Fig 1.
A multiscale model for early embryo development from fertilization to late blastocyst stage.
(a) Embryo shapes in different stages. The circle color indicates the cell type: Grey for unspecified cell; Green for Trophectoderm (TE) cell; Red for inner Cell Mass: double positive of Nanog and Gata6 (DP); Yellow for Nanog high and Gata6 low (Nanog+); Blue for Gata6 high and Nanog low (Gata6+). (b) Gene regulation models for ICM specification before early blastocyst stage. The grey color represents weak cell contact or weak gene expression. (c) Gene regulation models for Nanog+/Gata6+ specification during early to late blastocyst stage. (d) Modeled selective adhesion between different cell types through early to late blastocyst stage. (e) A schematic illustration of the multiscale model incorporating spatial and gene expression dynamics of the cells. The correspondence to equations are as follows: GRNs, Eqs (1)–(5); intercellular forces, Eq (7); intercellular gene regulation, Eqs (5) and (6); external forces, S1 Text Eqs (3) and (4). (f) Simulated embryo with Nanog/Gata6 and Fgf4/Fgfr2 expression at different stages.
Fig 2.
Data-informed selective adhesion model leads to successful cell arrangement at 128 cell stage.
(a) Histogram of z-score of summation of log([EphA4] + 1) and log([EphrinB2] + 1) at E4.5 stage. The green curve shows the distribution of z-score. The red and blue curves show two components of Gaussian Mixture to fit the distribution. (b) Percentage of high/low adhesive gene expression levels in Nanog+/Gata6+/DP cells at E4.5 stage. (c) An EphA4/EphrinB2 driven selective adhesion mechanism between Nanog+/Gata6+/DP cells, where higher adhesion score (AS) indicates stronger adhesion, and a positive AS means strengthened adhesion. (d) Success rate for Nanog+/Gata6+ cells arrangement in simulations with different selective adhesion hypotheses: (H1) no selective adhesion; (H2) symmetric selective adhesion where adhesion between Nanog+/Nanog+, Gata6+/Gata6+ and DP/DP cells are the same; (H3) asymmetric selective adhesion where DP cells have same adhesion with Nanog+ and with Gata6+; (H4) asymmetric selective adhesion where DP cells have stronger adhesion with Nanog+ cells than with Gata6+ cells; (H5) asymmetric selective adhesion where DP cells have stronger adhesion with both Nanog+ and Gata6+ cells; (H6) the EphA4/EphrinB2 driven selective adhesion; (H7) the EphB2/EphrinB2 driven selective adhesion. (e) Pattern loss score of the simulations. Each data point corresponds to one simulation. A loss score of 0 indicates a perfect pattern and random cell type assignments have an expected loss score of 1. (f) Representative terminal Nanog+/Gata6+ cell arrangements for successful, partially successful, and failed cases.
Fig 3.
Sensitivity of selective adhesion starting time.
(a) Ratio of Nanog+/Gata6+/DP/DN at 128-cell stage for different selective adhesion (SA) starting time; (b) Success rate for embryo development at 128-cell stage for different SA starting time. (c) Spatial pattern of simulation where selective adhesion starts from 128-cell stage (a partially successful case) and simulation where selective adhesion starts from 64-cell stage (a successful case).
Fig 4.
Nanog/Gata6 pattern for different Fgf4 ceasing time.
(a) Single cell gene expression level in different cell stages in baseline simulation. (b) Cell number percentage of DP/Nanog+/Gata6+/DN cells at different 128C (simulation)/ 100C-150C (experiment) stages with different Fgf ceasing time in simulations and experiments. The horizontal dashed line shows the percentage of Nanog+ cells in wild type experiment. (c) Fgf4/Fgfr2 expression levels (log1p transformed) in Nanog+/Gata6+ cells in different cell stages from scRNA-seq data. The vertical bar shows the standard deviation. T-tests were used to compare between Nanog+ and Gata6+ cells the Fgf4 or Fgfr2 expression levels from E4.5 to E6.5. The (t-statistic, two-tailed p-value) for Fgf4 at E4.5, E5.5, and E6.5 are (11.75, <1e-16), (-0.80, 0.43), and (-1.29, 0.20), respectively; and for Fgfr2 at E4.5, E5.5, and E6.5 are (-3.83, 2.2e-4), (-0.27, 0.78), and (-1.37, 0.17), respectively. (d) Gene expression level of Nanog and Gata6 at 128 cell stage if Fgf ceases at 128C and if Fgf is always on. (e) Violin plot of Gata6 level of Nanog+ cell (red) and Nanog level of Gata6+ cell (blue) for simulation where Fgf4 is always on and simulation where Fgf4 ceases at 128 cell stage. The hollow circle shows the median. The t-statistic and two-tailed p-value are 7.44 and 1.7e-12 between the first two columns, and -0.54 and 0.59 between the last two columns.
Fig 5.
(a) Trajectory of Nanog/Gata6 expression over time for different Fgf on-time. Each dot represents one cell. The color of the cell represents the stage of the cell. Dashed circles represent the range of Nanog/Gata6 expression levels for different stages: dark blue for 16C-32C, little blue for 32C-64C and orange for 64C-128C. (b) Bias of Nanog or Gata6 gene expression level from the initial state (16C) in simulation with different Fgf on-time. Red curve shows the cells whose Nanog expression is higher than cells in initial state; Blue curve shows the cells whose Gata6 expression is higher than cells in initial state. The vertical line shows the error bar with one standard deviation.