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