Differential Cellular Stiffness Contributes to Tissue Elongation on an Expanding Surface

Pattern formation and morphogenesis of cell populations is essential for successful embryogenesis. Steinberg proposed the differential adhesion hypothesis, and differences in cell-cell adhesion and interfacial tension have proven to be critical for cell sorting. Standard theoretical models such as the vertex model consider not only cell-cell adhesion/tension but also area elasticity of apical cell surfaces and viscous friction forces. However, the potential contributions of the latter two parameters to pattern formation and morphogenesis remain to be determined. In this theoretical study, we analyzed the effect of both area elasticity and the coefficient of friction on pattern formation and morphogenesis. We assumed the presence of two cell populations, one population of which is surrounded by the other. Both populations were placed on the surface of a uniformly expanding environment analogous to growing embryos, in which friction forces are exerted between cell populations and their expanding environment. When the area elasticity or friction coefficient in the cell cluster was increased relative to that of the surrounding cell population, the cell cluster was elongated. In comparison with experimental observations, elongation of the notochord in mice is consistent with the hypothesis based on the difference in area elasticity but not the difference in friction coefficient. Because area elasticity is an index of cellular stiffness, we propose that differential cellular stiffness may contribute to tissue elongation within an expanding environment.