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