Dear Dr. Berret,

Thank you very much for submitting your manuscript "Co-Contraction Embodies Uncertainty: An Optimal Feedforward Strategy for Robust Motor Control" 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 were generally positive about the contribution of the paper, but raised a few issues that should be addressed, as well as making a number of constructive suggestions to improve the paper. In light of the reviews (below this email), we would like to invite the resubmission of a 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,

Adrian M Haith

Academic Editor

PLOS Computational Biology

Andrea E. Martin

Section 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: Review of “Co-Contraction Embodies Uncertainty: An Optimal Feedforward Strategy for Robust Motor Control” by Berret et al.

This paper presents theoretical analysis and experimental evidence that feedforward modulation of muscle co-activation and mechanical impedance is a strategy to deal with uncertain external perturbations. The paper is generally well written and the experimental results are largely consistent with the model predictions.

However, the experiment considered only a single-joint pointing task which is hardly a “seminal motor control task” (line 89). This significantly reduced enthusiasm for the findings reported.

Moreover, the finding that for \\alpha of 0.25, 0.50 and 0.75, performance converged within 10 to 20 trials (figure 5C) would appear to indicate that this was not a particularly challenging task. How then can extrapolation to more general tasks be justified?

It appears (equation 1) that the external disturbance process \\xi was stationary and independent of the system state. While that is an important case, it seems like a rather impoverished model of tool use, where the user’s actions significantly affect the stochasticity of the interaction as well as its stability.

Indeed, due to the apparent absence of state-dependent disturbances, it is not clear how equation (1) was applied to the simulation of figure 3. That may reflect this reviewers ignorance of the mathematics but if so, this should be clarified in the text.

The results presented in figure 2 are interesting but they indicate an approximately trapezoidal time profile of stiffness. How can this be reconciled with the results reported by Bennett et al. (ref. 31) which clearly showed a substantial reduction of stiffness in the middle of movement? Indeed, might Bennett et al.’s results invalidate the analysis presented here? This should at least be discussed briefly.

The paper is focused on stiffness modulation but neuromuscular mechanical impedance may have other components. Was there any evidence of modulation of apparent neuromuscular damping?

I would like to know more about the exoskeleton. How “back-drivable” was it? For example, if its static friction or apparent inertia were significant (which is typical for a geared electric motor) they would evoke enhanced muscle activation and thereby enhance apparent mechanical impedance with no relation to external perturbations.

Minor suggestions:

The use of the symbol u to represent either (i) generic control input (ii) torque and (iii) stiffness (e.g. in figure 2) was quite confusing; torque and stiffness require different units. It would be helpful to distinguish these different meanings of this variable.

Abstract line 7, Line 108, Line 268: Do you mean “singular” in the mathematical sense or do you mean “unique”? If the former, please clarify.

Line 13: re-arrange the sentence to read: “… predict co-contraction well …”

Line 21: while direct measurement of output mechanical impedance requires external perturbation, it may also be estimated from a model. Remarkably, there is evidence that humans do so [1], [2] . This might support the argument for predictive feedforward control of mechanical impedance.

In equation (1) should the symbol be \\w_t or w as defined in the subsequent text?

Line 259: delete “of”

Line 236: suggest replacing “At last” with “Finally”.

Line 454: rearrange the sentence to read: “… the considered reaching movement.”

[1] M. E. Huber, C. Folinus, and N. Hogan, “Visual Perception of Joint Stiffness from Multi-Joint Motion,” J. Neurophysiol., vol. 122, no. 1, pp. 51–59, 2019, doi: 10.1152/jn.00514.2018.

[2] A. M. J. West, M. E. Huber, and N. Hogan, “Role of Path Information in Visual Perception of Joint Stiffness,” PLoS Comput. Biol., vol. 18, no. 11, p. e1010729, 2022, doi: 10.1371/journal.pcbi.1010729.

Reviewer #2: This paper presents a new mathematical framework to explain human sensorimotor behavior in the face of environmental uncertainty. The framework and the experimental evaluations focus on feedforward (open-loop) control, showing that muscle co-contraction is related to environmental uncertainty. The results provide an insightful first step towards understanding why and how co-contraction occurs, and can be a valuable addition to the literature. However, I have some general thoughts that the authors might consider addressing to further strengthen the paper.

One point for further consideration is the potentially restrictive formulation of the problem. The authors model “trial-by-trial” uncertainty, where the uncertain effects are fixed within the scope of one trial (encoded in \\xi), but we live in a continuous world; trial-by-trial effects are artifacts of our experimental designs. I recognize the limitations of our current experimental and theoretical tools, and that answering such real-world questions will require decades of research. Nevertheless, I encourage the authors to discuss this issue further. I personally would be very interested to learn their perspective on how these results might be extended to more real-world applications, such as implementing the framework within a receding horizon control scheme.

My second comment is regarding the level of detail. The paper presents the general problem that the nervous system may need to solve (eqs. 1 and 2) and then converts the original problem to an equivalent ODE problem. However, the final step—solving the problem—is not fully detailed. Depending on the reader's goal—whether learning about the functioning of the brain or implementing/extending the method—the level of detail might be either too much or too little. Adjusting the level of detail to better match the overall objective of the paper would be beneficial.

Another philosophical point concerns the paper's conclusion: “Co-contraction embodies uncertainty.” The presented optimal feedforward control model indeed supports this conclusion. However, a short discussion on whether this is the sole reason for co-contraction in uncertain environments might be beneficial. The authors’ 2020 SOOC paper is a good example; it provided an alternative explanation for some behavioral observations that were previously modeled differently, e.g., the minimal intervention principle. Could there be alternative explanations for co-contraction yet to be discovered (maybe a feedback-driven one)?

Lastly, the manuscript is well-written, though a round of copy-editing could enhance its clarity and impact.

Here are some additional comments

Line 63. Problem 1. The dynamics of the nonlinear model must be approximated (linearized) to arrive at this augmented-state ODE description. However, the Discussion (lines 253-254) tries to contrast the model with “linear” theories like H-infinity. Further discussion is appreciated to expand on when and how the presented method can be applied to full nonlinear system equations (i.e., without approximation), or how the approximation is still superior to other methods.

Equations 6, 7, 10, and 25 need parentheses in the integral.

115. How was the multiplicative noise included in the model? Please provide more details.

Fig 1C. Why do the grey traces have two separate values for a given variance? In other words, why isn’t the shape shown in Fig 1A symmetric? Is it because of some combined effects of intrinsic and extrinsic noise?

120. A brief description of the model is appreciated here. Is it a linear or nonlinear model? How were stiffness and muscle activity related? I suggest including the equations of motion in the Methods section.

136. Fig 3 or Fig 4?

141. Please provide more details of this model as well.

150. Torques are mentioned, but there are 3 traces in Fig 3C,D, which implies muscle groups. Please provide further details to clarify.

151. In the statement “mean stiffness and co-contraction”: Mean over time and over muscles? Further details are appreciated.

Figure 3C. It is curious that co-contraction is zero in the first quarter of movement. Is it just an artifact of the combination of reach direction, initial condition, disturbance magnitude, etc. in the simulation? Or is there some exciting explanation behind it?

165. Was the disturbance always in the flexion direction (or extension)? Also, when describing the experimental protocol, it is mentioned in line 410 both flexion and extension movements, but the results (and line 421) imply only flexion movements were tested. The description of the results and experimental protocol require further expansion and clarification.

303. Why are A, B assumed to be functions of u? Is it, for example to include muscle activation-dependent dynamics? What would be the applications/implications of this assumption?

**********

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: Yes: Reza Sharif Razavian

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. Berret,

Thank you very much for submitting your manuscript "Co-Contraction Embodies Uncertainty: An Optimal Feedforward Strategy for Robust Motor Control" for consideration at PLOS Computational Biology.

The reviewers were satisfied with the responses and revisions to the paper. However, Reviewer 1 noted a number of small issues that require attention before formal acceptance.

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,

Adrian M Haith

Academic Editor

PLOS Computational Biology

Andrea E. Martin

Section 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:

Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #1: Please see the attached review

Reviewer #2: Thank you for addressing my comments. I have no further 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 #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: Yes: Reza Sharif Razavian

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.

Attachments

Attachment

Submitted filename: Re-review Berret 2024.pdf

Dear Dr. Berret,

We are pleased to inform you that your manuscript 'Co-Contraction Embodies Uncertainty: An Optimal Feedforward Strategy for Robust Motor Control' 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,

Adrian M Haith

Academic Editor

PLOS Computational Biology

Andrea E. Martin

Section Editor

PLOS Computational Biology

Feilim Mac Gabhann

Editor-in-Chief

PLOS Computational Biology

Jason Papin

Editor-in-Chief

PLOS Computational Biology

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