\frac{dx_{1}}{dt} = \left(-1 \cdot k_{52} \cdot k_{6} \cdot x_{1} + -1 \cdot k_{52} \cdot k_{8} \cdot x_{1} + 1 \cdot k_{52} \cdot 6 \cdot 10^{-6} \cdot k_{51} \cdot x_{14} \cdot x_{3} + 1 \cdot k_{52} \cdot \frac{12}{5} \cdot 10^{-5} \cdot k_{51} \cdot x_{14} \cdot x_{2}\right) / k_{52}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{52} \cdot k_{6} \cdot x_{1} + -1 \cdot k_{52} \cdot k_{9} \cdot x_{2} + 1 \cdot k_{52} \cdot \frac{6}{5} \cdot 10^{-5} \cdot k_{51} \cdot x_{14} \cdot x_{4} + -1 \cdot k_{52} \cdot \frac{12}{5} \cdot 10^{-5} \cdot k_{51} \cdot x_{14} \cdot x_{2} + 1 \cdot k_{52} \cdot \frac{6}{5} \cdot 10^{-7} \cdot k_{51} \cdot x_{14} \cdot x_{5}\right) / k_{52}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{52} \cdot k_{8} \cdot x_{1} + -1 \cdot k_{52} \cdot k_{7} \cdot x_{3} + -1 \cdot k_{52} \cdot 6 \cdot 10^{-6} \cdot k_{51} \cdot x_{14} \cdot x_{3} + 1 \cdot k_{52} \cdot \frac{6}{5} \cdot 10^{-5} \cdot k_{51} \cdot x_{14} \cdot x_{4}\right) / k_{52}\\
\frac{dx_{4}}{dt} = \left(1 \cdot k_{52} \cdot k_{7} \cdot x_{3} + -1 \cdot k_{52} \cdot \frac{6}{5} \cdot 10^{-5} \cdot k_{51} \cdot x_{14} \cdot x_{4} + -1 \cdot k_{52} \cdot \frac{6}{5} \cdot 10^{-5} \cdot k_{51} \cdot x_{14} \cdot x_{4}\right) / k_{52}\\
\frac{dx_{5}}{dt} = \left(1 \cdot k_{52} \cdot k_{9} \cdot x_{2} + -1 \cdot k_{52} \cdot \frac{6}{5} \cdot 10^{-7} \cdot k_{51} \cdot x_{14} \cdot x_{5}\right) / k_{52}\\
\frac{dx_{8}}{dt} = \left(-1 \cdot k_{52} \cdot k_{11} \cdot x_{7} \cdot x_{8} / \left(k_{12} + x_{8}\right) \cdot \left(1 - \left(x_{9} + x_{10}\right) / \left(x_{6} \cdot k_{10}\right)\right) + 1 \cdot k_{52} \cdot k_{15} \cdot x_{11}\right) / k_{52}\\
\frac{dx_{9}}{dt} = \left(1 \cdot k_{52} \cdot k_{11} \cdot x_{7} \cdot x_{8} / \left(k_{12} + x_{8}\right) \cdot \left(1 - \left(x_{9} + x_{10}\right) / \left(x_{6} \cdot k_{10}\right)\right) + -1 \cdot k_{52} \cdot k_{11} \cdot x_{7} \cdot x_{9} / \left(k_{12} + x_{9}\right) + -1 \cdot k_{52} \cdot \left(k_{13} \cdot x_{9} \cdot x_{12} - k_{14} \cdot x_{11}\right) + 1 \cdot k_{52} \cdot k_{15} \cdot x_{13}\right) / k_{52}\\
\frac{dx_{10}}{dt} = \left(1 \cdot k_{52} \cdot k_{11} \cdot x_{7} \cdot x_{9} / \left(k_{12} + x_{9}\right) + -1 \cdot k_{52} \cdot \left(k_{13} \cdot x_{10} \cdot x_{12} - k_{14} \cdot x_{13}\right)\right) / k_{52}\\
\frac{dx_{11}}{dt} = \left(1 \cdot k_{52} \cdot \left(k_{13} \cdot x_{9} \cdot x_{12} - k_{14} \cdot x_{11}\right) + 1 \cdot k_{52} \cdot k_{16} \cdot x_{13} + -1 \cdot k_{52} \cdot k_{15} \cdot x_{11}\right) / k_{52}\\
\frac{dx_{12}}{dt} = \left(-1 \cdot k_{52} \cdot \left(k_{13} \cdot x_{9} \cdot x_{12} - k_{14} \cdot x_{11}\right) + -1 \cdot k_{52} \cdot \left(k_{13} \cdot x_{10} \cdot x_{12} - k_{14} \cdot x_{13}\right) + 1 \cdot k_{52} \cdot k_{15} \cdot x_{13} + 1 \cdot k_{52} \cdot k_{15} \cdot x_{11}\right) / k_{52}\\
\frac{dx_{13}}{dt} = \left(1 \cdot k_{52} \cdot \left(k_{13} \cdot x_{10} \cdot x_{12} - k_{14} \cdot x_{13}\right) + -1 \cdot k_{52} \cdot k_{15} \cdot x_{13} + -1 \cdot k_{52} \cdot k_{16} \cdot x_{13}\right) / k_{52}\\
\frac{dx_{15}}{dt} = \left(1 \cdot k_{52} \cdot k_{17} \cdot x_{7} \cdot x_{16} / \left(k_{18} + x_{16}\right) + -1 \cdot k_{52} \cdot k_{19} \cdot x_{14} \cdot x_{15} / \left(k_{20} + x_{15}\right) + -1 \cdot k_{52} \cdot \left(k_{21} \cdot x_{15} \cdot x_{17} - k_{22} \cdot x_{18}\right)\right) / k_{52}\\
\frac{dx_{16}}{dt} = \left(-1 \cdot k_{52} \cdot k_{17} \cdot x_{7} \cdot x_{16} / \left(k_{18} + x_{16}\right) + 1 \cdot k_{52} \cdot k_{19} \cdot x_{14} \cdot x_{15} / \left(k_{20} + x_{15}\right)\right) / k_{52}\\
\frac{dx_{17}}{dt} = -1 \cdot k_{52} \cdot \left(k_{21} \cdot x_{15} \cdot x_{17} - k_{22} \cdot x_{18}\right) / k_{52}\\
\frac{dx_{18}}{dt} = 1 \cdot k_{52} \cdot \left(k_{21} \cdot x_{15} \cdot x_{17} - k_{22} \cdot x_{18}\right) / k_{52}\\
\frac{dx_{20}}{dt} = \left(1 \cdot k_{52} \cdot k_{23} \cdot x_{7} \cdot x_{21} / \left(k_{24} + x_{21}\right) + -1 \cdot k_{52} \cdot k_{25} \cdot x_{14} \cdot x_{20} / \left(k_{26} + x_{20}\right) + -1 \cdot k_{52} \cdot \left(k_{27} \cdot x_{20} \cdot x_{24} - k_{28} \cdot x_{23}\right)\right) / k_{52}\\
\frac{dx_{21}}{dt} = \left(-1 \cdot k_{52} \cdot k_{23} \cdot x_{7} \cdot x_{21} / \left(k_{24} + x_{21}\right) + 1 \cdot k_{52} \cdot k_{25} \cdot x_{14} \cdot x_{20} / \left(k_{26} + x_{20}\right)\right) / k_{52}\\
\frac{dx_{22}}{dt} = \left(1 \cdot k_{52} \cdot k_{29} \cdot x_{7} \cdot x_{23} + -1 \cdot k_{52} \cdot k_{30} \cdot x_{7} \cdot x_{22}\right) / k_{52}\\
\frac{dx_{23}}{dt} = \left(1 \cdot k_{52} \cdot \left(k_{27} \cdot x_{20} \cdot x_{24} - k_{28} \cdot x_{23}\right) + -1 \cdot k_{52} \cdot k_{29} \cdot x_{7} \cdot x_{23}\right) / k_{52}\\
\frac{dx_{24}}{dt} = -1 \cdot k_{52} \cdot \left(k_{27} \cdot x_{20} \cdot x_{24} - k_{28} \cdot x_{23}\right) / k_{52}\\
\frac{dx_{25}}{dt} = 1 \cdot k_{52} \cdot k_{30} \cdot x_{7} \cdot x_{22} / k_{52}\\
\frac{dx_{28}}{dt} = \left(1 \cdot k_{52} \cdot k_{31} \cdot x_{25} \cdot x_{29} + -1 \cdot k_{52} \cdot \left(k_{32} \cdot x_{28} \cdot x_{31} - k_{33} \cdot x_{38}\right)\right) / k_{52}\\
\frac{dx_{29}}{dt} = -1 \cdot k_{52} \cdot k_{31} \cdot x_{25} \cdot x_{29} / k_{52}\\
\frac{dx_{31}}{dt} = -1 \cdot k_{52} \cdot \left(k_{32} \cdot x_{28} \cdot x_{31} - k_{33} \cdot x_{38}\right) / k_{52}\\
\frac{dx_{32}}{dt} = -1 \cdot k_{52} \cdot \left(k_{34} \cdot x_{38} \cdot x_{32} - k_{35} \cdot x_{33}\right) / k_{52}\\
\frac{dx_{33}}{dt} = \left(1 \cdot k_{52} \cdot \left(k_{34} \cdot x_{38} \cdot x_{32} - k_{35} \cdot x_{33}\right) + -1 \cdot k_{52} \cdot k_{36} \cdot x_{25} \cdot x_{33}\right) / k_{52}\\
\frac{dx_{37}}{dt} = 1 \cdot k_{52} \cdot k_{36} \cdot x_{25} \cdot x_{33} / k_{52}\\
\frac{dx_{38}}{dt} = \left(1 \cdot k_{52} \cdot \left(k_{32} \cdot x_{28} \cdot x_{31} - k_{33} \cdot x_{38}\right) + -1 \cdot k_{52} \cdot \left(k_{34} \cdot x_{38} \cdot x_{32} - k_{35} \cdot x_{33}\right)\right) / k_{52}