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PLoS Comput Biol. 2007 Mar 16;3(3):e45.

Modeling networks of coupled enzymatic reactions using the total quasi-steady state approximation.

Author information

1
The FIRC Institute for Molecular Oncology, Milan, Italy. andrea.ciliberto@ifom-ieo-campus.it

Abstract

In metabolic networks, metabolites are usually present in great excess over the enzymes that catalyze their interconversion, and describing the rates of these reactions by using the Michaelis-Menten rate law is perfectly valid. This rate law assumes that the concentration of enzyme-substrate complex (C) is much less than the free substrate concentration (S0). However, in protein interaction networks, the enzymes and substrates are all proteins in comparable concentrations, and neglecting C with respect to S0 is not valid. Borghans, DeBoer, and Segel developed an alternative description of enzyme kinetics that is valid when C is comparable to S0. We extend this description, which Borghans et al. call the total quasi-steady state approximation, to networks of coupled enzymatic reactions. First, we analyze an isolated Goldbeter-Koshland switch when enzymes and substrates are present in comparable concentrations. Then, on the basis of a real example of the molecular network governing cell cycle progression, we couple two and three Goldbeter-Koshland switches together to study the effects of feedback in networks of protein kinases and phosphatases. Our analysis shows that the total quasi-steady state approximation provides an excellent kinetic formalism for protein interaction networks, because (1) it unveils the modular structure of the enzymatic reactions, (2) it suggests a simple algorithm to formulate correct kinetic equations, and (3) contrary to classical Michaelis-Menten kinetics, it succeeds in faithfully reproducing the dynamics of the network both qualitatively and quantitatively.

PMID:
17367203
PMCID:
PMC1828705
DOI:
10.1371/journal.pcbi.0030045
[Indexed for MEDLINE]
Free PMC Article

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