Dear Dr. Mukherjee,

Thank you very much for submitting your manuscript "Cluster Size Distribution of Cells Disseminating from a Primary Tumor" 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.

In particular, as the reviewers comment, how well do the results agree with biological observations, and can they be tested experimentally? Are there experimental observations that the model can help explain, or are there key discrepancies with data that warrant further research? Apart from the detailed comments by reviewers #2 and #3, the biological insight coming from your model and the biological interpretation of your results will be key for deciding on the manuscript's suitability for PLOS Computational Biology. The reviewers further remark that the figures are difficult to interpret. Ensure that figures can be read  fairly independently from the main text - see for example the labels "similar", "increasing" in Fig. 8 and the detailed remarks of reviewer #1.

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,

Roeland M.H. Merks, Ph.D

Associate Editor

PLOS Computational Biology

Douglas Lauffenburger

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: In this study the authors carried out numerical simulations of cellular Potts model to investigate cluster size of disseminating cells from primary tumor. It was confirmed that the cluster size increases for larger adhesion while decreases for larger motility, for which scaling relation were determined. Mixture of different cell types were also investigated, where combination of different cell types can facilitate larger cluster size.

Overall, the author has shown many results in various simulation settings, but the analysis is rather descriptive for each setting and the results are not very surprising. I'm not sure if the results are general and / or insightful enough to understand the actual process of metastasis.

1. Some figures are too small and messy, due to which I’m afraid that I misunderstand the results, e.g., Figs. 3C,D, 4F, 5, 6.

2. Comparison with experimental data are scattered in the main text and are not sufficiently addressed. For example, I’m not sure whether experimental data shown in Fig. 3f are similar to numerical results. The authors should make a more detailed discussion of the interpretation of the obtained results in the light of experimental observation. This will help the readers understand the motivation and purpose of this study.

3. What is the biological meaning of the parameter tau? Is it possible to experimentally disturb it?

4. The author numerically determined powers of scaling behaviors of N and f on mu and Gamma. Are these values are universal, in other words, simulation with other model schemes can also reproduce the same results? Is it possible to theoretically derive these powers?

5. How mu_min scales with Gamma? Using mu – mu_min instead of mu seems more natural choice (I might be wrong).

6. Fig. 7A and L313. The authors claim “N remains almost constant up to sigma = 2, ..”, but it is unclear this statement is valid from Figs 7A and B.

7. Fig. 7D and E: adding error bars is preferable.

8. The section “Cell shape driven cluster size distribution” seems interesting. Are the results related with jamming transition reported in Bi, et al. Nat. Phys. (2015)?

9. Typos: L226 “fall rapidly fall as N ..”, L420 “Nevertheless” N is capital.

Reviewer #2: Review is uploaded as an attachment.

Reviewer #3: The manuscript presents a detailed study of a cellular Potts model with the aim of chracterizing clusters of metastatic cells in terms of the simulted EMT state of the individual cells comprising the cluster. Understanding how the phsyical organization of metastatic cells depends on the gene regulated phenotype of the individual cells undergoing EMT is an interesting topic worth investigating. The present computational study could guide further experimental studies. In this respect, I woul encourage the authors to discuss in the conclusions possible avenues for experimental investigation of the same problem. In general the manuscript is well written and I would thus suggest publication.

I have some minor issues that should be fixed before acceptance:

The analysis presented in Fig. 3 should be improved. The author state that the fit in Fig. 3A yields an exponent of 1.98 +- 0.01. Yet ,the fit is performed over three points with huge error bars. How is it possible that the error bar on the exponent is so tiny. Was the error on the data included in the estimate of the error bar on the fit (my guess is that the authors reported what the fitting routine gave). Also, it is not clear, here and in other instances what the error bar actually is. It is the SD or the SE on the mean? Please provide the definition of the error bars in all the captions. I have similar considerations for the fit p=0.999 +- 0.001 in Fig. 3c. It is clear that a line fits the data, but I do not believe the tiny error bar. Since the author are fitting multiple curves in a parameter dependent way, the most correct way to proceed is to fit collectively all the curves with a single scaling function with unknown parameters. In this way, all the parameters are fit simultaneously over multiple curves.

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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: No: I did not notice code and detailed data list. The results themselves are reproducible by the given explanation.

Reviewer #2: No: 

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.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

Figure Files:

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org.

Data Requirements:

Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.

Reproducibility:

To enhance the reproducibility of your results, we recommend that you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols

Attachments

Attachment

Submitted filename: Report PCOMPBIOL-D-21-00759 2021.pdf

Dear Dr. Mukherjee,

Thank you very much for submitting your manuscript "Cluster Size Distribution of Cells Disseminating from a Primary Tumor" 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. The reviewers appreciated the attention to an important topic. Based on the reviews, we are likely to accept this manuscript for publication, providing that you modify the manuscript according to the review recommendations.

Please prepare and submit your revised manuscript within 30 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email.

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

[1] A letter containing a detailed list of your responses to all 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.

Thank you again for your submission to our journal. 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,

Roeland M.H. Merks, Ph.D

Associate Editor

PLOS Computational Biology

Douglas Lauffenburger

Deputy Editor

PLOS Computational Biology

***********************

A link appears below if there are any accompanying review attachments. If you believe any reviews to be missing, please contact ploscompbiol@plos.org immediately:

[LINK]

Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #1: The authors answered my comments and questions, and the revised manuscript is much improved. I now agree the manuscript meets publication from the PLOS Compt. Biol.

Reviewer #2: The authors satisfactorily answered my comments, except the one about fragmentation, which has been overlooked. The authors claimed that they work in a region of parameter space where fragmentation events are very rare, as they observe fragmentation at p0>30. However, this represents 37.5% of the range they scanned ([20,36]).

As this has been shown recently (M. Durand, PLOS Comp. Biol. 17, e1008576, 2021), apparition of fragments can significantly affect the results of CPM simulations. Therefore, the results presented in Fig. 8, S12 and S13 should be presented with proper warnings, at least.

Reviewer #3: The authors modified the paper in order to respond to the remarks of the referees. I am satisfied by the response.

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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

**********

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

Figure Files:

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org.

Data Requirements:

Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.

Reproducibility:

To enhance the reproducibility of your results, we recommend that you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols

References:

Review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript.

If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Dear Dr. Mukherjee,

We are pleased to inform you that your manuscript 'Cluster Size Distribution of Cells Disseminating from a Primary Tumor' 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.

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,

Roeland M.H. Merks, Ph.D

Associate Editor

PLOS Computational Biology

Douglas Lauffenburger

Deputy Editor

PLOS Computational Biology

***********************************************************

Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #2: The authors satisfactorily answered all my comments, and the revised manuscript is now suitable for publication in PLOS Comput. Biol.

**********

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 #2: Yes

**********

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 #2: No