Bi-Symmetric Polyhedral Cages with Nearly Maximally Connected Faces and Small Holes

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. The manuscript focuses on theoretical modeling but should bridge to experimental studies sonochemistry process or etc, on nanoparticle synthesis, which could validate the predicted p-cage geometries.
2. Clarify the choice of parameters (e.g., cooling rate, stopping criteria) in the optimization algorithm.
3. Justify the 10% deformation threshold—does this align with experimental feasibility in protein cages?
4. The manuscript notes some p-cages are "degenerate" (Sec. 4). Could these still be experimentally relevant, or should they be excluded?
5. The abstract is too short and needs to be rewritten by the authors.
6. The introduction briefly mentions artificial protein cages but lacks a detailed discussion on existing synthetic approaches. The authors should incorporate references to: Discuss structural characterization of Zn(II) complexes, relevant to metal-organic cages, covering Ag(I) metal-organic coordination polymers, which could parallel the p-cage design, explore sonochemical synthesis of Pb(II) coordination polymers, a method applicable to p-cage fabrication, and discuss nanostructured Cd(II) complexes, relevant to deformation analysis in p-cages. a)Journal of Molecular Structure 1231 (2021): 129947. b)Journal of Solid State Chemistry 310 (2022): 123013. c) Ultrasonics sonochemistry 42 (2018): 310-319.d)Ultrasonics sonochemistry 39 (2017): 129-136. e) Applied Organometallic Chemistry35.5 (2021): e6181. F) Rev. Roum. Chim., 2022, 67(8–9), 493–501
7. Figure 1 (Graphical Representation): Add labels to distinguish hole-polyhedron edges vs. p-cage faces.
8. Table A1 (Graph List): Include a column noting experimental feasibility (e.g., "likely synthesizable").
9. The supplementary files (OFFS.tar.gz) are helpful but should include a README for non-specialists.
10. Some sections are overly passive (e.g., "It was found that..."). Revise for clarity.
11. Expand Citations: Include more recent works (e.g., **2023–2025**) on protein cage design.

 

 

 

Comments for author File: Comments.pdf

Author Response

All the changes in the paper have been coloured in red except for the extra references.

1)    The manuscript focuses on theoretical modelling but should bridge to
experimental studies sonochemistry process or etc, on nanoparticle synthesis,
which could validate the predicted p-cage geometries.
#

RESPONSE 1 : I have added a statement in the introduction to suggest the use of such technique to
facilitate the synthesis of protein nano-cages.

COMMENT 2) Clarify the choice of parameters (e.g., cooling rate, stopping criteria)
in the optimisation algorithm.
#
RESPONSE 2 : I have added a paragraph in the methodology section to describe the parameters used for the
simulated annealing optimisation.

COMMENT 3) Justify the 10% deformation threshold—does this align with experimental
feasibility in protein cages?
#
RESPONSE 3 :I have added a justification for this choice of 10% where it is first mentioned in the
introduction.

COMMENT 4) The manuscript notes some p-cages are "degenerate" (Sec. 4). Could these
   still be experimentally relevant, or should they be excluded?
#
RESPONSE 4 :I have added a paragraph in section 4 to justify keeping these degenerate geometries.

COMMENT 5) The abstract is too short and needs to be rewritten by the authors.
#
RESPONSE 5 :I have extended the abstract.

COMMENT 6) The introduction briefly mentions artificial protein cages but lacks a
detailed discussion on existing synthetic approaches. The authors should
incorporate references to: Discuss structural characterisation of Zn(II)
complexes, relevant to metal-organic cages, covering Ag(I) metal-organic
coordination polymers, which could parallel the p-cage design, explore
sonochemical synthesis of Pb(II) coordination polymers, a method applicable
to p-cage fabrication, and discuss nanostructured Cd(II) complexes, relevant
to deformation analysis in p-cages.

 a) Journal of Molecular Structure 1231 (2021): 129947.
 b) Journal of Solid State Chemistry 310 (2022): 123013.
 c) Ultrasonics sonochemistry 42 (2018): 310-319.
 d) Ultrasonics sonochemistry 39 (2017): 129-136.
 e) Applied Organometallic Chemistry35.5 (2021): e6181.
 F) Rev. Roum. Chim., 2022, 67(8–9), 493–501
#
RESPONSE 5 : I have added a paragraph in the introduction to link the protein nano-cages to these other
other type of nano-structures. 

COMMENT 7)    Figure 1 (Graphical Representation): Add labels to distinguish
      hole-polyhedron edges vs. p-cage faces.
#
RESPONSE 7 : I have coloured the hole-edges in green leaving the shared edges in black and I have
adjusted the figure caption accordingly.
      
COMMENT 8)    Table A1 (Graph List): Include a column noting experimental feasibility
      (e.g., "likely synthesizable").

RESPONSE 8 : The geometries which will be realisable as protein cages will depend on the properties
of the  constitutive proteins i.e. their flexibility as well as the type of
linkers between the faces. So they are potentially all realisable. 
The Heddle lab  has created experimentally protein nanocages
with deformations close to 4% and so I have added a columns in the appendix tables
providing the number of configurations with deformations below 5%.

COMMENT 9)    The supplementary files (OFFS.tar.gz) are helpful but should include a
      README for non-specialists.
#
RESPONSE 9 : I have added a README.txt file listing a number of software, mostly on them free, to
visualise the off and ply files.

COMMENT 10)    Some sections are overly passive (e.g., "It was found that...").
       Revise for clarity.
#
RESPONSE 10 : I have added some clarifications and improved the narrative flow in a several places.

COMMENT 11)    Expand Citations: Include more recent works (e.g., **2023–2025**)
       on protein cage design.
#
RESPONSE 11 : I have added a few references to more recent work on protein cage design.

 

Reviewer 2 Report

Comments and Suggestions for Authors

In this manuscript Piette describes the classification and characterization of symmetric p-cages. The topic is interesting and the manuscript can be useful for classification of this type of materials by symmetry considerations. The manuscript has been prepared with high care and quality. Thus, I recommend publication of manuscript after addressing following comments:

1) In order to improve the quality and strength of the report I strongly suggest to provide some other examples in the main text or int he supporting information file to support the findings and also provide extra examples to the readers for using the method described in this manuscript.

2) The next issue is the use of this method for other similar materials like MOFs with similar cages. It can be attractive if the author try to evaluate that whether this method can be useful in MOFs or not. 

 

Author Response

All the changes in the paper have been coloured in red except for the extra references.

COMMENTS 1) In order to improve the quality and strength of the report I strongly
suggest to provide some other examples in the main text or int he supporting
information file to support the findings and also provide extra examples to
the readers for using the method described in this manuscript.
#
RESPONSE 1 : I have added an extra 2 example of derivation of the p-cages in section 3.

COMMENTS 2) The next issue is the use of this method for other similar materials like
MOFs with similar cages. It can be attractive if the author try to evaluate
that whether this method can be useful in MOFs or not. 
#
RESPONSE 2 : I have added a sentence in the introduction suggesting that the geometries
described in the paper could be relevant to MOFs if they can be extended
into a lattice but this would obviously require a completely separate study.

 

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript describes a report identifying p-cages made out of 2 families of equivalent polygonal faces/protein rings, where each face has at least 4 neighbours, and where at most 4 faces contribute to the holes.  Additionally, they started construction from a planar graph made out of 2 families of equivalent nodes. Overall, the manuscript is suitable for publication in this journal after minor modifications. 

1. Conclusion part should be more precise, descriptive, and separated from the results and discussion parts.
2. Some of the content needs to be rephrased for better understanding of the results.

Author Response

All the changes in the paper have been coloured in red except for the extra references.

COMMENTS 1)    Conclusion part should be more precise, descriptive, and
separated from the results and discussion parts.
#
RESPONSE 1 : I have added a separate conclusion section at then end of the paper
to summarise our results.

COMMENTS 2)    Some of the content needs to be rephrased for better
understanding of the results.
#
RESPONSE 2 : I have added some clarifications and improved the narrative
flow in a several places.

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript can be accepted in this form