Available online at www.sciencedirect.com Mathematics and Computers in Simulation 79 (2008) 1010–1019 The total quasi-steady-state approximation for complex enzyme reactions Morten Gram Pedersen a,∗ , Alberto M. Bersani b , Enrico Bersani c,1 , Giuliana Cortese d a Department of Mathematics, Technical University of Denmark, Lyngby, Denmark b Department of Mathematical Methods and Models, “La Sapienza” University, Rome, Italy c Datalink Informatica, Rome, Italy d Department of Statistical Sciences, University of Padova, Italy Available online 13 February 2008 Abstract 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. © 2008 IMACS. Published by Elsevier B.V. All rights reserved. Keywords: Signal transduction; Enzyme kinetics; Reverse engineering 1. Introduction One of the principal components of the mathematical approach to Systems Biology is the model of biochemical reactions set forth by Henri in 1901 [8–10] and Michaelis and Menten in 1913 [12], and further developed by Briggs and Haldane in 1925 [4]. This formulation considers a reaction where a substrate S binds to an enzyme E reversibly to form a complex C. The complex can then decay irreversibly to a product P and the enzyme, which is then free to bind ∗ Corresponding author. Present address: Department of information Engineering, University of Padova, Via Gradenigo 6/A, 35131 Padova, Italy. Tel.: +39 049 8277863; fax: +39 049 8277699. E-mail address: pedersen@dei.unipd.it (M.G. Pedersen). 1 Present address: ISMAC, Genova, Italy. 0378-4754/$32.00 © 2008 IMACS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.matcom.2008.02.009