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