\frac{dx_{1}}{dt} = \left(-1 \cdot k_{1} \cdot x_{1} \cdot k_{18} / \left(x_{4} + k_{18}\right) + 1 \cdot \left(1 - k_{9} - k_{15} \cdot k_{16} / \left(x_{4} + k_{16}\right)\right) \cdot k_{6} \cdot x_{1} \cdot \left(1 - \left(x_{1} + x_{2} + x_{3} + x_{4}\right) / k_{5}\right)\right) / k_{21}\\ \frac{dx_{2}}{dt} = \left(1 \cdot k_{9} \cdot k_{6} \cdot x_{1} \cdot \left(1 - \left(x_{1} + x_{2} + x_{3} + x_{4}\right) / k_{5}\right) + -1 \cdot k_{2} \cdot x_{2} \cdot k_{19} / \left(x_{4} + k_{19}\right) + 1 \cdot \left(1 - k_{13}\right) \cdot k_{10} \cdot x_{2} \cdot \left(1 - \left(x_{1} + x_{2} + x_{3} + x_{4}\right) / k_{5}\right)\right) / k_{21}\\ \frac{dx_{3}}{dt} = \left(1 \cdot k_{13} \cdot k_{10} \cdot x_{2} \cdot \left(1 - \left(x_{1} + x_{2} + x_{3} + x_{4}\right) / k_{5}\right) + -1 \cdot k_{3} \cdot x_{3} \cdot k_{20} / \left(x_{4} + k_{20}\right)\right) / k_{21}\\ \frac{dx_{4}}{dt} = \left(1 \cdot k_{15} \cdot k_{16} / \left(x_{4} + k_{16}\right) \cdot k_{6} \cdot x_{1} \cdot \left(1 - \left(x_{1} + x_{2} + x_{3} + x_{4}\right) / k_{5}\right) + -1 \cdot k_{17} \cdot x_{4}\right) / k_{21}