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