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