The massless two-loop two-point function and zeta functions in counterterms of Feynman diagrams

The main part of this thesis describes a method of calculating the massless two-loop two-point function which allows expanding the integral up to an arbitrary order in the dimensional regularization parameter epsilon by rewriting it as a double Mellin-Barnes integral. Closing the contour and collecting the residues then transforms this integral into a form that enables us to utilize S. Weinzierl's computer library nestedsums. We could show that multiple zeta values and rational numbers are sufficient for expanding the massless two-loop two-point function to all orders in epsilon. We then use the Hopf algebra of Feynman diagrams and its antipode, to investigate the appearance of Riemann's zeta function in counterterms of Feynman diagrams in massless Yukawa theory and massless QED. The class of Feynman diagrams we consider consists of graphs built from primitive one-loop diagrams and the non-planar vertex correction, where the vertex corrections only depend on one external momentum. We showed the absence of powers of pi in the counterterms of the non-planar vertex correction and diagrams built by shuffling it with the one-loop vertex correction. We also found the invariance of some coefficients of zeta functions under a change of momentum flow through these vertex corrections.

Analysis of nonlinear diffusion equations of second and fourth order

Wegen der fortschreitenden Miniaturisierung von Halbleiterbauteilen spielen Quanteneffekte eine immer wichtigere Rolle. Quantenphänomene werden gewöhnlich durch kinetische Gleichungen beschrieben, aber manchmal hat eine fluid-dynamische Beschreibung Vorteile: die bessere Nutzbarkeit für numerische Simulationen und die einfachere Vorgabe von Randbedingungen. In dieser Arbeit werden drei Diffusionsgleichungen zweiter und vierter Ordnung untersucht. Der erste Teil behandelt die implizite Zeitdiskretisierung und das Langzeitverhalten einer degenerierten Fokker-Planck-Gleichung. Der zweite Teil der Arbeit besteht aus der Untersuchung des viskosen Quantenhydrodynamischen Modells in einer Raumdimension und dessen Langzeitverhaltens. Im letzten Teil wird die Existenz von Lösungen einer parabolischen Gleichung vierter Ordnung in einer Raumdimension bewiesen, und deren Langzeitverhalten studiert.

Vibrational spectroscopic and electrochemical investigations of multi-centered heme proteins in biomimetic membrane architectures

Membrane proteins play a major role in every living cell. They are the key factors in the cell’s metabolism and in other functions, for example in cell-cell interaction, signal transduction, and transport of ions and nutrients. Cytochrome c oxidase (CcO), as one of the membrane proteins of the respiratory chain, plays a significant role in the energy transformation of higher organisms. CcO is a multi centered heme protein, utilizing redox energy to actively transport protons across the mitochondrial membrane. One aim of this dissertation is to investigate single steps in the mechanism of the ion transfer process coupled to electron transfer, which are not fully understood. The protein-tethered bilayer lipid membrane is a general approach to immobilize membrane proteins in an oriented fashion on a planar electrode embedded in a biomimetic membrane. This system enables the combination of electrochemical techniques with surface enhanced resonance Raman (SERRS), surface enhanced reflection absorption infrared (SEIRAS), and surface plasmon spectroscopy to study protein mediated electron and ion transport processes. The orientation of the enzymes within the surface confined architecture can be controlled by specific site-mutations, i.e. the insertion of a poly-histidine tag to different subunits of the enzyme. CcO can, thus, be oriented uniformly with its natural electron pathway entry pointing either towards or away from the electrode surface. The first orientation allows an ultra-fast direct electron transfer(ET) into the protein, not provided by conventional systems, which can be leveraged to study intrinsic charge transfer processes. The second orientation permits to study the interaction with its natural electron donor cytochrome c. Electrochemical and SERR measurements show conclusively that the redox site structure and the activity of the surface confined enzyme are preserved. Therefore, this biomimetic system offers a unique platform to study the kinetics of the ET processes in order to clarify mechanistic properties of the enzyme. Highly sensitive and ultra fast electrochemical techniques allow the separation of ET steps between all four redox centres including the determination of ET rates. Furthermore, proton transfer coupled to ET could be directly measured and discriminated from other ion transfer processes, revealing novel mechanistic information of the proton transfer mechanism of cytochrome c oxidase. In order to study the kinetics of the ET inside the protein, including the catalytic center, time resolved SEIRAS and SERRS measurements were performed to gain more insight into the structural and coordination changes of the heme environment. The electrical behaviour of tethered membrane systems and membrane intrinsic proteins as well as related charge transfer processes were simulated by solving the respective sets of differential equations, utilizing a software package called SPICE. This helps to understand charge transfer processes across membranes and to develop models that can help to elucidate mechanisms of complex enzymatic processes.

3D-ultrastructure, functions and stress responses of rhogocytes from the freshwater gastropods Biomphalaria glabrata and Lymnaea stagnalis

Rhogocytes, also termed ‘pore cells’, exist free in the hemolymph or embedded in the connective tissue of different body parts of molluscs, notably gastropods. These unique cells can be round, elongated or irregularly shaped, and up to 30 μm in diameter. Their hallmark is the so-called slit apparatus: i.e. pocket-like invaginations of the plasma membrane creating extracellular lacunae, bridged by cytoplasmic bars. These bars form distinctive slits of ca. 20 nm width. A slit diaphragm composed of proteins establishes a molecular sieve with holes of 20 x 20 nm. Different functions have been assigned to this special molluscan cell type, notably biosynthesis of the hemolymph respiratory protein hemocyanin. It has further been proposed, but not proven, that in the case of red-blooded snail species rhogocytes might synthesize the hemoglobin. However, the secretion pathway of these hemolymph proteins, and the functional role of the enigmatic slit apparatus remained unclear. Additionally proposed functions of rhogocytes, such as heavy metal detoxification or hemolymph protein degradation, are also not well studied. This work provides more detailed electron microscopical, histological and immunobiochemical information on the structure and function of rhogocytes of the freshwater snails Biomphalaria glabrata and Lymnaea stagnalis. By in situ hybridization on mantle tissues, it proves that B. glabrata rhogocytes synthesize hemoglobin and L. stagnalis rhogocytes synthesize hemocyanin. Hemocyanin is present, in endoplasmic reticulum lacunae and in vesicles, as individual molecules or pseudo-crystalline arrays. The first 3D reconstructions of rhogocytes are provided by means of electron tomography and show unprecedented details of the slit apparatus. A highly dense material in the cytoplasmic bars close to the diaphragmatic slits was shown, by immunogold labeling, to contain actin. By immunofluorescence microscopy, the protein nephrin was localized at the periphery of rhogocytes. The presence of both proteins in the slit apparatus supports the previous hypothesis, hitherto solely based on similarities of the ultrastructure, that the molluscan rhogocytes are phylogenetically related to mammalian podocytes and insect nephrocytes. A possible secretion pathway of respiratory proteins that includes a transfer mechanism of vesicles through the diaphragmatic slits is proposed and discussed. We also studied, by electron microscopy, the reaction of rhogocytes in situ to two forms of animal stress: deprivation of food and cadmium contamination of the tank water. Significant cellular reactions to both stressors were observed and documented. Notably, the slit apparatus surface and the number of electron-dense cytoplasmic vesicles increased in response to cadmium stress. Food deprivation led to an increase in hemocyanin production. These observations are also discussed in the framework of using such animals as potential environmental biomarkers.

Conceptual and normative issues of memory enhancement

Our growing understanding of human mind and cognition and the development of neurotechnology has triggered debate around cognitive enhancement in neuroethics. The dissertation examines the normative issues of memory enhancement, and focuses on two issues: (1) the distinction between memory treatment and enhancement; and (2) how the issue of authenticity concerns memory interventions, including memory treatments and enhancements. rnThe first part consists of a conceptual analysis of the concepts required for normative considerations. First, the representational nature and the function of memory are discussed. Memory is regarded as a special form of self-representation resulting from a constructive processes. Next, the concepts of selfhood, personhood, and identity are examined and a conceptual tool—the autobiographical self-model (ASM)—is introduced. An ASM is a collection of mental representations of the system’s relations with its past and potential future states. Third, the debate between objectivist and constructivist views of health are considered. I argue for a phenomenological account of health, which is based on the primacy of illness and negative utilitarianism.rnThe second part presents a synthesis of the relevant normative issues based on the conceptual tools developed. I argue that memory enhancement can be distinguished from memory treatment using a demarcation regarding the existence of memory-related suffering. That is, memory enhancements are, under standard circumstances and without any unwilling suffering or potential suffering resulting from the alteration of memory functions, interventions that aim to manipulate memory function based on the self-interests of the individual. I then consider the issue of authenticity, namely whether memory intervention or enhancement endangers “one’s true self”. By analyzing two conceptions of authenticity—authenticity as self-discovery and authenticity as self-creation, I propose that authenticity should be understood in terms of the satisfaction of the functional constraints of an ASM—synchronic coherence, diachronic coherence, and global veridicality. This framework provides clearer criteria for considering the relevant concerns and allows us to examine the moral values of authenticity. rn