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Die zentralen Objekte der Dissertation sind Translationsflächen. Dabei handelt es sich um Riemann’sche Flächen, die aus in die euklidische Ebene eingebetteten Polygonen durch Verkleben von parallelen gleichlangen Seiten entstehen. Zwei Translationsflächen sind gleich, wenn es möglich ist, die Polygone durch ”Zerschneiden und mittels Translationen neu Zusammenkleben“ ineinander zu überführen. Die Gruppe GL_2(R) operiert auf der Menge der Translationsflächen via der linearen Abbildungen auf den Polygonen. Der Stabilisator einer Translationsfläche X unter dieser Operation wird die Veech-Gruppe von X genannt und mit SL(X) bezeichnet. Die Veech-Gruppe ist eine diskrete Untergruppe von SL_2(R) und damit eine Fuchs’sche Gruppe.
Fuchs’sche Gruppen werden je nach ihrer Limesmenge in elementare und nicht-elementare Gruppen eingeteilt. Letztere wiederum unterteilt man in Gruppen erster oder zweiter Art. Fuchs’sche Gruppen mit endlichem co-Volumen heißen Gitter und sind genau die endlich erzeugten Gruppen erster Art. Translationsflächen, deren Veech-Gruppe ein Gitter ist, heißen Veech-Flächen und sind von besonderem Interesse, da für sie die Veech Alternative gilt.
Ein feineres Maß für die Größe einer Fuchs’schen Gruppe ist der kritische Exponent. Er ist definiert als das Infimum aller reellen Zahlen, für die die Poincaré Reihe konvergiert und liegt für alle unendlichen Fuchs’schen Gruppen zwischen 0 und 1. Hauptziel der Dissertation ist der Beweis von Theorem 1. Es gibt Translationsflächen, für die der kritische Exponent ihrer Veech-Gruppe echt zwischen 1/2 und 1 liegt.
Der kritische Exponent von elementaren Gruppen ist höchstens 1/2, Translationsflächen mit elementaren Veech-Gruppen sind also als Kandidaten für das Theorem ausgeschlossen. Der kritische Exponent von Gittern ist 1. Also scheiden auch Veech-Flächen für das Theorem aus.
Bis zum Jahr 2003 waren Gitter die einzigen bekannten nicht-elementaren Veech-Gruppen. McMullen klassifizierte die Veech-Flächen vom Geschlecht 2 und zeigte, dass jede solche Fläche, die nur eine Singularität besitzt, in der GL_2(R)-Bahn der Fläche L_D liegt, die aus einem L-förmigen Polygon mit geeigneten von D abhängigen Seitenlängen entsteht.
Während auch heute noch keine Translationsfläche mit Veech-Gruppe zweiter Art bekannt ist, fanden McMullen und unabhängig davon Hubert und Schmidt Konstruktionen unendlich erzeugter Veech-Gruppen erster Art. Eine Abschätzung des kritischen Exponenten dieser Gruppen war 10 Jahre lang eine wichtige offene Frage, die nun durch Theorem 1 beantwortet wird.
Zentral in der Konstruktion von Hubert und Schmidt sind spezielle Punkte, nämlich Verbindungspunkte. Hubert und Schmidt konstruieren Translationsflächen, deren Veech-Gruppen kommensurabel zum Stabilisator SL(X;P) von P sind und damit den gleichen kritischen Exponenten haben. Für Verbindungspunkte mit unendlicher SL(X)- Bahn (diese Punkte heißen nicht-periodisch) ist SL(X;P) unendlich erzeugt und von erster Art.
Wir zeigen Theorem 1, indem wir zeigen, dass für jedes D kongruent 0 mod 4, (kein Quadrat), und jeden nicht-periodischen Verbindungspunkt P in L_D der kritische Exponent der Gruppe SL(L_D;P) echt zwischen 1/2 und 1 liegt.
Eine natürliche Frage in diesem Zusammenhang ist die Abhängigkeit von P: Punkte Q in der SL(L_D)-Bahn von P sind auch er nicht-periodische Verbindungspunkte und die zugehö̈rigen Gruppen SL(L_D;P) und SL(L_D;Q) sind konjugiert zueinander. Daher widmen wir uns in Kapitel 4 der Bestimmung der Bahnen nicht-periodischer Verbindungspunkte.
Die Verbindungspunkte haben die Form P=(x_r+x_iw;y_r+y_iw) mit x_r,x_i,y_r,y_i aus Q. Wir zeigen, dass der Hauptnenner N(P) dieser (gekürzten) Brüche eine Invariante der Bahn ist. Daraus folgt:
Theorem 2. Es gibt unendlich viele verschiedene Bahnen von Verbindungspunkten von L_D.
Wir kennen die Operation der horizontalen und der vertikalen Scherungen A und B aus SL(L_D). Im Spezialfall D=8 erzeugen diese beiden Elemente die ganze Gruppe und wir geben je ein Verfahren an, um eine untere und eine obere Schranke an die Anzahl der Bahnen von nicht-periodischen Verbindungspunkten P mit fixiertem Hauptnenner N(P) zu finden. Damit zeigen wir:
Theorem 3. Die Menge der Verbindungspunkte P mit festem Wert N(P) zerfällt in eine endliche Anzahl von SL(L_8)-Bahnen.
Im Beweis von Theorem 1 ist es nötig, die Nicht-Mittelbarkeit eines Graphen zu zeigen. Da wir nur sehr wenige Informationen über dessen Struktur in unserer konkreten Situation haben, entwickeln wir in Kapitel 1 die folgende Methode:
Theorem 4. Sei G ein Graph, den man durch Weglassen von Kanten in einen Wald G′ ohne Blätter überführen kann, bei dem das Supremum der Längen von zusammenhängenden Valenz-2-Teilgraphen von G′ beschränkt ist. Dann ist G nicht mittelbar.
Um diese Methode anzuwenden, ordnen wir jeder Ecke P von G ein Komplexitätsmaß s(P) zu und weisen nach, dass dieser Wert für die Operation von Worten in A- und B-Potenzen mit wachsender Wortlänge ”tendenziell wächst“.
Lichens are present in most land ecosystems, frequently occupying habitats where few other organisms are able to survive. Their contribution to the ecosystems in terms of biomass and ground cover increases with latitude and altitude, being, together with bryophytes, the most conspicuous component of alpine and polar landscapes. Whereas some polar lichens have reduced distributions and are restricted to high latitudes, most of them have very wide distributional ranges, which oven extend over several climatic regions. Many of them are common to Polar Regions of both hemispheres, a distributional pattern that has been denominated as bipolar, antitropical or amphitropical. Bipolar distributions are not exclusive to lichens, but common to many groups of organisms. The bipolar element in lichens is exceptional as it includes a large number of species, while in most other land organisms it includes genera or families but very seldom species.
In this dissertation I use the bipolar lichen Cetraria aculeata to give a first insight into the phylogeography of this biogeographic element in lichens. I discuss how and when the disjunct distribution of C. aculeata came to be, and try to partial out the roles that historical and ecological processes played in shaping its distribution.
Sampling was designed to cover a wide geographic extension. The main e"ort was made to collect in boreal, temperate and tropical mountain ranges in North and South America, as well to include Mediterranean populations in which specimens with deviant morphologies are observed.
I found that Cetraria aculeata forms a genetically congruent taxon. Although whether it should include C. muricata remains unsolved, I excluded all specimens identified as the latter from our analyses. Thee populations of both algal and fungal symbionts have a strong geographic structure. The study of the lichen fungus suggested that the species originated in the Eurasian continent and later expanded to acquire its current distribution during the Pleistocene. The results showed that all American populations originated from an ancestral population, more similar to the extant Arctic populations than to the Mediterranean ones.
The comparison between the structure of fungal and algal populations showed a high degree of coherence between them. However, the similarity in photobiont use between Arctic and Antarctic populations suggests that photobiont use responds not only to a history of codispersal in vegetative propagula, but it is also a result of a selective process related to climate. Since this climatic pattern of similarity is also found in the community of Alphaproteobacteria associated with C. aculeata, we concluded that lichens might be able to accommodate or to respond to different environmental conditions by selectively associating with different symbiotic partners.
Lastly, we found the Mediterranean populations of C. aculeata to be genetically differentiated in algal and fungal symbionts from the rest of the populations. While we found no grounds to believe that the overgrown morphs encountered in the region are due to the association with different algal lineages, I believe that a switch in photobiont use might be responsible for the pattern of genetic isolation encountered. Furthermore, I suggest that the Mediterranean and bipolar C. aculeata could be two different species, since both are ecologically, genetically and at least in part morphologically divergent.
During this study clumped isotope analysis of carbonates was established at the Goethe University of Frankfurt, Germany. Therefore, preparation protocols and analytical parameters were elaborated to obtain precise and accurate Δ47 data. Briefly, analyte CO2 was cleaned cryogenically using glass extraction lines to remove traces of water that enable re-equilibration of C–O bonds in the gases. Furthermore, analyte CO2 was passed through a gas chromatograph (GC) to clean it from contaminants that produce isobaric interferences with m/z 47. Initially, phosphoric acid digestions of carbonates was conducted at 25 °C in McCrea-type reaction vessels. Afterwards samples were reacted at 90 °C using a common acid bath. Mass spectrometric analyses were performed using a MAT 253 equipped with a dual inlet system. Δ47 values were directly projected to the absolute scale using CO2 gases equilibrated at distinct temperatures.
In cooperation with Stefano Bernasconi and his research group at ETH Zurich we studied the non-linearity that occurs for the measurement of m/z 47. This effect results from secondary electrons created by the m/z 44 beam. These electrons cause a negative background on the m/z 47 collector. A correction procedure was proposed that relies on the determination of the negative background on the m/z 47 Faraday cup. This approach might reduce time-consuming analyses of heated gases which were used so far to account for the observed non-linearity. However, the suggested correction of the negative background on the m/z 47 cup is only applicable if the slit width of the m/z 44 beam is significantly wider than that of the m/z 47 beam.
This thesis, furthermore, presents a comparison of the different phosphoric acid digestion techniques which are commonly used for carbonate clumped isotope analysis. For calcitic and aragonitic material digested at 25 °C in McCrea-type vessels we observed that the sample size has an effect on Δ47 data: higher mean Δ47 values and a larger scatter of data were received for samples <7 mg than for larger aliquots. For carbonate samples digested at 90 °C in a common acid bath no sample size effect was determined. We assume that secondary re-equilibration of CO2 with water preferentially occurs at 25 °C producing the observed differences. However, a sample size effect can be avoided if reaction temperature is increased to 90 °C.
In order to make carbonate Δ47 data obtained from acid digestions at 90 °C comparable to Δ47 data received from reactions at 25 °C the difference of the acid fractionation factores (Δ47*25-90) between both temperatures has to be known. For the determination of the Δ47*25-90 value we have considered Δ47 data made at 25 °C from samples >7 mg only. For calicte and aragonite we obtained differences in fractionation factores of 0.075‰ and 0.066‰, respectively. These Δ47*25-90 values are coincident with the theoretical prediction of 0.069‰ proposed for calcite (Guo et al., 2009).
Moreover, this dissertation comprises a calibration study of the clumped isotope thermometer based on various natural calcites that grew between 9 and 38 °C. The samples include a brachiopod shell, a bivalve shell, an eggshell of an ostrich and foraminifera tests which formed from distinct biomineralizing processes. Furthermore we included an authigenic carbonate crystallized from biological-induced precipitation. The following linear relationship between 1/T2 and Δ47 was determined (with Δ47 in ‰ and T in K):
Δ47 = 0.0327 (± 0.0026) x 106 / T2 + 0.3030 (± 0.0308) (R2 = 0.9915)
This equation differs from the pioneering Ghosh et al. (2006a) calibration. However, our regression line is statistically indistinguishable from that of Henkes et al. (2013) which is based on aragonitic mollusks and calcitic brachiopod shells. Both studies have in common that calibration data were, at first, directly referenced to the absolute scale. In addition, both datasets rely on similar digestion techniques. Furthermore, the two calibrations are conform with the theoretical prediction of Guo et al. (2009).
The calcite calibration of the clumped isotope paleothermometer received in this study was applied to Δ47 data measured for Silurian brachiopods shells from Gotland/Sweden. Prior to isotopic analysis the fossils were intensively investigated for their preservation state (CL, SEM, trace elements). The lowest T(Δ47) values of ca. 28 to 33 °C were estimated from ultrastructurally well-preserved regions of some shells. For these samples also the lowest δ18Ow values of Silurian seawater were determined. These estimates of ca. −1‰ confirm the assumption that the δ18O value of the Silurian ocean was buffered to (0 ± 1)‰.
Nevertheless, most studied shells were characterized by a patchwork of pristine and altered shell portions resulting in elevated T(Δ47) values which plot mostly between 40 and 60 °C. Our results indicate that the clumped isotopic composition of the shells were altered at low water-rock ratios, not affecting the δ18O values. Δ47 and δ18O data of associated diagenetic phases (sparitic and micritic phases of the inner fillings of the fossils) provide evidence that the sparitic cements grew during several diagenetic events which occurred at different temperatures in fluid-buffered systems. We, furthermore, conclude that the micritic phases lithified at a very early diagenetic stage with the δ18O values being most probably close to a Silurian seawater composition
The Chikungunya virus (CHIKV) is a mosquito-transmitted alphavirus that causes high fever, rash, and recurrent arthritis in humans. The majority of symptoms disappear after about one week. However, arthritis can last for months or even years (in about 30% of cases), which makes people unable to work during this period. The virus is endemic in Sub-Saharan Africa, the Indian Ocean islands, India, and Southeast Asia. It has additionally caused several large outbreaks in the last few years, affecting millions of people. The mortality rate is very low (0.1%), but the infection rates are high (sometimes 30%) and the number of asymptomatic cases is rare (about 15%). The first CHIKV outbreak in a country with a moderate climate was detected in Italy in 2007. Furthermore, the virus has spread to the Caribbean in late 2013. Due to climate change, globalization, and vector switching, the virus will most likely continue to cause new worldwide outbreaks. Additionally, more temperate regions of the world like Europe or the USA, which have recently reported their first cases, will likely become targets. Alarmingly, there is no specific treatment or vaccination against CHIKV available so far.
The cell entry process of CHIKV is also not understood in detail, and was thusly the focus of study for this project. The E2 envelope protein is responsible for cell attachment and entry. It consists of the domain C, located close to the viral membrane, domain A, in the center of the protein, and domain B, at the distal end, prominently exposed on the viral surface.
In this work, the important role of cell surface glycosaminoglycans (GAGs) for CHIKV cell attachment was uncovered. GAGs consist of long linear chains of heavily sulfated disaccharide units and can be covalently linked to membrane associated proteins. They play an important role in different cell signaling pathways. So far, solely cell culture passage has revealed an increased GAG-dependency of CHIKV due to mutations in E2 domain A, which was associated with virus attenuation in vivo. However, in this work it could be shown that cell surface GAGs promote CHIKV entry using non-cell culture adapted CHIKV envelope (Env) proteins. Transduction and infection of cell surface GAG-deficient pgsA-745 cells with CHIKV Env pseudotyped vector particles (VPs) and with wild-type CHIKV revealed decreased transduction and replication rates. Furthermore, cell entry and transduction rates of GAG-containing cells were also dose-dependently decreased in the presence of soluble GAGs. In contrast, transduction of pgsA-745 cells with CHIKV Env pseudotyped VPs was enhanced by the addition of soluble GAGs. This data suggests a mechanism by which GAGs activate CHIKV particles for subsequent binding to a cellular receptor. However, at least one GAG-independent entry pathway might exist, as CHIKV entry could not be totally inhibited by soluble GAGs and entry into pgsA-745 was, albeit at a lower rate, still possible. Further binding experiments using recombinant CHIKV E2 domains A, B, and C suggest that domain B is responsible for the GAG binding, domain A possibly for receptor binding, and domain C is not involved in cell binding. These results are in line with the geometry of CHIKV Env on the viral surface. They altogether reveal that GAG binding promotes viral cell entry and that the E2 domain B plays a central role for this mechanism.
As no vaccine against CHIKV has been approved so far, another goal of this project was to test new vaccination approaches. It has been published that a single linear epitope of E2 is the target of the majority of early neutralizing antibodies against CHIKV in patients. Artificial E2-derived proteins were created, expressed in E.coli, and successfully purified. They consisted of 5 repeats of the mentioned linear epitope (L), the surface exposed regions of domain A linked by glycine-serine linkers (sA), the whole domain B plus a part of the β-ribbon connector (B+), or a combination of these 3 modules. Vaccination experiments revealed that B+ was necessary and sufficient to induce a neutralizing immune response in mice, with the protein sAB+ yielding the best results. sAB+, as a protein vaccine, efficiently and significantly reduced viral titers in mice upon CHIKV challenge, which was not the case for recombinant Modified Vaccinia virus Ankara (MVA; MVA-CHIKV-sAB+), as a vaccine platform expressing the same protein. These experiments show that a small rationally designed CHIKV Env derived protein might, after optimization of some vaccination parameters, be sufficient as a safe, easy-to-produce, and cheap CHIKV vaccine.
Epigallocatechin-3-gallate (EGCG) is a catechin found in green tea and was, in this work, found to inhibit the CHIKV life cycle at the entry state in in vitro experiments using CHIKV Env VPs and wild-type virus. EGCG was recently published to inhibit attachment of several viruses to cell surface GAGs, which is in line with the role for GAGs in CHIKV entry revealed in this work. EGCG might serve as a lead compound for the development of a small molecule treatment against CHIKV.
RNA modifications are present in all three kingdoms of life and detected in all classes of cellular RNAs. RNA modifications are diverse, with more than 100 types of chemical modifications identified to date. These chemical modifications expand the topological repertoire of RNAs and are expected to fine-tune their functions. Ribosomal RNA (rRNA) contains two types of covalent modifications, either methylation on the sugar (Nm) or bases (mN), or base isomerization (conversion of uridine into pseudouridines, "). Pseudouridylations and ribose methylations are catalyzed by site-specific H/ACA and C/D box snoRNPs, respectively. The RNA component (snoRNA) of both types of snoRNPs is responsible for the site selection by base pairing with the rRNA substrate, whereas the protein component catalyzes the modification reaction: Nop1 in C/D box and Cbf5 in H/ACA box snoRNPs. Contrastingly, base methylations are performed by snoRNA independent, ‘protein-only’, methyltransferases (MTases). rRNA modifications occur at highly conserved positions, all clustering around functional ribosomal sites. Mutations in factors involved in rRNA modification have been linked to severe human diseases (e.g. X-linked Dyskeratosis congenita). Emerging evidences indicate that heterogeneity in RNA modification prevails, i.e. not all positions are modified at all time, and the concept of ‘specialized ribosomes’ has been coined. rRNA modification heterogeneity has been correlated with disease etiology (cancer), and shown to play a role in cell differentiation(hematopoiesis). Remarkably, alteration in rRNA modification patterns profoundly affects the preference of ribosomes for cap- versus IRESdependent translation initiation, with major consequences on cell physiology.
Alzheimer’s disease (AD) is a common, age associated neurodegenerative disease that manifests as progressive dementia and is characterized by accumulation of the amyloid beta (Aβ) peptide which is a processing product of a transmembrane protein termed Alzheimer Amyloid Precursor Protein (APP). The Aβ peptide is generated by a sequential proteolytic processing of APP by two distinct proteases that are termed β- and γ-secretase. The β-secretase, also called BACE-1 or memapsin 2, belongs to the family of aspartyl proteases. BACE-1 evidently cleaves APP in an acidic endosomal compartment after endocytosis of APP, thereby facilitating Aβ peptide generation.
Sorting of transmembrane proteins is generally controlled by sorting signals in the cytoplasmic domains of the cargo proteins. The short cytoplasmic tail of BACE-1 with 23 amino acids contains a sorting signal of the acidic cluster, di-leucine (ACDL) type. The two Leu residues in this determinant are important for the clathrin mediated endocytosis of BACE-1, whereas the acidic residues together with the Leu are required for the endosomal sorting and recycling of BACE-1 back to the plasma membrane. The ACDL motif binds to the members of the GGA (Golgi-localized γ ear-containg ARF- binding proteins) family (GGA1-GGA3) that are involved in the sorting of BACE-1.
One of the major aims of this study was to address the role of flotillins in the intracellular sorting of BACE-1. This study shows that flotillin-1 directly binds to the di-leucine motif in the cytoplasmic tail of BACE-1, whereas flotillin-2 only shows an association mediated by flotillin-1. Flotillin-1 competes with GGA2 for the binding to BACE-1 tail, and thus influences the endosomal sorting of BACE-1. Importantly, depletion of flotillins results in an altered localization of the wildtype BACE-1, whereas the plasma membrane resident Leu to Ala (LLAA) mutant is not affected. Flotillin knockdown results in an accumulation of BACE-1, implicating reduced degradation and enhanced stability of this protease. Thus, flotillins appear to be important for the cellular targeting of BACE-1 and also influence the amyloidogenic processing of APP, as demonstrated by an increase in the amyloidogenic C-99 processing fragments.
When flotillin depleted cells were subjected to apoptotic stresses including Aβ25-35 synthetic peptide (inducer of the extrinsic apoptosis pathway) or several chemotherapeutic agents (staurosporine, brefeldin A, doxorubicin, carboplatin and paclitaxel: intrinsic apoptosis pathway) and cytotoxicity was determined, various apoptotic markers were activated in flotillin depleted cells. Caspase-3 and GGA3 are well accepted apoptosis markers and an enhanced caspase-3 cleavage was detected upon STS induced apoptosis in SH-SY5Y, HeLa, and HaCaT cell lines and increased GGA3 cleavage was observed in MCF7 cell line.
One of the major reasons for the apoptotic sensitivity in the absence of flotillins was a PI3K/Akt signaling defect. Neuroblastoma cells depleted of flotillins showed diminished levels of total Akt, phospho-Akt and phospho-ERK upon STS induced apoptosis. Since PI3K/Akt was the primary survival pathway affected upon STS induced apoptosis, ectopic expression of Akt in neuroblastoma cell line reduced caspase-3 cleavage and retarded apoptosis.
The direct downstream target of Akt is FOXO3a, whose localization was investigated in flotillin depleted cells. A major proportion of FOXO3a was localized in the nucleus of flotillin knockdown cells, implicating that FOXOs are active in these cells and subsequently trigger the transcription of death genes. Strikingly, an essential anti-apoptotic molecule and a major cancer target, Mcl-1, was inherently downregulated in flotillin knockdown cells. Mcl-1 is a chief member of the Bcl-2 family as it plays a pivotal role in cell survival and it is a critical protein in cancer therapeutics as suppression of Mcl-1 protein can curtail the survival and growth of tumorous cells.
Neuroblastoma cells were rescued from undergoing permanent damage due to STS induced apoptosis by overexpression of anti-apoptotic Bcl-2. Phorbol esters are well known PKC activators, and pre-treatment of neuroblastoma cells with phorbol esters along with staurosporine reduced caspase-3 cleavage.
These results demonstrate that absence of flotillins can sensitize cellular systems to apoptosis induction. The two main characteristics of cancer cells include resistance to apoptosis and unresponsiveness to chemotherapeutic agents. It is a well established fact that impaired apoptosis is central to tumour development. This study implicates that the downregulation of flotillin function can trigger cellular susceptibility and enhances apoptosis in response to conventional chemotherapeutic agents. Therefore, flotillins can serve as vital regulators in providing a more rational approach in molecular-targeted therapies for receding cancer growth and survival.