Dear Dr. Wan,

Thank you very much for submitting your manuscript "Dynamic inference of cell developmental complex energy landscape from time series single-cell transcriptomic data" 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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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).

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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,

Qing Nie

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 work, the authors propose an approach to infer cell state transition dynamics and uncover cell-cell interactions from time series single-cell RNA-seq data, by constructing the energy landscape of the system. Based on a nonlinear Fokker-Planck equation on Graph based model, they solve the model inference problem in a dynamic optimal transport framework. They further illustrate the validity of their approach by applying it to a time series scRNA-seq data set of embryonic murine cerebral cortex development.

Overall, this is an interesting work, aiming to address a critical problem in dynamic model inference and data-driven approach in biology. However, I have some concerns that need to be addressed.

1, The authors assume that the cell-cell interaction matrix W is symmetric, what does this assumption mean in biology? And why is this a reasonable assumption? For example, should cells with different differentiation potency have symmetric interactions?

2, Fig.2 (a)(b)(c), the use of color for different cell types is very confusing. Please try to make them consistent.

3, It’s interesting to get cell-cell interaction matrix W as in Fig.2. However, the biological indication needs to be further discussed. For example, from Fig. 2 (g and h) it is found that cell type 3 (Aps/RPs) has positive interaction with cell type 6 (Young Neurons), and negative interaction with cell type 4 (IPs) or 2 (Young Neurons). What could be the biological meaning here based on the linage commitment route in Fig. 2(a)? Why do the two Young Neurons populations (cell type 6 and 2) have opposite types of interactions with cell type 3 (Aps/RPs)?

4, The energy landscape here is defined for each cell type, could it be expanded to single cell? i.e., each cell has a potential energy?

5, Current work focus on the cell-cell interactions, and molecular expression data is used only for estimating probability of cell types at different time point. As we know, the molecular interactions are important to cell fate transition determinations, and corresponding landscape construction approaches have been proposed (Kang, Advanced Science, 8, 2003133 (2021)). The authors may want to discuss the relationship between the two types of approaches.

Reviewer #2: The authors consider the dynamic inference of an evolving cell population from the time series scRNA-seq data. The main idea of their approach is to apply the optimal transport theory on graph with a free energy consists of the potential, mean field interaction, and the entropy terms. The parameters describing the potential and interaction terms are estimated by fitting the model to the available data. The computation applied to embryonic murine cerebral cortex development gives reasonable results. The literature review is also fair. Overall, I think the paper is interesting and present simple yet useful tool to analyze the time series scRNA-seq data.

Some major and minor points are as below.

Major:

1. The computational cost and robustness. The authors state that the method will be applied to the cell states/types in a complete graph. If it is only for cell types, which have a small number, the DOF is small and the computation cost should be light. If it is for the whole cell states, the DOF might be huge and the computation is difficult to be done. BTW, in different time points, how will the authors choose the common cell states if they do not do grouping at first? How will the different grouping affect the result?

2. Quantification of the cell stemness. This is an important issue in scRNA-seq data analysis. Will the proposed method give a quantification on this problem? I would like to see some tests and comments on this point.

3. The authors choose the optimal transport (OT) approach and and Wasserstein distance to the scRNA-seq data analysis, which is a hot topic in this area and machine learning community. Yes, it is fancy to take OT. But it is also possible to utilize other simpler model and optimization approach to accomplish similar task. I wonder whether the authors have some reason to take OT instead of other methods. Some comments and discussion on this point should be added.

Minor:

1. Some typo or gramatical errors.

Line 73: double periods in the text.

Line 121: as follows

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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

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.

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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. Wan,

Thank you very much for submitting your manuscript "Dynamic inference of cell developmental complex energy landscape from time series single-cell transcriptomic data" 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,

Qing Nie

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 have addressed my concerns thoroughly. I have only a few minor comments.

1, Line 483, is ref. 37 the right reference here? It seems that ref. 37 is not talking about data-driven landscape.

2, The final word of the paper (Line 533), “adopt” should be adopted?

3, Fig. 3 (c and d), the y axis seems to be labeled incorrectly.

Reviewer #2: The authors responded to my concerns perfectly. Now I recommend it for publication.

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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

**********

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, 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. Wan,

We are pleased to inform you that your manuscript 'Dynamic inference of cell developmental complex energy landscape from time series single-cell transcriptomic data' 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,

Qing Nie

Associate Editor

PLOS Computational Biology

Douglas Lauffenburger

Deputy Editor

PLOS Computational Biology

Feilim Mac Gabhann

Editor-in-Chief

PLOS Computational Biology

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