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Cyclin-Dependent Kinases (CDKs)

A family of protein kinases that regulate the progression of the cell cycle by phosphorylating target proteins, their activity controlled by cyclins.
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The statement of the theorem

Let C(t)C(t) be the concentration of the Cyclin and D(t)D(t) be the concentration of the CDK. The instantaneous activity of the kinase, A(t)A(t), is defined by the mass-action kinetics: A(t)=kcat⋅C(t)⋅D(t)KM+C(t)⋅D(t)A(t) = k_{cat} \cdot \frac{C(t) \cdot D(t)}{K_M + C(t) \cdot D(t)} where kcatk_{cat} is the catalytic rate constant and KMK_M is the apparent Michaelis constant for the substrate. The phosphorylation rate of a target protein PP is then given by the differential equation: d[Pphos]dt=(A(t)Ksub+[Punphos])[Punphos]−kdephos[Pphos]\frac{d[P_{phos}]}{dt} = \left( \frac{A(t)}{K_{sub} + [P_{unphos}]} \right) [P_{unphos}] - k_{dephos} [P_{phos}] where [Punphos][P_{unphos}] and [Pphos][P_{phos}] are the concentrations of unphosphorylated and phosphorylated protein, respectively.
Source: Wikipedia