\frac{dx_{1}}{dt} = \left(1 \cdot k_{13} \cdot k_{1} + -1 \cdot k_{13} \cdot k_{4} \cdot x_{1} \cdot x_{2}^{k_{10}} / \left(k_{7}^{k_{10}} + x_{2}^{k_{10}}\right)\right) / k_{13}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{13} \cdot k_{3} \cdot \left(1 - x_{2}\right) \cdot x_{3}^{k_{12}} / \left(k_{9}^{k_{12}} + x_{3}^{k_{12}}\right) + -1 \cdot k_{13} \cdot k_{6} \cdot x_{2}\right) / k_{13}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{13} \cdot k_{2} \cdot \left(1 - x_{3}\right) \cdot x_{1}^{k_{11}} / \left(k_{8}^{k_{11}} + x_{1}^{k_{11}}\right) + -1 \cdot k_{13} \cdot k_{5} \cdot x_{3}\right) / k_{13}