des jeux adéquats et plus faciles à étudier vu que leurs équilibres sont distingués. Cette partie est divisée en deux chapitres. Dans le premier chapitre, nous établissons une décomposition canonique de tout jeu arbitraire fini en trois composantes et nous caractérisons les équilibres approximatifs d'un jeu donné par les équilibres uniformément mixtes et en stratégies dominantes lesquels apparaissent sur ses composantes. Dans le deuxième chapitre, nous introduisons sur l'espace des jeux finis une famille de produits scalaires et nous définissons la classe des jeux harmoniques relativement au produit scalaire choisi dans cette famille. Inspiré par la décomposition de Helmholtz-Hodge appliquée aux jeux par Candogan et al. (2011), nous établissons une décomposition orthogonale de l'espace des jeux finis, par rapport au produit scalaire choisi, en les sous espaces des jeux potentiels, des jeux harmoniques et des jeux non­stratégiques c nous généralisons les résultats de Candogan et al. (2011). / The problems addressed and results obtained in this thesis are divided in two parts. The first part concerns the study of the asymptotic value of frequency-dependent games (FD-games). We introduce a differential game associated to the FD-game whose value leads to a Hamilton-Jacob-Bellman-lsaacs equation. Although an irregularity occurs at the origin, we prove existence of the value in the differential game played over [0.1 ], which allows to prove that the value of the FD-game, as the number of stages tend to infinity, converges to the value of the continuous-time game with initial state 0. ln the second part, the objective is the decomposition of the space of finite games in subspaces of suitable games which admit disguised equilibria and more tractable analysis. This part is divided in two chapters. In the first chapter, we establish a canonical decomposition of an arbitrary game into three components and we characterize the approximate equilibria of a given game in terms of the uniform equilibrium and the equilibrium in dominant strategies that appear in its components. In the second part, we introduce a family of inner products in the space of finite games and we define the class of harmonic games relatively to the chosen inner product. Inspired of the Helmholtz-Hodge decomposition applied to games by Candogan et al (2011 ), we establish an orthogonal decomposition of the space of finite games with respect to the chosen inner product, in the subspaces of potential harmonic and non-strategic games and we further generalize several results of Candogan et al (2011).

Cette thèse porte sur l’adaptation de la réalisabilité et la paramétricité au cas des types dépendants dans le cadre des Systèmes de Types Purs. Nous décrivons une méthode systématique pour construire une logique à partir d’un langage de programmation, tous deux décrits comme des systèmes de types purs. Cette logique fournit des formules pour exprimer des propriétés des programmes et elle offre un cadre formel adéquat pour développer une théorie de la réalisabilité au sein de laquelle les réalisateurs des formules sont exactement les programmes du langage de départ. Notre cadre permet alors de considérer les théorèmes de représentation pour le système T de Gödel et le système F de Girard comme deux instances d'un théorème plus général.Puis, nous expliquons comment les relations logiques de la théorie de la paramétricité peuvent s'exprimer en terme de réalisabilité, ce qui montre que la logique engendrée fournit un cadre adéquat pour développer une théorie de la paramétricité du langage de départ. Pour finir, nous montrons comment cette théorie de la paramétricité peut-être adaptée au système sous-jacent à l'assistant de preuve Coq et nous donnons un exemple d'application original de la paramétricité à la formalisation des mathématiques. / This thesis focuses on the adaptation of realizability and parametricity to dependent types in the framework of Pure Type Systems. We describe a systematic method to build a logic from a programming language, both described as pure type systems. This logic provides formulas to express properties of programs and offers a formal framework that allows us to develop a theory of realizability in which realizers of formulas are exactly programs of the starting programming language. In our framework, the standard representation theorems of Gödel's system T and Girard's system F may be seen as two instances of a more general theorem. Then, we explain how the so-called « logical relations » of parametricity theory may be expressed in terms of realizability, which shows that the generated logic provides an adequate framework for developping a general theory of parametricity. Finally, we show how this parametricity theory can be adapted to the underlying type system of the proof assistant Coq and we give an original example of application of parametricity theory to the formalization of mathematics.

No description available.

Ahnak ist ein ubiquitäres Protein, das an einer Vielzahl biologischer Prozesse beteiligt ist. In der Herzmuskelzelle ist Ahnak überwiegend am Sarkolemma lokalisiert und bindet an Aktin und an die regulatorischen Beta2-Untereinheit des L-Typ-Kalzium-Kanals. Das Ziel dieser Arbeit war die Funktion von Ahnak im Herzen mit Hilfe eines Knock-out-Maus-Modells und in Bindungsstudien zu untersuchen. Morphologische Untersuchungen zeigten, dass das Längenwachstum adulter Kardiomyozyten bei Ahnakdefizienz signifikant reduziert war. Die Kontraktionseigenschaften adulter isolierter Ahnak-defizienter Kardio-myozyten (im Alter von 6 Monaten) waren ebenfalls verändert. Die Kontraktions- und Relaxaktionsgeschwindigkeiten waren erhöht. Eine Erhöhung des diastolischen Kalzium-Spiegels zeigten die Kardiomyozyten schon im Alter von 3 Monaten. Diese beobachteten phänotypischen Veränderungen lassen vermuten, dass die Aktivität des L-Typ-Kalzium-Kanals erhöht ist. In dieser Arbeit konnte das PXXP-Motiv, in der C-terminalen Ahnak-Domäne, als die hochaffine Beta2-Bindungsstelle (KD ~ 60 nM) identifiziert werden. Substitution von Prolin gegen Alanin verringerte zwar die Bindung zur Beta2-Untereinheit dramatisch (KD ~ 1 µM), hob sie aber nicht auf. In weiteren Bindungsstudien zeigte sich, dass die natürlich vorkommende Missensmutation I5236T die Bindung zur regulatorischen Beta2-Untereinheit verstärkte, dagegen verminderte die PKA-abhängige Phosphorylierung der beiden Proteinpartner die Bindung. Experimente am ganzen isoliert perfundierten Herzen zeigten, dass Ahnak-Knock-Out-Herzen geringer Beta-adrenerg stimulierbar waren. Ahnak scheint wie eine physiologische Bremse des kardialen Kalzium-Kanals zu wirken. / Ahnak is an ubiquitous protein with in unique structure, which has been implicated in cell type specific functions. In cardiomyocytes, ahnak is predominantly localized at the sarcolemma and is associated with actin and with the regulatory beta2 subunit of the L-type calcium-channel. The aim of this work was to unravel the function of ahnak in the heart, using a knock-out-mouse model and binding studies. Morphological studies showed a significant decrease in the cell-length of ahnak deficient cardiomyocytes. The contractile parameters of isolated adult ahnak deficient cardiomyocytes (in the age of 6 month) were altered. The development of tension and relaxation were increased. An increase of diastolic calcium was already observed at the age of 3 month. In general the observed phenotypic changes suggested an increased activity of the L-type calcium-channel. In this study, a PXXP-motif, which locates in ahnaks C-terminus, was identified as the high affinity beta2 subunit binding site (KD ~ 60 nM). Substitution of both proline residues by alanine reduced, but did not abolish the binding (KD ~ 1 µM). Further binding studies revealed that the natural occurring ahnak missense mutation I5236T increases the binding affinity to the regulatory beta2 subunit. By contrast PKA dependant phosphorylation of both protein partners decreases the interaction. In studies with isolated perfused working heart preparations, the ahnak deficient hearts were less beta-adrenergic stimulated than hearts from wild type. Taken together ahnak seems to be a physiological brake of the cardiac calcium-channel.