PCOMPBIOL-D-24-02090

Mathematical modelling of mechanotransduction via RhoA signalling pathways

PLOS Computational Biology

Dear Dr. Verhees,

Thank you for submitting your manuscript to PLOS Computational Biology. After careful consideration, we feel that it has merit but does not fully meet PLOS Computational Biology'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 within 60 days May 10 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 ploscompbiol@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcompbiol/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

* A rebuttal letter that responds to each point raised by the editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. This file does not need to include responses to formatting updates and technical items listed in the 'Journal Requirements' section below.

* 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 you would like to make changes to your financial disclosure, competing interests statement, or data availability statement, please make these updates within the submission form at the time of resubmission. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter

We look forward to receiving your revised manuscript.

Kind regards,

Jochen Hub

Academic Editor

PLOS Computational Biology

Jason Papin

Editor-in-Chief

PLOS Computational Biology

Additional Editor Comments (if provided):

Both reviewers acknowledge the novelty and relevance of the study. However, they have identified weaknesses that require a thorough major revision, which may involve modifying the mathematical model and running new simulations.

The main manuscript contains an exceptionally large number of figures (20). Please consider whether key results can be presented more concisely in the main text and whether control simulations can be moved to the Supporting Information.

I look forward to your revised manuscript.

Journal Requirements:

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: This manuscript "Mathematical modelling of mechanotransduction via RhoA signalling pathways" presents a well-structured mathematical model describing the bidirectional coupling between RhoA signaling and cellular mechanics. Using a bulk-surface finite element method, the authors solve nonlinear reaction-diffusion equations alongside elasticity equations to simulate cellular deformations. Their findings highlight the influence of cell shape on RhoA dynamics and the role of mechanotransduction in maintaining mechanical homeostasis. While the study is novel and insightful, certain aspects require further refinement.

Detailed comments are listed below:

1. The authors assume that the cell follows a linear elasticity model, whereas many studies suggest that biological cells exhibit viscoelastic or poroelastic properties, especially over long time scales. It is recommended to discuss the validity of this assumption and consider incorporating viscoelastic effects to improve the biological realism of the model.

2. The model parameters (e.g., RhoA reaction rates, diffusion coefficients, substrate stiffness) are not well justified. The authors should provide references to experimental studies or parameter sensitivity analyses to strengthen the biological basis of their choices.

3. RhoA primarily regulates actin cytoskeleton remodeling, influencing cellular contractility and adhesion dynamics. However, the current model does not explicitly incorporate F-actin dynamics. Computational studies on cytoskeletal remodeling have been extensively explored in the literature, and these sources must be acknowledged and integrated into the manuscript. The authors may refer to the following studies:

• Predicting YAP/TAZ nuclear translocation in response to ECM mechanosensing.

• Directed cell migration towards softer environments.

Reviewer #2: The Authors propose a model describing the two-way feedback between FAK and mechanical characteristics of the environment. Though the subject is interesting and the attention to mechanotransduction is growing the model presents several unclear points.

In fact, in describing the evolution of the concentrations of active and inactive FAK (ϕ_a and ϕ_d, respectively) and of active RhoA (ρ_a) the model presents the following weak points

1- It is stated that "inactive species are assumed to be cytoplasm resident and activated forms membrane resident". However, while it appears that the latter actually evolves on the membrane Gamma, FAK seems to live in the cytoplasm in both forms.

2- This confusion transfers to the figures, where it is not clear what is shown. For instance, in the 2D case, is Fig.1 showing a section of the cell, or the membrane with an axisymmetric geometry? And then what about Fig.2? Ans so on ....

3- The fact that an evolution equation depends on an initial value is odd (say last equation in (1)). Since the total mass of rhoA seems to be conserved, it is better to refer to such a quantity, that is related to rho_d^0+rho_a^0/n_r.

4- A big problem regards the dimensions of the quantities introduced. This makes unclear what are the parameters actually used. For instance,

4.1- rhoA and phi are said to be concentrations, but the former is measured in #/m^2 and the latter in moles (which is not a concentration)

4.2- In Eq.(2) the dimensions of k₈ will depend on the power p, as well as the dimensions of k₇ in order to eventually have an E_c that is measured in Pascal. Certainly k₇ and k₈ are not s^-1 as stated in Table 2. However, it would be better to define E_c (that I believe is then called f) as E_c = k₇(1+(k₈ ϕ_a)^p) where the dimensions of k₈ are the inverse of those of ϕ_a

4.3- C_1 seems to be a pure number but its dimensions are 1/(Pa s). Then being either 0 or 1 like an on-off switch makes little sense. There must be a parameter measuring the stress-induced activation of FAK.

Regarding the presentation of the results

5- The presentation of the figures can be improved. In addition to the confusion mentioned above, I suggest to replace C=0 and C=1 with a more descriptive notation, such as σ ↛ FAK and σ → FAK. Similarly, I would use FAK ↛ E and FAK → E for the columns. Then, does E_c = 0.6 corresponds to the parameters used for f when the effect of FAK on the Young modulus is switched off?

6- In addition, graphically speaking, while one figure presents both concentrations (why not phi_d?) the other presents the deformation only (with some confusion induced by a reordering of the "table" of cases). Would it be possble to use the same format for all variables? Or put phi, rho, and u for instance one below the other for the different cases? Or split in three figures one per state variable?

7- The so-called lamellipodium configuration is not clear starting from its introduction at line 177. In addition, the results of the simulations give an axisymmetric distribution of the concentrations and deformations that are not axisymmetric. Why is that? Are the Authors sure they are using the correct boundary conditions on the sector they study?

Finally, as a minor comment, in Eq.(5) \cdot is used to mean different operations, a scalar product between two vectors and the multiplication of a matrix (the stress) by a vector (the normal). The following sentence is a bit obscure as it is written. After all, Pi_r is just the shear stress at the surface.

For the above reasons the paper can not be accepted for publication, but because of the novelty of the topic and the approach I think it can be reconsidered for publication after a strong and careful revision.

**********

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: None

**********

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

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

Figure resubmission:

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. Registration is free. 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 PLOS at figures@plos.org. Please note that Supporting Information files do not need this step. If there are other versions of figure files still present in your submission file inventory at resubmission, please replace them with the PACE-processed versions.

Reproducibility:

To enhance the reproducibility of your results, we recommend that authors of applicable studies 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. 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

PCOMPBIOL-D-24-02090R1

Mathematical modelling of mechanotransduction via RhoA signalling pathways

PLOS Computational Biology

Dear Dr. Verhees,

Thank you for submitting your manuscript to PLOS Computational Biology. After careful consideration, we feel that it has merit but does not fully meet PLOS Computational Biology'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 within 30 days Aug 30 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 ploscompbiol@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcompbiol/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

* A rebuttal letter that responds to each point raised by the editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. This file does not need to include responses to formatting updates and technical items listed in the 'Journal Requirements' section below.

* 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 you would like to make changes to your financial disclosure, competing interests statement, or data availability statement, please make these updates within the submission form at the time of resubmission. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

We look forward to receiving your revised manuscript.

Kind regards,

Jochen Hub

Academic Editor

PLOS Computational Biology

Feilim Mac Gabhann

Editor-in-Chief

PLOS Computational Biology

Additional Editor Comments (if provided):

The reviewers acknowledged that the manuscript has been greatly improved and recommended it for acceptance.

Reviewer 2 suggests two additions that would further improve the clarity of the manuscript. Please indicate whether you will follow this recommendation or whether you disagree. Further review will not be needed, irrespective of your decision.

Journal Requirements:

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: no further comments

Reviewer #2: The Authors considerably improved the paper answering all question.

I only have two suggestions:

What about insert a sketch of the protein relations and their location at the beginning of the modeling section?

What about recalling that (5) represents a shear stress-free condition?

**********

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: None

Reviewer #2: None

**********

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

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

Figure resubmission:

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. Registration is free. 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 PLOS at figures@plos.org. Please note that Supporting Information files do not need this step. If there are other versions of figure files still present in your submission file inventory at resubmission, please replace them with the PACE-processed versions.

Reproducibility:

To enhance the reproducibility of your results, we recommend that authors of applicable studies 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. 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 Ms Verhees,

We are pleased to inform you that your manuscript 'Mathematical modelling of mechanotransduction via RhoA signalling pathways' 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,

Jochen Hub

Academic Editor

PLOS Computational Biology

Feilim Mac Gabhann

Editor-in-Chief

PLOS Computational Biology

***********************************************************