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The vertebrate spinal cord is composed of billions of neurons and glia cells, which are formed in a highly coordinated manner during early neurogenesis. Specification of these cells at distinct positions along the dorsoventral (DV) axis of the developing spinal cord is controlled by a ventrally located signaling center, the medial floor plate (MFP). Currently, the origin and time frame of specification of this important organizer are not clear. During my PhD thesis, I have analyzed the function of the novel secreted growth factor Midkine-a (Mdka) in zebrafish. In higher vertebrates, mdk and the related factor pleiotrophin (ptn) are widely expressed during embryogenesis and are implicated in a variety of processes. The in-vivo function of both factors, however, is unclear, as knock-out mice show no embryonic phenotype. We have isolated two mdk co-orthologs, mdka and mdkb, and one single ptn gene in zebrafish. Molecular phylogenetic analyses have shown that these genes evolved after two large gene block duplications. In contrast to higher vertebrates, zebrafish mdk and ptn genes have undergone functional divergence, resulting in mostly non-redundant expression patterns and functions. I have shown by overexpression and knock-down analyses that Mdka is required for MFP formation during zebrafish neurulation. Unlike the previously known MFP inducing factors, mdka is not expressed within the embryonic shield or tailbud but is dynamically expressed in the paraxial mesoderm. I used epistatic and mutant analyses to show that Mdka acts independently from these factors. This indicates a novel mechanism of Mdka dependent MFP formation during zebrafish neurulation. To get insight into the signaling properties of zebrafish Mdka, the function of both Mdk proteins and the candidate receptor Anaplastic lymphoma kinase (Alk) have been compared. Knock-down of mdka and mdkb resulted in the same reduction of iridophores as in mutants deficient for Alk. This indicates that Alk could be a putative receptor of Mdks during zebrafish embryogenesis. In most vertebrate species a lateral floor plate (LFP) domain adjacent to the MFP has been defined. In higher vertebrates it has been shown that the LFP is located within the p3 domain, which forms V3 interneurons. It is unclear, how different cell types in this domain are organized during early embryogenesis. I have analyzed a novel homeobox gene in zebrafish, nkx2.2b, which is exclusively expressed in the LFP. Overexpression, mutant and inhibitor analyses showed that nkx2.2b is activated by Sonic hedgehog (Shh), but repressed by retinoids and the motoneuron-inducing factor Islet-1 (Isl1). I could show that in zebrafish LFP and p3 neuronal cells are located at the same level along the DV axis, but alternate along the anteroposterior (AP) axis. Moreover, these two different cell populations require different levels of HH signaling and nkx2.2 activities. This provides new insights into the structure of the vertebrate spinal cord and suggests a novel mechanism of neural patterning.
The biotransformation of 1,1,1,3,3-pentafluoropropane was investigated in rats and in in vitro systems. First, the metabolites were identified in vivo using GC/MS and 19F NMR analysis. The main metabolite was identified as trifluoroacetic acid, the minor metabolite as 3,3,3-trifluoropropionic acid and as a cleavage product, inorganic fluoride was found. As the in vitro system, liver microsomes from rat and human samples and rat liver homogenates were used. Trifluoroacetic acid and 3,3,3 trifluoropropionic acid were confirmed in vitro as metabolic intermediates, following biotransformation of 1,1,1,3,3-pentafluoropropane by the cytochrome P-450-system. Studies, designed for clarifying the cardiotoxicity of 1,1,1,3,3-pentafluoropropane were driven by the hypothesis that 3,3,3-trifluoropropionic acid is the toxic agent. This was based on the lethal toxicity, which was observed in previous in vivo experiments. In addition, the point of its structural similarity to toxic agents as for example monofluoroacetic acid or of possible metabolic intermediates like difluoroacrylic acid with known toxicity were considered to support this assumption. However, trifluoroacetic acid was neglected as the sought-after toxic agent because of its different toxic effects, known from literature. Investigations on the biotransformation of 3,3,3-trifluoropropionic acid were performed and resulted in no metabolic activity and in poor elimination of 3,3,3-trifluoropropionic acid in vivo. The histopathological effects on the heart, which were observed in the 90-day oral toxicity study of 1,1,1,3,3-pentafluoropropane in rats, namely mononuclear inflammatory cell infiltrations and degenerated myocardial fibers, were not observed after a 28 day repeated exposure of up to 10 mg/kg b.w. of 3,3,3-trifluoropropionic acid. However, a single high dose of 3,3,3-trifluoropropionic acid lead to severe toxicological effects. The difference in the observed toxic effects after a single and repeated administration may be due to adaptive mechanisms in rats. The toxicological effects included clinical signs like ataxia, coma and cramps. The conditions of the rats suggested possible inhibition of the energy supply to the organism. Furthermore, the interference of 3,3,3-trifluoropropionic acid in the functionality of the organism was investigated. Experiments were performed in vitro in rat liver and heart mitochondria to investigate effects on the mitochondrial ß-oxidation. However, the transformation of the substrate [U14C] palmitic acid in the ß oxidation pathway was not inhibited by 3,3,3-trifluoropropionic acid. In addition, no cytotoxicity of 3,3,3 trifluoropropionic acid was observed in the cell culture systems. The main effect after a single dose of 3,3,3-trifluoropropionic acid was seen in clinical pathology and metabonomic analysis. The decrease in blood glucose is considered to have the most far-reaching consequences for the toxicity of 3,3,3-trifluoropropionic acid. If considering this change as the primary effect after a single dose, secondary effects, for example, the above-mentioned clinical signs could be explained. In addition, the observed high level of ketone bodies might have been responsible for life-threatening possible ketoacidosis. In general, ketoacidosis occurs after an imbalance between glycolysis, lipolysis, TCA cycle activity and respiratory function. Based on the results, ß-oxidation of fatty acids was not affected, and due to the decrease in glucose levels and the high levels of acetyl CoA, glycolysis was considered not to be impaired. Increased amounts of acetyl CoA might be a result of insufficient activity of the TCA cycle. However, the inhibition of the TCA cycle can be based on the impairment of specific enzymes and/or on the involvement of messenger substrates like insulin. Supporting the first mentioned aspect are decreased levels of TCA cycle intermediates, like α-ketoglutarate or citrate, as seen in 1H-NMR spectra of urine. However, the second aspect would explain the drop in blood glucose with the impairment of glucose transporters or the impairment of the insulin balance. If a single dose of 3,3,3-trifluoropropionic acid had stimulated the insulin release, glycolysis would be activated, and high amounts of acetyl CoA would be produced. In case of impaired use by the TCA cycle, levels of ketone bodies would be increased. Experiments were designed to characterize the direct effect of 3,3,3-trifluoropropionic acid on rat insulinoma-derived INS-1 cells as possible increase in insulin release. Further investigations are necessary to answer in which step of the metabolic pathway 3,3,3-trifluoropropionic acid interferes or finally which specific enzyme is inhibited or activated by 3,3,3-trifluoropropionic acid, leading to the drop in blood glucose and finally in lethal toxicity.
Flagellar motility and chemotaxis are essential virulence traits required for the ability of Helicobacter pylori to colonize the gastric mucosa. The flagellar regulatory network and the complex chemotaxis system of H. pylori are fundamentally different from other bacteria, despite many similarities. In H. pylori expression of the flagella is controlled by a complex regulatory cascade involving the two-component system FlgR-HP244, the sigma factors 54 and 28 and the anti-sigma 28 factor FlgM. Thus far, the input signal for histidine kinase HP244, which activates the transcriptional regulator FlgR, which triggers sigma factor 54-dependent transcription of the flagellar class 2 genes, is not known. Based on a yeast two-hybrid screen a highly significant protein-protein interaction between the H. pylori protein HP137 and both the histidine kinase HP244 and the flagellar hook protein HP908 (FlgE´) has been reported recently (Rain et al., 2001). So far, no function could be assigned to HP137. Interestingly, the interaction between HP137 and histidine kinase HP244 was observed in the characteristic block N sequence motif of the C-terminal ATP-binding kinase domain. In this work a potential role of HP137 in a feedback regulatory mechanism controlling the activity of histidine kinase HP244 in the flagellar regulation of H. pylori was investigated. Although the substitution of the gene encoding HP137 by a kanamycin cassette resulted in non-motile bacteria, the failure to restore motility by the reintroduction of hp137 in cis into the mutant strain, and the observation that HP137 has no significant effect on the activity of histidine kinase HP244 in vitro indicated that HP137 is not directly involved in flagellar regulation. Therefore, it was demonstrated that HP137 does not participate in the regulation of flagellar gene expression, neither in H. pylori nor in the closely related bacterium C. jejuni. Chemotactic signal transduction in H. pylori differs from the enterobacterial paradigm in several respects. In addition to a CheY response regulator protein (CheY1) H. pylori contains a CheY-like receiver domain (CheY2) which is C-terminally fused to the histidine kinase CheA. Furthermore, the genome of H. pylori encodes three CheV proteins consisting of an N-terminal CheW-like domain and a C-terminal receiver domain, while there are no orthologues of the chemotaxis genes cheB, cheR, and cheZ. To obtain insight into the mechanism controlling the chemotactic response of H. pylori the phosphotransfer reactions between the purified two-component signalling modules were investigated in vitro. Using in vitro phosphorylation assays it was shown that both H. pylori histidine kinases CheAY2 and CheA´ lacking the CheY-like domain (CheY2) act as ATP-dependent autokinases. Similar to other CheA proteins CheA´ shows a kinetic of phosphorylation represented by an exponential time course, while the kinetics of phosphorylation of CheAY2 is characterized by a short exponential time course followed by the hydrolysis of CheAY2~P. Therefore, it was demonstrated that the presence of the CheY2-like receiver domain influences the stability of the phosphorylated P1 domain of the CheA part of the bifunctional protein. Furthermore, it was proven that both CheY1 and CheY2 are phosphorylated by CheAY2 and CheA´~P and that the three CheV proteins mediate the dephosphorylation of CheA´~P, although with a clearly reduced efficiency as compared to CheY1 and CheY2. Moreover, CheA´ is capable of donating its phospho group to the CheY1 protein from C. jejuni and to CheY protein from E. coli. Retrophosphorylation experiments indicated that CheY1~P is able to transfer the phosphate group back to the HK CheAY2 and the receiver domain present in the bifunctional CheAY2 protein acts as a phosphate sink fine tuning the activity of the freely diffusible CheY1 protein, which is thought to interact with the flagellar motor. Hence, in this work evidence of a complex phosphorelay in the chemotaxis system was obtained which has similarities to other systems with multiple CheY proteins. The role of the CheV proteins remain unclear at the moment, but they might be engaged in a further fine regulation of the phosphate flow in this complex chemotaxis system and the independent function of the two domains CheA´ and CheY2 is not sufficient for normal chemotactic signalling in vivo.
In the experiments presented in this work, linear and non-linear femtosecond time-resolved spectrsocopy were applied to investigate the structure-function and functiondynamics relationship in biological and artificially designed systems. The experiments presented in this work utilize femtosecond time-resolved transient absorption and transient grating as well as picosecond time-resolved fluorescence spectroscopy to investigate the photophysics and photochemistry of biological photoreceptors and address the light-induced excited-state processes in a particular molecular device that serves as a - structurally - very simple light-harvesting antenna and potentially as a catalysis-switch for the production of hydrogen in solution. The combination of white-light probe transient absorption and coherent transient grating spectroscopies yields spectral information about the excited state absorption in concert with high quality, high signal-to-noise kinetic transients, which allow for precise fitting and therefore very accurate time-constants to be extracted from the data. The use of femtosecond time-resolved transient grating spectroscopy is relatively uncommon in addressing questions concerning the excited-state reaction pathways of complex (biological) systems, and therefore the experiments presented in this work constitute according to the literature the first studies applying this technique to a a metalloporphyrin and an artificial light-harvesting antenna.
Although spintronics has aroused increasing interest, much fundamental research has to be done. One important issue is the control over the electronic spin. Therefore, spin and phase coherent transport are very important phenomena. This thesis describes experiments with mercury based quantum well structures. This narrow gap material provides a very good template to study spin related effects. It exhibits large Zeeman spin splitting and Rashba spin-orbit splitting. The latter is at least four to five times larger than in III-V semiconductors. Initially a short review on the transport theory was presented. The main focus as on quantisation effects that are important to understand the related experiments. Thus, Shubnikov-de Haas and the quantum Hall effect have been analysed. Due to the first fabrication of nanostructures on Hg-based quantum well samples, the observation of ballistic transport effects could be expected. Hence, the Landauer-B¨uttiker theory has been introduced which gives the theoretical background to understand such effects. With respect to the main topic of this thesis, phase coherence has been introduced in detail. Experiments, where coherence effects could be observed, have been explained theoretically. Here, possible measurement setups have been discussed, e.g., a ring shaped structure to investigate the Aharonov-Bohm and related effects. Due to the fact, that all experiments, described in this thesis, were performed on Hg-based samples, the exceptional position of such samples among the “classical” semiconductors has been clarified. Hg1-xMnx Te quantum wells are type-III QWs in contrast to the type-I QWs formed by e.g., GaAs/AlGaAs heterostructures. With a well width of more than 6 nm and a manganese content of less than 7% they exhibit an inverted band alignment. Band structure calculations based on self consistent Hartree calculations have been presented. The common description of a diluted magnetic semiconductor with the Brillouin function has been introduced and the experiments to obtain the empiric parameters T0 and S0 have been presented. Rashba spin-orbit splitting and giant Zeeman splitting have been explained theoretically and the magnetic ordering of a spin glass as well as the relevant interactions therein have been discussed. The next chapter describes the first realisation of nanostructures on Hg-based heterostructures. Several material specific problems have been solved, but the unique features of this material system mentioned above justify the effort. Interesting new insight could be found and will be found with these structures. Onto a series of QW samples, cross-shaped structures with several lead widths have been patterned. With the non-local resistance measurement setup, evidence for quasiballistic transport was demonstrated in cross-shaped structures with lead widths down to 0.45 mm. The non-local bend resistance and a regime of rebound trajectories as well as the anomalous Hall effect could be identified. Monte-Carlo simulations of the classical electron trajectories have been performed. A good agreement with the experimental data has been achieved by taking a random scattering process into account. Encouraged by this success the technology has been improved and ring-shaped structures with radii down to 1 mm have been fabricated. Low temperature (below 100 mK), four terminal resistance measurements exhibit clear Aharonov-Bohm oscillations. The period of the oscillations agrees very well with a calculation that takes only the sample geometry into account. One goal using such a structure is the experimental prove of the spin-orbit Berry phase. Therefore an additional Shottky gate on top of the ring was needed. With this structure evidence for the Aharonov-Casher effect was observed. Here, a perpendicular applied electric field causes analogous oscillations as does the magnetic field in the AB effect. A subsequent change in the Rashba SO splitting due to several applied gate voltages while measuring the AB effect should reveal the SO Berry phase. Although initially evidence of a phase change was detected, a clear proof for the direct measurement of the SO Berry phase could not be found. In the future, with an advanced sample structure, e.g., with an additional Hall bar next to the ring, which permits a synchronous measurement of the Rashba splitting, it might be possible to measure the SO Berry phase directly. In manganese doped HgTe QWs two different effects simultaneously cause spin splitting: the giant Zeeman and the Rashba effect. By analysing the Shubnikovde Haas oscillations and the node positions of their beating pattern, it has been possible to separate these two effects. Whereas the Rashba effect can be identified by its dependence on the structure inversion asymmetry, varied by the applied gate voltage, the giant Zeeman splitting is extracted from its strong temperature dependence, because Rashba splitting is temperature independent. The analysis revealed, that the Rashba splitting is larger than or comparable to the giant Zeeman splitting even at moderately high magnetic fields. In an extraordinary HgMnTe QW sample, that exhibits the n= 1 quantum Hall plateau from less than 1 T up to 28 T, the anomalous Hall effect could be excluded. Intense studies on the temperature dependence of the QHE as well as band structure calculations have revealed this extraordinary behaviour to be an ordinary band structure effect of this system. In a series of mesoscopic structures on nonmagnetic and magnetic QWs, an investigation of the universal conductance uctuations have been carried out. In the
It has been known for a long time that Drosophila can learn to discriminate not only between different odorants but also between different concentrations of the same odor. Olfactory associative learning has been described as a pairing between odorant and electric shock and since then, most of the experiments conducted in this respect have largely neglected the dual properties of odors: quality and intensity. For odorant-coupled short-term memory, a biochemical model has been proposed that mainly relies on the known cAMP signaling pathway. Mushroom bodies (MB) have been shown to be necessary and sufficient for this type of memory, and the MB-model of odor learning and short-term memory was established. Yet, theoretically, based on the MB-model, flies should not be able to learn concentrations if trained to the lower of the two concentrations in the test. In this thesis, I investigate the role of concentration-dependent learning, establishment of a concentration-dependent memory and their correlation to the standard two-odor learning as described by the MB-model. In order to highlight the difference between learning of quality and learning of intensity of the same odor I have tried to characterize the nature of the stimulus that is actually learned by the flies, leading to the conclusion that during the training flies learn all possible cues that are presented at the time. The type of the following test seems to govern the usage of the information available. This revealed a distinction between what flies learned and what is actually measured. Furthermore, I have shown that learning of concentration is associative and that it is symmetrical between high and low concentrations. I have also shown how the subjective quality perception of an odor changes with changing intensity, suggesting that one odor can have more than one scent. There is no proof that flies perceive a range of concentrations of one odorant as one (odor) quality. Flies display a certain level of concentration invariance that is limited and related to the particular concentration. Learning of concentration is relevant only to a limited range of concentrations within the boundaries of concentration invariance. Moreover, under certain conditions, two chemically distinct odorants could smell sufficiently similarly such, that they can be generalized between each other like if they would be of the same quality. Therefore, the abilities of the fly to identify the difference in quality or in intensity of the stimuli need to be distinguished. The way how the stimulus is analyzed and processed speaks in favor of a concept postulating the existence of two separated memories. To follow this concept, I have proposed a new form of memory called odor intensity memory (OIM), characterized it and compared it to other olfactory memories. OIM is independent of some members of the known cAMP signaling pathway and very likely forms the rutabaga-independent component of the standard two-odor memory. The rutabaga-dependent odor memory requires qualitatively different olfactory stimuli. OIM is revealed within the limits of concentration invariance where the memory test gives only sub-optimal performance for the concentration differences but discrimination of odor quality is not possible at all. Based on the available experimental tools, OIM seems to require the mushroom bodies the same as odor-quality memory but its properties are different. Flies can memorize the quality of several odorants at a given time but a newly formed memory of one odor interferes with the OIM stored before. In addition, the OIM lasts only 1 to 3 hours - much shorter than the odor-quality memory.
Emery-Dreifuss muscular dystrophy (EDMD) is a rare genetic disorder characterised by early contractures of the elbows, Achilles tendons and spine, slowly progressive muscle wasting and cardiomyopathy associated with cardiac conduction defect. The autosomal dominant form is caused by mutations in the LMNA gene which gives rise to lamin A and lamin C proteins by alternative splicing. These A-type lamins, together with B-type lamins, form the nuclear lamina, a network of intermediate filament proteins underlining the nuclear envelope. In order to ascertain the role lamin A and C separately contribute to the molecular phenotype, we analysed ten LMNA mutations and one single nucleotide polymorphism (SNP) in transfection studies in COS7 fibroblasts and, partially, in C2C12 myoblasts. The EGFP or DsRed2 tagged lamins were exogenously expressed either individually or both A-types together and examined by light and electron microscopy. The protein mobility of lamin A mutants was determined by FRAP analysis. Additionally, a co-immunoprecipitation binding assay of in vitro synthesised A-type lamins and emerin was performed.Eight of the LMNA mutations (R50S, R133P, E358K, E358K+C<T1698, E361K, R527P, L530P, R541S and G602S) and the SNP C<T1698, when expressed in lamin A, exhibited a range of nuclear mis-localisation patterns from a wild type phenotype to the formation of nuclear aggregates. Two mutations (T150P and delQ355) led to the severe mis-localisation of the exogenous protein and additionally affected nuclear envelope reassembly and mid-body protein composition after mitosis. Exogenously expressed DsRed2 tagged wild type and mutant lamin C was only inserted into the nuclear lamina if co-expressed with the equivalent EGFP tagged lamin A construct, except for the T150P mutation which prevented either lamin from reaching the nuclear lamina. The T150P, R527P and L530P mutations reduced the ability of lamin A, but not lamin C from binding to emerin. These data indicate that mutations in the rod domain of lamin A mainly impair its function as a structural protein, whereas mutations of the globular tail domain appear to disrupt protein-protein interactions important for gene regulation and signal transduction processes. In addition, our results suggest specific functional roles for the emerin-lamin A and emerin-lamin C containing protein complexes; this is the first report to propose that the A-type lamin mutations may be differentially dysfunctional for the same LMNA mutation.
In this thesis, I introduce the Virtual Brain Protocol, which facilitates applications of the Standard Brain of Drosophila melanogaster. By providing reliable and extensible tools for the handling of neuroanatomical data, this protocol simplifies and organizes the recurring tasks involved in these applications. It is demonstrated that this protocol can also be used to generate average brains, i.e. to combine recordings of several brains with the same features such that the common features are emphasized. One of the most important steps of the Virtual Insect Protocol is the aligning of newly recorded data sets with the Standard Brain. After presenting methods commonly applied in a biological or medical context to align two different recordings, it is evaluated to what extent this alignment can be automated. To that end, existing Image Processing techniques are assessed. I demonstrate that these techniques do not satisfy the requirements needed to guarantee sensible alignments between two brains. Then, I analyze what needs to be taken into account in order to formulate an algorithm which satisfies the needs of the protocol. In the last chapter, I derive such an algorithm using methods from Information Theory, which bases the technique on a solid mathematical foundation. I show how Bayesian Inference can be applied to enhance the results further. It is demonstrated that this approach yields good results on very noisy images, detecting apparent boundaries between structures. The same approach can be extended to take additional knowledge into account, e.g. the relative position of the anatomical structures and their shape. It is shown how this extension can be utilized to segment a newly recorded brain automatically.
Diese Arbeit wurde durch Experimente zur Potential- und Stromverteilung in Quanten-Hall- Systemen motiviert, die in den letzten Jahren in der Abteilung von Klitzing am MPI für Festkörperforschung durchgeführt wurden und ergaben, dass elektrostatische Abschirmungseffekte in zweidimensionalen Elektronensystemen (2DES), die den ganzzahligen Quanten-Hall-Effekt (QHE) zeigen, sehr wichtig für das Verständnis der Stromverteilung innerhalb der Probe und der extremen Genauigkeit der gemessenen quantisierten Werte des Hall-Widerstands sind. Daraus ergab sich für die hier vorgelegte Arbeit das folgende Programm. Zunächst wird, nach einem einleitenden Kapitel, in Kapitel 2 der Formalismus vorgestellt, mit dem in den späteren Kapiteln Elektronendichten und elektrostatische Potentiale, die z.B. das 2DES auf eine Probe mit Streifengeometrie eingrenzen, selbstkonsistent berechnet werden. Diese Selbstkonsistenz besteht aus zwei Teilen. Erstens wird, bei vorgegebenem Potential, die Elektronendichte berechnet. Zweitens wird aus vorgegebener Ladungsverteilung, bestehend aus (positiven) Hintergrundladungen und der (im ersten Schritt berechneten) Elektronenladungsdichte, und geeigneten Randbedingungen (konstantes Potential auf metallischen Gates) durch Lösen der Poisson-Gleichung das elektrostatische Potential berechnet. Wenn wir im ersten Schritt, unter Berücksichtigung der Fermi-Dirac-Statistik, die Elektronendichte quantenmechanisch aus den Energieeigenfunktionen und -werten berechnen, erhalten wir die Hartree-Näherung, die die Dichte als nichtlokales Funktional des Potentials liefert. Wenn man die Ausdehnung der Wellenfunktionen auf der Längenskala, auf der sich das Potential typischerweise ändert, vernachlässigen kann, so vereinfacht sich die Hartree-Näherung zur Thomas- Fermi-Näherung, die einen lokalen Zusammenhang zwischen Elektronendichte und Potential beschreibt. Die meisten der konkreten Rechnungen wurden im Rahmen dieser selbstkonsistenten Thomas-Fermi-Poisson-Näherung durchgeführt. Im Kapitel 3 wird allgemein das Abschirmverhalten eines 2DES im hohen Magnetfeld untersucht. Wir betrachten die Antwort auf eine harmonische Potentialmodulation im unbegrenzten 2DES und in streifenförmig begrenzten Systemen mit zwei unterschiedlichen Arten von Randbedingungen. Bei tiefen Temperaturen und hohen Magnetfeldern finden wir extrem nichtlineare Abschirmung. Im unbegrenzten 2DES charakterisieren wir die Abschirmung, indem wir die gesamte Variation des selbstkonsistent berechneten Potentials als Funktion der Amplitude des aufgeprägten cosinus-Potentials berechnen. Bei festem Magnetfeld ergeben sich so Stufenfunktionen, deren Gestalt stark vom Füllfaktor der Landau-Niveaus im homogenen Zustand ohne aufgeprägtes Potential abhängt (siehe Abbildungen 3.2- 3.6). Vielleicht noch unerwartetere Kurven ergeben sich, wenn man bei festem Modulationspotential die Varianz des selbstkonsistenten Potentials gegen das Magnetfeld B aufträgt (Abb. 3.9). Die Resultate lassen sich aber leicht verstehen und (bei Temperatur T = 0) in einem einfachen Schema (Abb. 3.7) zusammenfassen. Als ordnendes Prinzip stellt sich heraus, dass sich stets Zustände einstellen, in denen die Elektronendichte möglichst wenig von der bei verschwindendem Magnetfeld abweicht. Wenn die Zyklotronenergie groß gegen die thermische Energie kBT ist, erfordert das, dass in den großen Bereichen, in denen die Dichte variiert, ein Landau-Niveau unmittelbar an dem, im Gleichgewicht konstanten, elektrochemischen Potential liegen muss (En, “pinning”). Man nennt diese Bereiche kompressibel. In den kompressiblen Bereichen können Elektronen leicht umverteilt werden, d.h. die Dichte ist leicht veränderbar und in diesen Bereichen gibt es extrem effektive Abschirmung. Existieren kompressible Bereiche mit unterschiedlichen Landau-Niveaus (En) am elektrochemischen Potential, z.B. bei großer Modulation oder weil die Dichte zum Probenrand hin abnimmt, so gibt es zwischen benachbarten kompressiblen Bereichen mit unterschiedlichen Landau-Quantenzahlen n “inkompressible” Bereiche, in denen zwischen zwei Landau-Niveaus liegt. Dort sind alle Landau-Niveaus unterhalb von besetzt, die oberhalb leer. Folglich ist dort der Füllfaktor ganzzahlig und die Dichte konstant. Das Wechselspiel zwischen kompressiblen und inkompressiblen Bereichen bestimmt das Abschirmverhalten. Randeffekte erweisen sich nur in solchen Magnetfeldintervallen als wichtig für die Abschirmung im Inneren einer streifenförmigen Probe, in denen (schon ohne aufgeprägte Modulation) in der Probenmitte ein neuer inkompressibler Streifen entsteht. Im Kapitel 4 wird die Rolle der inkompressiblen Streifen in einer idealisierten, streifenförmigen Hall-Probe untersucht. Mithilfe einer lokalen Version des Ohmschen Gesetzes berechnen wir bei vorgegebenen Gesamtstrom die Stromdichte und das nun ortsabhängige elektrochemische Potential, dessen Gradient die Stromdichte treibt. Für den lokalen Leitfähigkeitstensor nehmen wir ein für homogenes 2DES berechnetes Resultat und ersetzen den Füllfaktor jeweils durch den lokalen Wert. Dadurch ergibt sich, dass bei Existenz inkompressibler Streifen der gesamte Strom auf diese Streifen eingeschränkt ist, in denen die Komponenten des spezifischen Widerstands die Werte des freien, idealen 2DES haben, also verschwindenden longitudinalen und quantisierten Hall-Widerstand. Aus Hartree-Rechnungen zeigen wir, dass es inkompressible Streifen nur in Magnetfeldintervallen endlicher Breite (um ganzzahlige Füllfaktoren) gibt und dass in der Nähe von Füllfaktor 4 es nur inkompressible Streifen mit dem lokalen Füll-faktor \nu(x) = 4 gibt, aber nicht solche mit \nu(x) = 2, in Gegensatz zu dem Ergebnis der Thomas-Fermi-Poisson-Näherung, die hier nicht gültig ist. Um diese Unzulänglichkeit der Thomas-Fermi-Poisson-Näherung und Artefakte des strikt lokalen Modells zu beheben, führen wir die Rechnungen mit einem (auf der Skala des mittleren Elektronenabstands) gemittelten Leitfähigkeitstensors aus. Damit erhalten wir, im Rahmen einer Linear-Response-Rechnung, sehr schöne Übereinstimmung mit den Potentialmessungen, die diese Dissertation motivierten, einen kausalen Zusammenhang zwischen der Existenz inkompressibler Streifen und der Existenz von Plateaus im QHE, und ein Verständnis der extremen Genauigkeit, mit der die quantisierten Widerstandswerte reproduziert werden können, unabhängig von Probenmaterial und -geometrie. Im Kapitel 5 untersuchen wir das Zufallspotential, in dem sich die Elektronen bewegen. Wir gehen davon aus, dass sich hinter einer undotierten Schicht eine Ebene mit zufällig verteilten ionisierten Donatoren befindet, deren Coulomb-Potentiale sich zu dem Zufallspotential überlagern. Wir weisen darauf hin, dass sich die langreichweitigen Fluktuationen dieses Potentials anders verhalten als die kurzreichweitigen. Die kurzreichweitigen klingen mit dem Abstand der Donatorebene von der Ebene des 2DES exponentiell ab, werden aber (bei B = 0) nur schwach durch das 2DES abgeschirmt. Diese Fluktuationen haben wir durch die endlichen Leitfähigkeiten und die Stoßverbreiterung der Landau-Niveaus berücksichtigt. Die langreichweitigen Fluktuationen, andererseits, sind nur schwach von der Entfernung der Donatorebene abhängig, werden aber stark vom 2DES abgeschirmt. Diese sollte man bei der selbstkonsistenten Abschirmungsrechnung explizit berücksichtigen. Erste Versuche in dieser Richtung zeigen, dass sie die Quanten-Hall-Plateaus verbreitern, verschieben und stabilisieren können. Sie sollten besonders bei breiten Proben wichtig werden, bei denen sie zusätzliche inkompressible Streifen im Probeninneren verursachen können. Schließlich diskutieren wir in Kapitel 6 Abschirmungseffekte in einem Doppelschichtsystem aus zwei parallelen 2DES. Interessante neue Effekte treten auf, wenn die Schichten verschiedene Dichten haben. Das Auftreten inkompressibler Streifen in der einen Schicht kann dann drastische Auswirkungen auf die andere Schicht haben. Widerstandsmessungen in Abhängigkeit vom Magnetfeld, die kürzlich an solchen Systemen durchgeführt wurden, zeigen, dass am Rande eines QH-Plateaus Hysterese auftritt, d.h. dass die für ansteigendes Magnetfeld gemessene Kurve nicht mit der für abfallendes Magnetfeld gemessenen Kurve übereinstimmt, wenn dieser Magnetfeldbereich in ein QH-Plateau der anderen Schicht fällt. Wir entwickeln ein Modell und beschreiben Modellrechnungen, die dieses Phänomen plausibel machen.
This thesis contributes to the field of silicon chemistry, with a special emphasis on the chemistry of penta- and hexacoordinate silicon.The spirocyclic zwitterionic Lambda5Si-silicates 1–6 with a (2,2,6,6-tetramethylpiperidinio)- methyl group and two identical bidentate chelate ligands derived from glycine, (S)-alanine, (S)-phenylalanine, (S)-valine, (S)-tert-leucine, or (S)-proline bound to the silicon(IV) coordination center were synthesized and structurally characterized for the first time.The hitherto unknown spirocyclic zwitterionic Lambda5Si-silicates 7–12 with an (ammonio)- methyl group and two identical bidentate chelate ligands derived from (S)-lactic acid, (S)-3- phenyllactic acid, or (S)-mandelic acid were synthesized and structurally characterized in the solid state (elemental analyses (C, H, N), crystal structure analyses, 15N and 29Si VACP/MAS solid-state NMR experiments) and in solution (except 10; 1H, 13C, and 29Si NMR experiments)The spirocyclic zwitterionic Lambda5Si-silicates 13, 15, and 16 with an (ammonio)methyl group and two bidentate meso-oxolane-3,4-diolato(2–) ligands bound to the silicon(IV) coordination center were synthesized for the first time. The already existent compound 14 was resynthesized in order to perform a crystal structure analysis. All compounds were characterized by elemental analyses (C, H, N), 29Si VACP/MAS solid-state NMR experiments, and solution NMR studies (1H, 13C, 15N, and 29Si NMR experiments), and compounds 14–16 were additionally studied by single-crystal X-ray diffraction.The already existent zwitterionic Lambda5Si-silicate 17 was synthesized by new methods, including a remarkable Si–C cleavage reaction with benzoin. To investigate the dynamic behavior of the known zwitterionic Lambda5Si-silicate 18 in solution, VT 1H NMR experiments in CD2Cl2 were performed in the temperature range –100 °C to 23 °C.The hexacoordinate silicon compounds 19–22 containing multidentate ligands derived from citric acid or (S)-malic acid were synthesized for the first time. The anionic Lambda6Si-silicates 19–22 were structurally characterized in the solid state by single-crystal X-ray diffraction and VACP/MAS NMR spectroscopy (13C, 15N, 29Si). Upon dissolution in water at 20 °C, spontaneous hydrolysis of the Lambda6Si-silicate anions was observed.