\frac{dx_{1}}{dt} = \left(-1 \cdot k_{32} \cdot x_{1} \cdot \left(k_{5} \cdot x_{3} / \left(k_{6} + x_{3}\right) + k_{7} \cdot x_{2} / \left(k_{8} + x_{2}\right) + k_{9} \cdot x_{3} \cdot x_{2} / \left(\left(k_{6} + x_{3}\right) \cdot \left(k_{8} + x_{2}\right)\right)\right) \cdot \left(1 - k_{10} \cdot x_{1} / \left(k_{11} + x_{1}\right) - k_{12} \cdot x_{4} / \left(k_{13} + x_{4}\right)\right) \cdot k_{4} + -1 \cdot k_{32} \cdot x_{1} \cdot k_{4} + 1 \cdot k_{32} \cdot k_{1} + 1 \cdot k_{32} \cdot k_{2} \cdot \left(1 - x_{1} / k_{3}\right) \cdot x_{1}\right) / k_{32}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{32} \cdot k_{14} \cdot \left(1 - x_{2} / k_{15}\right) \cdot x_{2} + -1 \cdot k_{32} \cdot k_{16} \cdot x_{2} + 1 \cdot k_{32} \cdot k_{14} \cdot \left(1 - x_{2} / k_{15}\right) \cdot \left(k_{17} \cdot x_{3} / \left(k_{18} + x_{3}\right) + k_{19} \cdot x_{1} / \left(k_{20} + x_{1}\right)\right) \cdot x_{2}\right) / k_{32}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{32} \cdot k_{21} + 1 \cdot k_{32} \cdot k_{22} \cdot \left(1 - x_{3} / k_{23}\right) \cdot x_{3} + 1 \cdot k_{32} \cdot k_{22} \cdot \left(1 - x_{3} / k_{23}\right) \cdot k_{25} \cdot x_{2} / \left(k_{26} + x_{2}\right) \cdot x_{3} + -1 \cdot k_{32} \cdot k_{24} \cdot x_{3}\right) / k_{32}\\
\frac{dx_{4}}{dt} = \left(-1 \cdot k_{32} \cdot k_{29} \cdot x_{4} + 1 \cdot k_{32} \cdot k_{27} \cdot \left(1 - x_{4} / k_{28}\right) \cdot x_{4} + 1 \cdot k_{32} \cdot k_{27} \cdot \left(1 - x_{4} / k_{28}\right) \cdot k_{30} \cdot x_{1} / \left(k_{31} + x_{1}\right) \cdot x_{4}\right) / k_{32}