Sensing relative signal in the Tgf-β/Smad pathway

Abstract

How signaling pathways function reliably despite cellular variation remains a question in many systems. In the transforming growth factor-β (Tgf-β) pathway, exposure to ligand stimulates nuclear localization of Smad proteins, which then regulate target gene expression. Examining Smad3 dynamics in live reporter cells, we found evidence for fold-change detection. Although the level of nuclear Smad3 varied across cells, the fold change in the level of nuclear Smad3 was a more precise outcome of ligand stimulation. The precision of the fold-change response was observed throughout the signaling duration and across Tgf-β doses, and significantly increased the information transduction capacity of the pathway. Using single-molecule FISH, we further observed that expression of Smad3 target genes (ctgf, snai1, and wnt9a) correlated more strongly with the fold change, rather than the level, of nuclear Smad3. These findings suggest that some target genes sense Smad3 level relative to background, as a strategy for coping with cellular noise.

Keywords: Smad; Tgf-β; fold-change detection; information; signal transduction.

Fig. 1.

Ligand-induced nuclear accumulation of NG-Smad3. (A) Illustration of Smad3 activation and nucleocytoplasmic shuttling in the Tgf-β pathway. Ligand stimulation leads to phosphorylation of Smad3. Phosphorylated Smad3 complexes with Smad4 are shown. The Smad complex translocates to the nucleus and regulates target genes. The Smad complex may also dissociate, allowing Smad3 dephosphorylation and export back to the cytoplasm. (B) NG-Smad3 in C2C12 clonal reporter cells responding to ligand stimulation. Purified Tgf-β1 (2.4 ng/mL) was added to the cells at the start of the experiment (denoted as t = 0 min). (Left) Cells are shown before stimulation. (Center) Two individual cells are tracked over time. (Right) Same cells 60 min after stimulation. (Scale bars: 20 μm.) (C) Quantitation of the level of nuclear NG-Smad3 during Tgf-β1 stimulation. Each line corresponds to an individual cell. The dashed line indicates when Tgf-β1 was added. au, arbitrary units. (D) Fold change in nuclear NG-Smad3 from the same cells measured in C. Basal level is measured as the average of the fluorescence level 24 min before ligand stimulation.

Fig. S1.

Immunofluorescent staining reveals overlap of the Smad3 level in unstimulated and stimulated cells. (A) Immunofluorescent staining of Smad3 in C2C12 cells: unstimulated (Left) and stimulated with 2.4 ng/mL Tgf-β1 (Right). (B) Quantitation of the fluorescence signal from unstimulated cells (gray, n = 152) and cells stimulated for 1 h with 2.4 ng/mL Tgf-β1 stimulation (red, n = 557). The overlap did not decrease at subsequent time points. For immunofluorescence, cells were grown overnight on 96-well glass-bottomed plates (Griener Bio-One; 655892). After Tgf-β stimulation, cells were fixed with 4% (wt/vol) paraformaldehyde for 20 min. Following fixation, cells were rinsed twice with 1×PBS, blocked, permeabilized with 5% (vol/vol) goat serum and 0.1% Triton X-100 in PBS, and then incubated with primary antibody diluted in blocking buffer overnight at 4 °C. Cells were then washed three times with 1×PBS + 0.05% Tween-20 for 5–10 min each time, and incubated in secondary antibody diluted in 1×PBS + 0.05% Tween-20 for 1 h in the dark at room temperature. The cells were washed again three times with 1×PBS + 0.05% Tween-20 for 5–10 min each time, with DAPI counterstain added in the third wash, followed by one more wash with 1×PBS for 5 min. Imaging was done in 1× PBS. Monoclonal rabbit anti-Smad3 (Cell Signaling; C67H9) was used at 1:100, and goat–anti-Rabbit DyLight 650 (Thermo Fisher Scientific; SA510034) was used at 1:2,000. au, arbitrary units.

Fig. S2.

Characterization of the NG-Smad3 construct. (A) Amino acid sequence of the NG-Smad3 used in the study. The asterisk denotes a stop codon. (B and C) Quantifying the level of NG-Smad3 relative to endogenous Smad3 using quantitative Western blotting. (B) Cell lysate was loaded at different concentrations to find the range where antibody staining is linear. IB, immunoblot. (C) Linear region (blue-shaded area) is where the change in lysate amount is proportional to the change in fluorescent signal. The relative expression of NG-Smad3 to Smad3 was determined by taking the average of two biological replicates. (D) Western blot against phosphorylated Smad3 (pSmad3) in the nuclear fraction. (E) Western blot against Smad3 in the nuclear fractions. In both D and E, cells were collected 1 h after Tgf-β stimulation (2.4 ng/mL). For Western blotting, cells were treated with Tgf-β1 or a carrier, harvested by trypsinization, and then either pelleted and frozen or fractionated into nuclear and cytoplasmic fractions using NE-PER Nuclear and Cytoplasmic Extraction Reagents (Thermo Scientific; 78833). Cell lysates were loaded on Bolt 4–12% gradient SDS/PAGE (Invitrogen) and transferred onto nitrocellulose membranes by wet transfer using a standard wet transfer buffer [25 mM Tris, 192 mM glycine, 20% (wt/vol) methanol] for 1 h at 200 mA at 4 °C. Membranes were dried, blocked using Odyssey blocking buffer (LI-COR; 927-50000) for 1 h at room temperature, and incubated with primary antibodies at 4 °C overnight and secondary antibodies for 1 h at room temperature. Imaging and quantification were performed using a LI-COR Odyssey infrared scanner. Primary antibodies were as follows: rabbit–anti-Smad3 (Cell Signaling; C67H9) at a 1:1,000 dilution, rabbit–anti-pSmad3 (Cell Signaling; C25A9) diluted at 1:1000, and mouse-anti–β-actin (Cell Signaling; 8H10D10) diluted at 1:20,000. All primary antibodies were diluted in blocking buffer. Secondary antibodies, goat–anti-rabbit IRDye 680LT (LI-COR; 925-68021), and goat–anti-mouse IgG (H+L) DyLight 800 Conjugate (Cell Signaling; 5257) were diluted at 1:5,000. All secondary antibodies were diluted in blocking buffer + 0.1% Tween-20 + 0.01% SDS.

Fig. S3.

Higher precision of fold-change response is reproducible across experiments and clonal lines. (A) Data from six of 20 independent experiments performed in the study. (Left) Distribution of the level of nuclear NG-Smad3 at 32 min after ligand stimulation (2.4 ng/mL Tgf-β1). (Right) Fold change in nuclear Smad3. (B) Data from three clonal cell lines. In each plot, the colored lines are traces from the indicated clone and the gray lines are traces from all clones together. The data are plotted as the absolute fluorescence level (Top) or relative to its basal level (Bottom). The dashed line indicates when Tgf-β1 was added (2.4 ng/mL). Data from clone 3 are presented in the main text.

Fig. S4.

Smad3 responses to stimulation are statistically different from unstimulated cells. (A, Left) We confirmed that cells only exposed to buffer showed no response. (A, Right) Cells exposed to 2.4 ng/mL Tgf-β show an increase in nuclear Smad3. (B) Exposure to all doses of Tgf-β tested produces Smad3 responses that are statistically different from unstimulated cells. Distributions of unstimulated cells at t = 60 min were compared with distributions of cells stimulated with the indicated doses of Tgf-β using the Student’s t test. P values are shown in the table. (C) Nuclear Smad3 level poststimulation correlates linearly with the basal nuclear Smad3 level. Each data point comes from a single cell. The entire plot comes from measurements of 299 cells. Shown on the y axis is the level of nuclear NG-Smad3 32 min (Left) and 56 min (Right) after ligand stimulation. The same linearity is observed at other time points. R² is the square of Pearson’s correlation coefficient.

Fig. 2.

Fold change in nuclear NG-Smad3 is a more precise response to ligand stimulation. (A and B) NG-Smad3 responding to 2.4 ng/mL Tgf-β1 stimulation. The dashed line indicates when Tgf-β1 was added. Each line is a trace from a single cell, plotted as the absolute fluorescence level (A) or relative to its basal level (B). Basal level was computed as the average of nuclear NG-Smad3 fluorescence in the cell over 24 min before ligand stimulation. These data came from multiple experiments. The fluorescence distribution from each experiment was adjusted so that the median fluorescence is equal across experiments. No systematic differences were observed across experiments (Fig. S3). Distribution of the level (C) and fold change in the level (D) of nuclear NG-Smad3 at 32 min after ligand stimulation are shown. Quartile coefficient of dispersion (QCD) is defined here as: (Q3 − Q1)/Q2, where Q1, Q2, and Q3 are the 25th, 50th, and 75th percentiles, respectively. (E) Illustration of the different response features examined in F. Response time was computed as the time from ligand addition until the inflection point in the response curve. Rate of change was computed as the maximum derivative of the response curve. Integrated response was computed over 52 min after ligand stimulation. (F) Distributions of the response time (purple), maximum rate of change, and integrated response computed from the absolute level (light blue) or fold change in nuclear NG-Smad3 (dark blue). The distributions are median-normalized to facilitate comparison. The distribution for response time is the same for fold change and absolute level, because it is defined as the time to maximum rate of change (the inflection point). Thus, only one distribution is shown.

Fig. S5.

Fold-change response is more precise and has higher information capacity throughout the duration of signaling. (A) Plotted is the quartile coefficient of dispersion (QCD) for the level (orange) and the fold change (blue) in the level of nuclear NG-Smad3. The QCD is defined here as follows: (Q3 − 1)/Q2, where Q1, Q2, and Q3 are the 25th, 50th, and 75th percentiles, respectively. The QCD values reported here are computed using the cell traces in Fig. 2 A and B. (B) Maximum mutual information between Tgf-β input and nuclear Smad3 level (orange) or fold change (blue) was determined at each time interval after Tgf-β addition (t = 0). Error bars are 90% confidence intervals computed using bootstrap resampling. The total number of cells examined for each calculation was 1,650.

Fig. 3.

Higher precision of fold-change response holds across doses of Tgf-β. Plotted is the median (bold line) bounded by the 25th percentile and 75th percentile of the data (shaded area) from traces of the level of nuclear NG-Smad3 (Upper) and the fold change of nuclear NG-Smad3 (Lower). The dashed line indicates the time of Tgf-β addition.

Fig. 4.

Fold-change response has higher information transduction capacity. (A) Noisy, overlapping response distributions provide low information about the strength of ligand input. (B and C) To compute the maximum mutual information, we stimulated the cells with different doses of Tgf-β1 (Fig. 3). The response distributions for three doses are shown here, of the absolute fluorescence level (B) or the fold change (C). (Bottom) Overlay of the distributions. For low, medium, and high doses, the number of cells examined was 277, 290, and 532, respectively. (D) We computed the maximum mutual information between ligand input and different features of the nuclear NG-Smad3 response. Features computed using the absolute response are shown in orange, and features computed using the fold-change response are shown in blue. Level and fold change of nuclear NG-Smad3 were evaluated at steady state, at 36 min after Tgf-β addition (comparison at different time points is shown in Fig. S5B). Rate of change in the NG-Smad3 response was computed as the maximum of the derivative of the response curve. To compute the integral of the NG-Smad3 response, the response was integrated over the first hour of ligand stimulation. For dynamic measurements, the level of nuclear NG-Smad3 was measured at multiple time points, as indicated, and mutual information was computed with a 2D distribution (Fig. S8). Error bars are 90% confidence intervals computed using bootstrap resampling. The total number of cells examined for each calculation was 1,650.

Fig. 5.

Expression of target genes correlates more strongly with the fold change in nuclear NG-Smad3. (A) To correlate NG-Smad3 dynamics and transcription response within a single cell, we combined live-cell imaging with smFISH. Cells were stimulated with Tgf-β1 and imaged. The same cells were then fixed, stained against specific mRNA, and imaged again. Foci corresponding to individual mRNA molecules were quantified using custom MATLAB scripts. The mRNA transcript counts were then plotted against features of NG-Smad3 response from the same cells. (B) Number of mRNA transcripts plotted against the level (Left) or fold change (Right) of nuclear NG-Smad3 measured in the same cell. The mRNA transcripts were counted after 1 h of Tgf-β stimulation, and plotted here with response features measured at 44 min (snail) and 28 min (ctgf) after ligand stimulation. (C) Plotted is the correlation between mRNA transcripts (at 1 h after ligand stimulation) and NG-Smad3 response measured throughout the entire signaling dynamics. The correlation coefficient is Spearman’s rank correlation coefficient. Error bars are 90% confidence intervals (CI), computed using bootstrap resampling. At each time point after ligand addition, the correlation with fold change (blue) is significantly higher than the correlation with level (orange) (P < 0.01, Steiger’s Z test; a complete statistical analysis is shown in Table S1).

Fig. S6.

Expression of wnt9a correlates more strongly with fold change in nuclear NG-Smad3. Plotted is the correlation between NG-Smad3 responses and wnt9a mRNA transcripts counted in the same cell. (A) Level of nuclear NG-Smad3 (Left) and the fold change in nuclear level of Smad3 (Right) plotted versus the number of wnt9a mRNA counts per cell. The mRNA transcripts were counted at 1 h after ligand stimulation as described in the main text. (B) Plotted is the correlation between wnt9a mRNA transcripts (at 1 h after ligand stimulation) and NG-Smad3 response measured throughout the entire signaling dynamics. The correlation coefficient is Spearman’s rank correlation coefficient. Error bars are 90% confidence intervals, computed using bootstrap resampling. At each time point after ligand addition, the correlation with fold change (blue) is significantly higher than the correlation with level (orange) (P < 0.01, Steiger’s Z test; Table S1).

Fig. 6.

Our finding suggests that, at least in some contexts, Smad signal in the Tgf-β pathway is sensed in a relative manner.

Fig. S7.

Mathematical model of Tgf-β pathway predicts fold-change robustness to parameter variation. We tested whether a mathematical model predicts robustness of Smad fold change to endogenous cellular variability. The mathematical model used is a system of ODEs describing R-Smad nucleocytoplasmic shuttling in response to Tgf-β (11). To test for robustness to cell-to-cell variation, we performed 1,000 simulations with random parameter variation. (A) Response dynamics of nuclear R-Smad level (Left) and fold change (Right) from 1,000 individual simulations with random parameter variation. (B) Response dynamics of nuclear Smad complex level (Left) and fold change (Right) from 1,000 individual simulations with random parameter variation. Plots of the normalized steady-state response (absolute level, red; fold change, green) vs. the total parameter variation for R-Smad (C) and the Smad complex (D) are shown. The responses were normalized to the median of all 1,000 simulations as a way of facilitating comparison. Each dot corresponds to an individual simulation. Plots of basal nuclear vs. final nuclear level of Smad3 (E) or the Smad complex (F) are shown. Each data point represents one simulation of the Tgf-β model either without (Left) or with (Right) random parameter variation. In each plot are data from 1,000 simulations. R² is the square of Pearson’s correlation coefficient. Simulations of the system of ordinary differential equations (ODEs) were performed in MATLAB using the numerical solver, ode15i. To perform parameter variation, parameter values were chosen randomly in each iteration of the simulation from a log-normal distribution whose mode is the parameter value of the published model. The log-normal distributions were generated by multiplying the parameter by a randomly generated log-normal distribution with mu equal to 0 and sigma equal to 0.1, except for the expression of R-Smad, where sigma was 0.4 (mu and sigma are the log-mean and log-standard deviation of the log-normal distribution, respectively). We began all simulations with a basal level of Tgf-β (i.e., 0.02 nM), followed by stimulation with 0.5 nM. Total parameter variation, k, is defined as: $\log \left(k\right)={\displaystyle \sum _{n=1}^L}\left|\text{log}(k_n/k_n^0)\right|$, where $k_n^0$ are the published biochemical parameters of the model and $k_n$ are the biochemical parameters of the altered system.

Fig. S8.

Mutual information computed with dynamic measurements. (A) Illustration of dynamic measurement. In dynamic measurement, the signaling response of a cell is defined as a vector containing multiple time points (e.g., t = [0,28 min] [Left] and t = [28,52 min] [Right]) instead of a single time point (as described in ref. 6). (B) Maximum mutual information between NG-Smad3 response and Tgf-β input using the specified dynamic measurement time point combinations. The data used for the information calculation are the same used in Fig. 4 (n = 1,650). Maximum mutual information was computed as described in Materials and Methods, with R in Eq. 1 as the multivariate. Each entry in R contains two time point measurements. (C) Shown is a matrix of the maximum mutual information between NG-Smad3 response and Tgf-β input for all time-point combinations. The x axis is the first time point, and the y axis is the second time point. The boxes indicate the location of the time point combinations from A and B.