The nature of the edge-on eclipsing binary Epsilon Aurigae remains perplexing, despite notable progress since the recent 2009-2011 eclipse. The binary involves an early F supergiant with a still unknown companion enshrouded in a disk. Although the eclipse geometry produces a significant broad band polarization signature, semiregular pulsations of the F supergiant are also a source of variable polarization, with an amplitude that is commensurate with the effect of the eclipse. This fact makes use of the polarization for studying the disk of the companion far more challenging. In an effort to better understand the pulsation nature of the supergiant, we explore a simple model for the stellar contribution to the polarization signal. The model does reasonably well in characterizing the gross properties of the time-variable polarization.

Les travaux présentés dans cette synthèse en vue d'une Habilitation à Diriger des Recherches concernent des problèmes aux limites non linéaires mixtes elliptiques hyperboliques auxquels on adjoint une contrainte inégalité. Ici nous présentons le cas significatif présenté par le problème aux limites résultant du modèle de Karman et Guderley avec condition d'entropie. Ce problème a l'avantage de se présenter simplement tout en présentant un terme non linéaire conduisant aux difficultés fondamentales des problèmes mixtes non linéaires. Ce problème aux limites est mal posé : il n'existe pas de cadre fonctionnel assurant l'existence de solutions. Notre propos est de proposer une méthode d'analyse assurant la cohérence entre les résultats fonctionnels et numériques. On commence par traiter le problème aux limites sans contrainte. L'utilisation d'une formulation variationnelle et de la formule de Green généralisée ramènent le problème à montrer qu'une projection adaptée s'annule. L'introduction d'une norme adaptée conduit à minimiser une fonctionnelle. On utilise des solutions généralisées à epsilon près correspondant aux quasi minima d'Ekeland. On considère ensuite le problème aux limites avec contrainte. Le paramètre d'entropie est recherché dans un intervalle réel suffisamment grand a priori. La contrainte est également transformée par la formule de Green généralisée ce qui conduit à une contrainte égalité. Une fonctionnelle pénalisée est minimisée.

Each cell division, the nuclear DNA must be replicated efficiently and with high accuracy to avoid mutations which can have an effect on cell function. There are three replicative DNA polymerases essential for the synthesis of DNA during replication in eukaryotic cells. DNA polymerase α (Pol α) synthesize short primers required for DNA polymerase δ (Pol δ) and DNA polymerase ε (Pol ε) to carry out the bulk synthesis. The role of Pol δ and Pol ε at the replication fork has been unclear. The aim of this thesis was to examine what role Pol ε has at the replication fork, compare the biochemical properties of Pol δ and Pol ε, and to study the function of the second largest and essential subunit of Pol ε, Dpb2. To identify where Pol ε replicates DNA in vivo, a strategy was taken where the active site of Pol ε was altered to create a mutator polymerase leaving a unique error-signature. A series of mutant pol ε proteins were purified and analyzed for enzyme activity and fidelity of DNA synthesis. Two mutants, M644F and M644G, exhibited an increased mutation rate and close to normal polymerase activity. One of these, the M644G gave rise to a specific increase of mismatch mutations resulting from T-dTMP mis-pairing during DNA synthesis in vitro. The M644G mutant was introduced in yeast strains carrying a reporter gene, URA3, on either side of an origin in different orientations. Mutations which inactivated the URA3 gene in the M644G mutant strains were analyzed. A strand specific signature was found demonstrating that Pol ε participates in the synthesis of the leading strand. Pol δ and Pol ε are both stimulated by the processivity clamp, PCNA, in in vitro replication assays. To clarify any differences they were challenged side by side in biochemical assays. Pol ε was found to require that single-stranded template (ssDNA) was entirely coated with RPA, whereas Pol δ was much less sensitive to uncoated ssDNA. The processivity of Pol δ was stimulated to a much higher degree by PCNA than of Pol ε. In presence of PCNA the processivity of Pol δ and Pol ε was comparable. In contrast, Pol ε was approximately four times slower than Pol δ when replicating a single-primed circular template in the presence of all accessory proteins and an excess of polymerase. The biochemical characterization of the system suggests that Pol ε and Pol δ are loaded onto the PCNA-primer-ternary complex by separate mechanisms. A model is proposed where the loading of Pol ε onto the leading strand is independent of the PCNA interaction motif which is required by enzymes acting on the lagging strand. The essential gene DPB2 encodes for the second largest subunit of Pol ε. We carried out a genetic screen in S.cerevisiae and isolated a lethal mutant allele of dpb2 (dpb2-200). When over-expressed together with the remaining three subunits of Polε, Pol2, Dpb3 and Dpb4, the dpb2-201 did not copurify. The biochemical property of Pol2/Dpb3/Dpb4 complex was compared with wild-type four-subunit Pol ε (Pol2/Dpb2/Dpb3/Dpb4) and a Pol2/Dpb2 complex in replication assays. The absence of Dpb2 in the complex did not significantly affect the specific activity or the processivity, but gave a slightly reduced efficiency in holoenzyme assays when compared to wild-type four-subunit Pol ε. We propose that Dpb2 is not essential for the enzyme activity of Pol ε.

In eukaryotes there are three DNA polymerases which are essential for the replication of chromosomal DNA: DNA polymerase alpha (Pol alpha), DNA polymerase delta (Pol delta) and DNA polymerase epsilon (Pol epsilon). In vitro studies of viral DNA replication showed that Pol alpha and Pol delta are sufficient for DNA replication on both leading and lagging DNA strands, thus leaving the function of Pol epsilon unknown. The low abundance and the reported protease sensitivity of Pol epsilon were holding back biochemical studies of the enzyme. The aim of this study was to characterize the structural and functional properties of eukaryotic Pol epsilon. We first developed a protocol for over-expression and purification of Pol epsilon from the yeast Saccharomyces cerevisiae. Pol epsilon consists of four subunits: Pol2 (catalytic subunit), Dpb2, Dpb3 and Dpb4. This four-subunit complex was purified to homogeneity by conventional chromatography and the subunit stoichiometry of purified Pol epsilon was estimated from colloidal coomassie-stained gels to be 1:1:1:1. The quaternary structure was determined by sedimentation velocity and gel filtration experiments. Molecular mass (371 kDa) was calculated from the experimentally determined Stokes radius (74.5 Å) and sedimentation coefficient (11.9 S) and was in good agreement with a theoretical molecular mass calculated for a heterotetramer (379 kDa). Analytical sedimentation equilibrium ultracentrifugation experiments supported the proposed heterotetrameric structure of Pol epsilon. By cryo-electron microscopy and single-particle image analysis we determined the structure of Saccharomyces cerevisiae Pol epsilon to 20-Å resolution. The four-subunit complex was found to consist of a globular domain, comprising the Pol2 subunit, flexibly connected to an elongated domain, including Dpb2, Dpb3 and Dpb4 subunits. We found that Pol epsilon requires a minimal length of 40 base pairs of primer-template duplex to be processive. This length corresponds to the dimensions of the elongated domain. To characterize the fidelity by which Pol epsilon synthesizes DNA, we purified wild type and exonuclease-deficient Pol epsilon. Wild type Pol epsilon synthesizes DNA with a very high accuracy. Analysis of the exonuclease-deficient Pol epsilon showed that Pol epsilon proofreads more than 90% of the errors made by its polymerase activity. Exonuclease-deficient Pol epsilon was shown to have a specific spectrum of errors not seen in other DNA polymerases: a high proportion of transversions resulting from T-dTTP, T-dCTP and C-dTTP mispairs. This unique error specificity and amino acid sequence alignment suggest that the structure of the polymerase active site of Pol epsilon differs from those of other members of B family DNA polymerases. With recombinant proteins and circular single-stranded DNA templates, we partially reconstituted DNA replication in vitro, in which we challenged Pol epsilon and Pol delta in side-by-side comparisons regarding functional assays for polymerase activity and processivity, as well as physical interactions with nucleic acids and PCNA. We found that Pol epsilon activity and “on-DNA” PCNA interactions are dependent on RPA-coated template DNA. By the surface plasmon resonance technique, we showed that Pol epsilon has a high affinity for DNA and low affinity for immobilized PCNA. By contrast, Pol delta was found to have low affinity for DNA and high affinity for PCNA. We suggest that a possible function of RPA is to regulate down the DNA synthesis through Pol epsilon, and that the mechanism by which Pol epsilon and Pol delta load onto the template is different due to different properties of the interaction with DNA and PCNA.

To transfer the information in the genome from mother cell to daughter cell, the DNA replication must be carried out only once and with very high fidelity prior to every cell division. In yeast there are several different DNA polymerases involved in DNA replication and/or DNA repair. The two replicative DNA polymerases, DNA polymerase delta (Pol delta) and DNA polymerase epsilon (Pol epsilon), which both include a proofreading 3´→5´exonuclease activity, can replicate and proofread the genome with a very high degree of accuracy. The aim of this thesis was to gain a better understanding of how the enigmatic DNA polymerase epsilon participates in DNA transactions. To investigate whether Pol epsilon or Pol delta is responsible for the synthesis of DNA on the lagging strand, the processing and assembly of Okazaki fragments was studied. Pol delta was found to have a unique property called “idling” which, together with the flap-endonuclease (FEN1), maintained a ligatable nick for DNA ligase I. In contrast, Pol epsilon was found to lack the ability to “idle” and interact functionally with FEN-1, indicating that Pol epsilon is not involved in processing Okazaki fragments. Together with previous genetic studies, it was concluded that Pol delta is the preferred lagging strand polymerase, leaving Pol epsilon to carry out some other function. The structure of Pol epsilon was determined by cryo-electron microscopy, to a resolution of ~20 Å. Pol epsilon is composed of a globular “head” domain consisting of the large catalytic subunit Pol2p, and a “tail” domain, consisting of the small subunits Dpb2p, Dpb3p, and Dpb4p. The two separable domains were found to be connected by a flexible hinge. Interestingly, the high intrinsic processivity of Pol epsilon depends on the interaction between the tail domain and double-stranded DNA. As a replicative DNA polymerase, Pol epsilon encounters different lesions in DNA. It was shown that Pol epsilon can perform translesion synthesis (TLS) through a model abasic site in the absence of external processivity clamps under single-hit conditions. The lesion bypass was dependent of the sequence on the template and also on a proper interaction of the “tail”domain with the primer-template. Yeast cells treated with a DNA damaging agent and devoid of all TLS polymerases showed improved survival rates in the presence of elevated levels of dNTPs. These genetic results suggested that replicative polymerases may be engaged in the bypass of some DNA lesions. In vitro, Pol epsilon was found to bypass 8-OxoG at elevated dNTP levels. Together, the in vitro and in vivo results suggest that the replicative polymerases may be engaged in bypass of less bulky DNA lesions at elevated dNTP levels. In conclusion, the low-resolution structure presented represents the first structural characterization of a eukaryotic multi-subunit DNA polymerase. The replicative DNA polymerase Pol epsilon can perform translesion synthesis due to an interaction between the tail domain and double-stranded DNA. Pol epsilon may also bypass less bulky DNA lesions when there are elevated dNTP concentrations in vivo.

This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for &epsilon;-randomizing maps, <em>n</em> + 2log(1/&epsilon;) + <em>c</em> bits required to &epsilon;-randomize an arbitrary <em>n</em>-qubit state by improving a scheme of Ambainis and Smith [5] based on small bias spaces [16, 3]. We show by a probabilistic argument that in fact the great majority of random schemes using slightly more than this many bits of key are also &epsilon;-randomizing. We provide the first known nontrivial lower bound for &epsilon;-randomizing maps, and develop several conditions on them which we hope may be useful in proving stronger lower bounds in the future.

This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for &epsilon;-randomizing maps, <em>n</em> + 2log(1/&epsilon;) + <em>c</em> bits required to &epsilon;-randomize an arbitrary <em>n</em>-qubit state by improving a scheme of Ambainis and Smith [5] based on small bias spaces [16, 3]. We show by a probabilistic argument that in fact the great majority of random schemes using slightly more than this many bits of key are also &epsilon;-randomizing. We provide the first known nontrivial lower bound for &epsilon;-randomizing maps, and develop several conditions on them which we hope may be useful in proving stronger lower bounds in the future.

The paper considers approximations of time-continuous epsilon-correlated random processes by interpolation of time-discrete Moving-Average processes. These approximations are helpful for Monte-Carlo simulations of the response of systems containing random parameters described by epsilon-correlated processes. The paper focuses on the approximation of stationary epsilon-correlated processes with a prescribed correlation function. Numerical results are presented.

In dieser Arbeit werden stochastische Charakteristiken der Lösung parabolischer Differentialgleichungen mit zufälligen Neumann-Randbedingungen mit Hilfe der Finite-Elemente-Methode angegeben. Dabei wird der Berechnung der Korrelations- bzw. Varianzfunktion besondere Bedeutung beigemessen. Das stochastische Randanfangswertproblem wird durch Anwendung von FEM-Techniken durch ein System gewöhnlicher Differentialgleichungen mit stochastischen inhomogenen Termen approximiert. Die Modellierung der stochastischen Eingangsparameter durch epsilon-korrelierte Felder gestattet Entwicklungen der Lösungscharakteristiken nach der Korrelationslänge. Numerische Beispiele enthalten den Vergleich zwischen analytischen Ergebnissen und Simulationsresultaten.

In dieser Arbeit werden parabolische Randanfangswertprobleme mit zufälliger Anfangs- und Neumann-Randbedingung betrachtet. Die zufälligen Einflußgrößen werden dabei als epsilon-korrelierte, zufällige Felder modelliert. Das Hauptinteresse liegt auf der Berechnung stochastischer Kenngrößen der auf Basis der Finite-Elemente Methode erhaltenen Lösung des Randanfangswertproblems. Für die Korrelationsfunktion der Lösung wird eine Entwicklung nach der Korrelationslänge sowie eine explizite Berechnung für spezielle Typen der Vernetzung vorgestellt. Anhand von numerischen Beispielen werden abschließend die auf den verschiedenen Wegen erhaltenen Varianzen mit der einer simulierten Lösung verglichen.