Wuppertal, Univ., Diss., 2005. / Computerdatei im Fernzugriff.

Wuppertal, Universiẗat, Diss., 2005.

Rhodopsin, der Rezeptor der visuellen Kaskade, gehört zu größten Klasse A der G-Protein-koppelnden Rezeptoren (GPCRs) und gilt als Modell-Rezeptor in der GPCR-Forschung. Über 3 % des humanen Genoms kodieren für GPCRs, doch trotz der physiologischen Bedeutung dieser Proteinfamilie sind die fundamentalen Mechanismen, mit denen diese Rezeptoren extrazelluläre Signale in das Zellinnere weiterleiten noch nicht verstanden. In der vorliegenden Dissertation werden Aspekte des Aktivierungsmechanismus von Rhodopsin sowie der Kopplung und Aktivierung des G-Proteins Transduzin untersucht. Die Arbeit ist in drei Schwerpunkte unterteilt: I. Es wurde ein in GPCR’s hochkonserviertes NPxxYx(5,6)F Motiv (Aminosäuresequenz Asn-Pro-x-x-Tyr-x(5,6)-Phe) in der siebten und achten Helix charakterisiert. In diesem konservierten Motiv sind mehrere für die Ausbildung der aktiven Rezeptorkonformation wichtige Funktionen vereint: Verknüpfung zu einem Wasserstoffbrückennetzwerk, Helixflexibilität sowie die exakte Positionierung der achten Helix. Letzteres hat nicht nur bei der Rezeptoraktivierung sondern auch bei der nachfolgenden Interaktion mit dem G-Protein eine Bedeutung. II. Anhand von chimären Rezeptoren, bei denen Teile der achten Helix durch homologe Sequenzen des beta2-adrenergen Rezeptors ausgetauscht wurden, wurde die Rolle der achten Helix bei der Rezeptor-Aktivierung und Bindung des G-Proteins untersucht. Auch bei dieser Studie wurde gezeigt, dass die exakte Positionierung der achten Helix essentiell für die Interaktion mit dem G-Protein ist. Zudem wurde ein bezüglich der G-Protein-Aktivierung funktionsfähiger chimärer Rezeptor gefunden, was auf einen übergeordneten Mechanismus bei der Aktivierung von G-Proteinen durch GPCRs hindeutet. III. Die Funktion des ß-Ionon-Rings des Retinals beim Aktivierungsmechanismus von Rhodopsin wurde an einem Retinal studiert, bei welchem Teile des Retinal-Rings fehlten (azyklisches Retinal). Auch diesem azyklischen Retinal können Eigenschaften eines partiellen Agonisten zugeschrieben werden. Beim Vergleich zu Pigmenten mit dem nativen 11-cis-Retinal wurden starke Analogien bei der initialen Energieaufnahme durch die Retinal-Isomerisierung sowie bei der Weiterleitung der Lichtenergie ins Protein gefunden. Allerdings wird die Energie schlechter auf das Protein übertragen, wodurch wesentlich weniger der aktiven G-Protein bindenden Rezeptorkonformation gebildet wird. Als wichtigste Funktion des Retinal-Rings wurde die Aufrechterhaltung der aktiven Meta-II-Konformation identifiziert. / Rhodopsin, the receptor of the visual cascade, belongs to the largest group A of G-protein coupled receptors (GPCRs) and can be seen as a model receptor in GPCR research. More than 3 % of the human genome code for GPCRs. But despite their physiological relevance, the detailed mechanism of signal transduction from extra cellular signal to different cellular pathways remains to be fully understood. Different aspects of receptor activation and the coupling and activation of the G-protein transducin are investigated in this dissertation. The thesis focuses on the following three subjects: I. A NPxxYx(5,6)F motif (amino acid sequence Asn-Pro-x-x-Tyr-x(5,6)-Phe) has been characterized for rhodopsin. It is localized in helix VII and VIII and is highly conserved throughout the GPCR family. Various roles for rhodopsin activation are combined in this motif: linkage to a hydrogen-bond network, helix flexibility and the exact positioning of helix VIII. The latter is not only relevant for the activation of the receptor but also for interaction with its G-protein. II. The role of helix VIII for receptor activation and G-protein coupling was studied on chimeric receptors, in which parts of helix VIII were exchanged against homologous sequences of the beta2 adrenergic receptor. This study confirmed the importance of helix VIII’s position for G-protein coupling. Furthermore, a chimeric receptor was found, which was fully functional concerning G-protein activation. This indicates that GPCRs might use a single, generic mechanism for G-protein activation. III. The role of the ß-ionone-ring for the activation mechanism of rhodopsin was studied by means of an acyclic retinal, which lacks four carbon atoms of the ß-ionone-ring. This modified retinal could be classified as a partial agonist for rhodopsin. Energy input by retinal isomerization and formation of the G-protein binding Meta-II conformation were found to be very similar to rhodopsin when bound to its native 11-cis-retinal. However, the lack of the ring structure resulted in a lower amount of Meta-II and a fast decay of activity. It was concluded that the main role of the ring structure is to maintain the active state of rhodopsin.

Be it in the weather forecast or while swimming in the Baltic Sea, in almost every aspect of every day life we are confronted with flow phenomena. A common model to describe the motion of viscous incompressible fluids are the Navier-Stokes equations. These equations are not only relevant in the field of physics, but they are also of great interest in a purely mathematical sense. One of the difficulties of the Navier-Stokes equations originates from a non-linear term. In this thesis, we consider the Oseen equations as a linearisation of the Navier-Stokes equations. We restrict ourselves to the two-dimensional case. Our domain will be the unit square. The aim of this thesis is to find a suitable numerical method to overcome known instabilities in discretising these equations. One instability arises due to layers of the analytical solution. Another instability comes from a divergence constraint, where one gets poor numerical accuracy when the irrotational part of the right-hand side of the equations is large. For the first cause, we investigate the layer behaviour of the analytical solution of the corresponding stream function of the problem. Assuming a solution decomposition into a smooth part and layer parts, we create layer-adapted meshes in Chapter 3. Using these meshes, we introduce a numerical method for equations whose solutions are of the assumed structure in Chapter 4. To reduce the instability caused by the divergence constraint, we add a grad-div stabilisation term to the standard Galerkin formulation. We consider Taylor-Hood elements and elements with a discontinous pressure space. We can show that there exists an error bound which is independent of our perturbation parameter and get information about the convergence rate of the method. Numerical experiments in Chapter 5 confirm our theoretical results.

Be it in the weather forecast or while swimming in the Baltic Sea, in almost every aspect of every day life we are confronted with flow phenomena. A common model to describe the motion of viscous incompressible fluids are the Navier-Stokes equations. These equations are not only relevant in the field of physics, but they are also of great interest in a purely mathematical sense. One of the difficulties of the Navier-Stokes equations originates from a non-linear term. In this thesis, we consider the Oseen equations as a linearisation of the Navier-Stokes equations. We restrict ourselves to the two-dimensional case. Our domain will be the unit square. The aim of this thesis is to find a suitable numerical method to overcome known instabilities in discretising these equations. One instability arises due to layers of the analytical solution. Another instability comes from a divergence constraint, where one gets poor numerical accuracy when the irrotational part of the right-hand side of the equations is large. For the first cause, we investigate the layer behaviour of the analytical solution of the corresponding stream function of the problem. Assuming a solution decomposition into a smooth part and layer parts, we create layer-adapted meshes in Chapter 3. Using these meshes, we introduce a numerical method for equations whose solutions are of the assumed structure in Chapter 4. To reduce the instability caused by the divergence constraint, we add a grad-div stabilisation term to the standard Galerkin formulation. We consider Taylor-Hood elements and elements with a discontinous pressure space. We can show that there exists an error bound which is independent of our perturbation parameter and get information about the convergence rate of the method. Numerical experiments in Chapter 5 confirm our theoretical results.:Acknowledgement III Notation IV 1 Introduction 1 1.1 Existence of solutions 2 1.2 Transformation into a fourth-order problem 4 2 Asymptotic analysis 6 2.1 A fourth-order problem in 1D 6 2.2 A fourth-order problem in 2D 14 2.2.1 Asymptotic expansion 19 2.2.2 Estimation of the residual 26 2.2.3 Asymptotic expansion without compatibility conditions 30 3 Solution decomposition and layer-adapted meshes 32 3.1 Solution decomposition 32 3.2 Layer-adapted meshes 33 3.3 Interpolation errors on layer-adapted meshes 36 4 Galerkin method and stabilisation 41 4.1 Discrete problem and stabilised formulation 41 4.2 A priori error estimates 44 5 Numerical results 48 5.1 Numerical evaluation of inf-sup constants 48 5.1.1 Theoretical aspects 48 5.1.2 Numerical results for β0 and B0 50 5.2 Convergence studies 53 5.2.1 Uniformity in ε 54 5.2.2 Convergence order 55 5.2.3 Necessity of stabilisation 56 5.2.4 Further experiments without known exact solution 56 6 Conclusions and outlook 60 A Numerical study of the stability estimate (2.35) 62 Bibliography 67

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We developed a three-step colloidal synthesis of near-infrared active Cu-In-Se (CISe)/ZnS core/shell nanocrystals (NCs) via a sequential partial cation exchange. In the first step binary highly copper deficient Cu2‒xSe NCs were synthesized, followed by a partial cation exchange of copper to indium ions yielding CISe NCs. In order to enhance the stability and the photoluminescence (PL) properties of the NCs, a subsequent ZnS shell was grown, resulting in CISe/ZnS core/shell NCs. These core/shell hetero-NCs exhibited a dramatic increase in size and a restructuring to trigonal pyramidal particles. The reaction parameters, e.g. the Cu:Se-ratio, the temperature and the time were carefully tuned enabling a distinct control over the size and the composition of the NCs. By varying only the size of the CISe/ZnS NCs (from 9 to 18 nm) the PL spectra could be tuned covering a wide range with maxima from 990 nm to 1210 nm. Thus, in these experiments we demonstrate a clear dependence of the optical properties of these materials on their size and extend the PL range of CISe-based nanoparticles further to the infrared part of the spectrum. Furthermore, the relatively large size of these NCs allows their detailed structural analysis via electron microscopy techniques, which is particularly challenging in the case of small particles and especially important to relate the size, composition and crystal structure to their optoelectronic properties.

Die salzhaltigen Abwässer des Kalibergbaues führen in natürlichen Süßwassersystemen zu Ionenimbalanzen und einer sekundären Versalzung der Werra in Deutschland. Die Auswirkungen dieser Ionenungleichgewichte auf die Reproduktion von Süßwasserfischen wurden unter Verwendung der Modellfischart Danio rerio untersucht. Angepasst an die aktuellen Grenzwerte für die Einleitung der Abwässer aus dem Kalibergbau wurden fünf verschiedene Kombinationen erhöhter Ionenkonzentrationen getestet. Während eines partiellen Lebenszyklustests wurden adulte Fische 35 Tage lang in den Salzkombinationen exponiert. Anschließend wurden die Nachkommen dieser Fische bis zum 8. Tag nach der Befruchtung den gleichen Salzkonzentrationen ausgesetzt. Zusätzlich wurden Early-Life-Stage-Tests (ELST) mit den Nachkommen von nicht exponierten Eltern durchgeführt. Im Vergleich zu natürlich vorkommenden Ionenkonzentrationen und -verhältnissen in Süßwassersystemen war die Befruchtungsrate der Eier für alle Ionenkombinationen signifikant niedriger, die Koagulations- und Deformationsrate jedoch signifikant höher. Die ELST ergaben bei den Embryonen und Larven u.a. vorzeitige und verlängerte Schlupfzeiten, verringerte Überlebensraten, erhöhte Deformationsraten und Herzschlagfrequenzen sowie Unregelmäßigkeiten des Ganzkörpergehalts von K, Mg, Na und Ca und des Ganzkörper-Ionenverhältnisses von Ca:Mg bei erhöhten Ionenkonzentrationen und Ionenimbalanzen. Im Vergleich zu den Effekten auf die Fortpflanzung und Entwicklung der Nachkommen waren die Effekte auf die adulten Tiere moderat. Die Ergebnisse dieser Dissertation zeigen, dass Teillebenszyklus-Tests besser als Fischeitests oder ELST geeignet sind, die Effekte von durch Abwasser verursachten Ionenimbalanzen, auf die Fortpflanzung und frühe Entwicklung von Süßwasserfischen, zu untersuchen. Weder die momentan gültigen noch die zukünftig herabgesetzten Grenzwerte bis 2027 sind danach als unschädlich, für die Reproduktion von Süßwasserfischen, zu betrachten. / The potash mining industry discharges saline effluents which generate ion imbalances in natural freshwater systems and cause severe secondary salinization in the river Werra in Germany. The effects of these ion imbalances on reproduction of freshwater fish were investigated using the fish model species Danio rerio. Five different combinations of elevated ion concentrations adjusted to the current threshold values for the discharge of potash mining effluents in Germany were tested. During a partial life cycle test, adult fish were exposed to the salt combinations for 35 days. Subsequently, the offspring were exposed to the same concentrations until hatch, and the larvae were further reared at the exposure concentrations from hatch until the 8th day post fertilization. Additionally, a standard early life stage test with offspring from unexposed parents was performed. Compared to naturally occurring ion concentrations and ratios in freshwater systems, the fertilization rate of the eggs was significantly lower for all ion combinations, while coagulation and deformation rates were significantly higher. Early life stage tests on embryos and larvae revealed premature and prolonged hatching times, reduced survival rates, increased deformation and heart rates and irregularities in whole body content of K, Mg, Na and Ca and whole body Ca:Mg ratios at elevated ion concentrations and imbalances of ion ratios. Compared to effects on reproduction and development of the offspring, effects on the parental generation were moderate. The results of this dissertation indicate that partial life cycle tests instead of fish egg tests or ELST are needed to examine most sensitively the effects of ion imbalances caused by potash mining effluents on reproduction and early development of freshwater fish. Neither the recent German threshold values nor the future reduced values until 2027 are safe for the reproduction of freshwater fish.