Dynamics and Structure in Cell Signaling Networks: Off-State Stability and Dynamically Positive Cycles

The signaling system is a fundamental part of the cell, as it regulates essential functions including growth, differentiation, protein synthesis, and apoptosis. A malfunction in this subsystem can disrupt the cell significantly, and is believed to be involved in certain diseases, with cancer being a very important example. While the information available about intracellular signaling networks is constantly growing, and the network topology is actively being analyzed, the modeling of the dynamics of such a system faces difficulties due to the vast number of parameters, which can prove hard to estimate correctly. As the functioning of the signaling system depends on the parameters in a complex way, being able to make general statements based solely on the network topology could be especially appealing. We study a general kinetic model of the signaling system, giving results for the asymptotic behavior of the system in the case of a network with only activatory interactions. We also investigate the possible generalization of our results for the case of a more general model including inhibitory interactions too. We find that feedback cycles made up entirely of activatory interactions (which we call dynamically positive) are especially important, as their properties determine whether the system has a stable signal-off state, which is desirable in many situations to avoid autoactivation due to a noisy environment. To test our results, we investigate the network topology in the Signalink database, and find that the human signaling network indeed has only significantly few dynamically positive cycles, which agrees well with our theoretical arguments.     

Data-Derived Modeling Characterizes Plasticity of MAPK Signaling in Melanoma

The majority of melanomas have been shown to harbor somatic mutations in the RAS-RAF-MEK-MAPK and PI3K-AKT pathways, which play a major role in regulation of proliferation and survival. The prevalence of these mutations makes these kinase signal transduction pathways an attractive target for cancer therapy. However, tumors have generally shown adaptive resistance to treatment. This adaptation is achieved in melanoma through its ability to undergo neovascularization, migration and rearrangement of signaling pathways. To understand the dynamic, nonlinear behavior of signaling pathways in cancer, several computational modeling approaches have been suggested. Most of those models require that the pathway topology remains constant over the entire observation period. However, changes in topology might underlie adaptive behavior to drug treatment. To study signaling rearrangements, here we present a new approach based on Fuzzy Logic (FL) that predicts changes in network architecture over time. This adaptive modeling approach was used to investigate pathway dynamics in a newly acquired experimental dataset describing total and phosphorylated protein signaling over four days in A375 melanoma cell line exposed to different kinase inhibitors. First, a generalized strategy was established to implement a parameter-reduced FL model encoding non-linear activity of a signaling network in response to perturbation. Next, a literature-based topology was generated and parameters of the FL model were derived from the full experimental dataset. Subsequently, the temporal evolution of model performance was evaluated by leaving time-defined data points out of training. Emerging discrepancies between model predictions and experimental data at specific time points allowed the characterization of potential network rearrangement. We demonstrate that this adaptive FL modeling approach helps to enhance our mechanistic understanding of the molecular plasticity of melanoma.     

Predictive modeling of signaling crosstalk during C. elegans vulval development

Caenorhabditis elegans vulval development provides an important paradigm for studying the process of cell fate determination and pattern formation during animal development. Although many genes controlling vulval cell fate specification have been identified, how they orchestrate themselves to generate a robust and invariant pattern of cell fates is not yet completely understood. Here, we have developed a dynamic computational model incorporating the current mechanistic understanding of gene interactions during this patterning process. A key feature of our model is the inclusion of multiple modes of crosstalk between the epidermal growth factor receptor (EGFR) and LIN-12/Notch signaling pathways, which together determine the fates of the six vulval precursor cells (VPCs). Computational analysis, using the model-checking technique, provides new biological insights into the regulatory network governing VPC fate specification and predicts novel negative feedback loops. In addition, our analysis shows that most mutations affecting vulval development lead to stable fate patterns in spite of variations in synchronicity between VPCs. Computational searches for the basis of this robustness show that a sequential activation of the EGFR-mediated inductive signaling and LIN-12 / Notch-mediated lateral signaling pathways is key to achieve a stable cell fate pattern. We demonstrate experimentally a time-delay between the activation of the inductive and lateral signaling pathways in wild-type animals and the loss of sequential signaling in mutants showing unstable fate patterns; thus, validating two key predictions provided by our modeling work. The insights gained by our modeling study further substantiate the usefulness of executing and analyzing mechanistic models to investigate complex biological behaviors.     

ECHO,the executable CHOndrocyte: A computational model to study articular chondrocytes in health and disease

Computational modeling can be used to investigate complex signaling networks in biology. However, most modeling tools are not suitable for molecular cell biologists with little background in mathematics. We have built a visual-based modeling tool for the investigation of dynamic networks. Here, we describe the development of computational models of cartilage development and osteoarthritis, in which a panel of relevant signaling pathways are integrated. In silico experiments give insight in the role of each of the pathway components and reveal which perturbations may deregulate the basal healthy state of cells and tissues.We used a previously developed computational modeling tool Analysis of Networks with Interactive Modeling (ANIMO) to generate an activity network integrating 7 signal transduction pathways resulting in a network containing over 50 nodes and 200 interactions. We performed in silico experiments to characterize molecular mechanisms of cell fate decisions. The model was used to mimic biological scenarios during cell differentiation using RNA-sequencing data of a variety of stem cell sources as input. In a case-study, we wet-lab-tested the model-derived hypothesis that expression of DKK1 (Dickkopf-1) and FRZB (Frizzled related protein, WNT antagonists) and GREM1 (gremlin 1, BMP antagonist) prevents IL1β (Interleukin 1 beta)-induced MMP (matrix metalloproteinase) expression, thereby preventing cartilage degeneration, at least in the short term. We found that a combination of DKK1, FRZB and GREM1 may play a role in modulating the effects of IL1β induced inflammation in human primary chondrocytes.     

Modeling systems-level regulation of host immune responses

Many pathogens are able to manipulate the signaling pathways responsible for the generation of host immune responses. Here we examine and model a respiratory infection system in which disruption of host immune functions or of bacterial factors changes the dynamics of the infection. We synthesize the network of interactions between host immune components and two closely related bacteria in the genus Bordetellae. We incorporate existing experimental information on the timing of immune regulatory events into a discrete dynamic model, and verify the model by comparing the effects of simulated disruptions to the experimental outcome of knockout mutations. Our model indicates that the infection time course of both Bordetellae can be separated into three distinct phases based on the most active immune processes. We compare and discuss the effect of the species-specific virulence factors on disrupting the immune response during their infection of naive, antibody-treated, diseased, or convalescent hosts. Our model offers predictions regarding cytokine regulation, key immune components, and clearance of secondary infections; we experimentally validate two of these predictions. This type of modeling provides new insights into the virulence, pathogenesis, and host adaptation of disease-causing microorganisms and allows systems-level analysis that is not always possible using traditional methods.     

Minimal Network Topologies for Signal Processing during Collective Cell Chemotaxis

Cell-cell communication plays an important role in collective cell migration. However, it remains unclear how cells in a group cooperatively process external signals to determine the group’s direction of motion. Although the topology of signaling pathways is vitally important in single-cell chemotaxis, the signaling topology for collective chemotaxis has not been systematically studied. Here, we combine mathematical analysis and simulations to find minimal network topologies for multicellular signal processing in collective chemotaxis. We focus on border cell cluster chemotaxis in the Drosophila egg chamber, in which responses to several experimental perturbations of the signaling network are known. Our minimal signaling network includes only four elements: a chemoattractant, the protein Rac (indicating cell activation), cell protrusion, and a hypothesized global factor responsible for cell-cell interaction. Experimental data on cell protrusion statistics allows us to systematically narrow the number of possible topologies from more than 40,000,000 to only six minimal topologies with six interactions between the four elements. This analysis does not require a specific functional form of the interactions, and only qualitative features are needed; it is thus robust to many modeling choices. Simulations of a stochastic biochemical model of border cell chemotaxis show that the qualitative selection procedure accurately determines which topologies are consistent with the experiment. We fit our model for all six proposed topologies; each produces results that are consistent with all experimentally available data. Finally, we suggest experiments to further discriminate possible pathway topologies.     

Regulatory Networks and Complex Interactions between the Insulin and Angiotensin II Signalling Systems: Models and Implications for Hypertension and Diabetes

The cross-talk between insulin and angiotensin II signalling pathways plays a significant role in the co-occurrence of diabetes and hypertension. We developed a mathematical model of the system of interactions among the biomolecules that are involved in the cross-talk between the insulin and angiotensin II signalling pathways. We have identified several feedback structures that regulate the dynamic behavior of the individual signalling pathways and their interactions. Different scenarios are simulated and dominant steady-state, dynamic and stability characteristics are revealed. The proposed mechanistic model describes how angiotensin II inhibits the actions of insulin and impairs the insulin-mediated vasodilation. The model also predicts that poor glycaemic control induced by diabetes contributes to hypertension by activating the renin angiotensin aystem.     

A mathematical model of metabolic insulin signaling pathways

We develop a mathematical model that explicitly represents many of the known signaling components mediating translocation of the insulin-responsive glucose transporter GLUT4 to gain insight into the complexities of metabolic insulin signaling pathways. A novel mechanistic model of postreceptor events including phosphorylation of insulin receptor substrate-1, activation of phosphatidylinositol 3-kinase, and subsequent activation of downstream kinases Akt and protein kinase C-zeta is coupled with previously validated subsystem models of insulin receptor binding, receptor recycling, and GLUT4 translocation. A system of differential equations is defined by the structure of the model. Rate constants and model parameters are constrained by published experimental data. Model simulations of insulin dose-response experiments agree with published experimental data and also generate expected qualitative behaviors such as sequential signal amplification and increased sensitivity of downstream components. We examined the consequences of incorporating feedback pathways as well as representing pathological conditions, such as increased levels of protein tyrosine phosphatases, to illustrate the utility of our model for exploring molecular mechanisms. We conclude that mathematical modeling of signal transduction pathways is a useful approach for gaining insight into the complexities of metabolic insulin signaling.     

Encephalomyocarditis virus induces PKR-independent mitogen-activated protein kinase activation in macrophages

In this study, we provide evidence that the double-stranded RNA-dependent protein kinase (PKR) is not required for virus-induced expression of inducible nitric oxide synthase (iNOS) or the activation of specific signaling pathways in macrophages. The infection of RAW264.7 cells with encephalomyocarditis virus (EMCV) induces iNOS expression and nitric oxide production, which are unaffected by a dominant-negative mutant of PKR. EMCV infection also activates the mitogen-activated protein kinase, cyclic AMP response element binding protein, and nuclear factor kappaB (NF-kappaB) signaling cascades at 15 to 30 min postinfection in PKR+/+ and PKR-/- macrophages. Activation of these signaling cascades does not temporally correlate with PKR activity or the accumulation of EMCV RNA, suggesting that an interaction between a structural component of the virion and the cell surface may activate macrophages. Consistent with this hypothesis, empty EMCV capsids induced comparable levels of iNOS expression, nitrite production, and activation of these signaling cascades to those induced by intact virions. These findings support the hypothesis that virion-host cell interactions are primary mediators of the PKR-independent activation of signaling pathways that participate in the macrophage antiviral response of inflammatory gene expression.     

Specification, annotation, visualization and simulation of a large rule-based model for ERBB receptor signaling

ABSTRACT: BACKGROUND: Mathematical/computational models are needed to understand cell signaling networks, which are complex. Signaling proteins contain multiple functional components and multiple sites of post-translational modification. The multiplicity of components and sites of modification ensures that interactions among signaling proteins have the potential to generate myriad protein complexes and post-translational modification states. As a result, the number of chemical species that can be populated in a cell signaling network, and hence the number of equations in an ordinary differential equation model required to capture the dynamics of these species, is prohibitively large. To overcome this problem, the rule-based modeling approach has been developed for representing interactions within signaling networks efficiently and compactly through coarse-graining of the chemical kinetics of molecular interactions. RESULTS: Here, we provide a demonstration that the rule-based modeling approach can be used to specify and simulate a large model for ERBB receptor signaling that accounts for site-specific details of protein-protein interactions. The model is considered large because it corresponds to a reaction network containing more reactions than can be practically enumerated. The model encompasses activation of ERK and Akt, and it can be simulated using a network-free simulator, such as NFsim, to generate time courses of phosphorylation for 55 individual serine, threonine, and tyrosine residues. The model is annotated and visualized in the form of an extended contact map. CONCLUSIONS: With the development of software that implements novel computational methods for calculating the dynamics of large-scale rule-based representations of cellular signaling networks, it is now possible to build and analyze models that include a significant fraction of the protein interactions that comprise a signaling network, with incorporation of the site-specific details of the interactions. Modeling at this level of detail is important for understanding cellular signaling.     

Signaling by the integrated stress response kinase PKR is fine-tuned by dynamic clustering

The double-stranded RNA sensor kinase PKR is one of four integrated stress response (ISR) sensor kinases that phosphorylate the α subunit of eukaryotic initiation factor 2 (eIF2α) in response to stress. The current model of PKR activation considers the formation of back-to-back PKR dimers as a prerequisite for signal propagation. Here we show that PKR signaling involves the assembly of dynamic PKR clusters. PKR clustering is driven by ligand binding to PKR’s sensor domain and by front-to-front interfaces between PKR’s kinase domains. PKR clusters are discrete, heterogeneous, autonomous coalescences that share some protein components with processing bodies. Strikingly, eIF2α is not recruited to PKR clusters, and PKR cluster disruption enhances eIF2α phosphorylation. Together, these results support a model in which PKR clustering may limit encounters between PKR and eIF2α to buffer downstream signaling and prevent the ISR from misfiring.     

An integrated pathway system modeling of Saccharomyces cerevisiae HOG pathway: a Petri net based approach

Biochemical networks comprise many diverse components and interactions between them. It has intracellular signaling, metabolic and gene regulatory pathways which are highly integrated and whose responses are elicited by extracellular actions. Previous modeling techniques mostly consider each pathway independently without focusing on the interrelation of these which actually functions as a single system. In this paper, we propose an approach of modeling an integrated pathway using an event-driven modeling tool, i.e., Petri nets (PNs). PNs have the ability to simulate the dynamics of the system with high levels of accuracy. The integrated set of signaling, regulatory and metabolic reactions involved in Saccharomyces cerevisiae’s HOG pathway has been collected from the literature. The kinetic parameter values have been used for transition firings. The dynamics of the system has been simulated and the concentrations of major biological species over time have been observed. The phenotypic characteristics of the integrated system have been investigated under two conditions, viz., under the absence and presence of osmotic pressure. The results have been validated favorably with the existing experimental results. We have also compared our study with the study of idFBA (Lee et al., PLoS Comput Biol 4:e1000–e1086, 2008) and pointed out the differences between both studies. We have simulated and monitored concentrations of multiple biological entities over time and also incorporated feedback inhibition by Ptp2 which has not been included in the idFBA study. We have concluded that our study is the first to the best of our knowledge to model signaling, metabolic and regulatory events in an integrated form through PN model framework. This study is useful in computational simulation of system dynamics for integrated pathways as there are growing evidences that the malfunctioning of the interplay among these pathways is associated with disease.     

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?β 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.     

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.     

The next step in systems biology: simulating the temporospatial dynamics of molecular network

As a result of the time- and context-dependency of gene expression, gene regulatory and signaling pathways undergo dynamic changes during development. Creating a model of the dynamics of molecular interaction networks offers enormous potential for understanding how a genome orchestrates the developmental processes of an organism. The dynamic nature of pathway topology calls for new modeling strategies that can capture transient molecular links at the runtime. The aim of this paper is to present a brief and informative, but not all-inclusive, viewpoint on the computational aspects of modeling and simulation of a non-static molecular network.