Abstract
During morphogenesis, three-dimensional (3D) multicellular structures emerge from biochemical and mechanical interplays among cells. In particular, by organizing their gradient within tissues, the diffusible signalling molecules play an essential role in producing the spatio-temporal patterns of cell status such as the differentiation states. Notably, this biochemical patterning can be dynamically coupled with multicellular deformations by signal-dependent cell activities such as contraction, adhesion, migration, proliferation and apoptosis. However, the mechanism by which these cellular activities mediate the interactions between multicellular deformations and patterning is still unknown. Herein, we propose a novel framework of a 3D vertex model to express molecular signalling among the mechanically deforming cells. By specifying a density of signalling molecules for each cell, we express their transport between neighbouring cells. By simulating signal-dependent epithelial growth, we found various types of tissue morphogenesis such as arrest, expansion, invagination and evagination. In the expansion phase, growth molecules were widely diffused with increasing tissue volume, which diluted the growth molecules in order to support the autonomous suppression of tissue growth. These results indicate that the proposed model successfully expresses 3D multicellular deformations dynamically coupled with biochemical patterning. We expect our proposed model to be a useful tool for predicting new phenomena emerging from mechanochemical coupling in multicellular morphogenesis.