Computational modeling of cambium activity provides a regulatory framework for simulating radial plant growth
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Evaluation Summary:
The paper presents a sequence of models, simulating with increasing accuracy the production of phloem and xylem in a cross-section of a generalized circularly symmetric plant organ. The results may serve as a stepping stone for the construction of predictive models.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #2 agreed to share their name with the authors.)
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Abstract
Precise organization of growing structures is a fundamental process in developmental biology. In plants, radial growth is mediated by the cambium, a stem cell niche continuously producing wood (xylem) and bast (phloem) in a strictly bidirectional manner. While this process contributes large parts to terrestrial biomass, cambium dynamics eludes direct experimental access due to obstacles in live-cell imaging. Here, we present a cell-based computational model visualizing cambium activity and integrating the function of central cambium regulators. Performing iterative comparisons of plant and model anatomies, we conclude that the receptor-like kinase PXY and its ligand CLE41 are part of a minimal framework sufficient for instructing tissue organization. By integrating tissue-specific cell wall stiffness values, we moreover probe the influence of physical constraints on tissue geometry. Our model highlights the role of intercellular communication within the cambium and shows that a limited number of factors are sufficient to create radial growth by bidirectional tissue production.
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Author Response
Reviewer #1 (Public Review):
The authors try to shed light on how plant stem cells located in a ring‐like structure in the (the procambial cells or cambium) can generate two distinct differentiated tissues, one filling the interior of the ring (the xylem) and the other one surrounding the ring (the phloem). To achieve this goal, the authors propose different models increasing in complexity, and perform a series of comparisons between the model outcomes and experimental data in the Arabidopsis hypocotyl. This work seems to provide for the first time a computational framework to model the radial formation of the cambium, xylem and phloem in the hypocotyl. Some of the features of the wild type and mutants could be qualitatively recapitulated, such as the radial organization of the xylem, cambium and phloem in wild type, …
Author Response
Reviewer #1 (Public Review):
The authors try to shed light on how plant stem cells located in a ring‐like structure in the (the procambial cells or cambium) can generate two distinct differentiated tissues, one filling the interior of the ring (the xylem) and the other one surrounding the ring (the phloem). To achieve this goal, the authors propose different models increasing in complexity, and perform a series of comparisons between the model outcomes and experimental data in the Arabidopsis hypocotyl. This work seems to provide for the first time a computational framework to model the radial formation of the cambium, xylem and phloem in the hypocotyl. Some of the features of the wild type and mutants could be qualitatively recapitulated, such as the radial organization of the xylem, cambium and phloem in wild type, and a striking phenotype upon the overexpression of CLE41 transgene.
We thank the reviewer for appreciating the novelty of this work.
Although this work is very well written and understandable at the introduction, when paying careful attention to the presented results, there are different aspects that would require further work and investigation, on both experimental and modelling sides: The authors chose to study different models increasing in complexity, reaching a more complete model (Model 3, Figure 5A‐D) that the authors claim it is recapitulating the experimental data and the explored experimental perturbations (Figure 5E‐F). This model is substantially more complex than Model 1 and Model 2, and it is difficult to understand all the claims by the authors, and the radial pattern formation capabilities of it. Yet, a feature that is clear to the eye, both in the pictures and in the movies, is that this model seems more likely to present a front instability of the cambium front progression, disrupting the radial organization of the different tissues (see Figure 5B), which does not seem to happen in the wild type hypocotyl from Arabidopsis. This effect is even more extreme when looking at the pxy mutant (Figure 5F) and when the xylem cell wall thickness is explored through the simulations (Figure 6). The authors claim this model is able to recapitulate a basic feature of the pxy mutant, which is the fact that the distal cambium appears in patches. Although these patches appear in the simulations, this effect in the model might be produced by the instability of the cambium front progression itself, which might be fundamentally different from what happens in the experimental data. In the experimental data, the PXYpro:CFP cambium does not seem to present such front instability, but rather is the xylem that gets fragmented. To make a link between the Model 3 and the pxy mutant, a careful study of the different stages of this phenotype could be useful to do, both on the modelling and experimental side.
Thanks for this valuable comment and for appreciating our writing style. Front stability was not part of our considerations but provides certainly a very interesting aspect to our study. The reviewer is correct when noticing that the front of domains observed in planta is very stable but that this is not the case for our computational simulations. We believe that instability in the computational models is due to local noise in the cellular pattern leading to differential diffusion of chemicals* with respect to its radial position and to a progressive deviation of domain from a perfect circle. Such a deviation seems to be corrected by an unknown mechanism in planta but such a corrective mechanism is, due to the absence of a good idea of its nature, not implemented in our models. In order to investigate this point and the contribution of front instability to phenotypes of perturbed lines, we performed a time course analysis of anatomies of wt, IRX3pro:CLE41 and pxy lines with the help of the PXYpro:CFP/SMXL5pro:YFP markers, now shown in Fig. S1, and compared their dynamics to the respective movies 4A, 5A, and 6A. For pxy mutants, we observed ‘gaps’ in the cambium domain already at early stages of development (Fig. S1I, J) arguing against the fact that the pxy anatomy is caused by increased front instability but rather by differential signaling within a circular domain leading to a breakdown of cambium patterning and cell fate determination. Although a corrective mechanism ensuring front stability in planta is difficult to predict, we believe that our model now allows to test respective ideas like directional movement of chemicals or stabilizing communication between cells within a particular circular domain. This aspect is now discussed in the discussion.
The authors have a parameter search strategy based on matching the proportion of cell types in Model 3. I am wondering how effective is this strategy in a system where these features are evolving in time, especially in Model 3, which seems to present a front instability. Moreover, this strategy does not tell anything about the model robustness for recapitulating the different features of the pattern.
We thank the reviewer for pointing out these aspects regarding the parameter search. We agree that there are some limitations to estimating dynamic parameters based on the proportion of cell types. As a consequence, we have focused our parameter search on those parameters that directly impact tissue formation: cell division thresholds, cell differentiation thresholds and maximal cell sizes. We have further expanded our parameter search until we obtained five distinct parameter sets that recapitulate central features of cambium activity. This increases the likelihood that the behavior we saw in the subsequent analyses was actually a feature of the system and not a characteristic of that particular parameter set. This strategy did not solve the front instability of model 3, which suggests that there are factors at play ‐ beyond the CLE41‐PXY module and cell wall stability – which are currently beyond the scope of our model.
In the last model, the authors try to link the cell wall thickness with the radiality of the divisions. Although the idea of looking at the division trajectories seems interesting, more clarity is needed to see how helpful is the radiality measure, and perhaps a better measure is needed ‐ note that the proliferation trajectory in Figure 6C might have the same amount of ramifications than in Figure 6B, and therefore, effectively speaking, the amount of periclinal divisions might be the same in both cases. The authors claim that the increase of xylem thickness contributes in having a more radial growth, but this could be related to the cambium front instability, which seems to be more pronounced as well for higher xylem thickness.
We agree with the reviewer that this is a critical point as a robust measurement of ‘radiality’ of cell lineages is central for accessing the degree of pericliniality of cell divisions with the computational model. After extensively considering different measurement methods, we indeed think that calculating R2 of cell* connectors is the most appropriate and quantitative one in the context of our computational model. In fact, the amount of ramifications is not considered by this method but the geometry of ‘cell* connectors’ which clearly shows a more ‘radial’ pattern of cell lineages when xylem cells are ‘stiffer’ (Fig. 6D). Ramifications would be a measurement of the amount of cell divisions, which we did not want to target in this case. We also did not claim that increased xylem thickness leads to more radial growth. In fact, Fig. S4 shows that this is rather the opposite. We expect that increased front instability when ‘xylem stiffness’ is increased, would rather decrease radiality of cell* lineages and mask respective positive effects. The fact that we still see increased ‘radiality’ argues against the assumption that front instability is causative.
On the experimental side, the claims about the proximal and distal cambium, together with the cell proliferation data are not very well supported with the presented data in Figures 2, 3A and S1. Moreover, these different figures seem to show different behaviors ‐ are these sections at different stages of the hypocotyl? Also, seeing more of the H4 marker in a region of the tissue not necessarily indicates a higher proliferation rate (it could also simply be that cells are more synchronized in the S phase in that region of the cambium, and/or the cell cycle lasts for longer in that part of the tissue). A quantification and the proper repeats to support these claims is lacking. A quantitative and more extensive study of the pxy mutant would enable a better comparison with the simulated model. Is there PXYpro:CFP expression between the fragmented xylem?
We agree with these concerns toward the H4 marker used in the initial submission. Because H4 expression is not specifically associated with cell division but with DNA synthesis in general and, thus, with endoreduplication, H4 expression does not report faithfully on cell division. As a response, we removed related figures and now reference our previous study characterizing cell division levels in different cambium domains based on cell linage analyses (Shi et al., 2019). Because this is a far more reliable analysis and convincingly supports our claims, we believe that we thereby addressed this concern. As mentioned above, we also added a more extensive analysis of the pxy mutant (Fig. S1) showing that there is no PXY expression between the fragmented xylem domains.
This work might help progress in the field of understanding radial patterning in plants. The introduction and the first models could attract a more general plant audience, but once the models increase in complexity, the narrative and presented results are more relevant to those scientists more specialized in xylem and phloem formation.
We thank the reviewer for appreciating the general relevance of our models for a larger audience.
Reviewer #2 (Public Review):
The paper uses computer modeling and simulations to show how a radially growing circular plant organ, such as a hypocotyl, can develop and maintain its organization into tissues including, in particular, cambium, xylem and phloem. The results are illustrated with useful movies representing the simulations. The paper is organized as a sequence of models, which has some rationale ‐ it presumably depicts the path of refinements through which the authors arrived at the final model ‐ but the intermediate steps are of limited interest. At the same time, mathematical details of the models are not presented to the full extent. Fortunately, the models can be downloaded over the Internet, and the supplementary materials include detailed instructions for executing them (using the VirtualLeaf framework). Consequently, the paper and its results can potentially serve as a stepping stone for further model‐assisted studies of radial tissue organization and growth.
Again, we thank the reviewer for appreciating the usefulness of our model and its general implications. In the revised version of the manuscript we substantially expanded explanations of the mathematical details in the main text and the supplemental methods. We still would argue that intermediate steps are of common interests as they illustrate why certain assumptions being extensively discussed within the field were refused providing important justifications for the final model.
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Reviewer #2 (Public Review):
The paper uses computer modeling and simulations to show how a radially growing circular plant organ, such as a hypocotyl, can develop and maintain its organization into tissues including, in particular, cambium, xylem and phloem. The results are illustrated with useful movies representing the simulations. The paper is organized as a sequence of models, which has some rationale - it presumably depicts the path of refinements through which the authors arrived at the final model - but the intermediate steps are of limited interest. At the same time, mathematical details of the models are not presented to the full extent. Fortunately, the models can be downloaded over the Internet, and the supplementary materials include detailed instructions for executing them (using the VirtualLeaf framework). Consequently, …
Reviewer #2 (Public Review):
The paper uses computer modeling and simulations to show how a radially growing circular plant organ, such as a hypocotyl, can develop and maintain its organization into tissues including, in particular, cambium, xylem and phloem. The results are illustrated with useful movies representing the simulations. The paper is organized as a sequence of models, which has some rationale - it presumably depicts the path of refinements through which the authors arrived at the final model - but the intermediate steps are of limited interest. At the same time, mathematical details of the models are not presented to the full extent. Fortunately, the models can be downloaded over the Internet, and the supplementary materials include detailed instructions for executing them (using the VirtualLeaf framework). Consequently, the paper and its results can potentially serve as a stepping stone for further model-assisted studies of radial tissue organization and growth.
-
Reviewer #1 (Public Review):
The authors try to shed light on how plant stem cells located in a ring-like structure in the (the procambial cells or cambium) can generate two distinct differentiated tissues, one filling the interior of the ring (the xylem) and the other one surrounding the ring (the phloem). To achieve this goal, the authors propose different models increasing in complexity, and perform a series of comparisons between the model outcomes and experimental data in the Arabidopsis hypocotyl.
This work seems to provide for the first time a computational framework to model the radial formation of the cambium, xylem and phloem in the hypocotyl. Some of the features of the wild type and mutants could be qualitatively recapitulated, such as the radial organization of the xylem, cambium and phloem in wild type, and a striking …
Reviewer #1 (Public Review):
The authors try to shed light on how plant stem cells located in a ring-like structure in the (the procambial cells or cambium) can generate two distinct differentiated tissues, one filling the interior of the ring (the xylem) and the other one surrounding the ring (the phloem). To achieve this goal, the authors propose different models increasing in complexity, and perform a series of comparisons between the model outcomes and experimental data in the Arabidopsis hypocotyl.
This work seems to provide for the first time a computational framework to model the radial formation of the cambium, xylem and phloem in the hypocotyl. Some of the features of the wild type and mutants could be qualitatively recapitulated, such as the radial organization of the xylem, cambium and phloem in wild type, and a striking phenotype upon the overexpression of CLE41 transgene.
Although this work is very well written and understandable at the introduction, when paying careful attention to the presented results, there are different aspects that would require further work and investigation, on both experimental and modelling sides:
The authors chose to study different models increasing in complexity, reaching a more complete model (Model 3, Figure 5A-D) that the authors claim it is recapitulating the experimental data and the explored experimental perturbations (Figure 5E-F). This model is substantially more complex than Model 1 and Model 2, and it is difficult to understand all the claims by the authors, and the radial pattern formation capabilities of it. Yet, a feature that is clear to the eye, both in the pictures and in the movies, is that this model seems more likely to present a front instability of the cambium front progression, disrupting the radial organization of the different tissues (see Figure 5B), which does not seem to happen in the wild type hypocotyl from Arabidopsis. This effect is even more extreme when looking at the pxy mutant (Figure 5F) and when the xylem cell wall thickness is explored through the simulations (Figure 6). The authors claim this model is able to recapitulate a basic feature of the pxy mutant, which is the fact that the distal cambium appears in patches. Although these patches appear in the simulations, this effect in the model might be produced by the instability of the cambium front progression itself, which might be fundamentally different from what happens in the experimental data. In the experimental data, the PXYpro:CFP cambium does not seem to present such front instability, but rather is the xylem that gets fragmented. To make a link between the Model 3 and the pxy mutant, a careful study of the different stages of this phenotype could be useful to do, both on the modelling and experimental side.
The authors have a parameter search strategy based on matching the proportion of cell types in Model 3. I am wondering how effective is this strategy in a system where these features are evolving in time, especially in Model 3, which seems to present a front instability. Moreover, this strategy does not tell anything about the model robustness for recapitulating the different features of the pattern.
In the last model, the authors try to link the cell wall thickness with the radiality of the divisions. Although the idea of looking at the division trajectories seems interesting, more clarity is needed to see how helpful is the radiality measure, and perhaps a better measure is needed - note that the proliferation trajectory in Figure 6C might have the same amount of ramifications than in Figure 6B, and therefore, effectively speaking, the amount of periclinal divisions might be the same in both cases. The authors claim that the increase of xylem thickness contributes in having a more radial growth, but this could be related to the cambium front instability, which seems to be more pronounced as well for higher xylem thickness.
On the experimental side, the claims about the proximal and distal cambium, together with the cell proliferation data are not very well supported with the presented data in Figures 2, 3A and S1. Moreover, these different figures seem to show different behaviors - are these sections at different stages of the hypocotyl? Also, seeing more of the H4 marker in a region of the tissue not necessarily indicates a higher proliferation rate (it could also simply be that cells are more synchronized in the S phase in that region of the cambium, and/or the cell cycle lasts for longer in that part of the tissue). A quantification and the proper repeats to support these claims is lacking. A quantitative and more extensive study of the pxy mutant would enable a better comparison with the simulated model. Is there PXYpro:CFP expression between the fragmented xylem?
This work might help progress in the field of understanding radial patterning in plants. The introduction and the first models could attract a more general plant audience, but once the models increase in complexity, the narrative and presented results are more relevant to those scientists more specialized in xylem and phloem formation.
-
Evaluation Summary:
The paper presents a sequence of models, simulating with increasing accuracy the production of phloem and xylem in a cross-section of a generalized circularly symmetric plant organ. The results may serve as a stepping stone for the construction of predictive models.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #2 agreed to share their name with the authors.)
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