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