\frac{dx_{1}}{dt} = 0\\
\frac{dx_{2}}{dt} = 0\\
\frac{dx_{3}}{dt} = 0\\
\frac{dx_{4}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{2} \cdot k_{51} / k_{3} \cdot k_{52} / k_{4} - k_{5} \cdot k_{53} / k_{6} \cdot x_{4} / k_{7}\right) / \left(\left(1 + k_{51} / k_{3} + k_{53} / k_{6}\right) \cdot \left(1 + k_{52} / k_{4} + x_{4} / k_{7}\right)\right) + -1 \cdot k_{1} \cdot \left(k_{8} \cdot x_{4} / k_{9} - k_{10} \cdot x_{5} / k_{11}\right) / \left(1 + x_{4} / k_{9} + x_{5} / k_{11}\right)\right) / k_{1}\\
\frac{dx_{5}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{8} \cdot x_{4} / k_{9} - k_{10} \cdot x_{5} / k_{11}\right) / \left(1 + x_{4} / k_{9} + x_{5} / k_{11}\right) + -1 \cdot k_{1} \cdot \left(k_{12} \cdot x_{5} / k_{13} - k_{14} \cdot x_{6} / k_{15}\right) / \left(1 + x_{5} / k_{13} + x_{6} / k_{15}\right) + -1 \cdot k_{1} \cdot \left(k_{36} \cdot x_{5} / k_{37} - k_{38} \cdot x_{8} / k_{39} \cdot x_{11} / k_{40}\right) / \left(1 + x_{5} / k_{37} + x_{8} / k_{39} + x_{11} / k_{40} + x_{5} / k_{37} \cdot x_{8} / k_{39} + x_{8} / k_{39} \cdot x_{11} / k_{40}\right)\right) / k_{1}\\
\frac{dx_{6}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{12} \cdot x_{5} / k_{13} - k_{14} \cdot x_{6} / k_{15}\right) / \left(1 + x_{5} / k_{13} + x_{6} / k_{15}\right) + -1 \cdot k_{1} \cdot \left(k_{16} \cdot x_{6} / k_{17} - k_{18} \cdot x_{7} / k_{19}\right) / \left(1 + x_{6} / k_{17} + x_{7} / k_{19}\right) + -1 \cdot k_{1} \cdot \frac{47}{250} \cdot \left(k_{47} \cdot x_{5} / k_{48} - k_{49} \cdot x_{6} / k_{50}\right) / \left(1 + x_{5} / k_{48} + x_{6} / k_{50}\right)\right) / k_{1}\\
\frac{dx_{7}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{16} \cdot x_{6} / k_{17} - k_{18} \cdot x_{7} / k_{19}\right) / \left(1 + x_{6} / k_{17} + x_{7} / k_{19}\right) + -1 \cdot k_{1} \cdot \left(k_{20} \cdot x_{7} / k_{21} - k_{22} \cdot x_{8} / k_{23}\right) / \left(1 + x_{7} / k_{21} + x_{8} / k_{23}\right)\right) / k_{1}\\
\frac{dx_{8}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{20} \cdot x_{7} / k_{21} - k_{22} \cdot x_{8} / k_{23}\right) / \left(1 + x_{7} / k_{21} + x_{8} / k_{23}\right) + -1 \cdot k_{1} \cdot \left(k_{24} \cdot x_{8} / k_{25} - k_{26} \cdot x_{9} / k_{27}\right) / \left(1 + x_{8} / k_{25} + x_{9} / k_{27}\right) + 1 \cdot k_{1} \cdot \left(k_{36} \cdot x_{5} / k_{37} - k_{38} \cdot x_{8} / k_{39} \cdot x_{11} / k_{40}\right) / \left(1 + x_{5} / k_{37} + x_{8} / k_{39} + x_{11} / k_{40} + x_{5} / k_{37} \cdot x_{8} / k_{39} + x_{8} / k_{39} \cdot x_{11} / k_{40}\right)\right) / k_{1}\\
\frac{dx_{9}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{24} \cdot x_{8} / k_{25} - k_{26} \cdot x_{9} / k_{27}\right) / \left(1 + x_{8} / k_{25} + x_{9} / k_{27}\right) + -1 \cdot k_{1} \cdot \left(k_{28} \cdot x_{9} / k_{29} - k_{30} \cdot x_{10} / k_{31}\right) / \left(1 + x_{9} / k_{29} + x_{10} / k_{31}\right)\right) / k_{1}\\
\frac{dx_{10}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{28} \cdot x_{9} / k_{29} - k_{30} \cdot x_{10} / k_{31}\right) / \left(1 + x_{9} / k_{29} + x_{10} / k_{31}\right) + -1 \cdot k_{1} \cdot \left(k_{32} \cdot x_{10} / k_{33} - k_{34} \cdot k_{52} / k_{35}\right) / \left(1 + x_{10} / k_{33} + k_{52} / k_{35}\right) + 1 \cdot k_{1} \cdot \left(k_{41} \cdot x_{11} / k_{42} \cdot k_{51} / k_{43} - k_{44} \cdot x_{10} / k_{45} \cdot k_{53} / k_{46}\right) / \left(\left(1 + x_{11} / k_{42} + x_{10} / k_{45}\right) \cdot \left(1 + k_{51} / k_{43} + k_{53} / k_{46}\right)\right)\right) / k_{1}\\
\frac{dx_{11}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{36} \cdot x_{5} / k_{37} - k_{38} \cdot x_{8} / k_{39} \cdot x_{11} / k_{40}\right) / \left(1 + x_{5} / k_{37} + x_{8} / k_{39} + x_{11} / k_{40} + x_{5} / k_{37} \cdot x_{8} / k_{39} + x_{8} / k_{39} \cdot x_{11} / k_{40}\right) + -1 \cdot k_{1} \cdot \left(k_{41} \cdot x_{11} / k_{42} \cdot k_{51} / k_{43} - k_{44} \cdot x_{10} / k_{45} \cdot k_{53} / k_{46}\right) / \left(\left(1 + x_{11} / k_{42} + x_{10} / k_{45}\right) \cdot \left(1 + k_{51} / k_{43} + k_{53} / k_{46}\right)\right)\right) / k_{1}\\
\frac{dx_{12}}{dt} = 0