  Quasi-steady state reductions for the irreversible Michaelis--Menten reaction
mechanism are of interest both from a theoretical and an experimental design
perspective. A number of publications have been devoted to extending the
parameter range where reduction is possible, via improved sufficient
conditions. In the present note, we complement these results by exhibiting
local conditions that preclude quasi-steady-state reductions
(anti-quasi-steady-state), in the classical as well as in a broader sense. To
this end, one needs to obtain necessary (as opposed to sufficient) conditions
and determine parameter regions where these do not hold. In particular, we
explicitly describe parameter regions where no quasi-steady-state reduction (in
any sense) is applicable (anti-quasi-steady-state conditions), and we also show
that -- in a well defined sense -- these parameter regions are small. From
another perspective, we obtain local conditions for the accuracy of standard or
total quasi-steady-state. Perhaps surprisingly, our conditions do not involve
initial substrate.
