\frac{dx_{1}}{dt} = \left(-1 \cdot k_{1} \cdot x_{1} + 1 \cdot k_{5} \cdot x_{1}\right) / k_{13}\\
\frac{dx_{2}}{dt} = \left(1 \cdot \left(k_{2} + k_{3} \cdot x_{1} / \left(x_{1} + k_{4}\right)\right) \cdot x_{1} + -1 \cdot k_{6} \cdot x_{2} + 1 \cdot k_{10} \cdot x_{2}\right) / k_{13}\\
\frac{dx_{3}}{dt} = \left(1 \cdot \left(k_{7} + k_{8} \cdot x_{2} / \left(x_{2} + k_{9}\right)\right) \cdot x_{2} + -1 \cdot k_{11} \cdot x_{3}\right) / k_{13}