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.

A domain-oriented approach to the reduction of combinatorial complexity in signal transduction networks.

BACKGROUND: Receptors and scaffold proteins possess a number of distinct domains and bind multiple partners. A common problem in modeling signaling systems arises from a combinatorial explosion of different states generated by feasible molecular species. The number of possible species grows exponentially with the number of different docking sites and can easily reach several millions. Models accounting for this combinatorial variety become impractical for many applications. RESULTS: Our results show that under realistic assumptions on domain interactions, the dynamics of signaling pathways can be exactly described by reduced, hierarchically structured models. The method presented here provides a rigorous way to model a large class of signaling networks using macro-states (macroscopic quantities such as the levels of occupancy of the binding domains) instead of micro-states (concentrations of individual species). The method is described using generic multidomain proteins and is applied to the molecule LAT. CONCLUSION: The presented method is a systematic and powerful tool to derive reduced model structures describing the dynamics of multiprotein complex formation accurately.

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

BACKGROUND: Structural 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. RESULTS: We 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. CONCLUSION: The 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.

An integrative model links multiple inputs and signaling pathways to the onset of DNA synthesis in hepatocytes.

During liver regeneration, quiescent hepatocytes re-enter the cell cycle to proliferate and compensate for lost tissue. Multiple signals including hepatocyte growth factor, epidermal growth factor, tumor necrosis factor α, interleukin-6, insulin and transforming growth factor ß orchestrate these responses and are integrated during the G(1) phase of the cell cycle. To investigate how these inputs influence DNA synthesis as a measure for proliferation, we established a large-scale integrated logical model connecting multiple signaling pathways and the cell cycle. We constructed our model based upon established literature knowledge, and successively improved and validated its structure using hepatocyte-specific literature as well as experimental DNA synthesis data. Model analyses showed that activation of the mitogen-activated protein kinase and phosphatidylinositol 3-kinase pathways was sufficient and necessary for triggering DNA synthesis. In addition, we identified key species in these pathways that mediate DNA replication. Our model predicted oncogenic mutations that were compared with the COSMIC database, and proposed intervention targets to block hepatocyte growth factor-induced DNA synthesis, which we validated experimentally. Our integrative approach demonstrates that, despite the complexity and size of the underlying interlaced network, logical modeling enables an integrative understanding of signaling-controlled proliferation at the cellular level, and thus can provide intervention strategies for distinct perturbation scenarios at various regulatory levels.

Exact model reduction of combinatorial reaction networks.

BACKGROUND: Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models. RESULTS: We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs) to a model with 87 ODEs. CONCLUSION: The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.

Dynamics of proximal signaling events after TCR/CD8-mediated induction of proliferation or apoptosis in mature CD8+ T cells.

Engagement of the TCR can induce different functional outcomes such as activation, proliferation, survival, or apoptosis. How the TCR-mediated signaling cascades generating these distinct cellular responses are organized on the molecular level is so far not completely understood. To obtain insight into this question, we analyzed TCR/CD8-mediated signaling events in mature OT-I TCR transgenic T cells under conditions of stimulation that lead to either proliferation or apoptosis. These experiments revealed major differences in the phosphorylation dynamics of LAT, ZAP70, protein kinase B, phospholipase C-gamma1, protein kinase D1, and ERK1/2. Moreover, input signals leading to apoptosis induced a strong, but transient activation of ERK1/2 mainly at sites of TCR-engagement. In contrast, stimuli promoting survival/proliferation generated a low and sustained activation of ERK1/2, which colocalizes with Ras in recycling endosomal vesicles. The transient activation of ERK1/2 under pro-apoptotic conditions of stimulation is at least partially due to the rapid polyubiquitination and subsequent degradation of ZAP70, whereas the sustained activation of ERK1/2 under survival promoting conditions is paralleled by the induction/phosphorylation of anti-apoptotic molecules such as protein kinase B and Bcl-x(L). Collectively, our data provide signaling signatures that are associated with proliferation or apoptosis of T cells.

Structural and functional analysis of cellular networks with CellNetAnalyzer.

BACKGROUND: Mathematical 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. RESULTS: Herein 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. CONCLUSION: CellNetAnalyzer 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.

The galactose switch in Kluyveromyces lactis depends on nuclear competition between Gal4 and Gal1 for Gal80 binding.

The Gal4 protein represents a universally functional transcription activator, which in yeast is regulated by protein-protein interaction of its transcription activation domain with the inhibitor Gal80. Gal80 inhibition is relieved via galactose-mediated Gal80-Gal1-Gal3 interaction. The Gal4-Gal80-Gal1/3 regulatory module is conserved between Saccharomyces cerevisiae and Kluyveromyces lactis. Here we demonstrate that K. lactis Gal80 (KlGal80) is a nuclear protein independent of the Gal4 activity status, whereas KlGal1 is detected throughout the entire cell, which implies that KlGal80 and KlGal1 interact in the nucleus. Consistently KlGal1 accumulates in the nucleus upon KlGAL80 overexpression. Furthermore, we show that the KlGal80-KlGal1 interaction blocks the galactokinase activity of KlGal1 and is incompatible with KlGal80-KlGal4-AD interaction. Thus, we propose that dissociation of KlGal80 from the AD forms the basis of KlGal4 activation in K. lactis. Quantitation of the dissociation constants for the KlGal80 complexes gives a much lower affinity for KlGal1 as compared with Gal4. Mathematical modeling shows that with these affinities a switch based on competition between Gal1 and Gal4 for Gal80 binding is nevertheless efficient provided two monomeric Gal1 molecules interact with dimeric Gal80. Consistent with such a mechanism, analysis of the sedimentation behavior by analytical ultracentrifugation demonstrates the formation of a heterotetrameric KlGal80-KlGal1 complex of 2:2 stoichiometry.

Metabolic design based on a coupled gene expression-metabolic network model of tryptophan production in Escherichia coli.

The presumably high potential of a holistic design approach for complex biochemical reaction networks is exemplified here for the network of tryptophan biosynthesis from glucose, a system whose components have been investigated thoroughly before. A dynamic model that combines the behavior of the trp operon gene expression with the metabolic network of central carbon metabolism and tryptophan biosynthesis is investigated. This model is analyzed in terms of metabolic fluxes, metabolic control, and nonlinear optimization. We compare two models for a wild-type strain and another model for a tryptophan producer. An integrated optimization of the whole network leads to a significant increase in tryptophan production rate for all systems under study. This enhancement is well above the increase that can be achieved by an optimization of subsystems. A constant ratio of control coefficients on tryptophan synthesis rate has been identified for the models regarding or disregarding trp operon expression. Although we found some examples where flux control coefficients even contradict the trends of enzyme activity changes in an optimized profile, flux control can be used as an indication for enzymes that have to be taken into account in optimization.

Bistability analyses of a caspase activation model for receptor-induced apoptosis.

Apoptosis is an important physiological process crucially involved in development and homeostasis of multicellular organisms. Although the major signaling pathways have been unraveled, a detailed mechanistic understanding of the complex underlying network remains elusive. We have translated here the current knowledge of the molecular mechanisms of the death-receptor-activated caspase cascade into a mathematical model. A reduction down to the apoptotic core machinery enables the application of analytical mathematical methods to evaluate the system behavior within a wide range of parameters. Using parameter values from the literature, the model reveals an unstable status of survival indicating the need for further control. Based on recent publications we tested one additional regulatory mechanism at the level of initiator caspase activation and demonstrated that the resulting system displays desired characteristics such as bistability. In addition, the results from our model studies allowed us to reconcile the fast kinetics of caspase 3 activation observed at the single cell level with the much slower kinetics found at the level of a cell population.

A benchmark for methods in reverse engineering and model discrimination: problem formulation and solutions.

A benchmark problem is described for the reconstruction and analysis of biochemical networks given sampled experimental data. The growth of the organisms is described in a bioreactor in which one substrate is fed into the reactor with a given feed rate and feed concentration. Measurements for some intracellular components are provided representing a small biochemical network. Problems of reverse engineering, parameter estimation, and identifiability are addressed. The contribution mainly focuses on the problem of model discrimination. If two or more model variants describe the available experimental data, a new experiment must be designed to discriminate between the hypothetical models. For the problem presented, the feed rate and feed concentration of a bioreactor system are available as control inputs. To verify calculated input profiles an interactive Web site (http://www.sysbio.de/projects/benchmark/) is provided. Several solutions based on linear and nonlinear models are discussed.