1. Network Features and Dynamical Landscape of Naive and Primed Pluripotency 
Benjamin Pfeuty, Clémence Kress, Bertrand Pain 
Biophysical Journal 
Volume 114, Issue 1, Pages (January 2018)
DOI: /j.bpj
Copyright © 2017 Biophysical Society Terms and Conditions

2. Figure 1
The pluripotency model: network architecture and cell fate data. (A) Pluripotency displays specific in vitro and in vivo transition patterns among a naive/mESC pluripotent state, N; a primed/mEpiSC pluripotent state, P; and a nonpluripotent differentiated state, D. (B) The regulatory network model is based on a selected set of signaling and transcription factors interacting with each other through various regulatory mechanisms (arrow legend box). (C) A set of perturbation experiments is used as target experimental dataset for the model optimization procedure. These experiments describe the fate outcome j′ = N,P,D of cells that are initially in a state j = N,P,D and then subjected to specific culture conditions (LIF, Activin, FGF) or to upregulation/downregulation (±) of specific factors. (D) Typical relative mRNA levels of pluripotency factors (Oct4-Sox2, Nanog, Esrrb, and Klf4) are associated with naive/mESC, primed/mEpiSC, and nonpluripotent states, which are determined from experiments (Fig. S4) and used for model optimization. To see this figure in color, go online.
Biophysical Journal  , DOI: ( /j.bpj )
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3. Figure 2
Model optimization through computational evolution. (A) The statistical distribution of the global error score Φ is computed over 103 randomized-parameter models. (B) An example of a computational evolutionary trial showing the decreasing score Φ from 0.8 to 0.2 and the parameter set of the fittest model individual of the family of the ith generation. The generation 0 is composed of NI = 20 model individuals k of parameter Pik=10ηk+ηi, where ηi,k values are uniformly distributed between [−1:1]. (C) The statistical distribution of the global error score Φ is computed for the fittest individuals of 103 evolutionary trials. (D) Given here are condition-specific scores ϕik of a set of optimal models satisfying Φ < 0.21: model-averaged value (lower panel) and fraction of models with ϕik > 0.5 (upper panel). (E) Three main classes of optimal models (green, class I; blue, class II; red, class III) are evidenced by the distance matrix of their condition-specific scores (Eq. 5). (F) The three model classes differ in their worst-condition-specific scores. To see this figure in color, go online.
Biophysical Journal  , DOI: ( /j.bpj )
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4. Figure 3
Parameter distribution and core topologies of optimized models. The systematic analysis of the i=1,49 optimized parameters is made for the k = 1,29 optimal models segregated into the three classes identified in Fig. 2 E (green, class I; blue, class II; red, class III). (A) The two left panels show parameter values Pik (k points in the ith line) and their class-averaged values 〈Pi〉k⊆class. The two right panels show parameter sensitivities γik (Eq. 4) and their class-averaged values 〈γik〉k⊆class, where the dashed line shows the threshold γ0 = 0.1 between relevant and irrelevant regulations (Fig. S6). (B) The three classes of optimal model differ in their topology, as evidenced by the distance matrix of model parameter sensitivities Dkl(log γi) (Eq. 5). (C) Core pluripotent circuitries for each model class are drawn by including only regulations whose removal results in a significant increase of error score Φ (〈γi〉k⊆class > γ0 in (A)). Model classes share 15 common regulations (thick network edges). To see this figure in color, go online.
Biophysical Journal  , DOI: ( /j.bpj )
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5. Figure 4
Multistability domains and asymmetric transitions between naive and primed states. Color code represents the three classes of optimal models (green, class I; blue, II; red, class III). (A) Normalized expression/activity levels Xj∞,j of the i protein species are associated with the stable states j = N,P,D (top, naive state with SLIF = 1; middle, primed state with SAct/FGF = 1; bottom, differentiated state with SLIF = SAct/FGF = 0). (B) Distinct multistable subdomains between these three states are depicted by their average expression levels of pluripotency factors 〈Xik〉i = Oct, Nan, Esr, Klf as a function of SLIF (and SAct/FGF = 0) and SAct/FGF (and SLIF = 0). (Lower panel) An example of multistable property with two bistability domains (shading) and two saddle-node bifurcation points (circles) is illustrated for one optimal model. (C) Dynamical trajectories of optimal models in a 2D section of the concentration space are shown for distinct transition scenarios between naive and primed pluripotent states. (Middle panel, insets) A set of trajectories from a heterogeneous naive state (X→0=X→∞N+η→) seems attracted to a slow manifold through the primed state. (D) Primed-to-naive reversion efficiencies ϵik = 1/θik are given for the strategy i (overexpression of a given pluripotency factor or 2i, with or without LIF) and optimal model k, where θi is the critical level of upregulation or downregulation αi or of SLIF that is required for successful reversion. To see this figure in color, go online.
Biophysical Journal  , DOI: ( /j.bpj )
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6. Figure 5
Identification of a modular network through systematic perturbation approach. (A) The approach consists in quantifying the effect of diverse network motif perturbations on the signaling thresholds and expression levels of the naive and primed states. (B) Model-average alterations 〈|ΔYk|〉k of expression levels (Y=〈X∞,i〉i=Oct,Nan,Klf,Esr(Sj=1) and signaling thresholds (Y = SCj) of the naive state (left, j = LIF) and the primed state (right, j = Act/FGF) are computed upon the deletion of a single or multiple (∗) regulatory links (a ↔ b: a → b ∪ b → a; a → b,c : a → b ∪ a → c). (C) Functional modular circuits are inferred from (B) regulating the naive and primed states. (Black arrows) Activatory regulation; (red circles) inhibitory regulation. (Solid lines) Effective regulation; (dashed line) ineffective regulation. To see this figure in color, go online.
Biophysical Journal  , DOI: ( /j.bpj )
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7. Figure 6
A low-dimensional modular model reproduces the pluripotent dynamics of detailed models. (A) Minimal circuit corresponding to Eq. 6 consists of regulatory modules xi = N,I,P, extrinsic signals si = L,A, and regulatory parameters aii′. (Black arrows) Activatory regulation (red circles) inhibitory regulation. (B) A signal-dependent multistability among three discrete states similar to Fig. 4 B is found for 381 parameter sets from a sample of 106 random parameter sets for which log10(aii′) values are uniformly distributed between [−1:1] except aNL = 1 and aPA = 1. (See Fig. S7 A for the quantitative multistability criteria used for parameter set selection.) (C) Three examples of canalized trajectories where heterogeneous initial conditions around the naive-like state (dark shaded circle) are quickly attracted to a slow 1D manifold that passes near the primed-like state (light shaded circle) toward the differentiated-like state (blank circle). (D and E) The 381-parameter set satisfying the multistability criteria in (B) shows specific distribution profiles for each parameter with peaks for high values (D), and significant positive correlations between the parameters aNN and aIN (lower panel of E) and between the parameters aNN and Δλ (upper panel of E). Δλ is a measure of stability of the naive state (Fig. S7, B and C). To see this figure in color, go online.
Biophysical Journal  , DOI: ( /j.bpj )
Copyright © 2017 Biophysical Society Terms and Conditions