Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript:

“Dynamics of the Aggregation of Cells with Internal Oscillators”, by T. Glimm and D. Gruszka (Ref. No.: mathematics-3887653-peer-review-v1),

contains an interesting material that may be suitable for publication in Mathematics. However, the manuscript is not well-organized and requires a significant elaboration. In particular, the objective and the novelty of this work is somewhat vague and, therefore, should be stronger emphasized. The authors should also discuss if the proposed model is completely new or a just modification of the known one. It would be desirable if the comparisons with other well-known models could be provided. Moreover, the advantages and disadvantages of the proposed model should also be discussed.

English is acceptable. However, the manuscript requires more citations.

Apart from this, the following should be taken into account:

Abstract
1) Key quantitative results, obtained in this study, should be shown.
2) Abstract should show the novelty or originality of this study.

1. Introduction
1) The sentence: “Once formed, these aggregates undergo compaction: clusters round up, compact, and, by growing in the third dimension, become spherical”, should be cited.

2) What are cAMP, Frz and MglAB? All abbreviations should be defined.

3) The sentence: “Specifically, we address the question how the oscillations in swarmalator-type behavior influence aggregation”. What is the specific novelty in this study?

4) The sentence: “In their model, cell-cell adhesion varies with clock phase, similar to the model in this paper”. Is your model is new? If not, how did you modify the existing model? More details are required.

2. The model
1) If this model is completely new, then it should be renamed as ‘Proposed model’. Otherwize, it should be called as ‘Modified model’.

2) The sentence: “Aggregation is modeled via the fact that two cells are more likely to move towards each other than away from each other”. It is not clear what can motivate two cells more likely to move towards each other than away from each other. The clarifications are required.

3) The sentence: “Each hexagonal node has six “channels”. Why hexagonal node has specifically six channels (why not 5 or 7, for example)?

4) All main equations should be cited.

5) The sentence: “Simulations were run on a standard PC with 64 GB RAM and an Intel Core 17-1370P 1.90 GHz processor”. It seems that it should be Intel Core i7-1370P, not 17-1370P.

6) The sentence: “To account for the periodic boundary conditions, we joined up copies of the image regions …”.

3. Results
1) The section ‘Results’ should be merged with section ‘Results and discussion’ as these results should be discussed in parallel.

2) The sentence: “As these aggregates grow in size, their number decreases, from initially about 1700 to around 100 within 40 time steps”. Why specifically these numbers are used?

3) All main equations should be cited.

4. Discussion
1) The sentence: “We investigated two different, but closely related models of the adhesion-mediated aggregation of cells with internal oscillators (’clocks’) and their synchronization”. Which model is more relevant for practical application?

2) What are the advantages and disadvantages of these two models?

3) The comparisons of the proposed model with our well-known models should be shown.

4) The section ‘Conclusion’ is needed.

The manuscript requires a major mandatory revision.

Author Response

We thank the reviewer for their careful reading of our manuscript and their many queries. Please see the attachment for our detailed replies.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

please see the attachment.

Comments for author File: Comments.pdf

Author Response

We thank the reviewer for their careful reading of our manuscript. Please see the attachment for our reply.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript:

“Dynamics of the Aggregation of Cells with Internal Oscillators”, by T. Glimm and D. Gruszka (Ref. No.: mathematics-3887653-peer-review-v2),

is improved after a major revision. In particular, the authors show the originality of their study. The authors clarified regarding the originality of their model and show how the internal oscillations in swarmalator-type behavior influence aggregation of cells. Therefore, the work may be considered suitable for publication. Moreover, the authors provided more material, clarification and citations. However, the manuscript still requires some amendments and the following should be taken into account:

1) All main equations should be cited.

2) The sentence: “We joined up 91 copies of the simulation domain to create one big picture with periodically repeating images arranged in a hexagonal shape”. Why specifically 91 copies were used? This should be justified.

3) The section '4. Conclusions’ is too excessive and looks like a discussion. The significant part of the section should be discussed in the section '3. Quantitative Results’

4) Is it possible accuracy of the models shown in [13] and current work? We do not know how the proposed models match with real data.

The manuscript requires a minor revision.

Author Response

We thank the referee again for their helpful comments. Please see the attachment for our replies.

Author Response File: Author Response.pdf