La quantité de données disponibles n'a jamais été aussi grande. Se poser les bonnes questions, c'est-à-dire des questions qui soient à la fois pertinentes et dont la réponse est accessible est difficile. L'analyse topologique de données tente de contourner le problème en ne posant pas une question trop précise mais en recherchant une structure sous-jacente aux données. Une telle structure est intéressante en soi mais elle peut également guider le questionnement de l'analyste et le diriger vers des questions pertinentes. Un des outils les plus utilisés dans ce domaine est l'homologie persistante. Analysant les données à toutes les échelles simultanément, la persistance permet d'éviter le choix d'une échelle particulière. De plus, ses propriétés de stabilité fournissent une manière naturelle pour passer de données discrètes à des objets continus. Cependant, l'homologie persistante se heurte à deux obstacles. Sa construction se heurte généralement à une trop large taille des structures de données pour le travail en grandes dimensions et sa robustesse ne s'étend pas au bruit aberrant, c'est-à-dire à la présence de points non corrélés avec la structure sous-jacente.Dans cette thèse, je pars de ces deux constatations et m'applique tout d'abord à rendre le calcul de l'homologie persistante robuste au bruit aberrant par l'utilisation de la distance à la mesure. Utilisant une approximation du calcul de l'homologie persistante pour la distance à la mesure, je fournis un algorithme complet permettant d'utiliser l'homologie persistante pour l'analyse topologique de données de petite dimension intrinsèque mais pouvant être plongées dans des espaces de grande dimension. Précédemment, l'homologie persistante a également été utilisée pour analyser des champs scalaires. Ici encore, le problème du bruit aberrant limitait son utilisation et je propose une méthode dérivée de l'utilisation de la distance à la mesure afin d'obtenir une robustesse au bruit aberrant. Cela passe par l'introduction de nouvelles conditions de bruit et l'utilisation d'un nouvel opérateur de régression. Ces deux objets font l'objet d'une étude spécifique. Le travail réalisé au cours de cette thèse permet maintenant d'utiliser l'homologie persistante dans des cas d'applications réelles en grandes dimensions, que ce soit pour l'inférence topologique ou l'analyse de champs scalaires. / Massive amounts of data are now available for study. Asking questions that are both relevant and possible to answer is a difficult task. One can look for something different than the answer to a precise question. Topological data analysis looks for structure in point cloud data, which can be informative by itself but can also provide directions for further questioning. A common challenge faced in this area is the choice of the right scale at which to process the data.One widely used tool in this domain is persistent homology. By processing the data at all scales, it does not rely on a particular choice of scale. Moreover, its stability properties provide a natural way to go from discrete data to an underlying continuous structure. Finally, it can be combined with other tools, like the distance to a measure, which allows to handle noise that are unbounded. The main caveat of this approach is its high complexity.In this thesis, we will introduce topological data analysis and persistent homology, then show how to use approximation to reduce the computational complexity. We provide an approximation scheme to the distance to a measure and a sparsifying method of weighted Vietoris-Rips complexes in order to approximate persistence diagrams with practical complexity. We detail the specific properties of these constructions.Persistent homology was previously shown to be of use for scalar field analysis. We provide a way to combine it with the distance to a measure in order to handle a wider class of noise, especially data with unbounded errors. Finally, we discuss interesting opportunities opened by these results to study data where parts are missing or erroneous.

Abrin is a potent toxin obtained from the seeds of Abrus precatorius. It is a heterodimeric glycoprotein consisting of an A and a B subunit linked together by a disulfide bond. The toxicity of the protein comes from the A subunit harboring RNA-N-glycosidase activity which cleaves the glycosidic bond between the ribose sugar and the adenine at position 4324 in 28S rRNA. The depurination of a specific adenine residue at position 4324 results in loss of conformation of the 28S rRNA at the α sarcin/ricin loop to which elongation factor-2 (EF-2) binds, during the transloction step of translation, leading to inhibition of protein synthesis. The B subunit of abrin is a galactose specific lectin. The lectin activity enables the toxin to gain entry inside cells on binding to receptors with terminal galactose. After entering cells, a few molecules of abrin reach the endoplasmic reticulum (ER) via the retrograde transport, where the disulfide bond between the A and the B subunits gets cleaved. Then the A chain escapes into the cytosol where it binds to its target, the α-sarcin loop of the 28S ribosomal RNA and inhibits protein synthesis. Apart from inhibition of protein synthesis, exposure of cells to abrin leads to the loss of mitochondrial membrane potential (MMP) resulting in the activation of caspases and finally apoptosis. However, whether apoptosis is dependent on the inhibition of protein synthesis has not been elucidated. The major objectives of this study are therefore to delineate the signaling pathways involved in abrin-induced apoptosis. The thesis is divided into 4 Chapters: Chapter 1. provides a overview of the general properties of RIPs, with a brief history, classification, trafficking and biological activities of the toxins. This chapter also discusses their potential use in bio-warfare and the treatments available for management of toxicity. Chapter 2 and 3 discuss the results obtained on studies aimed at gaining insights into the signaling pathways involved in abrin-induced apoptosis. Chapter 4 focuses on the research carried out to understand the mechanisms of neutralization of abrin by the mAb D6F10. Towards the first objective, chapter 2 elucidates the role of endoplasmic reticulum (ER) stress signaling in abrin-induced apoptosis using the human T-cell line, Jurkat as a model system. It could be concluded that the inhibition of protein synthesis by the catalytic A subunit of abrin could result in accumulation of unfolded proteins in the ER leading to ER stress which triggers the unfolded protein response (UPR) pathway. The ER resident trans-membrane sensors IRE1 (Inositol-requiring enzyme 1), PERK (PKR-like ER kinase) and ATF6 (Activating transcription factor 6) are the important players of UPR in mammalian cells. These sensors inhibit translation and increase the levels of chaperones to restore protein homeostasis. However, if the ER stress is prolonged, apoptotic pathways get activated to remove severely damaged cells in which protein folding defects cannot be resolved. Recent studies have shown that endoplasmic reticulum (ER) stress induces apoptosis by activating initiater caspases such as caspase-2 and -8 which eventually trigger mitochondrial membrane potential loss and activation of downstream effector capases-9 and -3. Phosphorylation of eukaryotic initiation factor 2α and upregulation of CHOP [CAAT/enhancer binding protein (C/EBP) homologous protein], important players involved in ER stress signaling by abrin, suggested activation of ER stress in the cells. ER stress is also known to induce apoptosis via stress kinases such as p38 MAPK and JNK. Activation of both the pathways was observed upon abrin treatment and found to be upstream of the activation of caspases. However, abrin-induced apoptosis was found be dependent on p38 MAPK but not JNK. We also observed that abrin induced activation of caspase-2 and caspase-8 and triggered Bid cleavage leading to mitochondrial membrane potential loss and thus connecting the signaling events from ER stress to mitochondrial death machinery. Few toxins belonging to the family of ribosome inactivating proteins such as Shiga toxin have been observed to induce DNA damage in human endothelial cells and activate p53/ATM-dependent signaling pathway in mammalian cells. To further investigate the role of abrin on activation of DNA damage signaling pathway, we analysed the phosphorylation of H2AX and ATM, which are markers for double strand DNA breaks. We observed phosphorylation of H2AX and ATM upon abrin treatment but not when cells were pretreated with the broad spectrum pan caspase inhibitor. This study suggested that the DNA damage observed was an indirect effect of caspase-activated DNase. We concluded from the studies in chapter 2 that inhibition of protein synthesis by abrin can trigger endoplasmic reticulum stress leading to mitochondria-mediated apoptosis. Further studies were conducted to understand the dependence of ER stress on inhibition of protein synthesis and are presented in chapter 3. For this study, we have used an active site mutant of abrin A chain (R167L) which exhibits lower protein synthesis inhibitory activity than the wild type abrin A chain. Recombinant wild type and mutant abrin A chains were expressed in E.coli and purified. Since, abrin A chain requires the B chain for internalization into cells, both wild type and mutant abrin A chains were conjugated to native ricin B chain to generate a hybrid toxin. Next, we have compared the toxic effects of the two conjugates in cells. The rate of inhibition of protein synthesis mediated by the mutant ricin B-rABRA (R167L) conjugate was slower than that of the wild type ricin B-rABRA conjugate but it could trigger ER stress leading to mitochondrial mediated apoptosis in cells though delayed, suggesting that inhibition of protein synthesis is the major factor contributing to abrin-mediated apoptosis. Abrin is extremely lethal and considered as a potential agent for use in biological warfare. Currently, there are no antidotes or effective therapies available for abrin poisoning. Antibody based antitoxins function by either preventing toxin binding to cell surface receptors or by translocation. Antibodies against the B chain of RIPs function by inhibiting the binding of B chain of the toxin to cells, whereas the exact mechanism by which antibodies against A chain function is still not clear. The only known neutralizing monoclonal antibody against abrin A chain, namely, D6F10, was generated in our laboratory and was shown to rescue cells and mice from abrin intoxication. Earlier experiments with confocal microscopy suggested that mAb D6F10 could internalize in HeLa cells along with abrin, suggesting that the antibody can function intracellularly. Chapter 4 discusses the work carried out to delineate the mechanism of intracellular neutralization of abrin by the mAb D6F10. We observed significant reduction in binding and delay in abrin internalization in the presence of the neutralizing monoclonal antibody (mAb) D6F10. Considering that the majority of the abrin after internalization is removed by lysosomal degradation, we studied the fate of abrin in the presence of mAb D6F10. Confocal images did not show any difference in the distribution of abrin in the lysosomes in the absence or presence of antibody. However, the antibody remained persistently colocalized with abrin in the cells, suggesting that the antibody might inhibit enzymatic activity of abrin at its cellular site of action.