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Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models.
The degradation of cytosol-invading pathogens by autophagy, a process known as xenophagy, is an important mechanism of the innate immune system. Inside the host, Salmonella Typhimurium invades epithelial cells and resides within a specialized intracellular compartment, the Salmonella-containing vacuole. A fraction of these bacteria does not persist inside the vacuole and enters the host cytosol. Salmonella Typhimurium that invades the host cytosol becomes a target of the autophagy machinery for degradation. The xenophagy pathway has recently been discovered, and the exact molecular processes are not entirely characterized. Complete kinetic data for each molecular process is not available, so far. We developed a mathematical model of the xenophagy pathway to investigate this key defense mechanism. In this paper, we present a Petri net model of Salmonella xenophagy in epithelial cells. The model is based on functional information derived from literature data. It comprises the molecular mechanism of galectin-8-dependent and ubiquitin-dependent autophagy, including regulatory processes, like nutrient-dependent regulation of autophagy and TBK1-dependent activation of the autophagy receptor, OPTN. To model the activation of TBK1, we proposed a new mechanism of TBK1 activation, suggesting a spatial and temporal regulation of this process. Using standard Petri net analysis techniques, we found basic functional modules, which describe different pathways of the autophagic capture of Salmonella and reflect the basic dynamics of the system. To verify the model, we performed in silico knockout experiments. We introduced a new concept of knockout analysis to systematically compute and visualize the results, using an in silico knockout matrix. The results of the in silico knockout analyses were consistent with published experimental results and provide a basis for future investigations of the Salmonella xenophagy pathway.
Author Summary
Salmonellae are Gram-negative bacteria, which cause the majority of foodborne diseases worldwide. Serovars of Salmonella cause a broad range of diseases, ranging from diarrhea to typhoid fever in a variety of hosts. In the year 2010, Salmonella Typhi caused 7.6 million foodborne diseases and 52 000 deaths, and Salmonella enterica was responsible for 78.7 million diseases and 59 000 deaths. After invasion of Salmonella into host epithelial cells, a small fraction of Salmonella escapes from a specialized intracellular compartment and replicates inside the host cytosol. Xenophagy is a host defense mechanism to protect the host cell from cytosolic pathogens. Understanding how Salmonella is recognized and targeted for xenophagy is an important subject of current research. To the best of our knowledge, no mathematical model has been presented so far, describing the process of Salmonella Typhimurium xenophagy. Here, we present a manually curated and mathematically verified theoretical model of Salmonella Typhimurium xenophagy in epithelial cells, which is consistent with the current state of knowledge. Our model reproduces literature data and postulates new hypotheses for future investigations.
Bioinformatics analysis quantifies neighborhood preferences of cancer cells in Hodgkin lymphoma
(2017)
Motivation Hodgkin lymphoma is a tumor of the lymphatic system and represents one of the most frequent lymphoma in the Western world. It is characterized by Hodgkin cells and Reed-Sternberg cells, which exhibit a broad morphological spectrum. The cells are visualized by immunohistochemical staining of tissue sections. In pathology, tissue images are mainly manually evaluated, relying on the expertise and experience of pathologists. Computational quantification methods become more and more essential to evaluate tissue images. In particular, the distribution of cancer cells is of great interest.
Results Here, we systematically quantified and investigated cancer cell properties and their spatial neighborhood relations by applying statistical analyses to whole slide images of Hodgkin lymphoma and lymphadenitis, which describes a non-cancerous inflammation of the lymph node. We differentiated cells by their morphology and studied the spatial neighborhood relation of more than 400,000 immunohistochemically stained cells. We found that, according to their morphological features, the cells exhibited significant preferences for and aversions to cells of specific profiles as nearest neighbor. We quantified differences between Hodgkin lymphoma and lymphadenitis concerning the neighborhood relations of cells and the sizes of cells. The approach can easily be applied to other cancer types.
isiKnock is a new software that automatically conducts in silico knockouts for mathematical models of biochemical pathways. The software allows for the prediction of the behavior of biological systems after single or multiple knockout. The implemented algorithm applies transition invariants and the novel concept of Manatee invariants. A knockout matrix visualizes the results. The tool enables the analysis of dependencies, for example, in signal flows from the receptor activation to the cell response at steady state.
Human lymph nodes play a central part of immune defense against infection agents and tumor cells. Lymphoid follicles are compartments of the lymph node which are spherical, mainly filled with B cells. B cells are cellular components of the adaptive immune systems. In the course of a specific immune response, lymphoid follicles pass different morphological differentiation stages. The morphology and the spatial distribution of lymphoid follicles can be sometimes associated to a particular causative agent and development stage of a disease. We report our new approach for the automatic detection of follicular regions in histological whole slide images of tissue sections immuno-stained with actin. The method is divided in two phases: (1) shock filter-based detection of transition points and (2) segmentation of follicular regions. Follicular regions in 10 whole slide images were manually annotated by visual inspection, and sample surveys were conducted by an expert pathologist. The results of our method were validated by comparing with the manual annotation. On average, we could achieve a Zijbendos similarity index of 0.71, with a standard deviation of 0.07.
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.
Our purpose was to analyze the robustness and reproducibility of magnetic resonance imaging (MRI) radiomic features. We constructed a multi-object fruit phantom to perform MRI acquisition as scan-rescan using a 3 Tesla MRI scanner. We applied T2-weighted (T2w) half-Fourier acquisition single-shot turbo spin-echo (HASTE), T2w turbo spin-echo (TSE), T2w fluid-attenuated inversion recovery (FLAIR), T2 map and T1-weighted (T1w) TSE. Images were resampled to isotropic voxels. Fruits were segmented. The workflow was repeated by a second reader and the first reader after a pause of one month. We applied PyRadiomics to extract 107 radiomic features per fruit and sequence from seven feature classes. We calculated concordance correlation coefficients (CCC) and dynamic range (DR) to obtain measurements of feature robustness. Intraclass correlation coefficient (ICC) was calculated to assess intra- and inter-observer reproducibility. We calculated Gini scores to test the pairwise discriminative power specific for the features and MRI sequences. We depict Bland Altmann plots of features with top discriminative power (Mann–Whitney U test). Shape features were the most robust feature class. T2 map was the most robust imaging technique (robust features (rf), n = 84). HASTE sequence led to the least amount of rf (n = 20). Intra-observer ICC was excellent (≥ 0.75) for nearly all features (max–min; 99.1–97.2%). Deterioration of ICC values was seen in the inter-observer analyses (max–min; 88.7–81.1%). Complete robustness across all sequences was found for 8 features. Shape features and T2 map yielded the highest pairwise discriminative performance. Radiomics validity depends on the MRI sequence and feature class. T2 map seems to be the most promising imaging technique with the highest feature robustness, high intra-/inter-observer reproducibility and most promising discriminative power.
The human immune system is determined by the functionality of the human lymph node. With the use of high-throughput techniques in clinical diagnostics, a large number of data is currently collected. The new data on the spatiotemporal organization of cells offers new possibilities to build a mathematical model of the human lymph node - a virtual lymph node. The virtual lymph node can be applied to simulate drug responses and may be used in clinical diagnosis. Here, we review mathematical models of the human lymph node from the viewpoint of cellular processes. Starting with classical methods, such as systems of differential equations, we discuss the values of different levels of abstraction and methods in the range from artificial intelligence techniques formalism.