Before revision:  However, our results indicate that this approximationcan be valid when initial enzyme and substrate concentrations are of equal magnitude . Consequently, this opens  the possibility of utilizing the rQSSA to model enzyme catalyzed reactions and estimate kinetic parameters in enzymatic assays at much lower enzyme to substrate ratios than was previously thought  .
After revision:  However, our results indicate that this approximationcan be valid when initial enzyme and substrate concentrations are of equal magnitude . Consequently, this opens the possibility of utilizing the rQSSA to model enzyme catalyzed reactions and estimate kinetic parameters in enzymatic assays at much lower enzyme to substrate ratios than was previously thought . Moreover, we show for the first time that the critical manifold of the reverse quasi-steady-state approximation contains a singular point where normal hyperbolicity is lost. Associated with this singularity is a transcritical bifurcation, and the corresponding normal form of this bifurcation is recovered through scaling analysis .