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M Phase Transition

The abrupt shift from the G2 phase to mitosis, characterized by chromosome condensation, spindle formation, and nuclear envelope breakdown.
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The statement of the theorem

Define the state variable Mstate∈[0,1]M_{state} \in [0, 1] representing the commitment to mitosis. The transition from G2 to M is governed by the activation of the Cyclin B-CDK complex, CDKB\text{CDK}_{B}. Let CB(t)C_B(t) be the concentration of Cyclin B and DG2(t)D_{G2}(t) be the DNA damage status. The transition rate λG2→M\lambda_{G2 \to M} is modeled by a cooperative switch function: λG2→M=kmax⋅CB(t)nKMn+CB(t)n⋅exp⁡(−DG2(t)Dcrit)\lambda_{G2 \to M} = k_{max} \cdot \frac{C_B(t)^n}{K_M^n + C_B(t)^n} \cdot \exp\left(-\frac{D_{G2}(t)}{D_{crit}}\right) where nn is the Hill coefficient, KMK_M is the Michaelis constant, and DcritD_{crit} is the critical damage threshold. The state transition is initiated when λG2→M>λthreshold\lambda_{G2 \to M} > \lambda_{threshold}.
Source: Wikipedia