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