Dear Dr. Uchinomiya,

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PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Yes

Reviewer #2: Partly

Reviewer #3: Yes

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2. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: N/A

Reviewer #2: N/A

Reviewer #3: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #1: No

Reviewer #2: Yes

Reviewer #3: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #1: Uchinomiya and Tomita present a mathematical model of the effect of competition between “intact” and “damaged” stem cells on the accumulation of damaged cells within the population. Interestingly, although the text is focused on low-dose radiation exposure, the model itself is not specific to radiation. Overall, I enjoyed reading the manuscript, but offer some comments and suggestions below.

Major comments

1. According to the introduction, the goal of this study is to investigate the influence of stem cell competition on accumulation of damage from low dose background radiation. However, the discussion and conclusion do not clearly or strongly tie the results back to this goal. That is, there is no discussion of what implications these results have for protective measures that may be taken against low dose rate exposure.

2. Lines 380-389. The discussion presented in these lines does not make sense. Please completely rewrite this section. Firstly, as far as this reviewer knows and can find, there exists no such definition of an “elemental dose” in this context. In addition, reference 8, which is given for this definition, does not discuss such a concept. What is the correct reference? Second, the calculation that it would take 18 days to reach 1mGy under the assumption of an exposure limit of 20mGy per year isn’t valid. The time it takes to accumulate any exposure would depend solely on the dose rate being experienced, not the upper limit of dose exposure. Third, it is not clear what approximation the authors are referring to in line 387.

3. During model development, several explicit or implicit assumptions were made that need to be discussed either in the methods or in the discussion section. For example, it is assumed that damage is irreversible. However, it is well known that radiation induced DNA damage is repairable and could even occur on the time scales considered in the article.

Minor comments

1. Lines 217-227. The text refers to data presented in Figure 3. There is a mismatch between the color of the data in the figure that corresponds to the values (green) and the color used in the text (pink).

2.Please provide information regarding the initial makeup of the population. Do the simulations begin with one damaged cell, or only intact cells?

3. The definition of Tabs isn’t clear. Is it when there is only damaged stem cells present?

4. Can the lattice-based model only support a certain number of cells, or does the lattice expand indefinitely?

5. How did the authors decide on performing 50 simulations per condition? Currently the first mention that 50 simulations were performed is in the caption of Figure 3. Please also mention this in the methods section. Further, please adapt the figures (where appropriate) to include the standard deviation as error bars.

6. Please include a brief explanation of how to the C values can be interpreted. For example, does C_(I←D)<1 indicate that damaged cells lower or increase the cost of intact cells?

7. The manuscript mentions “low dose-rate” conditions as being when λ is “very small”. In Figure 3, λ ranges from 10^-3 to 1. Are all of these values considered to be low dose rate?

8. According to lines 252-254 “…Tabs could be normalized to 1” in Figure 4 (a). Has Tabs been normalized to one in the rest of Figure 4, or has it been normalized to the value of Tabs from Figure 4(a)? It is not clear.

9. Lines 377-378 states “For example, the influence of cell competition was significant under low dose-rate condition..”. Please clarify if this refers to a statistically significant difference or not.

10. Lines 93, 134, 190. Please replace the word abstract with abstraction.

11. Line 109-110 is not clear. Please rephrase.

12. Lines 163-164 state “The well-mixed model is a Markov process, and the absorbing state is only when damaged cells occupy the cell pool.” Do the authors have a proof for this statement? If so, please include it in the appendix or supplemental information.

13. Line 175-176 “Then, one cell is randomly chosen from the removed cell and surrounding cells to divide and fill the removed space.” So the removed cell proliferates? Please clarify.

14. I encourage the authors to be consistent with the tenses used throughout the manuscript. In some places they have used past tense, and in some they use present tense.

15. Lines 255-256 and 258-259. I believe the authors have switched the descriptions. In Figure 4(b), Tabs monotonically decreases with N, and in Figure 4(c) it monotonically increases with N.

16. In line 292, there is a typo. I believe “closed” should be “close”.

17. In line 302, it should be “therefore”.

18. The description of figure 5, and how the dotted and dash dotted lines were chosen and what they mean is unclear. Please rephrase the explanation.

Reviewer #2: Title: A Mathematical Model assuming Frequency-dependent Cost for Analyzing the Influence of Cell Competition on Radiation Effects

Summary: authors use standard Moran process with state-switching model to determine the influence of radiation on stem cell damaged cell’s expanding over intact stem cells. Then the authors extend the model to a standard spatial Moran process with 8 nearest neighbors.

Overall the research question is important, but the methods are standard and the connection to existing theoretical literature is weak, including any discussion of types of payoff matrices (e.g. prisoner’s dilemma; hawk-dove; etc) rather than relying on hard-coded payoff values. There are some theoretical analysis of the rate of mutant expansion that might be helpful here, too. For a good example, check Heyde et. al. Cell, 2021.

The most interesting part of the manuscript is the connection between frequency-dependent competition and radiation dose. However the dose parameter, \lambda, is not contained in the equations of the competition model in equation 3, making it difficult to determine its influence. Secondly, I assume that \lambda will have an effect on stem cell pool size, N, and that radiation may influence the competition parameters in the matrix too.

One of the central claims of the paper, that “When the dose rate is very low, some stem cells may be damaged and mixed with intact stem cells in the stem cell pool” isn’t sufficiently explored in the model. For example, an effect of radiation dose is linear, and thus there is no qualitative regime change between high and low doses of radiation.

Many claim in the introduction or conclusion section are true claims, but do not have associated references; for example:

1. Line 36: “Ionizing radiation is a well-known external factor that increases the risk of cancer. “

2. Line 59: “The hypothesis that stem cell competition suppresses the effects of radiation has been supported by experiments.”

3. Line 462: “In recent years, the effects of cell-cell interactions have begun to be measured quantitatively.”

Reviewer #3: I have read the article “A Mathematical Model assuming Frequency-dependent Cost for Analyzing the Influence of Cell Competition on Radiation Effects.” In this manuscript, the authors analyze the effect of cell-cell competition on the accumulation of cells damaged by radiation. They constructed mathematical model of radiation damage which used a Moran process to model growth and death of cells, a Markov model for transition probabilities between induced and damaged cells, and an evolutionary game of interaction between cells. They analyzed this under a well-mixed and spatially explicit model. They showed that frequency-dependent competition between cells can slow down the rate of damaged cell takeover, at least under low-dose radiation. Overall, this is a good paper with an appropriate model that shows interesting results. I cannot find serious flaws with the methodology or analysis. I list my comments regarding the manuscript below.

My first comment is that elements of the manuscript could be made more clearly. Firstly, the authors mention cell fitness. It would be good to define fitness in the context of cells. I have an understanding of what they mean but a formal definition would help. They also mention stem cell competition but it seems like this model could be broadened to any kind of cell. I would either state the reasons for focusing on stem cells (i.e., why they are biologically important/relevant) and keep that consistency throughout or just generalize the model to all cells. This would help focus the reader’s mind. As well, the authors use the inequalities to describe the scenarios. I think substituting the inequalities with words like positive-frequency dependence, negative-frequency dependence, damaged cells dominant, and intact cells dominant would help with readability. Overall, less wording and being more direct would improve the paper.

The figures for the most part work although it looks like they have been taken from screenshots of a previous paper. This is my biggest concern, that the results have not been already duplicated elsewhere. An explanation of why they look like that would be helpful. I would also modify figure 3 so that there is a second figure (perhaps figure 3b) that shows the difference between theoretical and simulations. One can kind of see the difference in figure 3 but it is quite busy. Having a separate panel that shows just the difference would be helpful especially because in some cases the difference is greater than zero and in other cases it is less than zero. Explaining when we see differences greater than zero versus less than zero and why would just generally be interesting. Perhaps there is a kind of pattern there.

I think the discussion could be better written with the results put in a broader context. I do appreciate discussion on fitting the values to real world data, but there isn’t much beyond that. Reaching into the cancer literature and general insect pest games may help. One potential paper to cite is Kaznatcheev et al. 2019 “Fibroblasts and Alectinib switch the evolutionary games played by non-small cell lung cancer”. In this paper, the authors show that the presence of fibroblasts favor sensitive cancer cells over resistant cancer cells in an evolutionary game, i.e. cell-cell interactions affected the composition and eventual takeover of resistant cancer cells. It seems pertinent to their work.

Did the authors look at all inequalities? I believe there are twelve, ordinally distinct symmetric games. It would be interesting to see how this process affects all twelve types of games.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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Dear Dr. Uchinomiya,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Nov 02 2025 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org . When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols . Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols .

We look forward to receiving your revised manuscript.

Kind regards,

Attila Csikász-Nagy

Academic Editor

PLOS ONE

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If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise. 

Please 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.

Additional Editor Comments:

Address the remaining concerns of reviewer 2.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #1: All comments have been addressed

Reviewer #2: (No Response)

Reviewer #3: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions??>

Reviewer #1: Yes

Reviewer #2: Partly

Reviewer #3: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: N/A

Reviewer #2: N/A

Reviewer #3: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #1: No

Reviewer #2: Yes

Reviewer #3: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

Reviewer #1: (No Response)

Reviewer #2: My previous concern that “the dose parameter, \lambda, is not contained in the equations of the competition model in equation 3, making it difficult to determine its influence” was not addressed. I remain concerned that the model methods still isn't written in such a way that is reproducible.

Based on the authors' response, i now understand that the Moran process has 3 steps: transition, birth, replacement. The equations in 3a, 3b, 3c, and 3d only describe birth and replacement. Please consider updating these equations to be explicit functions of lambda, to include the transition step.

All my other comments have been addressed satisfactorily.

Reviewer #3: The reviewers have taken all my concerns into account, and I am pleased with the state of the manuscript.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

**********

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A Mathematical Model assuming Frequency-dependent Cost for Analyzing the Influence of Cell Competition on Radiation Effects

PONE-D-25-19152R2

Dear Dr. Uchinomiya,

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Kind regards,

Attila Csikász-Nagy

Academic Editor

PLOS ONE

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