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Fluids in Gravitational Fields – Well-Balanced Modifications for Astrophysical Finite-Volume Codes
(2021)
Stellar structure can -- in good approximation -- be described as a hydrostatic state, which which arises due to a balance between gravitational force and pressure gradient. Hydrostatic states are static solutions of the full compressible Euler system with gravitational source term, which can be used to model the stellar interior. In order to carry out simulations of dynamical processes occurring in stars, it is vital for the numerical method to accurately maintain the hydrostatic state over a long time period. In this thesis we present different methods to modify astrophysical finite volume codes in order to make them \emph{well-balanced}, preventing them from introducing significant discretization errors close to hydrostatic states. Our well-balanced modifications are constructed so that they can meet the requirements for methods applied in the astrophysical context: They can well-balance arbitrary hydrostatic states with any equation of state that is applied to model thermodynamical relations and they are simple to implement in existing astrophysical finite volume codes. One of our well-balanced modifications follows given solutions exactly and can be applied on any grid geometry. The other methods we introduce, which do no require any a priori knowledge, balance local high order approximations of arbitrary hydrostatic states on a Cartesian grid. All of our modifications allow for high order accuracy of the method. The improved accuracy close to hydrostatic states is verified in various numerical experiments.
In recent years <mi>PI</mi>-conjugated organoboron polymers and BN-doped polycyclic aromatic hydrocarbons have attracted a lot of interest due to their great potential in organic electronics. However, there are only few known examples of conjugated polymers with BN units in their main chain. Within this work silazane cleavage with silicon-boron (Si/B) exchange for the synthesis of a novel class of inorganic-organic hybrid polymers is demonstrated. These polymers consist of alternating NBN and para-phenylene units in the main chain. Photophysical studies and TD-DFT calculations for the polymer and molecular model systems were carried out, revealing a low extent of <mi>PI</mi>-conjugation across the NBN units. The new polymers can be used as macromolecular polyligands by a cross-linking reaction with a ZrIV compound. In the next chapter the synthesis and characterization of the first poly(p-phenylene iminoborane) is presented. This novel inorganic–organic hybrid polymer can be described as a BN analogue of the well-known poly(p-phenylene vinylene) (PPV) and is also accessible using the previously described Si/B exchange as synthetic strategy. Photophysical investigations and TD-DFT calculations on the polymer and corresponding model oligomers provide clear evidence for <mi>PI</mi>-conjugation across the B=N units and extension of the conjugation path with increasing chain length. Furthermore, a possible application of Si/B exchange for the synthesis of polysulfoximines was explored. Herein, diaryl sulfoximines and a p-phenylene bisborane serve as building blocks for new BN- and BO-doped alternating inorganic–organic hybrid copolymers. While the BN-linked polymers were accessible by a facile silicon/boron exchange protocol, the synthesis of polymers with B–O linkages in the main chain is achieved by salt elimination. In the last chapter the concept of Si/B exchange was investigated for the synthesis of BP-linked oligomers. Herein oligomers with sterically less demanding substituents (substituents: 2,4,6-trimethylphenyl or 2,4,6-tri-iso-propylphenyl) at the phosphorus are accessible using Si/B exchange, but the oligomer with Mes* (2,4,6-tri-tert-butylphenyl) as substituent needed a salt elimination pathway to give the desired product. Experimental data and theoretical investigations indicate, that the P-substituent has a high influence on the geometry of the phosphorus center and therefore on the possible conjugation over the BP units.
Bacterial small non-coding RNAs (sRNAs) play fundamental roles in controlling and finetuning gene expression in a wide variety of cellular processes, including stress responses, environmental signaling and virulence in pathogens. Despite the identification of hundreds of sRNA candidates in diverse bacteria by genomics approaches, the mechanisms and regulatory capabilities of these posttranscriptional regulators have most intensively been studied in Gram-negative Gammaproteobacteria such as Escherichia coli and Salmonella. So far, almost nothing is known about sRNA-mediated regulation (riboregulation) in Epsilonproteobacteria, including the major human pathogen Helicobacter pylori. H. pylori was even thought to be deficient for riboregulation as none of the sRNAs known from enterobacteria are conserved in Helicobacter and since it lacks the major RNA chaperone Hfq, which is crucial for sRNA function as well as stability in many bacteria. Nonetheless, more than 60 cis- and trans-acting sRNA candidates were recently identified in H. pylori by a global RNA sequencing approach, indicating that this pathogen, in principle, has the capability to use riboregulation for its gene expression control. However, the functions and underlying mechanisms of H. pylori sRNAs remained unclear.
This thesis focused on the first functional characterization and target gene identification of a trans-acting sRNA, RepG (Regulator of polymeric G-repeats), in H. pylori. Using in-vitro and in-vivo approaches, RepG was shown to directly base-pair with its C/Urich terminator loop to a variable homopolymeric G-repeat in the 5’ untranslated region (UTR) of the tlpB mRNA, thereby regulating expression of the chemotaxis receptor TlpB. While the RepG sRNA is highly conserved, the length of the G-repeat in the tlpB mRNA leader varies among different H. pylori isolates, resulting in a strain-specific tlpB regulation. The modification of the number of guanines within the G-stretch in H. pylori strain 26695 demonstrated that the length of the homopolymeric G-repeat determines the outcome of posttranscriptional control (repression or activation) of tlpB by RepG. This lengthdependent targeting of a simple sequence repeat by a trans-acting sRNA represents a new twist in sRNA-mediated regulation and a novel mechanism of gene expression control, since it uniquely links phase variation by simple sequence repeats to posttranscriptional regulation.
In almost all sequenced H. pylori strains, tlpB is encoded in a two gene operon upstream of HP0102, a gene of previously unknown function. This study provided evidence that HP0102 encodes a glycosyltransferase involved in LPS O-chain and Lewis x antigen production. Accordingly, this glycosyltransferase was shown to be essential for mice colonization by H. pylori. The coordinated posttranscriptional regulation of the tlpB-HP0102 operon by antisense base-pairing of RepG to the phase-variable G-repeat in the 5’ UTR of the tlpB mRNA allows for a gradual, rather than ON/OFF, control of HP0102 expression, thereby affecting LPS biosynthesis in H. pylori. This fine-tuning of O-chain and Lewis x antigen expression modulates H. pylori antibiotics sensitivity and thus, might be advantageous for Helicobacter colonization and persistence.
Whole transcriptome analysis based on microarray and RNA sequencing was used to identify additional RepG target mRNAs and uncover the physiological role of this riboregulator in H. pylori. Altogether, repG deletion affected expression of more than 40 target gene candidates involved various cellular processes, including membrane transport and adhesion, LPS modification, amino acid metabolism, oxidative and nitrosative stress, and nucleic acid modification. The presence of homopolymeric G-repeats/G-rich sequences in almost all target mRNA candidates indicated that RepG hijacks a conserved motif to
recognize and regulate multiple target mRNAs in H. pylori.
Overall, this study demonstrates that H. pylori employs riboregulation in stress response and virulence control. In addition, this thesis has successfully established Helicobacter as a new model organism for investigating general concepts of gene expression control by Hfq-independent sRNAs and sRNAs in bacterial pathogens.