Anti-resonance in developmental signaling regulates cell fate decisions

Samuel J Rosen
Olivier Witteveen
Naomi Baxter
Ryan S Lach
Erik Hopkins
Marianne Bauer author has email address
Maxwell Z Wilson author has email address

Interdisciplinary Program in Quantitative Biosciences, University of California Santa Barbara, Santa Barbara, United States
Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Technische Universiteit Delft, Delft, Netherlands
Department of Molecular, Cellular, and Development Biology, University of California Santa Barbara, Santa Barbara, United States
Integrated Biosciences, Inc, Redwood City, United States
Center for Bioengineering, University of California Santa Barbara, Santa Barbara, United States
Neuroscience Research Institute, University of California Santa Barbara, Santa Barbara, United States

https://doi.org/10.7554/eLife.107794.1

Open access
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Figures and data

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 24hrs of 405nm light illumination delivered every 2 minutes. Images are shown using the same lookup table. (C) Single-cell unsmoothed mean fluorescent intensity (MFI) traces (N = 321-567 cells, 4 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. Blue background indicates light on, white indicates light off. Black line represents population mean. (D) Population smoothed means of live, single-cell β-catenin (top) and TopFlash (bottom) MFI traces from indicated conditions (N = 321-595 cells, 4 biological replicates per condition, see Methods for significance values).

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 21hrs compared against our unsmoothed experimental results (light) from Figure 1D. Post-26 hours, experimental data was corrected for over confluency effects in both 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.

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 MFI in the top right corner (N = 106-590 cells, 4 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, 4 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 to differentiate our experimental results heatmap from our computational heatmap.

A hidden variable approach relates the anti-resonance to the timescales of Wnt activation and deactivation.
(A) A hidden variable a(t) is activated upon optogenetic Wnt activation at a rate k_on and deactivates at rate k_off when the light is turned off. In turn, a(t) is coupled to first-order β-catenin dynamics b(t). (B-D) Systematic exploration of the parameter space shows that the rates k_on and k_off tune the concavity. (B) Concavity of anti-resonance is dependent on the combination of k_on and k_off rates. (C) Shape of the anti-resonance for five different points (A-E) in parameter space. As we enter the region k_off < 1+k_a) k_on the anti-resonance appears, consistent with our analytical result (see Supplemental Text for details about equations and parameter values). (D) Anti-resonant frequency is dependent on the combination of k_on and k_off rates.

Anti-resonant dynamics drive mesodermal stem cell differentiation in 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 24hrs 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, 6 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 to differentiate 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).

Model variables

Model parameters.

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