Figure 2

Bifurcation analysis. Stability of cell fates change as a function of strength of lateral stabilization. Bifurcation diagram showing stable attractors (solid) and unstable states (dashed) for a minimal tissue consisting of three-cells (hexagons). Arrows indicate trajectories after loss of stabilization. (A) In presence of lateral inhibition, a>a _c , loss of stabilization, b<b _c , causes dedifferentiation towards a progenitor-like multipotent state. If lateral stabilization is recovered at this early stage, the developmental process is recapitulated and a mixed pattern of both cell fates arises. In contrast, if stabilization remains inhibited, cells redifferentiate into islet cells. (B) In absence of lateral inhibition, a<a _c , loss of stabilization results in direct lineage conversion, due to the absence of a progenitor-like multipotent state. This unstable multipotent state vanishes at a _c in a saddle-node bifurcation with another solution branch of similar Y-values but higher Z activity which is additionally unstable against perturbations in Z and therefore omitted in (A). Note that Σ Y is a projection of a high (12)-dimensional space, such that intersections do not imply bifurcations or changes in stability as these need not intersect in the actual state space. In the legend, the stability of X or Y means (un)stable with respect to perturbations in variable X or Y, respectively. With parameters as in Table 1, a _c ≈0.0017 and b _c ≈0.012.