Anti-resonance in developmental signaling regulates cell fate decisions

Reviewer #1 (Public review):

Summary:

This report demonstrates that the gene expression output of the Wnt pathway, when controlled precisely by a synthetic light-based input, depends substantially on the frequency of stimulation. The particular frequency-dependent trend that is observed - anti-resonance, a suppression of target gene expression at intermediate frequencies given a constant duty cycle - is a novel aspect that has not been clearly shown before for this or other signaling pathways. The paper provides both clear experimental evidence of the phenomenon with engineered cellular systems and a model-based analysis of how the pairing of rate constants in pathway activation/deactivation could result in such a trend.

Strengths:

This report couples in vitro experimental data with an abstracted mathematical model. Both of these approaches appear to be technically sound and to provide consistent and strong support for the main conclusion. The experimental data are particularly clear, and the demonstration that Brachyury expression is subject to anti-resonance in ESCs is particularly compelling. The modeling approach is reasonably scaled for the system at the level of detail that is needed in this case, and the hidden variable analysis provides some insight into how the anti-resonance works.

Weaknesses:

(1) The anti-resonance phenomenon has not been demonstrated using physiological Wnt ligands; however, I view this as only a minor weakness for an initial report of the phenomenon. The potential significance of the phenomenon for Wnt outweighs the amount of effort it would take to carry the demonstration further - testing different frequencies/duty cycles at the level of ligand stimulus using microfluidics could get quite involved, and would likely take quite some time. Adding some more discussion about how the time scales of ligand-receptor binding could play into the reduced model would further ameliorate this issue.

(2) While the model is fully consistent with the data, it has not been validated using experimental manipulations to establish that the mechanisms of the cell system and the model are the same. There may be some ways to make such modifications, for example, using a proteasome inhibitor. An alternative would be to more explicitly mention the need to validate the model's mechanism with experiments.

(3) I think the manuscript misses an opportunity to discuss the potential of the phenomenon in other pathways. The hedgehog pathway, for example, involves GSK3-mediated partial proteolysis of a transcription factor, which could conceivably be subject to similar behaviors, and there are certainly other examples as well.

(4) Some aspects of the modeling and hidden variable analysis are not optimally presented in the main text, although when considered together with the Supplemental Data, there are no significant deficiencies.

Reviewer #2 (Public review):

Summary:

By combining optogenetics with theoretical modelling, the authors identify an anti-resonance behavior in the WnT signaling pathway. This behavior is manifested as a minimal response at a certain stimulation frequency. Using an abstracted hidden variable model, the authors explain their findings by a competition of timescales. Furthermore, they experimentally show that this anti-resonance influences the cell fate decision involved in human gastrulation.

Strengths:

(1) This interdisciplinary study combines precise optogenetic manipulation with advanced modelling.

(2) The results are directly tested in two different systems: HEK293T cells and H9 human embryonic stem cells.

(3) The model is implemented based on previous literature and has two levels of detail: i) a detailed biochemical model and ii) an abstract model with a hidden parameter.

Weaknesses:

(1) While the experiments provide both single-cell data and population data, the model only considers population data.

(2) Although the model captures the experimental data for TopFlash very well, the beta-Cat curves (Figure 2B) are only described qualitatively. This discrepancy is not discussed.

Overall Assessment:

The authors convincingly identified an anti-resonance behavior in a signaling pathway that is involved in cell fate decisions. The focus on a dynamic signal and the identification of such a behavior is important. I believe that the model approach of abstracting a complicated pathway with a hidden variable is an important tool to obtain an intuitive understanding of complicated dependencies in biology. Such a combination of precise ontogenetic manipulation with effective models will provide a new perspective on causal dependencies in signaling pathways and should not be limited only to the system that the authors study.