# Studying gastrulation by invagination: The bending of a cell sheet by mechanical cell properties using 3D deformable cell based simulations

## TL;DR

This paper uses 3D simulations to study how cell properties affect embryo shape during gastrulation, revealing that cell number is more important than shape for invagination.

## Contribution

A 3D deformable cell-based model was developed to simulate gastrulation, showing the impact of mechanical properties on embryo shape.

## Key findings

- Changing mechanical properties like cell stiffness and adhesion directly affects cell behavior and embryo shape.
- The number of cells involved in invagination is more critical than the shape of the endodermal region.
- 3D simulations revealed shape transitions during invagination that differ from real embryos, suggesting additional mechanisms are at play.

## Abstract

Studying the bending of a cell sheet in vivo, like invagination in embryos, can be complex due to a multitude of cellular processes and properties that interact with each other. Computer simulations can help to unravel this process. 2D computer simulations, however, lack the ability to take into account the effect three-dimensional properties, like endodermal plate shape and cell number, have on the shape of an embryo. Therefore, we developed a 3D cell-based model, that is able to simulate cells as separate deformable entities with a conserved cell volume. A blastula is formed by adhering the cells together as a sphere. The simulation results showed that changing individual mechanical properties, like cell stiffness, cell-cell adhesion, and the apical constriction factor, had a direct effect on the cell’s behavior and future shape. These properties influenced the ability of a cell sheet to bend and eventually change the global shape of the embryo. The observed shape transitions the endodermal region goes through during the inward bending of the cell sheet in the simulation, can give an insight into the mechanisms involved, and timing of events in biological model organisms. Changing geometrical properties (endodermal plate shape, endodermal cell number and the start position of constriction), which is not possible in 2D models, showed that the inwards bending is more dependent on the number of cells involved than on the shape of the endodermal region, and thus that the invagination process is very robust to irregularities. When qualitatively comparing our simulation results to biological data from literature, we saw that our simulations did not exactly reproduce the shapes observed in nature. This might indicate that additional mechanisms are playing a role during invagination.

Organisms that develop from a fertilized egg into a complex multicellular organism, go through multiple shape changes. One of the first changes that occurs, takes place during gastrulation, where a part of the embryo bends inward to form the germ layers, creating a multilayered embryo. Examining how this process takes place and which mechanical properties are necessary to change the local cell shape tells us something about the development of an organism and how robust the process is. We used a computer model to simulate a 3D embryo with cells that can deform and adhere together to investigate the bending of a cell sheet. Locally deforming a cell that is connected to other cells transfers this deformation to the surrounding cells. Thereby transforming a part of the embryo. The number of cells and the pattern formed by the interconnected cells determine the embryo’s shape. 3D simulation outcomes differed from real embryos, suggesting that there are more mechanisms necessary for full gastrulation, that are not captured by 2D simulations.