Apical constriction requires patterned apical surface remodeling to synchronize cellular deformation

Reviewer #1 (Public Review):

Summary:

Satoshi Yamashita et al., investigate the physical mechanisms driving tissue bending using the cellular Potts Model, starting from a planar cellular monolayer. They argue that apical length-independent tension control alone cannot explain bending phenomena in the cellular Potts Model, contrasting with the vertex model. However, the evidence supporting this claim is incomplete. They conclude that an apical elastic term, with zero rest value (due to endocytosis/exocytosis), is necessary in constricting cells and that tissue bending can be enhanced by adding a supracellular myosin cable. Notably, a very high apical elastic constant promotes planar tissue configurations, opposing bending.

Strengths:

- The finding of the required mechanisms for tissue bending in the cellular Potts Model provides a more natural alternative for studying bending processes in situations with highly curved cells.

- Despite viewing cellular delamination as an undesired outcome in this particular manuscript, the model's capability to naturally allow T1 events might prove useful for studying cell mechanics during out-of-plane extrusion.

Weaknesses:

- The authors claim that the cellular Potts Model is unable to obtain the vertex model simulation results, but the lack of a substantial comparison undermines this assertion. No references are provided with vertex model simulations, employing similar setups and rules, and explaining tissue bending solely through an increase in a length-independent apical tension.

- The apparent disparity between the two models is attributed to straight versus curved cellular junctions, with cells with a curved lateral junction achieving lower minimum energies at steady-state. However, a critical discussion on the impact of T1 events, allowing cellular delamination, is absent. Note that some of the cited vertex model works do not allow T1 events while allowing curvature.

- The suggested mechanism for inducing tissue bending in the cellular Potts Model, involving an apical elastic term, has been utilized in earlier studies, including a cited vertex model paper (Polyakov 2014). Consequently, the physical concept behind this implementation is not novel and warrants discussion.

- The absence of information on parameter values, initial condition creation, and boundary conditions in the manuscript hinders reproducibility. Additionally, the explanation for the chosen values and their unit conversion is lacking.

Reviewer #2 (Public Review):

Summary:

In their work, the authors study local mechanics in an invaginating epithelial tissue. The mostly computational work relies on the Cellular Potts model. The main result shows that an increased apical "contractility" is not sufficient to properly drive apical constriction and subsequent tissue invagination. The authors propose an alternative model, where they consider an alternative driver, namely the "apical surface elasticity".

Strengths:

It is surprising that despite the fact that apical constriction and tissue invagination are probably most studied processes in tissue morphogenesis, the underlying physical mechanisms are still not entirely understood. This work supports this notion by showing that simply increasing apical tension is perhaps not sufficient to locally constrict and invaginate a tissue.

Weaknesses:
The findings and claims in the manuscript are only partially supported. With the computational methodology for studying tissue mechanics being so well developed in the field, the authors could probably have done a more thorough job of supporting the main findings of their work.

Author Response

Public Reviews:

Reviewer #1 (Public Review):

Summary:

Satoshi Yamashita et al., investigate the physical mechanisms driving tissue bending using the cellular Potts Model, starting from a planar cellular monolayer. They argue that apical length-independent tension control alone cannot explain bending phenomena in the cellular Potts Model, contrasting with the vertex model. However, the evidence supporting this claim is incomplete. They conclude that an apical elastic term, with zero rest value (due to endocytosis/exocytosis), is necessary in constricting cells and that tissue bending can be enhanced by adding a supracellular myosin cable. Notably, a very high apical elastic constant promotes planar tissue configurations, opposing bending.

Strengths:

• The finding of the required mechanisms for tissue bending in the cellular Potts Model provides a more natural alternative for studying bending processes in situations with highly curved cells.

• Despite viewing cellular delamination as an undesired outcome in this particular manuscript, the model's capability to naturally allow T1 events might prove useful for studying cell mechanics during out-of-plane extrusion.

We thank the reviewer for the careful comments and insightful suggestions.

Weaknesses:

• The authors claim that the cellular Potts Model is unable to obtain the vertex model simulation results, but the lack of a substantial comparison undermines this assertion. No references are provided with vertex model simulations, employing similar setups and rules, and explaining tissue bending solely through an increase in a length-independent apical tension.

We did not copy the parameters of the vertex models in the preceding studies because we also found that the apical, lateral, and basal surface tensions must be balanced otherwise the epithelial cell could not maintain the integrity (Supplementary Figure 1), while the ratio was outside of the suitable range in the preceding studies.

• The apparent disparity between the two models is attributed to straight versus curved cellular junctions, with cells with a curved lateral junction achieving lower minimum energies at steady-state. However, a critical discussion on the impact of T1 events, allowing cellular delamination, is absent. Note that some of the cited vertex model works do not allow T1 events while allowing curvature.

We appreciate the comment, and will add it to the discussion.

• The suggested mechanism for inducing tissue bending in the cellular Potts Model, involving an apical elastic term, has been utilized in earlier studies, including a cited vertex model paper (Polyakov 2014). Consequently, the physical concept behind this implementation is not novel and warrants discussion.

The reviewer is correct but Polyakov et al. assumed “that the cytoskeletal components lining the inside membrane surfaces of the cells provide these surfaces with springlike elastic properties” without justification. We assumed that the myosin activity generated not the elasticity but the contractility based on Labouesse et al. (2015), and expected that the surface elasticity corresponded with the membrane elasticity. Also, in the physical concept, we clarified how the contractility and the elasticity differently deformed the cells and tissue, and demonstrated why the elasticity was important for the apical constriction. We will add it to the discussion.

• The absence of information on parameter values, initial condition creation, and boundary conditions in the manuscript hinders reproducibility. Additionally, the explanation for the chosen values and their unit conversion is lacking.

We agree with the comment, and will add them to the methods.

Reviewer #2 (Public Review):

Summary:

In their work, the authors study local mechanics in an invaginating epithelial tissue. The mostly computational work relies on the Cellular Potts model. The main result shows that an increased apical "contractility" is not sufficient to properly drive apical constriction and subsequent tissue invagination. The authors propose an alternative model, where they consider an alternative driver, namely the "apical surface elasticity".

Strengths:

It is surprising that despite the fact that apical constriction and tissue invagination are probably most studied processes in tissue morphogenesis, the underlying physical mechanisms are still not entirely understood. This work supports this notion by showing that simply increasing apical tension is perhaps not sufficient to locally constrict and invaginate a tissue.

We thank the reviewer for recognizing the importance and novelty of our work.

Weaknesses:

The findings and claims in the manuscript are only partially supported. With the computational methodology for studying tissue mechanics being so well developed in the field, the authors could probably have done a more thorough job of supporting the main findings of their work.

We thank the reviewer for the careful assessment and suggestions. However our simulation was computationally expensive, modeling the epithelium in an analytically calculable expression requires a lot of work, and it is beyond the scope of the present study.