Computable early Caenorhabditis elegans embryo with a phase field model
Fig 4
The role of timely cell division to protect the 3D embryo structure and cell-cell contact map.
(A). Morphological evolution during 7-cell stage, with simulation time long enough for the whole system to reach mechanical equilibrium. The curves of average velocity (upper) and its change rate (lower) are illustrated side by side. The solid and dashed vertical black lines denote the extreme points in the two curves respectively, while the 3D structures at those time points are illustrated on top and bottom, pointed by gray arrows originating from their corresponding lines. The last structure in the bottom right is the system’s terminal state approaching mechanical equilibrium. The change of cell-cell contact map is illustrated by different colors in the background, while the detail is written between two consecutive structures. The time point of the first quasi-steady state is indicated by a black triangle. The relationship between cell identity and color is listed in the bottom left corner. (B). Linear fitting of time scale between simulation and experiment systems. The durations in simulation are obtained from the quasi-steady states (Figs 4A, S6, and S7B), while the ones in experiment are obtained from 222 wild-type embryos in a previous dataset [2]. The intercept is predetermined as −Δt0 = −2.2784 min, obtained from 4 wild-type embryos in another dataset [34]. The time step in computation is consistently set as h = 0.1 for all stages. (C). An evolutionary tree composed of 8 developmental paths diversified by different cell division timing. The branch of the normal developmental path is plotted with a solid red line while the ones with disturbed cell division timing are plotted with dashed black lines. The cell division timing is denoted with a solid point; the perturbed cell division timing is set at the critical time points (i.e., extreme points) in the curves of average velocity and its change rate (Figs 4A and S6), and only the ones with developmental path differentiated from the others are plotted. The final state is determined by the first and second quasi-steady states for 7- and 8-cell stages respectively, and the 3D structures at the time points with cell divisions activated or in the end are illustrated near the corresponding nodes. A scale bar representing the in silico and in vivo time scales is placed in the top right corner. The terminal embryo morphology and cell-cell contact map of branches ⓪ ~ ⑦ can be found in S9 Fig. The relationship between cell identity and color is listed in the bottom right corner.