  The standard two-step model of homogeneous-catalyzed reactions had been
theoretically analyzed at various levels of approximations from time to time.
The primary aim was to check the validity of the quasi-steady-state
approximation, and hence emergence of the Michaelis-Menten kinetics, with
various substrate-enzyme ratios. But, conclusions vary. We solve here the
desired set of coupled nonlinear differential equations by invoking a new set
of dimensionless variables. Approximate solutions are obtained via the
power-series method aided by Pade approximants. The scheme works very
successfully in furnishing the initial dynamics at least up to the region where
existence of any steady state can be checked. A few conditions for its validity
are put forward and tested against the findings. Temporal profiles of the
substrate and the product are analyzed in addition to that of the complex to
gain further insights into legitimacy of the above approximation. Some recent
observations like the reactant stationary approximation and the notions of
different timescales are revisited. Signatures of the quasi-steady-state
approximation are also nicely detected by following the various reduced
concentration profiles in triangular plots. Conditions for the emergence of
Michaelis-Menten kinetics are scrutinized and it is stressed how one can get
the reaction constants even in the absence of any steady state.
