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Cyclisches Adenosinmonophosphat ist ein ubiquitärer zweiter Botenstoff zahlreicher Signalwege im menschlichen Körper. Auf eine Vielzahl verschiedenster extrazellulärer Signale folgt jedoch eine Erhöhung desselben intrazellulären Botenstoffs - cAMP. Nichtsdestotrotz schafft es die Zelle, Signalspezifität aufrecht zu erhalten. Ein anerkanntes, wenn auch bisher unverstandenes Modell, um dieses zu ermöglichen, ist das Prinzip der Kompartimentierung. Die Zelle besitzt demnach Areale verschieden hoher cAMP-Konzentrationen, welche lokal begrenzt einzelne Signalkaskaden beeinflussen und somit eine differenzierte Signalübertragung ermöglichen. Eine mögliche Ursache für die Ausbildung solcher Bereiche geringerer cAMP- Konzentrationen (hier als Domänen bezeichnet), ist die hydrolytische Aktivität von Phosphodiesterasen (PDEs), welche als einzige Enzyme die Fähigkeiten besitzen, cAMP zu degradieren.
In dieser Arbeit wird der Einfluss der cAMP-Hydrolyse verschiedener PDEs auf die Größe dieser Domänen evaluiert und mit denen der PDE4A1 verglichen, welche bereits durch unsere Arbeitsgruppe aufgrund ihrer Größe als Nanodomänen definiert wurden. Der Fokus wird dabei auf den Einfluss von kinetischen Eigenschaften der Phosphodiesterasen gelegt. So werden eine PDE mit hoher Umsatzgeschwindigkeit (PDE2A3) und eine PDE mit hoher Substrataffinität (PDE8A1) verglichen. Mithilfe sogenannter Linker, Abstandshaltern definierter Länge, werden zusätzlich die Nanodomänen ausgemessen, um einen direkten Zusammenhang zwischen Größe und kinetischer Eigenschaft anzugeben. Die Zusammenschau der Ergebnisse zeigt, dass die maximale Umsatzgeschwindigkeit der Phosphodiesterasen direkt mit der Größe der Nanodomänen korreliert.
Durch den unmittelbaren Vergleich der gesamten PDE mit ihrer katalytischen Domäne wird zusätzlich der Einfluss von regulatorischen Domänen evaluiert. Es wird gezeigt, dass diese cAMP-Gradienten modulieren können. Bei der PDE2A3 geschieht die Modulation u.a. durch Stimulation mit cGMP, welche höchstwahrscheinlich dosisabhängig ist und somit graduell verläuft. Hiermit präsentieren sich die Domänen als dynamische Bereiche, d.h. sie können in ihrer Ausprägung reguliert werden. In dieser Arbeit wird die Hypothese bestätigt, dass Phosphodiesterasen eine wichtige Rolle in der Kompartimentierung von cAMP spielen, die Gruppe jedoch inhomogener ist, als bislang angenommen. Die Gradienten-Bildung lässt sich nicht bei jeder Phosphodiesterase darstellen (PDE8A1). Einige Phosphodiesterasen (PDE2A3) jedoch bilden Kompartimente, die durch externe Stimuli in ihrer Größe reguliert werden können.
Die Arbeit legt den Grundstein zur breiteren Charakterisierung des spezifischen Einflusses weiterer PDEs auf cAMP-Kompartimentierung, welches nicht nur das Verständnis der Kompartimentierungs-Strategien voranbringt, sondern auch essentiell für das Verständnis der Pathophysiologie zahlreicher Krankheitsbilder, aber auch für das Verständnis bereits angewandter aber auch potentiell neuer Medikamente ist.
The second messenger cyclic AMP (cAMP) plays an important role in synaptic plasticity. Although there is evidence for local control of synaptic transmission and plasticity, it is less clear whether a similar spatial confinement of cAMP signaling exists. Here, we suggest a possible biophysical basis for the site-specific regulation of synaptic plasticity by cAMP, a highly diffusible small molecule that transforms the physiology of synapses in a local and specific manner. By exploiting the octopaminergic system of Drosophila, which mediates structural synaptic plasticity via a cAMP-dependent pathway, we demonstrate the existence of local cAMP signaling compartments of micrometer dimensions within single motor neurons. In addition, we provide evidence that heterogeneous octopamine receptor localization, coupled with local differences in phosphodiesterase activity, underlies the observed differences in cAMP signaling in the axon, cell body, and boutons.
The pleiotropic function of 3′,5′-cyclic adenosine monophosphate (cAMP)-dependent pathways in health and disease led to the development of pharmacological phosphodiesterase inhibitors (PDE-I) to attenuate cAMP degradation. While there are many isotypes of PDE, a predominant role of PDE4 is to regulate fundamental functions, including endothelial and epithelial barrier stability, modulation of inflammatory responses and cognitive and/or mood functions. This makes the use of PDE4-I an interesting tool for various therapeutic approaches. However, due to the presence of PDE4 in many tissues, there is a significant danger for serious side effects. Based on this, the aim of this review is to provide a comprehensive overview of the approaches and effects of PDE4-I for different therapeutic applications. In summary, despite many obstacles to use of PDE4-I for different therapeutic approaches, the current data warrant future research to utilize the therapeutic potential of phosphodiesterase 4 inhibition.
This work is concerned with the numerical approximation of solutions to models that are used to describe atmospheric or oceanographic flows. In particular, this work concen- trates on the approximation of the Shallow Water equations with bottom topography and the compressible Euler equations with a gravitational potential. Numerous methods have been developed to approximate solutions of these models. Of specific interest here are the approximations of near equilibrium solutions and, in the case of the Euler equations, the low Mach number flow regime. It is inherent in most of the numerical methods that the quality of the approximation increases with the number of degrees of freedom that are used. Therefore, these schemes are often run in parallel on big computers to achieve the best pos- sible approximation. However, even on those big machines, the desired accuracy can not be achieved by the given maximal number of degrees of freedom that these machines allow. The main focus in this work therefore lies in the development of numerical schemes that give better resolution of the resulting dynamics on the same number of degrees of freedom, compared to classical schemes.
This work is the result of a cooperation of Prof. Klingenberg of the Institute of Mathe- matics in Wu¨rzburg and Prof. R¨opke of the Astrophysical Institute in Wu¨rzburg. The aim of this collaboration is the development of methods to compute stellar atmospheres. Two main challenges are tackled in this work. First, the accurate treatment of source terms in the numerical scheme. This leads to the so called well-balanced schemes. They allow for an accurate approximation of near equilibrium dynamics. The second challenge is the approx- imation of flows in the low Mach number regime. It is known that the compressible Euler equations tend towards the incompressible Euler equations when the Mach number tends to zero. Classical schemes often show excessive diffusion in that flow regime. The here devel- oped scheme falls into the category of an asymptotic preserving scheme, i.e. the numerical scheme reflects the behavior that is computed on the continuous equations. Moreover, it is shown that the diffusion of the numerical scheme is independent of the Mach number.
In chapter 3, an HLL-type approximate Riemann solver is adapted for simulations of the Shallow Water equations with bottom topography to develop a well-balanced scheme. In the literature, most schemes only tackle the equilibria when the fluid is at rest, the so called Lake at rest solutions. Here a scheme is developed to accurately capture all the equilibria of the Shallow Water equations. Moreover, in contrast to other works, a second order extension is proposed, that does not rely on an iterative scheme inside the reconstruction procedure, leading to a more efficient scheme.
In chapter 4, a Suliciu relaxation scheme is adapted for the resolution of hydrostatic equilibria of the Euler equations with a gravitational potential. The hydrostatic relations are underdetermined and therefore the solutions to that equations are not unique. However, the scheme is shown to be well-balanced for a wide class of hydrostatic equilibria. For specific classes, some quadrature rules are computed to ensure the exact well-balanced property. Moreover, the scheme is shown to be robust, i.e. it preserves the positivity of mass and energy, and stable with respect to the entropy. Numerical results are presented in order to investigate the impact of the different quadrature rules on the well-balanced property.
In chapter 5, a Suliciu relaxation scheme is adapted for the simulations of low Mach number flows. The scheme is shown to be asymptotic preserving and not suffering from excessive diffusion in the low Mach number regime. Moreover, it is shown to be robust under certain parameter combinations and to be stable from an Chapman-Enskog analysis.
Numerical results are presented in order to show the advantages of the new approach.
In chapter 6, the schemes developed in the chapters 4 and 5 are combined in order to investigate the performance of the numerical scheme in the low Mach number regime in a gravitational stratified atmosphere. The scheme is shown the be well-balanced, robust and stable with respect to a Chapman-Enskog analysis. Numerical tests are presented to show the advantage of the newly proposed method over the classical scheme.
In chapter 7, some remarks on an alternative way to tackle multidimensional simulations are presented. However no numerical simulations are performed and it is shown why further research on the suggested approach is necessary.
In this thesis we consider a reactive transport model with precipitation dissolution reactions from the geosciences. It consists of PDEs, ODEs, algebraic equations (AEs) and complementary conditions (CCs). After discretization of this model we get a huge nonlinear and nonsmooth equation system. We tackle this system with the semismooth Newton method introduced by Qi and Sun. The focus of this thesis is on the application and convergence of this algorithm. We proof that this algorithm is well defined for this problem and local even quadratic convergent for a BD-regular solution. We also deal with the arising linear equation systems, which are large and sparse, and how they can be solved efficiently. An integral part of this investigation is the boundedness of a certain matrix-valued function, which is shown in a separate chapter. As a side quest we study how extremal eigenvalues (and singular values) of certain PDE-operators, which are involved in our discretized model, can be estimated accurately.