Ernst Dieter Gilles

Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors

We present a computational model that offers an integrated quantitative, dynamic, and topological representation of intracellular signal networks, based on known components of epidermal growth factor (EGF) receptor signal pathways. The model provides insight into signal–response relationships between the binding of EGF to its receptor at the cell surface and the activation of downstream proteins in the signaling cascade. It shows that EGF-induced responses are remarkably stable over a 100-fold range of ligand concentration and that the critical parameter in determining signal efficacy is the initial velocity of receptor activation. The predictions of the model agree well with experimental analysis of the effect of EGF on two downstream responses, phosphorylation of ERK-1/2 and expression of the target gene, c-fos.

Metabolic network structure determines key aspects of functionality and regulation

The relationship between structure, function and regulation in complex cellular networks is a still largely open question. Systems biology aims to explain this relationship by combining experimental and theoretical approaches. Current theories have various strengths and shortcomings in providing an integrated, predictive description of cellular networks. Specifically, dynamic mathematical modelling of large-scale networks meets difficulties because the necessary mechanistic detail and kinetic parameters are rarely available. In contrast, structure-oriented analyses only require network topology, which is well known in many cases. Previous approaches of this type focus on network robustness or metabolic phenotype, but do not give predictions on cellular regulation. Here, we devise a theoretical method for simultaneously predicting key aspects of network functionality, robustness and gene regulation from network structure alone. This is achieved by determining and analysing the non-decomposable pathways able to operate coherently at steady state (elementary flux modes). We use the example of Escherichia coli central metabolism to illustrate the method.

Structural and functional analysis of cellular networks with CellNetAnalyzer

BackgroundMathematical modelling of cellular networks is an integral part of Systems Biology and requires appropriate software tools. An important class of methods in Systems Biology deals with structural or topological (parameter-free) analysis of cellular networks. So far, software tools providing such methods for both mass-flow (metabolic) as well as signal-flow (signalling and regulatory) networks are lacking.ResultsHerein we introduce CellNetAnalyzer, a toolbox for MATLAB facilitating, in an interactive and visual manner, a comprehensive structural analysis of metabolic, signalling and regulatory networks. The particular strengths of CellNetAnalyzer are methods for functional network analysis, i.e. for characterising functional states, for detecting functional dependencies, for identifying intervention strategies, or for giving qualitative predictions on the effects of perturbations. CellNetAnalyzer extends its predecessor FluxAnalyzer (originally developed for metabolic network and pathway analysis) by a new modelling framework for examining signal-flow networks. Two of the novel methods implemented in CellNetAnalyzer are discussed in more detail regarding algorithmic issues and applications: the computation and analysis (i) of shortest positive and shortest negative paths and circuits in interaction graphs and (ii) of minimal intervention sets in logical networks.ConclusionCellNetAnalyzer provides a single suite to perform structural and qualitative analysis of both mass-flow- and signal-flow-based cellular networks in a user-friendly environment. It provides a large toolbox with various, partially unique, functions and algorithms for functional network analysis.CellNetAnalyzer is freely available for academic use.

A methodology for the structural and functional analysis of signaling and regulatory networks

BackgroundStructural analysis of cellular interaction networks contributes to a deeper understanding of network-wide interdependencies, causal relationships, and basic functional capabilities. While the structural analysis of metabolic networks is a well-established field, similar methodologies have been scarcely developed and applied to signaling and regulatory networks.ResultsWe propose formalisms and methods, relying on adapted and partially newly introduced approaches, which facilitate a structural analysis of signaling and regulatory networks with focus on functional aspects. We use two different formalisms to represent and analyze interaction networks: interaction graphs and (logical) interaction hypergraphs. We show that, in interaction graphs, the determination of feedback cycles and of all the signaling paths between any pair of species is equivalent to the computation of elementary modes known from metabolic networks. Knowledge on the set of signaling paths and feedback loops facilitates the computation of intervention strategies and the classification of compounds into activators, inhibitors, ambivalent factors, and non-affecting factors with respect to a certain species. In some cases, qualitative effects induced by perturbations can be unambiguously predicted from the network scheme. Interaction graphs however, are not able to capture AND relationships which do frequently occur in interaction networks. The consequent logical concatenation of all the arcs pointing into a species leads to Boolean networks. For a Boolean representation of cellular interaction networks we propose a formalism based on logical (or signed) interaction hypergraphs, which facilitates in particular a logical steady state analysis (LSSA). LSSA enables studies on the logical processing of signals and the identification of optimal intervention points (targets) in cellular networks. LSSA also reveals network regions whose parametrization and initial states are crucial for the dynamic behavior.We have implemented these methods in our software tool CellNetAnalyzer (successor of FluxAnalyzer) and illustrate their applicability using a logical model of T-Cell receptor signaling providing non-intuitive results regarding feedback loops, essential elements, and (logical) signal processing upon different stimuli.ConclusionThe methods and formalisms we propose herein are another step towards the comprehensive functional analysis of cellular interaction networks. Their potential, shown on a realistic T-cell signaling model, makes them a promising tool.

A logical model provides insights into T cell receptor signaling

Cellular decisions are determined by complex molecular interaction networks. Large-scale signaling networks are currently being reconstructed, but the kinetic parameters and quantitative data that would allow for dynamic modeling are still scarce. Therefore, computational studies based upon the structure of these networks are of great interest. Here, a methodology relying on a logical formalism is applied to the functional analysis of the complex signaling network governing the activation of T cells via the T cell receptor, the CD4/CD8 co-receptors, and the accessory signaling receptor CD28. Our large-scale Boolean model, which comprises 94 nodes and 123 interactions and is based upon well-established qualitative knowledge from primary T cells, reveals important structural features (e.g., feedback loops and network-wide dependencies) and recapitulates the global behavior of this network for an array of published data on T cell activation in wild-type and knock-out conditions. More importantly, the model predicted unexpected signaling events after antibody-mediated perturbation of CD28 and after genetic knockout of the kinase Fyn that were subsequently experimentally validated. Finally, we show that the logical model reveals key elements and potential failure modes in network functioning and provides candidates for missing links. In summary, our large-scale logical model for T cell activation proved to be a promising in silico tool, and it inspires immunologists to ask new questions. We think that it holds valuable potential in foreseeing the effects of drugs and network modifications.

Minimal cut sets in biochemical reaction networks

MOTIVATION Structural studies of metabolic networks yield deeper insight into topology, functionality and capabilities of the metabolisms of different organisms. Here, we address the analysis of potential failure modes in metabolic networks whose occurrence will render the network structurally incapable of performing certain functions. Such studies will help to identify crucial parts in the network structure and to find suitable targets for repressing undesired metabolic functions. RESULTS We introduce the concept of minimal cut sets for biochemical networks. A minimal cut set (MCS) is a minimal (irreducible) set of reactions in the network whose inactivation will definitely lead to a failure in certain network functions. We present an algorithm which enables the computation of the MCSs in a given network related to user-defined objective reactions. This algorithm operates on elementary modes. A number of potential applications are outlined, including network verifications, phenotype predictions, assessing structural robustness and fragility, metabolic flux analysis and target identification in drug discovery. Applications are illustrated by the MCSs in the central metabolism of Escherichia coli for growth on different substrates. AVAILABILITY Computation and analysis of MCSs is an additional feature of the FluxAnalyzer (freely available for academic users upon request, special contracts for industrial companies; see web page below). SUPPLEMENTARY INFORMATION http://www.mpi-magdeburg.mpg.de/projects/fluxanalyzer

FluxAnalyzer: exploring structure, pathways, and flux distributions in metabolic networks on interactive flux maps

MOTIVATION The analysis of structure, pathways and flux distributions in metabolic networks has become an important approach for understanding the functionality of metabolic systems. The need of a user-friendly platform for stoichiometric modeling of metabolic networks in silico is evident. RESULTS The FluxAnalyzer is a package for MATLAB and facilitates integrated pathway and flux analysis for metabolic networks within a graphical user interface. Arbitrary metabolic network models can be composed by instances of four types of network elements. The abstract network model is linked with network graphics leading to interactive flux maps which allow for user input and display of calculation results within a network visualization. Therein, a large and powerful collection of tools and algorithms can be applied interactively including metabolic flux analysis, flux optimization, detection of topological features and pathway analysis by elementary flux modes or extreme pathways. The FluxAnalyzer has been applied and tested for complex networks with more than 500,000 elementary modes. Some aspects of the combinatorial complexity of pathway analysis in metabolic networks are discussed. AVAILABILITY Upon request from the corresponding author. Free for academic users (license agreement). Special contracts are available for industrial corporations. SUPPLEMENTARY INFORMATION http://www.mpi-magdeburg.mpg.de/projects/fluxanalyzer.

Dynamics of the direct methanol fuel cell (DMFC) : experiments and model-based analysis

Abstract A laboratory-scale liquid-feed direct methanol fuel cell (DMFC) was operated with different methanol feeding strategies. A proton exchange membrane (PEM) was used as the elecytrolyte. The cell voltage response to dynamic feeding of methanol revealed that a significant voltage increase can be obtained from dynamic changes in methanol feed concentration. The observed fuel cell behaviour was analysed with a mathematical model which consists of anode mass balances, charge balances of both electrodes and electrode kinetic expressions. Anode kinetics were derived from a four-step reaction mechanism with several intermediates bound to the catalyst surface. The model also accounts for the undesired cross-over of methanol, through the PEM, towards the cathode catalyst layer. First, the model is applied to predict steady-state current–voltage characteristics. Then, the cell voltage response to dynamic changes of methanol feed concentration is simulated. The simulated results are in full agreement to experimental observations. It turns out that methanol cross-over can be reduced by periodically pulsed methanol feeding.

A quantitative approach to catabolite repression in Escherichia coli

A dynamic mathematical model was developed to describe the uptake of various carbohydrates (glucose, lactose, glycerol, sucrose, and galactose) in Escherichia coli. For validation a number of isogenic strains with defined mutations were used. By considering metabolic reactions as well as signal transduction processes influencing the relevant pathways, we were able to describe quantitatively the phenomenon of catabolite repression in E. coli. We verified model predictions by measuring time courses of several extra- and intracellular components such as glycolytic intermediates, EII-ACrr phosphorylation level, both LacZ and PtsG concentrations, and total cAMP concentrations under various growth conditions. The entire data base consists of 18 experiments performed with nine different strains. The model describes the expression of 17 key enzymes, 38 enzymatic reactions, and the dynamic behavior of more than 50 metabolites. The different phenomena affecting the phosphorylation level of EIIACrr, the key regulation molecule for inducer exclusion and catabolite repression in enteric bacteria, can now be explained quantitatively.

Correlation between Growth Rates, EIIACrr Phosphorylation, and Intracellular Cyclic AMP Levels in Escherichia coli K-12

In Escherichia coli K-12, components of the phosphoenolpyruvate-dependent phosphotransferase systems (PTSs) represent a signal transduction system involved in the global control of carbon catabolism through inducer exclusion mediated by phosphoenolpyruvate-dependent protein kinase enzyme IIA(Crr) (EIIA(Crr)) (= EIIA(Glc)) and catabolite repression mediated by the global regulator cyclic AMP (cAMP)-cAMP receptor protein (CRP). We measured in a systematic way the relation between cellular growth rates and the key parameters of catabolite repression, i.e., the phosphorylated EIIA(Crr) (EIIA(Crr) approximately P) level and the cAMP level, using in vitro and in vivo assays. Different growth rates were obtained by using either various carbon sources or by growing the cells with limited concentrations of glucose, sucrose, and mannitol in continuous bioreactor experiments. The ratio of EIIA(Crr) to EIIA(Crr) approximately P and the intracellular cAMP concentrations, deduced from the activity of a cAMP-CRP-dependent promoter, correlated well with specific growth rates between 0.3 h(-1) and 0.7 h(-1), corresponding to generation times of about 138 and 60 min, respectively. Below and above this range, these parameters were increasingly uncoupled from the growth rate, which perhaps indicates an increasing role executed by other global control systems, in particular the stringent-relaxed response system.