The extra-embryonic space is a geometric constraint regulating cell arrangement in nematodes

In multicellular systems, cells communicate with adjacent cells to decide their positions and fates. Cellular arrangement in space is thus important for development. Orientation of cell division, cell-cell interaction (i.e., attraction and repulsion), and geometrical constraints are the three major factors that define cell arrangement. Here we found that the amount and location of extra-embryonic space (ES), the empty space within the eggshell not occupied by embryonic cells, are critical to define cell arrangement in the 4-cell stage embryo of nematodes. This discovery was motivated by observations of a T-reversed-type arrangement, which was not explained by a model assuming simplified shapes of the eggshell, in our previous experiments. In this study, we incorporated the precise shape of the C. elegans eggshell in our newly developed multicellular morphology model based on the phase-field method. The new model succeeded in reproducing the T-reverse arrangement, demonstrating the importance of the precise shape of the eggshell. Further analyses revealed that the amount and location of ES is critical to develop various cell arrangements. Overall, our analyses characterized the roles of new geometrical contributors to cell arrangements, which should be considered for any multicellular system.