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