\frac{dx_{1}}{dt} = -k_{1} \cdot x_{1} \cdot x_{17}\\
\frac{dx_{2}}{dt} = k_{1} \cdot x_{1} \cdot x_{17}\\
\frac{dx_{3}}{dt} = 4 \cdot \left(x_{2} - x_{3}\right) / k_{12}\\
\frac{dx_{4}}{dt} = 4 \cdot \left(x_{3} - x_{4}\right) / k_{12}\\
\frac{dx_{5}}{dt} = 4 \cdot \left(x_{4} - x_{5}\right) / k_{12}\\
\frac{dx_{6}}{dt} = 4 \cdot \left(x_{5} - x_{6}\right) / k_{12}\\
\frac{dx_{7}}{dt} = k_{3} \cdot x_{2} \cdot x_{18} / \left(1 + k_{11} \cdot x_{16}\right) - k_{5} \cdot x_{7}\\
\frac{dx_{8}}{dt} = k_{5} \cdot x_{7} - k_{4} \cdot x_{8}\\
\frac{dx_{9}}{dt} = 4 \cdot \left(x_{8} - x_{9}\right) / k_{13}\\
\frac{dx_{10}}{dt} = 4 \cdot \left(x_{9} - x_{10}\right) / k_{13}\\
\frac{dx_{11}}{dt} = 4 \cdot \left(x_{10} - x_{11}\right) / k_{13}\\
\frac{dx_{12}}{dt} = 4 \cdot \left(x_{11} - x_{12}\right) / k_{13}\\
\frac{dx_{13}}{dt} = 4 \cdot \left(x_{20} - x_{13}\right) / k_{14}\\
\frac{dx_{14}}{dt} = 4 \cdot \left(x_{13} - x_{14}\right) / k_{14}\\
\frac{dx_{15}}{dt} = 4 \cdot \left(x_{14} - x_{15}\right) / k_{14}\\
\frac{dx_{16}}{dt} = 4 \cdot \left(x_{15} - x_{16}\right) / k_{14}\\
\frac{dx_{17}}{dt} = -k_{1} \cdot x_{1} \cdot x_{17}\\
\frac{dx_{18}}{dt} = k_{2} \cdot x_{6} + k_{9} \cdot x_{19} - k_{8} \cdot x_{18} - k_{3} \cdot x_{2} \cdot x_{18} / \left(1 + k_{11} \cdot x_{16}\right)\\
\frac{dx_{19}}{dt} = k_{8} \cdot x_{18} - k_{9} \cdot x_{19} + k_{4} \cdot x_{8}\\
\frac{dx_{20}}{dt} = k_{10} + k_{6} \cdot x_{12} - k_{7} \cdot x_{20}