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