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