\frac{dx_{1}}{dt} = \left(-1 \cdot k_{1} \cdot k_{3} \cdot x_{1} / \left(x_{1} + k_{4} \cdot \left(1 + x_{2} / k_{5} + x_{6} / k_{6} + x_{9} / k_{7} + x_{21} / k_{8} + k_{78} / k_{9}\right)\right) + 1 \cdot k_{1} \cdot k_{35} \cdot x_{13} \cdot x_{16} / \left(\left(x_{13} + k_{36} \cdot \left(1 + x_{2} / k_{37} + x_{1} / k_{38} + x_{21} / k_{39}\right)\right) \cdot \left(x_{16} \cdot \left(1 + x_{17} / k_{40}\right) + k_{41} \cdot \left(1 + x_{17} / k_{42}\right)\right)\right)\right) / k_{1}\\
\frac{dx_{2}}{dt} = \left(2 \cdot k_{1} \cdot k_{3} \cdot x_{1} / \left(x_{1} + k_{4} \cdot \left(1 + x_{2} / k_{5} + x_{6} / k_{6} + x_{9} / k_{7} + x_{21} / k_{8} + k_{78} / k_{9}\right)\right) + -1 \cdot k_{1} \cdot \left(k_{10} \cdot x_{2} \cdot x_{16} - k_{11} \cdot x_{3} \cdot x_{17}\right) + -1 \cdot k_{1} \cdot k_{60} \cdot x_{2} / \left(x_{2} \cdot \left(1 + k_{61} / k_{81}\right) + k_{62} \cdot \left(1 + \left(1 + k_{61} / k_{81}\right) \cdot \left(x_{21} / k_{63} + x_{4} / k_{64} + x_{5} / k_{65}\right)\right)\right)\right) / k_{1}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{10} \cdot x_{2} \cdot x_{16} - k_{11} \cdot x_{3} \cdot x_{17}\right) + -1 \cdot k_{1} \cdot \left(k_{12} \cdot x_{3} \cdot k_{78} \cdot k_{80} - k_{13} \cdot x_{4} \cdot k_{79} \cdot x_{21}\right)\right) / k_{1}\\
\frac{dx_{4}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{12} \cdot x_{3} \cdot k_{78} \cdot k_{80} - k_{13} \cdot x_{4} \cdot k_{79} \cdot x_{21}\right) + -1 \cdot k_{1} \cdot \left(k_{14} \cdot x_{4} - k_{15} \cdot x_{5}\right) + -1 \cdot k_{1} \cdot \left(k_{16} \cdot x_{5} \cdot x_{4} - k_{17} \cdot x_{6}\right) + -1 \cdot k_{1} \cdot \left(k_{22} \cdot x_{4} \cdot x_{7} - k_{23} \cdot x_{11} \cdot x_{8}\right) + -1 \cdot k_{1} \cdot \left(k_{29} \cdot x_{4} \cdot x_{10} - k_{30} \cdot x_{11} \cdot x_{12}\right) + -1 \cdot k_{1} \cdot k_{66} \cdot x_{4} / \left(x_{4} \cdot \left(1 + k_{67} / k_{81}\right) + k_{68} \cdot \left(1 + \left(1 + k_{67} / k_{81}\right) \cdot \left(x_{21} / k_{69} + x_{2} / k_{70} + x_{5} / k_{71}\right)\right)\right)\right) / k_{1}\\
\frac{dx_{5}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{14} \cdot x_{4} - k_{15} \cdot x_{5}\right) + -1 \cdot k_{1} \cdot \left(k_{16} \cdot x_{5} \cdot x_{4} - k_{17} \cdot x_{6}\right) + -1 \cdot k_{1} \cdot \left(k_{24} \cdot x_{5} \cdot x_{8} - k_{25} \cdot x_{9}\right) + -1 \cdot k_{1} \cdot k_{72} \cdot x_{5} / \left(x_{5} \cdot \left(1 + k_{73} / k_{81}\right) + k_{74} \cdot \left(1 + \left(1 + k_{73} / k_{81}\right) \cdot \left(x_{21} / k_{75} + x_{2} / k_{76} + x_{4} / k_{77}\right)\right)\right)\right) / k_{1}\\
\frac{dx_{6}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{16} \cdot x_{5} \cdot x_{4} - k_{17} \cdot x_{6}\right) + -1 \cdot k_{1} \cdot k_{18} \cdot x_{6} / \left(x_{6} + k_{19} \cdot \left(1 + x_{7} / k_{20} + x_{21} / k_{21}\right)\right)\right) / k_{1}\\
\frac{dx_{7}}{dt} = \left(1 \cdot k_{1} \cdot k_{18} \cdot x_{6} / \left(x_{6} + k_{19} \cdot \left(1 + x_{7} / k_{20} + x_{21} / k_{21}\right)\right) + -1 \cdot k_{1} \cdot \left(k_{22} \cdot x_{4} \cdot x_{7} - k_{23} \cdot x_{11} \cdot x_{8}\right) + -1 \cdot k_{1} \cdot \left(k_{43} \cdot x_{7} - k_{44} \cdot x_{14}\right)\right) / k_{1}\\
\frac{dx_{8}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{22} \cdot x_{4} \cdot x_{7} - k_{23} \cdot x_{11} \cdot x_{8}\right) + -1 \cdot k_{1} \cdot \left(k_{24} \cdot x_{5} \cdot x_{8} - k_{25} \cdot x_{9}\right)\right) / k_{1}\\
\frac{dx_{9}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{24} \cdot x_{5} \cdot x_{8} - k_{25} \cdot x_{9}\right) + -1 \cdot k_{1} \cdot k_{26} \cdot x_{9} / \left(x_{9} + k_{27} \cdot \left(1 + x_{21} / k_{28}\right)\right)\right) / k_{1}\\
\frac{dx_{10}}{dt} = \left(1 \cdot k_{1} \cdot k_{26} \cdot x_{9} / \left(x_{9} + k_{27} \cdot \left(1 + x_{21} / k_{28}\right)\right) + -1 \cdot k_{1} \cdot \left(k_{29} \cdot x_{4} \cdot x_{10} - k_{30} \cdot x_{11} \cdot x_{12}\right)\right) / k_{1}\\
\frac{dx_{11}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{22} \cdot x_{4} \cdot x_{7} - k_{23} \cdot x_{11} \cdot x_{8}\right) + 1 \cdot k_{1} \cdot \left(k_{29} \cdot x_{4} \cdot x_{10} - k_{30} \cdot x_{11} \cdot x_{12}\right) + -1 \cdot k_{1} \cdot \left(k_{33} \cdot x_{11} - k_{34} \cdot x_{13}\right)\right) / k_{1}\\
\frac{dx_{12}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{29} \cdot x_{4} \cdot x_{10} - k_{30} \cdot x_{11} \cdot x_{12}\right) + -1 \cdot k_{1} \cdot \left(k_{31} \cdot x_{12} - k_{32} \cdot x_{13}\right)\right) / k_{1}\\
\frac{dx_{13}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{31} \cdot x_{12} - k_{32} \cdot x_{13}\right) + 1 \cdot k_{1} \cdot \left(k_{33} \cdot x_{11} - k_{34} \cdot x_{13}\right) + -1 \cdot k_{1} \cdot k_{35} \cdot x_{13} \cdot x_{16} / \left(\left(x_{13} + k_{36} \cdot \left(1 + x_{2} / k_{37} + x_{1} / k_{38} + x_{21} / k_{39}\right)\right) \cdot \left(x_{16} \cdot \left(1 + x_{17} / k_{40}\right) + k_{41} \cdot \left(1 + x_{17} / k_{42}\right)\right)\right)\right) / k_{1}\\
\frac{dx_{14}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{43} \cdot x_{7} - k_{44} \cdot x_{14}\right) + -1 \cdot k_{1} \cdot \left(k_{45} \cdot x_{14} - k_{46} \cdot x_{15}\right)\right) / k_{1}\\
\frac{dx_{15}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{45} \cdot x_{14} - k_{46} \cdot x_{15}\right) + -1 \cdot k_{1} \cdot k_{47} \cdot x_{15} \cdot x_{16} / \left(\left(x_{15} + k_{48}\right) \cdot \left(1 + x_{17} / k_{50}\right) \cdot \left(x_{16} + k_{49} \cdot \left(1 + k_{49} \cdot x_{21} / \left(k_{51} \cdot x_{2} + k_{52} \cdot x_{7} + k_{53} \cdot x_{6}\right)\right)\right)\right) + 1 \cdot k_{1} \cdot k_{54} \cdot x_{21} / \left(x_{21} + k_{55} \cdot \left(1 + x_{15} / k_{56}\right)\right)\right) / k_{1}\\
\frac{dx_{16}}{dt} = \left(-1 \cdot k_{1} \cdot \left(k_{10} \cdot x_{2} \cdot x_{16} - k_{11} \cdot x_{3} \cdot x_{17}\right) + -1 \cdot k_{1} \cdot k_{35} \cdot x_{13} \cdot x_{16} / \left(\left(x_{13} + k_{36} \cdot \left(1 + x_{2} / k_{37} + x_{1} / k_{38} + x_{21} / k_{39}\right)\right) \cdot \left(x_{16} \cdot \left(1 + x_{17} / k_{40}\right) + k_{41} \cdot \left(1 + x_{17} / k_{42}\right)\right)\right) + -1 \cdot k_{1} \cdot k_{47} \cdot x_{15} \cdot x_{16} / \left(\left(x_{15} + k_{48}\right) \cdot \left(1 + x_{17} / k_{50}\right) \cdot \left(x_{16} + k_{49} \cdot \left(1 + k_{49} \cdot x_{21} / \left(k_{51} \cdot x_{2} + k_{52} \cdot x_{7} + k_{53} \cdot x_{6}\right)\right)\right)\right) + 1 \cdot k_{1} \cdot k_{57} \cdot x_{17} \cdot x_{21} / \left(\left(x_{17} + k_{58}\right) \cdot \left(x_{21} + k_{59}\right)\right)\right) / k_{1}\\
\frac{dx_{18}}{dt} = 0\\
\frac{dx_{19}}{dt} = 0\\
\frac{dx_{20}}{dt} = 0\\
\frac{dx_{22}}{dt} = 0