,p>Example of collective behaviour during the zebrafish epiboly.

See Supplementary Movie 3. (a) 2D section from live imaging 3D data (‘oblong’ stage, 3.7 hpf), highlighting the EVL, the external and internal YSL, and the interface between the blastoderm and the yolk cell (credit: BioEmergences). Scale bar 150 μm. (b) Simplified GRN controlling the bipolar protrusion of mesenchymal deep cells via protein Ubi, oriented by a gradient of extracellular ligand Lig. (c) Their polarization axes are oriented by chemotaxis (Supplementary Note 3, equations (43)–(46)) along a radial gradient of ligand (purple) released from the EVL (not shown). (d) Sagittal section of the whole simulated embryo (4 hpf), containing 1,595 deep cells (purple and grey polyhedra) and showing the EVL cell centres (purple dots), yolk particles (yellow dots) and yolk membrane (peripheral yellow edges). EVL and yolk take part only in passive relaxation forces. (e) In the bipolar domain of cell i (green cones) containing three neighbours, protrusive forces comprise ‘intrinsic’ (dashed green arrows) and ‘extrinsic’ components (dashed red; equation (21) and Supplementary Fig. 9), resulting in (solid green arrow).

Parameter exploration of the zebrafish epiboly study.

See Fig. 5. (a) Macroscopic measurements of the epibolic deformation (pasted on a Nomarski 2D picture at the level of the sagittal plane by Karlstrom and Kane⁴⁵, with permission). Landmarks: vegetal pole (VP), animal pole (APe), yolk animal pole (APy). Distances: embryo height (EH), yolk height (YH), margin height (MH) and margin diameter (MD). Scale bar 200 μm. (b) Temporal evolution of the last three measurements normalized by EH in the live embryo (dashed lines) and the best simulated embryo (solid lines). (c) Snapshots at four intermediate stages (time arrows in b). As deep cells divide (mitosis equations (24)–(29) based on empirical data^29,32), their number increases to 3,095. See parameters in Supplementary Table 4. (d) Fitness landscapes as a function of the protrusive force intensity ϕ and a noise factor λ_ran controlling the regularity of the polarization axes’ orientation. The global fitness function F is the average of the yolk height fitness F_YH, the margin height fitness F_MH and the margin diameter fitness F_MD. A lower fitness value (green) means a better similarity with the live embryo. The blue cross highlights the parameter values used in b, which are: ≈ (0.025, 28.5E-04).