Figure 3

The critical impact of adaptation on cell-fate heterogeneity. Fate decision probability is studied in presence of molecular noise level (a–e) or other sources of cell-cell variability (f–g). (a) Fate probability curves as function of relative stimulus for the cases of strong/slow adaptation (red squares) and weak/fast adaptation (gray circles). (b–c) Sample of noisy single-cell trajectories associated with a \(\pm 2\%\) change of stimulus level around \(s=s_{50}\) (dashed line of panel a), which are plotted in the \(\{x_1,x_3\}\) state space where steady-state branches \(\vec {x}(s)\) are also represented. (d) Fractionality index \(\eta\) as function of noise with their asymptotic scaling exponents. (e) Fractionality index \(\eta\) as a function of adaptation parameters \(\tau\) and \(\beta\) for molecular noise level \(\sigma =0.01\). White line delimits the parameter domains of saddle-collision and saddle-node transition scenario (redrawn from Fig. 2c). Red squares (\(\beta =1\) and \(\tau =10\)) and grey circles (\(\beta =0.3\) and \(\tau =3\)) correspond to the two archetypical parameter sets associated to each scenario, which are compared in panels a–d. (f–g) Fractionality index \(\eta\) as function of \(\beta\) and \(\tau\) for two sources of cell-cell variability: (f) a uniform distribution of stimulus exposure \(s^l\) with \(\langle \delta s^l \delta s^{l'} \rangle =0.01 \delta _{l,l'}\); (g) a uniform distribution of initial conditions \(\vec {x}_{st1}(s=0)+ \vec {\delta x}\) with \(\langle \delta x_i^l \delta x_j^{l'} \rangle =0.1 \delta _{i,j}\delta _{l,l'}\).