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