theoretical biology - Is it possible to get (an estimation of) reaction rates from the Michaelis constant?

I want to apply the Gillespie Algorithm to a biological system so I need to know the reaction rates for the relevant reactions. However, for all those reactions, I only know the Michaelis constant $K_M$ and the maximum rate $V_{max}$ (see Wikipedia). Is it possible to derive (an estimation of) the reaction rates $k_f$, $k_r$ and $k_{cat}$ (see image below) given $K_M$ and $V_{max}$? If so, how can it be done?

Answer

$K_M$ is a ratio and for QSSA it is $\dfrac{k_{cat}+k_r}{k_f}$ and for equilibrium approximation it is $\dfrac{k_r}{k_f}$.

It is clear from the formula that you cannot obtain all the constants simulataneously. If you know two (in case of QSSA) you can get the third.