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