Effective mechanical potential of cell–cell interaction explains three-dimensional morphologies during early embryogenesis
Fig 2
Validation of inference method using simulation data. Simulations were performed on the basis of a distance–force (DF) curve obtained from the Lenard–Jones potential (LJ).
The DF curve is shown in A–i. The simulation conditions contain “Assembling process” (A), “Steady state” (B), and “Cell proliferation” (C). For A–C, snapshots of the simulations are shown where the particles are of the mean size of cells (i). In A–ii, the procedure of data analyses is exemplified, where a colored heat map representing the frequencies of the data points (Frequency index (FI)). Averaged values of the forces are shown in yellow (binned average). In A–iii, B–ii, and C–ii, the resultant effective DF curves are shown with the DF curves from the LJ potential. Normalized L2 norms = {Finferred(D)–FLJ(D)}2 / (FLJ_max)2 were calculated along D, and then the mean values along D were calculated; FLJ_max is the maximum attractive force in the LJ potential, and the range of D was set that the absolute values of attractive forces at D are ≥ (0.1×|FLJ_max|). The normalize L2 norms are: in A–iii, 0.035 (0%), 0.034 (10%), 0.033 (100%), and 0.024 (1000%); in B–ii, 0.032 (1min), 0.046 (3min), and 0.15 (5min); in C–ii, 0.068 (1min), 0.035 (3min), and 0.095 (10min). Related figures: S2 and S3 Figs (in the case of other given potential and random walk).