Kinetic and affinity analysis of hybridization reactions between PNA probes and DNA targets using surface plasmon field-enhanced fluorescence spectroscopy (SPFS)

Sequenz spezifische biomolekulare Analyseverfahren erweisen sich gerade im Hinblick auf das Humane Genom Projekt als äußerst nützlich in der Detektion von einzelnen Nukleotid Polymorphismen (SNPs) und zur Identifizierung von Genen. Auf Grund der hohen Anzahl von Basenpaaren, die zu analysieren sind, werden sensitive und effiziente Rastermethoden benötigt, welche dazu fähig sind, DNA-Proben in einer geeigneten Art und Weise zu bearbeiten. Die meisten Detektionsarten berücksichtigen die Interaktion einer verankerten Probe und des korrespondierenden Targets mit den Oberflächen. Die Analyse des kinetischen Verhaltens der Oligonukleotide auf der Sensoroberfläche ist infolgedessen von höchster Wichtigkeit für die Verbesserung bereits bekannter Detektions - Schemata. In letzter Zeit wurde die Oberflächen Plasmonen feld-verstärkte Fluoreszenz Spektroskopie (SPFS) entwickelt. Sie stellt eine kinetische Analyse - und Detektions - Methode dar, die mit doppelter Aufzeichnung, d.h. der Änderung der Reflektivität und des Fluoreszenzsignals, für das Interphasen Phänomen operiert. Durch die Verwendung von SPFS können Kinetikmessungen für die Hybridisierung zwischen Peptid Nukleinsäure (PNA), welche eine synthetisierte Nukleinsäure DNA imitiert und eine stabilere Doppelhelix formt, und DNA auf der Sensoroberfläche ausgeführt werden. Mittels einzel-, umfassend-, und titrations- Experimenten sowohl mit einer komplementär zusammenpassenden Sequenz als auch einer mismatch Sequenz können basierend auf dem Langmuir Modell die Geschwindigkeitskonstanten für die Bindungsreaktion des oligomer DNA Targets bzw. des PCR Targets zur PNA ermittelt werden. Darüber hinaus wurden die Einflüsse der Ionenstärke und der Temperatur für die PNA/DNA Hybridisierung in einer kinetischen Analyse aufgezeigt.

Virtual Compton scattering in baryon chiral perturbation theory

This thesis is concerned with the calculation of virtual Compton scattering (VCS) in manifestly Lorentz-invariant baryon chiral perturbation theory to fourth order in the momentum and quark-mass expansion. In the one-photon-exchange approximation, the VCS process is experimentally accessible in photon electro-production and has been measured at the MAMI facility in Mainz, at MIT-Bates, and at Jefferson Lab. Through VCS one gains new information on the nucleon structure beyond its static properties, such as charge, magnetic moments, or form factors. The nucleon response to an incident electromagnetic field is parameterized in terms of 2 spin-independent (scalar) and 4 spin-dependent (vector) generalized polarizabilities (GP). In analogy to classical electrodynamics the two scalar GPs represent the induced electric and magnetic dipole polarizability of a medium. For the vector GPs, a classical interpretation is less straightforward. They are derived from a multipole expansion of the VCS amplitude. This thesis describes the first calculation of all GPs within the framework of manifestly Lorentz-invariant baryon chiral perturbation theory. Because of the comparatively large number of diagrams - 100 one-loop diagrams need to be calculated - several computer programs were developed dealing with different aspects of Feynman diagram calculations. One can distinguish between two areas of development, the first concerning the algebraic manipulations of large expressions, and the second dealing with numerical instabilities in the calculation of one-loop integrals. In this thesis we describe our approach using Mathematica and FORM for algebraic tasks, and C for the numerical evaluations. We use our results for real Compton scattering to fix the two unknown low-energy constants emerging at fourth order. Furthermore, we present the results for the differential cross sections and the generalized polarizabilities of VCS off the proton.

Mathematical aspects of Feynman integrals

In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals.rnrnThe integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph.rnrnStarting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative step to an abstract combinatorial problem, known as Hironaka's polyhedra game. We present a publicly available implementation of the improved algorithm. Furthermore we explain the relationship of the sector decomposition method with the resolution of singularities of a variety, given by a sequence of blow-ups, in algebraic geometry.rnrnMotivated by the connection between Feynman integrals and topics of algebraic geometry we consider the set of periods as defined by Kontsevich and Zagier. This special set of numbers contains the set of multiple zeta values and certain values of polylogarithms, which in turn are known to be present in results for Laurent coefficients of certain dimensionally regularized Feynman integrals. By use of the extended sector decomposition algorithm we prove a theorem which implies, that the Laurent coefficients of an arbitrary Feynman integral are periods if the masses and kinematical invariants take values in the Euclidean momentum region. The statement is formulated for an even more general class of integrals, allowing for an arbitrary number of polynomials in the integrand.

Investigations on asymptotic safety of metric, tetrad and Einstein-Cartan gravity

Among the different approaches for a construction of a fundamental quantum theory of gravity the Asymptotic Safety scenario conjectures that quantum gravity can be defined within the framework of conventional quantum field theory, but only non-perturbatively. In this case its high energy behavior is controlled by a non-Gaussian fixed point of the renormalization group flow, such that its infinite cutoff limit can be taken in a well defined way. A theory of this kind is referred to as non-perturbatively renormalizable. In the last decade a considerable amount of evidence has been collected that in four dimensional metric gravity such a fixed point, suitable for the Asymptotic Safety construction, indeed exists. This thesis extends the Asymptotic Safety program of quantum gravity by three independent studies that differ in the fundamental field variables the investigated quantum theory is based on, but all exhibit a gauge group of equivalent semi-direct product structure. It allows for the first time for a direct comparison of three asymptotically safe theories of gravity constructed from different field variables. The first study investigates metric gravity coupled to SU(N) Yang-Mills theory. In particular the gravitational effects to the running of the gauge coupling are analyzed and its implications for QED and the Standard Model are discussed. The second analysis amounts to the first investigation on an asymptotically safe theory of gravity in a pure tetrad formulation. Its renormalization group flow is compared to the corresponding approximation of the metric theory and the influence of its enlarged gauge group on the UV behavior of the theory is analyzed. The third study explores Asymptotic Safety of gravity in the Einstein-Cartan setting. Here, besides the tetrad, the spin connection is considered a second fundamental field. The larger number of independent field components and the enlarged gauge group render any RG analysis of this system much more difficult than the analog metric analysis. In order to reduce the complexity of this task a novel functional renormalization group equation is proposed, that allows for an evaluation of the flow in a purely algebraic manner. As a first example of its suitability it is applied to a three dimensional truncation of the form of the Holst action, with the Newton constant, the cosmological constant and the Immirzi parameter as its running couplings. A detailed comparison of the resulting renormalization group flow to a previous study of the same system demonstrates the reliability of the new equation and suggests its use for future studies of extended truncations in this framework.