Anisotropic Network Patterns in Kinetic and Diffusive Chemotaxis Models

Round 1

Reviewer 1 Report

In this work, authors have presented an anisotropic chemotaxis model to study network formation. The work is interesting. however, there are a number of points that authors need to address.

1. From the title, it appears that authors will discuss multiple models, however, they are focusing on a single model. The title needs to be amended to reflect that they are discussing a single model and their focus on endothelial cells.
2. The introduction is very short and does not clearly state why the work is significant and it's future impact.
3. The authors claim that they have conducted experiments to validate the results. However, it appears they are referring to their numerical simulation as an experiment.  Authors need to clarify this and not refer to different iterations and numerical evaluations as experiments with cells. If any such experiments were conducted, authors need to provide methods and materials including culture conditions and platforms used to study chemotaxis.
4. Authors should provide a quantitative plot of velocity mixing vs cell density with variable cell densities.
5. Diffusion plots as a function of cell densities and time should be provided as well.
6. Authors should proof read the document as there are a number of grammatical and sentence formation errors.

Author Response

Referee #1

In this work, authors have presented an anisotropic chemotaxis model to study network formation. The work is interesting, however, there are a number of points that authors need to address.

1. From the title, it appears that authors will discuss multiple models, however, they are focusing on a single model. The title needs to be amended to reflect that they are discussing a single model and their focus on endothelial cells.

Response: The plural was used to indicate a mesoscopic and a macroscopic model. We changed the title to clarify this:  Anisotropic Network Patterns in  kinetic and diffusive Chemotaxis Models

1. The introduction is very short and does not clearly state why the work is significant and it's future impact. 

Response: Some of the material that is typically in an introduction was presented in the Background section. We re-arranged some of this material and also added a paragraph on the significance and impact. 

1. The authors claim that they have conducted experiments to validate the results. However, it appears they are referring to their numerical simulation as an experiment.  Authors need to clarify this and not refer to different iterations and numerical evaluations as experiments with cells. If any such experiments were conducted, authors need to provide methods and materials including culture conditions and platforms used to study chemotaxis. 

Response: We are sorry that we were not very clear here. We used experiments only in the context of numerical experiments. We clarified this now throughout the text. 

1. Authors should provide a quantitative plot of velocity mixing vs cell density with variable cell densities. 
2. Diffusion plots as a function of cell densities and time should be provided as well.

Response: Thank you for this great idea. We added plots in Figure 6, where we show the amplitude of the anisotropic flux and the amplitude of the chemotactic flux as functions of space and time. This presentation helps to understand how these fluxes interact, and how they relate to orientation and to particle density. It allowed us to make a much stronger argument.  

1. Authors should proof read the document as there are a number of grammatical and sentence formation errors. 

Response: Upon careful editing, we found about 50 small errors. We are sorry for the sloppy editing of the first version and we hope that these issues are fixed now. 

Reviewer 2 Report

I suggest a minor revision to improve the quality of the presentation of the methodology here applied.

The present work is interesting from a  modeling point of view, even if it borrows pre-existent elements from other studies.

In my opinion, the main novelty here is the numerical study about the competition between the chemotaxis directionality and the tissue anisotropy. 

However, the authors should devote a better care in describing their approach and stress the novelty in comparison to the previous literature (also of the same authors) about this topic and in particular, respect to the works by Serini and Kumar.

Author Response

I suggest a minor revision to improve the quality of the presentation of the methodology here applied. The present work is interesting from a  modeling point of view, even if it borrows pre-existent elements from other studies. In my opinion, the main novelty here is the numerical study about the competition between the chemotaxis directionality and the tissue anisotropy. 

However, the authors should devote a better care in describing their approach and stress the novelty in comparison to the previous literature (also of the same authors) about this topic and in particular, respect to the works by Serini and Kumar.

Response: Thank you for this comment. A similar remark was made by Referee #1. We extended the Introduction section and we clearly highlight the previous work of Serini and Kumar. We also added two more references of those authors. 

Round 2

Reviewer 1 Report

Authors have appropriately addressed the reviewer comments.