On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

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.

Genetic dynamics across early life stages in the tropical tree Prunus africana (Rosaceae)

In many plant species, the genetic template of early life-stages is formed by animal-mediated pollination and seed dispersal and has profound impact on further recruitment and population dynamics. Understanding the impact of pollination and seed dispersal on genetic patterns is a central issue in plant population biology. In my thesis, I investigated (i) contemporary dispersal and gene flow distances as well as (ii) genetic diversity and spatial genetic structure (SGS) across subsequent recruitment stages in a population of the animal-pollinated and dispersed tree Prunus africana in Kakamega Forest, West Kenya. Using microsatellite markers and parentage analyses, I inferred distances of pollen dispersal (father-to-mother), seed dispersal/maternal gene flow (mother-to-offspring) as well as paternal gene flow (father-to-offspring) for four early life stages of the species (seeds and fruits, current year seedlings, seedlings ≤ 3yr, seedlings > 3yr). Distances of pollen and seed dispersal as well as paternal gene flow were significantly shorter than expected from the spatial arrangement of trees and sampling plots. They were not affected by the density of conspecific trees in the surrounding. At the propagule stage, mean pollen dispersal distances were considerably (23-fold) longer than seed dispersal distances, and paternal gene flow distances exceeded maternal gene flow by a factor of 25. Seed dispersal distances were remarkably restricted, potentially leading to a strong initial SGS. The initial genetic template created by pollination and seed dispersal was extensively altered during later recruitment stages. Potential Janzen-Connell effects led to markedly increasing distances between offspring and both parental trees in older life stages. This showed that distance and density-dependent mortality factors are not exclusively related to the mother tree, but also to the father. Across subsequent recruitment stages, the pollen to seed dispersal ratio and the paternal to maternal gene flow ratio dropped to 2.1 and 3.4, respectively, in seedlings > 3yr. The relative changes in effective pollen dispersal, seed dispersal, and paternal gene flow distances across recruitment stages elucidate the mechanisms affecting the contribution of the two processes pollen and seed dispersal to overall gene flow. Using the same six microsatellite loci, I analyzed genetic diversity and SGS across five life stages, from seed rain to adults. Levels of genetic diversity within the studied P. africana population were comparable to other Prunus species and did not vary across life stages. In congruence with the short seed dispersal distances, I found significant SGS in all life stages. SGS decreased from seed and early seedling stages to older juvenile stages, and it was higher in adults than in late juveniles of the next generation. A comparison of the data with direct assessments of contemporary gene flow patterns indicate that distance- or density-dependent mortality, potentially due to Janzen-Connell effects, led to the initial decrease in SGS. Intergeneration variation in SGS could have been driven by variation in demographic processes, the effect of overlapping generations, and local selection processes. Overall, my study showed that complex sequential processes during recruitment contribute to the spatial genetic structure of tree populations. It highlights the importance of a multistage perspective for a comprehensive understanding of the impact of animal-mediated pollen and seed dispersal on spatial population dynamics and genetic patterns of trees.