\frac{dx_{1}}{dt} = \left(1 \cdot k_{2} + -1 \cdot k_{4} \cdot x_{1} \cdot \left(1 + x_{1}\right) \cdot 1 + x_{2}^{2} / \left(k_{3} + 1 + x_{1}^{2} \cdot 1 + x_{2}^{2}\right)\right) / k_{1}\\
\frac{dx_{2}}{dt} = \left(50 \cdot k_{4} \cdot x_{1} \cdot \left(1 + x_{1}\right) \cdot 1 + x_{2}^{2} / \left(k_{3} + 1 + x_{1}^{2} \cdot 1 + x_{2}^{2}\right) + -1 \cdot k_{7} \cdot x_{2} \cdot \left(1 + k_{6} \cdot x_{2}\right) \cdot 1 + x_{3}^{2} / \left(k_{5} + 1 + k_{6} \cdot x_{2}^{2} \cdot 1 + x_{3}^{2}\right)\right) / k_{1}\\
\frac{dx_{3}}{dt} = \left(\frac{1}{50} \cdot k_{7} \cdot x_{2} \cdot \left(1 + k_{6} \cdot x_{2}\right) \cdot 1 + x_{3}^{2} / \left(k_{5} + 1 + k_{6} \cdot x_{2}^{2} \cdot 1 + x_{3}^{2}\right) + -1 \cdot k_{8} \cdot x_{3}\right) / k_{1}