\frac{dx_{1}}{dt} = \left(1 \cdot k_{13} \cdot k_{1} \cdot x_{1} + -1 \cdot k_{13} \cdot k_{2} \cdot x_{2} \cdot x_{1} / \left(x_{4} + k_{3}\right)\right) / k_{13}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{13} \cdot k_{4} \cdot x_{1} \cdot x_{2} / \left(x_{4} + k_{3}\right) + 1 \cdot k_{13} \cdot k_{5} \cdot x_{3} \cdot x_{2} / \left(x_{4} + k_{3}\right) + -1 \cdot k_{13} \cdot k_{7} \cdot x_{2} \cdot x_{1} + -1 \cdot k_{13} \cdot k_{8} \cdot x_{2}\right) / k_{13}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{13} \cdot k_{10} + -1 \cdot k_{13} \cdot k_{9} \cdot x_{3} + -1 \cdot k_{13} \cdot k_{11} \cdot x_{2} \cdot x_{3}\right) / k_{13}\\
\frac{dx_{4}}{dt} = \left(1 \cdot k_{13} \cdot k_{6} + -1 \cdot k_{13} \cdot k_{12} \cdot x_{4}\right) / k_{13}