\frac{dx_{1}}{dt} = \left(-1 \cdot k_{1} \cdot x_{1} + 1 \cdot \left(1 - k_{9}\right) \cdot k_{6} \cdot x_{1} \cdot \left(1 - \left(x_{1} + x_{2} + x_{3}\right) / k_{5}\right)\right) / k_{14}\\
\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}\right) / k_{5}\right) + -1 \cdot k_{2} \cdot x_{2} + 1 \cdot \left(1 - k_{13}\right) \cdot k_{10} \cdot x_{2} \cdot \left(1 - \left(x_{1} + x_{2} + x_{3}\right) / k_{5}\right)\right) / k_{14}\\
\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}\right) / k_{5}\right) + -1 \cdot k_{3} \cdot x_{3}\right) / k_{14}