\frac{dx_{1}}{dt} = \left(1 \cdot k_{23} \cdot k_{1} / \left(1 + k_{9} \cdot x_{3}^{k_{14}}\right) \cdot \left(k_{15} - x_{1}\right) \cdot k_{4} / \left(1 + k_{11} \cdot x_{3}^{k_{14}}\right) \cdot x_{1} + -1 \cdot k_{23} \cdot \left(1 - k_{1} / \left(1 + k_{9} \cdot x_{3}^{k_{14}}\right)\right) \cdot k_{4} / \left(1 + k_{11} \cdot x_{3}^{k_{14}}\right) \cdot x_{1}\right) / k_{23}\\
\frac{dx_{2}}{dt} = \left(2 \cdot k_{23} \cdot \left(1 - k_{1} / \left(1 + k_{9} \cdot x_{3}^{k_{14}}\right)\right) \cdot k_{4} / \left(1 + k_{11} \cdot x_{3}^{k_{14}}\right) \cdot x_{1} + 1 \cdot k_{23} \cdot k_{2} / \left(1 + k_{10} \cdot x_{3}^{k_{14}}\right) \cdot \left(k_{16} - \left(x_{2} + x_{4}\right)\right) \cdot k_{5} / \left(1 + k_{12} \cdot x_{3}^{k_{14}}\right) \cdot x_{2} + -1 \cdot k_{23} \cdot \left(1 - k_{2} / \left(1 + k_{10} \cdot x_{3}^{k_{14}}\right)\right) \cdot k_{5} / \left(1 + k_{12} \cdot x_{3}^{k_{14}}\right) \cdot x_{2}\right) / k_{23}\\
\frac{dx_{3}}{dt} = \left(2 \cdot k_{23} \cdot \left(1 - k_{2} / \left(1 + k_{10} \cdot x_{3}^{k_{14}}\right)\right) \cdot k_{5} / \left(1 + k_{12} \cdot x_{3}^{k_{14}}\right) \cdot x_{2} + -1 \cdot k_{23} \cdot k_{7} \cdot x_{3}\right) / k_{23}\\
\frac{dx_{4}}{dt} = \left(1 \cdot k_{23} \cdot k_{3} \cdot \left(k_{16} - \left(x_{2} + x_{4}\right)\right) \cdot k_{6} \cdot x_{4} + -1 \cdot k_{23} \cdot \left(1 - k_{3}\right) \cdot k_{6} \cdot x_{4}\right) / k_{23}\\
\frac{dx_{5}}{dt} = \left(2 \cdot k_{23} \cdot \left(1 - k_{3}\right) \cdot k_{6} \cdot x_{4} + -1 \cdot k_{23} \cdot k_{8} \cdot x_{5}\right) / k_{23}