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