SimuCell3D: three-dimensional simulation of tissue mechanics with cell polarization

The three-dimensional (3D) organization of cells determines tissue function and integrity, and changes markedly in development and disease. Cell-based simulations have long been used to define the underlying mechanical principles. However, high computational costs have so far limited simulations to either simplified cell geometries or small tissue patches. Here, we present SimuCell3D, an efficient open-source program to simulate large tissues in three dimensions with subcellular resolution, growth, proliferation, extracellular matrix, fluid cavities, nuclei and non-uniform mechanical properties, as found in polarized epithelia. Spheroids, vesicles, sheets, tubes and other tissue geometries can readily be imported from microscopy images and simulated to infer biomechanical parameters. Doing so, we show that 3D cell shapes in layered and pseudostratified epithelia are largely governed by a competition between surface tension and intercellular adhesion. SimuCell3D enables the large-scale in silico study of 3D tissue organization in development and disease at a great level of detail.

-Please provide more explanation on whether or not the contact stiffness between the cells or the parameters with respect to surface tension are realistic.
-Regarding the lumen-based system, please discuss whether or not any ECM on the apical side, or an apical actin ring, is taken into account.
-With regard to the adhesion model, please show whether or not it scales consistently with the resolution of the cell triangulation.
-Please indicate or demonstrate how the lack of stochastic forces in the simulations affects the results.
-The literature review section lacks enough discussion on previous cell-based methods for tissue simulation and should be elaborated.
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We look forward to hearing from you soon.This paper presents a tissue simulation software based on agent-based technology whereby the cells are represented as highly deformable objects ("Deformable Cell Model", DCM).The DCM is not a new methodology, and many aspects, as presented in this paper, are state-of-the-art and already described in earlier works.Here, the authors present a software package that they claim can simulate several 1000 to 100,000 cells in a time frame of 1 day of simulation time.This result is impressive, as it may increase the overall interest in the method significantly , which is now somewhat plagued by the large computational times.

Best,
Overall, the paper is well written and I find the results interesting and partially convincing.In this regard, some more explanation on the results is necessary and the method descriptions lacks some detail on several occasions.

My most important comments are:
1. Regarding the computational time diagram: Is this result obtained for cells each containing a nucleus inside ?Furthermore, despite the claim of being able to simulate growing systems up to 100,00 cells, there is no clear visual proof.Can the authors give more detail which system they actually simulate to achieve this ?2. In my opinion, the friction model is somewhat simplified because it does not take friction between the cells into account.As a result, pure shearing effects between cells are not capture in the model.This simplification also greatly simplifies the system to solve and probably explains why the authors are capable of simulating such high cell numbers.I think the authors should clearly discuss this issue.3. The large timestep (1000 s in the overdamped case) also explains why the simulations can handle such large cell numbers.However the maximum timestep that can be used in a stable simulation is usually determined by several parameters, for example stiffness values.I am bit surprised that such a large timesteps can be used in this DCM.Can the authors give more explanation on whether the contact stiffnesses between the cells or the parameters with respect to surface tension are realistic ?What are the limitations here ?Are the results sufficiently independent of the used timestep?4. Regarding the lumen-based system.Did the authors take any ECM on the apical side, or an apical actin ring into account?This is often observed in organoids.Furthermore I have some doubts about the results in Figure 3 in the sense that cells are not dividing.Cells dividing will create large mechanical perturbations and as such I am not sure whether the observed structures (or the phase diagram Fig 3e) would be the same after several cell divisions.5.I am puzzled with how the authors achieved to simulate a cell splitting up almost completely in two parts (Fig 4c).The two cell parts are apparently only separated with a cord.Where does this cord come from ?Can the authors be more clear on whether this is an emerging effect of the remeshing?I am a bit doubtful whether this splitting effect will not introduce artifacts in the simulations.In principle, a more indept analysis of the remeshing scheme should be present, for example by showing that remeshing algorithm does not increase or decreasing the energy for one cell.6.With regard to the adhesion model, I have my doubts whether it scales consistently with the resolution of the cell triangulation.In my opinion the authors should prove that experiments that measure contact angles between cells, or pull off forces between cells, can be reproduced with the model.In the work by Smeets et al. (e.g.https://www.sciencedirect.com/science/article/pii/S0006349523002680#fig4)this has been investigated thoroughly.7. Stochastic forces may play an important role in cellular systems.Surprisingly there seems to be no stochastic components (due to thermal fluctuations) in the simulations.Is there any reason for that ?Can the authors indicate how this affects the simulation results?
Reviewer #1 (Remarks on code availability): I had no time to review the code.Note that code for such models can be very large, and it may take a long time to review and test them thoroughly.

Reviewer #2 (Remarks to the Author):
This manuscript represents promising work in modelling the mechanics of large assemblies of cells in 3D.As the authors note, it accounts for growth, proliferation, extracellular matrix, fluid cavities, nuclei, and non-uniform mechanical properties of polarised epithelia at subcellular resolution.It therefore is relevant to spheroids, vesicles, sheets, tubes, and other tissue structures whose geometries can be obtained from microscopy images and their mechanics can be modelled.The authors also have presented two simulations of 3D many-cell structures that are impressive: the formation and maintenance of layered epithelia, and cellular organization in a "pseudostratified" epithelium.The computational treatment is detailed and uses a range of techniques in triangulation, mesh refinement and rezoning.The mechanics is treated by nodal force balance over the quasi-static, second-and first-order (overdamped) dynamic regimes.The forces themselves are obtained as the gradients of an energy functional accounting for area, volume and curvature elasticities.
My opinion, however, is that to qualify for Nature Comp Sci, work of this type needs to be either (a) of much greater scope drawing from a range of multiscale of multiphysics methods (for example using molecular, particlle scale and continuum models or coupling chemistry, transport and mechanics in cells), or (b) the culmination of a series of focused earier works, each of them going into significant depth in different aspects (the foundational physics, numerical methods, a few case studies...).The current manuscript does fall into either of these classes (a) or (b).It does, however fulfill the role of a manuscript representing a first step along Path b above.For this reason, I suggest that it may be more suitable for a forum in computational cell biology.
Reviewer #2 (Remarks on code availability): No, but from the examples presented here, I expect it works as advertised.
Reviewer #3 (Remarks to the Author): The paper "SimuCell3D: 3D Simulation of Tissue Mechanics with Cell Polarization" is a very well structured and written article.
Here, the authors present a novel simulation implementation for individual cell-based modelling, which can produce (computationally) efficiently large tissues in 3D, representative of the real biological processes.The software is open-source, and to be made available to the public upon publication.The authors detail how their software is capable of describing subcellular resolution, growth, proliferation, extracellular matrices, fluid cavities, cell nuclei and cell polarity.The then present how their implementation can easily model spheroids, vesicles, epithelial sheets and tubes, as well as monolayer, pseudostratified and stratified tissue structures.The basis for the model implementation is class of Deformable Cell Model, implemented in 3D.
I have a some minor comments.This article was a pleasure to read, and following these comments being address, I would recommend the article for publication.
Comment 1: The authors may wish to include a reference to the 2023 Advanced Materials paper by Schamberger et.al. which will emphasis this papers relevance and usefulness even more.
Comment 2: The literature review section lacks enough discussion on previous cell-based methods for tissue simulation.
Comment 3: The statement: "The high level of spatio-temporal details of cell-based models, however, entails a substantial computational cost which forces them to a tradeoff between the number of cells they can simulate and the spatial resolution of their representation." Is made without any discussion or reference -a relevant reference or explanation should assist this statement, as the authors seem to provide a counter example to this statement in this very paper.
Comment 4: Similar justification is needed for the statement: "vertex models are unsuitable for tissues that possess complex cell shapes or undergo phenomena such as cell extrusion or luminogenesis." Comment 5: On Page 3, the statement is made: "SimuCell3D overcomes the classical trade-off that has so far constrained cell-based models between their resolutions and the number of cells they can simulate."

Without providing reasoning or justification.
Comment 6: There is a word (one/us/…) missing in the sentence: "In addition, our program natively allows ____ to represent intra…" Comment 7: The statement: "which preserves numerical stability of the program even under large cell deformations." Is made, but there is no discussion about numerical stability.Please expand upon this point.Is it sensitive to time step, and what type of stability is being describe?Comment 8: Following Equation 1, please state that the "W" in dW/dV is work, as this may not be immediately obvious (it's clear in the methods but not here).
Comment 9: Please expand upon how the time complexity for the presented approach is found to be order N_{c}^{4/3}, as I would have thought it scaled with the number of nodes, rather than cells.
Comment 10: On page 5, 4 lines from the bottom, I believe the words "study case" may need to be flipped?
Comment 11: On page 6, I believe a word (one/us/…) may be missing: "SimuCell3D also allows ___ to directly modulate the shapes …" Comment 12: In the Methods section, can you please provide explanation why l_{max} = 3 x l_{min} is sufficient?Is this arbitrary, and how sensitive are the results to this? Comment 13: On page 7, the final paragraph again describes sources of numerical stability.Please provide some further explanation as to why this occurs and how it may be prevented.
Comment 14: Throughout the article, the jet colour pallet is used, except for Figure 4f.This jet colour pallet makes it difficult to observe small changes in variation, particularly nonmonotonic variation (e.g. Figure 3e).Is it please possible the colour pallet used in Figure 4f is used throughout?Comment 15: I would really enjoy to see some simulation output videos to accompany the Vesicle, spheroid, sheet, and tube in Figure 1.
Comment 16: I am curious to know if the software has been optimised for parallel computation across all 16 threads?If so, in the comparison to other method of Table 1, are these other implementations similarly optimised/parrellel?If these are single thread implementations, I am curious to see how SimuCell3D compares on a single thread also.
Comment 17: All equations should be punctuated."." if the end of a sentence as for first equation on page 3 and 9 and a "," if its in the middle of a sentence as on page 8 (and others).
Comment 18: There is a reversed bracket in one of the limits in Equation (2).
Reviewer #4 (Remarks to the Author): The paper "SimuCell3D: 3D Simulation of Tissue Mechanics with Cell Polarization" is a very well structured and written article.
Here, the authors present a novel simulation implementation for individual cell-based modelling, which can produce (computationally) efficiently large tissues in 3D, representative of the real biological processes.The software is open-source, and to be made available to the public upon publication.The authors detail how their software is capable of describing subcellular resolution, growth, proliferation, extracellular matrices, fluid cavities, cell nuclei and cell polarity.The then present how their implementation can easily model spheroids, vesicles, epithelial sheets and tubes, as well as monolayer, pseudostratified and stratified tissue structures.The basis for the model implementation is class of Deformable Cell Model, implemented in 3D.
I have a some minor comments.This article was a pleasure to read, and following these comments being address, I would recommend the article for publication.
Comment 1: The authors may wish to include a reference to the 2023 Advanced Materials paper by Schamberger et.al. which will emphasis this papers relevance and usefulness even more.
Comment 2: The literature review section lacks enough discussion on previous cell-based methods for tissue simulation.

Comment 3:
The statement: "The high level of spatio-temporal details of cell-based models, however, entails a substantial computational cost which forces them to a tradeoff between the number of cells they can simulate and the spatial resolution of their representation." Is made without any discussion or reference -a relevant reference or explanation should assist this statement, as the authors seem to provide a counter example to this statement in this very paper.
Comment 4: Similar justification is needed for the statement: "vertex models are unsuitable for tissues that possess complex cell shapes or undergo phenomena such as cell extrusion or luminogenesis." Comment 5: On Page 3, the statement is made: "SimuCell3D overcomes the classical trade-off that has so far constrained cell-based models between their resolutions and the number of cells they can simulate."

Without providing reasoning or justification.
Comment 6: There is a word (one/us/…) missing in the sentence: "In addition, our program natively allows ____ to represent intra…" Comment 7: The statement: "which preserves numerical stability of the program even under large cell deformations." Is made, but there is no discussion about numerical stability.Please expand upon this point.Is it sensitive to time step, and what type of stability is being describe?Comment 8: Following Equation 2, please state that the "W" in dW/dV is work, as this may not be immediately obvious.
Comment 9: Please expand upon how the time complexity for the presented approach is found to be order N_{c}^{4/3}, as I would have thought it scaled with the number of nodes, rather than cells.
Comment 10: On page 5, 4 lines from the bottom, I believe the words "study case" may need to be flipped?
Comment 11: On page 6, I believe a word (one/us/…) may be missing: "SimuCell3D also allows ___ to directly modulate the shapes …" Comment 12: In the Methods section, can you please provide explanation why l_{max} = 3 x l_{min} is sufficient?Is this arbitrary, and how sensitive are the results to this? Comment 13: On page 7, the final paragraph again describes sources of numerical stability.Please provide some further explanation as to why this occurs and how it may be prevented.
Comment 14: Throughout the article, the jet colour pallet is used, except for Figure 4f.This jet colour pallet makes it difficult to observe small changes in variation, particularly nonmonotonic variation (e.g. Figure 3e).Is it please possible the colour pallet used in Figure 4f is used throughout?Comment 15: I would really enjoy to see some simulation output videos to accompany the Vesicle, spheroid, sheet, and tube in Figure 1.
Comment 16: I am curious to know if the software has been optimised for parallel computation across all 16 threads?If so, in the comparison to other method of Table 1, are these other implementations similarly optimised/parrellel?If these are single thread implementations, I am curious to see how SimuCell3D compares on a single thread also.
Comment 17: All equations should be punctuated."." if the end of a sentence as for first equation on page 3 and 9 and a "," if its in the middle of a sentence as on page 8 (and others).
Comment 18: There is a reversed bracket in one of the limits in Equation (2).Thank you for submitting your revised manuscript "SimuCell3D: 3D Simulation of Tissue Mechanics with Cell Polarization" (NATCOMPUTSCI-23-0381B).It has now been seen by the original referees and their comments are below.The reviewers find that the paper has improved in revision, and therefore we'll be happy in principle to publish it in Nature Computational Science, pending minor revisions to satisfy the referees' final requests and to comply with our editorial and formatting guidelines.

Author Rebuttal to
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Best, Fernando
--Fernando Chirigati, PhD Chief Editor, Nature Computational Science Nature Portfolio ORCID IMPORTANT: Non-corresponding authors do not have to link their ORCIDs but are encouraged to do so.Please note that it will not be possible to add/modify ORCIDs at proof.Thus, please let your co-authors know that if they wish to have their ORCID added to the paper they must follow the procedure described in the following link prior to acceptance: https://www.springernature.com/gp/researchers/orcid/orcid-fornature-researchReviewer #1 (Remarks to the Author): I appreciate vey much the improvements in particular the test of the model verification with the contact law of Young Dupré.Some (minor) remarks -Please check the value of the omega ( adhesion strength) in FIG S4 as compared to Table 2 as they differ multiple orders of magnitude.
-I understand the behavior of the cells in Fig4 better now.However, with regard to the mesh deformation, the authors write in the rebuttal letter that the term "unphysiological" behavior corresponding to Fig4c left, right was mentioned in the manuscript; however I could not find this in manuscript.Perhaps the behavior explained in the letter could be transferred (or parts of it) to the manuscript.
-I remain a bit critical about how the computational efficiency of the code is communicated in the paper (Fig1e).I have little reason to doubt that their code is efficient compared to other codes, yet the example simulation of a spheroid up to 100000 cells in a day from one cell is a bit misleading because of the unphysiologically large growth rates to achieve this.As the authors mention themselves, this creates an out of equilibrium system cannot be realistic.In my opinion, code efficiency should be tested by comparing the computational time needed to complete T timesteps for various cells numbers (or nodes), or to compare the time needed to simulate production N cells (with physiological growth parameter, i.e. t_div ~ 24h ) with that of the real system.This would allow the user to have a clear view on how long a simulation will take.
-Please indicate whether the code will be able to be run in Windows or Mac (I assume that it is only Linux , as stated in the code files) ?-My impression is that the documentation of the code for now is rather limited; in addition working with xml files might be an obstacle for non expert users Reviewer #1 (Remarks on code availability): I have been able to download the code but I haven't been able to install or test it because of lack of time and I am currently only working with a Windows systems (which seems not to be supported).I have given the code to a student to test the efficiency and user friendliness it but so far I have no more information.remarks : in the readme, I was not able to download information from the provided link : https://github.com/SteveRunser/SimuCell3D_v2.gitReviewer #3 (Remarks to the Author): I thank the authors for responding to all my comments.I am satisfied with the responses and believe the manuscript is acceptable for publication.
I do recommend some changes to make the tool more useable see code availability box.
Reviewer #3 (Remarks on code availability): I would reccomend providing a docker container or similar to provide easy access to the code and tool.As it stands a potential user requires a linux machine to use (or they need to use a VM as was the case for this reviewer).In addition for a tool of this size I would expect a wiki or similar documentation along with the mentioned git repository.This may be in place for post publication but all I can asses is the downloaded zip which is not sufficient support.wide readership and conforms to house style.We look particularly carefully at the titles of all papers to ensure that they are relatively brief and understandable.
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