The unreasonable effectiveness of the total quasi-steady state approximation, and its limitations

In this note, we discuss the range of parameters for which the total quasi-steady-state approximation of the Michaelis–Menten reaction mechanism holds validity. We challenge the prevalent notion that total quasi-steady-state approximation is “roughly valid” across all parameters, showing that its validity cannot be assumed, even roughly, across the entire parameter space — when the initial substrate concentration is high. On the positive side, we show that the linearized one-dimensional equation for total substrate is a valid approximation when the initial reduced substrate concentration s 0 /K M is small. Moreover, we obtain a precise picture of the long-term time course of both substrate and complex.