Dear Dr. Zhang,

Thank you very much for submitting your manuscript "4D nucleome equation predicts gene expression controlled by long-range enhancer-promoter interaction" 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.

As you will see from the reports copied below, the reviewers find the modeling framework to be potentially valuable. However, they raise several concerns, in particular with regards to the novelty relative to Ref 10.

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,

Maxwell Wing Libbrecht, Ph.D.

Academic Editor

PLOS Computational Biology

Kiran Patil

Section Editor

PLOS Computational Biology

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

As you will see from the reports copied below, the reviewers find the modeling framework to be potentially valuable. However, they raise several concerns, in particular with regards to the novelty relative to Ref 10.

Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #1: In the manuscript ‘4D nucleosome equation predicts gene expression controlled by long-range enhancer promoter interaction’ Wang et al. proposed a theoretical framework for studying gene expression dynamics as a result of enhancer promoter (E-P) interaction. The fundamental concept of the framework is the description of chromatin dynamics and gene expression dynamics in a single equation, as well as the separation of the timescales for the two types of dynamics. The authors showed that simulations based on this framework produced results consistent with both the general understanding of E-P regulation and specific experimental data. Overall, the modeling framework is rigorous and novel. The manuscript is well-written overall. I have a few comments/suggestions regarding the connection between the models and data, as well as the clarity of the manuscript.

1. The biological interpretation of the ‘monomer’ is unclear. It was introduced generically on Page 5 without a description of its meaning. On Page 7, however, it was indicated that each monomer is one nucleosome. When fitting the model to the mESC data, a monomer became a 5kb region, which is more than 10-fold longer than a region spanned by a nucleosome. The confusing usages of the monomer’s meaning needs to be addressed. While the authors can make the interpretation flexible, doing so would mean that the biological meanings for all parameters of the model will change accordingly. This can be problematic when interpreting the simulation results. In addition, it will be helpful if the authors can use realistic distributions of genomic E-P distances to explain the scales of their structural model.

2. The comparison of multimodality of mRNA distribution from simulations and experimental data seems weak. Out of the three references mentioned in that section on Page 16, none of them showed the relationship between E-P regulation and modality of mRNA distribution. It is therefore unclear whether the simulation results are realistic.

3. I suggest that the authors use their framework to explain the source of the multimodality. Is this a result of the chromatin dynamics which produced multiple structural configurations that are more stable than others? If yes, some analysis of the structural model component will be helpful.

4. Page 3, Line 56. ‘Its’ should be ‘whose’, and ‘chromatin’ is misspelled.

5. Page 14, the last sentence. ‘Decrease’ should be ‘decreases’, and ‘trends’ should be ‘tends’.

Reviewer #2: The paper introduces the 4D nucleome equation as a comprehensive theoretical framework for investigating the impact of long-range enhancer-promoter (E-P) interactions on gene expression dynamics. The framework incorporates upstream chromatin motion, downstream mRNA production, and the temporal connection between these processes. The authors derive analytical mRNA distribution and explore how E-P interactions qualitatively influence the characteristics of mRNA distribution. The 4D nucleome equation provides a valuable modeling framework for studying the influence of chromatin dynamics on gene expression kinetics.

However, it is unclear what specific contributions the authors have made compared to previous work. Although the authors briefly discuss a comparison with the model presented in Ref. 10, most of the discussion is relegated to the Supplementary Information (SI). It appears that the authors' model is identical to the one in Ref. 10 in the fast chromatin dynamics regime. In this limit, the contact probability used in Ref. 10 can be directly replaced with the distance used in Eq. 3 of the SI.

Additionally, the authors introduce expressions for the slow chromatin dynamics limit, which are new. However, they do not discuss the contribution of slow dynamics to the fitting of experimental data. While the authors emphasize that their model fits experimental data better than the expression in Ref. 10, this improvement may be expected since the new model has more parameters. It would be interesting if the authors could provide insight into the obtained value for w in Eq. 12 and its impact on fitting with experimental data. Is the contribution from slow chromatin dynamics important for the observed improvement in fitting?

To justify the publication of the manuscript, the authors need to highlight novel observations that were not reported in Ref. 10. Many of the analytical expressions presented in the manuscript are standard for polymer physics and stochastic gene expression models. While it is commendable that the authors report these expressions and combine the two models, the expressions alone may not present sufficiently interesting results for publication.

Furthermore, one of the most notable findings in Ref. 10 is the non-linear dependence of the activation rate on E-P contacts, as demonstrated in Eq. 3 of the SI. Surprisingly, the authors do not mention this non-linearity in the main text and simply adopt the same assumptions as in Ref. 10. This omission prevents the authors from providing alternative explanations for the underlying molecular mechanisms that give rise to the observed non-linearity.

Lastly, there are some minor comments that the authors should address.

1) Firstly, if Eq. 9 in the main text has been derived previously, the authors should provide appropriate citations or clarify the novelty of the expression.

2) Secondly, for the fitting presented in Fig. 5, it would be useful to list the parameters in the SI.

3) Lastly, for Fig. S4, the authors should refer to the SI text that provides the definition of the KS distances.

Addressing these points will strengthen the manuscript and enhance its potential for publication.

Reviewer #3: The authors developed a modeling framework to couple enhancer-promoter interaction with gene expression at different timescales and applied the model to study how the enhancer-promoter interaction affects gene expression dynamics. It considered upstream chromatin motion on a fast timescale and downstream mRNA production on a slow timescale. The authors derived analytical mRNA distribution by following timescale separation method and also numerically solved the equation. They showed that E-P interaction could give rise to multiple shapes of mRNA distributions including bimodal and trimodal distributions. A power-law scaling of gene expression levels in the E-P genomic distance was also demonstrated through both theoretical analysis and numerical simulations. Analysis of experimental data showed consistent results as predicted by the model in mRNA distribution and E-P contact probability under different E-P interactions. The manuscript was clearly written to describe the modeling framework, main results and conclusions, except some grammar mistakes. I would suggest publishing this work if the following comments can be addressed:

On page 6, in the equation F(r,s;t)=V(r,s:t)-∇_r∙(Dlogp(r;t)), it should be ∇_r (Dlogp(r;t)) instead of ∇_r∙(Dlogp(r;t)).

On page 8, please explain why overdamped Langevin equation was applied to model the chromatin dynamics in more detail.

On page 10, when minimizing the total cross entropy function Eq. [6], was it possible to obtain multiple local minimizers? In that case, how were the parameter values determined? Will conclusions still be valid for different parameter values?

On page 13 line 265, V(r)=[(k_NN/d_G +k_EP ) d_s ]/bγ should be V(r)=[(k_NN/d_G +k_EP ) d_s ]/(bγ)?

On page 15 line 318, the last one of the five modes should be unimodal with NOP.

In Fig. S2, the titles of subfigures should be U(1 NOP).

On page 16 line 328-331, the authors discussed different scenarios that the evolution of the mRNA distribution may undergo. I would suggest to add more detailed discussion on the critical conditions or sensitive parameters giving rise to different scenarios and what biological insights can be obtained. What are the different conditions giving rise to results presented in S2 and S3?

On page 17 line 355, different values of d_G were chosen by fitting the experimental data. This information should be provided to clarify how those values were obtained.

Grammar mistakes:

Page 10 line 205, mothod -> method

Page 11 line 223, challenge-> challenging

Page 11 line 236, or a a frozen E-P -> or a frozen E-P

Page 13 line 260, given vs -> given as

Page 14 line 285, CV downregulated by -> CV is downregulated by

Page 14 line 297, the mRNA level decrease and trends -> the mRNA level decreases and tends

Page 16 line 329, it should be ‘still changes from unimodal to the bimodal and then to unimodal again’.

**********

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

Reviewer #3: 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

Reviewer #3: 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. Zhang,

We are pleased to inform you that your manuscript '4D nucleome equation predicts gene expression controlled by long-range enhancer-promoter interaction' 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,

Maxwell Wing Libbrecht, Ph.D.

Academic Editor

PLOS Computational Biology

Kiran Patil

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: The authors have addressed all my comments adequately.

Reviewer #2: The authors have successfully addressed all my concerns.

**********

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