Anti-resonance in developmental signaling regulates cell fate decisions
- Interdisciplinary Program in Quantitative Biosciences, University of California Santa Barbara, United States
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Technische Universiteit Delft, Netherlands
- Department of Molecular, Cellular, and Development Biology, University of California Santa Barbara, United States
- Integrated Biosciences, Inc., United States
- Center for Bioengineering, University of California Santa Barbara, United States
- Neuroscience Research Institute, University of California Santa Barbara, United States
Figures
Figure 1 with 1 supplement
A human cell line for all optical visualization and control of Wnt signaling dynamics.
(A) Schematic of HEK293T Wnt I/O cells containing lentiviral optogenetic LRP6c-Cry2Clust, CRISPR tdmRuby3-β-cat, lentiviral 8X-TOPFlash-tdIRFP, clonally FACS-sorted. (B) Live cell imaging of HEK293T Wnt I/O cells exposed to no light and 24 hr of 405 nm light illumination delivered every 2 min. Images are shown using the same lookup table. (C) Single-cell mean fluorescent intensity (MFI) traces (N=321–567 cells, four biological replicates per condition) of tdmRuby3-β-cat and (TopFlash) tdiRFP measurements from live HEK293T Wnt I/O cells tracked during exposure to activating blue light (right) or no light (left) controls. A blue background indicates light on, and a white indicates light off. Black line represents population mean. (D) Population means of live, single-cell β-catenin (top) and TopFlash (bottom) MFI traces from indicated conditions (N=321–595 cells, four biological replicates per condition, see Methods for significance values).
Figure 1—figure supplement 1
Optogenetic Activation of Wnt Signaling Enables Quantitative Single-Cell Analysis of β-Catenin Dynamics and Transcriptional Output.
(A) FACS data for Wnt I/O cell line with (+)/without (-) 24 hr of light exposure. Axes are of β-catenin (mCherry) v. TopFlash (APC-Cy5.5) (B) Live cell imaging of CRISPR tdmRuby3-β-cat, lentiviral 8X-TOPFlash-tdIRFP and DAPI, 16 hr after adding CHIR99021 (+CHIR) and Wnt3a (+Wnt3 a). (C) Quantifications of β-catenin and TopFlash fluorescence for no light, +16 hr light, +Wnt3 a, and +CHIR, where the mean of each condition was normalized to the mean of the no light condition and error bars represent SEM. (D) Flow for cell segmentation and heatmap generation from experimental data, using CellPose add TrackMate. From left to right: magenta (β-catenin) and cyan (TopFlash) images are passed into CellPose + Trackmate for segmentation and tracking. An example image of CellPose segmentation is shown under ‘segmented images,’ where the different colors correspond to the cell’s segmentation ID. Final images under ‘quantify and plot’ show quantification of β-catenin and TopFlash. (E) Mean fluorescent intensity (MFI) of β-catenin in the 24 hr light on condition, normalized to light off β-catenin. (F) MFI of TopFlash in the 24 hr light on condition, normalized to light off TopFlash. (G) Population mean MFI of β-catenin from live, single cell traces in indicated conditions, normalized to light off β-catenin. Initial drop in fluorescence is due to media bleaching. (H) Population mean MFI of TopFlash from live, single cell traces from indicated conditions, normalized to light off TopFlash. (I) Jitter plot of β-catenin mean nuclear fluorescent intensity (MFI) at the maximum intensity point in continuous light exposure conditions. Each point represents a single cell and the black line represents the mean of the population. (J) Jitter plot of TopFlash mean nuclear fluorescent intensity (MFI). Each point represents a single cell and the black line represents the mean of the population.
Figure 2 with 1 supplement
A model of Wnt signaling dynamics predicts anti-resonance.
(A) Schematic of ordinary differential equation (ODE) model of Wnt signaling. Dotted lines represent light-dependent parameters. For information on model variables and parameters, refer to Methods, ODE Model for Wnt Signaling. (B) ODE model predictions (solid) of β-cat mean fluorescent intensity (MFI) for 6, 15, and 24 hr compared against our unsmoothed experimental results (light) from Figure 1D. Post-26 hr, experimental data was corrected for over-confluency effects in both β-catenin (β-cat) and TopFlash. (C) ODE model predictions (solid) of TopFlash MFI compared against our unsmoothed experimental results (light) from Figure 1D. (D) Visualization of duty cycle and frequency. Left: Constant frequency with varying duty cycle. Right: Constant duty cycle with varying frequency. (E) ODE model generated heatmap of endpoint TopFlash MFI for various combinations of duty cycle and frequency conditions. (F) Line graph of 45–75% duty cycles vs frequency with 1/24, 1/3, and 4 cycles/hr labeled as A, B, and C.
Figure 2—figure supplement 1
ODE-Based Predictions of Wnt Signal Decoding Are Recapitulated by Experimental TOPFlash Dynamics.
(A) Ordinary differential equation (ODE) model generated heatmap of endpoint β-catenin mean fluorescent intensity (MFI) for various combinations of duty cycle and frequency conditions.(B) ODE model generated TopFlash MFI dynamic traces for points A, B, and C from Figure 2F. (C) Experimentally generated TopFlash MFI dynamic traces for point A, B, and C from Figure 2F. Error bars represent standard error of the mean (SEM).
Figure 3 with 1 supplement
The Wnt pathway of HEK cells displays anti-resonance.
(A) Schematic of our experimental method of the LITOS illumination device. (B) Qualitative images of end point β-catenin fluorescence post LITOS illumination with the heatmap of end point β-catenin mean fluorescent intensity (MFI) in the top right corner (N=106–590 cells, four biological replicates per condition). (C) Error bar plot of end point β-catenin MFI post frequency and duty cycle screen. Error bars represent standard error of the mean (SEM). (D) Qualitative images of end point TopFlash fluorescence post LITOS illumination (N=106–590 cells, four biological replicates per condition). (E) Error bar plot of end point TopFlash MFI post frequency and duty cycle screen. Error bars represent SEM. (F) Averaged heatmap of end point TopFlash MFI from two replicates of duty cycle and frequency experiment. Replicate heatmaps were normalized by the logarithm of the cell count at each well prior to averaging. Heatmap labels are displayed in categorical format, differentiating our experimental results heatmap from our computational heatmap.
Figure 3—figure supplement 1
Endpoint β-Catenin and Wnt Transcriptional Outputs Reveal Frequency-Dependent Signal Decoding.
(A) β-catenin and LiveNuc stained Wnt I/O HEK293T cells imaged post duty cycle and frequency experiment, ran for 48 hr. (B) Heatmap of end point β-catenin mean fluorescent intensity (MFI) post duty cycle and frequency experiment where values were normalized to the maximum β-catenin MFI. (C) Heatmap of total cell count for each duty cycle and frequency condition. (D) Heatmap of the total integrated amount of light for each duty cycle and frequency condition, obtained from the LITOS conditions used in the experiment. (E) TopFlash and LiveNuc stained Wnt I/O HEK293T cells imaged post duty cycle and frequency experiment, ran for 48 hr. (F) Rearranged LITOS stimulation plate set up for the replicate duty cycle and frequency experiment. (G) Heatmap of end point TopFlash MFI from our original duty cycle and frequency experiment, normalized to the maximum TopFlash MFI. (H) Heatmap of end point TopFlash MFI from our replicate duty cycle and frequency experiment, normalized to the maximum TopFlash MFI.
Figure 4
A hidden variable approach relates the anti-resonance to the timescales of Wnt activation and deactivation.
(A) A hidden variable is activated upon optogenetic Wnt activation at a rate and deactivates at rate when the light is turned off. In turn, is coupled to first-order β-catenin dynamics. (B–D) Systematic exploration of the parameter space shows that the rates and tune the concavity. (B) Concavity of anti-resonance is dependent on the combination of and rates. (C) Shape of the anti-resonance for five different points (A–E) in parameter space. As we enter the region the anti-resonance appears, consistent with our analytical result (see Appendix 3 for details about equations and parameter values). (D) Anti-resonant frequency is dependent on the combination of and rates.
Figure 5 with 1 supplement
Anti-resonant dynamics drive mesodermal stem cell differentiation in human embryonic stem cell (hESC) H9s.
(A) Schematic of H9 Wnt I/O cells containing PiggyBac optogenetic LRP6c-Cry2Clust and CRISPR tdmRuby3-β-catenin. (B) Representative examples of tdmRuby3-β-cat and Brachyury (BRA) accumulating in response to 24 hr of blue light activation in H9 Wnt I/O cells, post puromycin selection. (C) Qualitative images of the end point Brachyury (BRA) fluorescence post LITOS illumination (N=862–3176 cells, six biological replicates per condition). (D) Heatmap of end point BRA MFI for various duty cycle and frequency conditions. Heatmap labels are displayed in categorical format, differentiating our experimental results heatmap from our computational heatmap. (E) Error bar plot of end point BRA MFI post-frequency and duty cycle experiment. Error bars represent standard error of the mean (SEM).
Figure 5—figure supplement 1
Temporal Structure of Wnt Signaling Governs β-Catenin Dynamics and Mesoderm Marker Expression.
(A) Heatmap of endpoint Brachyury (BRA) in H9 Wnt I/O cells following duty cycle and frequency stimulation, ran for 48 hr. This experiment replicates the conditions shown in Figure 5 but extends the stimulation duration from 24 hr to 48 hr. (B) Line plot of endpoint BRA in H9 Wnt I/O cells following duty cycle and frequency stimulation, ran for 48 hr. This experiment replicates the conditions shown in Figure 5 but extends the stimulation duration from 24 hr to 48 hr. Error bars represent standard error of the mean (SEM). (C) Qualitative images of the end point β-catenin fluorescence post LITOS illumination (N=862–3176 cells, six biological replicates per condition). (D) Qualitative images of the end point β-catenin and DAPI fluorescent stain post LITOS illumination. (E) Qualitative images of the end point BRA and DAPI fluorescent stain post LITOS illumination. (F) Error bar plot of end point β-catenin mean fluorescent intensity (MFI). Error bars represent SEM.
Appendix 2—figure 1
Inter-Pulse Timing Effects on β-Catenin and Wnt Transcriptional Memory.
(A) β-catenin traces from computational model for two 6 hr pulses with a pause duration of 2 hr. (B) TopFlash traces from a computational model for two 6 hr pulses with a pause duration of 2 hr. (C) Final TopFlash expression level (at hrs) after two 6 hr pulses with varying pause duration. Blue shading indicates opto-Wnt activation during these time intervals.
Appendix 3—figure 1
Hidden-Variable Model of β-Catenin and TOPFlash Dynamics at Multiple Light-Exposure Times.
(A) Traces from the hidden-variable model of β-catenin at 6, 15, and 24 hr light exposure times. Dynamics in this regime are dictated by kb and ka. Low-alpha lines show experimental data. (B) Traces from the hidden-variable model of TopFlash at 6, 15, and 24 hr light exposure times. Dynamics in this regime are dictated by and . Low-alpha lines show experimental data. (C) TopFlash heatmap from the hidden-variable model displaying anti-resonance for and .
Videos
Video 1
Video of clonal HEK293T Wnt I/O under 24 hr of continuous light exposure, delivered as 100 ms long pulses every 2 min followed by an 8 hr relaxation period.
Top Left: Wnt I/O HEK293T cell line β-catenin fluorescent channel, imaged every 10 min. In the absence of 405 nm blue light stimulation, β-catenin fails to accumulate in the nucleus due to no optogenetic activation of the opto-Wnt tool. Top Right: Wnt I/O HEK293T cell line TopFlash fluorescent channel, imaged every 10 min. In the absence of 405 nm blue light stimulation, TopFlash fails to accumulate due to no optogenetic activation of the opto-Wnt tool. Bottom Left: Wnt I/O HEK293T cell line β-catenin fluorescent channel, imaged every 10 minutes. In the presence of 405 nm blue light stimulation, β-catenin accumulates in the nucleus due to optogenetic activation of the opto-Wnt tool. Bottom Right: Wnt I/O HEK293T cell line TopFlash fluorescent channel, imaged every 10 min. In the presence of 405 nm blue light stimulation, TopFlash accumulates due to optogenetic activation of the opto-Wnt tool.
Tables
Table 1
P-value and corresponding symbol.
| p-value range | Symbol |
|---|---|
| p>0.05 | n.s. |
| 0.01<p<0.05 | * |
| 0.001<p<0.01 | ** |
| p<0.001 | *** |
Table 2
Model variables.
| Variable | Description |
|---|---|
| Active disheveled | |
| Inactive disheveled | |
| Free destruction complex | |
| β-catenin bound to destruction complex | |
| Inactive destruction complex | |
| Free β-catenin | |
| TopFlash expression | |
| Light status () |
Table 3
Model parameters.
| Parameter | Dimensions* | Description |
|---|---|---|
| min−1 | Rate of disheveled activation | |
| min−1 | Rate of disheveled deactivation | |
| min−1 | Inactivation rate of destruction complex by disheveled | |
| min−1 | Activation rate of destruction complex | |
| min−1 | Dissociation of phosphorylated β-catenin from the destruction complex | |
| min−1 | Binding and phosphorylation of β-catenin with/by destruction complex | |
| min−1 | β-catenin synthesis rate | |
| . | Conserved concentration of disheveled | |
| . | Conserved concentration of destruction complex | |
| . | Hill coefficient | |
| . | Dissociation constant | |
| min−1 | Maximum TopFlash transcription rate | |
| min | Time delay between β-catenin accumulation and onset of TopFlash transcription |
-
*
In our system of units, concentration is dimensionless.
Appendix 1—table 1
T-test results from TopFlash (TF) and β-catenin (β-cat) traces from Figure 1D.
| Names | P-value TF | P-value β-cat | P-value TF stars | P-value β-cat stars |
|---|---|---|---|---|
| 6HR and 9HR | 8.65E-20 | 5.94E-05 | *** | *** |
| 6HR and 15HR | 2.19E-61 | 4.76E-12 | *** | *** |
| 6HR and 18HR | 4.56E-94 | 6.43E-19 | *** | *** |
| 6HR and 21HR | 1.11E-85 | 2.46E-12 | *** | *** |
| 6HR and 24HR | 9.14E-05 | 2.60E-12 | *** | *** |
| 9HR and 15HR | 9.05E-24 | 1.06E-05 | *** | *** |
| 9HR and 18HR | 6.39E-49 | 3.20E-14 | *** | *** |
| 9HR and 21HR | 2.88E-54 | 2.41E-08 | *** | *** |
| 9HR and 24HR | 7.52E-40 | 4.73E-06 | *** | *** |
| 15HR and 18HR | 1.93E-08 | 2.92E-06 | *** | *** |
| 15HR and 21HR | 6.50E-23 | 0.00795 | *** | ** |
| 15HR and 24HR | 1.12E-95 | 0.90173 | *** | n.s. |
| 18HR and 21HR | 4.16E-08 | 0.05985 | *** | n.s. |
| 18HR and 24HR | 1.86E-139 | 3.08E-07 | *** | *** |
| 21HR and 24HR | 2.06E-124 | 0.00334 | *** | ** |
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Anti-resonance in developmental signaling regulates cell fate decisions
eLife 14:RP107794.
https://doi.org/10.7554/eLife.107794.3
