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