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DNA Damage Response

A cellular pathway activated in response to DNA damage, halting the cell cycle to allow for repair or initiating programmed cell death if damage is irreparable.
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The statement of the theorem

Define the DNA damage state D\mathcal{D} as a binary variable, D=1\mathcal{D}=1 if damage is present, and D=0\mathcal{D}=0 otherwise. The DDR pathway activates a signaling cascade involving kinases (e.g., ATM, ATR). Let PactiveP_{active} be the concentration of the activated checkpoint protein. The activation rate is modeled by a Michaelis-Menten type function dependent on damage: \nd[Pactive]dt=kon⋅D⋅[Pinactive]−koff[Pactive]⋅(1+[Pactive]KD)\frac{d [P_{active}]}{d t} = k_{on} \cdot \mathcal{D} \cdot [P_{inactive}] - k_{off} [P_{active}] \cdot \left( 1 + \frac{[P_{active}]}{K_D} \right) \nIf D=1\mathcal{D}=1, the resulting high [Pactive][P_{active}] concentration triggers the activation of CDK\text{CDK} inhibitors (e.g., p21\text{p21}), mathematically enforcing a cell cycle arrest by setting the effective transition rate λG1→S=0\lambda_{G1 \to S} = 0 until D\mathcal{D} returns to 00.
Source: Wikipedia