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