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