Fig. 3. Bifurcation analysis of mitotic progression and mitotic collapse.

One- and two-parameter bifurcation diagrams are shown for normal mitotic progression (A,B), Wee1/Myt1 inhibition (C,D) and Wee1/Myt1 and Cdc25 double inhibition (E,F). One parameter bifurcation diagrams (A,C,E). CycB level is used as the bifurcation parameter while phosphorylated mitotic substrate indicates the state of the mitotic controls system. The black and the red curves represent the bifurcation diagrams before (ε = 1) and after (ε = 0.25) nuclear envelope breakdown, respectively. Solid lines represent stable while dashed lines unstable steady states. Normal mitotic progression (A), Wee1/Myt1 inhibition (C) and Wee1/Myt1 and Cdc25 double inhibition (E). The cyclin thresholds (labelled by Greek θ) for mitotic substrate phosphorylation and dephosphorylation are indicated with subscripts one and two, respectively. Between the two corresponding cyclin thresholds the mitotic susbtrate has two alternative stable steady states (G2 and M). Two parameter bifurcation diagrams (B,D,F). CycB and epsilon (ε) are chosen as the two parameters. The left black curve records the values of the cyclin thresholds (θ₂ values) for the mitotic substrate (S) dephosphorylation at different ε values. Its value is θ₂ when ε = 1 and its value is θ₂′ when ε = 0.25. The right black curve records the values of the cyclin thresholds for the mitotic susbtrate phosphorylation, which is θ₁ when ε = 1 and θ₁′ when ε = 0.25. The bistability region is between these two curves. The red lines record the time dependent trajectory of the system during mitotic progression. During normal mitotic progression (B) the trajectory starts from the G2 state in the bistable regime (red dot) and moves to the right at constant epsilon (ε) value until it crosses the cyclin threshold for phosphorylation of the mitotic substrate. As cells enter mitosis, NEBD triggers epsilon to decrease so the trajectory drops vertically and ends up the M phase state of the bistable regime. After Wee1/Myt1 inactivation (D), mitotic entry is triggered without the requirement of CycB production and the only stable steady state is in M phase (red dot). NEBD causes ε to decrease which drives the system vertically down, but it does not leave the M phase regime. When the two inhibitors for Wee1/Myt1 and Cdc25 are added after S phase (F), the system trajectory also drops vertically. The decrease of epsilon (ε) causes the system to enter the region with unphosphorylated mitotic substrate (mitotic collapse).