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Antimicrobial resistance became a serious threat to the worldwide public health in this century. A better understanding of the mechanisms, by which bacteria infect host cells and how the host counteracts against the invading pathogens, is an important subject of current research. Intracellular bacteria of the Salmonella genus have been frequently used as a model system for bacterial infections. Salmonella are ingested by contaminated food or water and cause gastroenteritis and typhoid fever in animals and humans. Once inside the gastrointestinal tract, Salmonella can invade intestinal epithelial cells. The host cell can fight against intracellular pathogens by a process called xenophagy. For complex systems, such as processes involved in the bacterial infection of cells, computational systems biology provides approaches to describe mathematically how these intertwined mechanisms in the cell function. Computational systems biology allows the analysis of biological systems at different levels of abstraction. Functional dependencies as well as dynamic behavior can be studied. In this thesis, we used the Petri net formalism to gain a better insight into bacterial infections and host defense mechanisms and to predict cellular behavior that can be tested experimentally. We also focused on the development of new computational methods.
In this work, the first realization of a mathematical model of the xenophagic capturing of Salmonella enterica serovar Typhimurium in epithelial cells was developed. The mathematical model expressed in the Petri net formalism was constructed in an iterative way of modeling and analyses. For the model verification, we analyzed the Petri net, including a computational performance of knockout experiments named in silico knockouts, which was established in this work. The in silico knockouts of the proposed Petri net are consistent with the published experimental perturbation studies and, thus, ensures the biological credibility of the Petri net. In silico knockouts that have not been experimentally investigated yet provide hypotheses for future investigations of the pathway.
To study the dynamic behavior of an epithelial cell infected with Salmonella enterica serovar Typhimurium, a stochastic Petri net was constructed. In experimental research, a decision like "Which incubation time is needed to infect half of the epithelial cells with Salmonella?" is based on experience or practicability. A mathematical model can help to answer these questions and improve experimental design. The stochastic Petri net models the cell at different stages of the Salmonella infection. We parameterized the model by a set of experimental data derived from different literature sources. The kinetic parameters of the stochastic Petri net determine the time evolution of the bacterial infection of a cell. The model captures the stochastic variation and heterogeneity of the intracellular Salmonella population of a single cell over time. The stochastic Petri net is a valuable tool to examine the dynamics of Salmonella infections in epithelial cells and generate valuable information for experimental design.
In the last part of this thesis, a novel theoretical method was introduced to perform knockout experiments in silico. The new concept of in silico knockouts is based on the computation of signal flows at steady state and allows the determination of knockout behavior that is comparable to experimental perturbation behavior. In this context, we established the concept of Manatee invariants and demonstrated the suitability of their application for in silico knockouts by reflecting biological dependencies from the signal initiation to the response. As a proof of principle, we applied the proposed concept of in silico knockouts to the Petri net of the xenophagic recognition of Salmonella. To enable the application of in silico knockouts for the scientific community, we implemented the novel method in the software isiKnock. isiKnock allows the automatized performance and visualization of in silico knockouts in signaling pathways expressed in the Petri net formalism. In conclusion, the knockout analysis provides a valuable method to verify computational models of signaling pathways, to detect inconsistencies in the current knowledge of a pathway, and to predict unknown pathway behavior.
In summary, the main contributions of this thesis are the Petri net of the xenophagic capturing of Salmonella enterica serovar Typhimurium in epithelial cells to study the knockout behavior and the stochastic Petri net of an epithelial cell infected with Salmonella enterica serovar Typhimurium to analyze the infection dynamics. Moreover, we established a new method for in silico knockouts, including the concept of Manatee invariants and the software isiKnock. The results of these studies are useful to a better understanding of bacterial infections and provide valuable model analysis techniques for the field of computational systems biology.
In pathology, tissue images are evaluated using a light microscope, relying on the expertise and experience of pathologists. There is a great need for computational methods to quantify and standardize histological observations. Computational quantification methods become more and more essential to evaluate tissue images. In particular, the distribution of tumor cells and their microenvironment are of special interest. Here, we systematically investigated tumor cell properties and their spatial neighborhood relations by a new application of statistical analysis to whole slide images of Hodgkin lymphoma, a tumor arising in lymph nodes, and inflammation of lymph nodes called lymphadenitis. We considered properties of more than 400, 000 immunohistochemically stained, CD30-positive cells in 35 whole slide images of tissue sections from subtypes of the classical Hodgkin lymphoma, nodular sclerosis and mixed cellularity, as well as from lymphadenitis. We found that cells of specific morphology exhibited significant favored and unfavored spatial neighborhood relations of cells in dependence of their morphology. This information is important to evaluate differences between Hodgkin lymph nodes infiltrated by tumor cells (Hodgkin lymphoma) and inflamed lymph nodes, concerning the neighborhood relations of cells and the sizes of cells. The quantification of neighborhood relations revealed new insights of relations of CD30-positive cells in different diagnosis cases. The approach is general and can easily be applied to whole slide image analysis of other tumor types.
Mathematical modeling of the molecular switch of TNFR1-mediated signaling pathways using Petri nets
(2021)
The paper describes a mathematical model of the molecular switch of cell survival, apoptosis, and necroptosis in cellular signaling pathways initiated by tumor necrosis factor 1. Based on experimental findings in the current literature, we constructed a Petri net model in terms of detailed molecular reactions for the molecular players, protein complexes, post-translational modifications, and cross talk. The model comprises 118 biochemical entities, 130 reactions, and 299 connecting edges. Applying Petri net analysis techniques, we found 279 pathways describing complete signal flows from receptor activation to cellular response, representing the combinatorial diversity of functional pathways.120 pathways steered the cell to survival, whereas 58 and 35 pathways led to apoptosis and necroptosis, respectively. For 65 pathways, the triggered response was not deterministic, leading to multiple possible outcomes. Based on the Petri net, we investigated the detailed in silico knockout behavior and identified important checkpoints of the TNFR1 signaling pathway in terms of ubiquitination within complex I and the gene expression dependent on NF-κB, which controls the caspase activity in complex II and apoptosis induction.