Dear Dr. Sarracino,

Thank you very much for submitting your manuscript "Critical behaviour of the stochastic Wilson-Cowan model" 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.

Of particular importance are the points raised by reviewer 2 about linking the results to other computational models of large-scale neural activity which address brain stability and criticality. A comprehensive review of the relevant literature, which covers different approaches and perspectives within the critical brain dynamics community, would be an important added value to the manuscript.

Assessing whether the stochastic WCM conforms with the “crackling noise” scaling relation, as suggested by reviewer 3, would also strengthen the results. 

We recognize that fully addressing the reviewers' comments may represent a significant challenge, and we leave it up to the authors if they prefer to submit the work elsewhere.

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,

Oren Shriki, PhD

Guest Editor

PLOS Computational Biology

Lyle Graham

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 #1: See attachment

Reviewer #2: see attachment

Reviewer #3: de Candia et al present a numerical and analytical study of the stochastic Wilson-Cowan model as a potential explanation for critical dynamics observed in experimental observations of diverse neural systems. Interestingly, the same model was used (about a decade ago also in PCB by Benayoun et al) to make approximately the opposite claim - that the stochastic Wilson-Cowan model creates something that looks like critical dynamics without actually having the right underlying mechanisms to really, truly be critical dynamics. de Candi et al show that multiple phenomena predicted to occur for real and true critical dynamics do, in fact, occur for the stochastic Wilson-Cowan model (WCM). Thus, de Candia et al draw the conclusion that the WCM does have a real, bona fide critical point. A key advance that allowed them to reach their conclusions (in contrast with Benayoun et al) was that they used the Gillespie algorithm to numerically simulate very large network sizes, thus revealing some of the predictions of critical phenomena.

In my view, this paper is interesting and on a timely topic with a long-lasting debate surrounding it. However, there are multiple ways the paper could be improved. Below I outline first the bigger concerns and comments, followed by smaller comments.

Big Comment 1: One of the more commonly used aspects of critical phenomena in modern system neuroscience is the “crackling noise” scaling relation, which relates the average avalanche duration to the avalanche size according to a third scaling exponent. This has been used by many prominent studies to make claims about criticality: Friedman et al PRL 2012; Shew et al Nature Phys 2015; Ma et al Neuron 2019 and others. Does the stochastic WCM also conform to this scaling law? In my view, adding this to the current paper would make it substantially stronger and more related to the state of the art in this field. Moreover, this would be a much more interesting addition to the paper than the current diversion about different ways of defining avalanches (time bins vs. time series thresholding), which could be moved to methods or supplementary material.

Big Comment 2: Building on Big Comment 1, in my view the large digression (Figs 5-7) about how to define avalanches is not a very interesting addition to the paper. This disrupts the flow of the paper and it is very easy for a reader to lose interest. Perhaps it would be better to combine Figs 5-7 into one figure. Maybe even move it to the methods section or supplementary materials.

Big Comment 3: The section titled “Requirements to assess critical behavior” is difficult to follow for someone who is not an expert on statistical physics of critical phenomena. As a step towards improving understandability, I suggest that the authors stick with a more explicit description of the Ising model and how it relates to assessing critical behavior. This would allow the authors to state more clearly what an order parameter is (magnetization), and what a control parameter is (temperature), and what an “external field” is, etc. By making it more specific, less general, the reader has a better chance of following along.

Medium Comment 1: Considering that omega_0 is your control parameter, it would be helpful to provide more interpretation of the meaning of omega_0. I guess it represents a sort of e/i imbalance? It would also be helpful if the authors remind the reader of this meaning in the figure captions (maybe even in the axes labels of the plots).

Medium comment 2: When discussing and introducing the different alternatives for defining avalanches (time bins vs. time series threshold) it would be appropriate to cite some of the original experimental uses of these methods. For instance, Beggs & Plenz J Neurosci 2003 were among the first (maybe the first?) to use the time bin method. And Gautam et al PLos Comp Biol 2015 were among the first to use the time series thresholding methods.

Small comments

Line 11: what is a “front of independent neurons”. Consider rewording

Line 215: Should cite some relevant experiments

Fig 3 caption: Either get rid of the panel labels A-F or mention them in the caption

Fig 3 caption: typo: single

**********

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: In the version sent to me there is no references to available code

Reviewer #2: Yes

Reviewer #3: No: I did not see a proposed plan to make the code publicly available

**********

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: Yes: Osame Kinouchi

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_PLoS.pdf

Attachment

Submitted filename: avalrep.pdf

Dear Dr. Sarracino,

We are pleased to inform you that your manuscript 'Critical behaviour of the stochastic Wilson-Cowan model' 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,

Oren Shriki, PhD

Guest Editor

PLOS Computational Biology

Lyle Graham

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 #1: The authors provided answers to all my concerns.

Reviewer #3: The authors have responded constructively and completely to all of my previous concerns. I have no further concerns and recommend publication now.

**********

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 #3: None

**********

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: Yes: Osame Kinouchi

Reviewer #3: Yes: Woodrow L Shew