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