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The main aim of this work was the classification of highly polar E–N (E = Al, Si, P) and Li–E’ (E’ = C, N, O) bonds in terms of ionic (closed-shell) or covalent (shared) interactions. To answer this question the experimentally determined electron density was analyzed using Bader’s theory of ‘Atoms in Molecules’ (AIM). This allows a quantitative evaluation of properties derived from the electron density, such as the Laplacian, the ellipticitiy and the ratio of the highest charge concentration perpendicular to the bond path, to the largest charge depletion along the bonding vector. Most of these properties were monitored along the entire bonding region and not limited to the BCP as in former studies. The analyses are completed by the calculation of the electronic energy densities Hl at the BCPs and the integration of atomic basins also defined within the AIM theory. The electrostatic potential (ESP) was computed from the multipole parameters to reveal preferred reactive sites of the structures under investigation. Apart from that, the multipole formalism was applied to problematic crystal structures in order to open this method for twinned samples or those including disordered groups in the molecule.
The first part of this work focuses on the characterization of systems which complex electronic structures require the application of multi-reference methods. The anti-tumor efficacy of the natural product Neocarzinostatin is based on the formation of diradicals and causes DNA cleavage and finally cytolysis. Computations on model systems performed in the present work show the influence of structural features on the mode of action and the efficacy of this antitumor-antibiotic. The cyclization of systems related to the enyne-cumulene framework like the enyne-allenes was investigated earlier and relations to the more unusual class of enyne-ketenes are analyzed. The class of enyne-ketenes (and also the enyne-allenes) show a broad spectrum of possible intermediates (diradicals, zwitterions, allenes). The electronic structures of these intermediates are also possible for the (heteroatom substituted) 1,2,4-cyclohexatriene and a model for their energetic sequence based on high-level multi-reference computations is proposed. In all three projects the application of multi-reference approaches is necessary to obtain a comprehensive picture of the reactivity and electronic structure but also shows up the limits inherently existing in the currently available programs with respect to the size of the molecules. In the second part, algorithms for a multi-reference Moller-Plesset perturbation theory (MR-MP2) program, designed to perform large-scale computations, were developed and implemented. The MR-MP2 approach represents the most cost-effective multireference ansatz and requires an efficient evaluation of the Hamilton matrix for which an algorithm is designed to instantly recognize only non-vanishing matrix elements and to employ the recurring interaction patterns of the Hamilton matrix. The direct construction of the Hamilton matrix is additionally parallelized to work on cluster environments.
This work is investigating the electronic structure of organic thin films. A central question in this respect is the influence of the interaction between the molecules in the condensed phase and the interaction at metal-organic interfaces on the electronic properties. For this purpose the experimental methods Photoelectron Spectroscopy (PES) and Near Edge X-ray Absorption Finestructure Spectroscopy (NEXAFS) were applied with highest energy resolution. In addition, ab initio calculations were performed for the theoretical simulation of NEXFAS spectra. The investigation is mainly focussing on thin, vacuum sublimated films of aromatic model molecules with oxygen-containing functional groups (NTCDA, PTCDA, NDCA, BPDCA and ANQ) and Ag(111) surfaces. Due to their large, delocalised p-systems these molecules have very interesting properties for their application in electronic devices. Due to the high energy resolution of third generation synchrotron sources the vibronic fine structure in the NEXAFS spectra of these large molecules could be resolved for the first time in the condensed phase. A comparison of the data of the different molecules provides interesting insight into the coupling between electronic transition and vibronic excitation. Although for these molecules a variety of different vibronic modes exist, the NEXAFS data show that preferentially only on mode couples to each electronic transition. The high-resolution PES spectra of the molecules NTCDA, PTCDA, NDCA, BPDCA and ANQ show distinct differences thus providing a fingerprint for each investigated substance. A comparative analysis of the spectra enabled us to define the 1s binding energies of all chemically different carbon and oxygen atoms. Additional structures in the spectra can be assigned as shake-up satellites. The five molecules are an ideal model system for the investigation of fundamental aspects of core electron spectroscopy, such as initial and final state effects and satellites, that are influenced by the intra- and intermolecular electron distribution in the ground and core ionized state. An important aspect in this thesis is the spectroscopic investigation of structurally different NTCDA monolayer phases on the Ag(111) surface. Marked differences in the electronic structures of the different phases, that can be assigned to differences in the metal-adsorbate interaction, could be demonstrated by XPS and NEXAFS. The substrate bonding can be characterized as chemisorptive for both, the compressed as well as the relaxed NTCDA monolayer, which can be unambiguously deduced from the analysis of satellite structures in the O 1s and C 1s XPS spectra. These satellites are due to dynamic screening by charge transfer from the substrate. The NEXAFS data show consistently, that the NTCDA LUMO becomes partly occupied upon adsorption. Highly interesting phase transitions into disordered low-temperature phases occur upon cooling to 160 K for both, the compressed and the relaxed NTCDA monolayer. Thereby, the adsorbate-substrate bonding is increased and the NTCDA LUMO becomes completely occupied. This can be observed in the NEXAFS data, where transitions involving LUMO final states are quenched. Simultaneously, the XPS data show a distinctly decreased intensity of unscreened photoemission states due to enhanced charge transfer screening. In addition, a hysteresis behaviour could be demonstrated for the phase transition of the relaxed monolayer by temperature dependent NEXAFS experiments and the hysteresis curve was determined. The hysteresis could be quantified to approx. 20 K. From SPA-LEED experiments the activating energy for the phase transition of the relaxed monolayer upon cooling could be determined to 60 meV. Finally, a NEXAFS investigation of polyethylene samples with different comonomer content is presented. Differences in the absorption spectra between samples with different comonomer content could be unambiguously assigned to the different crystallinities of the samples by heating a highly crystalline sample in situ close to the melting temperature. Ab initio calculations on a model matrix of butane molecules show, that the spectra of crystalline and amorphous polyethylene differ distinctly due to the intermolecular interaction, which can be observed best for resonances with strong Rydberg character. Thus, the differences in the PE spectra can be explained by the superposition of the signatures of crystalline and amorphous moieties, that are mixed according to the respective crystallinity.
The geologic barrier represents the final contact between a landfill and the environment. Ideally suited are clays and mudstones because of sufficient vertical and lateral extent, low hydraulic conductivities and high sorptive characteristics. Since hydraulic conductivity is no longer the single criteria to determine transport and retardation of contaminants in geologic landfill barrier materials, diffusive and sorptive characteristics of 4 different clay and mudstone lithologies in Northern Bavaria, were investigated. Cored samples from various depths were included in this study and subjected to evaluations of geochemistry, mineralogy, physical parameters, sorption and diffusion. A transient double reservoir with decreasing source concentration was designed and constructed using clear polycarbonate cylinders for undisturbed clay plugs of 2 to 4cm thickness. Samples were also fitted with internal electrical conductivity probes to determine the migration of the diffusive front. A multi chemical species synthetic landfill leachate was contrived to simulate and evaluate natural pollutant conditions. A computational method for determining mineralogy from geochemical data was also developed. It was found that sorptive processes are mostly controlled by the quality and type of fine grained phyllosilicates and the individual chemical species involved exhibited linear, Freundlich, as well as Langmuir sorption properties. Effective diffusion and sorption coefficients were also determined using POLLUTEv6 (GAEA, 1997) software and receptor reservoir concentrations for K, Na, Ca, Cu, NH4, Cl, NO3, SO4, and concentration totals at predetermined time intervals. Anion exclusion proved to be a major factor in the diffusion process and was used to explain many observed anomalies. Furthermore, diffusion coefficients were found not to be static with a multi chemical species leachate, but actually varied during the course of the experiment. Strong indications point toward the major role of pore space quality, shape, and form as control of diffusive properties of a geologic barrier. A correlation of CECNa of the samples with De may point to a possible deduction of diffusive properties for multi species leachates without extensive and time consuming laboratory tests
The first goal of this study was to develop cell lines with a stable expression of bio-fluorescent topo II and topo I. This was successfully achieved using a bicistronic vector system. Control experiments showed that proteins of expected size were expressed, and that GFP-tagged topos I, IIa, and IIb were active in the cells and fully integrated in the endogenous pools of the enzymes. These cell-lines provided a novel tool for investigating the cell biology of human DNA topoisomerases. Our most important finding was, that both types of mammalian topoisomerases are entirely mobile proteins that are in continuous and rapid flux between all compartments of the nucleus and between the cytososl and the chromosomes of mitotic cells. This was particularly surprising with regard to topo II, which is considered to be a structural component of the nuclear matrix and the chromosome scaffold. We must conclude that if this was the case, then these architectural structures appear to be much more dynamic than believed until now. In this context it should also be mentioned, that the alignment of topo II with the central axes of the chromosome arms, which has until now been considered a hall-mark of the enzyme’s association with the chromosomal scaffold, is not seen in vivo and can be demonstrated to be to some extent an artefact of immunohistochemistry. Furthermore, we show that the two isoforms of topo II (a and b) have a different localisation during mitotic cell division, supporting the general concept that topo II functions at mitosis are exclusively assigned to the a-form, whereas at interphase the two isoenzymes work in concert. Despite unrestricted mobility within the entire nuclear space, topoisomerases I and II impose as mostly nucleolar proteins. We show that this is due to the fact that in the nucleoli they are moving slower than in the nucleoplasm. The decreased nucleolar mobility cannot be due to DNA-interactions, because compounds that fix topoisomerases to the DNA deplete them from the nucleoli. Interestingly, the subnucleolar distribution of topoisomerases I and II was complementary. The type II enzyme filled the entire nucleolar space, but excluded the fibrial centers, whereas topo I accumulated at the fibrial centers, an allocation directed by the enzyme’s N-terminus. During mitosis, it also mediates association with the nucleolar organising regions of the acrocentric chromosomes. Thus, topo I stays associated with the rDNA during the entire cell-cycle and consistently colocalizes there with RNA-polymerase I. Finally, we show that certain cancer drugs believed to act by stabilising covalent catalytic DNA-intermediates of topoisomerases, do indeed immobilize the enzymes in living cells. Interestingly, these drugs do not target topoisomerases in the nucleoli but only in the nucleoplasm.
This work presents the analysis, 3D modeling and interpretation of gravity and aeromagnetic data of Jordan and Middle East. The potential field data delineate the location of the major faults, basins, swells, anticlines, synclines and domes in Jordan. The surface geology of Jordan and the immediate area east of the Rift is dominated by two large basins, the Al-Jafr basin in the south and the Al-Azraq-Wadi as Sirhan basin to the northeast. These two basins strike southeast-northwest and are separated by an anticlinal axis, the Kilwah-Bayir swell. The Karak Wadi El Fayha fault system occurs along the western flank of the swell. The Swaqa fault occurs on the southwest hinge of Al-Azraq basin and the Fuluq fault occurs on its northeast hinge. In the south west of Jordan, Wadi Utm-Quwaira and Disi-Mudawara fault zones are shown clearly in the aeromagnetic and gravity maps. The previous major faults are well correlated with the structural map of Jordan published by Bender (1968). 3D modeling of gravity data in the Dead Sea basin (DSB) was used together with existing geological and geophysical information to give a complete structural picture of the basin. The 3D models of the DSB show that the internal structure of the Dead Sea basin (DSB) is controlled by longitudinal faults and the basin is developed as a full graben bounded by sub-vertical faults along its long sides. In the northern planes of the 3D model, the accumulation of Quaternary (salt and marl) and Mesozoic (pre-rift) sediments are thinner than in the central and southern planes of the model. In the northern planes, the thickness of the Quaternary sediments is about 4 km, 5 km in the southern planes and it exceeds 8 km in the central planes of the DSR. The thickness of the pre-rift sediments reaches 10-12 km in the northern and southern planes and exceeds 15 km in the central planes of the DSR. The planes of the 3D models show that the depth to the crystalline basement under the eastern shoulders of the DSR is shallower than those beneath the western shoulders. It is about 3-5 km beneath the eastern shoulders and 7-9 km under the western shoulder of the DSR. The gravity anomaly maps of residual and first derivative gravity delineate the subsurface basins of widely varying size, shape, and depth along the Rift Valley. The basins are created by the combination of the lateral motion along a right-tending step over and normal faulting along the opposite sides. Al Bakura basin occupies the upper Jordanian River valley and extends into the southern Tiberias Lake. Bet Shean basin to the south of Al Bakura basin plunges asymmetrically toward the east. The Damia basin, comprising the central Jordan Valley and Jericho areas to the north of the Dead Sea is shallow basin (~600-800m deep). The Lisan basin is the deepest basin in the Rift. The 3D gravity models indicate a maximum of ~12 km of basin fill. Three basins are found in Wadi Araba area, Gharandal, Timna (Qa'-Taba) and Aqaba (Elat) basin. The three basins become successively wider and deeper to the south. The three regional gravity long E-W profiles (225 km) from the Mediterranean Sea crossing the Rift Valley to the east to the Saudi Arabia borders, show the positive correlation between topography and free air anomaly and strong negative Bouguer anomaly under the central part of the Dead Sea Basin (DSB) and normal regional Bouguer anomaly outside of the DSB in the transform valley. Depth to the top of the bedrock in the under ground of Jordan was calculated from potential field data. The basement crops out in the south west of Jordan and becomes deeper to northwards and eastwards to be about ~ 8 km below ground surface in the Risha area.
The present work consists of two parts. The first one deals with theoretical questions and tests the performance of orbitals obtained from a self-interaction free KS method, the LHFapproach, in multireference ab initio methods. The purpose of this part is to enable a more efficient computation of excitation energies, which is important for the spectroscopic characterization of many organic and bioorganic molecules. The second part focuses on bioorganic questions and studies the base pairing properties of the purine base xanthine in order to explain, e.g., the unusually high stability of selfpairing xanthine alanyl-PNA double strands and the mutagenicity of xanthine formed in DNA. Part1: In contrast to HF- and standard DFT-methods, the LHF-approach leads to a fully bound virtual orbital spectrum, because Coulomb self interactions are exactly canceled in the LHFansatz. Furthermore, the energies of the occupied orbitals are not upshifted, like it is the case for standard DFT-methods, so that Koopmans' theorem remains valid. In line with this, also the occupied LHF-orbitals are somewhat more compact than standard DFT-orbitals. The present work shows that both properties are of great benefit for MR methods. The virtual LHF-orbitals are well optimized and allow an efficient description of excited states and static correlation in both MRCI- and MRPT2-approaches. Furthermore, the higher compactness of the occupied LHF- compared to standard DFT-orbitals leads to a better description of the center ion of Rydberg states. However, for each of the two advantages mentioned at least one example molecule has been found, for which LHF-orbitals actually perform worse than HF-and/or standard DFT-orbitals. This shows, that even though LHF virtual orbitals allow an excellent MRCI- and MRPT2-description for the electronically excited states of a large number of molecules, this cannot be generalized and their performance needs to be tested for each individual case. In the second part of the present work, the base pairing properties of xanthine and xanthine derivatives were studied. The purpose of this part was to find an explanation for the unexpectedly high stability of the xanthine alanyl PNA double strand. Furthermore, it was analyzed, why xanthine, that is formed from guanine in DNA under chemical stress, is able to form mismatched base pairs with the pyrimidine base thymine. Stability of xanthine alanyl PNA: In the first step, the regioisomer present in the considered alanyl PNA was identified to be the N7-regioisomer of xanthine by a theoretical analysis of the 13C-NMR spectrum. To analyze the stability of the xanthine self-pairing, a simplified model was set up, in which the stability of the PNA double strand was explained solely by the energy contributions from H-bonding and base stacking. For that purpose, the dimerization and stacking energies for the xanthine-xanthine, guaninecytosine, adenine-thymine and xanthine-2,6-diaminopurine base pairs were computed using DFT and MP2 methods. Solvent effects were taken into account by the conductor like screening model. The influence of the peptide backbone on the stacking geometry was considered by force field optimizations. While the individual contributions from hydrogen bonding and stacking do not correlate with the melting temperature Tm, the sum of both correlates linearly with Tm. This correlation is somewhat surprising, because this means that the effects of the entropy and the molecular water environment either cancel or are similar for all systems compared. In this model, the stability of the xanthine selfpairing mainly stems from an enlarged stacking interaction, while the H-bonds give only minor contributions to the stability of the xanthine selfpaired double strand of alanyl-PNA. Base pairing properties of N9-Xanthine: The computation of the base pairing properties of N9-xanthine revealed a strong variation in the individual H-bond strengths for the selfpairing of xanthine, that range from -4 to -11 kcal/mol in the gas phase and -2.5 to -5 kcal/mol in polar solvent. By comparison with model systems it was shown that the strong variance of the H-bond strength is mainly due to attractive or repulsive secondary electrostatic interactions. For the homodimer of hypoxanthine it was shown that the increase of aromaticity in the pyrimidine ring upon dimer formation leads to a strengthening of the hydrogen bonds. Mutagenicity of hypoxanthine and xanthine: Several neutral and anionic Watson-Crick base pairs of xanthine were computed with MP2- and DFT-methods in order to explain the mutagenicity of hypoxanthine and xanthine. Also basepairs involving tautomeric forms of xanthine and hypoxanthine were considered. To evaluate the dimerization energies found, the dimers were classified into pairings that have the exact geometry of the canonical base pairs and those that realize a distorted Watson-Crick pairing mode. The computations show that a stable pairing which realizes the exact geometry of a canonical Watson Crick base pairing is only possible for the pairing of xanthine to cytosine, however, the base pairs are only weakly bound. The dimerization energies of both the neutral and the anionic pairing is around 0 kcal/mol, so that the xanthine-cytosine base pairs are incorporated into DNA solely because the base pairs fulfill the geometric demands of DNA polymerase, but it does not profit from any additional stabilization due to hydrogen bonding. The bonding that in the Watson-Crick pairing mode xanthine has almost no affinity to cytosine is in correspondence with the experimental result that the cytosine-xanthine base pair is incorporated into DNA at a much lower rate than the cytosine-guanine base pair, which has a very strong hydrogen bonding. While the affinity of xanthine to cytosine is very low, the computations predict that xanthine is able to form a stable Watson-Crick pairing with thymine. However, the pairing has a somewhat distorted Watson-Crick geometry, so that its high stability is outbalanced by the worsened fit to the binding pocket of DNA-polymerase. As a consequence, the xanthinethymine pairing is incorporated into DNA not at a faster, but only at a rate comparable to that of the xanthine-cytosine pairing.
Cellular proliferation, differentiation and survival in response to extracellular signals are controlled by the signal transduction pathway of Ras, Raf and MAP kinase. The Raf proteins are serine/threonine kinases with essential function in growth/differentiation/survival - related signal transduction events. In mammals, three functional (A-, B-, and C-Raf) genes were described. Biochemical studies suggest overlapping and differential utilization of Raf isozymes. However, the frequent co-expression of Raf isozymes and their multiple activators and effectors impedes the full understanding of their specific roles. The elucidation of these roles is important due to the involvement of the Ras/Raf/MEK/MAP kinase cascade in human disorders especially in tumor development and progression. B-Raf was shown to posses the strongest kinase activity among Raf kinases and display antiapoptotic properties. Mice deficient in B-Raf show overall growth retardation and die between E10.5 and E12.5 of vascular defects caused by excessive death of differentiated endothelial cells. To elucidate the redundancy of Raf isozymes during embryonic development and to rescue B-Raf-/- (KO) phenotype, B-Raf alleles were disrupted by introducing A-Raf cDNA under the control of endogenous B-Raf promoter. The resulting BRaf A-Raf/A-Raf (KIN) phenotype depends on genetic background. The living embryos displaying normal development but size reduction were found with low incidence at E12.5d-16.5d. All of them displayed the rescue of vascular system. One adult p20 mouse without any visible defects in development and behavior was obtained. On the other hand, the processes of neurogenesis and neural precursors migration in survived embryos were disturbed which led in some cases to underdevelopment of different brain compartments. TUNEL and cell proliferation (PCNA staining) assays revealed more apoptotic (E13.5d) and less proliferating(E12.5d cells within ventricular and sub-ventricular zones of brain ventricles and in striatum of KIN embryos. In addition, more apoptotic cells were detected in many other tissues of E13.5d and in lung of E16.5d KIN embryos but not in adult KIN mouse. p20 KIN mouse demonstrated reduced fraction of neural precursor cells in sub-granular zone of hippocampus and mature neurons in olfactory bulb. The other processes of neurogenesis were not disturbed in adult KIN animal. Fibroblasts obtained from KIN embryos demonstrated less proliferative ability and were more susceptible to apoptotic stimuli compared to WT. This was accompanied by the reduction of active ERK and Akt required for survival, and with decrease of inactive phosphorylated BAD. The kinetic of both ERK and Akt phosphorylation upon serum stimulation was delayed. All these data indicate that moderate A-Raf kinase activity can prevent the endothelial apoptosis but is not enough to completely rescue the other developmental consequences.
This thesis is concerned with the development of an on-line in-situ device for a chemical characterisation of flowing aerosols. The thesis describes the principles and most important features of such a system, allowing also on-line measurements using Raman spectroscopy as a diagnostic technique An analysis of the effect of forced oscillations on the motion of the particle dispersed in a gas flow is given in Chapter 2. Also the most important particle parameters are introduced. A review of the particle/fluid interaction in laminar air flows and the response of the particle is presented. In Chapter 3 the behaviour of the particle under different external conditions (ion bombardment and electric fields) is extended. A brief review of the most important particle charging theories (diffusion, field, and alternating potential charging) shows, that the effect of the electrical properties (represented by the dielectric constant) of the particles affects the charging process. A non-contact method for particle charge measurement was also presented. In the second part of the chapter, the interaction between the electric field and the charged particle for the purpose of particle trapping is illustrated. The most common systems like the two or four ring electrodynamic balance and the quadrupole trap are pointed out. In Chapter 4 a short review of the possibility of using scattered light to study aerosol particles is presented. First, the conditions and the facilities of using the Mie theory for particle size and refractive index determination are mentioned, then some features concerning the classical treatment of the Raman effect are presented Supported by the theoretical considerations exposed in Chapter 2, 3, and 4 the construction and the tests of different devices are presented in Chapter 5. Following the goal of the thesis, first an overview of the used materials and methods for particle generation is presented. Then, the constructed charging devices are described (from the mechanical and electrical point of view) and compared by measuring the acquired charge on the particle. Charged particles can be trapped in different containers. Two types of axially symmetric electrodynamic balances (two ring or an extended four ring configuration) were presented. For a deeper understanding these systems were studied using analytic and numerical methods. Considering the presented purpose of the work another type of trapping system has been developed, namely the quadrupole trap. A similar theoretical characterisation (in term’s of Mathieu equation) as for the electrodynamic balance was presented pointing out some specific features of this system. The incoming particle stream will be focused to the centre of the system simultaneously also the applied DC and AC potential onto the tube electrodes, yields a stable trapping of one or more particles. Chapter 6 consists of two parts: the system for single particle and for many particles investigation. The individual devices presented in Chapter 5 are now put together. The first part presents the method and the experimental realisation of a set-up for solid particle injection. In order to suppress the phase injection disadvantage found for the electrodynamic balance a developed program processes the information obtained from a particle cloud through an adequate electronic detection system, and reduces the number of particles until just one single particle is trapped. The method for one particle investigation can be extended for many particles. Using the presented set-up the particles are moved from one quadrupole to another and transformed from a particle cloud to a particle stream. A linearity between an external vertical mounted detector and the formed image of the particle stream on the CCD camera has been observed and used for simultaneous detection of many particles by Raman spectroscopy. For both methods Raman results are presented. One limitation of Raman Spectroscopy is the relatively long integration time needed for adequate signal-to-noise ratio. There are two factors which influence the integration time: first the incident radiation and the detector sensitivity, and second the intensity of the Raman bands. Using a CCD detector, the desired detector sensitivity should be achieved. So, the improvement of the signal-to-noise ratio should be the next goal in the system development. In order to reduce the integration time an optical system including optic fibres and the integration of an FT-Raman module operating in the visible region is planed. The goal of this work was to develop and construct an instrument for on-line in-situ single particle investigation by Raman spectroscopy. With the presented experimental set-up and the developed program the purpose of the work, the on-line in-situ near atmospheric pressure aerosol investigation was achieved. The Raman spectroscopy has been used successfully for a chemical characterisation of the aerosol particles.
The point of departure for the present work has been the following free boundary value problem for analytic functions $f$ which are defined on a domain $G \subset \mathbb{C}$ and map into the unit disk $\mathbb{D}= \{z \in \mathbb{C} : |z|<1 \}$. Problem 1: Let $z_1, \ldots, z_n$ be finitely many points in a bounded simply connected domain $G \subset \mathbb{C}$. Show that there exists a holomorphic function $f:G \to \mathbb{D}$ with critical points $z_j$ (counted with multiplicities) and no others such that $\lim_{z \to \xi} \frac{|f'(z)|}{1-|f(z)|^2}=1$ for all $\xi \in \partial G$. If $G=\mathbb{D}$, Problem 1 was solved by K?nau [5] in the case of one critical point, and for more than one critical point by Fournier and Ruscheweyh [3]. The method employed by K?nau, Fournier and Ruscheweyh easily extends to more general domains $G$, say bounded by a Dini-smooth Jordan curve, but does not work for arbitrary bounded simply connected domains. In this paper we present a new approach to Problem 1, which shows that this boundary value problem is not an isolated question in complex analysis, but is intimately connected to a number of basic open problems in conformal geometry and non-linear PDE. One of our results is a solution to Problem 1 for arbitrary simply connected domains. However, we shall see that our approach has also some other ramifications, for instance to a well-known problem due to Rellich and Wittich in PDE. Roughly speaking, this paper is broken down into two parts. In a first step we construct a conformal metric in a bounded regular domain $G\subset \mathbb{C}$ with prescribed non-positive Gaussian curvature $k(z)$ and prescribed singularities by solving the first boundary value problem for the Gaussian curvature equation $\Delta u =-k(z) e^{2u}$ in $G$ with prescribed singularities and continuous boundary data. This is related to the Berger-Nirenberg problem in Riemannian geometry, the question which functions on a surface R can arise as the Gaussian curvature of a Riemannian metric on R. The special case, where $k(z)=-4$ and the domain $G$ is bounded by finitely many analytic Jordan curves was treated by Heins [4]. In a second step we show every conformal pseudo-metric on a simply connected domain $G\subseteq \mathbb{C}$ with constant negative Gaussian curvature and isolated zeros of integer order is the pullback of the hyperbolic metric on $\mathbb{D}$ under an analytic map $f:G \to \mathbb{D}$. This extends a theorem of Liouville which deals with the case that the pseudo-metric has no zeros at all. These two steps together allow a complete solution of Problem 1. Contents: Chapter I contains the statement of the main results and connects them with some old and new problems in complex analysis, conformal geometry and PDE: the Uniformization Theorem for Riemann surfaces, the problem of Schwarz-Picard, the Berger-Nirenberg problem, Wittich's problem, etc.. Chapter II and III have preparatory character. In Chapter II we recall some basic results about ordinary differential equations in the complex plane. In our presentation we follow Laine [6], but we have reorganized the material and present a self-contained account of the basic features of Riccati, Schwarzian and second order differential equations. In Chapter III we discuss the first boundary value problem for the Poisson equation. We shall need to consider this problem in the most general situation, which does not seem to be covered in a satisfactory way in the existing literature, see [1,2]. In Chapter IV we turn to a discussion of conformal pseudo-metrics in planar domains. We focus on conformal metrics with prescribed singularities and prescribed non-positive Gaussian curvature. We shall establish the existence of such metrics, that is, we solve the corresponding Gaussian curvature equation by making use of the results of Chapter III. In Chapter V we show that every constantly curved pseudo-metric can be represented as the pullback of either the hyperbolic, the euclidean or the spherical metric under an analytic map. This is proved by using the results of Chapter II. Finally we give in Chapter VI some applications of our results. [1,2] Courant, H., Hilbert, D., Methoden der Mathematischen Physik, Erster/ Zweiter Band, Springer-Verlag, Berlin, 1931/1937. [3] Fournier, R., Ruscheweyh, St., Free boundary value problems for analytic functions in the closed unit disk, Proc. Amer. Math. Soc. (1999), 127 no. 11, 3287-3294. [4] Heins, M., On a class of conformal metrics, Nagoya Math. J. (1962), 21, 1-60. [5] K?nau, R., L?gentreue Randverzerrung bei analytischer Abbildung in hyperbolischer und sph?ischer Geometrie, Mitt. Math. Sem. Giessen (1997), 229, 45-53. [6] Laine, I., Nevanlinna Theory and Complex Differential Equations, de Gruyter, Berlin - New York, 1993.