  In this paper we prove that the well-known quasi-steady state approximations,
commonly used in enzyme kinetics, which can be interpreted as the reduced
system of a differential system depending on a perturbative parameter,
according to Tihonov theory, are asymptotically equivalent to the center
manifold of the system. This allows to give a mathematical foundation for the
application of a mechanistic method to determine the center manifold of (at
this moment, still simple) enzyme reactions.
