Repeatability of evolution on epistatic landscapes

Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an evolutionary process under varying mutation rates as well as varying fitness is still an open question. Experimental procedures, however, do include these complexities along with fluctuating population sizes and stochastic events such as extinctions. We investigate the mutational path probabilities of systems having epistatic effects on both fitness and mutation rates using a theoretical and computational framework. In contrast to previous models, we do not limit ourselves to the typical strong selection, weak mutation (SSWM)-regime or to fixed population sizes. Rather we allow epistatic interactions to also affect mutation rates. This can lead to qualitatively non-trivial dynamics. Pathways, that are negligible in the SSWM-regime, can overcome fitness valleys and become accessible. This finding has the potential to extend the traditional predictions based on the SSWM foundation and bring us closer to what is observed in experimental systems

Cancer initiation with epistatic interactions between driver and passenger mutations

We investigate the dynamics of cancer initiation in a mathematical model with one driver mutation and several passenger mutations. Our analysis is based on a multi type branching process: We model individual cells which can either divide or undergo apoptosis. In case of a cell division, the two daughter cells can mutate, which potentially confers a change in fitness to the cell. In contrast to previous models, the change in fitness induced by the driver mutation depends on the genetic context of the cell, in our case on the number of passenger mutations. The passenger mutations themselves have no or only a very small impact on the cell's fitness. While our model is not designed as a specific model for a particular cancer, the underlying idea is motivated by clinical and experimental observations in Burkitt Lymphoma. In this tumor, the hallmark mutation leads to deregulation of the MYC oncogene which increases the rate of apoptosis, but also the proliferation rate of cells. This increase in the rate of apoptosis hence needs to be overcome by mutations affecting apoptotic pathways, naturally leading to an epistatic fitness landscape. This model shows a very interesting dynamical behavior which is distinct from the dynamics of cancer initiation in the absence of epistasis. Since the driver mutation is deleterious to a cell with only a few passenger mutations, there is a period of stasis in the number of cells until a clone of cells with enough passenger mutations emerges. Only when the driver mutation occurs in one of those cells, the cell population starts to grow rapidly

Bench-to-bedside review: Carbon monoxide – from mitochondrial poisoning to therapeutic use

Carbon monoxide (CO) is generated during incomplete combustion of carbon-containing compounds and leads to acute and chronic toxicity in animals and humans depending on the concentration and exposure time. In addition to exogenous sources, CO is also produced endogenously by the activity of heme oxygenases (HOs) and the physiological significance of HO-derived CO has only recently emerged. CO exerts vasoactive, anti-proliferative, anti-oxidant, anti-inflammatory and anti-apoptotic effects and contributes substantially to the important role of the inducible isoform HO-1 as a mediator of tissue protection and host defense. Exogenous application of low doses of gaseous CO might provide a powerful tool to protect organs and tissues under various stress conditions. Experimental evidence strongly suggests a beneficial effect under pathophysiological conditions such as organ transplantation, ischemia/reperfusion, inflammation, sepsis, or shock states. The cellular and molecular mechanisms mediating CO effects are only partially characterized. So far, only a few studies in humans are available, which, however, do not support the promising results observed in experimental studies. The protective effects of exogenous CO may strongly depend on the pathological condition, the mode, time point and duration of application, the administered concentration, and on the target tissue and cell. Differences in bioavailability of endogenous CO production and exogenous CO supplementation might also provide an explanation for the lack of protective effects observed in some experimental and clinical studies. Further randomized, controlled clinical studies are needed to clarify whether exogenous application of CO may turn into a safe and effective preventive and therapeutic strategy to treat pathophysiological conditions associated with inflammatory or oxidative stress

Transmission Electron Microscopy on GaAs Nanowires – Spontaneous Polarization and MnAs Nanocrystals

The research on semiconductor nanowires – tiny semiconductor crystals of sub-micron diameter and some microns length – has, although around only for about one and a half decade, already significantly diversified and developed. However, it has relied on characterization methods provided by electron microscopy since the earliest days, on the one hand as their sheer size keeps them out of reach of light-based imaging techniques and on the other hand due to their interesting structural properties down to the atomic level, which is one of the core capabilities of transmission electron microscopy when it comes to characterization. While the first years of research were governed mainly by exploration of their most fundamental properties and finding out the mechanisms of their synthesis, meanwhile already a lot of progress has been made towards the controlled growth and manipulation of their properties. Also, people quite early extended the activities beyond practising nanowire research for its own sake and started to seek ways to make use of their unique features for applications – both in the literal sense, i.e. the development of nanowire based devices and functionalization, as well as in the less applied sense, where the nanowires are used as a model system to investigate fundamental material properties. Applying several transmission electron microscopical techniques, this thesis contains contributions to both of the fields mentioned above: Concerning the research on fundamental material properties spontaneous polarization is a property unique to the wurtzite crystal structure, which was within the III–V semiconductors up to now only known to be present in the nitride based ones since they are the only ones that grow by default in the wurtzite crystal structure. Only since the discovery of nanowire growth this crystal structure has gotten available also for the other III–V semiconductor materials and provides a model system to access its properties experimentally and verify the theoretical calculations that have been done on such (up to then hypothetical) crystal structures. The first part of this work therefore contains the first direct experimental observation of the spontaneous polarization in the III–V semiconductor materials gallium arsenide (GaAs) and gallium phosphide (GaP). More towards the application oriented side is the field of spintronics, i.e. the development of electronic devices that make use of the electron spin instead of the charge as the fundamental property to transfer, process and store information. This field requires the fabrication of ferromagnetic device structures that allow to generate and detect spin polarized electrons within the semiconductor materials it should integrate with. One candidate for such a ferromagnetic material is manganese arsenide (MnAs) which includes semiconducting and ferromagnetic properties within one material and is hence considered to be an important building block with respect to the development of spin-based electronic devices. The second part of this work is the characterization of such MnAs nanocrystals that have been grown on top of GaAs nanowires. The document at hand is organized in five main chapters of which the first three describe the theoretical and experimental framework in which this work took place, while the remaining two present the results that have been achieved. Chapter 2 gives an introduction into the topic of semiconductor nanowires, about their synthesis, and their properties of interest, with a special focus on III–V semiconductor nanowires and especially gallium arsenide (GaAs) and gallium phosphide (GaP) nanowires. Since one of the features of semiconductor nanowires is their polytypism, i.e. the possibility to adopt different crystal structures, in Chapter 3 the occurring crystal structures and some of their properties and implications are discussed. Chapter 4 explains the transmission electron microscope – the experimental instrument used – and the analytical methods available in this device which were employed in this work. The first experimental chapter, Chapter 5, presents the experimental evidence of spontaneous polarization in gallium arsenide and gallium phosphide. In addition, based on the issues that arose with the quantitative evaluation of the measurements, the properties and experimental limitations of the differential phase contrast (DPC) microscopy technique are discussed. Finally in Chapter 6, the second experimental chapter, the characterization of samples from a growth study on the route towards the inclusion of manganese arsenide (MnAs) is described

Quasi-universality of Reeb graph distances

We establish bi-Lipschitz bounds certifying quasi-universality (universality up to a constant factor) for various distances between Reeb graphs: the interleaving distance, the functional distortion distance, and the functional contortion distance. The definition of the latter distance is a novel contribution, and for the special case of contour trees we also prove strict universality of this distance. Furthermore, we prove that for the special case of merge trees the functional contortion distance coincides with the interleaving distance, yielding universality of all four distances in this case.Comment: 17 pages + 6 pages appendix, 5 figures; this version includes the appendix to the conference paper for SoCG 2022 with the same content otherwis

Universality of the Bottleneck Distance for Extended Persistence Diagrams

The extended persistence diagram is an invariant of piecewise linear functions, introduced by Cohen-Steiner, Edelsbrunner, and Harer. The bottleneck distance has been introduced by the same authors as an extended pseudometric on the set of extended persistence diagrams, which is stable under perturbations of the function. We address the question whether the bottleneck distance is the largest possible stable distance, providing an affirmative answer.Comment: 20 pages + 12 pages appendix, 18 figures, LaTeX; removal of appendix on "stable functors on M" which has moved to arXiv:2108.09298, added and improved figures, added a note of caution regarding variants of the bottleneck distance, rewrote the proof of lemma 4.6 (formerly lemma 4.4), added appendix B including the connection to the original definition of extended persistence, several minor edit

A “Push and Slide” Mechanism Allows Sequence-Insensitive Translocation of Secretory Proteins by the SecA ATPase

SummaryIn bacteria, most secretory proteins are translocated across the plasma membrane by the interplay of the SecA ATPase and the SecY channel. How SecA moves a broad range of polypeptide substrates is only poorly understood. Here we show that SecA moves polypeptides through the SecY channel by a “push and slide” mechanism. In its ATP-bound state, SecA interacts through a two-helix finger with a subset of amino acids in a substrate, pushing them into the channel. A polypeptide can also passively slide back and forth when SecA is in the predominant ADP-bound state or when SecA encounters a poorly interacting amino acid in its ATP-bound state. SecA performs multiple rounds of ATP hydrolysis before dissociating from SecY. The proposed push and slide mechanism is supported by a mathematical model and explains how SecA allows translocation of a wide range of polypeptides. This mechanism may also apply to hexameric polypeptide-translocating ATPases