(A) Cartoon depicting the response of an isolated cell to EGF doses, based on experimental evidence, obtained either by varying their distance from the EGF source [14] or using a tunable promoter driving EGF synthesis [11]. (B) Signal response curve in an isolated simulated cell showing the concentrations at 300 min of Lip1 (red) and Egl17 (blue) for increasing EGF doses. The cell fate trajectory is shown below. (C) Network diagram indicating the strength of the interactions characteristic of solutions that can stabilize an isolated cell in any of the three cell fates, without intermediate fates (summarizing Table S4 and Fig S3). Thick solid lines indicate stronger interactions, and thin dotted lines weaker interactions compared to wild-type solutions, as defined by the parameter values for the corresponding step: a low k value is expressed as a strong interaction. A spiral indicates high cooperativity. An example of parameter distribution histogram is displayed on the bottom right, plotting the binned number of solutions where kMAPKdsl has the corresponding parameter value on the x axis. (D) Vulval induction network summary showing the feedback and crosstalk (green) of the MAPK and the Notch pathways within a cell. M↵: MAPK pathway positive feedback loop; M → N: MAPK-mediated activation of DSL production; M ⊣N: MAPK-mediated inhibition of Notch; N ⊣M: Notch-mediated inhibition of MAPK. (E) Experimental proportions of fates adopted by an isolated cell in wild-type and dsl-1(0) worms in the C. elegans N2 background (Table S2). In the laser ablation, all competent Pn.p cells except P4.p were killed. In unc-84 mutant animals with defective Pn.p formation, only animals with a single Pn.p cell were scored. We separated the cases where the two daughters adopted 2° and 1° fates, respectively, as such 2° fates are not isolated from a 1° fate. The 2° fate proportion differs significantly between the dsl-1(+) and dsl-1(0) groups: p=0.006 in the laser ablation and p<0.001 in the unc-84 experiment See also Figure S2 and Table S2.