\frac{dx_{1}}{dt} = \left(1 \cdot k_{23} \cdot k_{17} \cdot k_{1} / \left(k_{6} + k_{1}\right) + -1 \cdot k_{23} \cdot k_{13} \cdot x_{1} / \left(k_{4} + x_{1}\right)\right) / k_{23}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{23} \cdot k_{21} \cdot \left(x_{7} - x_{2}\right) / \left(k_{9} + x_{7} - x_{2}\right) \cdot \left(x_{1} + x_{3}\right) + -1 \cdot k_{23} \cdot k_{22} \cdot x_{2} / \left(k_{10} + x_{2}\right) \cdot x_{4}\right) / k_{23}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{23} \cdot k_{18} \cdot x_{2} + -1 \cdot k_{23} \cdot k_{14} \cdot x_{4} \cdot x_{3} / \left(k_{5} + x_{3}\right)\right) / k_{23}\\
\frac{dx_{4}}{dt} = \left(1 \cdot k_{23} \cdot k_{15} \cdot x_{2} + -1 \cdot k_{23} \cdot k_{11} \cdot x_{6} \cdot x_{4} / \left(k_{2} + x_{4}\right)\right) / k_{23}\\
\frac{dx_{5}}{dt} = \left(1 \cdot k_{23} \cdot k_{16} \cdot x_{4} + -1 \cdot k_{23} \cdot k_{12} \cdot x_{6} \cdot x_{5} / \left(k_{3} + x_{5}\right)\right) / k_{23}\\
\frac{dx_{6}}{dt} = \left(1 \cdot k_{23} \cdot k_{19} \cdot x_{5} \cdot \left(x_{8} - x_{6}\right) / \left(k_{7} + x_{8} - x_{6}\right) + -1 \cdot k_{23} \cdot k_{20} \cdot x_{6} / \left(k_{8} + x_{6}\right)\right) / k_{23}\\
\frac{dx_{7}}{dt} = 0 / k_{23}\\
\frac{dx_{8}}{dt} = 0 / k_{23}