\frac{dx_{1}}{dt} = \left(-k_{9}\right) \cdot x_{1}\\ \frac{dx_{2}}{dt} = k_{4} \cdot x_{2} \cdot \left(1 - \left(x_{2} + x_{3} + x_{4}\right) / k_{10}\right) + k_{6} \cdot x_{4} - k_{5} \cdot x_{2} - k_{8} \cdot x_{1} \cdot k_{9} \cdot x_{2}\\ \frac{dx_{3}}{dt} = k_{5} - k_{8} \cdot x_{1} \cdot k_{9} \cdot x_{3}\\ \frac{dx_{4}}{dt} = k_{8} \cdot x_{1} \cdot k_{9} \cdot x_{3} - k_{6} \cdot x_{4} - k_{7} \cdot x_{4}