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The standard two-step model of homogeneous-catalyzed reactions had beentheoretically analyzed at various levels of approximations from time to time.The primary aim was to check the validity of the quasi-steady-stateapproximation, and hence emergence of the Michaelis-Menten kinetics, withvarious substrate-enzyme ratios. But, conclusions vary. We solve here thedesired set of coupled nonlinear differential equations by invoking a new setof dimensionless variables. Approximate solutions are obtained via thepower-series method aided by Pade approximants. The scheme works verysuccessfully in furnishing the initial dynamics at least up to the region whereexistence of any steady state can be checked. A few conditions for its validityare put forward and tested against the findings. Temporal profiles of thesubstrate and the product are analyzed in addition to that of the complex togain further insights into legitimacy of the above approximation. Some recentobservations like the reactant stationary approximation and the notions ofdifferent timescales are revisited. Signatures of the quasi-steady-stateapproximation are also nicely detected by following the various reducedconcentration profiles in triangular plots. Conditions for the emergence ofMichaelis-Menten kinetics are scrutinized and it is stressed how one can getthe reaction constants even in the absence of any steady state.

Enzyme Kinetics: A critique of the quasi-steady-state approximation