Cell Fate Specification Based on Tristability in the Inner Cell Mass of Mouse Blastocysts

Abstract

During development, interactions between transcription factors control the specification of different cell fates. The regulatory networks of genetic interactions often exhibit multiple stable steady states; such multistability provides a common dynamical basis for differentiation. During early murine embryogenesis, cells from the inner cell mass (ICM) can be specified in epiblast (Epi) or primitive endoderm (PrE). Besides the intracellular gene regulatory network, specification is also controlled by intercellular interactions involving Erk signaling through extracellular Fgf4. We previously proposed a model that describes the gene regulatory network and its interaction with Erk signaling in ICM cells. The model displays tristability in a range of Fgf4 concentrations and accounts for the self-organized specification process observed in vivo. Here, we further investigate the origin of tristability in the model and analyze in more detail the specification process by resorting to a simplified two-cell model. We also carry out simulations of a population of 25 cells under various experimental conditions to compare their outcome with that of mutant embryos or of embryos submitted to exogenous treatments that interfere with Fgf signaling. The results are analyzed by means of bifurcation diagrams. Finally, the model predicts that heterogeneities in extracellular Fgf4 concentration play a primary role in the spatial arrangement of the Epi/PrE cells in a salt-and-pepper pattern. If, instead of heterogeneities in extracellular Fgf4 concentration, internal fluctuations in the levels of expression of the transcription factors are considered as a source of randomness, simulations predict the occurrence of unrealistic switches between the Epi and the PrE cell fates, as well as the evolution of some cells toward one of these states without passing through the previous ICM state, in contrast to what is observed in vivo.

Figure 1

Intracellular GRN controlling the differentiation of the ICM into Epi and PrE. Gata6 and Nanog inhibit each other and self-activate. Fgf/Erk signaling, which is activated through the binding of Fgf4 to the receptor FGFR2, activates Gata6 and inhibits Nanog. The synthesis of the receptor FGFR2 is activated by Gata6 and inhibited by Nanog. The extracellular concentration of Fgf4 perceived by the cell (Fp) is considered as a control parameter (redrawn from our previous work (6)).

Figure 2

Tristability in the intracellular GRN controlling the differentiation of ICM cells into Epi and PrE. (A and B) Bifurcation diagrams of the model defined by Eqs. 1–4 as a function of parameter Fp, which represents the extracellular concentration of Fgf4. Three stable steady states coexist in the (0.0575,0.0663) interval. (C) Time evolutions in the (Gata6, Nanog) phase space from different initial conditions, showing the basins of attraction of the three stable steady states. Simulations correspond to Fp = 0.06, which value belongs to the domain of tristability. Parameter values are given in Table S1. (D) Sensitivity analysis of tristability. For each parameter listed, the bar indicates the range of relative variation—expressed as a change in percentage in the parameter value with respect to its default value—in which tristability is maintained. Default parameter values are listed in Table S1. Bifurcation diagrams were generated with AUTO (45).

Figure 3

Cell fate specification mechanism in the two-cell system. (A and B) Time evolution for Nanog and Gata6 in cells 1 and 2. Cell 1 and cell 2 direct themselves toward the ICM-like state, before cell 1 is finally attracted by the Epi-like state (and thus increases its rate of Fgf4 secretion). In consequence, cell 2 goes to the PrE-like state (and stops producing Fgf4). (C) Trajectories in the phase space. (D) Corresponding evolution of Fgf4 (variables Fp₁ and Fp₂). The dashed line shows the average concentration of Fgf4 in the extracellular medium (F), whereas the plain lines represent the concentrations of Fgf4 perceived by both cells (Fp₁ and Fp₂), i.e., F − γ and F + γ, respectively. The gray-shaded region corresponds to the domain of tristability. Variability is set to γ = 3%. Parameter values are listed in Table S1. Initial conditions are: G_1/2 = N_1/2 = 0, FR_1/2 = 2.8, ERK_1/2 = 0.25, and F = 0.066.

Figure 4

Spontaneous evolution of ICM cells to a salt-and-pepper pattern of Epi and PrE cells and effect of the rate of degradation of extracellular Fgf4. (A) A population of 25 cells defined by the same GRN and interacting through Fgf4 is simulated on a 5 × 5 grid. Frames are colored depending on the fate of the cell at the end of the simulation (100 arbitrary time units): light gray (red) for Epi, dark gray (blue) for PrE, and white (gray) for ICM. (B) Trajectories of all individual cells shown in (A) in the (Gata6, Nanog) phase plane. (C) Influence of the rate of degradation of Fgf4, kdf, on the proportion of PrE cells in the final population. Statistics were performed on 10 simulations. Parameter values are listed in Table S1. All γ_i values are randomly chosen in the (−10%,+10%) interval. Initial conditions are identical for each cell and, as in Fig. 3, G_i = N_i = 0, FR_i = 2.8, ERK_i = 0.25, and Fs_i = 0.066 (i = 1,…25). To see this figure in color, go online.

Figure 5

Effect of exogenous compounds interfering with the Fgf/Erk signaling pathway on cell-fate specification. White arrows indicate the times during which Fgf/Erk inhibitors are administered (the rate of Erk activation, va, is set equal to zero), whereas black arrows indicate the times during which exogenous Fgf4 has been added (the rate of addition of exogenous Fgf4, vex, is set equal to 0.12). Gray corresponds to the control medium. Column 3 indicates the outcomes of the simulations, performed as in Fig. 4A. The last column indicates the corresponding experiment in the literature. The last protocol is a theoretical prediction.

Figure 6

Influence of the time of administration of Fgf/Erk inhibitors on cell fate in Nanog^−/− embryos. (A) Scheme of the GRN corresponding to the Nanog^−/− mutant. (B) Proportions of cells maintaining Gata6 expression as a function of the time at which Fgf/Erk inhibitors are administered, simulated by setting va = 0 for all cells of the population. The histogram shows the average values for 10 simulations of the 25-cell model. γ_i is randomly chosen for each cell in the (−10%,+10%) interval. Parameter values and initial conditions are the same as in Fig. 4, with vsn1 = vsn2 = 0. (C) Time evolution of Gata6 simulated for the single-cell model. Cell 1, no inhibitor; cell 2, Fgf/Erk inhibitors administered at t = 1.5; cell 3, Fgf/Erk inhibitors administered at t = 1. (D) Bifurcation diagram of Gata6 as a function of ERK (taken as a control parameter) in the single-cell model (black curves), with the trajectories of the three cells shown in (C) (gray curves).

Figure 7

Salt-and-pepper pattern of Epi and PrE cells driven by internal noise. Shown is the spontaneous evolution of a population of ICM cells in the same conditions as in Fig. 4, except that internal fluctuations in the number of molecules are taken into account and external noise is absent. Reactions are listed in Table S3 and parameter values are given in Table 1. Ω = 500 and γ_i = 0 for all cells. The color code is the same as in Fig. 4. Stochastic simulations are performed by means of the algorithm of Gillespie (35). As discussed in the text, two cells of the simulated population switch from the Epi to the PrE state and one cell does not pass through an ICM-like state before becoming an Epi cell. To see this figure in color, go online.

Figure 8

Behavior of the model with internal noise compared to that with external noise. (A) Statistics of the final outcomes of the stochastic simulations with Gillespie’s algorithm in the absence of variability on Fgf4 (γ_i = 0 for all cells), where medium gray indicates the average number of cells in the PrE state, light gray the average number of cells in the Epi state, white the average number of cells in the ICM state, and dark gray the average number of cells that switch at least once from Epi to PrE or vice versa during the simulation (100 arbitrary time units). (B) Statistics of the time spent in the ICM state in the same conditions as in (A). The cells are considered to be in the ICM state as long as |G_i − N_i| < 1.2. (C) Statistics of the final outcomes of deterministic simulations including variability on Fgf4 (γ_i randomly chosen in the (−γ, + γ%) interval for each cell of the population). The color code is the same as in (A). (D) Statistics of the time spent in the ICM state in the same conditions as in (C). For all graphs, parameter values are given in Table S1 and initial conditions are as in Fig. 4.