\frac{dx_{1}}{dt} = \left(-1 \cdot \left(k_{13} \cdot x_{1} \cdot \left(x_{21} \cdot k_{51} - x_{4} \cdot k_{51} - x_{5}\right) \cdot k_{51} - k_{14} \cdot x_{4} \cdot k_{51}\right) + -1 \cdot \left(k_{1} \cdot x_{1} \cdot k_{51} - k_{2} \cdot x_{9} \cdot k_{52}\right) + 1 \cdot k_{21} \cdot x_{7} \cdot k_{51}\right) / k_{51}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{15} \cdot x_{4} \cdot k_{51} + -1 \cdot \left(k_{13} \cdot x_{2} \cdot \left(x_{21} \cdot k_{51} - x_{5} \cdot k_{51} - x_{4}\right) \cdot k_{51} - k_{14} \cdot x_{5} \cdot k_{51}\right) + -1 \cdot \left(k_{3} \cdot x_{2} \cdot k_{51} - k_{4} \cdot x_{10} \cdot k_{52}\right) + 1 \cdot k_{18} \cdot x_{8} \cdot k_{51} + -1 \cdot \left(k_{19} \cdot x_{2} \cdot x_{6} / \frac{47}{50} \cdot k_{51} - k_{20} \cdot x_{7}\right) \cdot k_{51}\right) / k_{51}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{15} \cdot x_{5} \cdot k_{51} + -1 \cdot \left(k_{5} \cdot x_{3} \cdot k_{51} - k_{6} \cdot x_{11} \cdot k_{52}\right) + -1 \cdot \left(k_{16} \cdot x_{3} \cdot x_{6} / \frac{47}{50} \cdot k_{51} - k_{17} \cdot x_{8}\right) \cdot k_{51}\right) / k_{51}\\
\frac{dx_{4}}{dt} = \left(1 \cdot \left(k_{13} \cdot x_{1} \cdot \left(x_{21} \cdot k_{51} - x_{4} \cdot k_{51} - x_{5}\right) \cdot k_{51} - k_{14} \cdot x_{4} \cdot k_{51}\right) + -1 \cdot k_{15} \cdot x_{4} \cdot k_{51}\right) / k_{51}\\
\frac{dx_{5}}{dt} = \left(1 \cdot \left(k_{13} \cdot x_{2} \cdot \left(x_{21} \cdot k_{51} - x_{5} \cdot k_{51} - x_{4}\right) \cdot k_{51} - k_{14} \cdot x_{5} \cdot k_{51}\right) + -1 \cdot k_{15} \cdot x_{5} \cdot k_{51}\right) / k_{51}\\
\frac{dx_{6}}{dt} = \left(-1 \cdot \left(k_{16} \cdot x_{3} \cdot x_{6} / \frac{47}{50} \cdot k_{51} - k_{17} \cdot x_{8}\right) \cdot k_{51} + 1 \cdot k_{18} \cdot x_{8} \cdot k_{51} + -1 \cdot \left(k_{19} \cdot x_{2} \cdot x_{6} / \frac{47}{50} \cdot k_{51} - k_{20} \cdot x_{7}\right) \cdot k_{51} + 1 \cdot k_{21} \cdot x_{7} \cdot k_{51}\right) / k_{51}\\
\frac{dx_{7}}{dt} = \left(1 \cdot \left(k_{19} \cdot x_{2} \cdot x_{6} / \frac{47}{50} \cdot k_{51} - k_{20} \cdot x_{7}\right) \cdot k_{51} + -1 \cdot k_{21} \cdot x_{7} \cdot k_{51}\right) / k_{51}\\
\frac{dx_{8}}{dt} = \left(1 \cdot \left(k_{16} \cdot x_{3} \cdot x_{6} / \frac{47}{50} \cdot k_{51} - k_{17} \cdot x_{8}\right) \cdot k_{51} + -1 \cdot k_{18} \cdot x_{8} \cdot k_{51}\right) / k_{51}\\
\frac{dx_{9}}{dt} = \left(1 \cdot \left(k_{1} \cdot x_{1} \cdot k_{51} - k_{2} \cdot x_{9} \cdot k_{52}\right) + 1 \cdot k_{32} \cdot x_{12} \cdot k_{52} + -1 \cdot \left(k_{7} \cdot x_{9} \cdot x_{14} / \frac{11}{50} \cdot k_{52} - k_{8} \cdot x_{15}\right) \cdot k_{52}\right) / k_{52}\\
\frac{dx_{10}}{dt} = \left(1 \cdot \left(k_{3} \cdot x_{2} \cdot k_{51} - k_{4} \cdot x_{10} \cdot k_{52}\right) + 1 \cdot k_{29} \cdot x_{13} \cdot k_{52} + -1 \cdot \left(k_{30} \cdot x_{10} \cdot x_{19} / \frac{11}{50} \cdot k_{52} - k_{31} \cdot x_{12}\right) \cdot k_{52} + -1 \cdot \left(k_{9} \cdot x_{10} \cdot x_{14} / \frac{11}{50} \cdot k_{52} - k_{10} \cdot x_{16}\right) \cdot k_{52}\right) / k_{52}\\
\frac{dx_{11}}{dt} = \left(1 \cdot \left(k_{5} \cdot x_{3} \cdot k_{51} - k_{6} \cdot x_{11} \cdot k_{52}\right) + -1 \cdot \left(k_{27} \cdot x_{11} \cdot x_{19} / \frac{11}{50} \cdot k_{52} - k_{28} \cdot x_{13}\right) \cdot k_{52} + -1 \cdot \left(k_{11} \cdot x_{11} \cdot x_{14} / \frac{11}{50} \cdot k_{52} - k_{12} \cdot x_{17}\right) \cdot k_{52}\right) / k_{52}\\
\frac{dx_{12}}{dt} = \left(1 \cdot \left(k_{30} \cdot x_{10} \cdot x_{19} / \frac{11}{50} \cdot k_{52} - k_{31} \cdot x_{12}\right) \cdot k_{52} + -1 \cdot k_{32} \cdot x_{12} \cdot k_{52}\right) / k_{52}\\
\frac{dx_{13}}{dt} = \left(1 \cdot \left(k_{27} \cdot x_{11} \cdot x_{19} / \frac{11}{50} \cdot k_{52} - k_{28} \cdot x_{13}\right) \cdot k_{52} + -1 \cdot k_{29} \cdot x_{13} \cdot k_{52}\right) / k_{52}\\
\frac{dx_{14}}{dt} = \left(-1 \cdot \left(k_{7} \cdot x_{9} \cdot x_{14} / \frac{11}{50} \cdot k_{52} - k_{8} \cdot x_{15}\right) \cdot k_{52} + -1 \cdot \left(k_{9} \cdot x_{10} \cdot x_{14} / \frac{11}{50} \cdot k_{52} - k_{10} \cdot x_{16}\right) \cdot k_{52} + -1 \cdot \left(k_{11} \cdot x_{11} \cdot x_{14} / \frac{11}{50} \cdot k_{52} - k_{12} \cdot x_{17}\right) \cdot k_{52}\right) / k_{52}\\
\frac{dx_{15}}{dt} = 1 \cdot \left(k_{7} \cdot x_{9} \cdot x_{14} / \frac{11}{50} \cdot k_{52} - k_{8} \cdot x_{15}\right) \cdot k_{52} / k_{52}\\
\frac{dx_{16}}{dt} = 1 \cdot \left(k_{9} \cdot x_{10} \cdot x_{14} / \frac{11}{50} \cdot k_{52} - k_{10} \cdot x_{16}\right) \cdot k_{52} / k_{52}\\
\frac{dx_{17}}{dt} = 1 \cdot \left(k_{11} \cdot x_{11} \cdot x_{14} / \frac{11}{50} \cdot k_{52} - k_{12} \cdot x_{17}\right) \cdot k_{52} / k_{52}\\
\frac{dx_{18}}{dt} = \left(1 \cdot k_{37} \cdot \left(1 + k_{38} \cdot x_{11}^{2} / \left(x_{11}^{2} \cdot k_{52} + k_{39}^{2}\right)\right) \cdot \frac{693}{1000} / k_{40} + -1 \cdot x_{18} \cdot \frac{693}{1000} / k_{40} \cdot k_{52}\right) / k_{52}\\
\frac{dx_{19}}{dt} = \left(-1 \cdot \left(k_{27} \cdot x_{11} \cdot x_{19} / \frac{11}{50} \cdot k_{52} - k_{28} \cdot x_{13}\right) \cdot k_{52} + 1 \cdot k_{29} \cdot x_{13} \cdot k_{52} + -1 \cdot \left(k_{30} \cdot x_{10} \cdot x_{19} / \frac{11}{50} \cdot k_{52} - k_{31} \cdot x_{12}\right) \cdot k_{52} + 1 \cdot k_{32} \cdot x_{12} \cdot k_{52} + 1 \cdot k_{41} \cdot x_{18} / \frac{11}{50} \cdot \frac{693}{1000} / k_{42} \cdot k_{52} + -1 \cdot x_{19} \cdot \frac{693}{1000} / k_{42} \cdot k_{52}\right) / k_{52}