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All-solid-state Li-ion batteries are one of the most promising energy storage devices for future automotive applications as high energy density metallic Li anodes can be safely used. However, introducing solid-state electrolytes needs a better understanding of the forming electrified electrode/electrolyte interface to facilitate the charge and mass transport through it and design ever-high-performance batteries. This study investigates the interface between metallic lithium and solid-state electrolytes. Using spectroscopic ellipsometry, we detected the formation of the space charge depletion layers even in the presence of metallic Li. That is counterintuitive and has been a subject of intense debate in recent years. Using impedance measurements, we obtain key parameters characterizing these layers and, with the help of kinetic Monte Carlo simulations, construct a comprehensive model of the systems to gain insights into the mass transport and the underlying mechanisms of charge accumulation, which is crucial for developing high-performance solid-state batteries., (© 2023. The Author(s).)

Background: Thermal damage to the muscle layer during mucosal application of argon plasma coagulation (APC) may be avoided by creating a fluid cushion within the submucosal layer, but the minimum injection volume needed or the ideal injection fluid are yet to be established. We conducted a systematic ex vivo study with this aim., Methods: All experiments were performed in an ex vivo porcine gastrointestinal tract model. Five different fluids (saline, Glyceol, Gelafundin, Voluven, and Eleview) of different volumes were injected into the submucosa of different parts of the gastrointestinal tract. APC was applied to the mucosa at different power settings. Immediately after APC treatment, the temperature was measured through a thermocouple placed inside the fluid cushion, just on top of the muscle layer. The minimum volume of fluid needed to protect the muscle layer from thermal damage was determined., Results: There was no difference in the temperature measured among the different injection fluids at the surface of the muscle, in all the locations, at equal injection volumes and power settings. The minimum amounts of fluid needed to protect the muscle layer were 2 and 3 mL for power settings of 30-90 W and 90-120 W, respectively., Conclusions: Normal saline and 4 commercially available submucosal injection fluids possess similar thermal protective effects. To reduce the likelihood of thermal damage to deeper layers when APC is applied, a minimum injection volume of 3 mL is recommended if less than 90 W power will be utilized over 3 sec., Competing Interests: Conflict of Interest: Roberta Maselli, Paul J. Belletrutti, Marco Spadaccini, Piera Alessia Galteri, Milena Di Leo and Alessandro Repici have no conflicts of interest or financial ties to disclose; Thomas Stäbler, Michael Ederer, Alexander Neugebauer, Markus D. Enderle are employees at the Research Department of Erbe Elektromedizin GmbH, (Copyright: © Hellenic Society of Gastroenterology.)

Background: Bipolar vessel sealing is an efficient electrosurgical procedure for the occlusion of blood vessels particularly during minimally invasive surgery. Reliable knowledge of the thermal spread is crucial for a safe application of bipolar vessel sealing instruments when operating close to thermo-sensitive structures, such as nerves. The evolution of the thermal spread over time and space depends on a variety of parameters, such as the biological tissue, the energy applied to the tissue, and the geometry of the vessel sealing instrument. Mathematical modeling has proven useful for the prediction of the thermal spread. It is, thus, a promising tool for the systematic analysis of the influence of geometrical changes on the thermal spread., Results: We present an experimentally validated in silico study to evaluate the impact of geometry variations on the progression of chicken egg white coagulation and the final shape of coagulated egg white as an approximation of the temporal and spatial evolution of the thermal spread during bipolar vessel sealing. Egg white has similar thermal and electrical properties to human tissue, with the advantage being that the spatial and temporal evolution of the thermal spread can be visually gauged. The simulations were performed using a mathematical model based on the finite element analysis of chicken egg white. The progression of egg white coagulation was predicted for two different peak voltages and various electrode geometries. Starting with two planar electrodes, one electrode was gradually changed to adopt a wedge shape. These changes to the geometry showed a distinct influence on the progression of egg white coagulation in the simulations. The predictions were successfully validated using an experimental setup with two different electrodes representing the extreme geometries., Discussion: The predicted spatial temperature distributions were experimentally validated for two geometries. Our simulation study shows that the geometry has a pronounced influence on the thermal spread and, thus, is a suitable parameter to reduce thermal damage. The in silico optimization of instrument designs is a suitable tool to accelerate the development of new vessel sealing instruments, with only a few promising designs having to be tested as prototypes.

Background: A common method for reconstruction of the anterior cruciate ligament (ACL) is it's replacement by a free avascular graft, using the gracilis and/or semitendinosus tendons. These grafts pass a vulnerable phase in the ligamentization-process during the 1 st year after reconstruction. The aims of this study were first to evaluate the vascularization of the pes anserinus superficialis (PAS) by the inferior medial genicular artery (IMGA) and second to develop a pedunculated surgical technique for ACL reconstruction, to preserve a maximal amount of natural vascularization of the tendons inserting at the PAS., Materials and Methods: First, the vascularization of the PAS was assessed in 12 fresh-frozen lower extremities. The IMGA was identified at its origin at the popliteal artery and perfused with a methylene blue solution. Second, a pedunculated ACL reconstruction was performed in 5 fresh-frozen lower extremities under maintenance of the distal tendon insertion at PAS., Results: The PAS is a highly vascularized structure. Vessels originate from the IMGA, running along the three tendons of the PAS in the paratendinous tissue. Histologically intratendinous vessels exist; however, perfusion of the inserting tendons through intratendinous vessels was not proven macroscopically. The pedunculated grafts could be positioned and fixed successfully into the bone tunnels in all knees., Conclusion: Although intratendinous vascularization of the tendons of the PAS via the IMGA was not proven, this study indicates a new possibility of ACL reconstruction. The described operation technique can be conducive to shorten the vulnerable phase of the graft-ligamentization after ACL reconstruction., Competing Interests: There are no conflicts of interest.

Macrophages are cells with remarkable plasticity. They integrate signals from their microenvironment leading to context-dependent polarization into classically (M1) or alternatively (M2) activated macrophages, representing two extremes of a broad spectrum of divergent phenotypes. Thereby, macrophages deliver protective and pro-regenerative signals towards injured tissue but, depending on the eliciting damage, may also be responsible for the generation and aggravation of tissue injury. Although incompletely understood, there is emerging evidence that macrophage polarization is critical for these antagonistic roles. To identify activation-specific expression patterns of chemokines and cytokines that may confer these distinct effects a systems biology approach was applied. A comprehensive literature-based Boolean model was developed to describe the M1 (LPS-activated) and M2 (IL-4/13-activated) polarization types. The model was validated using high-throughput transcript expression data from murine bone marrow derived macrophages. By dynamic modeling of gene expression, the chronology of pathway activation and autocrine signaling was estimated. Our results provide a deepened understanding of the physiological balance leading to M1/M2 activation, indicating the relevance of co-regulatory signals at the level of Akt1 or Akt2 that may be important for directing macrophage polarization.

Background: Urethral pressure profilometry (UPP) is used in the diagnosis of stress urinary incontinence (SUI) which is a significant medical, social, and economic problem. Low spatial pressure resolution, common occurrence of artifacts, and uncertainties in data location limit the diagnostic value of UPP. To overcome these limitations, high definition urethral pressure profilometry (HD-UPP) combining enhanced UPP hardware and signal processing algorithms has been developed. In this work, we present the different signal processing steps in HD-UPP and show experimental results from female minipigs., Methods: We use a special microtip catheter with high angular pressure resolution and an integrated inclination sensor. Signals from the catheter are filtered and time-correlated artifacts removed. A signal reconstruction algorithm processes pressure data into a detailed pressure image on the urethra's inside. Finally, the pressure distribution on the urethra's outside is calculated through deconvolution. A mathematical model of the urethra is contained in a point-spread-function (PSF) which is identified depending on geometric and material properties of the urethra. We additionally investigate the PSF's frequency response to determine the relevant frequency band for pressure information on the urinary sphincter., Results: Experimental pressure data are spatially located and processed into high resolution pressure images. Artifacts are successfully removed from data without blurring other details. The pressure distribution on the urethra's outside is reconstructed and compared to the one on the inside. Finally, the pressure images are mapped onto the urethral geometry calculated from inclination and position data to provide an integrated image of pressure distribution, anatomical shape, and location., Conclusions: With its advanced sensing capabilities, the novel microtip catheter collects an unprecedented amount of urethral pressure data. Through sequential signal processing steps, physicians are provided with detailed information on the pressure distribution in and around the urethra. Therefore, HD-UPP overcomes many current limitations of conventional UPP and offers the opportunity to evaluate urethral structures, especially the sphincter, in context of the correct anatomical location. This could enable the development of focal therapy approaches in the treatment of SUI.

The coccolithophorid unicellular alga Emiliania huxleyi is known to form large blooms, which have a strong effect on the marine carbon cycle. As a photosynthetic organism, it is subjected to a circadian rhythm due to the changing light conditions throughout the day. For a better understanding of the metabolic processes under these periodically-changing environmental conditions, a genome-scale model based on a genome reconstruction of the E. huxleyi strain CCMP 1516 was created. It comprises 410 reactions and 363 metabolites. Biomass composition is variable based on the differentiation into functional biomass components and storage metabolites. The model is analyzed with a flux balance analysis approach called diurnal flux balance analysis (diuFBA) that was designed for organisms with a circadian rhythm. It allows storage metabolites to accumulate or be consumed over the diurnal cycle, while keeping the structure of a classical FBA problem. A feature of this approach is that the production and consumption of storage metabolites is not defined externally via the biomass composition, but the result of optimal resource management adapted to the diurnally-changing environmental conditions. The model in combination with this approach is able to simulate the variable biomass composition during the diurnal cycle in proximity to literature data.

Sustained inflammation may increase the susceptibility of hepatocytes to apoptotic cell death and therefore exacerbate liver damage. Here we report that the pro-inflammatory cytokine IL-1β sensitizes primary murine hepatocytes to Fas ligand (FasL)-induced caspase-3/-7 activity. This process was dependent on JNK1/2 and the BH3-only proteins Bim and Bid. Mathematical modeling revealed that incubation of hepatocytes with IL-1β depleted the anti-apoptotic Bcl-2 protein pool and thus shifted hepatocytes to mitochondrial type II apoptosis following Fas activation. As a consequence, IL-1β and FasL treatment enhanced cytochrome c release. Surprisingly, despite increased caspase-3/-7 activation, FasL-induced cell death was reduced by IL-1β pre-treatment. This protective effect was independent of JNK1/2, Bim or Bid. Furthermore, elevated caspase-3/-7 activity upon IL-1β and FasL treatment did not result in enhanced PARP cleavage. The protective effect of IL-1β was seen after 3 h of pre-incubation, indicating an anti-apoptotic transcriptional response. Indeed, NF-κB DNA binding was increased in response to IL-1β plus FasL and gene-expression profiling of NF-κB regulated genes revealed a transcriptional and translational upregulation of the caspase-8 inhibitor A20. A mathematical model was developed to explain the contradictious occurrence of both increased caspase-3/-7 activity and elevated cell viability by including a heterogeneous distribution of Bcl-2 proteins and variations in Fas signaling resulting in different subpopulations of hepatocytes.

For adaptation between anaerobic, micro-aerobic and aerobic conditions Escherichia coli's metabolism and in particular its electron transport chain (ETC) is highly regulated. Although it is known that the global transcriptional regulators FNR and ArcA are involved in oxygen response it is unclear how they interplay in the regulation of ETC enzymes under micro-aerobic chemostat conditions. Also, there are diverse results which and how quinones (oxidised/reduced, ubiquinone/other quinones) are controlling the ArcBA two-component system. In the following a mathematical model of the E. coli ETC linked to basic modules for substrate uptake, fermentation product excretion and biomass formation is introduced. The kinetic modelling focusses on regulatory principles of the ETC for varying oxygen conditions in glucose-limited continuous cultures. The model is based on the balance of electron donation (glucose) and acceptance (oxygen or other acceptors). Also, it is able to account for different chemostat conditions due to changed substrate concentrations and dilution rates. The parameter identification process is divided into an estimation and a validation step based on previously published and new experimental data. The model shows that experimentally observed, qualitatively different behaviour of the ubiquinone redox state and the ArcA activity profile in the micro-aerobic range for different experimental conditions can emerge from a single network structure. The network structure features a strong feed-forward effect from the FNR regulatory system to the ArcBA regulatory system via a common control of the dehydrogenases of the ETC. The model supports the hypothesis that ubiquinone but not ubiquinol plays a key role in determining the activity of ArcBA in a glucose-limited chemostat at micro-aerobic conditions.

The efficient redesign of bacteria for biotechnological purposes, such as biofuel production, waste disposal or specific biocatalytic functions, requires a quantitative systems-level understanding of energy supply, carbon, and redox metabolism. The measurement of transcript levels, metabolite concentrations and metabolic fluxes per se gives an incomplete picture. An appreciation of the interdependencies between the different measurement values is essential for systems-level understanding. Mathematical modeling has the potential to provide a coherent and quantitative description of the interplay between gene expression, metabolite concentrations, and metabolic fluxes. Escherichia coli undergoes major adaptations in central metabolism when the availability of oxygen changes. Thus, an integrated description of the oxygen response provides a benchmark of our understanding of carbon, energy, and redox metabolism. We present the first comprehensive model of the central metabolism of E. coli that describes steady-state metabolism at different levels of oxygen availability. Variables of the model are metabolite concentrations, gene expression levels, transcription factor activities, metabolic fluxes, and biomass concentration. We analyze the model with respect to the production capabilities of central metabolism of E. coli. In particular, we predict how precursor and biomass concentration are affected by product formation.

Stress urinary incontinence is a significant social, medical, and economic problem. It is caused, at least in part, by degeneration of the sphincter muscle controlling the tightness of the urinary bladder. This muscular degeneration is characterized by a loss of muscle cells and a surplus of a fibrous connective tissue. In Western countries approximately 15% of all females and 10% of males are affected. The incidence is significantly higher among senior citizens, and more than 25% of the elderly suffer from incontinence. When other therapies, such as physical exercise, pharmacological intervention, or electrophysiological stimulation of the sphincter fail to improve the patient's conditions, a cell-based therapy may improve the function of the sphincter muscle. Here, we briefly summarize current knowledge on stem cells suitable for therapy of urinary incontinence: mesenchymal stromal cells, urine-derived stem cells, and muscle-derived satellite cells. In addition, we report on ways to improve techniques for surgical navigation, injection of cells in the sphincter muscle, sensors for evaluation of post-treatment therapeutic outcome, and perspectives derived from recent pre-clinical studies.

A simple, rapid, and inexpensive extraction method for carotenoids and other non-polar compounds present in phototrophic bacteria has been developed. The method, which has been extensively tested on the phototrophic purple non-sulphur bacterium Rhodospirillum rubrum, is suitable for extracting large numbers of samples, which is common in systems biology studies, and yields material suitable for subsequent analysis using HPLC and mass spectroscopy. The procedure is particularly suitable for carotenoids and other terpenoids, including quinones, bacteriochlorophyll a and bacteriopheophytin a, and is also useful for the analysis of polar phospholipids. The extraction procedure requires only a single step extraction with a hexane/methanol/water mixture, followed by HPLC using a Spherisorb C18 column, with a mobile phase consisting of acetone-water and a non-linear gradient of 50%-100% acetone. The method was employed for examining the carotenoid composition observed during microaerophilic growth of R. rubrum strains, and was able to determine 18 carotenoids, 4 isoprenoid-quinones, bacteriochlorophyll a and bacteriopheophytin a as well as four different phosphatidylglycerol species of different acyl chain compositions. The analytical procedure was used to examine the dynamics of carotenoid biosynthesis in the major and minor pathways operating simultaneously in a carotenoid biosynthesis mutant of R. rubrum.

: Transcriptional regulation networks are often modeled as Boolean networks. We discuss certain properties of Boolean functions (BFs), which are considered as important in such networks, namely, membership to the classes of unate or canalizing functions. Of further interest is the average sensitivity (AS) of functions. In this article, we discuss several algorithms to test the properties of interest. To test canalizing properties of functions, we apply spectral techniques, which can also be used to characterize the AS of functions as well as the influences of variables in unate BFs. Further, we provide and review upper and lower bounds on the AS of unate BFs based on the spectral representation. Finally, we apply these methods to a transcriptional regulation network of Escherichia coli, which controls central parts of the E. coli metabolism. We find that all functions are unate. Also the analysis of the AS of the network reveals an exceptional robustness against transient fluctuations of the binary variables.a.

: Bacterial strains that were genetically blocked in important metabolic pathways and grown under selective conditions underwent a process of adaptive evolution: certain pathways may have been deregulated and therefore allowed for the circumvention of the given block. A block of endogenous pyruvate synthesis from glycerol was realized by a knockout of pyruvate kinase and phosphoenolpyruvate carboxylase in E. coli. The resulting mutant strain was able to grow on a medium containing glycerol and lactate, which served as an exogenous pyruvate source. Heterologous expression of a pyruvate carboxylase gene from Corynebacterium glutamicum was used for anaplerosis of the TCA cycle. Selective conditions were controlled in a continuous culture with limited lactate feed and an excess of glycerol feed. After 200-300 generations pyruvate-prototrophic mutants were isolated. The genomic analysis of an evolved strain revealed that the genotypic basis for the regained pyruvate-prototrophy was not obvious. A constraint-based model of the metabolism was employed to compute all possible detours around the given metabolic block by solving a hierarchy of linear programming problems. The regulatory network was expected to be responsible for the adaptation process. Hence, a Boolean model of the transcription factor network was connected to the metabolic model. Our model analysis only showed a marginal impact of transcriptional control on the biomass yield on substrate which is a key variable in the selection process. In our experiment, microarray analysis confirmed that transcriptional control probably played a minor role in the deregulation of the alternative pathways for the circumvention of the block.

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.

Activation of nuclear factor κB (NF-κB) by interleukin-1β (IL-1) usually results in an anti-apoptotic activity that is rapidly terminated by a negative feedback loop involving NF-κB dependent resynthesis of its own inhibitor IκBα. However, apoptosis induced by ultraviolet B radiation (UVB) is not attenuated, but significantly enhanced by co-stimulation with IL-1 in human epithelial cells. Under these conditions NF-κB remains constitutively active and turns into a pro-apoptotic factor by selectively repressing anti-apoptotic genes. Two different mechanisms have been separately proposed to explain UV-induced lack of IκBα recurrence: global translational inhibition as well as deactivation of the Ser/Thr phosphatase PP2Ac. Using mathematical modelling, we show that the systems behaviour requires a combination of both mechanisms, and we quantify their contribution in different settings. A mathematical model including both mechanisms is developed and fitted to various experimental data sets. A comparison of the model results and predictions with model variants lacking one of the mechanisms shows that both mechanisms are present in our experimental setting. The model is successfully validated by the prediction of independent data. Weak constitutive IKKβ phosphorylation is shown to be a decisive process in IκBα degradation induced by UVB stimulation alone, but irrelevant for (co-)stimulations with IL-1. In silico knockout experiments show that translational inhibition is predominantly responsible for lack of IκBα recurrence following IL-1+UVB stimulation. In case of UVB stimulation alone, cooperation of both processes causes the observed decrease of IκBα. This shows that the processes leading to activation of transcription factor NF-κB upon stimulation with ultraviolet B radiation with and without interleukin-1 costimulation are more complex than previously thought, involving both a cross talk of UVB induced translational inhibition and PP2Ac deactivation. The importance of each of the mechanisms depends on the specific cellular setting.

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.

Stimulation of human epithelial cells with IL-1 (10 ng/ml) + UVB radiation results in sustained NFκB activation caused by continuous IKKβ phosphorylation. We have recently published a strictly reduced ordinary differential equation model elucidating the involved mechanisms. Here, we compare model extensions for low IL-1 doses (0.5 ng/ml), where delayed IKKβ phosphorylation is observed. The extended model including a positive regulatory element, most likely auto-ubiquitination of TRAF6, reproduces the observed experimental data most convincingly. The extension is shown to be consistent with the original model and contains very sensitive processes which may serve as potential intervention targets.

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.

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 CO(2) 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, AtbetaFruct4, 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.

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-alpha, UV-B irradiation, interleukin-1beta 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.

Background: The 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., Results: This 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., Conclusion: A 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.

Background: Combinatorial 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., Results: We 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., Conclusion: The 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.

The dynamics of biological reaction networks are strongly constrained by thermodynamics. An holistic understanding of their behavior and regulation requires mathematical models that observe these constraints. However, kinetic models may easily violate the constraints imposed by the principle of detailed balance, if no special care is taken. Detailed balance demands that in thermodynamic equilibrium all fluxes vanish. We introduce a thermodynamic-kinetic modeling (TKM) formalism that adapts the concepts of potentials and forces from irreversible thermodynamics to kinetic modeling. In the proposed formalism, the thermokinetic potential of a compound is proportional to its concentration. The proportionality factor is a compound-specific parameter called capacity. The thermokinetic force of a reaction is a function of the potentials. Every reaction has a resistance that is the ratio of thermokinetic force and reaction rate. For mass-action type kinetics, the resistances are constant. Since it relies on the thermodynamic concept of potentials and forces, the TKM formalism structurally observes detailed balance for all values of capacities and resistances. Thus, it provides an easy way to formulate physically feasible, kinetic models of biological reaction networks. The TKM formalism is useful for modeling large biological networks that are subject to many detailed balance relations.