PONE-D-23-16506Coherent feedback leads to robust background compensation in oscillatory and non-oscillatory homeostatsPLOS ONE

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Reviewer #1: Yes

Reviewer #2: Partly

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Reviewer #2: N/A

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: Yes

Reviewer #2: No

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Reviewer #1: The manuscript titled ‘Coherent feedback leads to robust background compensation in oscillatory and nonoscillatory homeostats’ by Nyg˚ard et al. proposes a control scheme that can provide disturbance rejections in the presence of multi-dimensional disturbances. The proposed scheme is technically rigorous and has been corroborated with sufficient case studies, thereby containing the potential to be a valuable addition to the literature. However, the following concerns may be addressed before the publication of this manuscript. Further, all the required details for the simulation studies have been made available.

 1. In the very first sentence of the abstract, the authors need to explicitly mention that the step perturbation is applied at the output terminal and, further, the sign of the step perturbation.

2. The term ‘background’ in the context of regulatory control would not be very clear to a control theorist. Therefore, the authors may consider spending a few lines on clarifying what changing background means in the language of systems theory. As I understand, the background in this manuscript, is mapped to the output of the control (also known as the error variable in control literature). Therefore, at the onset of step perturbations, in the absence of additional supervisory control, the existing integral control scheme can not drive the output to the previous steady state due to the change in the control output of the controller— This needs to be reflected properly in the manuscript.

3. Is it not already well-established in the literature of regulator theory that an integral control scheme is robust to parametric fluctuations as long as 1) the fluctuated parameters belong to the process and 2) the overall stability is not altered?. Further, this has also been shown to be the case by Bhattacharya et al. (2023), Mathematical biosciences. The K10 or the background species, only appears at the process dynamics. Therefore, any perturbations on K1 should ideally have no effect in dictating the steady state of the system. Therefore, I request the authors to clarify and rephrase the contributions of this manuscript in light of this observation.

4. A large part of the manuscript assumes zero-order kinetics. While I appreciate the fact that the zeroth-order kinetics is mathematically convenient both for analysis and demonstration, it also limits the generalizability of the results to a great extent. Therefore, at least a brief discussion of possible generalizations to other rate kinetics is warranted.

Minor: Please perform a thorough reading of the manuscript. Although the manuscript is well-written, and the language is quite good at most of the time, I can spot multiple proofing errors throughout.

Reviewer #2: Referee's report: PLOS ONE (PONE-D-23-16506)\\\\

Title:{\\it ``Coherent feedback leads to robust background compensation in oscillatory and non-oscillatory homeostats'' }\\\\

Author: M. Nygard, P. Ruoff\\\\

Although the authors do a good job on the technical part of the manuscript (ms), which is more of an engineering analysis than a dynamic study, I cannot recommend the ms in its present form. The English scientific prose needs to be revised and improved. In general, the ms is awkward because the dynamic variables are never explicitly related to measurable physical properties of a biological system. The authors mention the photoadaptation of photoreceptors but never connect the dynamic variables ($A, E, I_1, I_2$) to the actual measurable properties of an experimental biological system. In summary, without a relationship between the dynamic variables in the ms, and real, measurable physical properties of a biological system, the ms is too vague to be of any interest to chemists, biologists, and physiologists. I would ask the authors, what is your target audience?

Although I could guess that the variables ($I_1, I_2$) are some kind of feedback inputs, I could not understand the dynamic variables `a' and `e,' which the authors do not mention in their ms. What is the difference between e, in Eq. 4, 12, and a, in Eqs. 20, 28? The physical interpretation of these dynamic variables is not explained in the ms.

In line 20, the authors try to explain the onset of oscillations. But why is it that the authors are not considering bifurcation diagrams to find, in particular, the Poincare-Andronov-Hopf (PAH) bifurcation? Bifurcation diagrams complement and determine the stable and unstable branches of the steady states of dynamic systems.

In line 258, the authors try to relate the Hill equation to the Michaelis-Menten equation. But the Michaelis-Menten is a particular case of the Hill equation with $\\alpha =1$, which is a more general equation. In the ms, one could interpret the generality of the Hill equation incorrectly. But more importantly, if the authors use Michaelis-Mente expressions, one may wonder if the authors are considering enzymatic reactions. If they are, the authors could give the readers some examples.

Here are some issues:\\\\

1 - Besides the issue of the ms belonging to an engineering journal, the revised ms does not, in my opinion, reaches an appropriate quality of the written modern scientific English prose.\\\\

2 - The authors ignored punctuation rules and missed too many commas. The ms should be revised for punctuation.\\\\

3 - Quotates should be revised and corrected. For example, in line 76, 'outer' should be `outer.' Notice the first quotation\\\\

4 - One cannot start a sentence with an abbreviation, like Fig 4a, or a symbol like E.\\\\

5 - in modern scientific English prose, one must write using complete sentences. In particular, all the figure captions should be written with complete sentences and should start with `` Figure ...,'' rather than ``Fig ...''.\\\\

6 - In general, the ms is written in awkward English prose. A knowledgeable person of written English prose should revise the ms.\\\\

7 - In line 60, the sentence `` In the below calculations we have used ..'' is missing the proper punctuation and is too awkward and should be rewritten.\\\\

8 In line 71, another awkward sentence, ``The type of oscillations we here focus on ..''.\\\\

9 - in modern scientific English prose, one must avoid short paragraphs, in particular one-sentence paragraphs, like in lines 20 and 125.\\\\

10 - In a paragraph starting at line 281, one should not quote other authors in an original research report. Authors should leave those quotations to review or historically relevant reports.\\\\

In modern scientific English prose, one writes in an active voice. The use of passive voice is restricted to cases where one does not know the subject or does not care about the subject. For example, in Figures 1 and 2, the authors write `` flashes were applied''. The natural question is who applied these flashes. It is unclear if the authors or other researchers gathered the information in Figures 1 and 2. Also notice line 27, where the authors write ``...control was previously observed by us ..'' The sentence is awkward and should be written in an active voice.

The ms lacks a relevant Conclusion section, where the authors should compare and relate their results with at least one physical system. In other words, if the authors are interested in retinal light adaptation, they should connect the dynamic variables $(A, E, I_1, I_2, e$ or $a$) to the measurable physical properties of a biological system.

Although I find the technical aspects developed by the authors publishable in an {\\bf engineering} journal, I do not recommend publication in PLOS ONE in its present form. Still, I strongly recommend thoroughly revising the ms for clarity.

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Reviewer #1: No

Reviewer #2: No

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Coherent feedback leads to robust background compensation in oscillatory and non-oscillatory homeostats

PONE-D-23-16506R1

Dear Dr. Ruoff,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Karthik Raman, Ph.D.

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

The authors have satisfactorily addressed all reviewer comments.