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