\frac{dx_{1}}{dt} = \left(-1 \cdot k_{1} \cdot \left(k_{3} \cdot x_{1} \cdot x_{4} - k_{4} \cdot x_{2}\right) + -1 \cdot k_{12} \cdot k_{1} \cdot \left(x_{1} - x_{13}\right)\right) / k_{1}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{3} \cdot x_{1} \cdot x_{4} - k_{4} \cdot x_{2}\right) + -1 \cdot k_{1} \cdot \left(k_{5} \cdot x_{2} - k_{6} \cdot x_{6} \cdot k_{19}\right)\right) / k_{1}\\
\frac{dx_{3}}{dt} = 0\\
\frac{dx_{4}}{dt} = \left(-1 \cdot k_{1} \cdot \left(k_{3} \cdot x_{1} \cdot x_{4} - k_{4} \cdot x_{2}\right) + 1 \cdot k_{1} \cdot \left(k_{9} \cdot x_{5} - k_{10} \cdot x_{8} \cdot x_{4}\right)\right) / k_{1}\\
\frac{dx_{5}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{7} \cdot x_{6} \cdot k_{20} - k_{8} \cdot x_{5}\right) + -1 \cdot k_{1} \cdot \left(k_{9} \cdot x_{5} - k_{10} \cdot x_{8} \cdot x_{4}\right)\right) / k_{1}\\
\frac{dx_{6}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{5} \cdot x_{2} - k_{6} \cdot x_{6} \cdot k_{19}\right) + -1 \cdot k_{1} \cdot \left(k_{7} \cdot x_{6} \cdot k_{20} - k_{8} \cdot x_{5}\right)\right) / k_{1}\\
\frac{dx_{7}}{dt} = 0\\
\frac{dx_{8}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{9} \cdot x_{5} - k_{10} \cdot x_{8} \cdot x_{4}\right) + -1 \cdot k_{11} \cdot k_{1} \cdot \left(x_{8} - x_{11}\right)\right) / k_{1}\\
\frac{dx_{9}}{dt} = 0 / k_{2}\\
\frac{dx_{10}}{dt} = \left(-1 \cdot \left(k_{13} \cdot x_{11} \cdot x_{10} - k_{14} \cdot x_{12}\right) \cdot k_{2} + 1 \cdot k_{2} \cdot k_{15} \cdot x_{12} \cdot x_{9} / \left(x_{12} + k_{16}\right)\right) / k_{2}\\
\frac{dx_{11}}{dt} = \left(1 \cdot k_{11} \cdot k_{1} \cdot \left(x_{8} - x_{11}\right) + -1 \cdot \left(k_{13} \cdot x_{11} \cdot x_{10} - k_{14} \cdot x_{12}\right) \cdot k_{2} + -1 \cdot k_{2} \cdot k_{17} \cdot x_{11} \cdot x_{9} / \left(k_{18} + x_{11}\right)\right) / k_{2}\\
\frac{dx_{12}}{dt} = \left(1 \cdot \left(k_{13} \cdot x_{11} \cdot x_{10} - k_{14} \cdot x_{12}\right) \cdot k_{2} + -1 \cdot k_{2} \cdot k_{15} \cdot x_{12} \cdot x_{9} / \left(x_{12} + k_{16}\right)\right) / k_{2}\\
\frac{dx_{13}}{dt} = \left(1 \cdot k_{12} \cdot k_{1} \cdot \left(x_{1} - x_{13}\right) + 1 \cdot k_{2} \cdot k_{15} \cdot x_{12} \cdot x_{9} / \left(x_{12} + k_{16}\right) + 1 \cdot k_{2} \cdot k_{17} \cdot x_{11} \cdot x_{9} / \left(k_{18} + x_{11}\right)\right) / k_{2}