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