Heating the Early Universe : Numerical Methods and Their Analysis

During the epoch when the first collapsed structures formed (6<z<50) our Universe went through an extended period of changes. Some of the radiation from the first stars and accreting black holes in those structures escaped and changed the state of the Intergalactic Medium (IGM). The era of this global phase change in which the state of the IGM was transformed from cold and neutral to warm and ionized, is called the Epoch of Reionization.In this thesis we focus on numerical methods to calculate the effects of this escaping radiation. We start by considering the performance of the cosmological radiative transfer code C2-Ray. We find that although this code efficiently and accurately solves for the changes in the ionized fractions, it can yield inaccurate results for the temperature changes. We introduce two new elements to improve the code. The first element, an adaptive time step algorithm, quickly determines an optimal time step by only considering the computational cells relevant for this determination. The second element, asynchronous evolution, allows different cells to evolve with different time steps. An important constituent of methods to calculate the effects of ionizing radiation is the transport of photons through the computational domain or ``ray-tracing''. We devise a novel ray tracing method called PYRAMID which uses a new geometry - the pyramidal geometry. This geometry shares properties with both the standard Cartesian and spherical geometries. This makes it on the one hand easy to use in conjunction with a Cartesian grid and on the other hand ideally suited to trace radiation from a radially emitting source. A time-dependent photoionization calculation not only requires tracing the path of photons but also solving the coupled set of photoionization and thermal equations. Several different solvers for these equations are in use in cosmological radiative transfer codes. We conduct a detailed and quantitative comparison of four different standard solvers in which we evaluate how their accuracy depends on the choice of the time step. This comparison shows that their performance can be characterized by two simple parameters and that the C2-Ray generally performs best.

Theoretical studies of Membrane Proteins : Properties, Prediction Methods and Genome-wide analysis

Membrane proteins are a large and important class of proteins. They are responsible for several of the key functions in a living cell, e.g. transport of nutrients and ions, cell-cell signaling, and cell-cell adhesion. Despite their importance it has not been possible to study their structure and organization in much detail because of the difficulty to obtain 3D structures. In this thesis theoretical studies of membrane protein sequences and structures have been carried out by analyzing existing experimental data. The data comes from several sources including sequence databases, genome sequencing projects, and 3D structures. Prediction of the membrane spanning regions by hydrophobicity analysis is a key technique used in several of the studies. A novel method for this is also presented and compared to other methods. The primary questions addressed in the thesis are: What properties are common to all membrane proteins? What is the overall architecture of a membrane protein? What properties govern the integration into the membrane? How many membrane proteins are there and how are they distributed in different organisms? Several of the findings have now been backed up by experiments. An analysis of the large family of G-protein coupled receptors pinpoints differences in length and amino acid composition of loops between proteins with and without a signal peptide and also differences between extra- and intracellular loops. Known 3D structures of membrane proteins have been studied in terms of hydrophobicity, distribution of secondary structure and amino acid types, position specific residue variability, and differences between loops and membrane spanning regions. An analysis of several fully and partially sequenced genomes from eukaryotes, prokaryotes, and archaea has been carried out. Several differences in the membrane protein content between organisms were found, the most important being the total number of membrane proteins and the distribution of membrane proteins with a given number of transmembrane segments. Of the properties that were found to be similar in all organisms, the most obvious is the bias in the distribution of positive charges between the extra- and intracellular loops. Finally, an analysis of homologues to membrane proteins with known topology uncovered two related, multi-spanning proteins with opposite predicted orientations. The predicted topologies were verified experimentally, providing a first example of "divergent topology evolution".