\frac{dx_{1}}{dt} = \left(1 \cdot k_{10} \cdot k_{1} \cdot x_{1} \cdot \left(1 - x_{1} / k_{2}\right) + -1 \cdot k_{10} \cdot k_{3} \cdot k_{4} \cdot x_{2} / \left(k_{5} + x_{2}\right)\right) / k_{10}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{10} \cdot k_{6} \cdot x_{2} \cdot \left(1 - x_{2} / k_{7}\right) + 1 \cdot k_{10} \cdot k_{8} \cdot x_{1} \cdot \left(1 - x_{1} / k_{9}\right)\right) / k_{10}