Singular perturbation techniques and asymptotic expansions for some complex enzyme reactions

We show some recent results related to the application of singular perturbation techniques in the framework of the so-called total quasi-steady-state approximation (tQSSA) for the approximation of some important enzyme reactions: the fully competitive inhibition, the Goldbeter-Koshland cycle, the double phosphorylation mechanism. We determine the uniform expansions up to the first order in terms of appropriate perturbation parameters, related to the initial conditions and to the kinetic parameters characterizing the reactions