(A) The inferred gene regulatory network from 10,000 sampled solutions that stabilize each of the nine cell states. Each circle represents a gene module. Mean positive and negative interactions between the modules are shown in red and green, respectively, and their thickness and transparency are proportional to the absolute magnitude of the mean and the coefficient of variation (c.v.), respectively. The colored circles represent the gene modules expressed uniquely in only one of the cell states (color code matched with Figure 3A for each state). (B, C) Subsets of the network consisting of gene modules that are expressed in (and stabilize) the naïve ES C0 state (B) and epiblast-like C1 (C) state. As cells transition from C0 to C1, expression of [Klf4], [Apex1], [Ets2], [Atf2] modules is downregulated (shown in gray) while [Hes6] and [Otx2] modules are upregulated, leading to changes in the effective interactions between gene modules that are common to both C0 and C1 states, such as [Sox2] and [Oct4]. (D) [Sox2] overexpression (x-axis) plotted against the probability of [Oct4] downregulation (y-axis) computed over 10,000 models (Materials and methods). In the C1 state (solid line), [Oct4] is downregulated in an increasing fraction of models following [Sox2] overexpression, while in C0, [Oct4] is stable in ~96% of the models (dotted line). In order to obtain the error bars for this and subsequent predictions, we randomly sampled three subsets of 3333 from the 10,000 models. For each set we computed the mean and standard error of the proportion of models that show downregulation of Oct4 in response to Sox2 overexpression. (E, F) Subsets of the model consisting of gene modules that are expressed in the epiblast-like C1 (E) and mesendoderm-like C2 (F) states, and their interactions with [Snai1], which is not normally expressed in C1 or C2. As cells transition from the C1 to C2 state, [Hes6], [Sox2], [Otx2], [Churc1] are downregulated (shown in gray), while [Hmga1], [T], [Atf2], [Hes1], [Ets2], [Apex1], [Brd7], [Hmgn2] and [Smarce1] are upregulated, leading to changes in the effective interactions between [Snai1] and modules that are common to both C1 and C2, such as [Oct4]. (G) The probability of [Oct4] being downregulated (y-axis) as a function of [Snai1] overexpression (x-axis). In the C1 state (solid line), the over expression of [Snai1] has no effect on [Oct4] levels in ~94.5% of the 10,000 models whereas in the C2 state (dotted line), the overexpression of [Snai1] leads to [Oct4] downregulation in up to 19% of the models. (H) The C3 state shows a downregulation of [Oct4] and [BMP], and upregulation of [Tead1], [Apex1], [Pax6], [Smarce1], [Ets2], [Atf2], [Hes1], [Fhl1], [Hmgn2] modules relative to C1. (I) Cells in different states are predicted to respond differently to morphogens. Plot showing the percentage of models (y-axis) where states C1 and C3 (x-axis) transition to C6 (characterized by unique marker gene module [Msx2]), in response to [LIF]+[BMP]. C1 cells remain stable in response to [LIF]+[BMP] signaling in >98% of the models whereas C3 cells are destabilized and move to the C6 state in ~11% of the models.