Mechanical basis and topological routes to cell elimination
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eLife assessment
In this work, Monfared et al. construct a useful three-dimensional phase-field model for cell layers and use this to investigate the link of extrusion events to defects in cellular arrangement. The extension of existing 2D phase field models to three dimensions is an important contribution of this paper. Here the model is used to study the importance of cell-cell and cell-substrate interaction in extrusion from cell monolayers. Their claim that extrusion events can be distinctly linked to defects in nematic and hexatic orders in the monolayer need to be better justified to be fully convincing.
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Abstract
Cell layers eliminate unwanted cells through the extrusion process, which underlines healthy versus flawed tissue behaviors. Although several biochemical pathways have been identified, the underlying mechanical basis including the forces involved in cellular extrusion remains largely unexplored. Utilizing a phase-field model of a three-dimensional cell layer, we study the interplay of cell extrusion with cell–cell and cell–substrate interactions in a flat monolayer. Independent tuning of cell–cell versus cell–substrate adhesion forces reveals that extrusion events can be distinctly linked to defects in nematic and hexatic orders associated with cellular arrangements. Specifically, we show that by increasing relative cell–cell adhesion forces the cell monolayer can switch between the collective tendency towards fivefold, hexatic, disclinations relative to half-integer, nematic, defects for extruding a cell. We unify our findings by accessing three-dimensional mechanical stress fields to show that an extrusion event acts as a mechanism to relieve localized stress concentration.
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eLife assessment
In this work, Monfared et al. construct a useful three-dimensional phase-field model for cell layers and use this to investigate the link of extrusion events to defects in cellular arrangement. The extension of existing 2D phase field models to three dimensions is an important contribution of this paper. Here the model is used to study the importance of cell-cell and cell-substrate interaction in extrusion from cell monolayers. Their claim that extrusion events can be distinctly linked to defects in nematic and hexatic orders in the monolayer need to be better justified to be fully convincing.
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Reviewer #1 (Public Review):
Monfared et al. construct a three-dimensional phase-field model of cell layers and use it to examine cellular extrusion by independently tuning cell-substrate and cell-cell adhesion. In line with earlier studies (in some of which some of the authors were involved), they find that extrusion is linked to topological defects in cellular arrangement and relieving stress.
The authors claim that their development of the three-dimensional phase field model is crucial for understanding cell extrusion (which I agree with the authors is inherently three-dimensional). However, I don't think the data they currently present clearly demonstrate that the three-dimensional model adds significantly more to our understanding of extrusion events than earlier two-dimensional models.In the end, I think that the more important …
Reviewer #1 (Public Review):
Monfared et al. construct a three-dimensional phase-field model of cell layers and use it to examine cellular extrusion by independently tuning cell-substrate and cell-cell adhesion. In line with earlier studies (in some of which some of the authors were involved), they find that extrusion is linked to topological defects in cellular arrangement and relieving stress.
The authors claim that their development of the three-dimensional phase field model is crucial for understanding cell extrusion (which I agree with the authors is inherently three-dimensional). However, I don't think the data they currently present clearly demonstrate that the three-dimensional model adds significantly more to our understanding of extrusion events than earlier two-dimensional models.In the end, I think that the more important achievement of this work -- and one that is likely to be more influential -- is developing a three-dimensional phase field model for cell monolayers rather than any specific result regarding extrusion.
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Reviewer #2 (Public Review):
The paper provides a natural extension of 2D multiphase field models for cell monolayers to 3D, addressing cell deformations, cell-cell interaction, cell-substrate interactions and active components for the cells. As known from 2D, the cell arrangement leads to positional (hexatic) defects and if the elongation of the cells is coarse-grained to define a global nematic order also to orientational (nematic) defects. These defects are characterized, see Figure 2. However, this is done in 2D and it remains unclear if the projected basal or apical side is considered in this figure and the following statistics. The authors identify correlations between orientational defects and extrusion events. In terms of positional defects such statistics seem not to be considered and the relation between positional defects and …
Reviewer #2 (Public Review):
The paper provides a natural extension of 2D multiphase field models for cell monolayers to 3D, addressing cell deformations, cell-cell interaction, cell-substrate interactions and active components for the cells. As known from 2D, the cell arrangement leads to positional (hexatic) defects and if the elongation of the cells is coarse-grained to define a global nematic order also to orientational (nematic) defects. These defects are characterized, see Figure 2. However, this is done in 2D and it remains unclear if the projected basal or apical side is considered in this figure and the following statistics. The authors identify correlations between orientational defects and extrusion events. In terms of positional defects such statistics seem not to be considered and the relation between positional defects and cell extrusion events remains vague. Also in-plane and out-of-plane stresses are computed. These results confirm a mechanical origin for cell extrusions. However, these are the only 3D information provided. The final claim that the results clearly demonstrate the existence of a mechanical route related with hexatic and nematic disclinations is not clear to me. 3D vertex models for such systems e.g. showed the importance of different mechanical behavior of the apical and basal side and identified scutoids as an essential geometric 3D feature in cell monolayers. These results are not discussed at all. A comparison of the 3D multiphase field model with such results would have been nice.
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Reviewer #3 (Public Review):
In this paper, the authors studied the influence of topological defects on extrusion events using 3D multi-phase field simulations. By varying cell-cell and cell-substrate parameters, this study helps to better understand the influence of mechanical and geometrical parameters on cell extrusion and their linkage to topological defects.
First the authors show that extrusion events and topological defects of nematic and hexatic order are typically found in their system, and then that extrusions occur, on average, at a distance of a few cell sizes from a + and - 1/2 defects. Next, the author analyse at extrusion events the temporal evolution of the local isotropic stress and the local out-of-plane shear stress, showing that near the instant of extrusion, the isotropic stresses relax and the shear stresses …
Reviewer #3 (Public Review):
In this paper, the authors studied the influence of topological defects on extrusion events using 3D multi-phase field simulations. By varying cell-cell and cell-substrate parameters, this study helps to better understand the influence of mechanical and geometrical parameters on cell extrusion and their linkage to topological defects.
First the authors show that extrusion events and topological defects of nematic and hexatic order are typically found in their system, and then that extrusions occur, on average, at a distance of a few cell sizes from a + and - 1/2 defects. Next, the author analyse at extrusion events the temporal evolution of the local isotropic stress and the local out-of-plane shear stress, showing that near the instant of extrusion, the isotropic stresses relax and the shear stresses fluctuate around a vanishing value. Finally, the authors analyse both the distribution of isotropic stress and the average isotropic stress pattern near +1/2 defects.
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Author Response:
Reviewer #1 (Public Review):
Monfared et al. construct a three-dimensional phase-field model of cell layers and use it to examine cellular extrusion by independently tuning cell-substrate and cell-cell adhesion. In line with earlier studies (in some of which some of the authors were involved), they find that extrusion is linked to topological defects in cellular arrangement and relieving stress.
The authors claim that their development of the three-dimensional phase field model is crucial for understanding cell extrusion (which I agree with the authors is inherently three-dimensional). However, I don't think the data they currently present clearly demonstrate that the three-dimensional model adds significantly more to our understanding of extrusion events than earlier two-dimensional models.In the end, I think that …
Author Response:
Reviewer #1 (Public Review):
Monfared et al. construct a three-dimensional phase-field model of cell layers and use it to examine cellular extrusion by independently tuning cell-substrate and cell-cell adhesion. In line with earlier studies (in some of which some of the authors were involved), they find that extrusion is linked to topological defects in cellular arrangement and relieving stress.
The authors claim that their development of the three-dimensional phase field model is crucial for understanding cell extrusion (which I agree with the authors is inherently three-dimensional). However, I don't think the data they currently present clearly demonstrate that the three-dimensional model adds significantly more to our understanding of extrusion events than earlier two-dimensional models.In the end, I think that the more important achievement of this work -- and one that is likely to be more influential -- is developing a three-dimensional phase field model for cell monolayers rather than any specific result regarding extrusion.
We sincerely thank the reviewer for their time examining our manuscript and providing critical feedback. We are confident that our detailed response provided below and additional analyses have further highlighted the importance of three-dimensional stresses.
Reviewer #2 (Public Review):
The paper provides a natural extension of 2D multiphase field models for cell monolayers to 3D, addressing cell deformations, cell-cell interaction, cell-substrate interactions and active components for the cells. As known from 2D, the cell arrangement leads to positional (hexatic) defects and if the elongation of the cells is coarse-grained to define a global nematic order also to orientational (nematic) defects. These defects are characterized, see Figure 2. However, this is done in 2D and it remains unclear if the projected basal or apical side is considered in this figure and the following statistics. The authors identify correlations between orientational defects and extrusion events. In terms of positional defects such statistics seem not to be considered and the relation between positional defects and cell extrusion events remains vague. Also in-plane and out-of-plane stresses are computed. These results confirm a mechanical origin for cell extrusions. However, these are the only 3D information provided. The final claim that the results clearly demonstrate the existence of a mechanical route related with hexatic and nematic disclinations is not clear to me. 3D vertex models for such systems e.g. showed the importance of different mechanical behavior of the apical and basal side and identified scutoids as an essential geometric 3D feature in cell monolayers. These results are not discussed at all. A comparison of the 3D multiphase field model with such results would have been nice.
We thank the reviewer for bringing to our attention the work on scutoids, which we now discuss in the manuscript as an important geometric feature of 3D layers on curved surfaces. We shall, however, emphasize that scutoids are specific to monolayers on curved surfaces, while we focus on a cell monolayer on flat substrates here. Moreover, we shall argue that the difference between apical and basal sides is just one element of the 3D complexity of cell layers. Here, we focus on another aspect of 3D complexity that is not accessible in 2D: the development of 3D mechanical stress and its role in an inherently 3D problem of cell extrusion. Nevertheless, as discussed in detail responses below we have now added additional analyses varying the monolayer interaction with the substrate on the basal side.
Reviewer #3 (Public Review):
In this paper, the authors studied the influence of topological defects on extrusion events using 3D multi-phase field simulations. By varying cell-cell and cell-substrate parameters, this study helps to better understand the influence of mechanical and geometrical parameters on cell extrusion and their linkage to topological defects.
First the authors show that extrusion events and topological defects of nematic and hexatic order are typically found in their system, and then that extrusions occur, on average, at a distance of a few cell sizes from a + and - 1/2 defects. Next, the author analyse at extrusion events the temporal evolution of the local isotropic stress and the local out-of-plane shear stress, showing that near the instant of extrusion, the isotropic stresses relax and the shear stresses fluctuate around a vanishing value. Finally, the authors analyse both the distribution of isotropic stress and the average isotropic stress pattern near +1/2 defects.
We are grateful to the reviewer for their time examining our manuscript and providing critical feedback that has certainly improved our manuscript. In what follows, we provide detailed responses to each comment, including additional statistics that we have computed and now include in the manuscript for completion.
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