\frac{dx_{4}}{dt} = 0\\
\frac{dx_{1}}{dt} = x_{1} \cdot \left(k_{1} - k_{3} \cdot x_{1} - k_{5} \cdot x_{2}\right) - k_{13} \cdot x_{1} \cdot k_{20}\\
\frac{dx_{2}}{dt} = x_{2} \cdot \left(k_{11} - k_{4} \cdot x_{2}\right) - k_{6} \cdot x_{3} \cdot x_{2} + k_{14} \cdot x_{1} \cdot k_{20}\\
\frac{dx_{3}}{dt} = k_{7} + k_{8} \cdot x_{3} \cdot x_{2} / \left(k_{9} + x_{2}\right) - k_{12} \cdot x_{3} \cdot x_{2} - k_{10} \cdot x_{3} - k_{15} \cdot x_{3} \cdot k_{20} / \left(k_{16} + k_{20}\right)