Tropical mirror symmetry for elliptic curves

Mirror symmetry relates Gromov-Witten invariants of an elliptic curve with certain integrals over Feynman graphs. We prove a tropical generalization of mirror symmetry for elliptic curves, i.e., a statement relating certain labeled Gromov-Witten invariants of a tropical elliptic curve to more refined Feynman integrals. This result easily implies the tropical analogue of the mirror symmetry statement mentioned above and, using the necessary Correspondence Theorem, also the mirror symmetry statement itself. In this way, our tropical generalization leads to an alternative proof of mirror symmetry for elliptic curves. We believe that our approach via tropical mirror symmetry naturally carries the potential of being generalized to more adventurous situations of mirror symmetry. Moreover, our tropical approach has the advantage that all involved invariants are easy to compute. Furthermore, we can use the techniques for computing Feynman integrals to prove that they are quasimodular forms. Also, as a side product, we can give a combinatorial characterization of Feynman graphs for which the corresponding integrals are zero. More generally, the tropical mirror symmetry theorem gives a natural interpretation of the A-model side (i.e., the generating function of Gromov-Witten invariants) in terms of a sum over Feynman graphs. Hence our quasimodularity result becomes meaningful on the A-model side as well. Our theoretical results are complemented by a Singular package including several procedures that can be used to compute Hurwitz numbers of the elliptic curve as integrals over Feynman graphs.Comment: comment on historical development adde

Redoxnetzwerke des Malariaerregers Plasmodium : Validierung von Schlüsselenzymen für neue chemotherapeutische Ansätze

Die Malaria-assozierte Pathologie wird durch die Entwicklung von Plasmodien in den Erythrozyten ihres Wirtes verursacht. Um ein reduzierendes intrazelluläres Milieu in diesem Sauerstoff-reichen Umfeld zu erhalten, haben Malaria-Parasiten ein komplexes antioxidatives Netzwerk entwickelt, welches auf zwei zentralen Elektronen-Donatoren beruht, dem Glutathion und dem Thioredoxin. Die intrazellulären Spiegel dieser beiden redox-aktiven Peptide in reduzierter – und damit reduzierender Form – werden durch die entsprechenden NADPH-abhängigen Flavoenzyme Thioredoxinreduktase (TrxR) und Glutathionreduktase (GR) aufrechterhalten. Da Katalase und eine klassische Selen-abhängige Glutathionperoxidase in Plasmodium fehlen, spielen die auf den Enzymen Thioredoxin- und Glutathionreduktase basierenden Systeme eine besondere Rolle. Weitere Bestandteile der antioxidativen Abwehr sind verschiedene Mitglieder der Thioredoxin-Familie, vor allem das Plasmodien-spezifische Plasmoredoxin (Plrx), welches als zusätzliche Verteidigungslinie der Parasiten gegen oxidativen Stress diskutiert wird. Im Rahmen der vorliegenden Arbeit wurden antioxidative Proteine der Parasiten untersucht, die als Zielmoleküle für die rationale Medikamentenentwicklung von Bedeutung sind. Um zu klären, welche der beteiligten Proteine sich aufgrund einer essentiellen Funktion in den Blutstadien-Parasiten insbesondere dafür eignen, wurden die zugrunde liegenden Gene dreier Redox-Proteine mit Methoden der reversen Genetik untersucht. Dies geschah durch stabile Gen-Inaktivierung unter Nutzung von Integrations- und replacement-Strategien, im Falle der Glutathionreduktase ergänzt durch Gen-Komplementation mit dem entsprechenden Ortholog. Die Targetvalidierung individueller redox-aktiver Proteine ist eine unerlässliche Voraussetzung für die rationale Entwicklung neuer effektiver Antimalaria-Medikamente. Die erfolgreiche Herstellung von Plasmoredoxin knock out-Mutanten in Nagetiermalaria-Modellparasiten und die phänotypischen Analysen im Verlauf des Lebenszyklus offenbarten in vitro und in vivo keine essentiellen Funktionen dieses Proteins. Dieses Ergebnis kann mit funktioneller Redundanz innerhalb der Mitglieder der Thioredoxin-Familie erklärt werden, somit bietet sich eine weitere Arzneimittelentwicklung allein auf der Basis Plasmoredoxin-spezifischer Inhibitoren nicht an. Weiterhin konnten Thioredoxinreduktase-defiziente P. berghei-Mutanten erzeugt werden. Eine systematische Analyse dieser Parasiten im Verlauf des Plasmodium-Lebenszyklus zeigte an keiner Stelle eine lebensnotwendige Funktion der Thioredoxinreduktase. Dies steht im Gegensatz zu früheren in vitro-Studien bei P. falciparum, welche diesem Enzym eine essentielle Funktion zuschrieben. Da ein praktikables in vivo-Modell für humanpathogene Malaria-Parasiten nicht verfügbar ist, verdeutlicht das hier vorgestellte Ergebnis der Targetvalidierung für Thioredoxinreduktase die Bedeutung funktioneller Studien in Nagetiermalaria-Modellen für die präklinische Entwicklung neuer Medikamente gegen Malaria. Für eines der viel versprechendsten drug targets von Malaria-Parasiten, der Glutathionreduktase, konnte auf genetischer Ebene der Beweis erbracht werden, dass durch den Verlust der Funktion dieses Enzyms die Parasiten nicht lebensfähig sind. Somit nimmt die Glutathionreduktase in dem komplexen antioxidativen Netzwerk von Plasmodium eine zentrale und essentielle Rolle ein. Zusätzlich wurde in dieser Arbeit die molekulare Wirkungsweise des seit mehr als 100 Jahren klinisch genutzten Medikaments Methylenblau auf Malaria-Parasiten untersucht. Hierbei zeigte sich, dass diese Verbindung neben ihren inhibierenden Eigenschaften interessante Charakteristika als subversives Substrat verschiedener Disulfidreduktasen besitzt. Bei Anwesenheit von Methylenblau werden diese Enzyme zu pro-oxidativen, H2O2-produzierenden Verbindungen, welche die reduzierenden zellulären Bedingungen herausfordern, statt sie zu bewahren.Malaria-associated pathology is caused by the continuous expansion of Plasmodium parasites inside host erythrocytes. To maintain a reducing intracellular milieu in this oxygen-rich environment, malaria parasites have evolved a complex antioxidative network based on two central electron donors, glutathione and thioredoxin. The intracellular levels of these redox-active peptides in reduced and thus reducing forms are maintained by the respective NADPH-dependent flavoenzymes thioredoxin reductase (TrxR) and glutathione reductase (GR). As catalase and classical selenium-dependant glutathione peroxidase are absent in Plasmodium, the systems based on thioredoxin reductase and glutathione reductase play a prominent role. Further components of the antioxidative defense comprise different members of the thioredoxin family, especially Plasmodium-specific plasmoredoxin which has been discussed as an additional defense line against oxidative stress. In the framework of this thesis, antioxidative parasite proteins that are of interest as targets for rational drug development were investigated. To clarify which proteins are particularly suitable as drug target due to an essential function for blood stage parasites, the respective genes of three redox proteins were studied employing reverse genetics. This was achieved by stable gene inactivation with integration and replacement strategies, in the case of glutathione reductase supplemented by gene complementation of the respective ortholog. Target validation of individual redox-active proteins is an indispensable prerequisite for the rational development of new and effective antimalarial drugs. The successful generation of plasmoredoxin knockout mutants in the rodent model malaria parasite and phenotypic analysis during life cycle progression revealed both in vitro and in vivo a non-vital function of this protein. This finding can be explained by functional redundancy among the members of the thioredoxin family and discourages future drug discovery efforts that aim at specifically targeting plasmoredoxin. Furthermore P. berghei thioredoxin reductase-deficient parasites could be generated in this thesis. A systematic phenotypic analysis of this mutant throughout the Plasmodium life cycle demonstrated no essential function for thioredoxin reductase at any phase of the parasite life cycle. This is in contrast to previous in vitro studies which attributed an essential role to thioredoxin reductase in P. falciparum. As a feasible in vivo model for human pathogen malaria parasites is not available, the presented target validation result of thioredoxin reductase highlights the importance of functional studies in rodent malaria models to guide preclinical development of novel antimalaria intervention strategies. For one of the most promising drug targets of malaria parasites, glutathione reductase, this work provides the genetic proof that in the case of this enzyme loss of function results in non-viable malaria parasites in vivo. Hence, glutathione reductase occupies an essential position in the complex antioxidant network of Plasmodium parasites. Furthermore, the molecular mode of action of methylene blue, which has been clinically used as an antimalarial drug for over 100 years, against malaria parasites has been investigated. It could be shown that this compound – besides its inhibitory potential – has interesting characteristics as a subversive substrate of different disulfide reductases. In the presence of methylene blue, they turn into pro-oxidant, H2O2-producing enzymes which challenge the reducing cellular milieu that they are meant to protect in the absence of this perturbing drug

CLIL in Mathematics Education: Student Motivation for Subject Matter and Language Learning

Vor dem Hintergrund der Beobachtung, dass Schülerinnen und Schüler häufig eine Präferenz entweder für das (fremd-)sprachliche oder das mathematische Lernen besitzen, ist bilingualer Mathematikunterricht als Kombination dieser beiden unterschiedlichen Lernbereiche insbesondere aus motivationaler Perspektive interessant. Das übergeordnete Anliegen der Dissertation ist es daher, das motivationsförderliche Potenzial des bilingualen Mathematikunterrichts zu untersuchen. Die Forschungsfrage lautet: Welche Auswirkungen hat bilingualer Mathematikunterricht auf die Motivation der Schülerinnen und Schüler für das fremdsprachliche und das mathematische Lernen? Zur Beantwortung dieser Frage wurde im Schuljahr 2011/12 in vier verschiedenen Schulklassen an niedersächsischen Gymnasien jeweils eine Themeneinheit im Fach Mathematik bilingual unterrichtet und wissenschaftlich mit Fragebogenerhebung und Lehrerinterviews begleitet. Die gewonnenen Daten ermöglichen einen Vergleich der Schülermotivation in den regulären Unterrichtskontexten (Englischunterricht und deutschsprachiger Mathematikunterricht) mit der Motivation im bilingualen Mathematikunterricht. Untersuchte Teilaspekte von Motivation sind hierbei u.a. Einstellungen zum Englisch-/Mathematikunterricht, das fachliche Selbstkonzept, Selbstwirksamkeitserwartungen, die Zufriedenheit mit der eigenen Leistung, die Angst im Unterricht, das Kompetenzerleben sowie die aktive Unterrichtsbeteiligung. Für fremdsprachlich interessierte Lerner zeigt sich im bilingualen Modul eine positivere motivationale Ausgangslage als im regulären Mathematikunterricht, wodurch mathematisches Lernen gefördert werden kann. Bei Schülerinnen und Schülern mit einem mathematisch-naturwissenschaftlich Interessenschwerpunkt ist im bilingualen Modul eine günstigere motivationale Disposition als im regulären Fremdsprachenunterricht zu erkennen, die sich positiv auf das Fremdsprachenlernen auswirken kann. Jedoch wird gegenüber dem deutschsprachigen Mathematikunterricht ein Motivationsverlust deutlich, der sich als nachteilig für das fachliche Lernen erweisen kann. Die beobachteten Unterschiede im emotionalen Erleben des bilingualen Mathematikunterrichts in Abhängigkeit vom Interessenschwerpunkt der Schülerinnen und Schüler bieten Lehrern Anhaltspunkte dafür, wo motivationsfördernde Maßnahmen ansetzen können.Students often have a preference either for (foreign) languages or for mathematics. Teaching mathematics in a foreign language as a combination of these two learning areas is therefore particularly interesting from a motivational perspective. The aim of this thesis is to analyze mathematics and language integrated learning and its potential for increasing learner motivation. The research question is as follows: How does CLIL in mathematics education influence students in their motivation for learning foreign languages and mathematics? To answer this question empirically, four classes at different high schools in Lower Saxony received mathematics instruction in English for the duration of a short teaching unit in the 2011-2012 school year. Student questionnaires and teacher interviews were used as research methods for assessing learner motivation in different teaching contexts (English as a foreign language classes, regular mathematics classes, mathematics unit taught in English). The collected data provide the basis for analyzing motivational differences between these three contexts with regard to, inter alia, the following aspects: attitudes towards English and mathematics, subject-related self-concept, self-efficacy, satisfaction with one’s academic performance, anxiety, feelings of competence as well as active participation in class. The data analysis shows that students with a preference for language classes find learning mathematics through a foreign language more interesting than learning it in the regular class setting. For this group of students, CLIL can help create a positive motivational basis for learning mathematics. For students interested in mathematics and the natural sciences, CLIL mathematics lessons are more motivating than regular foreign language classes, however less motivating than mathematics lessons in German (mother tongue for most of the students and regular language of instruction). Thus, teaching mathematics in English can on the one hand be beneficial for this learner group regarding their motivation for foreign language learning. This comes, on the other hand, at the cost of decreasing motivation for subject matter learning. Knowing about the impact of CLIL in mathematics on different groups of students helps teachers find measures to address motivational problems

Nachhaltiges Konsumverhalten durch ökologische Dienstleistungen und organisierte Gemeinschaftsnutzungen im großstädtischen Wohnumfeld: Abschlussbericht

"Ziel des Forschungsvorhabens „Nachhaltiges Konsumverhalten durch ökologische Dienstleistungen und organisierte Gemeinschaftsnutzungen im großstädtischen Wohnumfeld“ war, neue Nutzungsstrategien in einem spezifischen Kontext umzusetzen, praktisch zu erproben und zu untersuchen. Dabei wurden sowohl die Möglichkeiten und Hemmnisse der Umsetzung von neuen Nutzungsstrategien im Wohnumfeld als auch ihr Beitrag zu nachhaltigerem Konsum bzw. einer nachhaltigen Entwicklung erkundet. Der Ansatz des Projektes greift Ergebnisse der Debatte zu den Genderaspekten von nachhaltigem Konsum auf, die auf den fehlenden Bezug auf die Handlungskontexte der privaten Haushalte als ein Defizit von Strategien zur Verbreitung von nachhaltigen Konsummustern verweisen. Vor diesem Hintergrund ist ein wesentliches konzeptionelles Element des Vorhabens, der Berücksichtigung von Alltagsanforderungen und den Bedingungen der Umsetzung von nachhaltigen Konsummustern im Alltag einen hohen Stellenwert beizumessen und zwar sowohl in seinen anwendungsorientierten als auch in seinen wissenschaftlichen Teilen: Über die Beteiligung der BewohnerInnen an der Gestaltung von neuen Nutzungsstrategien im Wohnumfeld wurde der Versuch unternommen, Interessen und Anforderungen von (potenziellen) NutzerInnen in die Planung und Umsetzung mit einzubeziehen. Gleichzeitig wurden damit die Möglichkeiten partizipativer Prozesse für die Erfassung von Alltagsanforderungen überprüft. Anhand detaillierter empirischer Untersuchungen der Nutzung von Gemeinschaftsnutzungsangeboten und ökologischen Dienstleistungen wurden Hemmnisse und Potenziale der Integration dieser nachhaltigen Konsumalternativen in den Alltag bestimmt. Die empirisch erhobenen Nutzungsmuster stellen eine wichtige Grundlage für die Abschätzung der Nachhaltigkeitseffekte der untersuchten Maßnahmen dar, da die Art und Weise der Umsetzung im Alltag erheblichen Einfluss auf die Nachhaltigkeitseffekte einer Nutzungsstrategie hat." (Textauszug

A High-Throughput Screen Targeting Malaria Transmission Stages Opens New Avenues for Drug Development

A major goal of the worldwide malaria eradication program is the reduction and eventual elimination of malaria transmission. All currently available antimalarial compounds were discovered on the basis of their activity against the asexually reproducing red blood cell stages of the parasite, which are responsible for the morbidity and mortality of human malaria. Resistance against these compounds is widespread, and there is an urgent need for novel approaches to reduce the emergence of resistance to new antimalarials as they are introduced. We have established and validated the first high-throughput assay targeting the red blood cell parasite stage required for transmission, the sexually reproducing gametocyte. This assay will permit identification of compounds specifically targeting the transmission stages in addition to the asexual stage parasites. Such stage-specific compounds may be used in a combination therapy, reducing the emergence of resistance by blocking transmission of resistant parasites that may be selected in a patient

Optimization of flow cytometric detection and cell sorting of transgenic Plasmodium parasites using interchangeable optical filters

Background: Malaria remains a major cause of morbidity and mortality worldwide. Flow cytometry-based assays that take advantage of fluorescent protein (FP)-expressing malaria parasites have proven to be valuable tools for quantification and sorting of specific subpopulations of parasite-infected red blood cells. However, identification of rare subpopulations of parasites using green fluorescent protein (GFP) labelling is complicated by autofluorescence (AF) of red blood cells and low signal from transgenic parasites. It has been suggested that cell sorting yield could be improved by using filters that precisely match the emission spectrum of GFP. Methods: Detection of transgenic Plasmodium falciparum parasites expressing either tdTomato or GFP was performed using a flow cytometer with interchangeable optical filters. Parasitaemia was evaluated using different optical filters and, after optimization of optics, the GFP-expressing parasites were sorted and analysed by microscopy after cytospin preparation and by imaging cytometry. Results: A new approach to evaluate filter performance in flow cytometry using two-dimensional dot blot was developed. By selecting optical filters with narrow bandpass (BP) and maximum position of filter emission close to GFP maximum emission in the FL1 channel (510/20, 512/20 and 517/20; dichroics 502LP and 466LP), AF was markedly decreased and signal-background improve dramatically. Sorting of GFP-expressing parasite populations in infected red blood cells at 90 or 95% purity with these filters resulted in 50-150% increased yield when compared to the standard filter set-up. The purity of the sorted population was confirmed using imaging cytometry and microscopy of cytospin preparations of sorted red blood cells infected with transgenic malaria parasites. Discussion Filter optimization is particularly important for applications where the FP signal and percentage of positive events are relatively low, such as analysis of parasite-infected samples with in the intention of gene-expression profiling and analysis. The approach outlined here results in substantially improved yield of GFP-expressing parasites, and requires decreased sorting time in comparison to standard methods. It is anticipated that this protocol will be useful for a wide range of applications involving rare events

Drug Screen Targeted at Plasmodium Liver Stages Identifies a Potent Multistage Antimalarial Drug

Plasmodium parasites undergo a clinically silent and obligatory developmental phase in the host’s liver cells before they are able to infect erythrocytes and cause malaria symptoms. To overcome the scarcity of compounds targeting the liver stage of malaria, we screened a library of 1037 existing drugs for their ability to inhibit Plasmodium hepatic development. Decoquinate emerged as the strongest inhibitor of Plasmodium liver stages, both in vitro and in vivo. Furthermore, decoquinate kills the parasite’s replicative blood stages and is active against developing gametocytes, the forms responsible for transmission. The drug acts by selectively and specifically inhibiting the parasite’s mitochondrial $bc_1$ complex, with little cross-resistance with the antimalarial drug atovaquone. Oral administration of a single dose of decoquinate effectively prevents the appearance of disease, warranting its exploitation as a potent antimalarial compound

Drug Screen Targeted at Plasmodium Liver Stages Identifies a Potent Multistage Antimalarial Drug

Plasmodium parasites undergo a clinically silent and obligatory developmental phase in the host's liver cells before they are able to infect erythrocytes and cause malaria symptoms. To overcome the scarcity of compounds targeting the liver stage of malaria, we screened a library of 1037 existing drugs for their ability to inhibit Plasmodium hepatic development. Decoquinate emerged as the strongest inhibitor of Plasmodium liver stages, both in vitro and in vivo. Furthermore, decoquinate kills the parasite's replicative blood stages and is active against developing gametocytes, the forms responsible for transmission. The drug acts by selectively and specifically inhibiting the parasite's mitochondrial bc1 complex, with little cross-resistance with the antimalarial drug atovaquone. Oral administration of a single dose of decoquinate effectively prevents the appearance of disease, warranting its exploitation as a potent antimalarial compoun

The chloride channel CFTR is not required for cyst growth in an ADPKD mouse model

Autosomal dominant polycystic kidney disease (ADPKD) is characterized by the development of bilateral renal cysts which enlarge continuously, leading to compression of adjacent intact nephrons. The growing cysts lead to a progressive decline in renal function. Cyst growth is driven by enhanced cell proliferation and chloride secretion into the cyst lumen. Chloride secretion is believed to occur mainly by the cAMP-activated cystic fibrosis transmembrane conductance regulator (CFTR), with some contribution by the calcium-activated chloride channel TMEM16A. However, our previous work suggested TMEM16A as a major factor for renal cyst formation. The contribution of CFTR to cyst formation has never been demonstrated in an adult ADPKD mouse model. We used mice with an inducible tubule-specific Pkd1 knockout, which consistently develop polycystic kidneys upon deletion of Pkd1. Cellular properties, ion currents, and cyst development in these mice were compared with that of mice carrying a co-deletion of Pkd1 and Cftr. Knockout of Cftr did not reveal any significant impact on cyst formation in the ADPKD mouse model. Furthermore, knockout of Cftr did not attenuate the largely augmented cell proliferation observed in Pkd1 knockout kidneys. Patch clamp analysis on primary renal epithelial cells lacking expression of Pkd1 indicated an only marginal contribution of CFTR to whole cell Cl− currents, which were clearly dominated by calcium-activated TMEM16A currents. In conclusion, CFTR does not essentially contribute to renal cyst formation in mice caused by deletion of Pkd1. Enhanced cell proliferation and chloride secretion is caused primarily by upregulation of the calcium-activated chloride channel TMEM16A

Loss of Polycystin-1 causes cAMP-dependent switch from tubule to cyst formation

Autosomal dominant polycystic kidney disease is the most common monogenic disease that causes end-stage renal failure. It primarily results from mutations in the PKD1 gene that encodes for Polycystin-1. How loss of Polycystin-1 translates into bilateral renal cyst development is mostly unknown. cAMP is significantly involved in cyst enlargement but its role in cyst initiation has remained elusive. Deletion of Polycystin-1 in collecting duct cells resulted in a switch from tubule to cyst formation and was accompanied by an increase in cAMP. Pharmacological elevation of cAMP in Polycystin 1-competent cells caused cyst formation, impaired plasticity, nondirectional migration, and mis-orientation, and thus strongly resembled the phenotype of Polycystin-1-deficient cells. Mis-orientation of developing tubule cells in metanephric kidneys upon loss of Polycystin-1 was phenocopied by pharmacological increase of cAMP in wildtype kidneys. In vitro, cAMP impaired tubule formation after capillary-induced injury which was further impaired by loss Polycystin-1