# How is the “quasi-steady-state” assumption of Michaelis-Menten kinetics different from the steady state assumption of ordinary kinetics?

In Wikipedia's article for Michaelis-Menten kinetics, it titles the "[ES] = constant" section the "Quasi-steady-state approximation". Lehninger's Principles of Biochemistry, 4th Ed. pp. 203ff call this "steady state kinetics".

I know that steady state is an assumption which is used for various kinetic models that have an intermediate, and I believe the term "steady state" is used in other settings as well. Is Wikipedia's use of "quasi" in the title for the enzyme kinetics reflective of $V_0$ only being the measurement of the initial rate, and thus the further assumption that [S] is constant also adds more uncertainty to the steady state assumption? If this isn't the reason (and I'm not certain that it is), why add a further descriptor that denotes uncertainty or inaccuracy when we already know that steady state is an assumption?

Is Wikipedia's use of "quasi" in the title for the enzyme kinetics reflective of [...] the further assumption that $$[S]$$ is constant[...]?
No I don't think the "quasi-steady state" hypothesis is related to whether $$[S]$$ varies with time.
I don't think there's a principled reason to prefer one term over another. If you solve the full differential equations for kinetic models that would normally invoke the PSSH, you'll see one problem. Before the reaction starts, the concentration of intermediate $$I$$ is zero. But when the reaction is going on, we assume the intermediate is at steady state, i.e. that $$\frac{dI}{dt}=0$$. But if $$I$$ starts at zero and has an initial concentration of zero, then it is everywhere zero, which violates the prinicple that intermediates actually occur in real-life chemical reactions. So there are two phases to such models: the first is the "burst" phase, also known as single-turnover conditions, or unsteady state kinetics. In that phase $$\frac{dI}{dt}$$ is not 0 but increases rapidly. That phase ends quickly and is replaced by the pseudo-steady phase for $$I$$. If you want to get precise about the strict definitions of the two phases, you'll need to invoke singular perturbation and asymptotic matching, as described in this thorough book chapter from Mathematical Biology by James D. Murray.