Dear Dr. Cooray,

Thank you very much for submitting your manuscript "Global dynamics of neural mass models" 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.

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,

Michael Breakspear

Guest Editor

PLOS Computational Biology

Lucy Houghton

Staff

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 their paper, Cooray et al. made a thorough analysis of a popular and effective type of brain dynamics models, i.e. neural mass models, which are a coarse-grained version of neural field models that has shown its relevance in many applications (e.g., epilepsy). The paper has the merit of proposing a detailed mathematical analysis that describes the behavior of those models not only around the fixed points, which is useful to understand the dynamical repertoire of those models.

However, in its current form the paper has some major drawbacks that are listed below:

1) The paper is difficult to follow for a non-specialist. The paper makes an extensive use of technical terms borrowed from different sub-fields of physics (dynamical itinerancy, adiabatic approximation, potential function, equations of motion...) which complexifies reading in an unnecessary manner. Extensive editing should improve this aspect to make the paper more accessible and increase its impact. Technical terms such as those, when unavoidable, should be defined operationally to facilitate reading of the paper.

2) The potential applications listed are not sufficiently described, which is not convincing: the authors should insist on why their approach will provide new insights in epilepsy (where much has been done in terms of neural mass modeling / analysis, more on this point below) at the onset of seizures, or for the description of beta bursts in Parkinson's disease. In its current form, this gives the impression that the authors have just listed some applications but without any specific reason or rationale (and there is likely one I am sure, but it is not obvious in the current form of the paper).

3) The authors mention that one innovation of their approach is the decomposition of the classical neural mass model (that they call "Canonical Microcircuit Model" or CMC) in terms of slow/fast sub-systems, and bifurcation analysis. However, slow-fast decomposition of the CMC, notably in the field of epilepsy, has been already performed previously (see for example this recent study uncited by the authors, https://doi.org/10.1371/journal.pcbi.1008430, which performs slow/fast decomposition at the initiation of seizures). Therefore, the innovation brought by the paper is unclear, and should be emphasized to clarify the potential impact of the paper and its interest for a broad readership.

4) It seems that previous literature (such as on the Epileptor model, https://doi.org/10.1093/brain/awu133) should be more discussed or taken into account, given the overlap with the present work.

Overall, my recommendation would be to request at least a major revision of the paper, along the lines suggested here, to increase its readability, clarify its original contribution and innovation, and accounting more accurately contributions from previous literature and how the present study goes beyond the state-of-the-art. I emphasize again however that the study seems technically sound, and that it has merit.

Reviewer #2: In this paper, the authors present a novel, elegant, and useful way to reduce the complexity of neural mass models of local cortical microcircuits by means of time scale separation, thus making them more accessible to model inversion, especially in larger portions of the state space away from fixed points. Although, personally, I would have liked a somewhat more elaborate evaluation of the methods using simulations and real data, I think the paper is worth publishing as it stands. The paper is very well written, so I have no further comments (which is a very rare case for me).

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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: Only general websites are listed, the information provided to access the code / data is not sufficiently specific.

Reviewer #2: 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: Yes: Thomas R. Knösche

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

Dear Dr. Cooray,

Thank you very much for submitting your manuscript "Global dynamics of neural mass models" 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.

Editorial Note: Please make a final read and edit of the paper, ensuring where possible a clear integration of the technical terms in the main text and subheadings with the glossary as per the reviewer's request

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,

Michael Breakspear

Guest Editor

PLOS Computational Biology

Lyle J. Graham

Section Editor

PLOS Computational Biology

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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:

Editorial Note: Please make a final read and edit of the paper, ensuring where possible a clear integration of the technical terms in the main text and subheadings with the glossary as per the reviewer's request

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 provided a revision that partly addresses the comments raised in the first review. The addition of an appendix with a lay definition of technical terms is very much welcome, however within the body of the paper, nothing has changed much in this regards, as is apparent in the "Track changes" version of the document. Therefore, the paper remains filled, including in the Section titles, with terms that are as I mentioned before unnecessarily complicated.

Furthermore, on the topic of Parkinson's disease, what has been added is very vague, and only "bursts" are mentioned: in which region, at rest, during tremor, during a task? Furthermore no reference is provided at all. I would suggest either to suppress Parkinson's disease from the paper, or to add precise and referenced content. The relevance of citing PD would also be an asset. Otherwise, the authors may as well cite almost any disease.

Also, the "arrow of causality" term is one of those terms that is technical for a large portion of the readership, should be defined, and also should be supported clearly by the results. If the authors want to keep such a term in the paper, this would deserve explaining this in more details.

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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

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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

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. Cooray,

We are pleased to inform you that your manuscript 'Global dynamics of neural mass models' 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,

Michael Breakspear

Guest Editor

PLOS Computational Biology

Lucy Houghton

Staff

PLOS Computational Biology

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

Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #1: All my comments have been addressed in a satisfactory manner.

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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: None

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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