A review on nonlinear DNA physics

The study and the investigation of structural and dynamical properties of complex systems have attracted considerable interest among scientists in general and physicists and biologists in particular. The present review paper represents a broad overview of the research performed over the nonlinear dynamics of DNA, devoted to some different aspects of DNA physics and including analytical, quantum and computational tools to understand nonlinear DNA physics. We review in detail the semi-discrete approximation within helicoidal Peyrard–Bishop model and show that localized modulated solitary waves, usually called breathers, can emerge and move along the DNA. Since living processes occur at submolecular level, we then discuss a quantum treatment to address the problem of how charge and energy are transported on DNA and how they may play an important role for the functioning of living cells. While this problem has attracted the attention of researchers for a long time, it is still poorly understood how charge and energy transport can occur at distances comparable to the size of macromolecules. Here, we review a theory based on the mechanism of ‘self-trapping’ of electrons due to their interaction with mechanical (thermal) oscillation of the DNA structure. We also describe recent computational models that have been developed to capture nonlinear mechanics of DNA in vitro and in vivo, possibly under topological constraints. Finally, we provide some conjectures on potential future directions for this field.

In the second part the authors consider the long-range polaron transport in DNA. This problem was also considered in paper [2] which need to be cited. With these improvements I recommend the paper for publication in Royal Society Open Science. Decision letter (RSOS-200774.R0) We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Dr Zdravkovic
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Reviewer comments to Author:
Reviewer: 1 Comments to the Author(s) The review reports on different aspects of DNA dynamics and stability, with special focus on theoretical frameworks that reproduce the emergence of breathing modes and explain the charge and energy transport along the chain. There is also a section of the numerical modelling of DNA.
Unfortunately, the overall feeling is that the manuscript reads as a collection of different parts rather than a single review revolving around a specific topic.
Sections II and III are the most coherent with the title, reporting a review of some of the theoretical models used to investigate the stability of double-stranded DNA with classical theories (although it should be noted that these sections reference 13 papers authored by the corresponding author, which makes this part of the review appear a bit too self-centred).
By contrast, in Section IV the authors discuss phenomena which have a quantum origin. However, differently from the previous sections, most of the work reported here seems original, or at least it is not clear whether the theory and results reported herein are new or reproduced from some other work (e.g. Figure 5). This in stark contrast with section III, which reports work already presented elsewhere.
Finally, Section V reviews some of the computational models used to investigate the structure and dynamics of DNA at different coarse-graining levels. However, the connection with the previous sections is tenuous at best. In fact, there is no connection with Section IV at all, whereas the discussion about the appearance of bubbles in simulations is only sketched.
All in all, I cannot recommend publication in its current form, as the manuscript does not feel as a single unit, and the inter-connections between the single parts are not strong enough to warrant their inclusion in a single review. The authors should make the effort to uniform the language and the style and to add more overlap between the different sections.
Here is a list of minor things: -The typesettings of some equations are a bit off (at least on my pdf reader). For instance, some vector signs and other symbols are not displayed correctly (e.g. eqq 2.4, 4.4a and b, 4.6b, eq 4.9).
-Stacking is at least as important as (if not more important than) hydrogen bonding in dictating the stability of the duplex (see e.g. https://academic.oup.com/nar/article/34/2/564/2401647) -I think a figure describing the theories introduced in Sections II and III would greatly help the reader grasping the nature of the models presented.
-I guess the sums in Section III run over all the nucleotides, but this is not specified in the text and in the equations.
-oxDNA has been used to investigate DNA melting (see e.g. https://doi.org/10.1093/nar/gkt687). The review considers nonlinear dynamics of DNA and is actual. In the first part of review the authors consider several models of DNA dynamics without electron. I recommend authors to read and refer the detailed review on this subject [1].
In the second part the authors consider the long-range polaron transport in DNA. This problem was also considered in paper [2] which need to be cited.
With these improvements I recommend the paper for publication in Royal Society Open Science.  one version identifying all the changes that have been made (for instance, in coloured highlight, in bold text, or tracked changes);  a 'clean' version of the new manuscript that incorporates the changes made, but does not highlight them. This version will be used for typesetting if your manuscript is accepted.
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Are the interpretations and conclusions justified by the results? Yes
Is the language acceptable? Yes

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? No

Recommendation?
Accept as is

Comments to the Author(s)
The revised version of the manuscript has been significantly improved by the authors, and while the review is still very broad in context, the authors explicity state in the text why this is the case.
In addition, they have also strengthened the connection between the sections and changed the title. I am happy to recommend publication.

Decision letter (RSOS-200774.R1)
We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Dr Zdravkovic,
It is a pleasure to accept your manuscript entitled "A Review on Nonlinear DNA Physics" in its current form for publication in Royal Society Open Science. The comments of the reviewer(s) who reviewed your manuscript are included at the foot of this letter.
You can expect to receive a proof of your article in the near future. Please contact the editorial office (openscience_proofs@royalsociety.org) and the production office (openscience@royalsociety.org) to let us know if you are likely to be away from e-mail contact --if you are going to be away, please nominate a co-author (if available) to manage the proofing process, and ensure they are copied into your email to the journal.
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Thank you for your fine contribution. On behalf of the Editors of Royal Society Open Science, we look forward to your continued contributions to the Journal. The revised version of the manuscript has been significantly improved by the authors, and while the review is still very broad in context, the authors explicity state in the text why this is the case.
In addition, they have also strengthened the connection between the sections and changed the title. I am happy to recommend publication.

Editor -Answer
For Editor's text small and bold letters are used.
Associate Editor Comments to Author: Two referees have commented on your paper -the first offers substantive feedback that we'd like you to address in a revision. The second offers a pair of references you may wish to consider including -please note, however, that the editors observe both references are from one author and it is not clear to the editors how critical these reference suggestions are. Please only include these references if you feel it adds value to your work and they can be critically considered in the review -otherwise, please consider disregarding their inclusion as a potential example of 'citation stacking'. This practice is not to be encouraged.
Thank you for encouraging us not to strictly follow the reviewer`s requirements. Authors are in dilemma sometimes either to follow the requirements with which they do not agree or their personal opinions. We belong to the second group of the authors but it is certainly relaxing to obtain the comment like the Editor`s above.
While writing our manuscript, we tried to escape overlapping with the references suggested by Reviewer 2, especially with Ref.
[1], which is larger review paper than our one. However, this is not reason not to mention them and, we think, we should have relied on them a little bit. Hence, we include these references in our manuscript believing that they add value to our work.
We thank the Editor for his work on our manuscript. We believe that the revised version is good enough to be published in RSOS.

Sincerely, The authors
Appendix A

Reviewer 1 -Answer
For Reviewer's text small and bold letters are used. New text in our revised manuscript is blue.
Unfortunately, the overall feeling is that the manuscript reads as a collection of different parts rather than a single review revolving around a specific topic.
We thank the referee for this comment. Our intention is to cover different problems within the broad field of DNA non-linear dynamics, to give a wide overview of the field. In particular, Sections 2 and 3 are free from moving charges and, consequently, free from quantum mechanics. In Section 4 free electrons are present, requiring quantum mechanical approach. While Section 4 may seem uncorrelated from the rest, it should be interpreted as a further layer of complexity that is added on top of the ones described in Sections 2 and 3. In particular, the model we discuss couples the motion of free electrons to the mechanical modes of the DNA structure thus creating a bridge between Section 4 and the others. We now highlight this connection in more detail in the revised text.
In Section 5 we review the state-of-the-art of numerical modelling of DNA mechanics and discuss in more detail recent numerical works that uncovered a coupling between twisting and bending modes in DNA. For instance, bending of the DNA generates twist waves that are reminiscent of the soliton solutions in the PB model. We also discuss that simulations can account for topological constraints, which are usually neglected in analytical models and may profoundly affect non-linear DNA dynamics. Accounting for topological constraints may be an interesting way forward for analytical models.
More generally, the composition of our review aims to target readers that are looking to familiarize themselves with the broad literature of DNA non-linear dynamics. Indeed, we feel that our review will satisfy a reader looking for a comprehensive review that covers not only the most popular analytical methods to treat DNA nonlinearities but also provides a broader context and information on quantum and computational methods. In the revised paper we have focused on strengthening the connections between sections so that a reader will feel that they are parts of a bigger picture. We finally thank the referee for pushing us to improve our work in this direction.
Sections II and III are the most coherent with the title, reporting a review of some of the theoretical models used to investigate the stability of double-stranded DNA with classical theories (although it should be noted that these sections reference 13 papers authored by the