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

Abstract

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.

Figure 1. The pathway diagram of Smad signaling (using symbols from BioCarta).

The dashed arrows indicate those reactions which are modeled in black box. The red arrows indicate the negative regulatory effects: (1) PPM1A dephosphorylating phospho-R-Smad; (2) Smurf2 induced proteasome degradation of phospho-R-Smad; (3) I-Smad induced receptor inhibition; (4) PPM1A upregulation by Smad signaling.

Figure 2. Model fitting results with different combinations of known negative regulatory effects.

(A–E) Dots: experimental data from Lin et al. . All P-Smad2 measurements used total cell lysate. Curves: the model simulations were fitted to the two sets of data simultaneously. (A) Model 1: R-Smad Dephosphorylation; (B) Model 2: R-Smad Dephosphorylation and Receptor Degradation; (C) Model 3: Receptor Degradation; (D) Model 4: P-Smad Degradation; (E) Model 5: R-Smad Dephosphorylation, Receptor Degradation and P-Smad Degradation. The reactions of each model are listed in the Supporting Information. (F–H) Predictions of the best-fit model (Model 5) in MG132 pre-treated cells. Simulation of MG132 treatment was performed by turning off the Smurf2-induced P-Smad Degradation (setting kdeg_pSmad2 = 0) in Model 5. (F) Comparison of the model prediction and experimental data from Lin et al. in the short-exposure experiment. (G) Model prediction in the long-exposure experiment. The green shaded area shows the cumulative difference between +MG132 and -MG132. (H) A histogram plots the cumulative differences seen in the short-exposure experiment (red) and the long-exposure experiment (blue).

Figure 3. Predictions and validations of Receptor Degradation.

(A) Different rates of I-Smad-induced Receptor Degradation (klid = 10⁻⁶∼10⁻²) were applied to Model 5, and the rate of Smurf-induced P-Smad Degradation (kdeg_pSmad2) was fitted to the short-exposure experimental data (red dots) and the long-exposure experimental data (blue dots). All the other parameters were kept the same as those in Model 5 (B) Different Receptor Degradation rates led to different levels of the type I receptor (T1R). Green curves were generated from all models in panel (A) with klid = 10⁻⁶∼10⁻² and kdeg_pSmad2 estimated. (C) In the fitted models in panel (A), the T1R level has negative correlation with the Receptor Degradation rate (klid) but positive correlation with the P-Smad Degradation rate (kdeg_pSmad2). (D) Quantified data from 3 replicates of the western blot in (E). There is no significant loss of the T1R comparing the first and last data points (P>0.05). (E) Western blot of the T1R from whole cell lysates of HaCaT cells treated with TGF-β for 24 hrs (representative of 3 replicates). (F) In the fitted models in panel (A), the rates of Receptor Degradation (klid) and P-Smad Degradation (kdeg_pSmad2) have negative correlation.

Figure 4. Simulations and experiments for P-Smad Degradation.

(A) Model 6 with P-Smad Degradation and R-Smad Dephosphorylation (but no Receptor Degradation) was fitted to both the short-exposure (red) and long-exposure (blue) experimental data. (B) Model 6 predicted significant loss of total R-Smad (green curve), while ELISA measurements showed insignificant change (P>0.05, comparing the first and last data points) in total R-Smad concentration (green dots). (C) ELISA measurements of phospho-R-Smad are consistent with previous measurements performed by Western blot . Cell lysates were from the same samples as panel B. (D) Model 7 was fitted to the phospho-R-Smad data while constraining the total R-Smad level to be constant.

Figure 5. Predictions and validation of PPM1A Upregulation.

(A) Western blot of PPM1A in HaCaT cells with 2 ng/ml TGF-β treatment, representative of 3 replicates. (B) Model 8 predicted PPM1A upregulation under long-exposure of TGF-β (green curve). Our experimental validation showed significant upregulation of PPM1A (green dots, quantification from 3 Western blots, P<0.05 comparing the untreated data point and the 1 hr data point). (C) Model 8 was fitted to the long-exposure and the short-exposure phospho-R-Smad experimental data. (D) Model 8 predicted unchanged T1R levels (green curve), in agreement with our experimental results (green dots). (E) Model 8 predicted unchanged total R-Smad levels (green curve), in agreement with our experimental results (green dots). (F) Red solid curve shows simulation of Model 8 with short-exposure (30 min) of TGF-β, while the yellow dotted curve shows the same simulation except with MG132 pre-treatment. MG132 was simulated as turning off Smurf2-induced P-Smad Degradation (kdeg_pSmad2 = 0), but having no impact on basal degradation of Receptors, unphosphorylated R-SMAD, or PPM1A. (G) The blue solid curve shows simulation of Model 8 with long-exposure (8 hr) of TGF-β, and the green dotted curve shows the same simulated except with MG132 pre-treatment. (H) The relative change in P-Smad2 levels after MG132 treatment, calculated from Eq. 1 and simulations of Model 8. The P-Smad2 change simulated using Model 8 in both short-exposure (30 min, red curve) and long-exposure (8 hr, blue curve) simulations was compared with the P-Smad2 changes in the experimental results of Lin et al. (30 min-exposure, red dots) and Alarcon et al. (6 hr-exposure, blue dots). Data points from Alarcon et al. were quantified from one published image. The discrepancy between our simulations and Alarcon et al. for the 7 hr measurement may be partially explained by MG132-independent differences. Their -MG132 control decreases much faster than that from Lin et al. and from our experiments.

Figure 6. Relative contributions of different negative regulatory effects in our final model (Model 8).

The effects of R-Smad Dephosphorylation, PPM1A Stabilization and P-Smad Degradation were removed one after another from Model 8, and the dynamics of P-Smad2 were simulated after 24 hr TGF-β treatment. In the absence of any negative regulatory effect (red curve), P-Smad2 levels climbed rapidly beyond the scale of the plot; and are not shown for time points after 1 hr.