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