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