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Effective mechanical potential of cell–cell interaction explains three-dimensional morphologies during early embryogenesis
Fig 4
Inference of effective force of cell–cell interaction in C.elegans embryos.
A. Snapshot of the nuclear positions in the C.elegans embryo with cell lineages at time frame = 76. B. Mean diameters of cells at each time frame estimated from cell numbers. Given that the volume of the embryos is constant (= Vol) during embryogenesis, the mean diameters were estimated from the cell numbers (Nc) at each time frame as follows: mean diameter 
. The diameters relative to that at time frame = 16 are shown with cell numbers. The sizes of the circles reflect the diameters, whose colors roughly correspond to the colors in the graph in F. C. Snapshots with inferred effective forces with the force values described by colored lines at t = 16, 76, and 195. Forces are depicted in arbitrary units (A.U.); 1 A.U. of the force can move a particle at 1μm/min. The nuclear tracking data were obtained from a previous report [31]. D. Uniqueness of solution of effective force inference was examined. The minimizations of the cost function G were performed from different initial force values as described in the x–and y–axes, and the inferred values of each cell–cell interaction were plotted by crosses. E. The inferred effective forces of cell–cell interactions were plotted against the distance of cell–cell interactions with binned averages at t = 76–115. F. Inferred DF and DP curves at various time frames. G. DP curves normalized by the distances at the potential minima at various time frames. Related figure: S6 (uniqueness of solution was examined), S7 (the inferred DP curves were fitted by previously used frameworks such as the Morse potential), and S8 (inferred potentials under the relative velocity–based model) Figs. Related movies: S1 (tracking data) and S2 (force map) Movies.
doi: https://doi.org/10.1371/journal.pcbi.1011306.g004