(A) CD71/Ter119 flow-cytometric histograms of fetal liver cells derived from embryos between E12 and E14.5. Developmental states 1 to 4 are noted.
(B) Cytospin preparations of E14.5 fetal liver cells sorted from each of states 1 to 4 show increasingly differentiated erythroid progenitors. Cells were stained for hemoglobin expression (brown) with diaminobenzidine and counterstained with Giemsa. Scale bar = 20 μm.
Developmental states 1 to 4 are defined as described in the text and in Protocol S1, section 1.1.

(A and B) ANXA5 binding in each of the four fetal liver states (B) and the corresponding frequency of each state in the same fetal livers (A) during E11–E15.5. Each data point is the mean ± standard error of the mean for embryos in one litter. x₁, x₂, and x₃ are the fraction of cells in states 1, 2, and 3, respectively. Av⁺₂ is the fraction of cells in state 2 that bind ANXA5. Individual embryo data for the same dataset are presented in Protocol S2, section 2.3.
(C and D) The fraction of cells expressing FAS in each state during E11–E15.5. Each data point in (C) is mean ± standard deviation for a litter of embryos. Individual embryos in the same dataset are shown in (D); each symbol denotes an independent experiment of one or more litters from the same embryonic age. Further analysis of embryos in this dataset, with the same symbols, is shown in Figure 6A and 6F. Φ₁, Φ₂, and Φ₃ are the fraction of cells expressing FAS in states 1, 2, and 3, respectively. All curves are second-order polynomials. In order to avoid overlapping data points in (D), the data for some litters were slightly displaced along the horizontal axis (e.g., E13.5 was plotted as E13.45).
(E) Fraction of cells that are ANXA5⁺ and FAS⁺ in states 1 to 3, measured in the same fetal livers (E12.5–E15.5) or in the same litters (E11.5, due to the small number of cells in fetal liver at this age). Each point represents a single embryo (E12.5–E15.5) or a single experiment (E11.5, mean of four litters). Each symbol denotes an independent experiment of one or more litters. Curve is a second-order polynomial.
(F) Fraction of cells that are FASL⁺ and FAS⁺ in states 1 to 3, measured in the same fetal livers (E12.5–E15.5). Each color denotes an independent experiment of one or more litters.

(A) All possible feedforward and feedback interactions are rank-ordered according to whether they are mostly present in the models of higher fit to the data in Figure 2A. Specifically, the fitness metric F_j is calculated for each interaction j by summing the inverse values of v_M, determined as described in Figure 2C, over all models M where the interaction j is present. The models are then ranked according to the values of F_j.
(B) All possible feedforward and feedback interactions are rank-ordered according to whether they are mostly present in the models of higher robustness. Specifically, the robustness to parameter variation metric R_j is calculated for each interaction j by summing the inverse values of f_M , determined as described in Figure 2C, over all models M where the interaction j is present. The models are then ranked according to the values of R_j.
(C) The consistency of parameter values corresponding to particular feedforward and feedback interactions is evaluated by plotting the parameter values for each model M in which the corresponding interaction is present. Each box has lines at the lower quartile (blue), median (red), and upper quartile (blue) values. The whiskers show the extent of the rest of the data. Outliers (red plus signs beyond the ends of the whiskers) indicate data with values more than 1.5 times the interquartile range away from the top or bottom of the box.
(D) A correlation matrix relating the control exercised by each feedback or feedforward interaction in each model in which it is present. Each row in the matrix corresponds to a single parameter, describing a single type of interaction. Each column represents one specific model topology. Models are arranged from left to right in descending order of their best fit to the experimental dataset. The color bar indicates the value of the control metric, defined as the correlation coefficient between the parameter values and their associated SSR values, obtained during the multivariate analysis illustrated in Figure 2C. Note that for ff23, ff34, and fb43 interactions, there is clustering of high negative correlation values for high-ranked models, suggesting the importance of these interactions in influencing the fitness of the high-ranked models.

(A) The relative numbers of cells in four states over the time course of the erythropoietic wave shown in Figure 1 were evaluated (Protocol S1, section 1.1) and plotted versus time. The fractions of cells in state 1 (blue triangles), 2 (green rhombs), 3 (red stars), and 4 (magenta squares) are shown.
(B) The model topologies were generated by allowing up to three independent feedback and feedforward interactions between different states, so that the fractions of cells in some of the states might affect the transition probabilities between pairs of successive states. Each model topology was then fitted to the data shown in (A). Two examples of the possible 298 topologies and the corresponding best fits are shown.
(C) For each model topology, the parameters determined during the fitting process were then varied within a 5% range, resulting in 200 predictions for the corresponding model topology, each with its associated SSR. The distributions of SSR values for two such model topologies are shown. The mean SSR value, f_M, is computed, as well as its variance in the distribution, v_M. These values are recorded for all the model topologies and then used to calculate the F_j and R_j metrics for each of the possible feedback and feedforward interactions, shown in Figure 4.

(A) The fraction of FAS⁺ cells in state 2 (Φ₂) is inversely proportional to the fraction of all fetal liver cells that are in state 2 (x₂). Each point represents an individual embryo from the same set of embryos shown in Figure 4D. The curve describes the equation y = 162x^−1.009 (R² = 0.63).
(B and C) The fraction of ANXA5⁺ cells in state 2 (Av⁺₂) is inversely proportional to x₂ between E12.5 and E15.5 (B), but not in earlier E11.5 embryos (C). Each point represents an individual embryo from the same set of embryos and with the same symbols as in Protocol S2, section 2.3. The curve describes the equation y = 0.03x^−0.6 (R² = 0.4).
(D) Four E11.5 embryos from the same litter, showing the distribution of cells in states 1 (x₁) and 2 (x₂) in the top panels, and a fraction of state 2 cells that are FAS⁺ (Φ₂) in the lower panels. Staining control for FAS shown in the leftmost panels. See additional data on these in Protocol S2, section 2.4.
(E) Potential time course of Φ, the fraction of cells that are FAS⁺, in a cohort of erythroblasts traversing state 2. t_st2 is the length of state 2. Φ₁ and Φ₃ are used as estimates for Φ when cells enter and exit state 2, respectively. The dashed red line represents a constant rate of decline in Φ throughout state 2. The solid red curve represents an alternative time course, with an initial rapid decline in Φ that slows down due to depletion of FAS⁺ cells.
(F) Comparison of Φ₂ with Φ_1,3, the arithmetic mean of Φ₁ and Φ₃, during E12.5 and E15.5. Data calculated for each embryo from values shown in Figure 4D. If the rate of decline in Φ in state 2 were constant, the ratio Φ_1,3/Φ₂ would be expected to be equal to one. Since Φ_1,3/Φ₂ is greater than one for embryos younger than E14.5, the rate of decline in Φ in these embryos resembles the solid red curve in (E).
(G) Approximate method for relating Φ₂ to Φ_1,3 when the rate of decline in Φ is nonlinear. Φ₂ equals the area under the red Φ curve (shaded red, panel i) divided by t_st2, and may be represented as the height of a rectangle (black dashed lines, panel ii) of height Φ₂ and base t_st2. The shaded red area is approximately equal to the area of a triangle (shaded blue, panel ii) of base t_a, where t_a is the length of time within state 2 when the rate of decline in Φ is relatively constant. The area of the blue triangle, given by Φ_1,3t_a, is therefore approximately equal to the area of the black dashed rectangle: Φ₂ t_st2 = Φ_1,3t_a.
(H) Graphical representation of Φ₂ and how it relates to the rate of decline in Φ. At E11.5, Φ declines rapidly as the first cohort of erythroblasts progresses through state 2, as suggested by data in (A) and (D). At E12.5–E13.5, Φ declines sufficiently rapidly so that it plateaus prior to completion of state 2, as suggested by (F). By E14.5, the rate of decline has slowed down and remains constant throughout state 2. Throughout, Φ₂ is directly proportional to t_a (from [G]), and both are inversely related to x₂ (from [A], and see text).

(A) Fraction of cells that are ANXA5⁺ in E14.5 gld embryos (circles) compared with strain- and age-matched wild-type embryos (triangles) in each of states 1, 2, and 3. Each data point represents the mean ± standard error of the mean for a litter of embryos; four litters containing 18 gld embryos were compared with three litters containing a total of 23 wild-type embryos; differences for state 2 were significant at the p < 0.0001 level using a two-tailed Student's t-test (non-equal variance).
(B) State 2 ANXA5 binding data shown in (A), plotted together with the ANXA5 binding data for the entire E11–E15.5 period from Figure 4B.
(C) Distribution of cells in the four fetal liver states shows an increase in state 2 cells in E14.5 and E13.5 lpr (magenta) and gld (orange) embryos, compared with strain- and age-matched wild-type embryos (blue). Each data point is the mean ± standard error of the mean of 5–12 embryos from the same litter. There is a 1.58-fold increase in x₂ in gld and lpr embryos at E14.5 (p < 0.0001) and a 1.29-fold increase at E13.5 (p < 0.0001).
(D) Median FAS expression per cell in the FAS⁺ cell population in states 1 and 2. Each point represents data from an individual embryo. Two experiments are shown; in each, two litters of different embryonic ages were examined simultaneously. No normalization was performed on the fluorescence data.