Isotropic expansion of external environment induces tissue elongation and collective cell alignment

Abstract

Cell movement is crucial for morphogenesis in multicellular organisms. Growing embryos or tissues often expand isotropically, i.e., uniformly, in all dimensions. On the surfaces of these expanding environments, which we call \"fields,\" cells are subjected to frictional forces and move passively in response. However, the potential roles of isotropically expanding fields in morphogenetic events have not been investigated well. In this study, we mathematically analyzed the effect of isotropically expanding fields using a vertex model, a standard type of multi-cellular model. We found that cells located on fields were elongated along a similar direction each other. Simultaneously, the cell clusters were also elongated, even though field expansion was absolutely isotropic. We then investigated the mechanism underlying these counterintuitive phenomena. In particular, we asked whether elongation was caused by the properties of the field, the cell cluster, or both. Theoretical analyses involving simplification of the model revealed that cell clusters have an intrinsic ability to asymmetrically deform, leading to their elongation. Importantly, this ability is effective only under the non-equilibrium conditions provided by field expansion. This may explain the elongation of the notochord, located on the surface of the growing mouse embryo. We established that passive cell movement induced by isotropically expanding external environments can contribute to both cell and tissue elongation, as well as collective cell alignment, providing key insight into morphogenesis involving multiple adjacent tissues.\n\nStatement of SignificanceIt is a central question of developmental biology how the symmetric shapes of eggs can develop the asymmetric structures of embryos. Embryos expand through their growth. Simultaneously, elongation of tissues such as the notochord occurs, which is fundamental phenomena of morphogenesis. However, possible relationships between tissue elongation and the expansion of embryos have not been investigated well. Here we mathematically present that, even if the expansion is isotropic, tissues located on the embryos are asymmetrically deformed by the expansion, resulting in elongation. We generalize the effect of expanding environments on tissue elongation through model reduction and uncover the mechanism underlying elongation. This process can be a novel key piece for symmetry breaking of embryos, together with previously established morphogenetic processes.