Also known as the quasisteadystate approximation, this condition is an important prerequisite for much of the mathematics used in deriving many of the equations that describe enzyme kinetics.
Any reaction in which a substrate and a catalyst combine to form a complex, inducing a change in the substrate to form a product, and subsequently irreversibly dissociate, can be represented with the reaction scheme below:
This reaction has a characteristic time course that consists of:
During the second phase mentioned above, the kinetic parameters k_{1}, k_{1}, and k_{2} determine the overall rate of the reaction. It therefore stands to reason that observations made during this phase could be used to measure these parameters. In practice, the time course is always curved over its entirety, with no 'linear' region corresponding to this second phase. It is accepted practice therefore to attempt to determine the initial velocity of the reaction from the timecourse graph, as that velocity will most closely approximate the ideal maximum reaction velocity for that set of reaction conditions.
This hypothetical second phase has several properties which make it useful for deriving mathematical descriptions of the reaction. First, in most cases it can be safely assumed that the rate of the reaction during this phase is determined solely by k_{2}, because this rate is generally orders of magnitude lower than k_{1}. Second, the reaction can be viewed as being in a kind of quasiequilibrium during this phase, because the rate of the reaction depends only on k_{2} and not at all on the concentrations of any of the species or any other timedependent quantity. This equilibrium leads to the useful deduction that the rate of the reaction leading from complex to product is equal to the sum of the enzymesubstrate association and dissociation reactions. A corrollary of this equilibrium is a third property: that the reaction is proceeding at approximately its theoretical maximum rate (for the extant set of reaction conditions). This is usually interpreted to mean that there is very little free enzyme present in the system, because as much enzyme as possible is combined with substrate.
All of the properties described above are made use of in the derivation of the MichaelisMenten equation. The slight distinction between the two expansions of the acronym 'QSSA' can now be made: the quasisteadystate assumption is the assumption that some period of time like the second phase described above exists and can be observed in the reaction of interest, and the quasisteadystate approximation describes the mathematics derived by assuming that the properties of this phase described in the preceeding paragraph hold.
All of these properties, and their mathematical consequences, are constrained by the mathematical relation below. As the expression on the left becomes smaller, the validity of the QSSA improves:
[E_{0}]

<< 1 
[Segel, Segel & Slemrod] 
The above discussion can be extended to attempt to describe systems in which some of the constraints of the standard quasisteadystate assumption (or sQSSA) do not hold. Other related sets of assumptions that have gained some attention include
[E_{0}] >> [S_{0}].  [Schnell and Maini] 
K[E_{0}]

<< 1 
[Borghans, et al.] 