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