\frac{dx_{1}}{dt} = \left(1 \cdot k_{24} \cdot k_{1} \cdot x_{5} \cdot x_{2} / \left(\left(k_{12} + x_{2}\right) \cdot \left(1 + k_{6} \cdot x_{4}\right)\right) + 1 \cdot k_{24} \cdot k_{2} \cdot x_{1} \cdot \left(1 - k_{4} \cdot x_{1}\right) / \left(1 + k_{6} \cdot x_{4}\right) + -1 \cdot k_{24} \cdot k_{3} \cdot x_{1} + -1 \cdot k_{24} \cdot k_{8} \cdot x_{2} \cdot x_{1}\right) / k_{24}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{24} \cdot k_{9} \cdot x_{2} \cdot \left(1 + k_{6} \cdot x_{4}\right) \cdot \left(1 - k_{10} \cdot x_{2}\right) / \left(1 + k_{7} \cdot x_{3}\right) + -1 \cdot k_{24} \cdot k_{11} \cdot x_{3} \cdot x_{2} / \left(k_{14} + x_{2}\right)\right) / k_{24}\\
\frac{dx_{3}}{dt} = \left(-1 \cdot k_{24} \cdot k_{16} \cdot x_{3} + 1 \cdot k_{24} \cdot \left(k_{19} \cdot x_{1} + k_{22}\right) \cdot x_{2} / \left(\left(k_{12} + x_{2}\right) \cdot \left(1 + k_{6} \cdot x_{4}\right)\right)\right) / k_{24}\\
\frac{dx_{4}}{dt} = \left(-1 \cdot k_{24} \cdot k_{17} \cdot x_{4} + 1 \cdot k_{24} \cdot \left(k_{20} \cdot x_{1} + k_{22}\right) \cdot x_{2} / \left(k_{12} + x_{2}\right) + 1 \cdot k_{24} \cdot k_{21} \cdot x_{2}^{2} / \left(k_{13}^{2} + x_{2}^{2}\right)\right) / k_{24}\\
\frac{dx_{5}}{dt} = \left(-1 \cdot k_{24} \cdot k_{15} \cdot x_{5} + 1 \cdot k_{24} \cdot \left(k_{18} \cdot x_{1} + k_{22}\right) \cdot x_{2} / \left(\left(k_{12} + x_{2}\right) \cdot \left(1 + k_{6} \cdot x_{4}\right)\right)\right) / k_{24}