\frac{dx_{1}}{dt} = k_{1} \cdot x_{1} \cdot x_{3} \cdot \left(k_{2} + 1\right) / \left(k_{2} + x_{1} + x_{3} + x_{2}\right) + k_{3} \cdot \left(1 + k_{8} \cdot x_{3}\right) - k_{4} \cdot x_{1} \cdot x_{3} \cdot x_{3} - k_{5} \cdot x_{1}\\
\frac{dx_{2}}{dt} = x_{2} \cdot \left(k_{2} + 1\right) / \left(k_{2} + x_{1} + x_{3} + x_{2}\right) - x_{2}\\
\frac{dx_{3}}{dt} = k_{7} \cdot x_{3} \cdot \left(k_{2} + 1\right) / \left(k_{2} + x_{1} + x_{3} + x_{2}\right) - x_{3} - k_{6} \cdot x_{1} \cdot x_{3} \cdot x_{3}