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