From Bistability to Oscillations

(A) The structure of the “1+2” subsystem. MAPKKK activation and MAPKKK* deactivation are indicated by the blue and red arrows, respectively.

(B) Limit cycle in the “1+2” system and its connection to the bistability in the “2” system. The limit cycle is plotted in red and the direction of time evolution is indicated by arrows. The hysteresis curve (black) is the I/O map of the system “2”, computed using the quantity KKK*tot as a bifurcation parameter. KKK*tot, defined as KKK*tot ≡ [KKK*] + [KK · KKK*] + [KK-P · KKK*], is a variable in system 1 + 2, but a parameter for system 2.

(C) Dynamics of the rates of MAPKKK activation (r1) and MAPKKK* deactivation (r2) along the periodic trajectory. The rates have been normalized by the maximum MAPKKK activation (r0). The arrows correspond to different phases of the periodic trajectory in (B).

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