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.

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.

Factorization method and irregular inclusions in electrical impedance tomography

In electrical impedance tomography, one tries to recover the conductivity inside a physical body from boundary measurements of current and voltage. In many practically important situations, the investigated object has known background conductivity but it is contaminated by inhomogeneities. The factorization method of Andreas Kirsch provides a tool for locating such inclusions. Earlier, it has been shown that under suitable regularity conditions positive (or negative) inhomogeneities can be characterized by the factorization technique if the conductivity or one of its higher normal derivatives jumps on the boundaries of the inclusions. In this work, we use a monotonicity argument to generalize these results: We show that the factorization method provides a characterization of an open inclusion (modulo its boundary) if each point inside the inhomogeneity has an open neighbourhood where the perturbation of the conductivity is strictly positive (or negative) definite. In particular, we do not assume any regularity of the inclusion boundary or set any conditions on the behaviour of the perturbed conductivity at the inclusion boundary. Our theoretical findings are verified by two-dimensional numerical experiments.