Figures and data
Schematic representation of cell fate decisions driven by noise (A) and signal (B) from a view of epigenetic landscape
(A-B) Valleys represent stable attractors. Cells (yellow balls) in stem cell fate (denoted as “S”, green well in landscape) differentiate into downstream fates, lineage X (denoted as “LX”, blue well) and lineage Y (denoted as “LY”, purple well). These abbreviations were used for following Figure 2–7.
Models of the Cross-Inhibition with Self-activation (CIS) network incorporated logic motifs
(A) A table listing the topologies with logic nodes, logic functions and Cis-Regulatory Elements (CRE) configurations in the CIS network incorporated AND-AND and OR-OR logic (denoted as AA motif and OO motif). X and Y are lineage-specifying transcription factors (TF). Xt+1 indicates the value of X at the next time step. X*, Y* represent activated forms of X and Y, respectively. The true or false signs denote whether gene X can be transcribed, respectively. These annotations were used for the following Figure 3-7.
(B) State spaces of the AA (top panel) and OO (bottom panel) motifs in Boolean models. Rectangles indicate cell states. Green, blue, purple represent S, LX, and LY, respectively. Solid arrows indicate transitions between states under corresponding Boolean models. Dotted arrows indicate forced transition imposed by external perturbations.
(C) State spaces of the AA (top panel) and OO (bottom panel) motifs in ODE models. Dark and red lines represent nullclines of dX/dt = 0, dY/dt = 0, respectively. Stable steady states (SSS) are denoted as orange dots. Unstable Steady States (USSs) are denoted as white dots. Each axis represents the concentration of each transcription factor. Blue, green and purple areas in state spaces indicate attractor basins representing LX, S and LY, respectively. These annotations were used for the following Figure 3-7.
(D) The solution landscape both for the AA and OO motifs. The crimson X-cross sign denotes the first-order saddle node. Blue, green, and purple circles indicate attractors. These annotations were used for the following Figure 3-7.
(E-F) Simulation result of stochastic differential equation models of the AA (E) and OO (F) motifs. Other than adding a white noise, parameters were identical with those in (C). Initial values were set to the attractor representing S fate in Figure 2C top panel (E) and Figure 2C bottom panel (F). Noise levels of X (σx) and Y (σy) are both set to 0.14 in the AA motif (E), and 0.1 in the OO motif (F). Stochastic simulation was preformed 3500 times, with each final state recorded as a dot on the plot. Color of heatmap corresponds to the density of points.
Two logic motifs exhibit opposite bias of fate decisions under the noise-driven mode
(A and C) Stochastic simulation in both the AA and OO motifs. σxis set to 0.18, and σyis 0.12. In both (A) and (C), initial values were identical with attractors of stem cell fate in Figure 2C (SSSs in green attractor basins). Simulation was preformed 1500 times, with each initial (A left and C left) and final (A right and C right) states recorded as a dot on the plot.
(B and D) Time courses of the percentage of cells in different fates in stochastic simulation, under the AA motif (B) and OO motif (D). Fates of cells were assigned by their final states according to the basins of the deterministic models in Figure 2C.
(E) Heatmaps showing the bias of cell fate decisions under different noise levels of X and Y. Color of heatmap indicates the extent of bias. Here, 
(F) Schematic illustration in that stem cell populations possessing the same bias of fate decisions need to have opposite noise patterns, according to whether they are in the AA or OO motif. The red and bold arrow indicates the bias of fate decisions.
Two logic motifs decide oppositely between differentiation and maintenance under the signal-driven mode
(A-B) Bifurcation diagrams for the AA motif (A) and OO motif (B) driven by parameter u (u = ux = uy) in the CIS model. SSSs and USSs are denoted as solid dots and hollow dots, respectively.
(C and F) Changes in the state spaces for the AA motif (C) and OO motif (F) with increasing parameter u, from top to down.
(D and G) Changes in the solution landscape with increasing of u, in company with these in (C and F). The crimson X-cross sign and yellow triangle denote first-order and second-order saddle nodes, respectively. Relative energy is quantified by the geometric minimum action method [88], see Methods.
(E) The solution landscape with parameter u = 0.0565 for the AA motif from a view of three dimensions. The crimson and yellow dots indicate saddle nodes in the state space. Color of the heatmap corresponds to the length of the acceleration at each point in the state space.
The progression-accuracy trade-off in cell fate decisions
(A) Schematic illustration of S-to-LX cell fate decisions with X-inducing signals. The red and bold arrow indicates the direction of fate decisions.
(B-C) Bifurcation diagrams for the AA motif (B) and OO motif (C) driven by parameter ux.
(D and F) Changes in the state spaces for the AA motif (D) and OO motif (F) with increasing values of ux, from top to down.
(E and G) Changes in the solution landscape with increasing of ux, in company with these in (D and F).
The CIS network performs differently during hematopoiesis and embryogenesis
(A) Schematic illustration of S differentiating into LX. We took fate transition labeled in light pink shade as an example in following simulation.
(B) Time courses on the coefficient of variation in expression levels of X and Y genes in silico during differentiation towards LX (ux switches from 0 to 0.08 from time point 1 to 9) in the AA motif. Initial values were set to the attractors of stem cell fate in Figure 2C top panel (SSS in green attractor basin). σxand σyare both set to 0.07. Stochastic simulation was preformed 1000 times for each pseudo-time point.
(C) Time courses on the coefficient of variation in expression levels of X and Y genes in silico during differentiation towards LX (uxswitches from 0 to 0.24 from time point 1 to 9) in the OO motif. Initial values were set to the attractors of stem cell fate in Figure 2C bottom panel (SSS in green attractor basin). σxand σyare both set to 0.05. Stochastic simulation was preformed 1000 times for each pseudo-time point.
(D) Schematic illustration of distinctive cell fate decision patterns under the AA and OO motifs in the state space. Dark and red gradients represent the extent of “AA” and “OO” in the actual regulatory network, respectively. Each axis represents expression levels of the lineage-specifying TFs. Blue, green, and purple circles indicate the cell fates of LX, S, and LY, respectively.
(E) Schematic illustration of Gata1-PU.1 circuit that dominates the primary fate decisions in hematopoiesis (CMP: Common myeloid progenitor; MEP: megakaryocyte-erythroid progenitor; GMP: Granulocyte-monocyte progenitor).
(F) Measured coefficient of variation of expression levels of Gata1 and PU.1 changing over time during differentiation from CMPs to MEPs and GMPs. Expression levels were quantified via single-cell RT-qPCR [83]. Error bars on points represent standard deviation (SD). For details of data processing, see Methods.
(G) Schematic illustration of the differentiation from mESCs in induction system [93].
(H) Measured expression levels of Gbx2 and Tbx3 among cells in embryogenesis quantified via single-cell SMART-seq2 [93]. For details of data processing, see Methods.
The chemical-induced reprogramming of human EB to iMK is the signal-driven fate decisions with an OO-like motif
(A) Schematic illustration of the differentiation from MEPs in vivo and in vitro. Red arrows represent the route of reprogramming [96]
(B) Measured expression levels of KLF1 and FLI1 in reprogramming quantified via single-cell 10X. For details of data processing, see Methods.
(C) Bifurcation diagrams for the OO motif driven by parameter uy in the CIS model.
(D) Fate transition representing reprogramming of EB to iMK in silico. Top panel: changes in the solution landscape with increasing of parameter uy, from left to right; Bottom panel: changes in the state spaces for the OO motif with increasing values of uy, in company with these in top panel.
(E) Left panel: coefficient of variation of expression levels of KLF1 and FLI1 changes in silico over time under given parameter (uy = 0.11) in the OO motif. Noise level of KLF1 (σx) and FLI1 (σy) are set to 0.087. Initial values were identical with LX attractor in Figure 2C bottom panel (SSS in blue attractor basin). Stochastic simulation was preformed 1000 times per round for each time point. We totally preformed 3 round simulations. Error bars on points represent SD; Right panel: measured coefficient of variation of expression levels of KLF1 and FLI1 changing over time in the processes from EBs to iMKs.
(F) Identification of distinct temporal patterns of noise by fuzzy c-means clustering. The x axis represents four time points, while the y axis represents scaled CV (coefficient of variation) in each time point. Dark trend lines in the middle indicate the average of scaled CV over genes in cluster.
(G) Enriched major Gene Ontology terms for cluster 5 and 10.
(H) Regulatory network of TFs in cluster 5 and 10. Circle size indicates the sum of in-degree and out-degree. Node colors indicate different Supermodules (adapted from [96]). Green and red edges indicate activation and inhibition, respectively. The light blue and light pink shades denote genes in cluster 5 and 10, respectively.
