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  1. Author Response

    Reviewer #3 (Public review):

    1. The central component of the model is the fast activation of AHA by BRI1, a rapid, non-transcriptional response. More experimental support is needed to establish that, in the root, AHAs are activated rapidly and not by the transcriptional pathway. Minami et al., 2019 showed that AHA activation in the hypocotyls requires tens of minutes and is likely mediated by the accumulation of SAUR proteins. In other words, the activation is not a rapid BRI1mediated phosphorylation. The model, however, uses the findings from Minami et al 2019 as the support for the immediate activation of AHAs by phosphorylation (at the line 143).

    The kinetics of AHA activation possibly through the accumulation of SAUR proteins is now discussed in detail in the Discussion section. In fact, this process is much slower compared to the mechanism presented here. As shown by the phosphoproteomics data of Lin et al. (2015), the rapid phosphorylation of AHAs within 5 min after BR application occurs at Ser315 and Thr 328 in the large cytoplasmic domain of the pumps and not at Thr947.

    1. Further, one of the crucial outputs that is used to compare experimental a modelled data - the apoplastic pH - seems very noisy in the provided figures. This is particularly apparent in the time-course response of apoplastic pH to 10nM BL application. Figure 4B should show that there is a rapid acidification that is maintained, however the figure shows rather a noisy behavior (in particular when we consider that the errors represent SEM) and, moreover, the figure 4B does not fit the results from 4A. Similar noisy results are shown in the figure 6A and B and the model does not seem to fit the experimental data in the meristematic cells. In the case of these figures, the conclusions in the text do not seem to fit with the data presented in the figures.

    We have now incorporated the statistics of the data (also) into Figures 4 and 6. Considering the statistical outcome, we see a good fit. The HPTS method is not technically straightforward in itself, to which some variability can be attributed. In addition, even the cells of the same tissue in different root samples show a variable response. Since the response in the meristematic zone is generally lower, the variability is particularly noticeable there and sometimes at the border of significance.

    1. Further, the cngc10 mutant pH responses are not very convincing: the cells of the meristematic zone of the control line do not respond to BL (Appendix Fig3) while in figure 7C the meristematic zone of control does respond to BL. However, I think other physiological phenotypes of the mutant lines should be tested that would determine whether CNGC10 is involved in the response of roots to brassinosteroids. What is the expression of CNGC10 - is it expressed in the same cells as BRI1 and AHA2? What are the densities of CNGC10 molecules along the root developmental gradient? Such questions should be clarified to substantiate the conclusion that this channel is a major player in the regulation of membrane potential.

    As far as the response of the MZ in Fig. 8 is concerned, we would like to refer to the answer to the statistics above and restrict the analysis of the CNGC10 function to the fast acidification process presented here. According to the data of the eFP browser, the accumulation of CNGC10 transcripts occurs quite evenly across all cells and tissues of the root and in the cells in which the other components of the mechanism described here are also expressed. A single cell annotation of CNGC10 transcript is not possible, as its expression is already induced by the protoplasting of the root cells.

    1. Why the predictions of the model regarding the BIR3 involvement were not tested experimentally? This could again show that the model predicts the cellular behavior correctly. It would be particularly interesting to test the model predictions along the longitudinal root axis, where the ratio of signaling components is changing.

    As suggested by the other reviewers, we have transferred the BIR3 modelling results to the Suppl. Data, but discuss them briefly in the Discussion. In fact, the modelling data are underpinned by experimental results published by Imkampe et al. (2017).

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  2. Evaluation Summary:

    This study addresses the effect of brassinosteroid hormones on acidification of the apoplast. The authors characterize a novel ionic channel involved in this process as well as a gradient of H+-ATPase activity, providing evidence for a fast brassinosteroid response that has so far received little attention. A combination of computational modeling and quantitative cell physiology is used to explain the regulation of proton pumping into Arabidopsis root cell walls. The authors show that regulation of AHA proton pump activity by the activated brassinosteroid receptor complex could potentially explain the experimentally determined zonation of root cell wall pH and growth. The work will be of interest to plant biologists as well as cell biologists in general.

    (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 #1 agreed to share their name with the authors.)

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  3. Reviewer #1 (Public Review):

    This work addresses a so far much overlooked aspect in plant signaling systems being the physiological reality of how components primarily identified by genetic means work together to achieve a functional physiological system. The genetically well-defined system of brassinosteroid signaling in Arabidopsis roots is employed as a convenient model system.
    For this accurate determination of the number of proteins involved, the kinetics of activation and ODE-based modelling are used by the authors.

    The results focus on one aspect of root brassinosteroid signaling, expansion of root cells as they enter into the extension zone of the root. Several parameters such as wall acidification and cell wall swelling are used as early output determinants of the BR signaling system.

    The authors show convincingly that BR signaling can be used to identify hitherto missing components of the system such as a potassium channel protein presumed to be used in rectifying the effects of the ion flow across the membrane.
    It would benefit from a clear perspective concerning the time frame of the events measured and a simplification by removing certain data sets from the main story.

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  4. Reviewer #2 (Public Review):

    The manuscript entitled "Computational modeling and quantitative cell physiology reveal central parameters for the brassinosteroid-regulated cell growth of the Arabidopsis root" by Ruth Grobeholz et al. presents a hybrid computational and experimental study on the fast response to brassinosteroids of epidermal cells in the elongation and in the meristematic zones of Arabidopsis primary root. The study focuses on the regulation of ionic transport through the plasma membrane that is elicited upon BL induction. This is supported by experimental data on ion fluxes and pH dependence with BRI1 receptor in Arabidopsis roots, analyzing WT and bri1-301 mutant. The combination of modeling and experimental data reveal a new component of the fast BR response. This new component is a cation channel, CNGC10, which the authors show, through the analysis of a CNGC10 loss-of-function mutant to be required in epidermal cells of the elongation zone to change the apoplastic pH upon BL application. In addition, the experimental results show a gradient of the proton pumping activity, through AHA2, along the root, with highest activity in the elongation zone. Finally, the study analyses the role of BIR3 on this fast response.
    The study is very interesting because it addresses a part of BR pathway that has been little investigated, which is that of the fast-response. The manuscript continues the proposal made by one of the leading authors of this manuscript on the existence of this fast response (Caesar et al, 2011) by extending it to epidermal cells in Arabidopsis primary root and by finding a novel factor involved, the cation channel CNGC10. The finding of AHA2 gradient is also promising, albeit, as discussed below, partially inconclusive in my opinion. The manuscript is also very appealing because of the many different techniques that have been used, both computational and experimental.

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  5. Reviewer #3 (Public Review):

    The authors create a computational model that aims to understand how the regulation of proton pumps by brassinosteroid receptor complexes translates into membrane potential changes and cell wall pH. They build the model using known facts from the brassinosteroid literature as well as published cell compartment volumes and membrane densities of some signaling components. To obtain further parameters for their model, the authors quantify the densities of BIR3 and AHA2 and found that the density of the proton pump increases along the differentiation gradient in the root, and that the ratio of AHA to BRI1 dramatically increases in the elongation zone.

    Their model focuses on the rapid responses to the external application of brassinosteroid BL, and as such it could predict the dose response of apoplastic pH to BL. The model was further broadened to involve the gradients of protein concentrations along the root developmental axis.

    The model predicted a significantly larger membrane hyperpolarization in response to BL than the one observed experimentally, indicating a missing component that would depolarize the PM, such as a cation channel. This prediction led the authors to identification of a missing component in the BRI1-BIR3-AHA module, the CNGC10 cation channel.

    The combination of quantitative cell physiology and mathematical modelling for the complex regulation of ion fluxes in the root cells is probably the only way how to understand the non-linear relationships and emergent properties that occur in growing root cells. This manuscript is an initial attempt to understand these phenomena in Arabidopsis roots, but as such it is, in my opinion, overly simplified, particularly when it comes to the involvement of ion channels that regulate and respond to membrane potential. The paper gives a somewhat unfinished impression, and most importantly, it lacks experimental validation of some of the crucial conclusions. Here I summarize the main points which I find problematic or weakly supported by the data:

    1. The central component of the model is the fast activation of AHA by BRI1, a rapid, non-transcriptional response. More experimental support is needed to establish that, in the root, AHAs are activated rapidly and not by the transcriptional pathway. Minami et al., 2019 showed that AHA activation in the hypocotyls requires tens of minutes and is likely mediated by the accumulation of SAUR proteins. In other words, the activation is not a rapid BRI1-mediated phosphorylation. The model, however, uses the findings from Minami et al 2019 as the support for the immediate activation of AHAs by phosphorylation (at the line 143).

    2. Further, one of the crucial outputs that is used to compare experimental a modelled data - the apoplastic pH - seems very noisy in the provided figures. This is particularly apparent in the time-course response of apoplastic pH to 10nM BL application. Figure 4B should show that there is a rapid acidification that is maintained, however the figure shows rather a noisy behavior (in particular when we consider that the errors represent SEM) and, moreover, the figure 4B does not fit the results from 4A. Similar noisy results are shown in the figure 6A and B and the model does not seem to fit the experimental data in the meristematic cells. In the case of these figures, the conclusions in the text do not seem to fit with the data presented in the figures.

    3. Further, the cngc10 mutant pH responses are not very convincing: the cells of the meristematic zone of the control line do not respond to BL (Appendix Fig3) while in figure 7C the meristematic zone of control does respond to BL. However, I think other physiological phenotypes of the mutant lines should be tested that would determine whether CNGC10 is involved in the response of roots to brassinosteroids. What is the expression of CNGC10 - is it expressed in the same cells as BRI1 and AHA2? What are the densities of CNGC10 molecules along the root developmental gradient? Such questions should be clarified to substantiate the conclusion that this channel is a major player in the regulation of membrane potential.

    4. Why the predictions of the model regarding the BIR3 involvement were not tested experimentally? This could again show that the model predicts the cellular behavior correctly. It would be particularly interesting to test the model predictions along the longitudinal root axis, where the ratio of signaling components is changing.

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