Abstract
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 s0/KM is small. Moreover, we obtain a precise picture of the long-term time course of both substrate and complex.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
e-mail: jse{at}ams.org
e-mail: santiago.schnell{at}nd.edu
e-mail: walcher{at}matha.rwth-aachen.de
Minor corrections to clarify the meaning of a couple of definitions.