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Wegner et al., (2012). Dynamics and feedback loops in the transforming growth factor β signaling pathway.

November 2012, model of the month by Martina Fröhlich
Original model: BIOMD0000000410

Ligand binding to the transforming growth factor β (TGF-β) receptor can lead to various cellular outputs, ranging from angiogenesis or the suppression of immune response to the inhibition of cell growth and the induction of apoptosis. A loss of TGF-β growth inhibition can be found in many human tumours [1].

Upon ligand binding, the preformed TGF-β type II receptors (TGFRII) bind to and phosphorylate TGF-β type I receptors (TGFRI). The activated TGFRI phosphorylate regulatory Smad proteins (RSmads), which can then form complexes with the co-Smadi, Smad4. The RSmad-Smad4 complexes translocate to the nucleus and activate or repress target genes. Feedback loops shaping the cellular response have been identified, i.e. via Smurf1/2 (ubiquitin E3 ligases), Smad7 (TGFRI antagonist), SARA (Smad anchor for receptor activation) or SnoN/Ski (oncoproteins).

Previously published models (e.g. BIOMD0000000101, BIOMD0000000112, BIOMD0000000342) focus mainly on receptor activation, internalization and the translocation of the signal to the nucleus, but less on the complex interaction of feedback loops. Wegner et al. [2, BIOMD0000000410] address the effects of the downstream network of positive and negative feedback loops and their influence on the dynamic outcome of the system (the formation of active Smad complexes as well as induced target gene expression).

Their model is based on ordinary differential equations (ODEs) and comprises 53 species involved in 91 reactions. They include translocation of model species between the nucleus and the cytoplasm (Figure 1). They apply mainly mass action kinetics as well as Michaelis-Menten type kinetics for the phosphorylation and dephosphorylation of Smad proteins. Furthermore, constitutive expression of components is implemented with constant production and linear degradation rates. The production of the feedback species Smurf1/2, Smad7, Sara and SnoN/Ski is dependent on gene activation by Smad complexes. Ubiquitination leads to the degradation of R-Smads.

Figure 2

Figure 2 Predicted oscillations of phosphorylated Smad2, the active Smad2-Smad4 complexes, and the target gene transcription in the nucleus. Simulation result taken from BIOMD0000000410.

For the selected oscillatory regime, manual variation of parameters showed that Smurf2 and Smad7 have a major impact on the appearance of oscillations. Although under different parameters, oscillations could still be observed while knocking out Smurf2 and Smad7 individually, it was not possible to restore oscillations in a Smurf2 Smad7 double mutant.

Global sensitivity analysis using massive random sampling followed by calculation of the concentration control coefficients revealed that Smad7 and the Smurfs have the strongest potential as negative feedback regulators ( Figure 3). SARA acts exclusively via positive feedback mechanism, but seems to have a minor role in general. By using RNAi experiments as well as a dominant-negative SARA mutant they confirmed that the interaction between SARA and Smads is negligible for the RSmad phosphorylation.

Figure 1

Figure 1 Schematic representation of the model. Figure taken from [2].

They used COPASI to perform numerical simulations, steady state-calculations, optimization, random sampling and sensitivity analysis. They focused on two major questions 1) if and under what conditions the pathway shows oscillations and 2) what effect the feedback loops in the system, have on the steady-state levels of the transcriptionally active Smad-complex as well as gene products. Furthermore, they performed experiments on AML12 mouse hepatoma cells and primary mouse hepatocytes to analyse their model predictions.

By varying the model parameters within well defined regions and optimizing them for the existence of oscillations they found large oscillatory regimes with periods between 30 min and 2h (Figure 2). The existence of a more complex dynamic behaviour potentially also including oscillations was demonstrated by quantitative Western plots analysis.

Figure 3

Figure 3 Distribution of concentration control coefficients of proteins affecting the active Smad complex. Shown on the x-axis are the obtained coefficients, the y-axis shows how often they were found during 500,000 runs of random sampling followed by subsequent sensitivity analysis. Sara->Smad2-P-Smad4 denotes the control coefficient of Sara with respect to the active Smad complex. Figure taken from [2].

Bibliographic references

  1. Liu et al. Ski/Sno and TGF-beta signaling. Cytokine Growth Factor Rev. 2001; Mar ;12(1):1-8
  2. Wegner et al. Dynamics and feedback loops in the transforming growth factor β signaling pathway. Biophys Chem. 2012; Mar ;162:22-34.