894 resultados para differential analysis
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Introduction: Wound healing process involves the activation of extracellular matrix components, remodeling enzymes, cellular adhesion molecules, growth factors, cytokines and chemokines genes. However, the molecular patterns underlying the healing process periapical environment remain unclear. Here we hypothesized that endodontic infection might result in an imbalance in the expression of wound healing genes involved in the pathogenesis of periapical lesions. Furthermore, we suggest that differential expression of wound healing markers in active and latent granulomas could account for different clinical outcomes for such lesions. Methods: Study samples consisted of 93 periapical granulomas collected after endodontic surgeries and 24 healthy periodontal ligament tissues collected from premolars extracted for orthodontic purposes as control samples. Of these, 10 periapical granulomas and 5 healthy periapical tissues were used for expression analysis of 84 wound healing genes by using a pathway-specific real-time polymerase chain reaction array. The remaining 83 granulomas and all 24 control specimens were used to validate the obtained array data by real-time polymerase chain reaction. Observed variations in expression of wound healing genes were analyzed according to the classification of periapical granulomas as active/progressive versus inactive/stable (as determined by receptor activator for nuclear factor kappa B ligand/osteoprotegerin expression ratio). Results: We observed a marked increase of 5-fold or greater in SERPINE1, TIMP1, COL1A1, COL5A1, VTN, CTGF, FGF7, TGFB1, TNF, CXCL11, ITGA4, and ITGA5 genes in the periapical granulomas when compared with control samples. SERPINE1, TIMP1, COL1A1, TGFB1, and ITGA4 mRNA expression was significantly higher in inactive compared with active periapical granulomas (P < .001), whereas TNF and CXCL11 mRNA expression was higher in active lesions (P < .001). Conclusions: The identification of novel gene targets that curb the progression status of periapical lesions might contribute to a more accurate diagnosis and lead to treatment modalities more conducive to endodontic success. (J Endod 2012;38:185-190)
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Abstract Background An important challenge for transcript counting methods such as Serial Analysis of Gene Expression (SAGE), "Digital Northern" or Massively Parallel Signature Sequencing (MPSS), is to carry out statistical analyses that account for the within-class variability, i.e., variability due to the intrinsic biological differences among sampled individuals of the same class, and not only variability due to technical sampling error. Results We introduce a Bayesian model that accounts for the within-class variability by means of mixture distribution. We show that the previously available approaches of aggregation in pools ("pseudo-libraries") and the Beta-Binomial model, are particular cases of the mixture model. We illustrate our method with a brain tumor vs. normal comparison using SAGE data from public databases. We show examples of tags regarded as differentially expressed with high significance if the within-class variability is ignored, but clearly not so significant if one accounts for it. Conclusion Using available information about biological replicates, one can transform a list of candidate transcripts showing differential expression to a more reliable one. Our method is freely available, under GPL/GNU copyleft, through a user friendly web-based on-line tool or as R language scripts at supplemental web-site.
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Abstract Background The search for enriched (aka over-represented or enhanced) ontology terms in a list of genes obtained from microarray experiments is becoming a standard procedure for a system-level analysis. This procedure tries to summarize the information focussing on classification designs such as Gene Ontology, KEGG pathways, and so on, instead of focussing on individual genes. Although it is well known in statistics that association and significance are distinct concepts, only the former approach has been used to deal with the ontology term enrichment problem. Results BayGO implements a Bayesian approach to search for enriched terms from microarray data. The R source-code is freely available at http://blasto.iq.usp.br/~tkoide/BayGO in three versions: Linux, which can be easily incorporated into pre-existent pipelines; Windows, to be controlled interactively; and as a web-tool. The software was validated using a bacterial heat shock response dataset, since this stress triggers known system-level responses. Conclusion The Bayesian model accounts for the fact that, eventually, not all the genes from a given category are observable in microarray data due to low intensity signal, quality filters, genes that were not spotted and so on. Moreover, BayGO allows one to measure the statistical association between generic ontology terms and differential expression, instead of working only with the common significance analysis.
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Abstract Background The etiology of Bell's palsy can vary but anterograde axonal degeneration may delay spontaneous functional recovery leading the necessity of therapeutic interventions. Corticotherapy and/or complementary rehabilitation interventions have been employed. Thus the natural history of the disease reports to a neurotrophic resistance of adult facial motoneurons leading a favorable evolution however the related molecular mechanisms that might be therapeutically addressed in the resistant cases are not known. Fibroblast growth factor-2 (FGF-2) pathway signaling is a potential candidate for therapeutic development because its role on wound repair and autocrine/paracrine trophic mechanisms in the lesioned nervous system. Methods Adult rats received unilateral facial nerve crush, transection with amputation of nerve branches, or sham operation. Other group of unlesioned rats received a daily functional electrical stimulation in the levator labii superioris muscle (1 mA, 30 Hz, square wave) or systemic corticosterone (10 mgkg-1). Animals were sacrificed seven days later. Results Crush and transection lesions promoted no changes in the number of neurons but increased the neurofilament in the neuronal neuropil of axotomized facial nuclei. Axotomy also elevated the number of GFAP astrocytes (143% after crush; 277% after transection) and nuclear FGF-2 (57% after transection) in astrocytes (confirmed by two-color immunoperoxidase) in the ipsilateral facial nucleus. Image analysis reveled that a seven days functional electrical stimulation or corticosterone led to elevations of FGF-2 in the cytoplasm of neurons and in the nucleus of reactive astrocytes, respectively, without astrocytic reaction. Conclusion FGF-2 may exert paracrine/autocrine trophic actions in the facial nucleus and may be relevant as a therapeutic target to Bell's palsy.
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Abstract Background Prostate cancer is a leading cause of death in the male population, therefore, a comprehensive study about the genes and the molecular networks involved in the tumoral prostate process becomes necessary. In order to understand the biological process behind potential biomarkers, we have analyzed a set of 57 cDNA microarrays containing ~25,000 genes. Results Principal Component Analysis (PCA) combined with the Maximum-entropy Linear Discriminant Analysis (MLDA) were applied in order to identify genes with the most discriminative information between normal and tumoral prostatic tissues. Data analysis was carried out using three different approaches, namely: (i) differences in gene expression levels between normal and tumoral conditions from an univariate point of view; (ii) in a multivariate fashion using MLDA; and (iii) with a dependence network approach. Our results show that malignant transformation in the prostatic tissue is more related to functional connectivity changes in their dependence networks than to differential gene expression. The MYLK, KLK2, KLK3, HAN11, LTF, CSRP1 and TGM4 genes presented significant changes in their functional connectivity between normal and tumoral conditions and were also classified as the top seven most informative genes for the prostate cancer genesis process by our discriminant analysis. Moreover, among the identified genes we found classically known biomarkers and genes which are closely related to tumoral prostate, such as KLK3 and KLK2 and several other potential ones. Conclusion We have demonstrated that changes in functional connectivity may be implicit in the biological process which renders some genes more informative to discriminate between normal and tumoral conditions. Using the proposed method, namely, MLDA, in order to analyze the multivariate characteristic of genes, it was possible to capture the changes in dependence networks which are related to cell transformation.
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Background Staphylococcus aureus is the most common agent of septic arthritis that is a severe, rapidly progressive and destructive joint disease. Superantigens produced by S. aureus are considered the major arthritogenic factors. In this study, we compared the arthritogenic potential of five superantigen-producing staphylococcal strains. Methods Male C57BL/6 mice were intravenously infected with ATCC 19095 SEC+, N315 ST5 TSST-1+, S-70 TSST-1+, ATCC 51650 TSST-1+ and ATCC 13565 SEA+ strains. Clinical parameters as body weight, arthritis incidence and clinical score were daily evaluated. Joint histopathological analysis and spleen cytokine production were evaluated at the 14th day after infection. Results Weight loss was observed in all infected mice. ATCC 19095 SEC+, N315 ST5 TSST-1+ and S-70 TSST-1+ were arthritogenic, being the highest scores observed in ATCC 19095 SEC+ infected mice. Intermediate and lower clinical scores were observed in N315 ST5 TSST-1+ and S-70 TSST-1+ infected mice, respectively. The ATCC 13565 SEA+ strain caused death of 85% of the animals after 48 h. Arthritis triggered by the ATCC 19095 SEC+ strain was characterized by accentuated synovial hyperplasia, inflammation, pannus formation, cartilage destruction and bone erosion. Similar joint alterations were found in N315 ST5 TSST-1+ infected mice, however they were strikingly more discrete. Only minor synovial proliferation and inflammation were triggered by the S-70 TSST-1+ strain. The lowest levels of TNF-α, IL-6 and IL-17 production in response to S. aureus stimulation were found in cultures from mice infected with the less arthritogenic strains (S-70 TSST-1+ and ATCC 51650 TSST-1+). The highest production of IL-17 was detected in mice infected with the most arthritogenic strains (ATCC 19095 SEC+ and N315 ST5 TSST-1+). Conclusions Together these results demonstrated that S. aureus strains, isolated from biological samples, were able to induce a typical septic arthritis in mice. These results also suggest that the variable arthritogenicity of these strains was, at least in part, related to their differential ability to induce IL-17 production.
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Abstract Background Cancer stem cell (CSC) hypothesis postulates that tumors are maintained by a self-renewing CSC population that is also capable of differentiating into non-self-renewing cell populations that constitute the bulk of tumor. Stem cells renewal and differentiation can be directly influenced by the oxygen levels of determined tissues, probably by the reduction of oxidative DNA damage in hypoxic regions, thus leading to a friendlier microenvironment, regarding to clonal expansion and for resistance to chemotherapeutic regimens. Furthermore, there have been strong data indicating a pivotal role of hypoxic niche in cancer stem cells development. There are evidence that hypoxia could drive the maintenance of CSC, via HIF-1α expression, but it still to be determined whether hypoxia markers are expressed in breast tumors presenting CD44+CD24-/low immunophenotype. Methods Immunohistochemical analysis of CD44+CD24-/low expression and its relationship with hypoxia markers and clinical outcome were evaluated in 253 samples of breast ductal carcinomas. Double-immunolabeling was performed using EnVision Doublestain System (Dako, Carpinteria, CA, USA). Slides were then scanned into high-resolution images using Aperio ScanScope XT and then, visualized in the software Image Scope (Aperio, Vista, CA, USA). Results In univariate analysis, CD44+CD24-/low expression showed association with death due to breast cancer (p = 0.035). Breast tumors expressing CD44+CD24-/low immunophenotype showed relationship with HIF-1α (p = 0.039) and negativity for HER-2 (p = 0.013). Conclusion Considering that there are strong evidences that the fraction of a tumour considered to be cancer stem cells is plastic depending upon microenvironmental signals, our findings provide further evidence that hypoxia might be related to the worse prognosis found in CD44+CD24-/low positive breast tumors.
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The thesis consists of three independent parts. Part I: Polynomial amoebas We study the amoeba of a polynomial, as de ned by Gelfand, Kapranov and Zelevinsky. A central role in the treatment is played by a certain convex function which is linear in each complement component of the amoeba, which we call the Ronkin function. This function is used in two di erent ways. First, we use it to construct a polyhedral complex, which we call a spine, approximating the amoeba. Second, the Monge-Ampere measure of the Ronkin function has interesting properties which we explore. This measure can be used to derive an upper bound on the area of an amoeba in two dimensions. We also obtain results on the number of complement components of an amoeba, and consider possible extensions of the theory to varieties of codimension higher than 1. Part II: Differential equations in the complex plane We consider polynomials in one complex variable arising as eigenfunctions of certain differential operators, and obtain results on the distribution of their zeros. We show that in the limit when the degree of the polynomial approaches innity, its zeros are distributed according to a certain probability measure. This measure has its support on the union of nitely many curve segments, and can be characterized by a simple condition on its Cauchy transform. Part III: Radon transforms and tomography This part is concerned with different weighted Radon transforms in two dimensions, in particular the problem of inverting such transforms. We obtain stability results of this inverse problem for rather general classes of weights, including weights of attenuation type with data acquisition limited to a 180 degrees range of angles. We also derive an inversion formula for the exponential Radon transform, with the same restriction on the angle.
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This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.
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Singularities of robot manipulators have been intensely studied in the last decades by researchers of many fields. Serial singularities produce some local loss of dexterity of the manipulator, therefore it might be desirable to search for singularityfree trajectories in the jointspace. On the other hand, parallel singularities are very dangerous for parallel manipulators, for they may provoke the local loss of platform control, and jeopardize the structural integrity of links or actuators. It is therefore utterly important to avoid parallel singularities, while operating a parallel machine. Furthermore, there might be some configurations of a parallel manipulators that are allowed by the constraints, but nevertheless are unreachable by any feasible path. The present work proposes a numerical procedure based upon Morse theory, an important branch of differential topology. Such procedure counts and identify the singularity-free regions that are cut by the singularity locus out of the configuration space, and the disjoint regions composing the configuration space of a parallel manipulator. Moreover, given any two configurations of a manipulator, a feasible or a singularity-free path connecting them can always be found, or it can be proved that none exists. Examples of applications to 3R and 6R serial manipulators, to 3UPS and 3UPU parallel wrists, to 3UPU parallel translational manipulators, and to 3RRR planar manipulators are reported in the work.
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[EN]Isogeometric analysis (IGA) has arisen as an attempt to unify the fields of CAD and classical finite element methods. The main idea of IGA consists in using for analysis the same functions (splines) that are used in CAD representation of the geometry. The main advantage with respect to the traditional finite element method is a higher smoothness of the numerical solution and more accurate representation of the geometry. IGA seems to be a promising tool with wide range of applications in engineering. However, this relatively new technique have some open problems that require a solution. In this work we present our results and contributions to this issue…
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Apple consumption is highly recomended for a healthy diet and is the most important fruit produced in temperate climate regions. Unfortunately, it is also one of the fruit that most ofthen provoks allergy in atopic patients and the only treatment available up to date for these apple allergic patients is the avoidance. Apple allergy is due to the presence of four major classes of allergens: Mal d 1 (PR-10/Bet v 1-like proteins), Mal d 2 (Thaumatine-like proteins), Mal d 3 (Lipid transfer protein) and Mal d 4 (profilin). In this work new advances in the characterization of apple allergen gene families have been reached using a multidisciplinary approach. First of all, a genomic approach was used for the characterization of the allergen gene families of Mal d 1 (task of Chapter 1), Mal d 2 and Mal d 4 (task of Chapter 5). In particular, in Chapter 1 the study of two large contiguos blocks of DNA sequences containing the Mal d 1 gene cluster on LG16 allowed to acquire many new findings on number and orientation of genes in the cluster, their physical distances, their regulatory sequences and the presence of other genes or pseudogenes in this genomic region. Three new members were discovered co-localizing with the other Mal d 1 genes of LG16 suggesting that the complexity of the genetic base of allergenicity will increase with new advances. Many retrotranspon elements were also retrieved in this cluster. Due to the developement of molecular markers on the two sequences, the anchoring of the physical and the genetic map of the region has been successfully achieved. Moreover, in Chapter 5 the existence of other loci for the Thaumatine-like protein family in apple (Mal d 2.03 on LG4 and Mal d 2.02 on LG17) respect the one reported up to now was demonstred for the first time. Also one new locus for profilins (Mal d 4.04) was mapped on LG2, close to the Mal d 4.02 locus, suggesting a cluster organization for this gene family, as is well reported for Mal d 1 family. Secondly, a methodological approach was used to set up an highly specific tool to discriminate and quantify the expression of each Mal d 1 allergen gene (task of Chapter 2). In aprticular, a set of 20 Mal d 1 gene specific primer pairs for the quantitative Real time PCR technique was validated and optimized. As a first application, this tool was used on leaves and fruit tissues of the cultivar Florina in order to identify the Mal d 1 allergen genes that are expressed in different tissues. The differential expression retrieved in this study revealed a tissue-specificity for some Mal d 1 genes: 10/20 Mal d 1 genes were expressed in fruits and, indeed, probably more involved in the allergic reactions; while 17/20 Mal d 1 genes were expressed in leaves challenged with the fungus Venturia inaequalis and therefore probably interesting in the study of the plant defense mechanism. In Chapter 3 the specific expression levels of the 10 Mal d 1 isoallergen genes, found to be expressed in fruits, were studied for the first time in skin and flesh of apples of different genotypes. A complex gene expression profile was obtained due to the high gene-, tissue- and genotype-variability. Despite this, Mal d 1.06A and Mal d 1.07 expression patterns resulted particularly associated with the degree of allergenicity of the different cultivars. They were not the most expressed Mal d 1 genes in apple but here it was hypotized a relevant importance in the determination of allergenicity for both qualitative and quantitative aspects of the Mal d 1 gene expression levels. In Chapter 4 a clear modulation for all the 17 PR-10 genes tested in young leaves of Florina after challenging with the fungus V. inaequalis have been reported but with a peculiar expression profile for each gene. Interestingly, all the Mal d 1 genes resulted up-regulated except Mal d 1.10 that was down-regulated after the challenging with the fungus. The differences in direction, timing and magnitude of induction seem to confirm the hypothesis of a subfunctionalization inside the gene family despite an high sequencce and structure similarity. Moreover, a modulation of PR-10 genes was showed both in compatible (Gala-V. inaequalis) and incompatible (Florina-V. inaequalis) interactions contribute to validate the hypothesis of an indirect role for at least some of these proteins in the induced defense responses. Finally, a certain modulation of PR-10 transcripts retrieved also in leaves treated with water confirm their abilty to respond also to abiotic stress. To conclude, the genomic approach used here allowed to create a comprehensive inventory of all the genes of allergen families, especially in the case of extended gene families like Mal d 1. This knowledge can be considered a basal prerequisite for many further studies. On the other hand, the specific transcriptional approach make it possible to evaluate the Mal d 1 genes behavior on different samples and conditions and therefore, to speculate on their involvement on apple allergenicity process. Considering the double nature of Mal d 1 proteins, as apple allergens and as PR-10 proteins, the gene expression analysis upon the attack of the fungus created the base for unravel the Mal d 1 biological functions. In particular, the knowledge acquired in this work about the PR-10 genes putatively more involved in the specific Malus-V. inaequalis interaction will be helpful, in the future, to drive the apple breeding for hypo-allergenicity genotype without compromise the mechanism of response of the plants to stress conditions. For the future, the survey of the differences in allergenicity among cultivars has to be be thorough including other genotypes and allergic patients in the tests. After this, the allelic diversity analysis with the high and low allergenic cultivars on all the allergen genes, in particular on the ones with transcription levels correlated to allergencity, will provide the genetic background of the low ones. This step from genes to alleles will allow the develop of molecular markers for them that might be used to effectively addressed the apple breeding for hypo-allergenicity. Another important step forward for the study of apple allergens will be the use of a specific proteomic approach since apple allergy is a multifactor-determined disease and only an interdisciplinary and integrated approach can be effective for its prevention and treatment.
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Das Hepatitis C Virus (HCV) ist ein umhülltes RNA Virus aus der Familie der Flaviviridae. Sein Genom kodiert für ein ca. 3000 Aminosäuren langes Polyprotein, welches co- und posttranslational in seine funktionellen Einheiten gespalten wird. Eines dieser viralen Proteine ist NS5A. Es handelt sich hierbei um ein stark phosphoryliertes Protein, das eine amphipatische α-Helix im Amino-Terminus trägt, welche für die Membran-Assoziation von NS5A verantwortlich ist. Welche Rolle die Phosphorylierung für die Funktion des Proteins spielt, bzw. welche Funktion NS5A überhaupt ausübt, ist zur Zeit noch unklar. Beobachtungen lassen Vermutungen über eine Funktion von NS5A bei der Resistenz infizierter Zellen gegenüber Interferon-alpha zu. Weiterhin wird vermutet, das NS5A als Komponente des membranständigen HCV Replikasekomplexes an der RNA Replikation beteiligt ist. Das Ziel dieser Doktorarbeit war es, die Funktion von NS5A für die RNA Replikation zu untersuchen. Zu diesem Zweck wurde eine Serie von Phosphorylierungsstellen-Mutanten generiert, die auf Ihre Replikationsfähigkeit und den Phosphorylierungsstatus hin untersucht wurden. Wir fanden, dass bestimmte Serin-Substitutionen im Zentrum von NS5A zu einer gesteigerten RNA Replikation führten, bei gleichzeitig reduzierter NS5A Hyperphosphorylierung. Weiterhin studierten wir den Einfluß von Mutationen in der Amino-terminalen amphipatischen α-Helix von NS5A auf die RNA-Replikation, sowie Phosphorylierung und subzelluläre Lokalisation des Proteins. Wir fanden, dass geringfügige strukturelle Veränderungen der amphipatischen Helix zu einer veränderten subzellulären Lokalisation von NS5A führten, was mit einer reduzierten oder komplett inhibierten RNA Replikation einherging. Zudem interferierten die strukturellen Veränderungen mit der Hyperphosphorylierung des Proteins, was den Schluß nahe legt, dass die amphipatische Helix eine wichtige strukturelle Komponente des Proteins darstellt, die für die korrekte Faltung und Phosphorylierung des Proteins essentiell ist. Als weitere Aspekte wurden die Trans-Komplementationsfähigkeit der verschiedenen viralen Komponenten des HCV Replikasekomplexes untersucht, sowie zelluläre Interaktionspartner von NS5A identifiziert. Zusammenfassend zeigen die Ergebnisse dieser Doktorarbeit, dass NS5A eine wichtige Rolle bei der RNA-Replikation spielt. Diese Funktion wird wahrscheinlich über den Phosphorylierungszustand des Proteins reguliert.
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Wegen der fortschreitenden Miniaturisierung von Halbleiterbauteilen spielen Quanteneffekte eine immer wichtigere Rolle. Quantenphänomene werden gewöhnlich durch kinetische Gleichungen beschrieben, aber manchmal hat eine fluid-dynamische Beschreibung Vorteile: die bessere Nutzbarkeit für numerische Simulationen und die einfachere Vorgabe von Randbedingungen. In dieser Arbeit werden drei Diffusionsgleichungen zweiter und vierter Ordnung untersucht. Der erste Teil behandelt die implizite Zeitdiskretisierung und das Langzeitverhalten einer degenerierten Fokker-Planck-Gleichung. Der zweite Teil der Arbeit besteht aus der Untersuchung des viskosen Quantenhydrodynamischen Modells in einer Raumdimension und dessen Langzeitverhaltens. Im letzten Teil wird die Existenz von Lösungen einer parabolischen Gleichung vierter Ordnung in einer Raumdimension bewiesen, und deren Langzeitverhalten studiert.
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In this thesis three measurements of top-antitop differential cross section at an energy in the center of mass of 7 TeV will be shown, as a function of the transverse momentum, the mass and the rapidity of the top-antitop system. The analysis has been carried over a data sample of about 5/fb recorded with the ATLAS detector. The events have been selected with a cut based approach in the "one lepton plus jets" channel, where the lepton can be either an electron or a muon. The most relevant backgrounds (multi-jet QCD and W+jets) have been extracted using data driven methods; the others (Z+ jets, diboson and single top) have been simulated with Monte Carlo techniques. The final, background-subtracted, distributions have been corrected, using unfolding methods, for the detector and selection effects. At the end, the results have been compared with the theoretical predictions. The measurements are dominated by the systematic uncertainties and show no relevant deviation from the Standard Model predictions.