Fluctuations in and out of equilibrium: Thermalization, quantum measurements and Coulomb disorder

This purely theoretical thesis covers aspects of two contemporary research fields: the non-equilibrium dynamics in quantum systems and the electronic properties of three-dimensional topological insulators. In the first part we investigate the non-equilibrium dynamics in closed quantum systems. Thanks to recent technologies, especially from the field of ultracold quantum gases, it is possible to realize such systems in the laboratory. The focus is on the influence of hydrodynamic slow modes on the thermalization process. Generic systems in equilibrium, either classical or quantum, in equilibrium are described by thermodynamics. This is characterized by an ensemble of maximal entropy, but constrained by macroscopically conserved quantities. We will show that these conservation laws slow down thermalization and the final equilibrium state can be approached only algebraically in time. When the conservation laws are violated thermalization takes place exponential in time. In a different study we calculate probability distributions of projective quantum measurements. Newly developed quantum microscopes provide the opportunity to realize new measurement protocols which go far beyond the conventional measurements of correlation functions. The second part of this thesis is dedicated to a new class of materials known as three-dimensional topological insulators. Also here new experimental techniques have made it possible to fabricate these materials to a high enough quality that their topological nature is revealed. However, their transport properties are not fully understood yet. Motivated by unusual experimental results in the optical conductivity we have investigated the formation and thermal destruction of spatially localized electron- and hole-doped regions. These are caused by charged impurities which are introduced into the material in order to make the bulk insulating. Our theoretical results are in agreement with the experiment and can explain the results semi-quantitatively. Furthermore, we study emergent lengthscales in the bulk as well as close to the conducting surface.

Improving safety and establishing episomal maintenance of Adeno-associated viral vectors

Adeno-associated viral (AAV) vectors are among the most widely used gene transfer systems in basic and pre-clinical research and have been employed in more than 160 clinical trials. AAV vectors are commonly produced in producer cell lines like HEK293 by co-transfection with a so-called vector plasmid and one (in this work) or two so-called helper plasmids. The vector plasmid contains the transgene cassette of interest (TEC) flanked by AAV’s inverted terminal repeats (ITRs) which serve as packaging signals, whereas the helper plasmid provides the required AAV and helper virus functions in trans. A pivotal aspect of AAV vectorology is the manufacturing of AAV vectors free from impurities arising during the production process. These impurities include AAV vector preparations that contain capsids containing prokaryotic sequences, e.g. antibiotic resistance genes originating from the producer plasmids. In the first part of the thesis we aimed at improving the safety of AAV vectors. As we found that encapsidated prokaryotic sequences (using the ampicillin resistance gene as indicator) cannot be re-moved by standard purification methods we investigated whether the producer plasmids could be replaced by Minicircles (MCs). MCs are circular DNA constructs which contain no functional or coding prokaryotic sequences; they only consist of the TEC and a short sequence required for production and purification. MC counterparts of a vector plasmid encoding for enhanced green fluorescent (eGFP) protein and a helper plasmid encoding for AAV serotype 2 (AAV2) and helper Adenovirus (Ad) genes were designed and produced by PlasmidFactory (Bielefeld, Germany). Using all four possible combinations of plasmid and MCs, single-stranded AAV2 vectors (ssAAV) and self-complementary AAV vectors (scAAV) were produced and characterized for vector quantity, quality and functionality. The analyses showed that plasmids can be replaced by MCs without decreasing the efficiency of vector production and vector quality. MC-derived scAAV vector preparations even exceeded plasmid-derived preparations, as they displayed up to 30-fold improved transduction efficiencies. Using MCs as tools, we found that the vector plasmid is the main source of encapsidated prokaryotic sequences. Remarkably, we found that plasmid-derived scAAV vector preparations contained a much higher relative amount of prokaryotic sequences (up to 26.1 %, relative to TEC) compared to ssAAV vector preparations (up to 2.9 %). By replacing both plasmids by MCs the amount of functional prokaryotic sequences could be decreased to below the limit of quantification. Additional analyses for DNA impurities other than prokaryotic sequences showed that scAAV vectors generally contained a higher amount of non-vector DNA (e.g. adenoviral sequences) than ssAAV vectors. For both, ssAAV and scAAV vector preparations, MC-derived vectors tended to contain lower amounts of foreign DNA. None of the vectors tested could be shown to induce immunogenicity. In summary we could demonstrate that the quality of AAV vector preparations could be significantly improved by replacing producer plasmids by MCs. Upon transduction of a target tissue, AAV vector genomes predominantly remain in an episomal state, as duplex DNA circles or concatemers. These episomal forms mediate long-term transgene expression in terminally differentiated cells, but are lost in proliferating cells due to cell division. Therefore, in the second part of the thesis, in cooperation with Claudia Hagedorn and Hans J. Lipps (University Witten/Herdecke) an AAV vector genome was equipped with an autonomous replication element (Scaffold/matrix attachment region (S/MAR)). AAV-S/MAR encoding for eGFP and a blasticidin resistance gene and a control vector with the same TEC but lacking the S/MAR element (AAV-ΔS/MAR) were produced and transduced into highly proliferative HeLa cells. Antibiotic pressure was employed to select for cells stably maintaining the vector genome. AAV-S/MAR transduced cells yielded a higher number of colonies than AAV-ΔS/MAR-transduced cells. Colonies derived from each vector transduction were picked and cultured further. They remained eGFP-positive (up to 70 days, maximum cultivation period) even in the absence of antibiotic selection pressure. Interestingly, the mitotic stability of both AAV-S/MAR and control vector AAV-ΔS/MAR was found to be a result of episomal maintenance of the vector genome. This finding indicates that, under specific conditions such as the mild selection pressure we employed, “common” AAV vectors persist episomally. Thus, the S/MAR element increases the establishment frequency of stable episomes, but is not a prerequisite.