The Status of the QSSA Approximation in Stochastic Simulations of Reaction Networks

Stochastic models of chemical reactions are needed in many contexts in which the copy numbers of species are low, but only the simplest models can be treated analytically. However, direct simulation of computational models for systems with many components can be very time-consuming, and approximate methods are frequently used. One method that has been used in systems with multiple time scales is to approximate the fast dynamics, and in this note we study one such approach, in which the deterministic QSSH is used for the fast variables and the result used in the rate equations for the slow variables. We examine the classical Michaelis-Menten kinetics using this approach to determine when it is applicable.

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