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