Constraint-based modeling and kinetic analysis of the Smad dependent TGF-beta signaling pathway

Abstract

Background: Investigation of dynamics and regulation of the TGF-beta signaling pathway is central to the understanding of complex cellular processes such as growth, apoptosis, and differentiation. In this study, we aim at using systems biology approach to provide dynamic analysis on this pathway.

Methodology/principal findings: We proposed a constraint-based modeling method to build a comprehensive mathematical model for the Smad dependent TGF-beta signaling pathway by fitting the experimental data and incorporating the qualitative constraints from the experimental analysis. The performance of the model generated by constraint-based modeling method is significantly improved compared to the model obtained by only fitting the quantitative data. The model agrees well with the experimental analysis of TGF-beta pathway, such as the time course of nuclear phosphorylated Smad, the subcellular location of Smad and signal response of Smad phosphorylation to different doses of TGF-beta.

Conclusions/significance: The simulation results indicate that the signal response to TGF-beta is regulated by the balance between clathrin dependent endocytosis and non-clathrin mediated endocytosis. This model is useful to be built upon as new precise experimental data are emerging. The constraint-based modeling method can also be applied to quantitative modeling of other signaling pathways.

Figure 1. Schematic representation of Smad dependent TGF-β signaling pathway.

Detailed information about this pathway is described in the text.

Figure 2. Comparison of experimental analysis and simulation results from the model obtained by constraint-based modeling method.

(A–B) for “in-sample fit”. (C–D) for “out-sample fit”. (A) Comparison of the model time course and experimental time course of Smad2 phosphorylation with 24 hours TGF-β treatment. The experimental data is normalized from Figure 1A in Lin et al. . (B) Effect of type I receptor kinase inhibitor SB431542. Cells were treated with TGF-β for 30 minutes, then were washed out TGF-β at 30th minute and added SB431542 to prevent rephosphorylation of Smad2. The experimental data is normalized from Figure 1C in Lin et al. . (C) Comparison of the model time course with an experimental time course of nuclear phosphorylated Smad2 after TGF-β treatment (80 pM, 2 ng/ml). The western-blot data reported by Inman et al. (Fig. 1A, top panel) is quantified with Scion Image software . (D) Subcellular location of Smad2 after TGF-β treatment (80 pM). The concentrations shown here refer to the local concentrations in cytoplasm and nucleus.

Figure 3. Effects on Smad2 phosphorylation by different doses of TGF-β.

Figure 4. Comparison of experimental analysis and simulation results from the model obtained by only fitting the time course data.

(A–B) The model has been over-fitted for “in-sample fit”. (C) The model has a bad prediction for “out-sample fit”. (A) Comparison of the model time course and experimental time course of Smad2 phosphorylation with 24 hours TGF-β treatment. Experimental data is the same as described in Figure 2A. (B) Effect of type I receptor kinase inhibitor SB431542. Experimental data is the same as described in Figure 2B. (C) Effects on Smad2 phosphorylation by different doses of TGF-β.

Figure 5. Sensitivity analysis of the rate constants on nuclear Smad phosphorylation.

The original values of the sensitivities are present Table S3

Figure 6. Computational simulations of the time course of nuclear phosphorylated Smad2 by the inhibition of different receptor endocytosis in 1000 parameter sets estimated by constraint-based modeling method.

The red lines refer the simulations for the parameter values listed in Table 1. Blue lines correspond to the 1000 parameter sets with the estimated parameter values listed in the Table S1. (A) Same parameter values as those in parameter sets with the exception that clathrin dependent internalization rate constant is decreased by a factor of 10: ki_EE = 0.033 min⁻¹. (B) Same parameters values as those in parameter sets. (C) Same parameter values as those in parameter sets with the exception that non-clathrin dependent internalization rate constant is decreased by a factor of 10: ki_Cave = 0.033 min⁻¹. (D) Same parameter values as those in parameter sets with the exception that ki_EE is decreased by a factor of 10 and ki_Cave is decreased by a factor of 2: ki_EE = 0.033 min⁻¹, ki_Cave = 0.165 min⁻¹. (E) Same parameter values as those in parameter sets with the exception that ki_EE and ki_Cave are decreased by a factor of 10: ki_EE = 0.033 min⁻¹, ki_Cave = 0.033 min⁻¹. (F) Same parameter values as those in parameter sets with the exception that ki_EE is decreased by a factor of 2 and ki_Cave is decreased by a factor of 10: ki_EE = 0.165 min⁻¹, ki_Cave = 0.033 min⁻¹.