\frac{dx_{1}}{dt} = \left(1 \cdot k_{8} \cdot \left(k_{62} \cdot k_{31} \cdot \left(k_{55} \cdot x_{7} - k_{54} \cdot x_{1} / k_{41}\right) / \left(k_{32} \cdot k_{33}\right) / \left(\left(1 + k_{55} / k_{32} + k_{54} / k_{34}\right) \cdot \left(1 + x_{7} / k_{33} + x_{1} / k_{35}\right)\right) + k_{58} \cdot k_{36} \cdot \left(k_{55} \cdot x_{7} - k_{54} \cdot x_{1} / k_{41}\right) / \left(k_{37} \cdot k_{38}\right) / \left(\left(1 + k_{55} / k_{37} + k_{54} / k_{39}\right) \cdot \left(1 + x_{7} / k_{38} + x_{1} / k_{40}\right)\right)\right) + -1 \cdot k_{8} \cdot k_{63} \cdot k_{42} \cdot \left(x_{8} \cdot x_{1} - k_{55} \cdot k_{54} / k_{43}\right) / \left(k_{2} \cdot k_{3}\right) / \left(\left(1 + x_{8} / k_{2} + k_{55} / k_{5}\right) \cdot \left(1 + x_{1} / k_{3} + k_{54} / k_{6} + x_{5} / k_{4} + x_{7} / k_{7}\right)\right) + -1 \cdot k_{8} \cdot k_{52} \cdot x_{1}\right) / k_{8}\\
\frac{dx_{2}}{dt} = \left(-1 \cdot k_{8} \cdot k_{61} \cdot k_{28} \cdot x_{2} / k_{29} / \left(1 + x_{2} / k_{29} + x_{4} / k_{30}\right) + 1 \cdot k_{8} \cdot k_{64} \cdot k_{46} \cdot x_{10} \cdot x_{9} / \left(k_{47} \cdot k_{48}\right) / \left(\left(1 + x_{10} / k_{47} + x_{2} / k_{49}\right) \cdot \left(1 + x_{9} / k_{48} + x_{3} / k_{50}\right)\right)\right) / k_{8}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{8} \cdot \left(k_{56} \cdot k_{9} \cdot x_{4} \cdot x_{9} / \left(k_{10} \cdot k_{11}\right) / \left(\left(1 + x_{4} / k_{10} + x_{6} / k_{12}\right) \cdot \left(1 + x_{9} / k_{11} + x_{3} / k_{13}\right)\right) + k_{57} \cdot k_{14} \cdot x_{4} \cdot x_{9} / \left(\left(1 + x_{4} / k_{15} + x_{6} / k_{17}\right) \cdot \left(1 + x_{9} / k_{16} + x_{3} / k_{18}\right)\right)\right) + 1 \cdot k_{8} \cdot k_{64} \cdot k_{46} \cdot x_{10} \cdot x_{9} / \left(k_{47} \cdot k_{48}\right) / \left(\left(1 + x_{10} / k_{47} + x_{2} / k_{49}\right) \cdot \left(1 + x_{9} / k_{48} + x_{3} / k_{50}\right)\right) + -1 \cdot k_{8} \cdot k_{51} \cdot x_{3}\right) / k_{8}\\
\frac{dx_{4}}{dt} = \left(-1 \cdot k_{8} \cdot \left(k_{56} \cdot k_{9} \cdot x_{4} \cdot x_{9} / \left(k_{10} \cdot k_{11}\right) / \left(\left(1 + x_{4} / k_{10} + x_{6} / k_{12}\right) \cdot \left(1 + x_{9} / k_{11} + x_{3} / k_{13}\right)\right) + k_{57} \cdot k_{14} \cdot x_{4} \cdot x_{9} / \left(\left(1 + x_{4} / k_{15} + x_{6} / k_{17}\right) \cdot \left(1 + x_{9} / k_{16} + x_{3} / k_{18}\right)\right)\right) + 1 \cdot k_{8} \cdot k_{61} \cdot k_{28} \cdot x_{2} / k_{29} / \left(1 + x_{2} / k_{29} + x_{4} / k_{30}\right)\right) / k_{8}\\
\frac{dx_{5}}{dt} = \left(1 \cdot k_{8} \cdot k_{59} \cdot k_{19} \cdot \left(x_{6} - x_{5} / k_{23}\right) / k_{20} / \left(1 + x_{6} / k_{20} + x_{5} / k_{21}\right) + -1 \cdot k_{8} \cdot k_{63} \cdot k_{44} \cdot \left(x_{8} \cdot x_{5} - k_{55} \cdot x_{7} / k_{45}\right) / \left(k_{2} \cdot k_{4}\right) / \left(\left(1 + x_{8} / k_{2} + k_{55} / k_{5}\right) \cdot \left(1 + x_{1} / k_{3} + k_{54} / k_{6} + x_{5} / k_{4} + x_{7} / k_{7}\right)\right) + -1 \cdot k_{8} \cdot k_{53} \cdot x_{5}\right) / k_{8}\\
\frac{dx_{6}}{dt} = \left(1 \cdot k_{8} \cdot \left(k_{56} \cdot k_{9} \cdot x_{4} \cdot x_{9} / \left(k_{10} \cdot k_{11}\right) / \left(\left(1 + x_{4} / k_{10} + x_{6} / k_{12}\right) \cdot \left(1 + x_{9} / k_{11} + x_{3} / k_{13}\right)\right) + k_{57} \cdot k_{14} \cdot x_{4} \cdot x_{9} / \left(\left(1 + x_{4} / k_{15} + x_{6} / k_{17}\right) \cdot \left(1 + x_{9} / k_{16} + x_{3} / k_{18}\right)\right)\right) + -1 \cdot k_{8} \cdot k_{59} \cdot k_{19} \cdot \left(x_{6} - x_{5} / k_{23}\right) / k_{20} / \left(1 + x_{6} / k_{20} + x_{5} / k_{21}\right) + -1 \cdot k_{8} \cdot k_{60} \cdot k_{24} \cdot \left(x_{6} - x_{8} / k_{27}\right) / k_{25} / \left(1 + x_{6} / k_{25} + x_{8} / k_{26}\right)\right) / k_{8}\\
\frac{dx_{7}}{dt} = \left(-1 \cdot k_{8} \cdot \left(k_{62} \cdot k_{31} \cdot \left(k_{55} \cdot x_{7} - k_{54} \cdot x_{1} / k_{41}\right) / \left(k_{32} \cdot k_{33}\right) / \left(\left(1 + k_{55} / k_{32} + k_{54} / k_{34}\right) \cdot \left(1 + x_{7} / k_{33} + x_{1} / k_{35}\right)\right) + k_{58} \cdot k_{36} \cdot \left(k_{55} \cdot x_{7} - k_{54} \cdot x_{1} / k_{41}\right) / \left(k_{37} \cdot k_{38}\right) / \left(\left(1 + k_{55} / k_{37} + k_{54} / k_{39}\right) \cdot \left(1 + x_{7} / k_{38} + x_{1} / k_{40}\right)\right)\right) + 1 \cdot k_{8} \cdot k_{63} \cdot k_{44} \cdot \left(x_{8} \cdot x_{5} - k_{55} \cdot x_{7} / k_{45}\right) / \left(k_{2} \cdot k_{4}\right) / \left(\left(1 + x_{8} / k_{2} + k_{55} / k_{5}\right) \cdot \left(1 + x_{1} / k_{3} + k_{54} / k_{6} + x_{5} / k_{4} + x_{7} / k_{7}\right)\right)\right) / k_{8}\\
\frac{dx_{8}}{dt} = \left(1 \cdot k_{8} \cdot k_{60} \cdot k_{24} \cdot \left(x_{6} - x_{8} / k_{27}\right) / k_{25} / \left(1 + x_{6} / k_{25} + x_{8} / k_{26}\right) + -1 \cdot k_{8} \cdot k_{63} \cdot k_{42} \cdot \left(x_{8} \cdot x_{1} - k_{55} \cdot k_{54} / k_{43}\right) / \left(k_{2} \cdot k_{3}\right) / \left(\left(1 + x_{8} / k_{2} + k_{55} / k_{5}\right) \cdot \left(1 + x_{1} / k_{3} + k_{54} / k_{6} + x_{5} / k_{4} + x_{7} / k_{7}\right)\right) + -1 \cdot k_{8} \cdot k_{63} \cdot k_{44} \cdot \left(x_{8} \cdot x_{5} - k_{55} \cdot x_{7} / k_{45}\right) / \left(k_{2} \cdot k_{4}\right) / \left(\left(1 + x_{8} / k_{2} + k_{55} / k_{5}\right) \cdot \left(1 + x_{1} / k_{3} + k_{54} / k_{6} + x_{5} / k_{4} + x_{7} / k_{7}\right)\right)\right) / k_{8}\\
\frac{dx_{11}}{dt} = 0\\
\frac{dx_{12}}{dt} = 0\\
\frac{dx_{13}}{dt} = 0\\
\frac{dx_{14}}{dt} = 0\\
\frac{dx_{15}}{dt} = 0\\
\frac{dx_{16}}{dt} = 0\\
\frac{dx_{17}}{dt} = 0\\
\frac{dx_{18}}{dt} = 0\\
\frac{dx_{19}}{dt} = 0\\
\frac{dx_{20}}{dt} = 0\\
\frac{dx_{21}}{dt} = 0