Dear Dr Treloar,

Thank you very much for submitting your manuscript "Deep Reinforcement Learning for Optimal Experimental Design in Biology" 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,

Vassily Hatzimanikatis

Associate Editor

PLOS Computational Biology

Mark Alber

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: This manuscript presents a deep reinforcement learning approach for the design of optimal experiments in biological systems.

Although this is a nice contribution, it needs to be improved in several ways. The main issues are:

1- the literature review in the introduction should be updated, especially regarding:

(i) links between OED and control theory (see e.g. surveys by Gevers, or Hjalmarsson; also papers from Pronzato such as https://doi.org/10.1016/j.automatica.2007.05.016 )

(ii) other recent related approaches, e.g. https://arxiv.org/abs/2202.00821

2- previous works (e.g. by Schenkendorf and others) have illustrated the use of global sensitivity analysis in OED to address some of the concerns outlined in this study. Such works should be cited/discussed.

3- the authors have focused on D-optimal design criterion. Previous works (also not cited in this study) have shown a trade-off between different FIM-based metrics (e.g. D and mod-E). Maybe a multicriteria approach could be used (as previously done by several groups). It would be nice if the authors discuss this aspect.

4- I think the author should also check (and cite/discuss) the excellent survey by Macchietto ( https://doi.org/10.1016/j.ces.2007.11.034 ) which, although not very recent, discusses in detail several of the above issues and the related literature

5- the authors show that a deep reinforcement learning approach performs favourably in comparison with a one-step ahead optimisation algorithm and a model predictive controller using a rather simple case study (bacterial growth in a chemostat). How scalable is their approach for more realistic applications?

6- also regarding scalability, recent alternative BO-based approaches should also be discussed (e.g. https://doi.org/10.23919/ACC45564.2020.9147824 )

Minor issues:

- some refs are incomplete

Reviewer #2: The manuscript by Treloar and colleagues presents a novel methodology to optimally design maximally informative experiments for the task of parameter inference for mathematical models describing biological systems. The method uses reinforcement learning to predict the informative content of potential experiments: while it does use a well-established technique (FIM-based metric) to estimate information content, the approach documented by the authors addresses a key problem in current approaches to OED, that is the need to either start from a neighbourhood of the actual value of the parameters when performing model calibration, or "paying the cost" of expensive Bayesian methods.

Overall the approach presented is sound, the paper is well structured and presented. I only have a few comments, offered, in order of importance, below:

- Given the audience of this journal, I believe that the manuscript would greatly benefit from a section that outlines the key elements of Reinforcement Learning and clarifies some of the jargon (Fitted Q, value function etc);

- While the authors compare their RL agents to MPC and one step ahead optimization I think that it would be helpful to show how the solutions the best agent identifies compares to other optimisation schemes commonly used in dynamic experimental design (e.g. eSS). Also, connected, RL is presented as a solution but the rationale for using ML in the first place is not entirely clear.

- In Section 4.4 I found the speculation on the reason for the underperformance ("problem too complex") requiring a level of suspension of judgement that I was not entirely comfortable with. Could the authors simplify the problem (less control intervals or less discrete values of the inputs) to show that "problem complexity" is indeed the issue?

- At page 5, where the chemotast model is introduced, the authors should review the vay the parameters are introduced as it seems inconsistent with the text that explains them;

- The manuscript is sprinkled with a parentheticals, some dispensable (e.g. I don't think this audience needs to be told what an auxotroph is). I would encourage the authors to go over the text and ask, for each sentence between parentheses, whether it is necessary. If so, make a proper sentence of it, otherwise eliminate;

- At page 11: "the determinant of the Fisher Information" should read "the determinant of the Fisher Information matrix"

Overall I genuinely believe this is an excellent piece of work and the authors should be commended for their contribution.

**********

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

Dear Dr Treloar,

Thank you very much for submitting your manuscript "Deep Reinforcement Learning for Optimal Experimental Design in Biology" 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,

Mark Alber, Ph.D.

Section Editor

PLOS Computational Biology

Mark Alber

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: I find the revised version satisfactory. There are a couple of minor things to be fixed:

- ref 10 must be corrected (it shows the funding info, not the journal)

- the annotated colored version is badly compiled regarding refs etc., but I was able to see the changes anyway

**********

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

**********

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

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 Treloar,

We are pleased to inform you that your manuscript 'Deep Reinforcement Learning for Optimal Experimental Design in Biology' 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,

Mark Alber, Ph.D.

Section Editor

PLOS Computational Biology

Mark Alber

Section Editor

PLOS Computational Biology

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