\frac{dx_{1}}{dt} = \left(1 \cdot k_{19} \cdot k_{1} \cdot x_{1} + -1 \cdot k_{19} \cdot \left(k_{2} \cdot x_{1} \cdot x_{1} + k_{3} \cdot x_{1} \cdot x_{3} + k_{4} \cdot x_{1} \cdot x_{5}\right)\right) / k_{19}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{19} \cdot \left(k_{5} \cdot x_{1} + k_{7} \cdot x_{1} \cdot x_{2}\right) + -1 \cdot k_{19} \cdot k_{6} \cdot x_{2}\right) / k_{19}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{19} \cdot \left(k_{8} \cdot x_{1} + k_{10} \cdot x_{1} \cdot x_{3} + k_{11} \cdot x_{2} \cdot x_{3}\right) + -1 \cdot k_{19} \cdot k_{9} \cdot x_{3}\right) / k_{19}\\
\frac{dx_{4}}{dt} = \left(1 \cdot k_{19} \cdot \left(k_{12} \cdot x_{1} + k_{14} \cdot x_{1} \cdot x_{4} + k_{15} \cdot x_{2} \cdot x_{4}\right) + -1 \cdot k_{19} \cdot k_{13} \cdot x_{4}\right) / k_{19}\\
\frac{dx_{5}}{dt} = \left(1 \cdot k_{19} \cdot k_{16} \cdot x_{4} + -1 \cdot k_{19} \cdot \left(k_{17} \cdot x_{5} + k_{18} \cdot x_{1} \cdot x_{5}\right)\right) / k_{19}