Fig. 7

Apical constriction is not sufficient to obtain a fold in a 3D biophysical model. a Ventral view of the virtual embryo before invagination. Ectodermal cell edges are in black and mesodermal cells in red. An: anterior, P: posterior, L: left, R: right. b Scheme of the apical constriction process. The cell constricts its apex (blue) until its surface area falls under a critical threshold. c Central region of the curved-shaped mesoderm in vivo. Apical area is color-coded (see color bar below h). d Comparison of cell area in the curved-shaped mesoderm in vivo and in the model. Graphs show the normalized cell area in vivo (mean: black line, s.d.: blue band, n = 3 embryos) and in simulations for different values of apical contractility increase τ_Γ (color-coded as indicated in g) with respect to the distance from the ventral midline. e Top row: Images show the central region of the curved-shaped mesoderm in simulated embryos for different values of apical contractility increase τ_Γ. Apical area is color-coded and cell edges are red in the mesoderm and black elsewhere. Bottom row: Tissue deformation (sagittal views) of the simulation results of curved-shaped embryos. For each simulation, the curved shape was defined as the time step when the invagination depth corresponds to the in vivo depth when the embryo adopts a curved shape. Scale bar: 25 µm. f Time-lapse images of the ventral part during mesoderm invagination showing apical extrusion of a few cells (marked in red). g Invagination depth as a function of time for different values of apical contractility increase τ_Γ (color-coded as indicated below). The black lines with a blue (resp. pink) border denote the average depth measured in vivo when the embryo adopts a curved (resp. at the end of invagination). h Same as (e) at full invagination stage for upper and middle rows. Bottom row: Tissue deformation (3D view) of the simulation results at full invagination stage. Scale bar: 25 µm. No apico-basal force was exerted in the above simulations (T^ab = 0)