Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

Expression profiling und rationale Expressionsoptimierung am Beispiel eines prokaryontischen Wirt-,Vektor-Systems

Durch globale Expressionsprofil-Analysen auf Transkriptom-, Proteom- oder Metabolom-Ebene können biotechnologische Produktionsprozesse besser verstanden und die Erkenntnisse für die zielgerichtete, rationale Optimierung von Expressionssystemen genutzt werden. In der vorliegenden Arbeit wurde die Überexpression einer Glukose-Dehydrogenase (EC 1.1.5.2), die von der Roche Diagnostics GmbH für die diagnostische Anwendung optimiert worden war, in Escherichia coli untersucht. Die Enzymvariante unterscheidet sich in sieben ihrer 455 Aminosäuren vom Wildtyp-Enzym und wird im sonst isogenen Wirt-/Vektor-System in signifikant geringeren Mengen (Faktor 5) gebildet. Das prokaryontische Expressionssystem wurde auf Proteom-Ebene charakterisiert. Die 2-dimensionale differenzielle Gelelektrophorese (DIGE) wurde zuvor unter statistischen Aspekten untersucht. Unter Berücksichtigung von technischen und biologischen Variationen, falsch-positiven (α-) und falsch-negativen (β-) Fehlern sowie einem daraus abgeleiteten Versuchsdesign konnten Expressionsunterschiede als signifikant quantifiziert werden, wenn sie um den Faktor ≥ 1,4 differierten. Durch eine Hauptkomponenten-Analyse wurde gezeigt, dass die DIGE-Technologie für die Expressionsprofil-Analyse des Modellsystems geeignet ist. Der Expressionsstamm für die Enzymvariante zeichnete sich durch eine höhere Variabilität an Enzymen für den Zuckerabbau und die Nukleinsäure-Synthese aus. Im Expressionssystem für das Wildtyp-Enzym wurde eine unerwartet erhöhte Plasmidkopienzahl nachgewiesen. Als potenzieller Engpass in der Expression der rekombinanten Glukose-Dehydrogenase wurde die Löslichkeitsvermittlung identifiziert. Im Expressionsstamm für das Wildtyp-Enzym wurden viele Proteine für die Biogenese der äußeren Membran verstärkt exprimiert. Als Folge dessen wurde ein sog. envelope stress ausgelöst und die Zellen gingen in die stationäre Wuchsphase über. Die Ergebnisse der Proteomanalyse wurden weiterführend dazu genutzt, die Produktionsleistung für die Enzymvariante zu verbessern. Durch den Austausch des Replikationsursprungs im Expressionsvektor wurde die Plasmidkopienzahl erhöht und die zelluläre Expressionsleistung für die diagnostisch interessantere Enzymvariante um Faktor 7 - 9 gesteigert. Um die Löslichkeitsvermittlung während der Expression zu verbessern, wurde die Plasmidkopienzahl gesenkt und die Coexpression von Chaperonen initiiert. Die Ausbeuten aktiver Glukose-Dehydrogenase wurden durch die Renaturierung inaktiven Produkts aus dem optimierten Expressionssystem insgesamt um einen Faktor von 4,5 erhöht. Somit führte im Rahmen dieser Arbeit eine proteombasierte Expressionsprofil-Analyse zur zielgerichteten, rationalen Expressionsoptimierung eines prokaryontischen Modellsystems.

Folic acid derivatives for PET imaging and therapy addressing folate receptor positive tumors

Folic acid, also known as vitamin B9, is the oxidized form of 5,6,7,8-tetrahydrofolate, which serves as methyl- or methylene donor (C1-building blocks) during DNA synthesis. Under physiological conditions the required amount of 5,6,7,8-tetrahydrofolate for survival of the cell is accomplished through the reduced folate carrier (RFC). In contrast, the supply of 5,6,7,8-tetrahydrofolate is insufficient under pathophysiological conditions of tumors due to an increased proliferation rate. Consequently, many tumor cells exhibit an (over)expression of the folate receptor. This phenomenon has been applied to diagnostics (PET, SPECT, MR) to image FR-positive tumors and on the other hand to treat malignancies related to a FR (over)expression. Based on this concept, a new 18F-labeled folate for PET imaging has been developed and was evaluated in vivo using tumor-bearing mice. The incorporation of oligoethylene spacers into the molecular structure led to a significant enhancement of the pharmacokinetics in comparison to previously developed 18F-folates. The liver uptake could be reduced by one sixth by remaining a tumor uptake of 3%ID/g leading to better contrast ratios. Encouraged by these results, a clickable 18F-labeled serine-based prosthetic group has been synthesized, again with the idea to improve the metabolic and pharmacokinetic profile of hydrophilic radiotracers. Therefore, an alkyne-carrying azido-functionalized serine derivative for coupling to biomolecules was synthesized and a chlorine leaving group for 18F-labeling, which could be accomplished using a microwave-assisted synthesis, a [K⊂2.2.2]+/carbonate system in DMSO. Radiochemical yields of 77±6% could be achieved.rnThe promising results obtained from the FR-targeting concept in the diagnostic field have been transferred to the boron neutron capture therapy. Therefore, a folate derivative was coupled to different boron clusters and cell uptake studies were conducted. The synthesis of the folate-boron clusters was straightforward. At first, a linker molecule based on maleic acid was synthesized, which was coupled to the boron cluster via Michael Addition of a thiol and alkene and subsequently coupled to the targeting moiety using CuAAC. The new conjugates of folate and boron clusters led to a significant increase of boron concentration in the cell of about 5-times compared to currently used and approved boron pharmaceuticals. rnMoreover, azido-folate derivatives were coupled to macromolecular carrier systems (pHPMA), which showed an enhanced and specific accumulation at target sites (up to 2.5-times) during in vivo experiments. A specific blockade could be observed up to 30% indicating an efficient targeting effect. A new kind of nanoparticles consisting of a PDLLA core and p((HPMA)-b-LMA)) as surfactants were developed and successfully radiolabeled via 18F-click chemistry in good RCYs of 8±3%rnThe nanoparticles were obtained via the miniemulsion technique in combination with solvent evaporation. The 18F-labeled nanoparticles were applied to in vivo testing using a mouse model. PET imaging showed a “mixed” biodistribution of low molecular weight as well as high molecular weight systems, indicating a partial loss of the 18F-labeled surfactant.rnIn conclusion, the presented work successfully utilized the FR-targeting concept in both, the diagnostic field (PET imaging) and for therapeutic approaches (BNCT, drug delivery systems). As a result, the high potential of FR-targeting in oncological applications has been shown and was confirmed by small animal PET imaging.rn