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