Fig 1.
Reconstruction of cellular developmental properties and establishment of phase field model.
(A). In vivo 3D time-lapse imaging experiment and quantification of cell location (nucleus; GFP, green) and cell morphology (membrane; mCherry, red), illustrated with strain ZZY0535 [40]. The images are obtained from a previous dataset for schematics [2]. (B). Cell lineage tree from 1- to 8-cell stages, including 6 conservatively-ordered cell division groups (i.e., P0 → AB → P1 → ABa and ABp → EMS → P2) and consequently 7 stages with the cell number increasing from 1 to 8 (noted on right). The 8-cell stage ends with the synchronous divisions of ABal, ABar, ABpl, and ABpr. The tree is plotted on an average of 222 wild-type embryos [2]. (C). The eggshell and cell in the phase field model. An ideal eggshell under compression is rebuilt as a boundary based on size measurements on 4 wild-type embryos [34]. The cells which interact via designated forces are constrained within the reconstructed eggshell and illustrated with the 4-cell stage. The x-z plane is highlighted with a rectangular frame and used to visualize the distribution of phase field in (D). The distribution of phase field across the x-z plane, illustrated with a heat map using the ABp cell as an example. The boundary of the eggshell is labeled by a solid white line and the boundaries of the other 3 cells (i.e., ABa, EMS, and P2) are labeled by dashed white lines. (E). A sketch map of the forces imposed on a cell in the phase field model. The relationship between force type and color is listed on right.
Table 1.
The symbols and parameters of phase-field functions.
Fig 2.
Embryo morphology reconstruction from 1- to 4-cell stages.
(A). Comparison of embryo morphology between simulation with cell-cell attraction and experiment from 1- to 4-cell stages (view from y / left-right axis). The 1st and 2nd columns, cell-arrangement progression in phase-field simulation; the time point of each embryonic structure is illustrated on its top; dashed arrows, cell division orientation measured by experiment and inputted into simulation; the 3rd column, a live embryo with mCherry fluorescence on cell membrane (strain ZZY0535 [40]); scale bar, 10 μm. (B). Comparison of cell surface area and cell-cell contact area between simulation and experiment at 4-cell stage, with globally symmetric attraction applied on all the cell-cell contacts (σ = 0.0, 0.3, 0.6, 0.9, 1.2 and 1.5). Inset, range from 0 to 500 μm2 in both coordinates. The quantitative experimental data is obtained at the last moment (time point) of 4-cell stage. (C). Comparison of cell surface area and cell-cell contact area between simulation and experiment at 4-cell stage, with globally symmetric attraction applied on the cell-cell contacts of ABa-ABp, ABa-EMS, ABp-EMS, and ABp-P2 (σ = 0.9), and weaker attraction on the contact of EMS-P2 (σEMS, P2 = 0.0, 0.2, 0.4, 0.6 and 0.8). Inset, range from 0 to 500 μm2 in both coordinates. The average δ reaches minimal (≈ 0.06) when σEMS, P2 = 0.2. The quantitative experimental data is obtained at the last moment (time point) of 4-cell stage. (D). Distribution of membrane-attached E-cadherin HMR-1 at 4-cell stage, with substantially higher accumulation in the cell-cell contacts of ABa-ABp, ABa-EMS, ABp-EMS, and ABp-P2 (indicated by blue arrows) than that in EMS-P2 contact (indicated by red arrow) (strain LP172 [48]); scale bar, 10 μm.
Fig 3.
Comparison of embryo morphology between simulation and experiment from 6- to 8-cell stages.
(A). The upper panel, embryo morphology at the last moment of 6-cell stage. (B). The middle panel, embryo morphology at the last moment of 7-cell stage. (C). The lower panel, embryo morphology at the last moment of 8-cell stage (with attraction motif on ABpl-E contact, i.e., σABpl, E = σW). In each panel, embryo morphology in simulation and experiment are respectively illustrated on the left and right in three orthogonal observation directions, while a cell-cell contact map is placed in their top left corners. About the map in simulation, dark and light gray shades denote relatively strong (σ = σS) and weak (σ = σW) attraction respectively, while black dots represent the contacted cell pairs. About the map in experiment, black dots represent the conserved contacted cell pairs, while empty circles represent the unconserved contacted cell pairs [34]. The relationship between cell identity and color is listed next to the contact maps. The quantitative experimental data is obtained at the last moment (time point) of each stage.
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.
Fig 5.
The selective impact of cell division orientation on the developmental path.
Simulation for 6- to 8-cell stages with cell division orientations aligned to the three orthogonal body axes. All the division orientations of ABa (1st column), ABp (2nd column), EMS (3rd column), and P2 (4th, 5th, 6th columns with different volume segregation ratio) are set along the experimental (1st row), anterior-posterior (2nd row; x / A-P), left-right (3rd row; y / L-R), and dorsal-ventral (4th row; z / D-V) directions, respectively. The 3D structures whose cell-cell contact map is the same as the one simulated with experimental orientation, are highlighted with red rectangles.
Fig 6.
High-dimensional diversity and regulatory potential of developmental paths provided by cell-cell attraction matrix and extra attraction motifs.
(A). A total of 17 single attraction motifs (σ = σW = 0.2 → σ = σS = 0.9 or σ = σS = 0.9 → σ = σW = 0.2) based on the cell-cell contact map at 8-cell stage (bottom left corner) are applied on the cell-cell attraction matrix default (top left corner) independently for simulation. The evolutionary sequence of cell-cell contact map is used to classify the developmental paths, illustrated on the right. Each color represents a unique developmental path originating from top and ending in bottom, with its corresponding attraction motif(s) indicated in the legend; the black diamond denotes the cell-cell contact map at the last moment of 7-cell stage (Topology 0 in S12 Fig); the black points denote the different cell-cell contact maps at 8-cell stage (Topologies 1 ~ 26 in S12 Fig), with a size positively correlated to the number of developmental paths passing through. (B). The migration trajectory of ABpl’s mass center when the 17 attraction motifs are added. The initial 8-cell structure is illustrated semi-transparently for visual comparison. The colors representing different cell identities are the same as those used in Fig 3C. The colors representing trajectories with different attraction motifs are the same as those used in Fig 6A. (C). The three types of developmental paths differentiated when different combinations of σABpl, E and σABpl, MS are applied (σABpl, E = 0.2, 0.9 and σABpl, MS = 0.2, 0.9, 1.6), highlighted with light yellow, purple, and green backgrounds. The 3D structures at their second quasi-steady states are illustrated. (D). The match of migration rate between simulated embryos with σABpl, E = σW = 0.2, σABpl, MS = σS = 0.9 and σABpl, E = σW = 0.2, σABpl, MS = σ’S = 1.6. A total of 16 critical time points selected according to the extreme points in the curves of average velocity and its change rate are used to compare the migration rate in the two simulations (S13 Fig and S10 Table).