Dear Dr Deritei,

Thank you very much for submitting your manuscript "Probabilistic Edge Weights Fine-tune Boolean Network Dynamics" 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.

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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,

Pedro Mendes, PhD

Associate 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: This manuscript presents a modeling framework that introduces noise at the edge level in Boolean networks. This framework could be useful for producing stochastic simulations of discrete models of biological systems. The authors applied their framework to two existing biological models and then showed the beneficial aspects of using their framework compared to the classic synchronous and asynchronous update modes. One limitation of this manuscript is that it does not address the problem of parameter estimation of the parameters this new framework requires. One positive aspect of the manuscript is that they provide the implementations of the discussed examples in Jupyter notebooks.

Overall, I found this manuscript mostly well-written and their results relevant. However, there are many issues in this manuscript that I suggest addressing them before recommending it for publication.

Major Revisions:

1. On page 3, in the last paragraph, it says that one of the earliest types of noisy BN were BNp in reference [27] which was published in 2013. However, PBN with noise (described in the PBN book from 2010) is much earlier than the BNp paper in reference [27]. Then, on page 4 it says PBNs address the lack of node-specificity of BNps. I think these two paragraphs were presented in a backward order. You could switch the order of the presentation by first describing PBNs as one of the earliest frameworks that introduces noise into the system and then describe that one can use BNps to make the system ergodic as in the case of PBNp.

2. The framework presented in this paper is very similar to SDDS for which there are methods for parameter estimation (see publication a) below) are well as method for control (see publication b) below). These references could be included when discussing the connections.

a) Estimating Propensity Parameters using Google PageRank and Genetic Algorithms. Frontiers in Neuroscience, 10:513, 2016

b) A Near-Optimal Control Method for Stochastic Boolean Networks. Letters in Biomathematics, 7(1), 67-80, 2020.

3. The initial states were not specified in Figure 2. Were these selected at random?

4. What does it mean that the stable motifs don’t loose their nonlinear attributes? What nonlinear attributes are you referring to in the caption of Figure 3?

5. Explain the axes of Figure 3. What is depicted in the horizontal axis?

6. Figure 4 appears on two separate pages. Merge the two panels so that they show up in the same page.

Minor Revisions:

1. On page 3, at the end of the second paragraph, it says “truly random”. It would be is best to remove the adjective “truly” and just go with random as it might create confusion.

2. It seems the acronym for the Transforming Growth Factor-beta should be TGF-beta instead of TGFB.

Reviewer #2: The author present an extension of Boolean Network Dynamics, by allowing probabilistic weights on network edges.

I am not convince that this present work is worth publishing, substantial modifications are necessary.

1) The presentation of the probabilistic grammar is clear, but the type of modeling output(s) is not described. Is it time-dependent? Probabilistic over Boolean node states? Probabilistic over the full set of Boolean node states?

2) What is the mathematical framework of this approach? Is it a discrete-time Markov chain? It seems to me that it is a special case of Probabilistic Boolean Networks, because there are different transition rules for a node, weighted by probabilities. Can the authors demonstrate that their approach is (or is not) a special case of Probabilistic Boolean Networks?

3) Although the authors show applications where their approach is efficient (in the first example) and more elegant (in the second), I am not convince that it is a major improvement of actual Boolean approaches. For that, the authors should show that a lot of biological reactions/influences are impossible to implement in any actual Boolean approaches and are only possible within their approach.

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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

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Reviewer #1: No

Reviewer #2: No

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Dear Dr Deritei,

We are pleased to inform you that your manuscript 'Probabilistic Edge Weights Fine-tune Boolean Network Dynamics' 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,

Pedro Mendes, PhD

Academic Editor

PLOS Computational Biology

Mark Alber

Section 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 my comments from the previous round of reviews. There is a small typo in the Author Summary: change "forunderstanding" to "for understanding". This can be implemented during the copy editing stage.

Reviewer #2: The author answer to all my comments in an efficient way. They modify the text accordingly; perhaps they should more explicitly describe the type of output they use: their ensemble average.

Nevertheless, I am not convince that this approach consists of an important enhancement of Boolean modeling. According to the authors, it is a generalization of PBN, with a more flexible choice of the noise function. In particular, this allows to consider partial inhibition of edges, in a more efficient way than for PBN. To my opinion, this has not a wide applicability. Why not just implement their approach in PBN existing tools?

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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

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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