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