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The quasi-steady-state approximation is widely used to develop simplifieddeterministic or stochastic models of enzyme catalyzed reactions. Indeterministic models, the quasi-steady-state approximation can bemathematically justified from singular perturbation theory. For several closedenzymatic reactions, the homologous extension of the quasi-steady-stateapproximation to the stochastic regime, known as the stochasticquasi-steady-state approximation, has been shown to be accurate under theanalogous conditions that permit the quasi-steady-state reduction of thedeterministic counterpart. However, it was recently demonstrated that theextension of the stochastic quasi-steady-state approximation to an openMichaelis--Menten reaction mechanism is only valid under a condition that isfar more restrictive than the qualifier that ensures the validity of itscorresponding deterministic quasi-steady-state approximation. In this paper, wesuggest a possible explanation for this discrepancy from the lens of geometricsingular perturbation theory. In so doing, we illustrate a misconception in theapplication of the quasi-steady-state approximation: timescale separation doesnot imply singular perturbation.

bulletin of mathematical biology

On the validity of the stochastic quasi-steady-state approximation in  open enzyme catalyzed reactions: Timescale separation or singular  perturbation?