Quantitative analysis of transient and sustained transforming growth factor-β signaling dynamics

Abstract

Mammalian cells can decode the concentration of extracellular transforming growth factor-β (TGF-β) and transduce this cue into appropriate cell fate decisions. How variable TGF-β ligand doses quantitatively control intracellular signaling dynamics and how continuous ligand doses are translated into discontinuous cellular fate decisions remain poorly understood. Using a combined experimental and mathematical modeling approach, we discovered that cells respond differently to continuous and pulsating TGF-β stimulation. The TGF-β pathway elicits a transient signaling response to a single pulse of TGF-β stimulation, whereas it is capable of integrating repeated pulses of ligand stimulation at short time interval, resulting in sustained phospho-Smad2 and transcriptional responses. Additionally, the TGF-β pathway displays different sensitivities to ligand doses at different time scales. While ligand-induced short-term Smad2 phosphorylation is graded, long-term Smad2 phosphorylation is switch-like to a small change in TGF-β levels. Correspondingly, the short-term Smad7 gene expression is graded, while long-term PAI-1 gene expression is switch-like, as is the long-term growth inhibitory response. Our results suggest that long-term switch-like signaling responses in the TGF-β pathway might be critical for cell fate determination.

Figure 1

Experimental and modeling analysis of P-Smad2 response to very short TGF-β stimulation. (A) Western blot analysis of P-Smad2 levels with different TGF-β stimulations. For a single pulse of 30 s of TGF-β stimulation, HaCaT cells were stimulated with TGF-β for 30 s. Then, they were washed with D-PBS and incubated with normal fresh medium without TGF-β. In the sustained TGF-β stimulation, cells were stimulated with TGF-β without washout. (B) Time course western blot analysis of P-Smad2 levels in HaCaT cells with single pulse of 30 s of TGF-β stimulation. (C) Comparison of model simulation with the experimental data. Blue and red curves represent model predictions of P-Smad2 response to sustained TGF-β stimulation and to single pulses of 30 s TGF-β stimulation, respectively. Circles and error bars are shown based on the scaled mean values and standard deviations of the quantified experimental data from 2 to 6 replicates, which were scaled to compare with model simulations in terms of molecules per cell. Source data is available for this figure at www.nature.com/msb.

Figure 2

Scheme of the mathematical model. A detailed description of mathematical model is given in the Supplementary information and Supplementary Tables S1–S4.

Figure 3

Dynamics of P-Smad2 response to pulses of TGF-β stimulation. For pulses of TGF-β stimulation, HaCaT cells were stimulated with TGF-β for a specific duration (TGF-β on time, T_on), then TGF-β was washed out and cells were immediately incubated with normal fresh medium for another specific duration (TGF-β off time, T_off). TGF-β was added and washed out at the indicated times. Green and blue curves represent model simulation results for medium TGF-β and P-Smad2 profiles, respectively. Experimental data from two replicates are scaled and plotted in red circles. (A–C) Pulses of TGF-β stimulation with 1 h stimulation and 1 h washout. (D–F) Pulses of TGF-β stimulation with 3 h stimulation and 3 h washout. Source data is available for this figure at www.nature.com/msb.

Figure 4

Signaling response to continuous short pulses of TGF-β stimulation. (A) Model prediction for P-Smad2 response to sustained TGF-β stimulation (the blue curve) and to pulses of 30 s TGF-β stimulation at 30 min intervals (the red curve). Circles and error bars are shown based on the scaled mean values and standard deviations of the quantified experimental data from six replicates (blue circles) and two replicates (red circles), respectively. The green curve on the top shows the medium TGF-β time course profile with pulses of 30 s TGF-β stimulation at 30 min intervals. (B) Western blot analysis of P-Smad2 response to pulses of 30 s TGF-β stimulation at 30 min intervals and sustained TGF-β stimulation in HaCaT cells. (C) Time course western blot analysis of P-Smad2 response to pulses of 30 s TGF-β stimulation at 30 min intervals in HaCaT cells. The last lane on the right was loaded with the cell lysates from 45 min of sustained TGF-β stimulation. (D) In HaCaT-lux cells, time course CAGA luciferase gene reporter activity with continuous short pulses of TGF-β stimulation is similar to those with sustained TGF-β stimulation. Standard deviations are shown from two experimental replicates. (E) Model prediction for P-Smad2 response to pulses of 30 s TGF-β stimulation at 3 h intervals. Experimental data from two replicates are scaled and plotted in red circles. (F) Time course western blot analysis of P-Smad2 response to pulses of 30 s TGF-β stimulation at 3 h intervals in HaCaT cells. Source data is available for this figure at www.nature.com/msb.

Figure 5

Short-term and long-term signaling responses to different doses of TGF-β stimulation. (A) Mathematical modeling predicts that short-term P-Smad2 response (near maximum at 45 min) is a graded response to different doses of sustained TGF-β stimulation. Experimental data from three replicates are scaled and plotted in red circles and they are fitted to Hill equation curve. The Hill coefficient (n_Hill) is 0.8 with 95% confidence interval of 0.7–0.9. (B) Mathematical modeling predicts that long-term P-Smad2 response (quasi steady state, at 24 h) is an ultrasensitive switch-like response to different doses of TGF-β stimulation. Experimental data from four replicates are scaled and plotted in red circles and they are fitted with a Hill function. The Hill coefficient (n_Hill) is 4.5 with 95% confidence interval of 4.0–5.1. (C) Western blot of P-Smad2 response at 45 min to different doses of TGF-β stimulation. (D) Western blot of P-Smad2 response at 24 h to different doses of TGF-β stimulation. The arrows in panels (A–D) indicate the dose of 60 000 TGF-β molecules/cell. (E) Quantitative PCR assay for Smad7 gene expression at 45 min with different doses of sustained TGF-β stimulation. The data are expressed as fold change by normalizing to the Smad7 gene expression level before TGF-β stimulation. The averages and standard deviations from two biological replicates are plotted and fitted with the Hill equation curve. The Hill coefficient (n_Hill) is 1.3 with 95% confidence interval of 1.1–1.4. (F) Western blot of PAI-1 protein expression at 24 h to different doses of TGF-β stimulation. Experimental data from two replicates are plotted in red circles and they are fitted with a Hill function. The Hill coefficient (n_Hill) is 5.3 with 95% confidence interval of 4.9–5.6. (G) Western blot of p21 protein expression at 24 h to different doses of TGF-β stimulation. Experimental data from two replicates are plotted in red circles and they are fitted using a Hill function. The Hill coefficient (n_Hill) is 2.0 with 95% confidence interval of 1.9–2.1. (H) BrdU assay of HaCaT cell proliferation with different doses of sustained TGF-β stimulation. HaCaT cells were seeded for 24 h and then were treated with TGF-β for 24 h. BrdU was added at 18 h after TGF-β stimulation. The data from three experimental replicates are plotted and fitted with a Hill function. The Hill coefficient (n_Hill) is 4.3 with 95% confidence interval of 4.1–4.5. Source data is available for this figure at www.nature.com/msb.

Figure 6

Perturbation of ligand depletion affects the ultrasensitivity of long-term P-Smad2 responses to different doses of TGF-β stimulation. (A) Model predictions for P-Smad2 responses at 24 h to different doses of sustained TGF-β stimulation with 2 and 10 ml medium. (B) Experimental data for P-Smad2 responses at 24 h to different doses of sustained TGF-β stimulation with 2 and 10 ml medium. The data were quantified from 4 to 6 replicates and were normalized to P-Smad2 signal with TGF-β dose of 120 000 molecules/cell. They are scaled and plotted in red circles in order to compare with the model predictions in (A). The Hill coefficient for P-Smad2 dose response with 10 ml medium is reduced from 4.5 (with 2 ml medium) to 1.8 with 95% confidence interval of 1.6–1.9. (C) Western blot analysis of P-Smad2 responses at 24 h to different doses of sustained TGF-β stimulation in HaCaT cells with 2 and 10 ml medium. Cell lysates were prepared from the same batch of cells that were stimulated with different volume of medium, but with the same doses of TGF-β in terms of molecules per cell. (D) Western blot analysis of P-Smad2 responses at 24 h to different doses of sustained TGF-β stimulation in HaCaT cells and used medium volume of 2 ml. (E) Western blot analysis of P-Smad2 responses at 24 h to different doses of sustained TGF-β stimulation in HaCaT cells and used medium volume of 10 ml. Cells were stimulated with similar doses of TGF-β as those in (D) in terms of molecules per cell. (F) Western blot analysis of P-Smad2 responses at 24 h to different doses of sustained TGF-β stimulation in HaCaT cells and used medium volume of 2 ml. The blots are the same as those shown in Figure 5D, but TGF-β doses were converted from TGF-β molecules per cell to TGF-β concentration in the medium. (G) Western blot analysis of P-Smad2 responses at 24 h to different doses of sustained TGF-β stimulation in HaCaT cells and used medium volume of 10 ml. Cells were stimulated with similar doses of TGF-β as those in (F) in terms of TGF-β concentration in the medium. Source data is available for this figure at www.nature.com/msb.

Figure 7

Contour landscape of the time-dependent P-Smad2 response profile to different doses of TGF-β stimulation in HaCaT cells. Model simulations indicate that when the TGF-β dose is less than a certain threshold (vertical white solid line), the stimulated cells have almost no signaling response. Within a certain dose range (between vertical white and black dashed line) of TGF-β stimulation, cells have a transient signaling response. Once the TGF-β dose is larger than a threshold (black solid line), cells rapidly switch from a transient short-term signaling response to a sustained long-term signaling response with the increase of TGF-β dose. More importantly, cells have different interpretations of signaling responses to different doses of TGF-β at different time scales. The short-term signaling response establishes a graded response to different doses of TGF-β. In contrast, the long-term signaling response (e.g., P-Smad2 at 24 h) is ultrasensitive or switch-like response. The long-term ultrasensitive signaling response is critical for cellular fate decisions, for example, cell growth arrest.