A spatial model of the plant circadian clock reveals design principles for coordinated timing
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Reviewer #1 (Evidence, reproducibility and clarity):
**A. Summary:**
In this modeling study, the authors devised a multicellular model to investigate how circadian clocks in different parts (organs) of plants coordinate their timing. The model uses a plausible mechanism to explain how having a different sensitivity to light leads to different phase and period of circadian clock, which is observed in different plant organs. The model allows for entrainment in Light-Dark (LD) cycles and then a release in always-light (LL) environments. The model disentangles numerous factors that have confounded previous experiments. In one instance, the authors assigned …
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Reply to the reviewers
Reviewer #1 (Evidence, reproducibility and clarity):
**A. Summary:**
In this modeling study, the authors devised a multicellular model to investigate how circadian clocks in different parts (organs) of plants coordinate their timing. The model uses a plausible mechanism to explain how having a different sensitivity to light leads to different phase and period of circadian clock, which is observed in different plant organs. The model allows for entrainment in Light-Dark (LD) cycles and then a release in always-light (LL) environments. The model disentangles numerous factors that have confounded previous experiments. In one instance, the authors assigned different light sensitivities to the different organs (e.g., root tip, hypocotyl, etc.) which unambiguously show that this one element alone - spatially differing sensitivity to light - is sufficient for recapitulating experimentally observed differences in periods and phases between plant organs. The model also recapitulates the spatial waves of gene expression within and between organs that experimentalists reported. At the sub-tissue level, the model-produced waves have similar patterns as the experimentally observed waves. This confirmation further validates the model. By having the cells share clock mRNA, from any clock component genes, showed the same, experimentally observed spatial dynamics. The main conclusion of the study is that regional differences (e.g., between different organs) in light senilities, when combined with cell-to-cell sharing of clock-gene mRNAs, enables a robust, yet flexible, circadian timing under noisy environmental cycles.
Thank you for your assessment of our work. We plan to make the following revisions based on your feedback.
**B. Specific points:**
1.Lines 125-127: "To simulate the variability observed in single cell clock rhythms, we multiplied the level of each mRNA and protein by a time scaling parameter that was randomly selected from a normal distribution." - Why not add a white (Gaussian) noise term to these equations? How does multiplying by a random variable (for rescaling time) different from my proposal? Some explanation should be given in the text here.
We opted for a time scaling approach as this generates between-cell period differences but avoids within-cell period differences. This is consistent with single cell experiments (S1 Fig; Gould et al., 2018, eLife). We will provide an explanation of this in the text.
2.Does the spatial network model simplify calculations by assuming separations of timescales (e.g., for equilibration in concentrations of mRNAs that diffuse between cells)? If so, it would be good to spell these out in the beginning of the Results section (where the model is described).
We agree that a more detailed discussion of the model assumptions would be beneficial and we will provide this in the text.
3.Lines 161-162: "....in a phase only model by local...." should be "....in a phase model only by local...."
Thank you for your correction.
4.Lines 188-190: The authors observed that qualitatively similar/indistinguishable behaviors arose regardless of which elements are varied (e.g., global versus local cell-cell coupling, setting light input to be equal in all regions of the seedling, etc.). Then they claim here that "...these results show that the assumptions of local cell-to-cell coupling and differential light sensitivity between regions are the key aspects of our model that allow a match to experimental data." - I don't see how this follows from the observation almost any of the variations lead to the same behaviors in this section (spatial waves). Show the reasoning in the text here.
We observed spatial waves with different local coupling regimes (4 v. 8 nearest neighbours). However, we did not observe spatial waves with global coupling (S10 Fig). This led us to conclude that local coupling is a key aspect. In addition, we do not observe waves when setting the light input to be equal in all regions of the seedling (S11 Fig). This confirms that local differences in light sensitivity are also required in our simulations to generate spatial waves. We will clarify these points with revisions to the text.
5.Pgs. 9-10: Section on "Cell-to-cell coupling maintains global coordination under noisy light-dark cycles": The simulation results rigorously support the authors' main conclusion here, which is that local cell-to-cell coupling allows for global coordination under noisy LD cycles. But I'm missing an intuitive explanation (or just any explanation) for why this is. At the end of this section, the authors should provide some intuition or qualitative explanation for the observations that they produced using their model in this section.
We will revise the text to provide an intuitive explanation of these results. The coupling decreases the within-region phase differences. Despite the between-regions phase differences persisting, this effect is sufficient to improve the overall global synchrony.
6.Lines 261-262: Replace the present tenses with past tenses.
Thank you for your correction.
7.Is the main idea that cell-to-cell coupling allows for averaging of fluctuations, between organs or cells within the same organ, while allowing for coordination of the average quantities? Is this responsible for both the flexibility and robustness observed under noisy environmental cycles?
The cell-to-cell-coupling allows for the averaging of fluctuations between cells and the regional flexibility arises from the different light sensitivities in each region. What was interesting to us was that under light-dark cycles the regional flexibility was not lost due to either the noise in the light or the averaging effect of the cell-to-cell coupling. We will revise the text to emphasize these points. Thank you for your prompts.
8.Line 304: Is it really true that the mammalian circadian rhythm is centralized? Don't some parts of our bodies have different circadian clock (e.g., slight differences in phase) than some other parts of our bodies?
There are indeed some small phase differences between parts of our bodies because the mammalian system, like the plant system, is imperfectly coupled. However, the mammalian system is considered more centralized because the suprachiasmatic nucleus in the brain receives the key entraining signal of light and then coordinates rhythms across the body (Bell-Pedersen et al., 2005, Nat Rev Gen; Brown & Azzi, 2013, Circadian Clocks). We will expand on these interesting points by adding a paragraph to the discussion.
Reviewer #1 (Significance):
**Overall assessment:**
I enthusiastically recommend this work for publication after the authors address my comments below (please see "Specific points").
The model's main strength is that the authors could vary each ingredient separately - light sensitivity of each cell/organ, which gene's mRNA diffuses between cells, cellular noise, local versus global cell-cell coupling, etc. Afterwards, the authors could determine which of these variations produces which experimentally observed behaviors. Another strength of the model is that it can reproduce not just one, but numerous, experimentally observed behaviors that are important for understanding circadian clocks in plants. Thus, the model is grounded in experimental truth and produces experimentally observed results. Crucially, since the authors could vary every single element in the model independently of the other elements, the authors are able to provide plausible explanations for why the experiments produced the results that they did (experimentally, a number of confounding factors prevented one from pinpointing to which element produced which observation).
Another strength of the model is also extendable, by other researchers to investigate other plant physiologies in the future (e.g., circadian clock's influence on cell division). The authors highlight these future uses in the discussion section. Therefore, I believe that this work will be valuable to plant biologists, non-plant biologists who are interested in circadian clocks, and systems biologists in general.
The manuscript is also well written and relatively easy to follow, even for non-plant biologists like myself.
Thank you for the positive feedback - we are pleased that you find the manuscript of broad interest to a range of readers.
Comment on Reviewer #2:
I agree with his/her major criticism #3 (ELF4 long-distance movement). I find this to be a reasonable request. Fulfilling it would increase the paper's impact.
Please see our response to reviewer #2.
Comment on Reviewer #3:
The reviewer's point (1) asks for a reasonable request.
Regarding his/her point (2): This is also reasonable. I'd recommend his/her suggestion (a). In the end, I'd be interested to see how the authors respond to this (what function they choose to let adjacent cells be subjected to some correlated light-input intensity. I'd be happy with something simple such as + noise, where is a deterministic term that, for example, decreases exponentially as one moves away from some central cell. Basically, I'd let the authors decide how to implement this and accept their current implementation - no correlation in light-intensity between adjacent cells - as an extreme scenario, as this reviewer points out.
Please see our response to reviewer #3.
Reviewer #2 (Evidence, reproducibility and clarity):
**Summary:**
The manuscript presents an improved model of the circadian clock network that accounts for tissue-specific clock behavior, spatial differences in light sensitivity, and local coupling achieved through intercellular sharing of mRNA. In contrast to whole-plant or "phase-only" models, the authors' approach enables them to address the mechanism behind coupling and how the clock maintains regional synchrony in a noisy environment. Using 34 parameters to describe clock activity and applying the properties mentioned above, the authors demonstrate that their model can recapitulate the spatial waves in circadian gene expression observed and can simulate how the plant maintains local synchrony with regional differences in rhythms under noisy LD cycles. Spatial models that incorporate cell-type-specific sensitivities to environmental inputs and local coupling mechanisms will be most accurate for simulating clock activity under natural environments.
Thank you for your assessment of our work. We plan to make the following revisions based on your feedback.
*We have the following **major criticisms** as follows*
- When assigning light sensitivities in different regions of the plant, the authors assign a higher sensitivity value to the root tip (L=1.03) than they do to the other part of the root (L=0.90). We are curious why the root tip would have higher light sensitivity than the rest of the root. Is this based on experimental data (if so, please cite in this section or methods)? It seems that these L values were assigned simply to make sure they recapitulated the period differences observed in Fig. 2A. Are these values based on PhyB expression in those organs? Or perhaps based on cell density in those locations?
We assign the light sensitivity to match observed experimental period differences across the plant (Fig 2A,B). This is based on previous experiments demonstrating that experimental period differences are dependent on light input through the light sensing gene PHYB (Greenwood et al., 2019, PLoS Bio; Nimmo et al., 2020, Physiologia Plantarum). For example, in WT seedlings, the root tip oscillates faster than the root, but this difference is lost in the phyb-9 mutant (Greenwood et al., 2019). Thus, we assume the root tip to be more sensitive to light than the roots.
Further supporting this assumption, there is evidence that expression of phytochromes and cryptochromes are increased in the root tip relative to the root (e.g., Somers & Quail, 1995, Plant J; Bognar et al., 1999, PNAS; Toth et al., 2001, Plant Physiol), as the reviewer proposes. However, further experiments would be needed to verify that these differences in expression are what lead to the differences in clock timing. We will add a discussion of these experiments to the text.
- In the discussion of the test where they set the "light inputs to be equal" in all regions to simulate the phyb-9 mutant, could the authors please clarify whether that means they set the L light sensitivity value equal in all regions?
This is indeed what we mean, we will rephrase the text for clarity.
a. If they are referring to setting the L value equal to all regions, we suggest that this discussion be moved to the section about different light sensitivities instead of the local sharing of mRNA section.
Thank you for your suggestion, we agree and will move this discussion.
b. Additionally, is it possible to set the light sensitivity to zero for all parts of the plant? We think this would be more suitable to simulate the phyb-9 mutant phenotype.
We thank the reviewer for this suggestion. We will include a simulation with light sensitivity set to zero in the revised manuscript, in addition to the existing simulations with light sensitivity set to 1.
- Based on the recent Chen et al. (2020) paper showing ELF4 long-distance movement, we think it would be of great interest for the authors to model ELF4 protein synthesis/translation as the coupling factor, in addition to the modeling using CCA1/LHY mRNA sharing. We understand you may be saving this analysis for a future modeling paper, but this addition to the paper could increase the impact of this paper.
Thank you for the suggestion to improve our manuscript. We agree it will be of interest to model ELF4 protein as the local coupling factor. In the revision, we will simulate each clock protein (including ELF4) as the local coupling factor and compare.
In addition, we will also modify the coupling mechanism to simulate the long-distance transport of ELF4 proposed by Chen et al., 2020. Our preliminary simulations show that we can couple shoot rhythms to those in the root tip, but that this long range coupling can not on its own generate the spatial structure observed in experiments. We agree with the reviewers that this analysis and an associated discussion will further increase the impact of the paper.
- This model is able to simulate circadian rhythms under 12:12 LD cycles, which represents two days of the year-the equinoxes. We are curious if the model can simulate rhythms under short days and long days as well. We understand this analysis may be outside the scope of this paper and may require changing the values of the 34 parameters used but think it could be a useful addition here or in future work.
We agree it would be interesting to observe the behavior of the model under different day lengths. We will include simulations under short and long days in the revision.
*And **minor criticisms** as follows*
- In the first paragraph of the results section, it would be helpful for the authors to reference Table S1 when they mention the 34 parameters used to model oscillator function
We agree and we will implement this helpful suggestion.
- In the first paragraph of the section titled "Local flexibility persists under idealized and noisy LD cycles", it would be helpful for the authors to reference S12 Fig after the last sentence that starts "However, ELF4/LUX appeared more synchronized..."
We agree and we will implement this helpful suggestion.
- In the first paragraph of the section titled "Cell-to-cell coupling maintains global communication under noisy light-dark cycles", the authors refer to a "Table 1" but I think they mean to refer to Table S1"
Thank you, we will implement this helpful suggestion.
- In Fig. 1, panel C is described as demonstrating the cell-to-cell coupling through the "level of CCA1/LHY". This phrasing is vague and we think could be improved to the "mRNA level of CCA1/LHY".
We agree and will implement this helpful suggestion.
Reviewer #2 (Significance (Required)):
This work would be broadly interesting to other researchers studying cell-to-cell signaling and coupling of circadian rhythms in plants and other species where spatial waves of gene expression have been observed (i.e., mice and humans). Additionally, the computational modeling aspect of this work was easily interpretable for someone outside this expertise. Our expertise lies in plant circadian biology.
We thank the reviewer for recognising the broad appeal of our work.
Reviewer #3 (Evidence, reproducibility and clarity):
**Summary:**
The authors start by taking a previously published model of the plant circadian clock and implement five changes: 1) updating the network topology to reflect some recent experimental findings, 2) make a spatial model loosely based on a seedling template 3) introduce coupling between cells based on shared levels of CCA1/LHY 4) randomly rescale time in each cell to induce inter-cell differences in period, 5) include a light sensitivity that depends on the region considered.
For a certain configuration of light sensitivities/intensities, the different periods of oscillations in each seedling region roughly match that of experiments. With a sufficiently high coupling between cells, the system can also generate spatial waves, which are also observed in the experimental system.
With pulsed light inputs the spatial pattern is still produced. The authors then investigate the robustness to environmental noise by generating stochastic light signals and show that the global synchrony, as measured with a synchronisation index, increases with cell-to-cell coupling strength. The paper is overall well-written, and the background and details of the analysis are well presented.
Thank you for your assessment of our work. We plan to make the following revisions based on your feedback.
**Major comments:**
For the first part of paper, the output of the model is certainly the focus. There is virtually no discussion of the inferred parameters and how much confidence the authors have in their values.
Thank you for this point. We will add discussion of the inferred parameters to the initial part of the results.
My main issue with the paper is about the section with noisy light signals, which is included in the title and is ultimately one of the main themes of the article.
Specifically, on line 224:
"This decrease in cell-to-cell variation revealed an underlying spatial structure (Fig 4D, middle and right, and S13 Fig), comparable to that observed under idealized LD cycles (Fig 4B, middle and right, and S12 Fig)."
Firstly, I don't feel these conclusions match with the data presented. Comparing figure 4D middle and right with figure 4B middle and right shows a clear and pronounced loss in spatial structure. In its current form, this statement has to change, but I believe there are at least two other major issues with this figure:
We agree there are some differences in the spatial structure between idealized (Fig 4B) and noisy (Fig 4D) LD cycles. Preliminary simulations suggest that this is due to the way the noisy LD cycles are programmed.
In the current implementation of noisy LD cycles, the maximum intensity of L, Lmax, differs between each region, such that relative differences in light sensitivity between regions are maintained. This means that some phase differences between regions are maintained. However, as the reviewer correctly points out in point 1 below, due to the noise fluctuations, the average level of light is lower than under idealized LD cycles, and with considerable day-to-day variation. We believe this is why the spatial structure differs.
Preliminary simulations suggest that if we normalize the mean light intensity such that the mean is equal between the two conditions (as the reviewer suggests in point 1 below), the spatial structure appears similar. We will present this analysis in the revision.
- The figure is clearly designed to invite a comparison between the noise-free light cycles on the left with the noisy cycles on the right. However, due to how the noisy light is simulated, the variance of light signal increases AND the average intensity of light decreases by 50%. When comparing the left and the right, we therefore don't know whether the changes are due to differences in the average signal or differences from the stochasticity. I think the authors should simulate a noisy light signal with the same mean intensity level as the deterministic signal.
As discussed above, we agree that the average intensity of the light decreases due to the noise, and this complicates interpretation. We will simulate idealized and noisy light cycles with the same mean light level upon revision.
- The noise model for the light doesn't seem realistic. On line 484 is says:
"We made the simplifying assumption that each cell is exposed to an independent noisy LD cycle due to their unique positions in the environment. LD cycles were input to the molecular model through the parameter L".
In fact, this could be considered as an incredibly complex signal, because for 800 cells it means drawing 800 random light signals. The implication is that two adjacent cells receive statistically independent light signals. Depending on chance, one cell might receive tropical levels of light while its neighbour experiences a cloudy day. This affects the interpretation and conclusions from figures 4 and 5. I propose two different ways of improving the simulation of the noisy light signal:
a) In one extreme case, all cells receive the same noisy light signal, and the other extreme, they all receive independent signals. You could consider a mixture model of light signals, where each cell receives \lambda L_global(t) + (1-\lambda) L_individual(t), where L_global(t) is a global light signal that is shared by all cells and L_individual(t) is a light signal unique to an individual cell. The mixing parameter \lambda controls how similar the light signal is between cells
b) Clearly the light signal will differ depending on the region, but there will be some spatial correlation. You could also consider methods of simulating light such that neighbouring cells receive correlated signals, although this might be difficult.
Thank you for your proposals. We agree that our current implementation of noisy LD cycles represents an extreme scenario. Given that there is no environmental data at sufficient resolution to reliably evaluate which implementation is most realistic, we will explore different approaches based on your suggestions and present them in our revision.
Assuming that the problem with the mean signal is corrected, do you expect the average spatial pattern to be the same between figure 4 B and D with no coupling (J=0) (although an increase in the variance between cells)? Perhaps not (owing to nonlinearities in the system), but it would be interesting to comment.
We agree that the decreased light intensity complicates interpretation of the spatial structure. Although in the current implementation relative light differences between regions are maintained, the spatial structure is altered because the mean intensities are lower. Preliminary simulations with the mean intensity fixed do result in spatial patterns more similar to that seen in Fig 4B, but with increased variance. Comprehensive simulations will be included in the revised manuscript.
The different periods in the different regions of the seedling are caused by differences in light sensitivity, which the authors claim is justified from refs 12-15. An alternative hypothesis is the that biochemical parameters such as degradation rates are different between regions. This is briefly alluded to in the introduction, but I think it would be interesting to discuss further. What would be the pros and cons of the two different mechanisms?
We agree that an alternative hypothesis is that biochemical parameters such as degradation rates may differ between regions. Experimental evidence, however, more supports the light sensitivity hypothesis. This is because, for example, mutations in light signalling remove the spatial differences between regions. We agree though that this is an important point, and will add a paragraph to the discussion discussing the pros and cons of the two different mechanisms.
I understand that the authors used a pre-existing model, but I must say that I find the way that light is incorporated into the model a bit confusing.
On line 345 it says:
"L(t) represents the input light signal (L = 0, lights off; L > 0, lights on) and D(t) denotes a corresponding darkness input signal (D = 1, lights off; D = 0, lights on)."
Surely the only thing that matters biophysically is the number of photons hitting the plant? Could you explain why the model needs to have a separate "darkness signal" compared to just a single light signal?
A darkness signal has been introduced in many circadian clock models because degradation rates of the clock genes can depend upon the light or dark condition. We agree with the reviewer that we should explain this clearer in the text.
In the model, the light intensity changes depending on the region. It might make more sense for interpretability if instead there is an additional light-sensitivity coefficient that depends on the region, because at the moment I'm not sure what units L(t) is supposed to take.
Thank you for your suggestion. We will try to implement this approach.
**Minor comments**
Could you more explicitly describe a possible molecular mechanism through which the coupling acts?
Thank you for your suggestion. We will more explicitly discuss likely transport mechanisms in the text.
In Figure 1C it looks like different genes are coupling to different genes, so you may need to rearrange it.
In our model, the level of CCA1/LHY is shared. Thus, CCA1/LHY from one cell can be considered to repress the expression of other interacting genes in the neighbour cell.
Line 103: "We found that regional differences persist even under LD cycles, but cell to-cell minimized differences between neighbor cells." Missing word.
Thank you for your correction.
Line 124: "The coupling strength was set to 2 (Methods)." This is meaningless in isolation, so it would be better to briefly explain what the coupling parameter is before mentioning its value.
Thank you for your suggestion, we will describe the coupling function in more detail.
Through the text, I think De Caluwe should be corrected to De Caluwé
Thank you for your correction.
Typo line 493
Thank you for your correction.
Code and data are not made available.
Model code will be made available from our project GitLab page: https://gitlab.com/slcu/teamJL/greenwood_tokuda_etal_2020
Output of analysis of experimental data and simulations will also be made available on the GitLab page.
Reviewer #3 (Significance (Required)):
The authors motivate the paper by highlighting that their proposed model improves on phase-based models in that it describes underlying molecular mechanisms.
From an experimental side, it's interesting that a model is developed and directly compared with measured spatio-temporal waves of gene expression. From a theoretical side, the authors address questions relating to oscillations, multi-scale modelling and noise robustness that also generalise to other systems. I therefore expect that both experimental and theoretical audiences will be interested in the results.
There are many possible additions and modifications that could be made to the model, and so the model and analysis could provide a platform for future research. However, I can't comment on whether there are similar pre-existing models of the plant circadian clock that contain both a molecular description of the circadian clock as well as a spatial scale.
We appreciate the reviewer’s view that the work is interesting to both experimental and theoretical audiences.
Comments on Review #1:
The time is rescaled in each cell, meaning that each cell has a unique period, but the dynamics remain deterministic and hence the peak-to-peak times will be exactly the same for each cell. I imagine this isn't completely consistent with single-cell data (if available), where peak-to-peak times are very likely to be variable due to noisy gene expression. In a future paper it would be interesting to analyse the system using stochastic differential equations.
Please see our response to reviewer #1.
Comments on Review #2:
I agree on the following two points:
- It would add value to discuss whether the different ranking of light sensitivities by organ matches any available experimental data.
Please see our response to reviewer #2.
- As the Reviewers point out, there are many possibilities for testing the robustness of the system to light clues, including varying the length of the day. Although outside of the scope of this paper, I wonder if it's possible to find data from a light sensor measuring light intensity across an entire year? Plugging such data into the model and measuring how the amplitude and period changes would be really interesting, in my opinion.
Thank you for your suggestion. We also see this as an interesting future direction.
-
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Referee #3
Evidence, reproducibility and clarity
Summary:
The authors start by taking a previously published model of the plant circadian clock and implement five changes: 1) updating the network topology to reflect some recent experimental findings, 2) make a spatial model loosely based on a seedling template 3) introduce coupling between cells based on shared levels of CCA1/LHY 4) randomly rescale time in each cell to induce inter-cell differences in period, 5) include a light sensitivity that depends on the region considered.
For a certain configuration of light sensitivities/intensities, the different periods of oscillations in each seedling region roughly match that of …
Note: This preprint has been reviewed by subject experts for Review Commons. Content has not been altered except for formatting.
Learn more at Review Commons
Referee #3
Evidence, reproducibility and clarity
Summary:
The authors start by taking a previously published model of the plant circadian clock and implement five changes: 1) updating the network topology to reflect some recent experimental findings, 2) make a spatial model loosely based on a seedling template 3) introduce coupling between cells based on shared levels of CCA1/LHY 4) randomly rescale time in each cell to induce inter-cell differences in period, 5) include a light sensitivity that depends on the region considered.
For a certain configuration of light sensitivities/intensities, the different periods of oscillations in each seedling region roughly match that of experiments. With a sufficiently high coupling between cells, the system can also generate spatial waves, which are also observed in the experimental system.
With pulsed light inputs the spatial pattern is still produced. The authors then investigate the robustness to environmental noise by generating stochastic light signals and show that the global synchrony, as measured with a synchronisation index, increases with cell-to-cell coupling strength. The paper is overall well-written, and the background and details of the analysis are well presented.
Major comments:
For the first part of paper, the output of the model is certainly the focus. There is virtually no discussion of the inferred parameters and how much confidence the authors have in their values.
My main issue with the paper is about the section with noisy light signals, which is included in the title and is ultimately one of the main themes of the article.
Specifically, on line 224:
"This decrease in cell-to-cell variation revealed an underlying spatial structure (Fig 4D, middle and right, and S13 Fig), comparable to that observed under idealized LD cycles (Fig 4B, middle and right, and S12 Fig)."
Firstly, I don't feel these conclusions match with the data presented. Comparing figure 4D middle and right with figure 4B middle and right shows a clear and pronounced loss in spatial structure. In its current form, this statement has to change, but I believe there are at least two other major issues with this figure:
- The figure is clearly designed to invite a comparison between the noise-free light cycles on the left with the noisy cycles on the right. However, due to how the noisy light is simulated, the variance of light signal increases AND the average intensity of light decreases by 50%. When comparing the left and the right, we therefore don't know whether the changes are due to differences in the average signal or differences from the stochasticity. I think the authors should simulate a noisy light signal with the same mean intensity level as the deterministic signal. .
- The noise model for the light doesn't seem realistic. On line 484 is says:
"We made the simplifying assumption that each cell is exposed to an independent noisy LD cycle due to their unique positions in the environment. LD cycles were input to the molecular model through the parameter L".
In fact, this could be considered as an incredibly complex signal, because for 800 cells it means drawing 800 random light signals. The implication is that two adjacent cells receive statistically independent light signals. Depending on chance, one cell might receive tropical levels of light while its neighbour experiences a cloudy day. This affects the interpretation and conclusions from figures 4 and 5. I propose two different ways of improving the simulation of the noisy light signal:
a) In one extreme case, all cells receive the same noisy light signal, and the other extreme, they all receive independent signals. You could consider a mixture model of light signals, where each cell receives \lambda L_global(t) + (1-\lambda) L_individual(t), where L_global(t) is a global light signal that is shared by all cells and L_individual(t) is a light signal unique to an individual cell. The mixing parameter \lambda controls how similar the light signal is between cells
b) Clearly the light signal will differ depending on the region, but there will be some spatial correlation. You could also consider methods of simulating light such that neighbouring cells receive correlated signals, although this might be difficult.
Assuming that the problem with the mean signal is corrected, do you expect the average spatial pattern to be the same between figure 4 B and D with no coupling (J=0) (although an increase in the variance between cells)? Perhaps not (owing to nonlinearities in the system), but it would be interesting to comment.
The different periods in the different regions of the seedling are caused by differences in light sensitivity, which the authors claim is justified from refs 12-15. An alternative hypothesis is the that biochemical parameters such as degradation rates are different between regions. This is briefly alluded to in the introduction, but I think it would be interesting to discuss further. What would be the pros and cons of the two different mechanisms?
I understand that the authors used a pre-existing model, but I must say that I find the way that light is incorporated into the model a bit confusing.
On line 345 it says: "L(t) represents the input light signal (L = 0, lights off; L > 0, lights on) and D(t) denotes a corresponding darkness input signal (D = 1, lights off; D = 0, lights on)."
Surely the only thing that matters biophysically is the number of photons hitting the plant? Could you explain why the model needs to have a separate "darkness signal" compared to just a single light signal?
In the model, the light intensity changes depending on the region. It might make more sense for interpretability if instead there is an additional light-sensitivity coefficient that depends on the region, because at the moment I'm not sure what units L(t) is supposed to take.
Minor comments
Could you more explicitly describe a possible molecular mechanism through which the coupling acts?
In Figure 1C it looks like different genes are coupling to different genes, so you may need to rearrange it.
Line 103: "We found that regional differences persist even under LD cycles, but cell to-cell minimized differences between neighbor cells." Missing word.
Line 124: "The coupling strength was set to 2 (Methods)." This is meaningless in isolation, so it would be better to briefly explain what the coupling parameter is before mentioning its value.
Through the text, I think De Caluwe should be corrected to De Caluwé
Typo line 493
Code and data are not made available.
Significance
The authors motivate the paper by highlighting that their proposed model improves on phase-based models in that it describes underlying molecular mechanisms.
From an experimental side, it's interesting that a model is developed and directly compared with measured spatio-temporal waves of gene expression. From a theoretical side, the authors address questions relating to oscillations, multi-scale modelling and noise robustness that also generalise to other systems. I therefore expect that both experimental and theoretical audiences will be interested in the results.
There are many possible additions and modifications that could be made to the model, and so the model and analysis could provide a platform for future research. However, I can't comment on whether there are similar pre-existing models of the plant circadian clock that contain both a molecular description of the circadian clock as well as a spatial scale.
REFEREE'S CROSS-COMMENTING
Comments on Review #1:
The time is rescaled in each cell, meaning that each cell has a unique period, but the dynamics remain deterministic and hence the peak-to-peak times will be exactly the same for each cell. I imagine this isn't completely consistent with single-cell data (if available), where peak-to-peak times are very likely to be variable due to noisy gene expression. In a future paper it would be interesting to analyse the system using stochastic differential equations.
Comments on Review #2:
I agree on the following two points:
It would add value to discuss whether the different ranking of light sensitivities by organ matches any available experimental data.
As the Reviewers point out, there are many possibilities for testing the robustness of the system to light clues, including varying the length of the day. Although outside of the scope of this paper, I wonder if it's possible to find data from a light sensor measuring light intensity across an entire year? Plugging such data into the model and measuring how the amplitude and period changes would be really interesting, in my opinion.
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Referee #2
Evidence, reproducibility and clarity
Summary:
The manuscript presents an improved model of the circadian clock network that accounts for tissue-specific clock behavior, spatial differences in light sensitivity, and local coupling achieved through intercellular sharing of mRNA. In contrast to whole-plant or "phase-only" models, the authors' approach enables them to address the mechanism behind coupling and how the clock maintains regional synchrony in a noisy environment. Using 34 parameters to describe clock activity and applying the properties mentioned above, the authors demonstrate that their model can recapitulate the spatial waves in circadian gene expression …
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Referee #2
Evidence, reproducibility and clarity
Summary:
The manuscript presents an improved model of the circadian clock network that accounts for tissue-specific clock behavior, spatial differences in light sensitivity, and local coupling achieved through intercellular sharing of mRNA. In contrast to whole-plant or "phase-only" models, the authors' approach enables them to address the mechanism behind coupling and how the clock maintains regional synchrony in a noisy environment. Using 34 parameters to describe clock activity and applying the properties mentioned above, the authors demonstrate that their model can recapitulate the spatial waves in circadian gene expression observed and can simulate how the plant maintains local synchrony with regional differences in rhythms under noisy LD cycles. Spatial models that incorporate cell-type-specific sensitivities to environmental inputs and local coupling mechanisms will be most accurate for simulating clock activity under natural environments.
We have the following major criticisms as follows
When assigning light sensitivities in different regions of the plant, the authors assign a higher sensitivity value to the root tip (L=1.03) than they do to the other part of the root (L=0.90). We are curious why the root tip would have higher light sensitivity than the rest of the root. Is this based on experimental data (if so, please cite in this section or methods)? It seems that these L values were assigned simply to make sure they recapitulated the period differences observed in Fig. 2A. Are these values based on PhyB expression in those organs? Or perhaps based on cell density in those locations?
In the discussion of the test where they set the "light inputs to be equal" in all regions to simulate the phyb-9 mutant, could the authors please clarify whether that means they set the L light sensitivity value equal in all regions? a. If they are referring to setting the L value equal to all regions, we suggest that this discussion be moved to the section about different light sensitivities instead of the local sharing of mRNA section. b. Additionally, is it possible to set the light sensitivity to zero for all parts of the plant? We think this would be more suitable to simulate the phyb-9 mutant phenotype.
Based on the recent Chen et al. (2020) paper showing ELF4 long-distance movement, we think it would be of great interest for the authors to model ELF4 protein synthesis/translation as the coupling factor, in addition to the modeling using CCA1/LHY mRNA sharing. We understand you may be saving this analysis for a future modeling paper, but this addition to the paper could increase the impact of this paper.
This model is able to simulate circadian rhythms under 12:12 LD cycles, which represents two days of the year-the equinoxes. We are curious if the model can simulate rhythms under short days and long days as well. We understand this analysis may be outside the scope of this paper and may require changing the values of the 34 parameters used but think it could be a useful addition here or in future work.
And minor criticisms as follows
In the first paragraph of the results section, it would be helpful for the authors to reference Table S1 when they mention the 34 parameters used to model oscillator function
In the first paragraph of the section titled "Local flexibility persists under idealized and noisy LD cycles", it would be helpful for the authors to reference S12 Fig after the last sentence that starts "However, ELF4/LUX appeared more synchronized..."
In the first paragraph of the section titled "Cell-to-cell coupling maintains global communication under noisy light-dark cycles", the authors refer to a "Table 1" but I think they mean to refer to Table S1"
In Fig. 1, panel C is described as demonstrating the cell-to-cell coupling through the "level of CCA1/LHY". This phrasing is vague and we think could be improved to the "mRNA level of CCA1/LHY".
Significance
This work would be broadly interesting to other researchers studying cell-to-cell signaling and coupling of circadian rhythms in plants and other species where spatial waves of gene expression have been observed (i.e., mice and humans). Additionally, the computational modeling aspect of this work was easily interpretable for someone outside this expertise. Our expertise lies in plant circadian biology.
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Referee #1
Evidence, reproducibility and clarity
A. Summary:
In this modeling study, the authors devised a multicellular model to investigate how circadian clocks in different parts (organs) of plants coordinate their timing. The model uses a plausible mechanism to explain how having a different sensitivity to light leads to different phase and period of circadian clock, which is observed in different plant organs. The model allows for entrainment in Light-Dark (LD) cycles and then a release in always-light (LL) environments. The model disentangles numerous factors that have confounded previous experiments. In one instance, the authors assigned different light sensitivities to the …
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Referee #1
Evidence, reproducibility and clarity
A. Summary:
In this modeling study, the authors devised a multicellular model to investigate how circadian clocks in different parts (organs) of plants coordinate their timing. The model uses a plausible mechanism to explain how having a different sensitivity to light leads to different phase and period of circadian clock, which is observed in different plant organs. The model allows for entrainment in Light-Dark (LD) cycles and then a release in always-light (LL) environments. The model disentangles numerous factors that have confounded previous experiments. In one instance, the authors assigned different light sensitivities to the different organs (e.g., root tip, hypocotyl, etc.) which unambiguously show that this one element alone - spatially differing sensitivity to light - is sufficient for recapitulating experimentally observed differences in periods and phases between plant organs. The model also recapitulates the spatial waves of gene expression within and between organs that experimentalists reported. At the sub-tissue level, the model-produced waves have similar patterns as the experimentally observed waves. This confirmation further validates the model. By having the cells share clock mRNA, from any clock component genes, showed the same, experimentally observed spatial dynamics. The main conclusion of the study is that regional differences (e.g., between different organs) in light senilities, when combined with cell-to-cell sharing of clock-gene mRNAs, enables a robust, yet flexible, circadian timing under noisy environmental cycles.
B. Specific points:
1.Lines 125-127: "To simulate the variability observed in single cell clock rhythms, we multiplied the level of each mRNA and protein by a time scaling parameter that was randomly selected from a normal distribution." - Why not add a white (Gaussian) noise term to these equations? How does multiplying by a random variable (for rescaling time) different from my proposal? Some explanation should be given in the text here.
2.Does the spatial network model simplify calculations by assuming separations of timescales (e.g., for equilibration in concentrations of mRNAs that diffuse between cells)? If so, it would be good to spell these out in the beginning of the Results section (where the model is described).
3.Lines 161-162: "....in a phase only model by local...." should be "....in a phase model only by local...."
4.Lines 188-190: The authors observed that qualitatively similar/indistinguishable behaviors arose regardless of which elements are varied (e.g., global versus local cell-cell coupling, setting light input to be equal in all regions of the seedling, etc.). Then they claim here that "...these results show that the assumptions of local cell-to-cell coupling and differential light sensitivity between regions are the key aspects of our model that allow a match to experimental data." - I don't see how this follows from the observation almost any of the variations lead to the same behaviors in this section (spatial waves). Show the reasoning in the text here.
5.Pgs. 9 -10: Section on "Cell-to-cell coupling maintains global coordination under noisy light-dark cycles": The simulation results rigorously support the authors' main conclusion here, which is that local cell-to-cell coupling allows for global coordination under noisy LD cycles. But I'm missing an intuitive explanation (or just any explanation) for why this is. At the end of this section, the authors should provide some intuition or qualitative explanation for the observations that they produced using their model in this section.
6.Lines 261-262: Replace the present tenses with past tenses.
7.Is the main idea that cell-to-cell coupling allows for averaging of fluctuations, between organs or cells within the same organ, while allowing for coordination of the average quantities? Is this responsible for both the flexibility and robustness observed under noisy environmental cycles?
8.Line 304: Is it really true that the mammalian circadian rhythm is centralized? Don't some parts of our bodies have different circadian clock (e.g., slight differences in phase) than some other parts of our bodies?
Significance
Overall assessment:
I enthusiastically recommend this work for publication after the authors address my comments below (please see "Specific points").
The model's main strength is that the authors could vary each ingredient separately - light sensitivity of each cell/organ, which gene's mRNA diffuses between cells, cellular noise, local versus global cell-cell coupling, etc. Afterwards, the authors could determine which of these variations produces which experimentally observed behaviors. Another strength of the model is that it can reproduce not just one, but numerous, experimentally observed behaviors that are important for understanding circadian clocks in plants. Thus, the model is grounded in experimental truth and produces experimentally observed results. Crucially, since the authors could vary every single element in the model independently of the other elements, the authors are able to provide plausible explanations for why the experiments produced the results that they did (experimentally, a number of confounding factors prevented one from pinpointing to which element produced which observation).
Another strength of the model is also extendable, by other researchers to investigate other plant physiologies in the future (e.g., circadian clock's influence on cell division). The authors highlight these future uses in the discussion section. Therefore, I believe that this work will be valuable to plant biologists, non-plant biologists who are interested in circadian clocks, and systems biologists in general.
The manuscript is also well written and relatively easy to follow, even for non-plant biologists like myself.
REFEREE'S CROSS-COMMENTING
Comment on Reviewer #2:
I agree with his/her major criticism #3 (ELF4 long-distance movement). I find this to be a reasonable request. Fulfilling it would increase the paper's impact.
Comment on Reviewer #3:
The reviewer's point (1) asks for a reasonable request. Regarding his/her point (2): This is also reasonable. I'd recommend his/her suggestion (a). In the end, I'd be interested to see how the authors respond to this (what function they choose to let adjacent cells be subjected to some correlated light-input intensity. I'd be happy with something simple such as < intensity > + noise, where <intensity> is a deterministic term that, for example, decreases exponentially as one moves away from some central cell. Basically, I'd let the authors decide how to implement this and accept their current implementation - no correlation in light-intensity between adjacent cells - as an extreme scenario, as this reviewer points out.
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