Dear Dr. Sun,

Thank you very much for submitting your manuscript "Inferring latent temporal progression and regulatory networks from cross-sectional transcriptomic data of cancer samples" 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 make sure that your code and data needed to reproduce the results of the paper are accessible at a valid URL.

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,

Sushmita Roy, Ph.D.

Deputy Editor

PLOS Computational Biology

Jian Ma

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: Gene regulatory network (GRN) reconstruction methods usually require time-course gene expression data or perturbation experiment data. However, most available omics data from cross-section studies of cancer patients often lack temporal information, making it challenging to reconstruct the GRN for the studied cancer progression. In this work, Sun et al. present a latent-temporal progression-based bayesian method, PROB, for the inference of GRNs from the cross-sectional transcriptomic data of tumor samples. Compared with other GRN methods, the proposed method has a number of advantages: (1) First, it was designed specifically to reconstruct GRNs from tumor samples, which utilizes a lot of cancer-specific information (staging) that are not utilized by others general methods (such as GENIE3). (2) Second, the authors mathematically proved the robustness of the proposed methods. The robustness is especially important in reconstructing GRNs from cancer samples, which are usually highly noisy. Third, the proposed method requires minimal prior knowledge. For example, in other GRN reference methods, the root (node) is usually needed to pick out by the users based on their prior knowledge. The proposed methods can automatically learn the root using a proposed distance-based approach. This significantly improves the usability of the proposed method. Overall, I think that this is a fantastic method and well fit the authorship of the journal. I highly recommend the publication of this manuscript. I only have a few minor comments :

(1) In equation (5), the authors described that the root is determined as the patient (x) with the largest distance to the patients the maximal grade score (e.g., stage 4). I would suggest limiting the candidate x \\ patients with the smallest grade (e.g., grade 0). If not, theoretically, it is likely that x0 will come from a later stage (e.g., stage 2 or even stage 4 (e.g., because of a few outliers that produce a considerable distance). In that case, the root x0 will come from stage 2 or stage 4, which would not make much sense to me. As the stage information is available, I would suggest to narrow down the selection of x0 among patients in stage 0

(2) In this work, the authors simulate Gaussian noise to examine the robustness of the method. I am amazed by the robustness of the method to Gaussian noise. However, the Gaussian noise is usually well dealt with. Did the authors also simulate other types of noise (e.g., drop-out noise is also a very common noise type)? It would be great if the methods can also be tested against other noises.

Reviewer #2: General Comments

Authors developed a latent-temporal progression-based Bayesian method, PROB, for inferring gene regulatory networks (GRNs) from the cross-sectional transcriptomic data of tumor samples. Mathematical proofs and numerical verification are provided to support the robustness of PROB to the measurement variabilities in the data. Benchmarking PROB with alternative methods of GRN inference shows advantages of PROB in both pseudotime inference and GRN inference. Authors also demonstrated the applications of PROB for identification of key regulators of cancer progression or drug targets as well as performed validations experiments. Overall, the manuscript is clear and accessible.

Specific comments

Pages 9-12: Section “Latent-temporal progression-based Bayesian (PROB) method to infer GRN”

This section can be rewritten more compactly to improve reading experience. Either put all details in the main text or keep only the main idea in the main text and leave the details in the supplementary text. Current main text is an abridged version of Text S1 and does not read consistent.

Page 9: “… the root was automatically identified with the aid of staging information.”

What is “root” meant here and in the subsequent context? Does it adapt a generally used and accepted mathematical meaning? Should it be called “optimizer”?

Page 11: “The above model is then transformed into a linear regression model …”

I think it’s better phrased as “a linear system”. Rigorously speaking Y is not linear in X.

Page 12: “Therefore, the above theorem theoretically guarantees the consistency and robustness of the estimates of the regulatory coefficients.”

It can be elaborated more the role of Theorem 1; for example, add 2-3 lines of equations.

Page 12: pseudo-code of PROB

Variable E is not defined in the main text.

Definition of phi should be readdressed in the algorithm.

Variable/function PPD is not defined.

Page 13: “To this end, we defined an outgoing causality score (OCS) …”

Does OCS have any mathematical/statistical meaning?

Page 21: “The code for PROB is available at https://github.com/SunXQlab/PROB.”

This page does not exist.

Page 28: Figure 2d

Why does not AUC decrease monotonically with CV?

Page 32: Figure 6: Details related to survival analysis are missing (e.g. how authors define

high and low risk groups. What is their cut-off?) Also role of FOXM1 on breast cancer progression is known and citations are missing.

Page S10: “The codes are available at https://github.com/dongbusun/PROB.”

This page does not exist.

Page S15: “PROB applied to realistic datasets”

Realistic -> real

**********

Have all data underlying the figures and results presented in the manuscript been provided?

Large-scale datasets should be made available via a public repository as described in the PLOS Computational Biology data availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.

Reviewer #1: Yes

Reviewer #2: No: 

**********

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

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, PLOS recommends that you deposit 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. For instructions see http://journals.plos.org/ploscompbiol/s/submission-guidelines#loc-materials-and-methods

Dear Dr. Sun,

We are pleased to inform you that your manuscript 'Inferring latent temporal progression and regulatory networks from cross-sectional transcriptomic data of cancer samples' has been provisionally accepted for publication in PLOS Computational Biology.

Please provide the numerical data underlying graphs described in the paper. 

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,

Sushmita Roy, Ph.D.

Deputy Editor

PLOS Computational Biology

Jian Ma

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: Authors addressed my concerns

**********

Have all data underlying the figures and results presented in the manuscript been provided?

Large-scale datasets should be made available via a public repository as described in the PLOS Computational Biology data availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.

Reviewer #2: No: Not all numerical data that underlies graphs or summary statistics provided

**********

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