The total quasi-steady-state approximation for complex enzyme reactions

Biochemistry in general and enzyme kinetics in particular have been heavily influenced by the model of biochemical reactions known as Michaelis-Menten kinetics. Assuming that the complex concentration is approximately constant after a short transient phase leads to the usual Michaelis-Menten (MM) approximation (or standard quasi-steady-state approximation (sQSSA)), which is valid when the enzyme concentration is sufficiently small. This condition is usually fulfilled for in vitro experiments, but often breaks down in vivo. The total QSSA (tQSSA), which is valid for a broader range of parameters covering both high and low enzyme concentrations, has been introduced in the last two decades. We extend the tQSSA to more complex reaction schemes, like fully competitive reactions, double phosphorylation, Goldbeter-Koshland switch and we show that for a very large range of parameters our tQSSA provides excellent fitting to the solutions of the full system, better than the sQSSA and the single reaction tQSSA. Finally, we discuss the need for a correct model formulation when doing "reverse engineering". which aims at finding unknown parameters by fitting the model to experimentally obtained data. We show that the estimated parameters are much closer to the real values when using the tQSSA rather than the sQSSA, which overestimates the parameter values greatly.