Dear Dr. Vu,

Thank you very much for submitting your manuscript "SPF: A Spatial and Functional Data Analytic Approach to cell Imaging 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.

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,

Martin Meier-Schellersheim

Associate Editor

PLOS Computational Biology

Jason Haugh

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 have proposed a novel approach to modelling the spatial interactions between cells in the tumour microenvironment (TME) to identify patterns associated with patient survival. The effectiveness of this approach has been demonstrated on publicly available data. While the focus of the manuscript is on the TME, this approach is clearly generalisable to other contexts and, because of this, I will likely be integrating components of their analysis strategy into any future analysis I perform.

## “Estimates from AFCM plots”

-- Could you center all of the colours on zero? Ie, red positive and blue negative.

## Line 122. “Specifically, tumor cells and their immediate neighboring stromal cells are negatively correlated in MHCII expression when they are less than 10 microns apart. As the cross-type cell distance increases, the correlation rises at different rates, and eventually drops close to 0.”

-- Given the average diameter of a cell, what does MHC11 becoming negatively correlated when cells are less than 10 microns mean? Are there worries about poor segmentation?

-- It would be helpful if the figure legends were more verbose, informative and/or repeated some of the information in the text. For example “Fig 4. Estimated surface from AFCM using lung cancer dataset. (a) Mcf curves and (b) Moran's I correlation using MHCII expression”. It would be very helpful for a reader (me) if you fleshed out how to interpret each axis, even though it is mentioned in the text. For example, what does a large mcf or small mcf mean? What does a positive (red) or negative (blue) F() mean?

## Line 181 “In particular, if tumor cells clustered together in the neighborhood of 25 { 75_m, the overall 182

survival improved, based on the negative estimate of the log hazard ratio. However, at distances beyond 183

75 _m, the more tumor cells clustered together, the higher the risk of mortality, while the increased 184

infiltration level of tumor-associated stromal cells reduced the hazard of death.”

-- A few points below:

1) This conclusion would be easier to make if the F() in Figure 4 was centered on white.

2) I am not a fan of the terminology “clustered together”. My preference would be something like, “if strong clustering of tumor cells is observed in the neighborhood of 25 - 75_m”. Or clustering more than expected maybe?

3) The difference in F() appears much larger for r>100 than 25<r<75. be="" considered="" interpreting="" is="" of="" or="" plots="" should="" significance="" some="" sort="" that="" there="" these="" threshold="" viewing="" when="">4) Can you elaborate any more on the complete flipping of interpretation/association that happens around r = 90 in 4a and 4b? It is a hard concept to wrap my head around.

5) As 4a and 4b are coloured by F(), would it also be useful for interpretation for 3b to be moved to Figure 4? Can the lines in Figure 3b also be coloured? Does that make any sense at all? Perhaps you could leave 3b in Figure 3, but then include it in Figure 4 with the top 10% “best survival” patients highlighted in red and bottom 10% “worst survival” patients highlighted in blue? Or some other highlighting that makes sense.

## Figure 5.

-- Why are 5c and 5d two plots? Wouldn’t it make more sense for them to be one plot coloured by mixed/not mixed?

## On line 246 “The authors concluded that P53 positivity associated with negative prognostic significance in breast cancer patients.” “In particular, a sample was defined as P53 positive if any cancer cells was positively expressed. “

-- Pan et al's conclusions appear to be about P53 positive cancer cells. Can you explain what it means for P53 to be correlated between cancer and immune cells? Is this a problem with cell segmentation? Or does P53 have the same function in immune cells as it does cancer cells?

-- The introduction could potentially benefit from some edits to make it easier and quicker to digest. For instance, in the paragraph starting on line 14, I would suggest spending more time talking about multiplexed imaging techniques and avoid detouring to mention bulk/sc sequencing without context.

-- This approach clearly extends beyond studying the TME, I’m not sure how or if it is worth emphasizing this?

-- The authors don’t appear to refer to p-values / statistical significance at any point. Are the “Estimates from AFCM plots” purely for qualitative interpretation? If I were to use your method for my own analysis, is there a single value I can report to provide evidence of a relationship? How would someone use these results?

-- The authors make reference to multiplex data which can quantify many cell types simultaneously however their examples only compare two types of cells (cancer vs immune). The authors briefly mention expanding the tests to include multiple or correlated objects in the conclusion. However, have the authors considered how they would simply apply this approach to multiple pairwise cell type comparisons? Or testing many markers for these comparisons? Is there a sensible way to rank pairwise comparisons? Or would I need to look at all pairwise plots and make a qualitative judgement?

-- Overall, I found the manuscript easy to read. However, I will leave it to the editors to comment on the structure as it does not follow the “manuscript organisation” outlined on PLOS Computational Biology’s website. Some components of the text could be moved from the results into the methods section and the discussion (conclusion) section.</r<75.>

Reviewer #2: This study aim to illustrate the use of established spatial statistics in studying cellular interactions. They motivate their work by discussing the role of tumour microenvironment in cancer evolution. They explore several spatial statistics in different datasets.

In general, the concepts presented in the paper are interesting. However, the presented results show that these metrics are not really very useful in reflecting the biology. For example: “if tumor cells clustered together in the neighborhood of 25 – 75μm, the overall 182 survival improved, based on the negative estimate of the log hazard ratio. However, at distances beyond 183 75 μm, the more tumor cells clustered together, the higher the risk of mortality”. This does not make sense as increased cancer cell density should reflect a worse outcome. Similarly, other statements regard the other analyses is again difficult to interpret. This applies to other statements in the paper.

Major concerns:

- except for the introduction, the paper is very hard to follow. It reads as disparate pieces of experiments that are put together and no clear link between the sections.

- Showing few survival values independent of any other information (e.g Fig. 3C) does not add any information.

- It is not clear how surface plots can be useful.

- It was not clear why simulation was used at the end.

- It was not clear why only the centres of the cells were shown and no original cell images.

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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: No: In my experience data is available upon request = “not available” . Code is available

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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.

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Reviewer #1: Yes: Ellis Patrick

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

Dear Dr. Vu,

Thank you very much for submitting your manuscript "SPF: A Spatial and Functional Data Analytic Approach to cell Imaging 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,

Martin Meier-Schellersheim

Associate Editor

PLOS Computational Biology

Jason Haugh

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: Thank you again for the opportunity to review this manuscript. The authors have addressed all of my comments and in doing so I believe the manuscript is more accessible.

Reviewer #2: The authors addressed most of the reviewers’ comments which improved the manuscript.

Comments:

- The proposed metrics can reveal interesting insights, however these are not always easy to interpret. It will be useful to discuss the limitations in the discussion.

- The authors did not report on the methods they used for image analysis which only appeared in their response to reviewer 1. Multiplexed images can be extremely challenging and reasonable segmentation accuracy is needed for reliable conclusions. Details of the image analysis and results (raw images and segmented images) should be included. I appreciate the paper is presenting a method for studying the resulting spatial single cell distribution. However, making it clear in the discussion of potential errors and challenges in data segmentation should be taken into consideration when interpreting the results.

- Following from that point, the red data points that in Figure 1 for Patient 131 are expected to be wrongly segmented cells as TMAs are usually cut as a round biopsy. These should be excluded from the data through QC. Could the author confirm this from the raw images or replace with another example.

- That AFCM does not result in any statistically significant signatures when using this metric, raises a concern regarding their utility of these metrics which make the study merely exploratory. Could the authors elaborate on the potential reason in the discussion?

- Fig. 2:

The text is difficult to read

The authors refer to r=10 in the text, it will be helpful to add a vertical line to indicate this on the figure

- There are few mistakes in referring to the supplementary material: e.g. Line 185 should refer to Fig S2 not S1 and line 283 should refer to Fig. S3 not S1. Line 298 should refer to Section 3 not 2.

- I am not sure why the ovarian dataset and the associated analysis was moved to the supplementary. It should be fit in the appropriate sections of the study.

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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: Yes: Ellis Patrick

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. Vu,

We are pleased to inform you that your manuscript 'SPF: A Spatial and Functional Data Analytic Approach to cell Imaging 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,

Martin Meier-Schellersheim

Associate Editor

PLOS Computational Biology

Jason Haugh

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: The authors addressed most of our comments.

**********

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 #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 #2: No