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