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