Loop Modeling of the Reciprocal Inhibition Between HPA and HPG Endocrine Axes Reveals Transitions to Bistability and Critical Bifurcation Parameters

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper aims to explain the important and poorly understood interactions between the HPA and HPG axis. While the mathematics involved are outside my area of expertise, the conclusions appear to be logical from the data presented. The authors make a compelling case for how HPA-HPG interactions may be associated with specific pathologies which can provide valuable insight into potential therapeutic targets.

Points to address:

• There could be greater transparency for "Literature survey" methods by following PRISMA guidelines. In particular, it would be helpful to give exact Boolean operators (Line 100) and the total number of papers this yielded (Line 105). It would also be helpful to know of any inclusion/exclusion criteria.
• "Pink boxes" appear orange on the PDF version reviewed - HEX #F2AA84 (Line 190). Likewise, "red lines" appear pink on PDF - HEX #FF2F92 (Line 195).
• For Figure 2, the variables used to describe specific components change between your 3 models. For example, across your models, X3 refers to both "DMH RFRP3 neurons" and "anterior pituitary ACTH cells", while X5 refers to both "gonadal progesterone cells" and "adrenal cortisol cells". For clarity, it may be worth either using consistent labelling between models, or being more explicit in the figure legends as done for Figure 3 & 4.
• The discussion mentions GR as a potential therapeutic target (Lines 691 & 701). While this is interesting, it must be noted that any attempt to manipulate GR pharmacologically is likely to lead to unwanted peripheral effects.

Author Response

• We thank the Editors and the Reviewer for the comments below, which have enabled us to improve the content of our article. Reviewer comments are reported in italics and our replies in Roman.
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• Comment 1. There could be greater transparency for "Literature survey" methods by following PRISMA guidelines. In particular, it would be helpful to give exact Boolean operators (Line 100) and the total number of papers this yielded (Line 105). It would also be helpful to know of any inclusion/exclusion criteria.
• Thank you for this comment. We added exact Pubmed Boolean operators and the number of results for each of them. (Page 3, Line 106)

• Comment 2. "Pink boxes" appear orange on the PDF version reviewed - HEX #F2AA84 (Line 190). Likewise, "red lines" appear pink on PDF - HEX #FF2F92 (Line 195).
• Thank you for this specification. In the caption of Figure 1, reference to colors has been changed as indicated by the reviewer.  (Page 5, Lines 198 and 203)

• Comment 3. For Figure 2, the variables used to describe specific components change between your 3 models. For example, across your models, X3 refers to both "DMH RFRP3 neurons" and "anterior pituitary ACTH cells", while X5 refers to both "gonadal progesterone cells" and "adrenal cortisol cells". For clarity, it may be worth either using consistent labelling between models, or being more explicit in the figure legends as done for Figure 3 & 4.
• We agree with this observation. The numbering of the variables follows the arrangement of the variable arrays in the Matlab codes. To address this point, we have included in the caption the correspondences between the variables and their biological counterparts, as also made explicit in Box 1. (Page 7, Line 334)

• Comment 4. The discussion mentions GR as a potential therapeutic target (Lines 691 & 701). While this is interesting, it must be noted that any attempt to manipulate GR pharmacologically is likely to lead to unwanted peripheral effects.
• We thank the Reviewer for this valuable observation. We have briefly addressed this point in the Discussion. (Page 17, Line 693)

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript titled “Loop modeling of the reciprocal inhibition between HPA and HPG endocrine axes reveals transitions to bistability and critical bifurcation parameters” provides a quantitative framework to explore how feedback structures generate emergent properties, such as bistability, where the system can reside in one of two stable states, and critical bifurcation points, which delineate transitions between these states. Overall, the topic holds merit, though it needs some improvements before possible publication in the journal.

 

1. It would be helpful to explain why a deterministic ODE framework was selected over stochastic or pulsatile approaches. Clarifying how this choice may influence the interpretation of the bistable states would strengthen the study.
2. A balanced discussion of limitations would further enhance the manuscript’s scientific impact.
3. Please discuss how future models might explore or validate this phenomenon in broader biological contexts.
4. The concluding statement on future directions is appropriate, but could be more impactful by suggesting 1–2 concrete research directions or applications that this work enables.
5. The references are sufficient in number, but some are outdated. Updating the references will ensure the manuscript remains timely and relevant.

Author Response

• We thank the Editors and the Reviewer for the comments below, which have enabled us to improve the content of our article. Reviewer comments are reported in italics and our replies in Roman.
•  
• Comment 1. It would be helpful to explain why a deterministic ODE framework was selected over stochastic or pulsatile approaches. Clarifying how this choice may influence the interpretation of the bistable states would strengthen the study.
• We thank the reviewer for this comment, which addresses the core meaning of our study. As more clearly emphasized now in the new subsection on the study’s limitations (Page 18, Line 717), our work is grounded in a general hypothesis that models life as a network of closed chains of interactions (loops) interconnected in various ways. Since such systems can be described as nonlinear dynamical systems with regular attractors, the hypothesis supports the view that life is fundamentally a deterministic process. In this framework, all life processes can be understood as the maintenance of single equilibrium points, or cyclic and quasi-cyclic attractors (homeostasis), or alternatively, as transitions from one equilibrium state to another (changes). This type of dynamics explains why life exhibits determinism—namely, the absence of butterfly effects and strange attractors—despite the presence of noisy components in its biochemical and biophysical processes. While noise may affect the trajectories of the system in phase space, the system is inevitably drawn toward a regular attractor, thereby ensuring a highly predictable outcome. This is the rationale for modeling the HPA–HPG interaction through sets of closed-chain interactions and deterministic ODEs. We acknowledge, of course, that endocrine processes are known to rely on pulsatile mechanisms that generate oscillations. To account for this, we incorporated oscillatory dynamics into two versions of the model: first, by expanding each endocrine axis into a negative loop (with oscillatory attractor), and second, by introducing a sinusoidal input to the HPA axis to represent the effect of the circadian clock. This latter oscillatory input is also assumed to arise from an underlying negative loop; however, expanding the model to include that system explicitly was beyond the scope of the present study.
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  Comment 2. A balanced discussion of limitations would further enhance the manuscript’s scientific impact.
• This is indeed an appropriate suggestion, which has led us to include a paragraph discussing the limitations of the study. Accordingly, we have divided the Discussion into two subsections: the first corresponding to the original content, and the second specifically dedicated to clarifying the study’s limitations. (Page 18, Line 717)

 

• Comment 3. Please discuss how future models might explore or validate this phenomenon in broader biological contexts.
• The new section of the Discussion, addressing the study’s limitations, critically examines the theoretical framework underlying this work and we think that, by generalizing its implications, also provides a response to the reviewer’s request. In other words, a general model has been already presented in previous papers, which has been now more explicitly stated in the new part of the text.

 

• Comment 4. The concluding statement on future directions is appropriate, but could be more impactful by suggesting 1–2 concrete research directions or applications that this work enables.
• The sentence to which the reviewer refers is in the Conclusions section, which, by its nature, provides a concise summary of the essential findings and perspectives of the work. In contrast, in the Discussion section, we have more clearly addressed the objectives that should be pursued to correct HPA–HPG impairments, specifically identifying the p_d parameter of our mathematical model as a key element for effectively manipulating the biological system, and proposing GRs as (part of) the potential biological counterparts of this mathematical component (Page 17, Line 690). This approach reflects the methodology that pathophysiological, biomedical, and pharmacological studies should adopt when seeking solutions for diseases. Furthermore, we provide examples of disorders to which the model developed in this study could be applied (Page 17, Line 700). Naturally, the model cannot deliver immediate solutions, as further data should be required because existing biological data are generally collected under a framework that largely disregards the modeling of the dynamic processes underlying life.
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• Comment 5. The references are sufficient in number, but some are outdated. Updating the references will ensure the manuscript remains timely and relevant.
• We acknowledge the reviewer’s observation and have replaced outdated references with more recent ones wherever possible. The following list shows, for each substitution, the original reference followed by the updated one; the position in the References is also indicated.

• {Runnebaum, 1972 #12} -> {Kottler, 1989 #12}

  {Russell, 2019 #6} -> {Agorastos, 2022 #6}

  {Donoso, 1986 #28} -> {Di Giorgio, 2019 #29}

  {Kessler, 2003 #62} -> {Albert, 2015 #62}

  {Holsboer, 2000 #64} -> {Anacker, 2011 #64}

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

None