Michael Ederer

ON/OFF and Beyond - A Boolean Model of Apoptosis

Apoptosis is regulated by several signaling pathways which are extensively linked by crosstalks. Boolean or logical modeling has become a promising approach to capture the qualitative behavior of such complex networks. Here we built a large-scale literature-based Boolean model of the central intrinsic and extrinsic apoptosis pathways as well as pathways connected with them. The model responds to several external stimuli such as Fas ligand, TNF-α, UV-B irradiation, interleukin-1β and insulin. Timescales and multi-value node logic were used and turned out to be indispensable to reproduce the behavior of the apoptotic network. The coherence of the model was experimentally validated. Thereby an UV-B dose-effect is shown for the first time in mouse hepatocytes. Analysis of the model revealed a tight regulation emerging from high connectivity and spanning crosstalks and a particular importance of feedback loops. An unexpected feedback from Smac release to RIP could further increase complex II formation. The introduced Boolean model provides a comprehensive and coherent description of the apoptosis network behavior. It gives new insights into the complex interplay of pro- and antiapoptotic factors and can be easily expanded to other signaling pathways.

Mathematical Modeling of the Central Carbohydrate Metabolism in Arabidopsis Reveals a Substantial Regulatory Influence of Vacuolar Invertase on Whole Plant Carbon Metabolism

A mathematical model representing metabolite interconversions in the central carbohydrate metabolism of Arabidopsis (Arabidopsis thaliana) was developed to simulate the diurnal dynamics of primary carbon metabolism in a photosynthetically active plant leaf. The model groups enzymatic steps of central carbohydrate metabolism into blocks of interconverting reactions that link easily measurable quantities like CO2 exchange and quasi-steady-state levels of soluble sugars and starch. When metabolite levels that fluctuate over diurnal cycles are used as a basic condition for simulation, turnover rates for the interconverting reactions can be calculated that approximate measured metabolite dynamics and yield kinetic parameters of interconverting reactions. We used experimental data for Arabidopsis wild-type plants, accession Columbia, and a mutant defective in vacuolar invertase, AtβFruct4, as input data. Reducing invertase activity to mutant levels in the wild-type model led to a correct prediction of increased sucrose levels. However, additional changes were needed to correctly simulate levels of hexoses and sugar phosphates, indicating that invertase knockout causes subsequent changes in other enzymatic parameters. Reduction of invertase activity caused a decline in photosynthesis and export of reduced carbon to associated metabolic pathways and sink organs (e.g. roots), which is in agreement with the reported contribution of vacuolar invertase to sink strength. According to model parameters, there is a role for invertase in leaves, where futile cycling of sucrose appears to have a buffering effect on the pools of sucrose, hexoses, and sugar phosphates. Our data demonstrate that modeling complex metabolic pathways is a useful tool to study the significance of single enzyme activities in complex, nonintuitive networks.

Reduced modeling of signal transduction – a modular approach

BackgroundCombinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. This subject has been discussed intensively and a lot of progress has been made within the last few years. A software tool (BioNetGen) was developed which allows an automatic rule-based set-up of mechanistic model equations. In many cases these models can be reduced by an exact domain-oriented lumping technique. However, the resulting models can still consist of a very large number of differential equations.ResultsWe introduce a new reduction technique, which allows building modularized and highly reduced models. Compared to existing approaches further reduction of signal transduction networks is possible. The method also provides a new modularization criterion, which allows to dissect the model into smaller modules that are called layers and can be modeled independently. Hallmarks of the approach are conservation relations within each layer and connection of layers by signal flows instead of mass flows. The reduced model can be formulated directly without previous generation of detailed model equations. It can be understood and interpreted intuitively, as model variables are macroscopic quantities that are converted by rates following simple kinetics. The proposed technique is applicable without using complex mathematical tools and even without detailed knowledge of the mathematical background. However, we provide a detailed mathematical analysis to show performance and limitations of the method. For physiologically relevant parameter domains the transient as well as the stationary errors caused by the reduction are negligible.ConclusionThe new layer based reduced modeling method allows building modularized and strongly reduced models of signal transduction networks. Reduced model equations can be directly formulated and are intuitively interpretable. Additionally, the method provides very good approximations especially for macroscopic variables. It can be combined with existing reduction methods without any difficulties.

Tumor Necrosis Factor α Sensitizes Primary Murine Hepatocytes to Fas/CD95-Induced Apoptosis in a Bim- and Bid-Dependent Manner

Fas/CD95 is a critical mediator of cell death in many chronic and acute liver diseases and induces apoptosis in primary hepatocytes in vitro. In contrast, the proinflammatory cytokine tumor necrosis factor α (TNFα) fails to provoke cell death in isolated hepatocytes but has been implicated in hepatocyte apoptosis during liver diseases associated with chronic inflammation. Here we report that TNFα sensitizes primary murine hepatocytes cultured on collagen to Fas ligand (FasL)–induced apoptosis. This synergism is time‐dependent and is specifically mediated by TNFα. Fas itself is essential for the sensitization, but neither Fas up‐regulation nor endogenous FasL is responsible for this effect. Although FasL is shown to induce Bid‐independent apoptosis in hepatocytes cultured on collagen, the sensitizing effect of TNFα is clearly dependent on Bid. Moreover, both c‐Jun N‐terminal kinase activation and Bim, another B cell lymphoma 2 homology domain 3 (BH3)–only protein, are crucial mediators of TNFα‐induced apoptosis sensitization. Bim and Bid activate the mitochondrial amplification loop and induce cytochrome c release, a hallmark of type II apoptosis. The mechanism of TNFα‐induced sensitization is supported by a mathematical model that correctly reproduces the biological findings. Finally, our results are physiologically relevant because TNFα also induces sensitivity to agonistic anti‐Fas–induced liver damage. Conclusion: Our data suggest that TNFα can cooperate with FasL to induce hepatocyte apoptosis by activating the BH3‐only proteins Bim and Bid. (HEPATOLOGY 2011.)

Integration of Boolean models exemplified on hepatocyte signal transduction

The number of mathematical models for biological pathways is rapidly growing. In particular, Boolean modelling proved to be suited to describe large cellular signalling networks. Systems biology is at the threshold to holistic understanding of comprehensive networks. In order to reach this goal, connection and integration of existing models of parts of cellular networks into more comprehensive network models is necessary. We discuss model combination approaches for Boolean models. Boolean modelling is qualitative rather than quantitative and does not require detailed kinetic information. We show that these models are useful precursors for large-scale quantitative models and that they are comparatively easy to combine. We propose modelling standards for Boolean models as a prerequisite for smooth model integration. Using these standards, we demonstrate the coupling of two logical models on two different examples concerning cellular interactions in the liver. In the first example, we show the integration of two Boolean models of two cell types in order to describe their interaction. In the second example, we demonstrate the combination of two models describing different parts of the network of a single cell type. Combination of partial models into comprehensive network models will take systems biology to the next level of understanding. The combination of logical models facilitated by modelling standards is a valuable example for the next step towards this goal.

Modeling the TNFα-Induced Apoptosis Pathway in Hepatocytes

The proinflammatory cytokine TNFα fails to provoke cell death in isolated hepatocytes but has been implicated in hepatocyte apoptosis during liver diseases associated with chronic inflammation. Recently, we showed that TNFα is able to sensitize primary murine hepatocytes cultured on collagen to Fas ligand-induced apoptosis and presented a mathematical model of the sensitizing effect. Here, we analyze how TNFα induces apoptosis in combination with the transcriptional inhibitor actinomycin D (ActD). Accumulation of reactive oxygen species (ROS) in response to TNFR activation turns out to be critical for sustained activation of JNK which then triggers mitochondrial pathway-dependent apoptosis. In addition, the amount of JNK is strongly upregulated in a ROS-dependent way. In contrast to TNFα plus cycloheximide no cFLIP degradation is observed suggesting a different apoptosis pathway in which the Itch-mediated cFLIP degradation and predominantly caspase-8 activation is not involved. Time-resolved data of the respective pro- and antiapoptotic factors are obtained and subjected to mathematical modeling. On the basis of these data we developed a mathematical model which reproduces the complex interplay regulating the phosphorylation status of JNK and generation of ROS. This model was fully integrated with our model of TNFα/Fas ligand sensitizing as well as with a published NF-κB-model. The resulting comprehensive model delivers insight in the dynamical interplay between the TNFα and FasL pathways, NF-κB and ROS and gives an example for successful model integration.

Modeling system states in liver cells: Survival, apoptosis and their modifications in response to viral infection

BackgroundThe decision pro- or contra apoptosis is complex, involves a number of different inputs, and is central for the homeostasis of an individual cell as well as for the maintenance and regeneration of the complete organism.ResultsThis study centers on Fas ligand (FasL)-mediated apoptosis, and a complex and internally strongly linked network is assembled around the central FasL-mediated apoptosis cascade. Different bioinformatical techniques are employed and different crosstalk possibilities including the integrin pathway are considered. This network is translated into a Boolean network (74 nodes, 108 edges). System stability is dynamically sampled and investigated using the software SQUAD. Testing a number of alternative crosstalk possibilities and networks we find that there are four stable system states, two states comprising cell survival and two states describing apoptosis by the intrinsic and the extrinsic pathways, respectively. The model is validated by comparing it to experimental data from kinetics of cytochrome c release and caspase activation in wildtype and Bid knockout cells grown on different substrates. Pathophysiological modifications such as input from cytomegalovirus proteins M36 and M45 again produces output behavior that well agrees with experimental data.ConclusionA network model for apoptosis and crosstalk in hepatocytes shows four different system states and reproduces a number of different conditions around apoptosis including effects of different growth substrates and viral infections. It produces semi-quantitative predictions on the activity of individual nodes, agreeing with experimental data. The model (SBML format) and all data are available for further predictions and development.

Towards a Systems Level Understanding of the Oxygen Response of Escherichia coli.

Escherichia coli is a facultatively anaerobic bacterium. With glucose if no external electron acceptors are available, ATP is produced by substrate level phosphorylation. The intracellular redox balance is maintained by mixed-acid fermentation, that is, the production and excretion of several organic acids. When oxygen is available, E. coli switches to aerobic respiration to achieve redox balance and optimal energy conservation by proton translocation linked to electron transfer. The switch between fermentative and aerobic respiratory growth is driven by extensive changes in gene expression and protein synthesis, resulting in global changes in metabolic fluxes and metabolite concentrations. This oxygen response is determined by the interaction of global and local genetic regulatory mechanisms, as well as by enzymatic regulation. The response is affected by basic physical constraints such as diffusion, thermodynamics and the requirement for a balance of carbon, electrons and energy (predominantly the proton motive force and the ATP pool). A comprehensive systems level understanding of the oxygen response of E. coli requires the integrated interpretation of experimental data that are pertinent to the multiple levels of organization that mediate the response. In the pan-European venture, Systems Biology of Microorganisms (SysMO) and specifically within the project Systems Understanding of Microbial Oxygen Metabolism (SUMO), regulator activities, gene expression, metabolite levels and metabolic flux datasets were obtained using a standardized and reproducible chemostat-based experimental system. These different types and qualities of data were integrated using mathematical models. The approach described here has revealed a much more detailed picture of the aerobic-anaerobic response, especially for the environmentally critical microaerobic range that is located between unlimited oxygen availability and anaerobiosis.

An approach for dividing models of biological reaction networks into functional units

Biological reaction networks consist of many substances and reactions between them. Like many other biological systems, they have a modular structure. Therefore, a division of a biological reaction network into smaller units highly facilitates its investigation. The authors propose an algorithm to divide an ordinary differential equation (ODE) model of a biological reaction network hierarchically into functional units. For every compound, an activity function dependent on concentration or concentration change rate is defined. After performing suitable simulations, distances between the compounds are computed by comparing the activities along the trajectories of the simulation. The distance information is used to generate a dendrogram revealing the internal structure of the reaction network. The algorithm identifies functional units in two models of different networks: catabolite repression in Escherichia coli and epidermal growth factor (EGF) signal transduction in mammalian cells.

A systems biology approach to analyse leaf carbohydrate metabolism in Arabidopsis thaliana

Plant carbohydrate metabolism comprises numerous metabolite interconversions, some of which form cycles of metabolite degradation and re-synthesis and are thus referred to as futile cycles. In this study, we present a systems biology approach to analyse any possible regulatory principle that operates such futile cycles based on experimental data for sucrose (Scr) cycling in photosynthetically active leaves of the model plant Arabidopsis thaliana. Kinetic parameters of enzymatic steps in Scr cycling were identified by fitting model simulations to experimental data. A statistical analysis of the kinetic parameters and calculated flux rates allowed for estimation of the variability and supported the predictability of the model. A principal component analysis of the parameter results revealed the identifiability of the model parameters. We investigated the stability properties of Scr cycling and found that feedback inhibition of enzymes catalysing metabolite interconversions at different steps of the cycle have differential influence on stability. Applying this observation to futile cycling of Scr in leaf cells points to the enzyme hexokinase as an important regulator, while the step of Scr degradation by invertases appears subordinate.