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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.
Background: Microarray analysis represents a powerful way to test scientific hypotheses on the functionality of cells. The measurements consider the whole genome, and the large number of generated data requires sophisticated analysis. To date, no gold-standard for the analysis of microarray images has been established. Due to the lack of a standard approach there is a strong need to identify new processing algorithms.
Methods: We propose a novel approach based on hyperbolic partial differential equations (PDEs) for unsupervised spot segmentation. Prior to segmentation, morphological operations were applied for the identification of co-localized groups of spots. A grid alignment was performed to determine the borderlines between rows and columns of spots. PDEs were applied to detect the inflection points within each column and row; vertical and horizontal luminance profiles were evolved respectively. The inflection points of the profiles determined borderlines that confined a spot within adapted rectangular areas. A subsequent k-means clustering determined the pixels of each individual spot and its local background.
Results: We evaluated the approach for a data set of microarray images taken from the Stanford Microarray Database (SMD). The data set is based on two studies on global gene expression profiles of Arabidopsis Thaliana. We computed values for spot intensity, regression ratio, and coefficient of determination. For spots with irregular contours and inner holes, we found intensity values that were significantly different from those determined by the GenePix Pro microarray analysis software. We determined the set of differentially expressed genes from our intensities and identified more activated genes than were predicted by the GenePix software.
Conclusions: Our method represents a worthwhile alternative and complement to standard approaches used in industry and academy. We highlight the importance of our spot segmentation approach, which identified supplementary important genes, to better explains the molecular mechanisms that are activated in a defense responses to virus and pathogen infection.
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.
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.
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.
Background: Signal transduction pathways are important cellular processes to maintain the cell’s integrity. Their imbalance can cause severe pathologies. As signal transduction pathways feature complex regulations, they form intertwined networks. Mathematical models aim to capture their regulatory logic and allow an unbiased analysis of robustness and vulnerability of the signaling network. Pathway detection is yet a challenge for the analysis of signaling networks in the field of systems biology. A rigorous mathematical formalism is lacking to identify all possible signal flows in a network model.
Results: In this paper, we introduce the concept of Manatee invariants for the analysis of signal transduction networks. We present an algorithm for the characterization of the combinatorial diversity of signal flows, e.g., from signal reception to cellular response. We demonstrate the concept for a small model of the TNFR1-mediated NF- κB signaling pathway. Manatee invariants reveal all possible signal flows in the network. Further, we show the application of Manatee invariants for in silico knockout experiments. Here, we illustrate the biological relevance of the concept.
Conclusions: The proposed mathematical framework reveals the entire variety of signal flows in models of signaling systems, including cyclic regulations. Thereby, Manatee invariants allow for the analysis of robustness and vulnerability of signaling networks. The application to further analyses such as for in silico knockout was shown. The new framework of Manatee invariants contributes to an advanced examination of signaling systems.
Synaptic release sites are characterized by exocytosis-competent synaptic vesicles tightly anchored to the presynaptic active zone (PAZ) whose proteome orchestrates the fast signaling events involved in synaptic vesicle cycle and plasticity. Allocation of the amyloid precursor protein (APP) to the PAZ proteome implicated a functional impact of APP in neuronal communication. In this study, we combined state-of-the-art proteomics, electrophysiology and bioinformatics to address protein abundance and functional changes at the native hippocampal PAZ in young and old APP-KO mice. We evaluated if APP deletion has an impact on the metabolic activity of presynaptic mitochondria. Furthermore, we quantified differences in the phosphorylation status after long-term-potentiation (LTP) induction at the purified native PAZ. We observed an increase in the phosphorylation of the signaling enzyme calmodulin-dependent kinase II (CaMKII) only in old APP-KO mice. During aging APP deletion is accompanied by a severe decrease in metabolic activity and hyperphosphorylation of CaMKII. This attributes an essential functional role to APP at hippocampal PAZ and putative molecular mechanisms underlying the age-dependent impairments in learning and memory in APP-KO mice.
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.
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.
Purpose: To identify transjugular intrahepatic portosystemic shunt (TIPS) thrombosis in abdominal CT scans applying quantitative image analysis.
Materials and methods: We retrospectively screened 184 patients to include 20 patients (male, 8; female, 12; mean age, 60.7 ± 8.87 years) with (case, n = 10) and without (control, n = 10) in-TIPS thrombosis who underwent clinically indicated contrast-enhanced and unenhanced abdominal CT followed by conventional TIPS-angiography between 08/2014 and 06/2020. First, images were scored visually. Second, region of interest (ROI) based quantitative measurements of CT attenuation were performed in the inferior vena cava (IVC), portal vein and in four TIPS locations. Minimum, maximum and average Hounsfield unit (HU) values were used as absolute and relative quantitative features. We analyzed the features with univariate testing.
Results: Subjective scores identified in-TIPS thrombosis in contrast-enhanced scans with an accuracy of 0.667 – 0.833. Patients with in-TIPS thrombosis had significantly lower average (p < 0.001), minimum (p < 0.001) and maximum HU (p = 0.043) in contrast-enhanced images. The in-TIPS / IVC ratio in contrast-enhanced images was significantly lower in patients with in-TIPS thrombosis (p < 0.001). No significant differences were found for unenhanced images. Analyzing the visually most suspicious ROI with consecutive calculation of its ratio to the IVC, all patients with a ratio < 1 suffered from in-TIPS thrombosis (p < 0.001, sensitivity and specificity = 100%).
Conclusion: Quantitative analysis of abdominal CT scans facilitates the stratification of in-TIPS thrombosis. In contrast-enhanced scans, an in-TIPS / IVC ratio < 1 could non-invasively stratify all patients with in-TIPS thrombosis.