\frac{dx_{1}}{dt} = \left(1 \cdot k_{22} \cdot \left(2 \cdot k_{1} / \left(1 + k_{8} \cdot x_{3}^{k_{13}}\right) - 1\right) \cdot k_{2} / \left(1 + k_{7} \cdot x_{3}^{k_{12}}\right) \cdot x_{1} + 1 \cdot k_{22} \cdot 2 \cdot k_{4} / \left(1 + k_{9} \cdot x_{3}^{k_{14}}\right) \cdot x_{2} \cdot k_{5} / \left(1 + k_{11} \cdot x_{1}^{k_{16}}\right) \cdot \left(1 - k_{3} / \left(1 + k_{10} \cdot x_{3}^{k_{15}}\right)\right)\right) / k_{22}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{22} \cdot 2 \cdot k_{2} / \left(1 + k_{7} \cdot x_{3}^{k_{12}}\right) \cdot x_{1} \cdot \left(1 - k_{1} / \left(1 + k_{8} \cdot x_{3}^{k_{13}}\right)\right) + 1 \cdot k_{22} \cdot \left(2 \cdot k_{3} / \left(1 + k_{10} \cdot x_{3}^{k_{15}}\right) - 1\right) \cdot k_{4} / \left(1 + k_{9} \cdot x_{3}^{k_{14}}\right) \cdot x_{2}\right) / k_{22}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{22} \cdot 2 \cdot k_{4} / \left(1 + k_{9} \cdot x_{3}^{k_{14}}\right) \cdot x_{2} \cdot \left(1 - k_{3} / \left(1 + k_{10} \cdot x_{3}^{k_{15}}\right)\right) \cdot \left(1 - k_{5} / \left(1 + k_{11} \cdot x_{1}^{k_{16}}\right)\right) + -1 \cdot k_{22} \cdot k_{6} \cdot x_{3}\right) / k_{22}