Quantitative modeling and analysis of the transforming growth factor beta signaling pathway

Optimal performance objectives in the highly conserved bone morphogenetic protein signaling pathway

Throughout development, complex networks of cell signaling pathways drive cellular decision-making across different tissues and contexts. The transforming growth factor β (TGF-β) pathways, including the BMP/Smad pathway, play crucial roles in determining cellular responses. However, as the Smad pathway is used reiteratively throughout the life cycle of all animals, its systems-level behavior varies from one context to another, despite the pathway connectivity remaining nearly constant. For instance, some cellular systems require a rapid response, while others require high noise filtering. In this paper, we examine how the BMP-Smad pathway balances trade-offs among three such systems-level behaviors, or "Performance Objectives (POs)": response speed, noise amplification, and the sensitivity of pathway output to receptor input. Using a Smad pathway model fit to human cell data, we show that varying non-conserved parameters (NCPs) such as protein concentrations, the Smad pathway can be tuned to emphasize any of the three POs and that the concentration of nuclear phosphatase has the greatest effect on tuning the POs. However, due to competition among the POs, the pathway cannot simultaneously optimize all three, but at best must balance trade-offs among the POs. We applied the multi-objective optimization concept of the Pareto Front, a widely used concept in economics to identify optimal trade-offs among various requirements. We show that the BMP pathway efficiently balances competing POs across species and is largely Pareto optimal. Our findings reveal that varying the concentration of NCPs allows the Smad signaling pathway to generate a diverse range of POs. This insight identifies how signaling pathways can be optimally tuned for each context.

Structure, unique biological properties, and mechanisms of action of transforming growth factor β

Transforming growth factor β (TGF-β) is a ubiquitous molecule that is extremely conserved structurally and plays a systemic role in human organism. TGF-β is a homodimeric molecule consisting of two subunits joined through a disulphide bond. In mammals, three genes code for TGF-β1, TGF-β2, and TGF-β3 isoforms of this cytokine with a dominating expression of TGF-β1. Virtually, all normal cells contain TGF-β and its specific receptors. Considering the exceptional role of fine balance played by the TGF-β in anumber of physiological and pathological processes in human body, this cytokine may be proposed for use in medicine as an immunosuppressant in transplantology, wound healing and bone repair. TGFb itself is an important target in oncology. Strategies for blocking members of TGF-β signaling pathway as therapeutic targets have been considered. In this review, signalling mechanisms of TGF-β1 action are addressed, and their role in physiology and pathology with main focus on carcinogenesis are described.

Optimal Performance Objectives in the Highly Conserved Bone Morphogenetic Protein Signaling Pathway

Throughout development, complex networks of cell signaling pathways drive cellular decision-making across different tissues and contexts. The transforming growth factor β (TGF-β) pathways, including the BMP/Smad pathway, play crucial roles in these cellular responses. However, as the Smad pathway is used reiteratively throughout the life cycle of all animals, its systems-level behavior varies from one context to another, despite the pathway connectivity remaining nearly constant. For instance, some cellular systems require a rapid response, while others require high noise filtering. In this paper, we examine how the BMP- Smad pathway balances trade-offs among three such systems-level behaviors, or "Performance Objectives (POs)": response speed, noise amplification, and the sensitivity of pathway output to receptor input. Using a Smad pathway model fit to human cell data, we show that varying non-conserved parameters (NCPs) such as protein concentrations, the Smad pathway can be tuned to emphasize any of the three POs and that the concentration of nuclear phosphatase has the greatest effect on tuning the POs. However, due to competition among the POs, the pathway cannot simultaneously optimize all three, but at best must balance trade-offs among the POs. We applied the multi-objective optimization concept of the Pareto Front, a widely used concept in economics to identify optimal trade-offs among various requirements. We show that the BMP pathway efficiently balances competing POs across species and is largely Pareto optimal. Our findings reveal that varying the concentration of NCPs allows the Smad signaling pathway to generate a diverse range of POs. This insight identifies how signaling pathways can be optimally tuned for each context.

Computational modeling of TGF-β2:TβRI:TβRII receptor complex assembly as mediated by the TGF-β coreceptor betaglycan

Transforming growth factor-β1, -β2, and -β3 (TGF-β1, -β2, and -β3) are secreted signaling ligands that play essential roles in tissue development, tissue maintenance, immune response, and wound healing. TGF-β ligands form homodimers and signal by assembling a heterotetrameric receptor complex comprised of two type I receptor (TβRI):type II receptor (TβRII) pairs. TGF-β1 and TGF-β3 ligands signal with high potency due to their high affinity for TβRII, which engenders high-affinity binding of TβRI through a composite TGF-β:TβRII binding interface. However, TGF-β2 binds TβRII 200-500 more weakly than TGF-β1 and TGF-β3 and signals with lower potency compared with these ligands. Remarkably, the presence of an additional membrane-bound coreceptor, known as betaglycan, increases TGF-β2 signaling potency to levels similar to TGF-β1 and -β3. The mediating effect of betaglycan occurs even though it is displaced from and not present in the heterotetrameric receptor complex through which TGF-β2 signals. Published biophysics studies have experimentally established the kinetic rates of the individual ligand-receptor and receptor-receptor interactions that initiate heterotetrameric receptor complex assembly and signaling in the TGF-β system; however, current experimental approaches are not able to directly measure kinetic rates for the intermediate and latter steps of assembly. To characterize these steps in the TGF-β system and determine the mechanism of betaglycan in the potentiation of TGF-β2 signaling, we developed deterministic computational models with different modes of betaglycan binding and varying cooperativity between receptor subtypes. The models identified conditions for selective enhancement of TGF-β2 signaling. The models provide support for additional receptor binding cooperativity that has been hypothesized but not evaluated in the literature. The models further showed that betaglycan binding to the TGF-β2 ligand through two domains provides an effective mechanism for transfer to the signaling receptors that has been tuned to efficiently promote assembly of the TGF-β2(TβRII)2(TβRI)2 signaling complex.

A novel strategy for dynamic modeling of genome-scale interaction networks

MOTIVATION

The recent availability of omics data allows the construction of holistic maps of interactions between numerous role-playing biomolecules. However, these networks are often static, ignoring the dynamic behavior of biological processes. On the other hand, dynamic models are commonly constructed on small scales. Hence, the construction of large-scale dynamic models that can quantitatively predict the time-course cellular behaviors remains a big challenge.

RESULTS

In this study, a pipeline is proposed for the automatic construction of large-scale dynamic models. The pipeline uses a list of biomolecules and their time-course trajectories in a given phenomenon as input. First, the interaction network of the biomolecules is constructed. To state the underlying molecular events of each interaction, it is translated into a map of biochemical reactions. Next, to define the kinetics of the reactions, an ordinary differential equation (ODE) is generated for each involved biomolecule. Finally, the parameters of the ODE system are estimated by a novel large-scale parameter approximation method. The high performance of the pipeline is demonstrated by modeling the response of a colorectal cancer cell line to different chemotherapy regimens. In conclusion, Systematic Protein Association Dynamic ANalyzer constructs genome-scale dynamic models, filling the gap between large-scale static and small-scale dynamic modeling strategies. This simulation approach allows for holistic quantitative predictions which are critical for the simulation of therapeutic interventions in precision medicine.

AVAILABILITY AND IMPLEMENTATION

Detailed information about the constructed large-scale model of colorectal cancer is available in supplementary data. The SPADAN toolbox source code is also available on GitHub (https://github.com/PooyaBorzou/SPADAN).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Modeling Cellular Signaling Variability Based on Single-Cell Data: The TGFβ-SMAD Signaling Pathway

Nongenetic heterogeneity is key to cellular decisions, as even genetically identical cells respond in very different ways to the same external stimulus, e.g., during cell differentiation or therapeutic treatment of disease. Strong heterogeneity is typically already observed at the level of signaling pathways that are the first sensors of external inputs and transmit information to the nucleus where decisions are made. Since heterogeneity arises from random fluctuations of cellular components, mathematical models are required to fully describe the phenomenon and to understand the dynamics of heterogeneous cell populations. Here, we review the experimental and theoretical literature on cellular signaling heterogeneity, with special focus on the TGFβ/SMAD signaling pathway.

Data-based stochastic modeling reveals sources of activity bursts in single-cell TGF-β signaling

Cells sense their surrounding by employing intracellular signaling pathways that transmit hormonal signals from the cell membrane to the nucleus. TGF-β/SMAD signaling encodes various cell fates, controls tissue homeostasis and is deregulated in diseases such as cancer. The pathway shows strong heterogeneity at the single-cell level, but quantitative insights into mechanisms underlying fluctuations at various time scales are still missing, partly due to inefficiency in the calibration of stochastic models that mechanistically describe signaling processes. In this work we analyze single-cell TGF-β/SMAD signaling and show that it exhibits temporal stochastic bursts which are dose-dependent and whose number and magnitude correlate with cell migration. We propose a stochastic modeling approach to mechanistically describe these pathway fluctuations with high computational efficiency. Employing high-order numerical integration and fitting to burst statistics we enable efficient quantitative parameter estimation and discriminate models that assume noise in different reactions at the receptor level. This modeling approach suggests that stochasticity in the internalization of TGF-β receptors into endosomes plays a key role in the observed temporal bursting. Further, the model predicts the single-cell dynamics of TGF-β/SMAD signaling in untested conditions, e.g., successfully reflects memory effects of signaling noise and cellular sensitivity towards repeated stimulation. Taken together, our computational framework based on burst analysis, noise modeling and path computation scheme is a suitable tool for the data-based modeling of complex signaling pathways, capable of identifying the source of temporal noise.

Transcriptional noise in intact and TGF-beta treated human kidney cells; the importance of time-series designs

The transforming growth factor (TGF)-β signaling pathway plays a key role in various cellular processes. However, insufficient knowledge about the complex and sometimes paradoxical functions of this pathway hinders its therapeutic targeting. In this study, the transcriptional profile of seven mediators and downstream elements of the TGF-β pathway were assessed in TGF-β treated and untreated human kidney derived cells for 2 weeks in a time course manner. As expected the up-regulation of ACTA2 and COL1A2 was evident in the treated cells. However, we observed remarkable fluctuations in gene expression, even in the supposedly steady states. The magnitude of noise was diverse in the examined genes. Our findings underscore the significance of time-course designs for gene expression analyses and clearly show that misleading data can be obtained in single point measurements. Furthermore, we propose specific considerations in the interpretation of time-course data in the context of noisy gene expression.

Deciphering Epithelial-Mesenchymal Transition Regulatory Networks in Cancer through Computational Approaches

Epithelial–mesenchymal transition (EMT), the process by which epithelial cells can convert into motile mesenchymal cells, plays an important role in development and wound healing but is also involved in cancer progression. It is increasingly recognized that EMT is a dynamic process involving multiple intermediate or “hybrid” phenotypes rather than an “all-or-none” process. However, the role of EMT in various cancer hallmarks, including metastasis, is debated. Given the complexity of EMT regulation, computational modeling has proven to be an invaluable tool for cancer research, i.e., to resolve apparent conflicts in experimental data and to guide experiments by generating testable hypotheses. In this review, we provide an overview of computational modeling efforts that have been applied to regulation of EMT in the context of cancer progression and its associated tumor characteristics. Moreover, we identify possibilities to bridge different modeling approaches and point out outstanding questions in which computational modeling can contribute to advance our understanding of pathological EMT.

TGF-β and IL-6 family signalling crosstalk: an integrated model

Mathematical models for TGF-β and IL-6 signalling have been linked, providing a platform for analyzing the crosstalk between the systems. An integrated IL-6:TGF-β model was developed via a reduced set of reaction equations which incorporate both feedback loops and appropriate time-delays for transcription and translation processes. The model simulates stable, robust and realistic responses to both ligands. Pulsatile (multiple pulses) inputs for both TGF-β and IL-6 have been simulated to investigate the effects of each ligand on the sensitivity, equilibrium and dynamic responses of the integrated signalling system. In our simulations the crosstalk between constant IL-6 and TGF-β signalling via SMAD7 does not appear to be sufficient to render the cells resistant to TGF-β inhibition. However, the simulations predict that pulsatile IL-6 stimulation would increase SMAD7 levels substantially and consequentially, lead to resistance to TGF-β. The model also allows the prediction of the integrated signalling pathway responses to the mutation of key components, e.g. Gp130 ^F/F.

Pattern formation in a nonlocal mathematical model for the multiple roles of the TGF-β pathway in tumour dynamics

The growth and invasion of cancer cells are very complex processes, which can be regulated by the cross-talk between various signalling pathways, or by single signalling pathways that can control multiple aspects of cell behaviour. TGF-β is one of the most investigated signalling pathways in oncology, since it can regulate multiple aspects of cell behaviour: cell proliferation and apoptosis, cell-cell adhesion and epithelial-to-mesenchimal transition via loss of cell adhesion. In this study, we use a mathematical modelling approach to investigate the complex roles of TGF-β signalling pathways on the inhibition and growth of tumours, as well as on the epithelial-to-mesenchimal transition involved in the metastasis of tumour cells. We show that the nonlocal mathematical model derived here to describe repulsive and adhesive cell-cell interactions can explain the formation of new tumour cell aggregations at positions in space that are further away from the main aggregation. Moreover, we show that the increase in cell-cell adhesion leads to fewer but larger aggregations, and the increase in TGF-β molecules - whose late-stage effect is to decrease cell adhesion - leads to many small cellular aggregations. Finally, we perform a sensitivity analysis on some parameters associated with TGF-β dynamics, and use it to investigate the relation between the tumour size and its metastatic spread.

Mathematical model of TGF-βsignalling: feedback coupling is consistent with signal switching

Background

Transforming growth factor β (TGF-β) signalling regulates the development of embryos and tissue homeostasis in adults. In conjunction with other oncogenic changes, long-term perturbation of TGF-β signalling is associated with cancer metastasis. Although TGF-β signalling can be complex, many of the signalling components are well defined, so it is possible to develop mathematical models of TGF-β signalling using reduction and scaling methods. The parameterization of our TGF-β signalling model is consistent with experimental data.

Results

We developed our mathematical model for the TGF-β signalling pathway, i.e. the RF- model of TGF-β signalling, using the “rapid equilibrium assumption” to reduce the network of TGF-β signalling reactions based on the time scales of the individual reactions. By adding time-delayed positive feedback to the inherent time-delayed negative feedback for TGF-β signalling. We were able to simulate the sigmoidal, switch-like behaviour observed for the concentration dependence of long-term (> 3 hours) TGF-β stimulation. Computer simulations revealed the vital role of the coupling of the positive and negative feedback loops on the regulation of the TGF-β signalling system. The incorporation of time-delays for the negative feedback loop improved the accuracy, stability and robustness of the model. This model reproduces both the short-term and long-term switching responses for the intracellular signalling pathways at different TGF-β concentrations. We have tested the model against experimental data from MEF (mouse embryonic fibroblasts) WT, SV40-immortalized MEFs and Gp130 ^F/F MEFs. The predictions from the RF- model are consistent with the experimental data.

Conclusions

Signalling feedback loops are required to model TGF-β signal transduction and its effects on normal and cancer cells. We focus on the effects of time-delayed feedback loops and their coupling to ligand stimulation in this system. The model was simplified and reduced to its key components using standard methods and the rapid equilibrium assumption. We detected differences in short-term and long-term signal switching. The results from the RF- model compare well with experimental data and predict the dynamics of TGF-β signalling in cancer cells with different mutations.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0421-5) contains supplementary material, which is available to authorized users.

Population Heterogeneity in the Epithelial to Mesenchymal Transition Is Controlled by NFAT and Phosphorylated Sp1

Epithelial to mesenchymal transition (EMT) is an essential differentiation program during tissue morphogenesis and remodeling. EMT is induced by soluble transforming growth factor β (TGF-β) family members, and restricted by vascular endothelial growth factor family members. While many downstream molecular regulators of EMT have been identified, these have been largely evaluated individually without considering potential crosstalk. In this study, we created an ensemble of dynamic mathematical models describing TGF-β induced EMT to better understand the operational hierarchy of this complex molecular program. We used ordinary differential equations (ODEs) to describe the transcriptional and post-translational regulatory events driving EMT. Model parameters were estimated from multiple data sets using multiobjective optimization, in combination with cross-validation. TGF-β exposure drove the model population toward a mesenchymal phenotype, while an epithelial phenotype was enhanced following vascular endothelial growth factor A (VEGF-A) exposure. Simulations predicted that the transcription factors phosphorylated SP1 and NFAT were master regulators promoting or inhibiting EMT, respectively. Surprisingly, simulations also predicted that a cellular population could exhibit phenotypic heterogeneity (characterized by a significant fraction of the population with both high epithelial and mesenchymal marker expression) if treated simultaneously with TGF-β and VEGF-A. We tested this prediction experimentally in both MCF10A and DLD1 cells and found that upwards of 45% of the cellular population acquired this hybrid state in the presence of both TGF-β and VEGF-A. We experimentally validated the predicted NFAT/Sp1 signaling axis for each phenotype response. Lastly, we found that cells in the hybrid state had significantly different functional behavior when compared to VEGF-A or TGF-β treatment alone. Together, these results establish a predictive mechanistic model of EMT susceptibility, and potentially reveal a novel signaling axis which regulates carcinoma progression through an EMT versus tubulogenesis response.

Semi-adaptive response and noise attenuation in bone morphogenetic protein signalling

Temporal dynamics of morphogen-driven signalling events are critical for proper embryonic development. During development, cells translate extracellular bone morphogenetic protein (BMP) gradients, often subject to noise, into graded intracellular tail-phosphorylated SMAD (TP-SMAD) levels. Using modelling and experimental approaches, we found that BMPs induce TP-SMAD responses in neural precursor cells in a concentration-dependent manner, which are semi-adaptive within a specific intermediate range of BMP concentration. These semi-adaptive TP-SMAD responses involve an intrinsically slow deactivation of BMP receptors, which attenuates noise by prolonging SMAD deactivation time after BMP withdrawal, but increases response time. Interestingly, negative feedback on BMP receptors is also required for semi-adaptation, which benefits both noise attenuation and response time, and therefore balances the trade-off seen with slow BMP receptor deactivation. These results highlight the rich dynamics of SMAD regulation in response to graded BMP concentration, and elucidate general design principles for balancing noise attenuation and activation speed in signalling systems.

Transcriptional activation by NFκB increases perlecan/HSPG2 expression in the desmoplastic prostate tumor microenvironment

Perlecan/HSPG2, a heparan sulfate proteoglycan typically found at tissue borders including those separating epithelia and connective tissue, increases near sites of invasion of primary prostatic tumors as previously shown for other proteins involved in desmoplastic tissue reaction. Studies of prostate cancer cells and stromal cells from both prostate and bone, the major site for prostate cancer metastasis, showed that cancer cells and a subset of stromal cells increased production of perlecan in response to cytokines present in the tumor microenvironment. In silico analysis of the HSPG2 promoter revealed two conserved NFκB binding sites, in addition to the previously reported SMAD3 binding sites. By systematically transfecting cells with a variety of reporter constructs including sequences up to 2.6 kb from the start site of transcription, we identified an active cis element in the distal region of the HSPG2 promoter, and showed that it functions in regulating transcription of HSPG2. Treatment with TNF-α and/or TGFβ1 identified TNF-α as a major cytokine regulator of perlecan production. TNF-α treatment also triggered p65 nuclear translocation and binding to the HSPG2 regulatory region in stromal cells and cancer cells. In addition to stromal induction of perlecan production in the prostate, we identified a matrix-secreting bone marrow stromal cell type that may represent the source for increases in perlecan in the metastatic bone marrow environment. These studies implicate perlecan in cytokine-mediated, innate tissue responses to cancer cell invasion, a process we suggest reflects a modified wound healing tissue response co-opted by prostate cancer cells.

Biomarkers from biosimulations: Transcriptome-To-Reactome™ Technology for individualized medicine

We validated a model of the TGF-β signaling pathway using reactions from Reactome. Using a patentpending technique, gene expression profiles from individual patients are used to determine model parameters. Gene expression profiles from 45 women, normal, or benign tumor and malignant breast cancer were used as training and validating sets for assessing clinical sensitivity and specificity. Biomarkers were identified from the biosimulation results using sensitivity analyses and derivative properties from the model. A membrane signaling marker had sensitivity of 80% and specificity of 60%; while a nuclear transcription factor marker had sensitivity of 80% and specificity of 90% to predict malignancy. Use of Fagan's nomogram increased probability from 7.5% for positive mammogram to 39% with positive results of the biosimulation for the nuclear marker. Our technology will allow researchers to identify and develop biomarkers and assist clinicians in diagnostic and treatment decision making.

The self-limiting dynamics of TGF-β signaling in silico and in vitro, with negative feedback through PPM1A upregulation

The TGF-β/Smad signaling system decreases its activity through strong negative regulation. Several molecular mechanisms of negative regulation have been published, but the relative impact of each mechanism on the overall system is unknown. In this work, we used computational and experimental methods to assess multiple negative regulatory effects on Smad signaling in HaCaT cells. Previously reported negative regulatory effects were classified by time-scale: degradation of phosphorylated R-Smad and I-Smad-induced receptor degradation were slow-mode effects, and dephosphorylation of R-Smad was a fast-mode effect. We modeled combinations of these effects, but found no combination capable of explaining the observed dynamics of TGF-β/Smad signaling. We then proposed a negative feedback loop with upregulation of the phosphatase PPM1A. The resulting model was able to explain the dynamics of Smad signaling, under both short and long exposures to TGF-β. Consistent with this model, immuno-blots showed PPM1A levels to be significantly increased within 30 min after TGF-β stimulation. Lastly, our model was able to resolve an apparent contradiction in the published literature, concerning the dynamics of phosphorylated R-Smad degradation. We conclude that the dynamics of Smad negative regulation cannot be explained by the negative regulatory effects that had previously been modeled, and we provide evidence for a new negative feedback loop through PPM1A upregulation. This work shows that tight coupling of computational and experiments approaches can yield improved understanding of complex pathways.

TGF-β signaling pathway regulates a variety of cellular responses, such as differentiation, migration and apoptosis. Phosphorylated R-Smad, the central signaling protein in this pathway, exhibits self-limiting behaviors: it not only decreases quickly after TGF-β is removed, but it also decreases slowly when TGF-β remains abundant. These two self-limiting behaviors are important to understand clearly because diseases such as cancer and fibrosis might benefit from treatments to decrease Smad signaling. Several negative regulatory effects have been reported previously, and we studied the dynamics of these effects with computational modeling. Analyzing the timing of negative regulation revealed that the three most widely accepted effects were not sufficient to explain the observed declines. After considering and excluding several alternative models, we arrived at a model in which TGF-β upregulated the phosphatase PPM1A. We tested for PPM1A upregulation in cell culture experiments. In addition, our model was able to explain why different durations of TGF-β exposure could cause seemingly opposite results about the importance of Smad degradation.

An integrative modeling framework reveals plasticity of TGF-β signaling

Background

The TGF-β transforming growth factor is the most pleiotropic cytokine controlling a broad range of cellular responses that include proliferation, differentiation and apoptosis. The context-dependent multifunctional nature of TGF-β is associated with complex signaling pathways. Differential models describe the dynamics of the TGF-β canonical pathway, but modeling the non-canonical networks constitutes a major challenge. Here, we propose a qualitative approach to explore all TGF-β-dependent signaling pathways.

Results

Using a new formalism, CADBIOM, which is based on guarded transitions and includes temporal parameters, we have built the first discrete model of TGF-β signaling networks by automatically integrating the 137 human signaling maps from the Pathway Interaction Database into a single unified dynamic model. Temporal property-checking analyses of 15934 trajectories that regulate 145 TGF-β target genes reveal the association of specific pathways with distinct biological processes. We identify 31 different combinations of TGF-β with other extracellular stimuli involved in non-canonical TGF-β pathways that regulate specific gene networks. Extensive analysis of gene expression data further demonstrates that genes sharing CADBIOM trajectories tend to be co-regulated.

Conclusions

As applied here to TGF-β signaling, CADBIOM allows, for the first time, a full integration of highly complex signaling pathways into dynamic models that permit to explore cell responses to complex microenvironment stimuli.

Literature-based automated reconstruction, expansion, and refinement of the TGF-β superfamily ligand-receptor network

The TGF-β pathway transduces a variety of extracellular signals into intracellular responses that control multiple cellular processes, including cell growth, apoptosis, and differentiation. It encompasses 33 ligands that interact with 7 type II receptors and 5 type I receptors at the plasma membrane to potentially form 1,155 ligand-receptor complexes in mammalian cells. Retrieving the information of the complexes that are actually formed from reading the literature might be tedious and prone to missing links. Here, we have developed an automated literature-mining procedure to obtain the interactions of the TGF-β ligand-receptor network. By querying the Information Hyperlinked over Proteins (iHOP) online service and processing the results, we were able to find pairwise interactions between ligands and receptors that allowed us to build the network automatically from the literature. Comparison with available published review papers indicates that this method is able to automatically reconstruct and expand the TGF-β superfamily ligand-receptor network. Retrieving and parsing the full text of the manuscripts containing the interactions allowed us to refine the network interactions for specific cell lines.

In silico identification of potential therapeutic targets in the TGF-β signal transduction pathway

The transforming growth factor-β (TGF-β) superfamily of cytokines controls fundamental cellular processes, such as proliferation, motility, differentiation, and apoptosis. This fundamental role is emphasized by the widespread presence of mutations of the core components of the TGF-β signal transduction pathway in a number of human diseases. Therefore, there is an increasing interest in the development of therapies to specifically target this pathway. Here we develop a computational approach to identify potential intervention points that are capable of restoring the normal signaling dynamics to the mutated system while maintaining the behavior of normal cells substantially unperturbed. We apply this approach explicitly to the TGF-β pathway to study the signaling dynamics of mutated and normal cells treated with inhibitory drugs and identify the processes in the pathway that are most susceptible to therapeutic intervention.

Characterization of negative feedback network motifs in the TGF-β signaling pathway

{Chung, 2009 #1}The transforming growth factor-β (TGF-β) superfamily of cytokines plays a fundamental role in a wide variety of cellular processes, including growth, differentiation, apoptosis, and tissue homeostasis. Its relevance is emphasized by the mutations of its core components that are associated with diverse human diseases, such as cancer and cardiovascular pathologies. A prominent regulator of the pathway is Smad7, which attenuates the signal and controls its duration in a cell-type-dependent manner through a negative feedback loop. Here, we characterize all the potential Smad7-mediated negative feedback network motifs and investigate their effects on the signaling dynamics upon stimulation with TGF-β and bone morphogenetic protein (BMP) ligands. The results show that the specific negative feedback implementation is a key determinant of both the response of the system to single and multiple ligands of the TGF-β superfamily and its robustness and sensitivity to parameter perturbations.

Computational modelling of Smad-mediated negative feedback and crosstalk in the TGF-β superfamily network

The transforming growth factor-β (TGF-β) signal transduction pathway controls many cellular processes, including differentiation, proliferation and apoptosis. It plays a fundamental role during development and it is dysregulated in many diseases. The factors that control the dynamics of the pathway, however, are not fully elucidated yet and so far computational approaches have been very limited in capturing the distinct types of behaviour observed under different cellular backgrounds and conditions into a single-model description. Here, we develop a detailed computational model for TGF-β signalling that incorporates elements of previous models together with crosstalking between Smad1/5/8 and Smad2/3 channels through a negative feedback loop dependent on Smad7. The resulting model accurately reproduces the diverse behaviour of experimental datasets for human keratinocytes, bovine aortic endothelial cells and mouse mesenchymal cells, capturing the dynamics of activation and nucleocytoplasmic shuttling of both R-Smad channels. The analysis of the model dynamics and its system properties revealed Smad7-mediated crosstalking between Smad1/5/8 and Smad2/3 channels as a major determinant in shaping the distinct responses to single and multiple ligand stimulation for different cell types.

Macrophage-specific deletion of transforming growth factor-β1 does not prevent renal fibrosis after severe ischemia-reperfusion or obstructive injury

Macrophage infiltration is a prominent feature of the innate immune response to kidney injury. The persistence of macrophages is associated with tubulointerstitial fibrosis and progression of chronic kidney disease. Macrophages are known to be major producers of transforming growth factor-β1 (TGF-β1), especially in the setting of phagocytosis of apoptotic cells. TGF-β1 has long been implicated as a central mediator of tissue scarring and fibrosis in many organ disease models, including kidney disease. In this study, we show that homozygous deletion of Tgfb1 in myeloid lineage cells in mice heterozygous for Tgfb1 significantly reduces kidney Tgfb1 mRNA expression and Smad activation at late time points after renal ischemia-reperfusion injury. However, this reduction in kidney Tgfb1 expression and signaling results in only a modest reduction of isolated fibrosis markers and does not lead to decreased interstitial fibrosis in either ischemic or obstructive injury models. Thus, targeting macrophage-derived TGF-β1 does not appear to be an effective therapy for attenuating progressive renal fibrosis after kidney injury.

A hybrid model of tumor-stromal interactions in breast cancer

Ductal carcinoma in situ (DCIS) is an early stage noninvasive breast cancer that originates in the epithelial lining of the milk ducts, but it can evolve into comedo DCIS and ultimately, into the most common type of breast cancer, invasive ductal carcinoma. Understanding the progression and how to effectively intervene in it presents a major scientific challenge. The extracellular matrix (ECM) surrounding a duct contains several types of cells and several types of growth factors that are known to individually affect tumor growth, but at present the complex biochemical and mechanical interactions of these stromal cells and growth factors with tumor cells is poorly understood. Here we develop a mathematical model that incorporates the cross-talk between stromal and tumor cells, which can predict how perturbations of the local biochemical and mechanical state influence tumor evolution. We focus on the EGF and TGF-β signaling pathways and show how up- or down-regulation of components in these pathways affects cell growth and proliferation. We then study a hybrid model for the interaction of cells with the tumor microenvironment (TME), in which epithelial cells (ECs) are modeled individually while the ECM is treated as a continuum, and show how these interactions affect the early development of tumors. Finally, we incorporate breakdown of the epithelium into the model and predict the early stages of tumor invasion into the stroma. Our results shed light on the interactions between growth factors, mechanical properties of the ECM, and feedback signaling loops between stromal and tumor cells, and suggest how epigenetic changes in transformed cells affect tumor progression.

Spatial aspects in the SMAD signaling pathway

Among other approaches, differential equations are used for a deterministic quantitative description of time-dependent biological processes. For intracellular systems, such as signaling pathways, most existing models are based on ordinary differential equations. These models describe temporal processes, while they neglect spatial aspects. We present a model for the SMAD signaling pathway, which gives a temporal and spatial description on the basis of reaction diffusion equations to answer the question whether cell geometry plays a role in signaling. In this article we simulate the ordinary differential equations as well as partial differential equations of parabolic type with suile numerical methods, the latter on different cell geometries. In addition to manual construction of idealized cells, we also construct meshes from microscopy images of real cells. The main focus of the paper is to compare the results of the model without and with spatial aspects to answer the addressed question. The results show that diffusion in the model can lead to significant intracellular gradients of signaling molecules and changes the level of response to the signal transduced by the signaling pathway. In particular, the extent of these observations depends on the geometry of the cell.

Dynamics of TGF-β/Smad signaling

The physiological responses to TGF-β stimulation are diverse and vary amongst different cell types and environmental conditions. Even though the principal molecular components of the canonical and the non-canonical TGF-β signaling pathways have been largely identified, the mechanism that underlies the well-established context dependent physiological responses remains a mystery. Understanding how the components of TGF-β signaling function as a system and how this system functions in the context of the global cellular regulatory network requires a more quantitative and systematic approach. Here, we review the recent progress in understanding TGF-β biology using integration of mathematical modeling and quantitative experimental analysis. These studies reveal many interesting dynamics of TGF-β signaling and how cells quantitatively decode variable doses of TGF-β stimulation.

Dynamic regulation of Tgf-B signaling by Tif1γ: a computational approach

TIF1γ (Transcriptional Intermediary Factor 1 γ) has been implicated in Smad-dependent signaling by Transforming Growth Factor beta (TGF-β). Paradoxically, TIF1γ functions both as a transcriptional repressor or as an alternative transcription factor that promotes TGF-β signaling. Using ordinary differential-equation models, we have investigated the effect of TIF1γ on the dynamics of TGF-β signaling. An integrative model that includes the formation of transient TIF1γ-Smad2-Smad4 ternary complexes is the only one that can account for TGF-β signaling compatible with the different observations reported for TIF1γ. In addition, our model predicts that varying TIF1γ/Smad4 ratios play a critical role in the modulation of the transcriptional signal induced by TGF-β, especially for short stimulation times that mediate higher threshold responses. Chromatin immunoprecipitation analyses and quantification of the expression of TGF-β target genes as a function TIF1γ/Smad4 ratios fully validate this hypothesis. Our integrative model, which successfully unifies the seemingly opposite roles of TIF1γ, also reveals how changing TIF1γ/Smad4 ratios affect the cellular response to stimulation by TGF-β, accounting for a highly graded determination of cell fate.

Inferring Biological Mechanisms by Data-Based Mathematical Modelling: Compartment-Specific Gene Activation during Sporulation in Bacillus subtilis as a Test Case

Biological functionality arises from the complex interactions of simple components. Emerging behaviour is difficult to recognize with verbal models alone, and mathematical approaches are important. Even few interacting components can give rise to a wide range of different responses, that is, sustained, transient, oscillatory, switch-like responses, depending on the values of the model parameters. A quantitative comparison of model predictions and experiments is therefore important to distinguish between competing hypotheses and to judge whether a certain regulatory behaviour is at all possible and plausible given the observed type and strengths of interactions and the speed of reactions. Here I will review a detailed model for the transcription factor σ(F), a regulator of cell differentiation during sporulation in Bacillus subtilis. I will focus in particular on the type of conclusions that can be drawn from detailed, carefully validated models of biological signaling networks. For most systems, such detailed experimental information is currently not available, but accumulating biochemical data through technical advances are likely to enable the detailed modelling of an increasing number of pathways. A major challenge will be the linking of such detailed models and their integration into a multiscale framework to enable their analysis in a larger biological context.

A control engineering approach to understanding the TGF-β paradox in cancer

TGF-β, a key cytokine that regulates diverse cellular processes, including proliferation and apoptosis, appears to function paradoxically as a tumour suppressor in normal cells, and as a tumour promoter in cancer cells, but the mechanisms underlying such contradictory roles remain unknown. In particular, given that this cytokine is primarily a tumour suppressor, the conundrum of the unusually high level of TGF-β observed in the primary cancer tissue and blood samples of cancer patients with the worst prognosis, remains unresolved. To provide a quantitative explanation of these paradoxical observations, we present, from a control theory perspective, a mechanistic model of TGF-β-driven regulation of cell homeostasis. Analysis of the overall system model yields quantitative insight into how cell population is regulated, enabling us to propose a plausible explanation for the paradox: with the tumour suppressor role of TGF-β unchanged from normal to cancer cells, we demonstrate that the observed increased level of TGF-β is an effect of cancer cell phenotypic progression (specifically, acquired TGF-β resistance), not the cause. We are thus able to explain precisely why the clinically observed correlation between elevated TGF-β levels and poor prognosis is in fact consistent with TGF-β's original (and unchanged) role as a tumour suppressor.

Trafficking coordinate description of intracellular transport control of signaling networks

Many cellular networks rely on the regulated transport of their components to transduce extracellular information into precise intracellular signals. The dynamics of these networks is typically described in terms of compartmentalized chemical reactions. There are many important situations, however, in which the properties of the compartments change continuously in a way that cannot naturally be described by chemical reactions. Here, we develop an approach based on transport along a trafficking coordinate to precisely describe these processes and we apply it explicitly to the TGF-β signal transduction network, which plays a fundamental role in many diseases and cellular processes. The results of this newly introduced approach accurately capture the distinct TGF-β signaling dynamics of cells with and without cancerous backgrounds and provide an avenue to predict the effects of chemical perturbations in a way that closely recapitulates the observed cellular behavior.

Plasticity of TGF-β signaling

Background

The family of TGF-β ligands is large and its members are involved in many different signaling processes. These signaling processes strongly differ in type with TGF-β ligands eliciting both sustained or transient responses. Members of the TGF-β family can also act as morphogen and cellular responses would then be expected to provide a direct read-out of the extracellular ligand concentration. A number of different models have been proposed to reconcile these different behaviours. We were interested to define the set of minimal modifications that are required to change the type of signal processing in the TGF-β signaling network.

Results

To define the key aspects for signaling plasticity we focused on the core of the TGF-β signaling network. With the help of a parameter screen we identified ranges of kinetic parameters and protein concentrations that give rise to transient, sustained, or oscillatory responses to constant stimuli, as well as those parameter ranges that enable a proportional response to time-varying ligand concentrations (as expected in the read-out of morphogens). A combination of a strong negative feedback and fast shuttling to the nucleus biases signaling to a transient rather than a sustained response, while oscillations were obtained if ligand binding to the receptor is weak and the turn-over of the I-Smad is fast. A proportional read-out required inefficient receptor activation in addition to a low affinity of receptor-ligand binding. We find that targeted modification of single parameters suffices to alter the response type. The intensity of a constant signal (i.e. the ligand concentration), on the other hand, affected only the strength but not the type of the response.

Conclusions

The architecture of the TGF-β pathway enables the observed signaling plasticity. The observed range of signaling outputs to TGF-β ligand in different cell types and under different conditions can be explained with differences in cellular protein concentrations and with changes in effective rate constants due to cross-talk with other signaling pathways. It will be interesting to uncover the exact cellular differences as well as the details of the cross-talks in future work.

The role of the microenvironment in tumor growth and invasion

Mathematical modeling and computational analysis are essential for understanding the dynamics of the complex gene networks that control normal development and homeostasis, and can help to understand how circumvention of that control leads to abnormal outcomes such as cancer. Our objectives here are to discuss the different mechanisms by which the local biochemical and mechanical microenvironment, which is comprised of various signaling molecules, cell types and the extracellular matrix (ECM), affects the progression of potentially-cancerous cells, and to present new results on two aspects of these effects. We first deal with the major processes involved in the progression from a normal cell to a cancerous cell at a level accessible to a general scientific readership, and we then outline a number of mathematical and computational issues that arise in cancer modeling. In Section 2 we present results from a model that deals with the effects of the mechanical properties of the environment on tumor growth, and in Section 3 we report results from a model of the signaling pathways and the tumor microenvironment (TME), and how their interactions affect the development of breast cancer. The results emphasize anew the complexities of the interactions within the TME and their effect on tumor growth, and show that tumor progression is not solely determined by the presence of a clone of mutated immortal cells, but rather that it can be 'community-controlled'.

Dynamic modeling and analysis of cancer cellular network motifs

With the advent of high-throughput biology, we now routinely scan cells and organisms at practically all levels, from genome to protein, metabolism, signaling and other cellular functions. This methodology allowed biological studies to move from a reductionist approach, such as isolation of specific pathways and mechanisms, to a more integrative approach, where biological systems are seen as a network of interconnected components that provide specific outputs and functions in response to stimuli. Recent literature on biological networks demonstrates two important concepts that we will consider in this review: (i) cellular pathways are highly interconnected and should not be studied separately, but as a network; (ii) simple, recurrent feedback motifs within the network can produce very specific functions that favor their modular use. The first theme differs from the traditional approach in biology because it provides a framework (i.e., the network view) in which large datasets are analyzed with an unbiased view. The second theme (feedback motifs) shows the importance of locally analyzing the dynamic properties of biological networks in order to better understand their functionality. We will review these themes with examples from cell signaling networks, gene regulatory networks and metabolic pathways. The deregulation of cellular networks (metabolism, signaling etc.) is involved in cancer, but the size of the networks and resulting non-linear behavior do not allow for intuitive reasoning. In that context, we argue that the qualitative classification of the 'building blocs' of biological networks (i.e. the motifs) in terms of dynamics and functionality will be critical to improve our understanding of cancer biology and rationalize the wealth of information from high-throughput experiments. From the examples highlighted in this review, it is clear that dynamic feedback motifs can be used to provide a unified view of various cellular processes involved in cancer and this will be critical for future research on personalized and predictive cancer therapies.

Immune response modeling of interferon beta-pretreated influenza virus-infected human dendritic cells

The pretreatment of human dendritic cells with interferon-beta enhances their immune response to influenza virus infection. We measured the expression levels of several key players in that response over a period of 13 h both during pretreatment and after viral infection. Their activation profiles reflect the presence of both negative and positive feedback loops in interferon induction and interferon signaling pathway. Based on these measurements, we have developed a comprehensive computational model of cellular immune response that elucidates its mechanism and its dynamics in interferon-pretreated dendritic cells, and provides insights into the effects of duration and strength of pretreatment.

Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: a mathematical model and experiments

It is well known that tumor and its microenvironment, or stroma, interact with each other and that this interaction plays a critical role in tumor initiation, growth, and metastasis. This interaction consists of complex relations between tumor cells, stromal cells such as fibroblasts, epithelial cells and immunocytes, the vascular system, the extracellular matrix, and cytokines secreted by the cells. Understanding these relationships may lead to new therapeutic approaches to cancer. In the present paper, we consider tumor-stroma crosstalk in a simple in vitro situation which involves interaction between tumor epithelial cells from breast cancer and a microenvironment consisting of just fibroblasts. The two populations of cells are separated by a semi-permeable membrane that allows only cytokines to cross over. We develop a mathematical model that includes two critical growth factors: TGF-beta, produced by the tumor cells, and EGF, secreted by the fibroblasts. The TGF-beta modifies the microenvironment by transforming fibroblasts into myofibroblasts. Myofibroblasts secrete higher concentrations of EGF than fibroblasts, thereby, increasing the proliferation of tumor cells. Thus already in this simple setup one sees a mutual interaction between tumor cells and their microenvironment. We conducted experiments which show good agreement with the model's simulations, hence confirming the model's ability to predict aspects of tumor cell behavior in response to signaling from fibroblasts.