The total quasi-steady state assumption: its justification by singular perturbation theory and its application to the chemical master equation

Abstract

Deterministic models of enzymatic reactions based on the quasi-steady state assumption (qssa) and total quasi-steady state assump-tion (tqssa) have been used successfully in the past. This is surprising as the qssa and tqssa can neither be verified mathematically nor by experiment for most cases of interest. Here, we discuss an approach using singular perturbation theory to justify the approximation ob-tained by tqssa. In addition, we extend the application of tqssa to the stochastic model to deal with stiff differential equations originating from the chemical master equation.