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  • https://math.libretexts.org/Bookshelves/Applied_Mathematics/Mathematical_Biology_(Chasnov)/06%3A_Biochemical_Reactions/6.05%3A_Cooperativity
    Application of the law of mass action results in \[\begin{aligned} \frac{d C_{1}}{d t} &=k_{1} S E+\left(k_{-3}+k_{4}\right) C_{2}-\left(k_{-1}+k_{2}+k_{3} S\right) C_{1} \\[4pt] \frac{d C_{2}}{d t} &...Application of the law of mass action results in \[\begin{aligned} \frac{d C_{1}}{d t} &=k_{1} S E+\left(k_{-3}+k_{4}\right) C_{2}-\left(k_{-1}+k_{2}+k_{3} S\right) C_{1} \\[4pt] \frac{d C_{2}}{d t} &=k_{3} S C_{1}-\left(k_{-3}+k_{4}\right) C_{2} \end{aligned} \nonumber \] Applying the quasi-equilibrium approximation \(\dot{C}_{1}=\dot{C}_{2}=0\) and the conservation law \(E_{0}=E+C_{1}+C_{2}\) results in the following system of two equations and two unknowns: \[\begin{align} \left(k_{-1}+k_{2}…

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