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