An asymptotic analysis at leading order of the Goldbeter–Koshland switch, the simplest futile cycle, is carried out in detail. After a nondimensionalization of the problem, we find the leading order uniform expansions of the reactants, identifying the proper time scales in a total setting. Comparison with numerical integration confirms the goodness of our analysis.
Asymptotic expansions Systems biology Enzyme kinetics
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J. Borghans, R. de Boer, L.A. Segel, Extending the quasi-steady state approximation by changing variables. Bull. Math. Biol. 58, 43–63 (1996)CrossRefGoogle Scholar
A. Ciliberto, F. Capuani, J.J. Tyson, Modeling networks of coupled anzymatic reactions using the total quasi-steady state approximation. PLoS Comput. Biol. 3, 463–472 (2007)CrossRefGoogle Scholar
G. Dell’Acqua, A.M. Bersani, A perturbation solution of Michaelis-Menten kinetics in a ‘total’ framework. J. Math. Chem. 50, 1136–1148 (2012)CrossRefGoogle Scholar
G. Dell’Acqua, A.M. Bersani, Quasi steady-state approximations and multistability in the double phosphorylation-dephosphorylation cycle. Comm. Com. Inf. Sc. 273, 155–172 (2013)Google Scholar
J.W. Dingee, A.B. Anton, A new perturbation solution to the Michaelis-Menten problem. AIChE J. 54, 1344–1357 (2008)CrossRefGoogle Scholar
A. Goldbeter, D.E. Koshland, An amplified sensitivity arising from covalent modification in biological system. Proc. Natl. Acad. Sci. 78, 6840–6844 (1981)CrossRefGoogle Scholar
A. Kumar, K. Josić, Reduced models of networks of coupled enzymatic reactions. J. Theor. Biol. 278, 87–106 (2011)CrossRefGoogle Scholar
C.C. Lin, L.A. Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences (Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1988)Google Scholar
M.G. Pedersen, A.M. Bersani, E. Bersani, G. Cortese, The total quasi-steady-state approximation for complex enzyme reactions. Math. Comput. Simulat. 79, 1010–1019 (2008)CrossRefGoogle Scholar