Fig. 4.

Dynamical system characteristics of the Notch–Delta–Jagged circuit. (A) Nullclines for the case of one cell interacting with fixed values of external proteins ($N_{ext}=500$, $D_{ext}=0$, $J_{ext}=1,750$). The blue nullcline is for condition $dN/dt=0$, $dD/dt=0$ and $dI/dt=0$, and the green nullcline is for condition $dD/dt=0$, $dJ/dt=0$ and $dI/dt=0$ (Eqs. 1–4). The red filled circles represent the three stable steady states––Sender (S), Receiver (R), and hybrid Sender/Receiver (S/R). Unfilled circles represent unstable steady states. (B) Nullclines for the case of two cells interacting with each other through Notch–Delta–Jagged. The blue nullcline is for condition of all ODEs being set to zero except for $d{N}_1/dt$ and the green nullcline is for condition of all ODEs being set to zero except for $d{N}_2/dt$ (Eqs. S22–S25). (C) Phenotype diagram when the one-cell Notch–Delta–Jagged circuit is driven by both the external Notch $\left(N_{ext}\right)$ and external Jagged $\left(J_{ext}\right)$, for $\left(D_{ext}=0\right)$. Each phase, denoted by a different color, corresponds to a different combination of coexisting phases. Same phenotype diagram is obtained when driven by $N_{ext}$ and $D_{ext}$, for $J_{ext}=0$, once Notch is considered to have the same binding affinity as $J_{ext}$ and $D_{ext}$. (D) Bifurcation of Notch protein levels on the membrane when driven by external Jagged for fixed levels of $N_{ext}=3,000$ proteins. This curve shows the existence of the monostable {S/R} phase (pink region) for a large range of external ligands. (E) Same as panel D for $N_{ext}=1,000$ proteins. In this case, the hybrid S/R state coexists with other states, i.e., seen only in bistable (blue and green regions) and tristable phases (gray region).