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