\frac{dx_{1}}{dt} = \left(1 \cdot k_{10} \cdot k_{1} \cdot x_{1} \cdot \left(1 - \left(x_{1} + x_{3}\right) / k_{2}\right) + -1 \cdot k_{10} \cdot k_{3} \cdot x_{1} \cdot x_{2}\right) / k_{10}\\
\frac{dx_{2}}{dt} = 1 \cdot k_{10} \cdot k_{4} \cdot x_{2} \cdot \left(1 - x_{2} / \left(k_{5} + k_{6} \cdot \left(x_{1} + \frac{1}{1000} \cdot x_{3}\right) \cdot x_{2}\right)\right) / k_{10}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{10} \cdot k_{7} \cdot x_{3} \cdot \left(1 - \left(x_{3} + x_{1}\right) / k_{2}\right) + -1 \cdot k_{10} \cdot k_{3} \cdot k_{9} \cdot x_{3} \cdot x_{2}\right) / k_{10}