\frac{dx_{1}}{dt} = \left(1 \cdot k_{13} \cdot k_{1} + -1 \cdot k_{13} \cdot k_{2} \cdot x_{1} + -1 \cdot k_{13} \cdot k_{3} \cdot x_{2} \cdot x_{1} / \left(k_{4} \cdot \left(1 + x_{3} / k_{5}\right) + x_{1}\right)\right) / k_{13}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{13} \cdot k_{6} \cdot x_{1} \cdot x_{4} / \left(k_{7} + x_{4}\right) + -1 \cdot k_{13} \cdot k_{8} \cdot x_{2} / \left(k_{9} + x_{2}\right)\right) / k_{13}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{13} \cdot k_{10} + -1 \cdot k_{13} \cdot k_{11} \cdot x_{3} + -1 \cdot k_{13} \cdot k_{12} \cdot x_{2} \cdot x_{3} / \left(k_{5} \cdot \left(1 + x_{1} / k_{4}\right) + x_{3}\right)\right) / k_{13}\\
\frac{dx_{5}}{dt} = 0