\frac{dx_{1}}{dt} = 0\\
\frac{dx_{2}}{dt} = \left(1 \cdot \left(k_{8} \cdot k_{2} - k_{1} \cdot x_{2}\right) + -1 \cdot \left(\left(-k_{5} \cdot x_{3}\right) + k_{6} \cdot x_{2} / \left(1 + x_{4}\right)\right) + -1 \cdot \left(\left(-k_{3} \cdot x_{4}\right) + k_{4} \cdot x_{2} / \left(1 + x_{4}\right)\right)\right) / k_{7}\\
\frac{dx_{3}}{dt} = 1 \cdot \left(\left(-k_{5} \cdot x_{3}\right) + k_{6} \cdot x_{2} / \left(1 + x_{4}\right)\right) / k_{7}\\
\frac{dx_{4}}{dt} = 1 \cdot \left(\left(-k_{3} \cdot x_{4}\right) + k_{4} \cdot x_{2} / \left(1 + x_{4}\right)\right) / k_{7}