The paper outlines a general approach to deriving quasi steady-state approximations (QSSAs) of the stochastic reaction networks describing the Michaelis-Menten enzyme kinetics. In particular it explains how different sets of assumptions about chemical species abundance and reaction rates lead to the standard QSSA (sQSSA), the total QSSA (tQSSA), and the reverse QSSA (rQSSA) approximations. These three QSSAs have been widely studied in the literature in deterministic ordinary differential equation (ODE) settings and several sets of conditions for their validity have been proposed. With the help of the multiscaling techniques introduced in [4, 27] it is seen that the conditions for deterministic QSSAs largely agree (with some exceptions) with the ones for stochastic QSSAs in the large volume limits. The paper also illustrates how the stochastic QSSA approach may be extended to more complex stochastic kinetic networks like, for instance, the Enzyme-Substrate-Inhibitor system. |