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