Dear Dr Turlier,

Thank you very much for submitting your manuscript "A hydro-osmotic coarsening theory of biological cavity formation" for consideration at PLOS Computational Biology.

As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.

All of three reviewers have favorable comments on the work, and suggest it is a well-performed theoretical study that will contribute to our understanding on the dynamics of lumens. They provide some constructive comments on improving the presentation. Reviewer 2 also suggests some aspects to make the model more realistic. I suggest the authors to consider them carefully.

I understand one concern the authors has is existence of a competitive study likely under review somewhere. We will try to expedite the process. If you have any concern, please don't hesitate on contacting me or the journal office.

We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments. Your revised manuscript is also likely to be sent to reviewers for further evaluation.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

Important additional instructions are given below your reviewer comments.

Please prepare and submit your revised manuscript within 60 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email. Please note that revised manuscripts received after the 60-day due date may require evaluation and peer review similar to newly submitted manuscripts.

Thank you again for your submission. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Jianhua Xing

Guest Editor

PLOS Computational Biology

Mark Alber

Deputy Editor

PLOS Computational Biology

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All of three reviewers have favorable comments on the work, and suggest it is a well-performed theoretical study that will contribute to our understanding on the dynamics of lumens. They provide some constructive comments on improving the presentation. Reviewer 2 also suggests some aspects to make the model more realistic. I suggest the authors to consider them carefully.

I understand one concern the authors has is existence of a competitive study likely under review somewhere. We will try to expedite the process. If you have any concern, please don't hesitate on contacting me or the journal office.

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: This is a comprehensive theoretical and computational study of the collective dynamics of lumens, as driven by flow of water and osmolytes between cavities and by pumping of osmolytes. The authors predict whether coarsening in a single lumen occurs and discuss applicability of their results to experiments. The work and results are of potential high interest to developmental biologists, to biophysicists, and to applied mathematicians. It is definitely worth publishing, though the clarity of the writing needs to be improved.

CONTENTS

- What would change in a more realistic 3D geometry, with lumens of finite size and bridges in the form of tubes?

- L186. Why a factor of 2 before the sum of L_i?

- L225. What is the meaning of the timescale of 1s to which tau_s is compared? Normally one should compare tau_s to another timescale defined by problem parameters.

- How relevant is this work to other types of lumens?

WRITING

- The beginnings of the abstract and introduction are too technical. Please define (or refrain from using): apical, basolateral, blastocoel…

- The author summary should be written for a scientist that is far from the field.

- In caption of Fig. 1: A_i and mu may be omitted, otherwise they need to be defined

- L78. Why isn’t sin(theta) absorbed in mu? What is the definition of mu?

- L87. Perhaps the definition of L_i should appear earlier.

- P4. Briefly explain why bridge thickness is considered to be constant.

- P5. It is not well thought to call dimensionless numbers ’screening lengths’. Why not ‘screening numbers’?

- Eqs. 6-8, why mix dimensionless quantities and time? This may be misleading.

- In insets of Fig.3A, the differences in size between lumens 1 and 2 are too small to be visible.

- P7. A brief description of coalescence events is needed.

- L247. What does \\bar{L}_{ij} stand for?

Reviewer #2: I read this paper by Le Verge–Serandour and Turlier with interest. The problem of lumen formation is an interesting biophysical problem, with numerous unknown subtopics that require some detailed understanding. The treatment by the author is quite elegant mathematically, and provides useful simplifications for the physical problem. The paper is nicely done and generally clear, and can be published. However, I find some simplifications in the current form are unrealistic biologically. Since this is a journal about computational biology, the treatment can include more biological detail. In particular models of active ion flux exist. The paper can improve substantially with some revision and additions.

1) A major problem is, j^a or the ion flux is not a constant. j^a should depend on concentration differences, and energy input by cells (it's a pump), and potentially tension in the membrane. There are models of j^a already in the literature, for example, Jiang & Sun, Biophysical J. 2013, and more detailed treatment in subsequent papers with different ionic species.

2) The active water flux across an epithelial barrier has been measured, e.g., see Li et al, Journal of Cell Science, 2020. For constant lumen osmolarity, the water flux was found to be maximum at Delta P=0, and decreases with increasing Delta P. The reason for this is can be traced to the properties of j^a. It is true that a detailed theory for j^a is lacking, but there has been work on this. The expression of j^a as a function of ion concentration will change the results qualitatively. Can the authors add some results with more realistic j^a?

3) In the presented physics, the rate at which l decreases is solely due to lumen expansion (Eq. 8) from water inflow. But another importance piece seems to be the break down of tight junctions that keep the junction zipped. One can imagine a scenario where P builds up sufficiently so the tension increases, and therefore unzips the tight junction. The rate of unzipping may depend on various factors. Where does this physics come in?

4) In a biologically realistic lumen, is it true that gamma, gamma_c and therefore mu are constants spatially and temporally within the lumen? Does the tension change with time? I would think there is an active adjustment process. Is the assumption with constant theta realistic?

5) What happens when 2 lumens collide and l for the bridge goes to zero? It seems that some assumptions break down here. At this moment, L_1+L_2=1, and you still have 2 lumen, how does this transition to 1 lumen? I didn't find details about this. Right now there would be a jump in overall mass of the lumen (Fig. 3A). This jump doesn't happen in reality, and the new lumen is filled slowly. How does this change the result for N(t) in Fig. 4. Does this take some time, and therefore change the time scale?

Reviewer #3: The review is uploaded as an attachment

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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Attachments

Attachment

Submitted filename: RefReportTurlier.pdf

Dear Dr Turlier,

We are pleased to inform you that your manuscript 'A hydro-osmotic coarsening theory of biological cavity formation' has been provisionally accepted for publication in PLOS Computational Biology.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests. Reviewer 3 listed a few minor change suggestions. I recommend you to consider and revise accordingly.

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

Should you, your institution's press office or the journal office choose to press release your paper, you will automatically be opted out of early publication. We ask that you notify us now if you or your institution is planning to press release the article. All press must be co-ordinated with PLOS.

Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology. 

Best regards,

Jianhua Xing

Guest Editor

PLOS Computational Biology

Mark Alber

Deputy Editor

PLOS Computational Biology

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Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: The authors have addressed all the points that I raised.

Reviewer #2: The authors have answered my concerns. I recommend publication.

Reviewer #3: The review is attached as a pdf to this form.

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

Attachments

Attachment

Submitted filename: RefReportTurlier2.pdf