Dynamics and distribution of immunoglobolin E receptors : a dialog between experiment and theory

This dissertation explores the dynamics and distribution of immunoglobulin E receptors (FceRI) on mast cells by drawing on the techniques of experimental and theoretical physics. The motivation for these investigations is provided by a considerable interest in the transmembrane signaling mechanisms of immunoreceptors, especially when triggered with membrane-bound ligands. Experimental investigations quantify the spatiotemporal dynamics of the redistribution of FceRI due to membrane-bound monovalent ligands, using total internal reflection fluorescence microscopy and single-particle tracking. When mast cells contact such substrates, receptor clusters form at cell-substrate contact points. The initial rate of accumulation of receptors into these contact points or cell protrusions is consistent with diffusion-limited trapping. Over longer timescales (\u3e10 s), individual clusters move with both diffusive and directed motion components and eventually coalesce to form a large central receptor patch surrounded by a receptor cluster depletion zone. Detailed analysis of single-particle trajectories show that receptors maintain their diffusivity when confined within receptor clusters, and increase their diffusivity (above that of monomeric unliganded FceRI) in central patches. To study the kinetics of central patch formation, a new coalescence theory described by a melding process, which is not instantaneous, was developed. In these theoretical investigations, the difficult problem of moving boundaries is encountered. To handle the complexity, which stems from boundary growth due to particle melding, the study is divided into three parts. The first is about stationary trapping problems investigated by the standard defect technique, and the second is about a validity study of an adiabatic approximation for moving boundaries. In the last part of this dissertation, a new coalescence theory is developed, which is based on a completely self-consistent approach. Here, the time dependence of the moving boundary is not prescribed but obtained through feedback. Comparison of experiment and theory shows that observed biological cluster coalescence is delayed at early times and occurs at a faster rate at later times than predicted by a simple theory. The incompatibility at early times is addressed by a generalization of the theory to incorporate a time-dependent melding process by a memory concept, which quantitatively explains the observed delay

Convergence of the tamed-Euler-Maruyama method for SDEs with discontinuous and polynomially growing drift

Numerical methods for SDEs with irregular coefficients are intensively studied in the literature, with different types of irregularities usually being attacked separately. In this paper we combine two different types of irregularities: polynomially growing drift coefficients and discontinuous drift coefficients. For SDEs that suffer from both irregularities we prove strong convergence of order $1/2$ of the tamed-Euler-Maruyama scheme from [Hutzenthaler, M., Jentzen, A., and Kloeden, P. E., The Annals of Applied Probability, 22(4):1611-1641, 2012]

Quantification of DNA-associated proteins inside eukaryotic cells using single-molecule localization microscopy

Development of single-molecule localization microscopy techniques has allowed nanometre scale localization accuracy inside cells, permitting the resolution of ultra-fine cell structure and the elucidation of crucial molecular mechanisms. Application of these methodologies to understanding processes underlying DNA replication and repair has been limited to defined in vitro biochemical analysis and prokaryotic cells. In order to expand these techniques to eukaryotic systems, we have further developed a photo-activated localization microscopy-based method to directly visualize DNA-associated proteins in unfixed eukaryotic cells. We demonstrate that motion blurring of fluorescence due to protein diffusivity can be used to selectively image the DNA-bound population of proteins. We designed and tested a simple methodology and show that it can be used to detect changes in DNA binding of a replicative helicase subunit, Mcm4, and the replication sliding clamp, PCNA, between different stages of the cell cycle and between distinct genetic backgrounds