  In biochemical systems the Michaelis-Menten (MM) scheme is one of the
best-known models of the enzyme- catalyzed kinetics. In the academic literature
the MM approximation has been thoroughly studied in the context of differential
equation models. At the level of the cell, however, molecular fluctuations have
many important consequences, and thus, a stochastic investigation of the MM
scheme is often necessary. In their work Barik et al. [Biophysical Journal, 95,
3563-3574, (2008)] presented a stochastic approximation of the MM scheme. They
suggested a substitution of the propensity function in the reduced master
equation with the total quasi-steady- state approximation (tQSSA) rate. The
justification of the substitution, however, was provided for a special case
only and did not cover the whole parameter domain of the tQSSA. In this
manuscript we present a derivation of the stochastic tQSSA that is valid for
the entire tQSSA parameter domain.
