This dissertation presents recent contributions to Ehrhart theory and its applications in Combinatorics. It investigates the enumeration and structure of integer points subject to linear inequalities from a geometric perspective.

We give an introduction in Chapter 1 and background on polyhedral geometry and combinatorial structures used in this work in Chapter 2.

In Chapter 3 we use Ehrhart polynomials to count combinatorial and geometric data in generalized permutahedra and hypergraphs. Generalized permutahedra are a class of polytopes with many interesting combinatorial subclasses. We introduce pruned inside-out polytopes, a generalization of inside-out polytopes introduced by Beck–Zaslavsky (2006), which have many applications such as recovering the famous reciprocity result for graph colorings by Stanley. We study the integer point count of pruned inside-out polytopes by applying classical Ehrhart polynomials and Ehrhart–Macdonald reciprocity. This yields a geometric perspective on and a generalization of a combinatorial reciprocity theorem for generalized permutahedra by Aguiar–Ardila (2023), Billera–Jia–Reiner (2009), and Karaboghossian (2022). Applying this reciprocity theorem to hypergraphic polytopes allows us to give a geometric proof of a combinatorial reciprocity theorem for hypergraph colorings by Aval–Karaboghossian–Tanasa (2020). Aside from the reciprocity for generalized permutahedra, this proof relies only on elementary geometric and combinatorial properties of hypergraphs and their associated polytopes.

In Chapter 4, which is joint work with Eleonore Bach and Matthias Beck, we investigate the coefficients of the Ehrhart polynomial for special classes of zonotopes associated with signed graphs. There is a well-established dictionary between zonotopes, hyperplane arrangements, and (oriented) matroids. Arguably one of the most famous examples is the class of graphical zonotopes, also called acyclotopes, which encode subzonotopes of the type-A root polytope, the permutahedron. Stanley gave a general interpretation of the coefficients of the Ehrhart polynomial (integer-point counting function for a polytope) of a zonotope via linearly independent subsets of its generators. Applying this to the graphical case shows that Ehrhart coefficients count (labeled) forests of the graph of fixed sizes. Our first goal is to extend and popularize this story to other root systems, which on the combinatorial side is encoded by signed graphs analogously to the work by Greene–Zaslavsky (1983). We compute the Ehrhart polynomial of the acyclotope in the signed case, and we give a matroid-dual construction. This gives rise to tocyclotopes and we compute their Ehrhart polynomials. Applying the same duality construction to a general integral matrix leads to a lattice Gale zonotope, whose face structure was studied by McMullen (1971). We describe the Ehrhart polynomials of lattice Gale zonotopes in terms of the given matrix.

Chapter 5 is joint work with Matthias Beck and Sophia Elia. Here, we extend Ehrhart theory to consider rational dilates of polytopes. The Ehrhart quasipolynomial of a rational polytope P encodes fundamental arithmetic data of P, namthe number of integer lattice points in positive integral dilates of P. The enumerative theory of lattice points in rational (equivalently, real) dilates of rational polytopes is much younger, starting with work by Linke (2011), Baldoni–Berline–Köppe–Vergne (2013), and Stapledon (2017). We introduce a generating-function ansatz for rational Ehrhart quasipolynomials, which unifies several known results in classical and rational Ehrhart theory. In particular, we define γ-rational Gorenstein polytopes, which extend the classical notion to the rational setting and encompass the generalized reflexive polytopes studied by Fiset–Kasprzyk (2008) and Kasprzyk–Nill (2012).

In Chapter 6, which is joint work with Alexander E. Black and Raman Sanyal we study poset permutahedra, an interesting class of polytopes arising as monotone path polytopes of order polytopes. Poset permutahedra are an amalgamation of order polytopes and permutahedra. We show that poset permutahedra give a unifying perspective on several recent classes of polytopes that occurred, for example, in connection with colorful subdivisions of polygons and Hessenberg varieties. As with order polytopes, the geometry and the combinatorics of poset permutahedra can be completely described in terms of the underlying poset. As applications of our results, we give a combinatorial description of the h-vectors of the partitioned permutahedra of Horiguchi–Masuda–Shareshian–Song (2024) and poset generalizations of Landau’s score sequences of tournaments. To prove our results, we show that poset permutahedra arise from order polytopes via the fiber polytope construction of Billera–Sturmfels (1992).

In ferroelectric materials, the properties such as Curie temperature, polarization switching and ferroelectric domain patterns, are very sensitive to the electrical, mechanical and chemical boundary conditions. This is particularly true at the nanoscale where minimization of the depolarization field drives the formation of new polarization patterns, including whirling ones. In this work, we explore the ferroelectric properties of epitaxial BaTiO3 nanostructures on silicon, with the objective to understand the effect of lateral scaling (< 500 nm) on ferroelectricity and to define routes to stabilize polar textures. The research begins with the investigation of He and Ne focused ion beam milling to fabricate BaTiO3 nanopillars with sub-500 nm diameters from single-crystalline BaTiO3. While He ion irradiation induces surface swelling and blistering due to He nanobubble formation, Ne ion milling proves to be a highly effective method to fabricate BaTiO3 nanopillars. They consist of a defect-free single-crystalline core surrounded on the top and lateral sidewalls by a defect-rich crystalline region and an outer Ne-implanted amorphous shell. We demonstrate that the geometry and beam-induced damage of the nanopillars can be precisely controlled via patterning parameters, establishing Ne ion milling as a useful technique for the rapid prototyping of crystalline nanostructures. Second, we investigate ferroelectricity in 20 nm-thick single-crystalline BaTiO3 nanodisks with diameters ranging from 400 nm down to 100 nm, fabricated using Ne ion milling from a 20 nm-thick epitaxial BaTiO3 film grown on SrTiO3-buffered silicon. The nanodisks are ferroelectric, with a Curie temperature ranging between 230 and 270 °C. Decreasing the diameter leads to an increased amount of Pup polarization relatively to Pdown. Signatures of polar textures emerge in the 100 nm nanodisks in both the lateral and vertical directions. Three distinct configurations are observed for the out-of-plane polarization patterns, consistent with existing theoretical predictions. The up-oriented polarization component can be progressively switched to a down-oriented state using electrical pulses. Third, we present the realization of chiral topological polar states in BaTiO3 nanostructures on silicon. The single crystalline nanoislands, grown by molecular beam epitaxy, are embedded in a continuous 20 nm-thick BaTiO3 layer on SrTiO3-buffered silicon and have a trapezoidal shape with lateral dimensions as small as 30-60 nm. They exhibit a center down-convergent polarization pattern with a swirling lateral component, which confers chirality. The center down-convergent pattern can be electrically switched to a center up-divergent one, occasionally passing through metastable states as experimentally observed and predicted in theoretical simulation. Engineering the shape of nanostructures (a trapezoidal shape similar to a narrowing funnel) is an original and highly promising route to design chiral polar textures. Finally, we investigate optical switching and domain modification in epitaxial BaTiO3 thin films on silicon. The as-grown films contains both a-domains (with in-plane polarization) and c-domains (with out-of-plane polarization). Upon UV laser irradiation (325 nm), ferroelastic and ferroelectric switchings occur leading to a mostly Pup single polarization orientation. Major structural changes are observed, which involve defect motions and full strain relaxation to bulk c-axis BaTiO3. We propose that this structural transformation and the resulting Pup domain configuration are triggered by high strain/stress fields resulting from internal electric fields created by the spatial separation of the photoexcited carriers and by internal heating. Our findings advance the understanding of nanoscale ferroelectrics on silicon, particularly in epitaxial BaTiO3 nanostructures and brings new perspectives particularly for the realization of chiral polar textures. By investigating the effects of lateral miniaturization on ferroelectricity and exploring both electrical and optical stimuli for domain control, this thesis highlights the potential of BaTiO3-based nanostructures for nanoelectronic applications in CMOS technology.

This dissertation explores novel mechanisms underlying ion channel function and regulation by examining three proteins with distinct external stimuli: the mechanosensitive channel of large conductance from Escherichia coli, EcMscL, the voltage-gated proton channel from Karlodinium veneficum, KvHv1, and the cation channel channelrhodopsin-1 from Chlamydomonas augustae, CaChR1. Initially, we tested the force-from-lipid gating model for EcMscL by incorporating a photoswitchable lipid into artificial membrane. This strategy enabled modulation of channel activity through light-driven manipulation and therefore providing us with support for the lipid-based gating hypothesis while presenting a novel technique for light-controlled ion channel activation. Additionally, chemical activation of the protein provided information about activation in the absence of mechanical stimuli and the gating model of the system. Furthermore, the structural simplicity of KvHv1, suggests it as a model protein for biophysical studies. Its functional properties and ion selectivity region offers fundamental insights into activation and regulation of voltage-gated proton channels. Mutation studies as well as spectroscopical investigation (in collaborations), shade light to the selectivity filter and its dynamics. Notably, inhibitory studies with the trivalent cation La3+ are suggesting a new model of activation. Finally, this work also presents for the first time the structural characterization of CaChR1 ground state obtained via CryoEM providing further support to previous spectroscopic results with detailed structural analysis. Comparative studies with a structurally homologous channelrhodopsin provided extra information over key amino acid residues governing its photocycle. Collectively, the investigation of EcMscL, KvHv1, and CaChR1 presented here enrich our understanding of ion channel’s function and manipulation, while offering substantial groundwork for future studies aimed at elucidating complex molecular mechanisms of channel activation and regulation.

The perfluorinated Cp* anion [C5(CF3)5]− is the extremely electron deficient counterpart of the well-studied Cp* ligand [C5(CH3)5]−. Although its first synthesis took place as early as 1980, the perfluorinated Cp* remained a synthetic dead end for decades, due to its low reactivity. Here, the preparation and full characterization of its first coordination complex [Rh(COD)(C5(CF3)5)] (COD = 1,5-cyclooctadiene) is presented. This allowed for extraordinary insights on the bonding situation between a metal and an electron-poor Cp ligand and revealed [C5(CF3)5]− as the weakest bound Cp ligand known.

The weakly bonding character of the perfluorinated Cp* is demonstrated by the quantitative and even reversible substitution by toluene to the cationic [Rh(COD)(PhMe)][C5(CF3)5] complex. Also the metallocenes [M(C5H5)(C5(CF3)5)] (M = Fe, Ru) are studied with respect to an unprecedented substitution lability of the perfluorinated Cp* ligand. Their photolysis in MeCN not only yields [M(C5H5)(MeCN)3][C5(CF3)5], but also reveals a unique photo/thermoswitchability by the back-reaction to the corresponding ruthenocene.

The low nucleophilicity and high oxidative resistance of [C5(CF3)5]− is further demonstrated by the coexistence with electrophilic and oxidizing cations and its introduction into the group of weakly coordinating carbanions (WCCAs). The prepared salts comprise hydride-accepting [(C6H5)3C]+, valuable Ag(I) reagents, oxidizing [Fe(C5H5)2]+ or [N(p-C6H4Br)3]+ and Brønsted acidic [H(m,m-NC5H3F2)2]+.

The preparation of the first complete series of coinage metal Cp coordination compounds with [M(C5(CF3)5)(PtBu3)] (M = Cu, Ag, Au) demonstrates the ability of the perfluorinated Cp* to stabilize metal centers by its extreme oxidative resistance. The binding modes between metal and ligand range from η3 to η1 and illustrate the coordinative versatility of [C5(CF3)5]−.

The impact of the perfluorinated Cp* ligand on the redox chemistry of metal complexes is demonstrated by the synthesis of the extremely electron deficient ferrocene [Fe(C5H5)(C5(CF3)5)]. Oxidation potentials of E1/2 = +1.35 V (vs. Fc/Fc+) represent the highest reported values obtained for any ferrocene. The corresponding stable and storable ferrocenium [Fe(C5H5)(C5(CF3)5)][AsF6] is the strongest organometallic oxidant to date and even capable of C-H activation.

Finally, the rhodocenium salt [Rh(C5(CH3)5)(C5(CF3)5)][BF4] is prepared. The surprisingly high reduction potentials E1/2 = −0.90 and −1.46 V (vs. Fc/Fc+) combined with the coordinative flexibility of [C5(CF3)5]− allow for the twofold reduction by decamethylcobaltocene [Co(C5(CH3)5)2]. The reported [Co(C5(CH3)5)2][Rh(C5(CH3)5)(C5(CF3)5)] not only represents the first structurally characterized 4d metallocene anion, but also shows an unprecedented coexistence with a metallocene cation.

Diese Habilitationsschrift vereint klinische und experimentelle Studien mit dem Ziel, diagnostische und therapeutische Verfahren in der Neurochirurgie zu optimieren und die Versorgung von Patient:innen mit Hirntumoren und vaskulären Erkrankungen des ZNS zu verbessern. Ein Schwerpunkt liegt auf der Weiterentwicklung der intraoperativen Tumorvisualisierung, der Etablierung molekularer und bildgebender Marker zur Charakterisierung von Gliomen sowie der Untersuchung biologischer Mechanismen, die Progression, Rezidivgeschehen und Therapieresistenz bestimmen.

In einer klinischen Phase-I-Studie wurde der Einsatz des Notch-Inhibitors RO4929097 in Kombination mit Temozolomid und Radiotherapie bei neu diagnostizierten malignen Gliomen untersucht. Die Behandlung erwies sich als sicher und gut verträglich und zeigte vielversprechende synergistische Effekte. Pharmakokinetische Analysen bestätigten das Eindringen des Wirkstoffs in das Parenchym, während Gewebestudien die Rolle des Notch-Signalwegs bei Gliomstammzellen und Angiogenese verdeutlichten. Gleichzeitig zeigte sich, dass Tumoren unter Therapie auf alternative angiogene Mechanismen ausweichen können, was die Notwendigkeit kombinierter Strategien unterstreicht.

Darüber hinaus wurde Fluorescein als optische Sonde für die Visualisierung von ZNS-Tumoren charakterisiert. Spektroskopische Untersuchungen belegten eine bathochrome Verschiebung und emissionsbandenabhängige Verbreiterung im Tumorgewebe, beeinflusst durch pH-Sensitivität und Konzentrationseffekte. Klinisch konnte gezeigt werden, dass fluoresceingestützte stereotaktische Biopsien die diagnostische Ausbeute erhöhen, die Anzahl notwendiger Biopsien um bis zu 50 % reduzieren und auch bei niedriggradigen Gliomen ohne Kontrastmittelanreicherung wertvolle Informationen liefern.

Weitere Arbeiten befassten sich mit der Pathophysiologie der Subarachnoidalblutung (SAB). Untersuchungen in Mausmodellen und an Patientenproben zeigten eine zeitlich-räumliche Akkumulation von neutrophilen extrazellulären Fallen (NETs). Die intravenöse Gabe von RNase A hob diese Ablagerungen auf und deutet auf eine mögliche Rolle von RNase in der angeborenen Immunantwort hin. Zur Standardisierung präklinischer SAB-Modelle wurde zudem ein MRT-gestützter Score zur Graduierung der Blutungsgröße etabliert. Insgesamt zeigen diese Arbeiten, dass die Kombination experimenteller und klinischer Ansätze Anknüpfungspunkte für die Weiterentwicklung diagnostischer und therapeutischer Verfahren in der Neurochirurgie bietet.

Eukaryotic precursor mRNAs contain noncoding regions or introns that must be removed, and the coding sequences or exons are ligated together to generate the mature mRNA. The spliceosome, an elaborate and dynamic multi-megadalton ribonucleoprotein complex, achieves RNA splicing. Alternative splicing enhances the genomes’ coding capacity and allows a quicker response to cellular stimuli via transcriptome-wide adjustments independent of de novo transcription. These transient responses, which are implemented immediately after cellular stimulation via changes in alternative splicing programs, are referred to as immediate early splicing switches. The role of immediate early splicing in controlling switches in gene expression in cell-type specific responses to stimuli has been underexplored. A transient alternative splicing switch upon T-cell activation is implemented via heterogenous ribonucleoprotein C (hnRNPC2 isoform) through transient phosphorylation. This study validated a possible mechanism for the hnRNPC2-phosphorylation-mediated alternative splicing switch in vitro using recombinantly produced hnRNPC WT and its phosphomimetic variant. The primary focus of this study was tool development to gain a deeper understanding of the splicing switches modulated by core spliceosomal components. Multiple highly conserved RNP remodeling enzymes guide and control the compositional and conformational rearrangements of the spliceosome that accompany each splicing event. Among these enzymes, the U5 snRNP-associated human BRR2 (SNRNP200) RNA helicase profoundly remodels the pre-catalytic spliceosome by unwinding U4/U6 di-snRNA to facilitate the transition to the activated spliceosome and therefore was targeted using small-molecule inhibitors. This dual cassette RNA helicase is tightly regulated to ensure splicing fidelity. Cryogenic electron microscopy (cryo-EM), in combination with single-particle analysis of these allosteric inhibitors, bound human BRR2, revealed large, global conformational changes in BRR2, altering the relative position of the helicase cassettes. Our findings underscore the utility of single-particle cryo-EM in uncovering ligand-induced conformational rearrangements that may be obscured in crystal structures and have implications for optimizing compounds that target the dynamic molecular machinery of the spliceosome. The mechanistic understanding of the small-molecule allosteric inhibition supported by high-resolution structures provided the basis for the rational design of next-generation compounds that could be utilized in studying splicing switches.

Carboxylic acids and organotrifluoroborate salts have been extensively explored as radical precursors for organic synthesis using photocatalysis or electrochemistry. Both approaches suffer from limitations in terms of price and sustainability due to the requirement of rare metals or complex setups. My doctoral thesis aimed to expand the applicability of these bench-stable precursors by exploring alternative approaches that do not require photocatalysts or electrochemical tools. In Chapter 2, I describe the development of a method for benzylic fluorination of phenylacetic acids that was realized by forming a charge-transfer complex between the fluorinating reagent Selectfluor and the organic base DMAP. This strategy is metal-free and does not require light irradiation to form C-centered radicals. The method described is two-fold, thanks to a solvent-dependent selectivity switch that allows selectively forming the decarboxylated product in aqueous conditions, or the α-fluoro-α-arylacetic acids in anhydrous conditions. In Chapter 3, I outlined the step-by-step development of a new paradigm for light-driven cross-couplings enabled by photoactive nickel complexes that can be activated through intramolecular charge transfer (ILCT) upon blue light irradiation. I studied donor-acceptor ligands formed by installing carbazole (Cz) units and bipyridine (bpy) motifs. These ligands accessed cross-coupling reactivity without adding exogenous photocatalysts, thus bypassing the use of rare metals. The first-generation ligand design (5,5'-Czbpy) enabled C(sp2)–heteroatom using aryl iodide starting materials. By synthesizing a small library of derivatives, I identified an improved ligand design (4,4'-Czbpy) that expanded the scope to aryl bromides. Moreover, this ligand facilitated light-mediated nickel-catalyzed C(sp2)–C(sp3) cross-couplings between aryl bromides and benzyl organotrifluoroborate salts. Thanks to extensive mechanistic studies, I could provide strong evidence for a new C(sp2)–C(sp3) cross-coupling mechanism. The key finding was that this ligand enabled the unprecedented transmetalation between a nickel intermediate and the organoboron starting material. This allowed me to propose a unified mechanistic paradigm for all cross-couplings enabled by Ni(Czbpy)X2-type catalysts, featuring a light-driven activation to access the key Ni(I) intermediate, followed by “dark” nickel cycles that proceed independently of light irradiation.

The process underlying vocal communication acquisition in humans, the most complex form of vocal communication, has been aptly named “Vocal Production Learning”. While human language remains unrivaled in complexity, a multitude of species have evolved individual hallmark features to approximate its intricacies and allow them to be ranked on a heterogenic spectrum. The zebra finch (Taeniopygia guttata) has been studied extensively and serves as an ideal model organism to investigate some of the characteristic features of vocal production learning: The auditory processing and integration of conspecific vocalizations and the potential for temporal and spectral adjustments of vocalizations during the critical developmental period. While behavioral approaches have provided insights into song learning, the neuronal mechanisms underlying this process remain poorly understood. The cortical vocal premotor nucleus HVC (proper name) is an integral part of the song system. In addition to receiving input from multiple upstream auditory nuclei, HVC innervates the downstream motor pathway, triggering song production, and sends efference copies of the motor program to the anterior forebrain pathway. To understand how representation of prominent temporal and spectral song features develops in the neuronal activity patterns of excitatory glutaminergic HVCRA/X projection- and local inhibitory GABAergic interneurons, I investigated their membrane potential during singing and listening to song, employing intracellular single- and extracellular multiunit recordings in awake juvenile and adult birds. During playback experiments, excitatory projection neurons of adult animals did not respond with consistent action potentials to either intact bird’s own song or to a pitch shifted or syllable swapped version thereof. In juvenile birds, however, precisely timed, highly robust response patterns temporally locked to individual syllables were elicited. These patterns occurred independent of the syllables position in the song. Furthermore, firing rates were altered in response to spectral shifts. Inhibitory interneurons in both adult and juvenile animals exhibited activity patterns precisely locked to the temporal aspects of the song while spectral song alterations only seemed to elicit limited responses in juvenile birds. In an additional set of experiments, I was able to provide evidence for a less efficient, less sparse representation of the premotor output program responsible for the elicitation of song production during singing in juvenile birds. These results indicate that the neuronal network in HVC undergoes a complex refinement process during song learning and maturation. The development of the inhibitory network is hypothesized to be responsible for the suppression of excitatory activity and ultimately the protection of the already learned temporal and spectral song features.

Background: Despite the control efforts, ascariasis remains a major public health concern. The introduction of regular preventive chemotherapy (PC) in endemic regions has led to a shift from high- to low-intensity Ascaris infections. These infections cannot be reliably detected by the standard diagnostic methods and thus act as reservoirs for sustained transmission. Furthermore, although the detrimental impacts of high-intensity Ascaris infections on nutrition, immunity, growth, and intellectual capacity are well established, both the short- and long-term impacts of low-intensity infections remain unknown. Additionally, Ascaris coexist in a dynamic interplay with the gut bacteria which are also linked to immune function and host metabolism. These interactions highlight the need to comprehensively examine Ascaris infections beyond their direct pathological effects, considering their broader impact on nutrition, microbiome and immune homeostasis. To address these gaps, we aimed to investigate the integrated effects of low-intensity Ascaris infections on nutrition, immunity and microbiome in schoolchildren living in an endemic setting. Additionally, by using the domestic pig as a human-relevant animal model, we aimed to gain preliminary insights into the natural killer (NK) cells functional disruptions triggered by a low-dose Ascaris infection and its potential to alter host susceptibility to Salmonella. Specifically, we aimed to: 1. Assess the diagnostic performance of copromicroscopy, multiplex-qPCR, and serology in the detection of low-intensity Ascaris infections. 2. Investigate the immune alterations associated with low-intensity Ascaris infections. 3. Determine the nutritional consequences of low-intensity Ascaris infections. 4. Analyze the gut microbiota composition and its associations with low-intensity Ascaris infection, immune responses, and nutritional status. 5. Evaluate how low-dose Ascaris infection modulates NK cell function in domestic pigs as a human-relevant model, to inform mechanisms relevant to human health outcomes during common coinfections in Ascaris-endemic human populations. Results: To precisely detect low-intensity Ascaris infections, we developed and optimized a multiplex-qPCR assay, which exhibited superior sensitivity compared to conventional microscopic techniques. Additionally, we identified IgG1 and IgG4 antibodies against adult Ascaris excretory-secretory products as potential accurate serological markers for current Ascaris infections and exposure, owing to their high accuracy and sensitivity, respectively. We observed a high prevalence of low-intensity Ascaris infections among schoolchildren four months following the administration of STH PC. The children's diet was predominantly carbohydrate-based with a low intake of protein-rich foods. Notably, we identified a relatively high prevalence of protein-energy malnutrition, reflected in low albumin levels, stunting and thinness, particularly among boys. Low-intensity Ascaris infections were negatively associated with zbfa (thinness) and zhfa (stunting) as well as ferritin levels. We show that Ascaris infection is associated with systemic memory CD4 responses, characterised by enhanced gut-homing capacity and a mixed Th1/Th2/Th17 cytokine profile and a mixed IgM/IgG/IgA/IgE antibody response. Notably, Ascaris-specific mucosal IgA1 responses correlated with Oscillospiraceae, Dorea formicigenerans, and Prevotella species which are all short-chain fatty acid-producing gut bacteria taxa known for their immunomodulatory properties. These microbial taxa were also linked to ferritin levels. Furthermore, we demonstrate that a low-dose Ascaris infection significantly impairs NK cells cytokine production and cytotoxicity both in the lungs and in the systemic circulation by altering transcription factors balance and upregulating inhibitory receptors. Conclusion: This study highlights the adverse effects of low-intensity Ascaris infections on nutrition, growth, and immunity. Low-intensity Ascaris infections may also modulate the gut microbiome indirectly by altering ferritin levels and mucosal immunity to foster specific microbial shifts. The profound suppression of NK cell functions by a low-dose Ascaris infection and during Ascaris-Salmonella coinfection indicate that Ascaris infection increases host susceptibility to coinfections and potentially influences disease outcomes. Our findings underscore the urgent need for highly sensitive diagnostic tools such as qPCR and serological markers to accurately ascertain the true burden of Ascaris infections. Future research should prioritize longitudinal human and parallel pig studies to understand the long-term impacts of low-intensity Ascaris infections and their broader implications for coinfections and disease outcomes in children to inform evidence-based interventions.

Computer‑aided drug design (CADD) plays a central role in modern drug development, expediting and streamlining the discovery process across a wide range of therapeutic targets. This dissertation focuses on the application of CADD to support the identification of novel inhibitors for two cancer‑relevant targets: Cytochrome P450 (CYP) 4A11 and protein phosphatase 1 (PP1). Cancer remains a major threat to human health, highlighting the need for advanced therapies with innovative pharmacological mechanisms. To date, no market‑approved anti‑cancer drugs targeting CYP4A11 or PP1 have been successfully developed, making both proteins highly promising targets. In this work, tailored computational strategies were employed to discover and optimize potential therapeutic candidates for these targets. In the first section, human CYP4A11, an enzyme critically involved in hepatic fatty acid oxidation, is analyzed. This reaction increases the generation of reactive oxygen species (ROS) and contributes to the pathogenesis of metabolic dysfunction‑associated steatotic liver disease (MASLD), leading to an increased risk of developing hepatocellular carcinoma (HCC). To identify novel CYP4A11 inhibitors, key structure‑based 3D pharmacophore interactions were extracted to enable virtual screening, followed by sequential filtering based on substructures and interaction patterns. The binding behavior of the most promising virtual hits was further assessed through both static and dynamic evaluations within the CYP4A11 binding site. The top candidates were experimentally tested using a luminescence‑based assay in permeabilized fission yeast cells. This workflow led to the identification of a novel set of imidazole‑ or triazole‑substituted small‑molecule inhibitors. Among these, the most potent candidates, C2 and C4, show nanomolar potency. In the second section, the serine/threonine phosphatase PP1 is investigated. This enzyme cat‑ alyzes the dephosphorylation of numerous essential proteins, thereby maintaining cellular homeostasis and regulating critical signaling pathways. Consequently, PP1 inhibition can induce cell death and is under investigation as a potential therapeutic mechanism in oncology. Microcystins (MCs) are high‑affinity PP1 binders that represent promising lead structures for anticancer drug development. However, their clinical application is hampered by challenges in selectivity and associated toxicity. In this dissertation, we present a structure‑guided analysis of PP1 aimed at improving the binding affinity of MC derivatives, conducted in collaboration with Professor Timo Niedermeyer, a leading expert in MC research with over a decade of experimental experience. We examined the flexibility of PP1 with a focus on its binding site and discovered a novel subpocket. To exploit this subpocket, semi‑synthetic MC derivatives were developed, and their binding modes were investigated in silico. Building on this analysis, a covalent docking protocol was applied to generate a shortlist of promising, optimized MC derivatives with potentially enhanced binding profiles. In summary, this thesis employs and develops integrated computational and experimental approaches for preclinical cancer drug discovery. Through molecular docking 3D pharmacophores, molecular dynamics simulations and experimental in vitro testing, we identified novel, potent CYP4A11 inhibitors and designed optimized PP1 binders.

The efficient exploration of chemical space is one of the great endeavours currently in the chemical sciences. This often relies on the construction of complex 3D molecules in a minimum number of steps, and the ability for these molecules to undergo late-stage functionalisation. In this pursuit, the fruitful merger of photochemistry and organoboron chemistry has provided a powerful platform for the generation of unique borylated scaffolds which can then undergo a variety of downstream derivatisations. Photochemistry allows for the mild access of high energy intermediates, which can undergo transformations otherwise unobtainable through thermally activated methods. Meanwhile the organoboron motif can act as the chameleon of organic chemistry, transforming into a variety of synthetically valuable functional groups. With the aim to “escape from flatland” in mind, this thesis describes the development of photochemical transformations generating 3D borylated organic molecules, which can provide a platform for the exploration of chemical space. Chapter 2 describes the development of a mild methodology to generate α-bimetalloid radicals from simple ambiphilic C1 units. The use of a Lewis base and light allowed for the selective activation of the C–I bond, which underwent homolytic scission. The generated radical could be intercepted with a variety of SOMOphiles, producing multifunctional 3D scaffolds that contain two synthetic handles. The mild mode of activation also allowed the strategic combination with EnT catalysis, providing access to the complimentary Z-stereoisomers of the allylic products. These highly functionalised molecules could then undergo several chemoselective manipulations to showcase there potential in exploring new chemical space. The mechanism for this reaction was then thoroughly studied via both experimental and computational investigations. Chapter 3 describes the novel excitation of simple borylated alkenes via EnT catalysis. Alkene scrambling provided a suitable reaction probe, with multiple boron residues reaching a photostationary state equilibrium indicative of excitation. The operating mechanism was supported via experimental mechanistic investigations including UV/Vis and CV analysis. Translation of this excitation model to an intermolecular [2+2] cycloaddition was unsuccessful, presumably due to short excited state lifetimes of the substrate. The modification to an intramolecular [2+2] cycloaddition alleviated this issue, allowing reactivity with acrylates and borylated alkenes. This provided access to valuable 3D borylated bicyclic scaffolds, which were derivatised to demonstrate there synthetic utility.

The synthesis of ribosomes is one of the major tasks in actively growing bacteria, where ribosomes can make up as much as 30% of the cellular dry mass. Therefore, diverse strategies are needed to regulate the synthesis of ribosomal proteins (r-proteins) and RNAs (rRNAs) to prevent energy waste during cell growth. Expression of the E. coli rpsJ operon, which encodes 11 r-proteins, is autogenously regulated by one of its products, r-protein L4. L4 is unique as it is the only E. coli r-protein that mediates autogenous control through transcriptional attenuation. An RNA element encoded by the operon’s leader region is involved in this attenuation process. The RNA can form five hairpin structures, HA to HE, followed by two attenuation sites, ATT and ATT’. L4 attenuates rpsJ transcription by stalling RNA polymerase at ATT and ATT’ sites, a process which is strictly dependent on NusA. To understand this regulatory event at a molecular level, single-particle cryogenic electron microscopy (cryo-EM) was used to determine the structures of E. coli transcription attenuation complexes (ATTCs) in the absence and presence of transcription factors, including NusA, L4, and the universal transcription factor NusG. These structures reveal hairpin-dependent stabilization of the paused transcription complex by NusA and L4, as well as the involvement of the NusA KH1 domain and the RNA polymerase (RNAP) β’ subunit in L4 binding. NusA contributes to transcription pausing by stabilizing the RNA hairpin HE at the RNA exit channel. An additional hairpin HD, sandwiched between L4 and NusA KH1-KH2 domains, is incorporated into the ATTC when L4 binds to the complex. In vitro transcription assays using a NusA variant that lacks the KH1-KH2 domains confirmed the importance of the NusA KH1-KH2 domains in the rpsJ attenuation process. Furthermore, the roles of L4 and its interactions with hairpin HD and RNAP were demonstrated through site-directed mutagenesis of L4 and RNAP, combined with in vitro transcription assays. E. coli has also evolved a transcription anti-termination complex (rrnTAC) to efficiently synthesize rRNAs. In rrnTACs, RNAP is modified at the RNA exit channel by a complex RNA chaperone composed of the transcription factors NusA, NusB, NusG, S10, and SuhB. This multi-factor RNA chaperone facilitates the co-transcriptional folding of nascent rRNA, which is a prerequisite for subsequent processing of the primary transcript into mature rRNAs. The first step in rRNA maturation is cleavage by RNase III. Upon completion of 16S rRNA transcription, a long, double-stranded RNA (dsRNA) stem (16S stem) is formed. This stem contains the recognition motif for RNase III cleavage, which generates the pre-16S rRNA. To investigate the molecular basis of co-transcriptional rRNA folding and processing, cryo-EM was used to determine structures of rrnTACs containing variants of the 16S stem that include the RNase III cleavage motif and resemble the pre-processed transcript of pre-16S RNA. NusA and the SuhB dimer anchor the 5’ end of the 16S stem near the RNA exit channel, creating a platform for dsRNA formation in a spatially defined region. Structures of rrnTACs bound by an inactive RNase III variant were also elucidated. The dimeric RNase III engages the 16S stem on the side opposite the RNAP-associated RNA chaperone and forms direct contacts not only with the dsRNA but also with NusA and one of the SuhB subunits. These findings reveal the structural basis of co-transcriptional, long-range RNA secondary structure formation by tethering the 5’ part of the nascent RNA to a multi-factor RNA chaperone, bringing it into proximity with the emerging 3’ part to promote dsRNA formation. Together, these molecular insights into ATTCs and rrnTACs provide a better understanding of the regulatory mechanisms governing ribosome synthesis during rapid bacterial growth and may inform the development of antibiotics targeting the bacterial ribosome synthesis pathway.

In this thesis, we report on several topics related to the stability of random dynamical systems. First, we show that a mechanism known as shear-induced chaos can induce chaotic behavior, as evidenced by a positive Lyapunov exponent, in a Stuart-Landau oscillator perturbed by additive white noise. This answers a question that has been raised several times in the literature . We then study a class of stochastic differential equations that allows for stronger shear than in the Stuart-Landau oscillator. This strong shear can cause the system to no longer admit a random attractor or to even lose strong completeness, i.e., to no longer admit a global stochastic flow. We call this mechanism shear-induced blowup. Furthermore, we derive two tight conditions on the growth of the shear term, under which the system is strongly complete and admits a set attractor, respectively. Combined with information about the sign of the largest Lyapunov exponent, this allows us to conclude whether the system is strongly and/or weakly synchronizing. For this, we introduce a new set of conditions for stochastic differential equations with additive noise under which the time-1 map satisfies a stable/unstable manifold theorem. These conditions are weaker than those previously available in the literature and, in particular, can handle cases for which the stochastic differential equation is not strongly complete. The final chapter of this dissertation deals with the stability of random dynamical systems in the context of machine learning. In particular, we study an overparameterized optimization task that is commonly encountered in modern deep learning. We characterize the set of interpolation solutions that are dynamically stable under two popular learning algorithms, gradient descent and stochastic gradient descent. Dynamical stability is related to generalization and implicit bias, a topic that is still poorly understood, despite the success of machine learning. Some of the results presented in this thesis are based on joint work with Maximilian Engel and Michael Scheutzow.

Mucins are heavily glycosylated proteins, with carbohydrates comprising up to 80% of their weight. They form the primary component of mucus, a complex protective hydrogel that covers all biointerfaces in mammals. Mucins play important biological roles in our body, e.g. protection against pathogens, yet the role of the glycans is still poorly understood. The primary objective of my doctoral research was to deconstruct mucin complexity by generating well-defined, fully synthetic mucin-like glyco-hydrogels using self-assembling systems. I worked on two approaches to create supramolecular mucin mimetics capable of forming hydrogels, which serve as models to study mucus and explore relationships between composition, structure, and properties. By mimicking natural mucin structures with previously established coiled-coil peptides or self-assembling oligosaccharides as backbones, and decorating them with carbohydrates, I aimed to understand the rules governing hydrogel formation to create tuneable and responsive synthetic mucin-like hydrogels. In Chapter 2 of the thesis, I synthesized various mucin-relevant well-defined oligosaccharides with Automated Glycan Assembly (AGA). I designed a novel building block (BB) for the installation of α-GalNAc with complete stereoselectivity, aiding access to mucin core structures. I also developed chemoenzymatic synthesis strategies to access sialylated structures, expanding the scope of this work. Five synthesized structures were used by the group of Prof. Dr. Koksch to decorate a hydrogel-forming peptide, hFF03, to generate simple mucus models. Regardless of the type of carbohydrate substitution, the hydrogels maintained similar secondary structures and exhibited consistent fiber morphology. In contrast, small differences in the carbohydrate composition affected the viscoelastic behavior. In Chapter 3 I analyzed how parameters connected to the solid-support affect the AGA outcomes for three model glycan sequences. The study showed that, while loading and reaction scale did not significantly influence the AGA outcome, the chemical nature of the linker dramatically altered the isolated yields. I identified that the major determinants of AGA yields are cleavage from the solid-support and post-AGA steps. The study suggests that loading and reaction scale don't significantly affect AGA, therefore offering insights for scaling up mucin-related glycan synthesis. In Chapter 4 I focused on cellulose-based (A8) supramolecular hydrogels with tunable properties to mimic native mucus. I synthesized three XA8C analogues carrying a 3,6-methylated glucose residue (C) and a saccharide epitope (X). Furthermore, I developed a chemoenzymatic method to create a sialylated analogue, Sia6GA8C, adding complexity to the toolbox of mucus-inspired hydrogels. In this thesis, I deconstructed the complexity of mucins by developing well-defined, artificial mucin-like glyco-hydrogels through innovative self-assembling systems. The established synthetic platforms and methodologies offer a versatile toolkit for further investigations into the biological roles of mucin-type glycosylation and the development of novel therapeutic strategies.

Infektionsprävention und -kontrolle sind essentiell zur Vorbereitung auf und Bekämpfung von Pandemien. Neben dem Einfluss auf die pandemische Resilienz ist Infektionsprävention ebenso entscheidend in Bezug auf antimikrobielle Resistenzen. Infektionsprävention generell und Händehygiene im Besonderen können dazu beitragen, sowohl die Entstehung als auch die Verbreitung von Resistenzen zu verhindern. In Westafrika treffen zwei entscheidende Herausforderungen aufeinander: begrenzte finanzielle Ressourcen im Gesundheitssystem mit lückenhafter infrastruktureller Ausstattung und häufige gesundheitliche Notlagen vor allem durch infektiöse Erkrankungen. Genau in dieser Region ist es demnach entscheidend Händehygiene als Grundpfeiler der Infektionsprävention zu stärken. Die vorliegende Habilitationsschrift stellt fünf wissenschaftliche Originalarbeiten zum Thema Herausforderungen der Infektionsprävention und -kontrolle in zwei westafrikanischen Ländern vor. Die Global Health-Perspektive wird dabei mit einem Mixed-Method-Ansatz vereint um so ein tiefgreifendes Verständnis zu schaffen, das eine kontextsensible Umsetzung ermöglicht. Besonderer Fokus liegt dabei auf der lokalen Produktion von Desinfektionsmittel als hochskalierbares und resilientes System zur Überwindung von globalen Abhängigkeiten. Die vorgelegten Arbeiten zeigen, dass die Multimodale Strategie der WHO zur Verbesserung der Händehygiene zum einen lokal adaptier- und anwendbar ist und sich zum anderen als effektiv zur Verbesserung von Wissen und Compliance auf allen Ebenen der Gesundheitsversorgung sowie zu Pandemiezeiten erweist. Durch die Einbeziehung kultureller sowie systemischer Gegebenheiten kann die Multimodale Strategie der WHO zur Verbesserung der Händehygiene, als globale Gesundheitsstrategie, in den vorliegenden Arbeiten lokal, evidenzbasiert und vor allem nachhaltig umgesetzt werden. Dadurch wird sowohl auf lokaler Ebene Infektionsprävention und Resilienz gestärkt, als auch auf globaler Ebene Pandemievorsorge und -bewältigung verbessert.

Biopolymers self-assemble to generate dynamic and complex functional materials that carry out sophisticated tasks. Inspired by nature, chemists have sought to create artificial analogs that mimic biopolymer self-assembly. Unlike peptides and nucleic acids, carbohydrates are less understood at the molecular level and have rarely been employed as scaffolds to construct self-assembling materials. Consequently, the potential of carbohydrates in supramolecular chemistry remains largely untapped. The primary objective of my doctoral research was to establish structure-property correlations for oligosaccharides and apply this understanding to develop design principles for creating carbohydrate foldamers and self-assembling materials. Molecular dynamic (MD) simulations played a central role in elucidating the structure, function, and stability of both natural and artificial oligosaccharide systems. In Chapter 2 of the thesis, I demonstrated that synthetic chitin oligomers self-assemble into platelets, which then aggregate into higher-order structures. Environmental humidity significantly affects their morphologies, emphasizing water's role in shaping chitin-based architectures. Different humidity levels produced various shapes, from undefined assemblies to well-defined chiral bundles, suggesting the potential to create multiple architectures on- demand. In Chapter 3, I conducted a systematic analysis of the factors affecting the conformational stability of a synthetic glycan hairpin. The modular design of the synthetic hairpin enabled the investigation of the effect of various chemical modifications, showing that longer strands enhance conformational stability and that the turn motif's intrinsic conformational proclivity is crucial for hairpin folding. These findings challenge the perception of glycans as flexible molecules, suggesting they can be designed to adopt rigid conformations. In Chapter 4, I developed a platform to screen the conformational space of glycans. By using a novel MD-based approach, multiple turn sequences were identified that fold into the unique conformation of an anti-parallel glycan hairpin, showcasing the platform's potential. The insights gained from studying carbohydrate materials and glycan foldamers culminated in the rational design of the world's first prototype for de novo glycan design. This work provides a foundation for the future design of oligosaccharides with potential applications in material science, medicine, and catalysis.

This dissertation addresses the synthesis, structural characterization, and physicochemical investigation of novel alkali-metal sulfido- and selenido-metalates containing 3d transition metals (such as iron, cobalt, chromium, and vanadium) as well as the post-transition metal bismuth. The research focuses on the structural, electronic, magnetic, optical, dielectric, and electrochemical properties of these compounds, aiming to systematically explore the relationship between crystal structure, coordination chemistry, and functionality. The study includes materials, such as, Na2[Fe3S4], K2[Fe3S4], K2[Co3S4] and K2[Cr3S4], where varying the chalcogen content and targeted substitutions led to the formation of structural motifs, such as, square-planar and square-pyramidal coordination geometries. These geometries are rare in classical transition metal chemistry and significantly influence the observed physical properties. The materials exhibit, among other things, antiferromagnetic behavior, frequency-dependent dielectric responses, and in some cases, noteworthy ionic conductivity. Additionally, the work explores how structural features, such as, metal-site defects or specific chalcogen-metal interactions, affect functional properties like conductivity and magnetic ordering. These findings provide a deeper understanding of structure–property relationships in this class of materials and serve as a foundation for the targeted development of such compounds with potential uses in energy and information technologies. Future studies should focus on more detailed electronic and transport analyses, particularly regarding the role of defects and substitution effects. Only on this basis can possible applications, such as, cathode materials, spintronic systems, or electrochemical storage devices, be meaningfully pursued.

This dissertation explores the context-dependent effects of tire wear particles and multiple concurrent anthropogenic stressors on soil ecosystems. In chapter 2, we address the impacts of TWPs with different delivery rates on soil physicochemical properties and microbial activities. By either adding TWPs to soils abruptly or gradually, this study showed that gradually-delivered TWPs negatively influenced the activity of carbon cycle-related enzymes, and abruptly-delivered TWPs had no significant effect. Abruptly-delivered TWPs increased the activity of nitrogen cycle-related enzymes, while gradually-delivered TWPs had no significant effect. It highlights that delivery rate of TWPs could be a key factor shaping the effects of TWPs on soil microbial activities. In chapter 3, we investigate if ageing influence the effects of TWP leachates on soil. TWPs were subjected to different ageing conditions, including mechanical-, thermal-, and UV-ageing. We found that comparing to pristine TWPs, the leachates of aged TWPs generated broader effects on soil physicochemical properties and microbial activities, and the response patterns were dependent on ageing conditions. This study suggested that ageing can alter the effects of TWP leachates on soil, and highlighted the necessity of considering ageing condition as a crucial factor when investigating the environmental effects of TWPs. In chapter 4, we explore how an increasing number of concurrent anthropogenic stressors affects plant-soil systems and the role of plant diversity in this process. Plant-soil systems with different plant diversity levels (3 vs. 9 species) were subjected to an increasing number of stressors (1, 2, 5 and 8) using random assemblages of plants and stressors from a predefined plant species pool and a stressor pool. We found not only directional changes in soil properties, functions and especially plant community composition, but also the diminishment of plant diversity effects as stressor number increased. This study broadens our insights into the ecological impacts of multifactorial environmental change and highlights the necessity of exploring the relationships between the number of anthropogenic stressors and the effect of plant diversity. Overall, this dissertation contributes to two critical areas of environmental research: the effects of TWPs on soil properties and functions, and key factors that alter these effects; how multiple anthropogenic stressors affect soil properties, functions, plant community composition, and the role of plant diversity in this process. Our work has advanced the knowledge about the ecological risks of global change, including microplastics and other anthropogenic stressors, in terrestrial ecosystems.

This dissertation systematically studied two emerging terrestrial microplastic pollutants, paint microplastics (MPs) and tire wear particles (TWPs), using innovative methodological approaches and comprehensive ecological assessments. Firstly, our research revealed a remarkably high concentration of paint MPs in urban soils, reaching up to 2.9 × 10⁷ particles per kilogram. Through chemical characterization of their polymeric constituents, we confirmed that these paint particles qualify as microplastics. This result represents the highest microplastic concentration reported in soils to date and highlights a clear vertical distribution pattern, with concentrations decreasing with increasing soil depth. Subsequent ecological evaluations demonstrated that paint MPs, especially those containing heavy metals, significantly affect soil physicochemical properties, microbial activity, and nutrient cycling. Their presence was associated with elevated soil pH and an enhancement of water-stable aggregate stability. Furthermore, the results underscored the influence of different polymeric compositions on particle size distribution and soil respiration dynamics. In addition, our research showed that soil storage conditions influence the observed ecological effects of TWPs, emphasizing the need for standardized experimental protocols to ensure comparability across studies. Moreover, the ecological effects of TWPs varied with environmental context, being modulated by soil properties and land-use intensity. These findings highlight the context-dependent nature of microplastic impacts in terrestrial ecosystems. Overall, this dissertation advances the field of terrestrial microplastic research through methodological innovation, ecological risk assessment, and the analysis of environmental modulators.

This dissertation demonstrates the interplay between perceptual and economic decision-making, two fields traditionally studied in isolation. It emphasizes how various forms of uncertainty both enable and necessitate their integration in real-world contexts. The research presented sheds light on the cognitive, computational, and psychophysiological mechanisms underlying this integration, while also exploring individual differences in adaptive behaviour.